From c86ea16622bf1e5efd91bae2f0239ad288e09066 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:21:59 +0530 Subject: [PATCH 0001/1001] proof: certify atlas Batch0001 (10:0 to 10:14) --- Collatz/Research/StoppingAtlas/Batch0001.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0001.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0001.lean b/Collatz/Research/StoppingAtlas/Batch0001.lean new file mode 100644 index 00000000..bc1c33c6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0001.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0001 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 0. -/ +theorem bounds_10_0 : exactInterval 10 0 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_0 (m : Nat) : + stoppingTime (2 ^ 10 * m + 0) 10 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_0 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_0 : oddCount 0 10 = 0 ∧ acceleratedOrbit 10 0 = 0 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_0 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 0) = 3 ^ 0 * m + 0 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_0.1, data_10_0.2] + +/-- Complete interval computation for depth 10, residue 1. -/ +theorem bounds_10_1 : exactInterval 10 1 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1) 10 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1 : oddCount 1 10 = 5 ∧ acceleratedOrbit 10 1 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1.1, data_10_1.2] + +/-- Complete interval computation for depth 10, residue 2. -/ +theorem bounds_10_2 : exactInterval 10 2 = ⟨1, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_2 (m : Nat) : + stoppingTime (2 ^ 10 * m + 2) 10 ↔ 1 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_2 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_2 : oddCount 2 10 = 5 ∧ acceleratedOrbit 10 2 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_2 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 2) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_2.1, data_10_2.2] + +/-- Complete interval computation for depth 10, residue 3. -/ +theorem bounds_10_3 : exactInterval 10 3 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_3 (m : Nat) : + stoppingTime (2 ^ 10 * m + 3) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_3 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_3 : oddCount 3 10 = 5 ∧ acceleratedOrbit 10 3 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_3 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 3) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_3.1, data_10_3.2] + +/-- Complete interval computation for depth 10, residue 4. -/ +theorem bounds_10_4 : exactInterval 10 4 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_4 (m : Nat) : + stoppingTime (2 ^ 10 * m + 4) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_4 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_4 : oddCount 4 10 = 4 ∧ acceleratedOrbit 10 4 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_4 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 4) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_4.1, data_10_4.2] + +/-- Complete interval computation for depth 10, residue 5. -/ +theorem bounds_10_5 : exactInterval 10 5 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_5 (m : Nat) : + stoppingTime (2 ^ 10 * m + 5) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_5 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_5 : oddCount 5 10 = 4 ∧ acceleratedOrbit 10 5 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_5 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 5) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_5.1, data_10_5.2] + +/-- Complete interval computation for depth 10, residue 6. -/ +theorem bounds_10_6 : exactInterval 10 6 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_6 (m : Nat) : + stoppingTime (2 ^ 10 * m + 6) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_6 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_6 : oddCount 6 10 = 4 ∧ acceleratedOrbit 10 6 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_6 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 6) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_6.1, data_10_6.2] + +/-- Complete interval computation for depth 10, residue 7. -/ +theorem bounds_10_7 : exactInterval 10 7 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_7 (m : Nat) : + stoppingTime (2 ^ 10 * m + 7) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_7 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_7 : oddCount 7 10 = 5 ∧ acceleratedOrbit 10 7 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_7 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 7) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_7.1, data_10_7.2] + +/-- Complete interval computation for depth 10, residue 8. -/ +theorem bounds_10_8 : exactInterval 10 8 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_8 (m : Nat) : + stoppingTime (2 ^ 10 * m + 8) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_8 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_8 : oddCount 8 10 = 4 ∧ acceleratedOrbit 10 8 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_8 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 8) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_8.1, data_10_8.2] + +/-- Complete interval computation for depth 10, residue 9. -/ +theorem bounds_10_9 : exactInterval 10 9 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_9 (m : Nat) : + stoppingTime (2 ^ 10 * m + 9) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_9 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_9 : oddCount 9 10 = 6 ∧ acceleratedOrbit 10 9 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_9 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 9) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_9.1, data_10_9.2] + +/-- Complete interval computation for depth 10, residue 10. -/ +theorem bounds_10_10 : exactInterval 10 10 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_10 (m : Nat) : + stoppingTime (2 ^ 10 * m + 10) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_10 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_10 : oddCount 10 10 = 4 ∧ acceleratedOrbit 10 10 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_10 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 10) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_10.1, data_10_10.2] + +/-- Complete interval computation for depth 10, residue 11. -/ +theorem bounds_10_11 : exactInterval 10 11 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_11 (m : Nat) : + stoppingTime (2 ^ 10 * m + 11) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_11 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_11 : oddCount 11 10 = 4 ∧ acceleratedOrbit 10 11 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_11 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 11) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_11.1, data_10_11.2] + +/-- Complete interval computation for depth 10, residue 12. -/ +theorem bounds_10_12 : exactInterval 10 12 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_12 (m : Nat) : + stoppingTime (2 ^ 10 * m + 12) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_12 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_12 : oddCount 12 10 = 4 ∧ acceleratedOrbit 10 12 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_12 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 12) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_12.1, data_10_12.2] + +/-- Complete interval computation for depth 10, residue 13. -/ +theorem bounds_10_13 : exactInterval 10 13 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_13 (m : Nat) : + stoppingTime (2 ^ 10 * m + 13) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_13 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_13 : oddCount 13 10 = 4 ∧ acceleratedOrbit 10 13 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_13 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 13) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_13.1, data_10_13.2] + +/-- Complete interval computation for depth 10, residue 14. -/ +theorem bounds_10_14 : exactInterval 10 14 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_14 (m : Nat) : + stoppingTime (2 ^ 10 * m + 14) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_14 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_14 : oddCount 14 10 = 5 ∧ acceleratedOrbit 10 14 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_14 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 14) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_14.1, data_10_14.2] + +end Collatz.Research.StoppingAtlas.Batch0001 From d45a9d0357929e40e7a7e958c22f1a299b7c6aeb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:21:59 +0530 Subject: [PATCH 0002/1001] proof: certify atlas Batch0002 (10:15 to 10:29) --- Collatz/Research/StoppingAtlas/Batch0002.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0002.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0002.lean b/Collatz/Research/StoppingAtlas/Batch0002.lean new file mode 100644 index 00000000..2381bf7f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0002.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0002 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 15. -/ +theorem bounds_10_15 : exactInterval 10 15 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_15 (m : Nat) : + stoppingTime (2 ^ 10 * m + 15) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_15 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_15 : oddCount 15 10 = 5 ∧ acceleratedOrbit 10 15 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_15 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 15) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_15.1, data_10_15.2] + +/-- Complete interval computation for depth 10, residue 16. -/ +theorem bounds_10_16 : exactInterval 10 16 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_16 (m : Nat) : + stoppingTime (2 ^ 10 * m + 16) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_16 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_16 : oddCount 16 10 = 3 ∧ acceleratedOrbit 10 16 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_16 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 16) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_16.1, data_10_16.2] + +/-- Complete interval computation for depth 10, residue 17. -/ +theorem bounds_10_17 : exactInterval 10 17 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_17 (m : Nat) : + stoppingTime (2 ^ 10 * m + 17) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_17 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_17 : oddCount 17 10 = 4 ∧ acceleratedOrbit 10 17 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_17 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 17) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_17.1, data_10_17.2] + +/-- Complete interval computation for depth 10, residue 18. -/ +theorem bounds_10_18 : exactInterval 10 18 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_18 (m : Nat) : + stoppingTime (2 ^ 10 * m + 18) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_18 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_18 : oddCount 18 10 = 5 ∧ acceleratedOrbit 10 18 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_18 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 18) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_18.1, data_10_18.2] + +/-- Complete interval computation for depth 10, residue 19. -/ +theorem bounds_10_19 : exactInterval 10 19 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_19 (m : Nat) : + stoppingTime (2 ^ 10 * m + 19) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_19 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_19 : oddCount 19 10 = 5 ∧ acceleratedOrbit 10 19 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_19 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 19) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_19.1, data_10_19.2] + +/-- Complete interval computation for depth 10, residue 20. -/ +theorem bounds_10_20 : exactInterval 10 20 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_20 (m : Nat) : + stoppingTime (2 ^ 10 * m + 20) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_20 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_20 : oddCount 20 10 = 3 ∧ acceleratedOrbit 10 20 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_20 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 20) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_20.1, data_10_20.2] + +/-- Complete interval computation for depth 10, residue 21. -/ +theorem bounds_10_21 : exactInterval 10 21 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_21 (m : Nat) : + stoppingTime (2 ^ 10 * m + 21) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_21 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_21 : oddCount 21 10 = 3 ∧ acceleratedOrbit 10 21 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_21 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 21) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_21.1, data_10_21.2] + +/-- Complete interval computation for depth 10, residue 22. -/ +theorem bounds_10_22 : exactInterval 10 22 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_22 (m : Nat) : + stoppingTime (2 ^ 10 * m + 22) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_22 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_22 : oddCount 22 10 = 4 ∧ acceleratedOrbit 10 22 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_22 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 22) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_22.1, data_10_22.2] + +/-- Complete interval computation for depth 10, residue 23. -/ +theorem bounds_10_23 : exactInterval 10 23 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_23 (m : Nat) : + stoppingTime (2 ^ 10 * m + 23) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_23 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_23 : oddCount 23 10 = 4 ∧ acceleratedOrbit 10 23 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_23 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 23) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_23.1, data_10_23.2] + +/-- Complete interval computation for depth 10, residue 24. -/ +theorem bounds_10_24 : exactInterval 10 24 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_24 (m : Nat) : + stoppingTime (2 ^ 10 * m + 24) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_24 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_24 : oddCount 24 10 = 3 ∧ acceleratedOrbit 10 24 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_24 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 24) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_24.1, data_10_24.2] + +/-- Complete interval computation for depth 10, residue 25. -/ +theorem bounds_10_25 : exactInterval 10 25 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_25 (m : Nat) : + stoppingTime (2 ^ 10 * m + 25) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_25 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_25 : oddCount 25 10 = 6 ∧ acceleratedOrbit 10 25 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_25 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 25) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_25.1, data_10_25.2] + +/-- Complete interval computation for depth 10, residue 26. -/ +theorem bounds_10_26 : exactInterval 10 26 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_26 (m : Nat) : + stoppingTime (2 ^ 10 * m + 26) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_26 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_26 : oddCount 26 10 = 3 ∧ acceleratedOrbit 10 26 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_26 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 26) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_26.1, data_10_26.2] + +/-- Complete interval computation for depth 10, residue 27. -/ +theorem bounds_10_27 : exactInterval 10 27 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_27 (m : Nat) : + stoppingTime (2 ^ 10 * m + 27) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_27 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_27 : oddCount 27 10 = 8 ∧ acceleratedOrbit 10 27 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_27 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 27) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_27.1, data_10_27.2] + +/-- Complete interval computation for depth 10, residue 28. -/ +theorem bounds_10_28 : exactInterval 10 28 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_28 (m : Nat) : + stoppingTime (2 ^ 10 * m + 28) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_28 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_28 : oddCount 28 10 = 5 ∧ acceleratedOrbit 10 28 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_28 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 28) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_28.1, data_10_28.2] + +/-- Complete interval computation for depth 10, residue 29. -/ +theorem bounds_10_29 : exactInterval 10 29 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_29 (m : Nat) : + stoppingTime (2 ^ 10 * m + 29) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_29 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_29 : oddCount 29 10 = 5 ∧ acceleratedOrbit 10 29 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_29 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 29) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_29.1, data_10_29.2] + +end Collatz.Research.StoppingAtlas.Batch0002 From 361a5ef59aa7ecbdf27e3fd4f6498043c23122ec Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:21:59 +0530 Subject: [PATCH 0003/1001] proof: certify atlas Batch0003 (10:30 to 10:45) --- Collatz/Research/StoppingAtlas/Batch0003.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0003.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0003.lean b/Collatz/Research/StoppingAtlas/Batch0003.lean new file mode 100644 index 00000000..e5258de4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0003.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0003 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 30. -/ +theorem bounds_10_30 : exactInterval 10 30 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_30 (m : Nat) : + stoppingTime (2 ^ 10 * m + 30) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_30 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_30 : oddCount 30 10 = 5 ∧ acceleratedOrbit 10 30 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_30 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 30) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_30.1, data_10_30.2] + +/-- Complete interval computation for depth 10, residue 31. -/ +theorem bounds_10_31 : exactInterval 10 31 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_31 (m : Nat) : + stoppingTime (2 ^ 10 * m + 31) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_31 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_31 : oddCount 31 10 = 8 ∧ acceleratedOrbit 10 31 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_31 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 31) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_31.1, data_10_31.2] + +/-- Complete interval computation for depth 10, residue 32. -/ +theorem bounds_10_32 : exactInterval 10 32 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_32 (m : Nat) : + stoppingTime (2 ^ 10 * m + 32) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_32 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_32 : oddCount 32 10 = 3 ∧ acceleratedOrbit 10 32 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_32 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 32) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_32.1, data_10_32.2] + +/-- Complete interval computation for depth 10, residue 33. -/ +theorem bounds_10_33 : exactInterval 10 33 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_33 (m : Nat) : + stoppingTime (2 ^ 10 * m + 33) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_33 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_33 : oddCount 33 10 = 6 ∧ acceleratedOrbit 10 33 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_33 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 33) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_33.1, data_10_33.2] + +/-- Complete interval computation for depth 10, residue 34. -/ +theorem bounds_10_34 : exactInterval 10 34 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_34 (m : Nat) : + stoppingTime (2 ^ 10 * m + 34) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_34 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_34 : oddCount 34 10 = 3 ∧ acceleratedOrbit 10 34 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_34 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 34) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_34.1, data_10_34.2] + +/-- Complete interval computation for depth 10, residue 35. -/ +theorem bounds_10_35 : exactInterval 10 35 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_35 (m : Nat) : + stoppingTime (2 ^ 10 * m + 35) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_35 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_35 : oddCount 35 10 = 3 ∧ acceleratedOrbit 10 35 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_35 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 35) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_35.1, data_10_35.2] + +/-- Complete interval computation for depth 10, residue 36. -/ +theorem bounds_10_36 : exactInterval 10 36 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_36 (m : Nat) : + stoppingTime (2 ^ 10 * m + 36) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_36 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_36 : oddCount 36 10 = 5 ∧ acceleratedOrbit 10 36 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_36 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 36) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_36.1, data_10_36.2] + +/-- Complete interval computation for depth 10, residue 37. -/ +theorem bounds_10_37 : exactInterval 10 37 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_37 (m : Nat) : + stoppingTime (2 ^ 10 * m + 37) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_37 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_37 : oddCount 37 10 = 5 ∧ acceleratedOrbit 10 37 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_37 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 37) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_37.1, data_10_37.2] + +/-- Complete interval computation for depth 10, residue 38. -/ +theorem bounds_10_38 : exactInterval 10 38 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_38 (m : Nat) : + stoppingTime (2 ^ 10 * m + 38) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_38 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_38 : oddCount 38 10 = 5 ∧ acceleratedOrbit 10 38 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_38 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 38) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_38.1, data_10_38.2] + +/-- Complete interval computation for depth 10, residue 39. -/ +theorem bounds_10_39 : exactInterval 10 39 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_39 (m : Nat) : + stoppingTime (2 ^ 10 * m + 39) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_39 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_39 : oddCount 39 10 = 6 ∧ acceleratedOrbit 10 39 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_39 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 39) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_39.1, data_10_39.2] + +/-- Complete interval computation for depth 10, residue 40. -/ +theorem bounds_10_40 : exactInterval 10 40 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_40 (m : Nat) : + stoppingTime (2 ^ 10 * m + 40) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_40 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_40 : oddCount 40 10 = 3 ∧ acceleratedOrbit 10 40 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_40 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 40) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_40.1, data_10_40.2] + +/-- Complete interval computation for depth 10, residue 41. -/ +theorem bounds_10_41 : exactInterval 10 41 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_41 (m : Nat) : + stoppingTime (2 ^ 10 * m + 41) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_41 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_41 : oddCount 41 10 = 7 ∧ acceleratedOrbit 10 41 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_41 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 41) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_41.1, data_10_41.2] + +/-- Complete interval computation for depth 10, residue 42. -/ +theorem bounds_10_42 : exactInterval 10 42 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_42 (m : Nat) : + stoppingTime (2 ^ 10 * m + 42) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_42 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_42 : oddCount 42 10 = 3 ∧ acceleratedOrbit 10 42 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_42 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 42) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_42.1, data_10_42.2] + +/-- Complete interval computation for depth 10, residue 43. -/ +theorem bounds_10_43 : exactInterval 10 43 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_43 (m : Nat) : + stoppingTime (2 ^ 10 * m + 43) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_43 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_43 : oddCount 43 10 = 5 ∧ acceleratedOrbit 10 43 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_43 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 43) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_43.1, data_10_43.2] + +/-- Complete interval computation for depth 10, residue 44. -/ +theorem bounds_10_44 : exactInterval 10 44 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_44 (m : Nat) : + stoppingTime (2 ^ 10 * m + 44) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_44 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_44 : oddCount 44 10 = 4 ∧ acceleratedOrbit 10 44 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_44 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 44) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_44.1, data_10_44.2] + +/-- Complete interval computation for depth 10, residue 45. -/ +theorem bounds_10_45 : exactInterval 10 45 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_45 (m : Nat) : + stoppingTime (2 ^ 10 * m + 45) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_45 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_45 : oddCount 45 10 = 4 ∧ acceleratedOrbit 10 45 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_45 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 45) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_45.1, data_10_45.2] + +end Collatz.Research.StoppingAtlas.Batch0003 From 1d3a7c0c78249307bc86cbf7781d7ff81c992822 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:21:59 +0530 Subject: [PATCH 0004/1001] proof: certify atlas Batch0004 (10:46 to 10:60) --- Collatz/Research/StoppingAtlas/Batch0004.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0004.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0004.lean b/Collatz/Research/StoppingAtlas/Batch0004.lean new file mode 100644 index 00000000..90224e01 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0004.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0004 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 46. -/ +theorem bounds_10_46 : exactInterval 10 46 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_46 (m : Nat) : + stoppingTime (2 ^ 10 * m + 46) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_46 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_46 : oddCount 46 10 = 4 ∧ acceleratedOrbit 10 46 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_46 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 46) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_46.1, data_10_46.2] + +/-- Complete interval computation for depth 10, residue 47. -/ +theorem bounds_10_47 : exactInterval 10 47 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_47 (m : Nat) : + stoppingTime (2 ^ 10 * m + 47) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_47 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_47 : oddCount 47 10 = 7 ∧ acceleratedOrbit 10 47 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_47 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 47) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_47.1, data_10_47.2] + +/-- Complete interval computation for depth 10, residue 48. -/ +theorem bounds_10_48 : exactInterval 10 48 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_48 (m : Nat) : + stoppingTime (2 ^ 10 * m + 48) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_48 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_48 : oddCount 48 10 = 3 ∧ acceleratedOrbit 10 48 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_48 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 48) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_48.1, data_10_48.2] + +/-- Complete interval computation for depth 10, residue 49. -/ +theorem bounds_10_49 : exactInterval 10 49 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_49 (m : Nat) : + stoppingTime (2 ^ 10 * m + 49) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_49 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_49 : oddCount 49 10 = 5 ∧ acceleratedOrbit 10 49 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_49 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 49) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_49.1, data_10_49.2] + +/-- Complete interval computation for depth 10, residue 50. -/ +theorem bounds_10_50 : exactInterval 10 50 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_50 (m : Nat) : + stoppingTime (2 ^ 10 * m + 50) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_50 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_50 : oddCount 50 10 = 5 ∧ acceleratedOrbit 10 50 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_50 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 50) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_50.1, data_10_50.2] + +/-- Complete interval computation for depth 10, residue 51. -/ +theorem bounds_10_51 : exactInterval 10 51 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_51 (m : Nat) : + stoppingTime (2 ^ 10 * m + 51) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_51 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_51 : oddCount 51 10 = 5 ∧ acceleratedOrbit 10 51 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_51 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 51) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_51.1, data_10_51.2] + +/-- Complete interval computation for depth 10, residue 52. -/ +theorem bounds_10_52 : exactInterval 10 52 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_52 (m : Nat) : + stoppingTime (2 ^ 10 * m + 52) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_52 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_52 : oddCount 52 10 = 3 ∧ acceleratedOrbit 10 52 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_52 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 52) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_52.1, data_10_52.2] + +/-- Complete interval computation for depth 10, residue 53. -/ +theorem bounds_10_53 : exactInterval 10 53 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_53 (m : Nat) : + stoppingTime (2 ^ 10 * m + 53) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_53 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_53 : oddCount 53 10 = 3 ∧ acceleratedOrbit 10 53 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_53 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 53) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_53.1, data_10_53.2] + +/-- Complete interval computation for depth 10, residue 54. -/ +theorem bounds_10_54 : exactInterval 10 54 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_54 (m : Nat) : + stoppingTime (2 ^ 10 * m + 54) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_54 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_54 : oddCount 54 10 = 7 ∧ acceleratedOrbit 10 54 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_54 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 54) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_54.1, data_10_54.2] + +/-- Complete interval computation for depth 10, residue 55. -/ +theorem bounds_10_55 : exactInterval 10 55 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_55 (m : Nat) : + stoppingTime (2 ^ 10 * m + 55) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_55 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_55 : oddCount 55 10 = 7 ∧ acceleratedOrbit 10 55 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_55 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 55) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_55.1, data_10_55.2] + +/-- Complete interval computation for depth 10, residue 56. -/ +theorem bounds_10_56 : exactInterval 10 56 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_56 (m : Nat) : + stoppingTime (2 ^ 10 * m + 56) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_56 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_56 : oddCount 56 10 = 4 ∧ acceleratedOrbit 10 56 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_56 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 56) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_56.1, data_10_56.2] + +/-- Complete interval computation for depth 10, residue 57. -/ +theorem bounds_10_57 : exactInterval 10 57 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_57 (m : Nat) : + stoppingTime (2 ^ 10 * m + 57) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_57 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_57 : oddCount 57 10 = 5 ∧ acceleratedOrbit 10 57 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_57 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 57) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_57.1, data_10_57.2] + +/-- Complete interval computation for depth 10, residue 58. -/ +theorem bounds_10_58 : exactInterval 10 58 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_58 (m : Nat) : + stoppingTime (2 ^ 10 * m + 58) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_58 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_58 : oddCount 58 10 = 4 ∧ acceleratedOrbit 10 58 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_58 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 58) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_58.1, data_10_58.2] + +/-- Complete interval computation for depth 10, residue 59. -/ +theorem bounds_10_59 : exactInterval 10 59 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_59 (m : Nat) : + stoppingTime (2 ^ 10 * m + 59) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_59 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_59 : oddCount 59 10 = 6 ∧ acceleratedOrbit 10 59 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_59 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 59) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_59.1, data_10_59.2] + +/-- Complete interval computation for depth 10, residue 60. -/ +theorem bounds_10_60 : exactInterval 10 60 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_60 (m : Nat) : + stoppingTime (2 ^ 10 * m + 60) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_60 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_60 : oddCount 60 10 = 4 ∧ acceleratedOrbit 10 60 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_60 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 60) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_60.1, data_10_60.2] + +end Collatz.Research.StoppingAtlas.Batch0004 From 67de8b07ef9b2567c0e286333c1c5d01c458ecc6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:00 +0530 Subject: [PATCH 0005/1001] proof: certify atlas Batch0005 (10:61 to 10:75) --- Collatz/Research/StoppingAtlas/Batch0005.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0005.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0005.lean b/Collatz/Research/StoppingAtlas/Batch0005.lean new file mode 100644 index 00000000..fda579aa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0005.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0005 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 61. -/ +theorem bounds_10_61 : exactInterval 10 61 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_61 (m : Nat) : + stoppingTime (2 ^ 10 * m + 61) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_61 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_61 : oddCount 61 10 = 4 ∧ acceleratedOrbit 10 61 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_61 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 61) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_61.1, data_10_61.2] + +/-- Complete interval computation for depth 10, residue 62. -/ +theorem bounds_10_62 : exactInterval 10 62 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_62 (m : Nat) : + stoppingTime (2 ^ 10 * m + 62) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_62 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_62 : oddCount 62 10 = 7 ∧ acceleratedOrbit 10 62 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_62 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 62) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_62.1, data_10_62.2] + +/-- Complete interval computation for depth 10, residue 63. -/ +theorem bounds_10_63 : exactInterval 10 63 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_63 (m : Nat) : + stoppingTime (2 ^ 10 * m + 63) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_63 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_63 : oddCount 63 10 = 7 ∧ acceleratedOrbit 10 63 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_63 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 63) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_63.1, data_10_63.2] + +/-- Complete interval computation for depth 10, residue 64. -/ +theorem bounds_10_64 : exactInterval 10 64 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_64 (m : Nat) : + stoppingTime (2 ^ 10 * m + 64) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_64 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_64 : oddCount 64 10 = 2 ∧ acceleratedOrbit 10 64 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_64 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 64) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_64.1, data_10_64.2] + +/-- Complete interval computation for depth 10, residue 65. -/ +theorem bounds_10_65 : exactInterval 10 65 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_65 (m : Nat) : + stoppingTime (2 ^ 10 * m + 65) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_65 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_65 : oddCount 65 10 = 5 ∧ acceleratedOrbit 10 65 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_65 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 65) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_65.1, data_10_65.2] + +/-- Complete interval computation for depth 10, residue 66. -/ +theorem bounds_10_66 : exactInterval 10 66 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_66 (m : Nat) : + stoppingTime (2 ^ 10 * m + 66) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_66 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_66 : oddCount 66 10 = 5 ∧ acceleratedOrbit 10 66 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_66 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 66) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_66.1, data_10_66.2] + +/-- Complete interval computation for depth 10, residue 67. -/ +theorem bounds_10_67 : exactInterval 10 67 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_67 (m : Nat) : + stoppingTime (2 ^ 10 * m + 67) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_67 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_67 : oddCount 67 10 = 5 ∧ acceleratedOrbit 10 67 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_67 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 67) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_67.1, data_10_67.2] + +/-- Complete interval computation for depth 10, residue 68. -/ +theorem bounds_10_68 : exactInterval 10 68 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_68 (m : Nat) : + stoppingTime (2 ^ 10 * m + 68) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_68 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_68 : oddCount 68 10 = 3 ∧ acceleratedOrbit 10 68 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_68 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 68) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_68.1, data_10_68.2] + +/-- Complete interval computation for depth 10, residue 69. -/ +theorem bounds_10_69 : exactInterval 10 69 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_69 (m : Nat) : + stoppingTime (2 ^ 10 * m + 69) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_69 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_69 : oddCount 69 10 = 3 ∧ acceleratedOrbit 10 69 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_69 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 69) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_69.1, data_10_69.2] + +/-- Complete interval computation for depth 10, residue 70. -/ +theorem bounds_10_70 : exactInterval 10 70 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_70 (m : Nat) : + stoppingTime (2 ^ 10 * m + 70) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_70 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_70 : oddCount 70 10 = 3 ∧ acceleratedOrbit 10 70 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_70 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 70) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_70.1, data_10_70.2] + +/-- Complete interval computation for depth 10, residue 71. -/ +theorem bounds_10_71 : exactInterval 10 71 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_71 (m : Nat) : + stoppingTime (2 ^ 10 * m + 71) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_71 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_71 : oddCount 71 10 = 7 ∧ acceleratedOrbit 10 71 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_71 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 71) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_71.1, data_10_71.2] + +/-- Complete interval computation for depth 10, residue 72. -/ +theorem bounds_10_72 : exactInterval 10 72 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_72 (m : Nat) : + stoppingTime (2 ^ 10 * m + 72) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_72 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_72 : oddCount 72 10 = 5 ∧ acceleratedOrbit 10 72 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_72 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 72) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_72.1, data_10_72.2] + +/-- Complete interval computation for depth 10, residue 73. -/ +theorem bounds_10_73 : exactInterval 10 73 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_73 (m : Nat) : + stoppingTime (2 ^ 10 * m + 73) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_73 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_73 : oddCount 73 10 = 7 ∧ acceleratedOrbit 10 73 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_73 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 73) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_73.1, data_10_73.2] + +/-- Complete interval computation for depth 10, residue 74. -/ +theorem bounds_10_74 : exactInterval 10 74 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_74 (m : Nat) : + stoppingTime (2 ^ 10 * m + 74) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_74 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_74 : oddCount 74 10 = 5 ∧ acceleratedOrbit 10 74 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_74 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 74) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_74.1, data_10_74.2] + +/-- Complete interval computation for depth 10, residue 75. -/ +theorem bounds_10_75 : exactInterval 10 75 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_75 (m : Nat) : + stoppingTime (2 ^ 10 * m + 75) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_75 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_75 : oddCount 75 10 = 3 ∧ acceleratedOrbit 10 75 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_75 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 75) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_75.1, data_10_75.2] + +end Collatz.Research.StoppingAtlas.Batch0005 From 9c3fea3962b993d8b7d9eeae0e47c929ccbe1934 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:00 +0530 Subject: [PATCH 0006/1001] proof: certify atlas Batch0006 (10:76 to 10:91) --- Collatz/Research/StoppingAtlas/Batch0006.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0006.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0006.lean b/Collatz/Research/StoppingAtlas/Batch0006.lean new file mode 100644 index 00000000..4895245a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0006.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0006 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 76. -/ +theorem bounds_10_76 : exactInterval 10 76 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_76 (m : Nat) : + stoppingTime (2 ^ 10 * m + 76) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_76 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_76 : oddCount 76 10 = 5 ∧ acceleratedOrbit 10 76 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_76 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 76) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_76.1, data_10_76.2] + +/-- Complete interval computation for depth 10, residue 77. -/ +theorem bounds_10_77 : exactInterval 10 77 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_77 (m : Nat) : + stoppingTime (2 ^ 10 * m + 77) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_77 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_77 : oddCount 77 10 = 5 ∧ acceleratedOrbit 10 77 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_77 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 77) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_77.1, data_10_77.2] + +/-- Complete interval computation for depth 10, residue 78. -/ +theorem bounds_10_78 : exactInterval 10 78 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_78 (m : Nat) : + stoppingTime (2 ^ 10 * m + 78) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_78 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_78 : oddCount 78 10 = 5 ∧ acceleratedOrbit 10 78 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_78 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 78) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_78.1, data_10_78.2] + +/-- Complete interval computation for depth 10, residue 79. -/ +theorem bounds_10_79 : exactInterval 10 79 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_79 (m : Nat) : + stoppingTime (2 ^ 10 * m + 79) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_79 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_79 : oddCount 79 10 = 5 ∧ acceleratedOrbit 10 79 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_79 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 79) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_79.1, data_10_79.2] + +/-- Complete interval computation for depth 10, residue 80. -/ +theorem bounds_10_80 : exactInterval 10 80 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_80 (m : Nat) : + stoppingTime (2 ^ 10 * m + 80) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_80 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_80 : oddCount 80 10 = 2 ∧ acceleratedOrbit 10 80 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_80 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 80) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_80.1, data_10_80.2] + +/-- Complete interval computation for depth 10, residue 81. -/ +theorem bounds_10_81 : exactInterval 10 81 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_81 (m : Nat) : + stoppingTime (2 ^ 10 * m + 81) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_81 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_81 : oddCount 81 10 = 5 ∧ acceleratedOrbit 10 81 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_81 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 81) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_81.1, data_10_81.2] + +/-- Complete interval computation for depth 10, residue 82. -/ +theorem bounds_10_82 : exactInterval 10 82 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_82 (m : Nat) : + stoppingTime (2 ^ 10 * m + 82) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_82 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_82 : oddCount 82 10 = 7 ∧ acceleratedOrbit 10 82 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_82 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 82) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_82.1, data_10_82.2] + +/-- Complete interval computation for depth 10, residue 83. -/ +theorem bounds_10_83 : exactInterval 10 83 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_83 (m : Nat) : + stoppingTime (2 ^ 10 * m + 83) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_83 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_83 : oddCount 83 10 = 7 ∧ acceleratedOrbit 10 83 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_83 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 83) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_83.1, data_10_83.2] + +/-- Complete interval computation for depth 10, residue 84. -/ +theorem bounds_10_84 : exactInterval 10 84 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_84 (m : Nat) : + stoppingTime (2 ^ 10 * m + 84) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_84 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_84 : oddCount 84 10 = 2 ∧ acceleratedOrbit 10 84 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_84 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 84) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_84.1, data_10_84.2] + +/-- Complete interval computation for depth 10, residue 85. -/ +theorem bounds_10_85 : exactInterval 10 85 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_85 (m : Nat) : + stoppingTime (2 ^ 10 * m + 85) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_85 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_85 : oddCount 85 10 = 2 ∧ acceleratedOrbit 10 85 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_85 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 85) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_85.1, data_10_85.2] + +/-- Complete interval computation for depth 10, residue 86. -/ +theorem bounds_10_86 : exactInterval 10 86 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_86 (m : Nat) : + stoppingTime (2 ^ 10 * m + 86) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_86 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_86 : oddCount 86 10 = 4 ∧ acceleratedOrbit 10 86 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_86 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 86) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_86.1, data_10_86.2] + +/-- Complete interval computation for depth 10, residue 87. -/ +theorem bounds_10_87 : exactInterval 10 87 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_87 (m : Nat) : + stoppingTime (2 ^ 10 * m + 87) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_87 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_87 : oddCount 87 10 = 4 ∧ acceleratedOrbit 10 87 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_87 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 87) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_87.1, data_10_87.2] + +/-- Complete interval computation for depth 10, residue 88. -/ +theorem bounds_10_88 : exactInterval 10 88 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_88 (m : Nat) : + stoppingTime (2 ^ 10 * m + 88) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_88 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_88 : oddCount 88 10 = 4 ∧ acceleratedOrbit 10 88 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_88 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 88) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_88.1, data_10_88.2] + +/-- Complete interval computation for depth 10, residue 89. -/ +theorem bounds_10_89 : exactInterval 10 89 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_89 (m : Nat) : + stoppingTime (2 ^ 10 * m + 89) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_89 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_89 : oddCount 89 10 = 5 ∧ acceleratedOrbit 10 89 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_89 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 89) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_89.1, data_10_89.2] + +/-- Complete interval computation for depth 10, residue 90. -/ +theorem bounds_10_90 : exactInterval 10 90 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_90 (m : Nat) : + stoppingTime (2 ^ 10 * m + 90) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_90 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_90 : oddCount 90 10 = 4 ∧ acceleratedOrbit 10 90 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_90 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 90) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_90.1, data_10_90.2] + +/-- Complete interval computation for depth 10, residue 91. -/ +theorem bounds_10_91 : exactInterval 10 91 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_91 (m : Nat) : + stoppingTime (2 ^ 10 * m + 91) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_91 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_91 : oddCount 91 10 = 8 ∧ acceleratedOrbit 10 91 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_91 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 91) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_91.1, data_10_91.2] + +end Collatz.Research.StoppingAtlas.Batch0006 From c3e0fc9ec57a7f4b7986297183930d28fe499b43 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:00 +0530 Subject: [PATCH 0007/1001] proof: certify atlas Batch0007 (10:92 to 10:106) --- Collatz/Research/StoppingAtlas/Batch0007.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0007.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0007.lean b/Collatz/Research/StoppingAtlas/Batch0007.lean new file mode 100644 index 00000000..bb3a8f47 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0007.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0007 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 92. -/ +theorem bounds_10_92 : exactInterval 10 92 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_92 (m : Nat) : + stoppingTime (2 ^ 10 * m + 92) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_92 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_92 : oddCount 92 10 = 4 ∧ acceleratedOrbit 10 92 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_92 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 92) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_92.1, data_10_92.2] + +/-- Complete interval computation for depth 10, residue 93. -/ +theorem bounds_10_93 : exactInterval 10 93 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_93 (m : Nat) : + stoppingTime (2 ^ 10 * m + 93) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_93 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_93 : oddCount 93 10 = 4 ∧ acceleratedOrbit 10 93 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_93 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 93) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_93.1, data_10_93.2] + +/-- Complete interval computation for depth 10, residue 94. -/ +theorem bounds_10_94 : exactInterval 10 94 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_94 (m : Nat) : + stoppingTime (2 ^ 10 * m + 94) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_94 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_94 : oddCount 94 10 = 7 ∧ acceleratedOrbit 10 94 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_94 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 94) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_94.1, data_10_94.2] + +/-- Complete interval computation for depth 10, residue 95. -/ +theorem bounds_10_95 : exactInterval 10 95 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_95 (m : Nat) : + stoppingTime (2 ^ 10 * m + 95) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_95 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_95 : oddCount 95 10 = 7 ∧ acceleratedOrbit 10 95 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_95 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 95) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_95.1, data_10_95.2] + +/-- Complete interval computation for depth 10, residue 96. -/ +theorem bounds_10_96 : exactInterval 10 96 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_96 (m : Nat) : + stoppingTime (2 ^ 10 * m + 96) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_96 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_96 : oddCount 96 10 = 2 ∧ acceleratedOrbit 10 96 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_96 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 96) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_96.1, data_10_96.2] + +/-- Complete interval computation for depth 10, residue 97. -/ +theorem bounds_10_97 : exactInterval 10 97 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_97 (m : Nat) : + stoppingTime (2 ^ 10 * m + 97) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_97 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_97 : oddCount 97 10 = 6 ∧ acceleratedOrbit 10 97 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_97 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 97) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_97.1, data_10_97.2] + +/-- Complete interval computation for depth 10, residue 98. -/ +theorem bounds_10_98 : exactInterval 10 98 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_98 (m : Nat) : + stoppingTime (2 ^ 10 * m + 98) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_98 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_98 : oddCount 98 10 = 5 ∧ acceleratedOrbit 10 98 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_98 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 98) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_98.1, data_10_98.2] + +/-- Complete interval computation for depth 10, residue 99. -/ +theorem bounds_10_99 : exactInterval 10 99 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_99 (m : Nat) : + stoppingTime (2 ^ 10 * m + 99) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_99 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_99 : oddCount 99 10 = 5 ∧ acceleratedOrbit 10 99 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_99 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 99) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_99.1, data_10_99.2] + +/-- Complete interval computation for depth 10, residue 100. -/ +theorem bounds_10_100 : exactInterval 10 100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_100 (m : Nat) : + stoppingTime (2 ^ 10 * m + 100) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_100 : oddCount 100 10 = 5 ∧ acceleratedOrbit 10 100 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_100 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 100) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_100.1, data_10_100.2] + +/-- Complete interval computation for depth 10, residue 101. -/ +theorem bounds_10_101 : exactInterval 10 101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_101 (m : Nat) : + stoppingTime (2 ^ 10 * m + 101) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_101 : oddCount 101 10 = 5 ∧ acceleratedOrbit 10 101 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_101 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 101) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_101.1, data_10_101.2] + +/-- Complete interval computation for depth 10, residue 102. -/ +theorem bounds_10_102 : exactInterval 10 102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_102 (m : Nat) : + stoppingTime (2 ^ 10 * m + 102) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_102 : oddCount 102 10 = 5 ∧ acceleratedOrbit 10 102 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_102 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 102) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_102.1, data_10_102.2] + +/-- Complete interval computation for depth 10, residue 103. -/ +theorem bounds_10_103 : exactInterval 10 103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_103 (m : Nat) : + stoppingTime (2 ^ 10 * m + 103) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_103 : oddCount 103 10 = 8 ∧ acceleratedOrbit 10 103 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_103 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 103) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_103.1, data_10_103.2] + +/-- Complete interval computation for depth 10, residue 104. -/ +theorem bounds_10_104 : exactInterval 10 104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_104 (m : Nat) : + stoppingTime (2 ^ 10 * m + 104) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_104 : oddCount 104 10 = 2 ∧ acceleratedOrbit 10 104 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_104 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 104) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_104.1, data_10_104.2] + +/-- Complete interval computation for depth 10, residue 105. -/ +theorem bounds_10_105 : exactInterval 10 105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_105 (m : Nat) : + stoppingTime (2 ^ 10 * m + 105) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_105 : oddCount 105 10 = 6 ∧ acceleratedOrbit 10 105 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_105 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 105) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_105.1, data_10_105.2] + +/-- Complete interval computation for depth 10, residue 106. -/ +theorem bounds_10_106 : exactInterval 10 106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_106 (m : Nat) : + stoppingTime (2 ^ 10 * m + 106) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_106 : oddCount 106 10 = 2 ∧ acceleratedOrbit 10 106 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_106 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 106) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_106.1, data_10_106.2] + +end Collatz.Research.StoppingAtlas.Batch0007 From d6b0b2454246fe9809337f8026b2f38fa33843d5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:00 +0530 Subject: [PATCH 0008/1001] proof: certify atlas Batch0008 (10:107 to 10:121) --- Collatz/Research/StoppingAtlas/Batch0008.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0008.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0008.lean b/Collatz/Research/StoppingAtlas/Batch0008.lean new file mode 100644 index 00000000..e49c3249 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0008.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0008 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 107. -/ +theorem bounds_10_107 : exactInterval 10 107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_107 (m : Nat) : + stoppingTime (2 ^ 10 * m + 107) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_107 : oddCount 107 10 = 7 ∧ acceleratedOrbit 10 107 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_107 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 107) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_107.1, data_10_107.2] + +/-- Complete interval computation for depth 10, residue 108. -/ +theorem bounds_10_108 : exactInterval 10 108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_108 (m : Nat) : + stoppingTime (2 ^ 10 * m + 108) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_108 : oddCount 108 10 = 7 ∧ acceleratedOrbit 10 108 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_108 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 108) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_108.1, data_10_108.2] + +/-- Complete interval computation for depth 10, residue 109. -/ +theorem bounds_10_109 : exactInterval 10 109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_109 (m : Nat) : + stoppingTime (2 ^ 10 * m + 109) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_109 : oddCount 109 10 = 7 ∧ acceleratedOrbit 10 109 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_109 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 109) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_109.1, data_10_109.2] + +/-- Complete interval computation for depth 10, residue 110. -/ +theorem bounds_10_110 : exactInterval 10 110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_110 (m : Nat) : + stoppingTime (2 ^ 10 * m + 110) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_110 : oddCount 110 10 = 7 ∧ acceleratedOrbit 10 110 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_110 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 110) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_110.1, data_10_110.2] + +/-- Complete interval computation for depth 10, residue 111. -/ +theorem bounds_10_111 : exactInterval 10 111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_111 (m : Nat) : + stoppingTime (2 ^ 10 * m + 111) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_111 : oddCount 111 10 = 8 ∧ acceleratedOrbit 10 111 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_111 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 111) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_111.1, data_10_111.2] + +/-- Complete interval computation for depth 10, residue 112. -/ +theorem bounds_10_112 : exactInterval 10 112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_112 (m : Nat) : + stoppingTime (2 ^ 10 * m + 112) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_112 : oddCount 112 10 = 4 ∧ acceleratedOrbit 10 112 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_112 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 112) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_112.1, data_10_112.2] + +/-- Complete interval computation for depth 10, residue 113. -/ +theorem bounds_10_113 : exactInterval 10 113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_113 (m : Nat) : + stoppingTime (2 ^ 10 * m + 113) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_113 : oddCount 113 10 = 2 ∧ acceleratedOrbit 10 113 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_113 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 113) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_113.1, data_10_113.2] + +/-- Complete interval computation for depth 10, residue 114. -/ +theorem bounds_10_114 : exactInterval 10 114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_114 (m : Nat) : + stoppingTime (2 ^ 10 * m + 114) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_114 : oddCount 114 10 = 5 ∧ acceleratedOrbit 10 114 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_114 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 114) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_114.1, data_10_114.2] + +/-- Complete interval computation for depth 10, residue 115. -/ +theorem bounds_10_115 : exactInterval 10 115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_115 (m : Nat) : + stoppingTime (2 ^ 10 * m + 115) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_115 : oddCount 115 10 = 5 ∧ acceleratedOrbit 10 115 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_115 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 115) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_115.1, data_10_115.2] + +/-- Complete interval computation for depth 10, residue 116. -/ +theorem bounds_10_116 : exactInterval 10 116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_116 (m : Nat) : + stoppingTime (2 ^ 10 * m + 116) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_116 : oddCount 116 10 = 4 ∧ acceleratedOrbit 10 116 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_116 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 116) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_116.1, data_10_116.2] + +/-- Complete interval computation for depth 10, residue 117. -/ +theorem bounds_10_117 : exactInterval 10 117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_117 (m : Nat) : + stoppingTime (2 ^ 10 * m + 117) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_117 : oddCount 117 10 = 4 ∧ acceleratedOrbit 10 117 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_117 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 117) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_117.1, data_10_117.2] + +/-- Complete interval computation for depth 10, residue 118. -/ +theorem bounds_10_118 : exactInterval 10 118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_118 (m : Nat) : + stoppingTime (2 ^ 10 * m + 118) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_118 : oddCount 118 10 = 5 ∧ acceleratedOrbit 10 118 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_118 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 118) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_118.1, data_10_118.2] + +/-- Complete interval computation for depth 10, residue 119. -/ +theorem bounds_10_119 : exactInterval 10 119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_119 (m : Nat) : + stoppingTime (2 ^ 10 * m + 119) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_119 : oddCount 119 10 = 5 ∧ acceleratedOrbit 10 119 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_119 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 119) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_119.1, data_10_119.2] + +/-- Complete interval computation for depth 10, residue 120. -/ +theorem bounds_10_120 : exactInterval 10 120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_120 (m : Nat) : + stoppingTime (2 ^ 10 * m + 120) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_120 : oddCount 120 10 = 4 ∧ acceleratedOrbit 10 120 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_120 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 120) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_120.1, data_10_120.2] + +/-- Complete interval computation for depth 10, residue 121. -/ +theorem bounds_10_121 : exactInterval 10 121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_121 (m : Nat) : + stoppingTime (2 ^ 10 * m + 121) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_121 : oddCount 121 10 = 7 ∧ acceleratedOrbit 10 121 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_121 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 121) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_121.1, data_10_121.2] + +end Collatz.Research.StoppingAtlas.Batch0008 From 31158b738234cf8749656bbb02c3fba49c63af1d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:01 +0530 Subject: [PATCH 0009/1001] proof: certify atlas Batch0009 (10:122 to 10:137) --- Collatz/Research/StoppingAtlas/Batch0009.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0009.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0009.lean b/Collatz/Research/StoppingAtlas/Batch0009.lean new file mode 100644 index 00000000..79a52ba1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0009.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0009 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 122. -/ +theorem bounds_10_122 : exactInterval 10 122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_122 (m : Nat) : + stoppingTime (2 ^ 10 * m + 122) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_122 : oddCount 122 10 = 4 ∧ acceleratedOrbit 10 122 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_122 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 122) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_122.1, data_10_122.2] + +/-- Complete interval computation for depth 10, residue 123. -/ +theorem bounds_10_123 : exactInterval 10 123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_123 (m : Nat) : + stoppingTime (2 ^ 10 * m + 123) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_123 : oddCount 123 10 = 6 ∧ acceleratedOrbit 10 123 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_123 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 123) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_123.1, data_10_123.2] + +/-- Complete interval computation for depth 10, residue 124. -/ +theorem bounds_10_124 : exactInterval 10 124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_124 (m : Nat) : + stoppingTime (2 ^ 10 * m + 124) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_124 : oddCount 124 10 = 6 ∧ acceleratedOrbit 10 124 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_124 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 124) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_124.1, data_10_124.2] + +/-- Complete interval computation for depth 10, residue 125. -/ +theorem bounds_10_125 : exactInterval 10 125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_125 (m : Nat) : + stoppingTime (2 ^ 10 * m + 125) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_125 : oddCount 125 10 = 6 ∧ acceleratedOrbit 10 125 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_125 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 125) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_125.1, data_10_125.2] + +/-- Complete interval computation for depth 10, residue 126. -/ +theorem bounds_10_126 : exactInterval 10 126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_126 (m : Nat) : + stoppingTime (2 ^ 10 * m + 126) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_126 : oddCount 126 10 = 6 ∧ acceleratedOrbit 10 126 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_126 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 126) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_126.1, data_10_126.2] + +/-- Complete interval computation for depth 10, residue 127. -/ +theorem bounds_10_127 : exactInterval 10 127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_127 (m : Nat) : + stoppingTime (2 ^ 10 * m + 127) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_127 : oddCount 127 10 = 8 ∧ acceleratedOrbit 10 127 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_127 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 127) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_127.1, data_10_127.2] + +/-- Complete interval computation for depth 10, residue 128. -/ +theorem bounds_10_128 : exactInterval 10 128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_128 (m : Nat) : + stoppingTime (2 ^ 10 * m + 128) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_128 : oddCount 128 10 = 2 ∧ acceleratedOrbit 10 128 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_128 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 128) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_128.1, data_10_128.2] + +/-- Complete interval computation for depth 10, residue 129. -/ +theorem bounds_10_129 : exactInterval 10 129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_129 (m : Nat) : + stoppingTime (2 ^ 10 * m + 129) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_129 : oddCount 129 10 = 6 ∧ acceleratedOrbit 10 129 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_129 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 129) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_129.1, data_10_129.2] + +/-- Complete interval computation for depth 10, residue 130. -/ +theorem bounds_10_130 : exactInterval 10 130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_130 (m : Nat) : + stoppingTime (2 ^ 10 * m + 130) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_130 : oddCount 130 10 = 4 ∧ acceleratedOrbit 10 130 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_130 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 130) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_130.1, data_10_130.2] + +/-- Complete interval computation for depth 10, residue 131. -/ +theorem bounds_10_131 : exactInterval 10 131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_131 (m : Nat) : + stoppingTime (2 ^ 10 * m + 131) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_131 : oddCount 131 10 = 4 ∧ acceleratedOrbit 10 131 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_131 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 131) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_131.1, data_10_131.2] + +/-- Complete interval computation for depth 10, residue 132. -/ +theorem bounds_10_132 : exactInterval 10 132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_132 (m : Nat) : + stoppingTime (2 ^ 10 * m + 132) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_132 : oddCount 132 10 = 4 ∧ acceleratedOrbit 10 132 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_132 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 132) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_132.1, data_10_132.2] + +/-- Complete interval computation for depth 10, residue 133. -/ +theorem bounds_10_133 : exactInterval 10 133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_133 (m : Nat) : + stoppingTime (2 ^ 10 * m + 133) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_133 : oddCount 133 10 = 4 ∧ acceleratedOrbit 10 133 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_133 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 133) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_133.1, data_10_133.2] + +/-- Complete interval computation for depth 10, residue 134. -/ +theorem bounds_10_134 : exactInterval 10 134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_134 (m : Nat) : + stoppingTime (2 ^ 10 * m + 134) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_134 : oddCount 134 10 = 4 ∧ acceleratedOrbit 10 134 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_134 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 134) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_134.1, data_10_134.2] + +/-- Complete interval computation for depth 10, residue 135. -/ +theorem bounds_10_135 : exactInterval 10 135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_135 (m : Nat) : + stoppingTime (2 ^ 10 * m + 135) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_135 : oddCount 135 10 = 6 ∧ acceleratedOrbit 10 135 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_135 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 135) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_135.1, data_10_135.2] + +/-- Complete interval computation for depth 10, residue 136. -/ +theorem bounds_10_136 : exactInterval 10 136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_136 (m : Nat) : + stoppingTime (2 ^ 10 * m + 136) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_136 : oddCount 136 10 = 3 ∧ acceleratedOrbit 10 136 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_136 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 136) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_136.1, data_10_136.2] + +/-- Complete interval computation for depth 10, residue 137. -/ +theorem bounds_10_137 : exactInterval 10 137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_137 (m : Nat) : + stoppingTime (2 ^ 10 * m + 137) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_137 : oddCount 137 10 = 8 ∧ acceleratedOrbit 10 137 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_137 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 137) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_137.1, data_10_137.2] + +end Collatz.Research.StoppingAtlas.Batch0009 From 56d0e4ad48716ffcf0962ce53819e2586b716401 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:01 +0530 Subject: [PATCH 0010/1001] proof: certify atlas Batch0010 (10:138 to 10:152) --- Collatz/Research/StoppingAtlas/Batch0010.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0010.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0010.lean b/Collatz/Research/StoppingAtlas/Batch0010.lean new file mode 100644 index 00000000..eef5493e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0010.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0010 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 138. -/ +theorem bounds_10_138 : exactInterval 10 138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_138 (m : Nat) : + stoppingTime (2 ^ 10 * m + 138) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_138 : oddCount 138 10 = 3 ∧ acceleratedOrbit 10 138 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_138 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 138) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_138.1, data_10_138.2] + +/-- Complete interval computation for depth 10, residue 139. -/ +theorem bounds_10_139 : exactInterval 10 139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_139 (m : Nat) : + stoppingTime (2 ^ 10 * m + 139) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_139 : oddCount 139 10 = 6 ∧ acceleratedOrbit 10 139 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_139 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 139) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_139.1, data_10_139.2] + +/-- Complete interval computation for depth 10, residue 140. -/ +theorem bounds_10_140 : exactInterval 10 140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_140 (m : Nat) : + stoppingTime (2 ^ 10 * m + 140) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_140 : oddCount 140 10 = 3 ∧ acceleratedOrbit 10 140 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_140 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 140) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_140.1, data_10_140.2] + +/-- Complete interval computation for depth 10, residue 141. -/ +theorem bounds_10_141 : exactInterval 10 141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_141 (m : Nat) : + stoppingTime (2 ^ 10 * m + 141) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_141 : oddCount 141 10 = 3 ∧ acceleratedOrbit 10 141 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_141 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 141) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_141.1, data_10_141.2] + +/-- Complete interval computation for depth 10, residue 142. -/ +theorem bounds_10_142 : exactInterval 10 142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_142 (m : Nat) : + stoppingTime (2 ^ 10 * m + 142) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_142 : oddCount 142 10 = 6 ∧ acceleratedOrbit 10 142 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_142 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 142) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_142.1, data_10_142.2] + +/-- Complete interval computation for depth 10, residue 143. -/ +theorem bounds_10_143 : exactInterval 10 143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_143 (m : Nat) : + stoppingTime (2 ^ 10 * m + 143) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_143 : oddCount 143 10 = 6 ∧ acceleratedOrbit 10 143 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_143 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 143) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_143.1, data_10_143.2] + +/-- Complete interval computation for depth 10, residue 144. -/ +theorem bounds_10_144 : exactInterval 10 144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_144 (m : Nat) : + stoppingTime (2 ^ 10 * m + 144) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_144 : oddCount 144 10 = 4 ∧ acceleratedOrbit 10 144 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_144 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 144) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_144.1, data_10_144.2] + +/-- Complete interval computation for depth 10, residue 145. -/ +theorem bounds_10_145 : exactInterval 10 145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_145 (m : Nat) : + stoppingTime (2 ^ 10 * m + 145) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_145 : oddCount 145 10 = 6 ∧ acceleratedOrbit 10 145 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_145 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 145) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_145.1, data_10_145.2] + +/-- Complete interval computation for depth 10, residue 146. -/ +theorem bounds_10_146 : exactInterval 10 146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_146 (m : Nat) : + stoppingTime (2 ^ 10 * m + 146) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_146 : oddCount 146 10 = 6 ∧ acceleratedOrbit 10 146 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_146 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 146) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_146.1, data_10_146.2] + +/-- Complete interval computation for depth 10, residue 147. -/ +theorem bounds_10_147 : exactInterval 10 147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_147 (m : Nat) : + stoppingTime (2 ^ 10 * m + 147) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_147 : oddCount 147 10 = 6 ∧ acceleratedOrbit 10 147 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_147 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 147) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_147.1, data_10_147.2] + +/-- Complete interval computation for depth 10, residue 148. -/ +theorem bounds_10_148 : exactInterval 10 148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_148 (m : Nat) : + stoppingTime (2 ^ 10 * m + 148) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_148 : oddCount 148 10 = 4 ∧ acceleratedOrbit 10 148 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_148 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 148) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_148.1, data_10_148.2] + +/-- Complete interval computation for depth 10, residue 149. -/ +theorem bounds_10_149 : exactInterval 10 149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_149 (m : Nat) : + stoppingTime (2 ^ 10 * m + 149) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_149 : oddCount 149 10 = 4 ∧ acceleratedOrbit 10 149 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_149 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 149) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_149.1, data_10_149.2] + +/-- Complete interval computation for depth 10, residue 150. -/ +theorem bounds_10_150 : exactInterval 10 150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_150 (m : Nat) : + stoppingTime (2 ^ 10 * m + 150) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_150 : oddCount 150 10 = 3 ∧ acceleratedOrbit 10 150 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_150 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 150) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_150.1, data_10_150.2] + +/-- Complete interval computation for depth 10, residue 151. -/ +theorem bounds_10_151 : exactInterval 10 151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_151 (m : Nat) : + stoppingTime (2 ^ 10 * m + 151) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_151 : oddCount 151 10 = 3 ∧ acceleratedOrbit 10 151 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_151 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 151) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_151.1, data_10_151.2] + +/-- Complete interval computation for depth 10, residue 152. -/ +theorem bounds_10_152 : exactInterval 10 152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_152 (m : Nat) : + stoppingTime (2 ^ 10 * m + 152) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_152 : oddCount 152 10 = 4 ∧ acceleratedOrbit 10 152 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_152 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 152) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_152.1, data_10_152.2] + +end Collatz.Research.StoppingAtlas.Batch0010 From 7f7dedd7bd09fe9602f279302d376eb376c08123 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:01 +0530 Subject: [PATCH 0011/1001] proof: certify atlas Batch0011 (10:153 to 10:167) --- Collatz/Research/StoppingAtlas/Batch0011.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0011.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0011.lean b/Collatz/Research/StoppingAtlas/Batch0011.lean new file mode 100644 index 00000000..8663361c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0011.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0011 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 153. -/ +theorem bounds_10_153 : exactInterval 10 153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_153 (m : Nat) : + stoppingTime (2 ^ 10 * m + 153) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_153 : oddCount 153 10 = 5 ∧ acceleratedOrbit 10 153 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_153 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 153) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_153.1, data_10_153.2] + +/-- Complete interval computation for depth 10, residue 154. -/ +theorem bounds_10_154 : exactInterval 10 154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_154 (m : Nat) : + stoppingTime (2 ^ 10 * m + 154) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_154 : oddCount 154 10 = 4 ∧ acceleratedOrbit 10 154 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_154 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 154) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_154.1, data_10_154.2] + +/-- Complete interval computation for depth 10, residue 155. -/ +theorem bounds_10_155 : exactInterval 10 155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_155 (m : Nat) : + stoppingTime (2 ^ 10 * m + 155) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_155 : oddCount 155 10 = 7 ∧ acceleratedOrbit 10 155 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_155 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 155) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_155.1, data_10_155.2] + +/-- Complete interval computation for depth 10, residue 156. -/ +theorem bounds_10_156 : exactInterval 10 156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_156 (m : Nat) : + stoppingTime (2 ^ 10 * m + 156) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_156 : oddCount 156 10 = 5 ∧ acceleratedOrbit 10 156 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_156 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 156) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_156.1, data_10_156.2] + +/-- Complete interval computation for depth 10, residue 157. -/ +theorem bounds_10_157 : exactInterval 10 157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_157 (m : Nat) : + stoppingTime (2 ^ 10 * m + 157) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_157 : oddCount 157 10 = 5 ∧ acceleratedOrbit 10 157 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_157 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 157) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_157.1, data_10_157.2] + +/-- Complete interval computation for depth 10, residue 158. -/ +theorem bounds_10_158 : exactInterval 10 158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_158 (m : Nat) : + stoppingTime (2 ^ 10 * m + 158) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_158 : oddCount 158 10 = 5 ∧ acceleratedOrbit 10 158 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_158 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 158) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_158.1, data_10_158.2] + +/-- Complete interval computation for depth 10, residue 159. -/ +theorem bounds_10_159 : exactInterval 10 159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_159 (m : Nat) : + stoppingTime (2 ^ 10 * m + 159) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_159 : oddCount 159 10 = 9 ∧ acceleratedOrbit 10 159 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_159 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 159) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_159.1, data_10_159.2] + +/-- Complete interval computation for depth 10, residue 160. -/ +theorem bounds_10_160 : exactInterval 10 160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_160 (m : Nat) : + stoppingTime (2 ^ 10 * m + 160) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_160 : oddCount 160 10 = 2 ∧ acceleratedOrbit 10 160 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_160 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 160) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_160.1, data_10_160.2] + +/-- Complete interval computation for depth 10, residue 161. -/ +theorem bounds_10_161 : exactInterval 10 161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_161 (m : Nat) : + stoppingTime (2 ^ 10 * m + 161) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_161 : oddCount 161 10 = 7 ∧ acceleratedOrbit 10 161 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_161 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 161) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_161.1, data_10_161.2] + +/-- Complete interval computation for depth 10, residue 162. -/ +theorem bounds_10_162 : exactInterval 10 162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_162 (m : Nat) : + stoppingTime (2 ^ 10 * m + 162) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_162 : oddCount 162 10 = 5 ∧ acceleratedOrbit 10 162 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_162 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 162) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_162.1, data_10_162.2] + +/-- Complete interval computation for depth 10, residue 163. -/ +theorem bounds_10_163 : exactInterval 10 163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_163 (m : Nat) : + stoppingTime (2 ^ 10 * m + 163) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_163 : oddCount 163 10 = 5 ∧ acceleratedOrbit 10 163 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_163 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 163) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_163.1, data_10_163.2] + +/-- Complete interval computation for depth 10, residue 164. -/ +theorem bounds_10_164 : exactInterval 10 164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_164 (m : Nat) : + stoppingTime (2 ^ 10 * m + 164) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_164 : oddCount 164 10 = 6 ∧ acceleratedOrbit 10 164 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_164 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 164) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_164.1, data_10_164.2] + +/-- Complete interval computation for depth 10, residue 165. -/ +theorem bounds_10_165 : exactInterval 10 165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_165 (m : Nat) : + stoppingTime (2 ^ 10 * m + 165) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_165 : oddCount 165 10 = 6 ∧ acceleratedOrbit 10 165 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_165 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 165) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_165.1, data_10_165.2] + +/-- Complete interval computation for depth 10, residue 166. -/ +theorem bounds_10_166 : exactInterval 10 166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_166 (m : Nat) : + stoppingTime (2 ^ 10 * m + 166) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_166 : oddCount 166 10 = 6 ∧ acceleratedOrbit 10 166 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_166 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 166) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_166.1, data_10_166.2] + +/-- Complete interval computation for depth 10, residue 167. -/ +theorem bounds_10_167 : exactInterval 10 167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_167 (m : Nat) : + stoppingTime (2 ^ 10 * m + 167) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_167 : oddCount 167 10 = 8 ∧ acceleratedOrbit 10 167 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_167 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 167) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_167.1, data_10_167.2] + +end Collatz.Research.StoppingAtlas.Batch0011 From d5e1a176c02156508f7f22c2ee5b0b3738ac0ce2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:01 +0530 Subject: [PATCH 0012/1001] proof: certify atlas Batch0012 (10:168 to 10:183) --- Collatz/Research/StoppingAtlas/Batch0012.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0012.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0012.lean b/Collatz/Research/StoppingAtlas/Batch0012.lean new file mode 100644 index 00000000..55622adc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0012.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0012 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 168. -/ +theorem bounds_10_168 : exactInterval 10 168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_168 (m : Nat) : + stoppingTime (2 ^ 10 * m + 168) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_168 : oddCount 168 10 = 2 ∧ acceleratedOrbit 10 168 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_168 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 168) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_168.1, data_10_168.2] + +/-- Complete interval computation for depth 10, residue 169. -/ +theorem bounds_10_169 : exactInterval 10 169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_169 (m : Nat) : + stoppingTime (2 ^ 10 * m + 169) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_169 : oddCount 169 10 = 8 ∧ acceleratedOrbit 10 169 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_169 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 169) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_169.1, data_10_169.2] + +/-- Complete interval computation for depth 10, residue 170. -/ +theorem bounds_10_170 : exactInterval 10 170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_170 (m : Nat) : + stoppingTime (2 ^ 10 * m + 170) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_170 : oddCount 170 10 = 2 ∧ acceleratedOrbit 10 170 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_170 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 170) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_170.1, data_10_170.2] + +/-- Complete interval computation for depth 10, residue 171. -/ +theorem bounds_10_171 : exactInterval 10 171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_171 (m : Nat) : + stoppingTime (2 ^ 10 * m + 171) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_171 : oddCount 171 10 = 5 ∧ acceleratedOrbit 10 171 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_171 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 171) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_171.1, data_10_171.2] + +/-- Complete interval computation for depth 10, residue 172. -/ +theorem bounds_10_172 : exactInterval 10 172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_172 (m : Nat) : + stoppingTime (2 ^ 10 * m + 172) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_172 : oddCount 172 10 = 4 ∧ acceleratedOrbit 10 172 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_172 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 172) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_172.1, data_10_172.2] + +/-- Complete interval computation for depth 10, residue 173. -/ +theorem bounds_10_173 : exactInterval 10 173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_173 (m : Nat) : + stoppingTime (2 ^ 10 * m + 173) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_173 : oddCount 173 10 = 4 ∧ acceleratedOrbit 10 173 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_173 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 173) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_173.1, data_10_173.2] + +/-- Complete interval computation for depth 10, residue 174. -/ +theorem bounds_10_174 : exactInterval 10 174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_174 (m : Nat) : + stoppingTime (2 ^ 10 * m + 174) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_174 : oddCount 174 10 = 4 ∧ acceleratedOrbit 10 174 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_174 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 174) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_174.1, data_10_174.2] + +/-- Complete interval computation for depth 10, residue 175. -/ +theorem bounds_10_175 : exactInterval 10 175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_175 (m : Nat) : + stoppingTime (2 ^ 10 * m + 175) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_175 : oddCount 175 10 = 7 ∧ acceleratedOrbit 10 175 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_175 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 175) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_175.1, data_10_175.2] + +/-- Complete interval computation for depth 10, residue 176. -/ +theorem bounds_10_176 : exactInterval 10 176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_176 (m : Nat) : + stoppingTime (2 ^ 10 * m + 176) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_176 : oddCount 176 10 = 3 ∧ acceleratedOrbit 10 176 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_176 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 176) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_176.1, data_10_176.2] + +/-- Complete interval computation for depth 10, residue 177. -/ +theorem bounds_10_177 : exactInterval 10 177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_177 (m : Nat) : + stoppingTime (2 ^ 10 * m + 177) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_177 : oddCount 177 10 = 5 ∧ acceleratedOrbit 10 177 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_177 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 177) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_177.1, data_10_177.2] + +/-- Complete interval computation for depth 10, residue 178. -/ +theorem bounds_10_178 : exactInterval 10 178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_178 (m : Nat) : + stoppingTime (2 ^ 10 * m + 178) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_178 : oddCount 178 10 = 5 ∧ acceleratedOrbit 10 178 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_178 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 178) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_178.1, data_10_178.2] + +/-- Complete interval computation for depth 10, residue 179. -/ +theorem bounds_10_179 : exactInterval 10 179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_179 (m : Nat) : + stoppingTime (2 ^ 10 * m + 179) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_179 : oddCount 179 10 = 5 ∧ acceleratedOrbit 10 179 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_179 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 179) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_179.1, data_10_179.2] + +/-- Complete interval computation for depth 10, residue 180. -/ +theorem bounds_10_180 : exactInterval 10 180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_180 (m : Nat) : + stoppingTime (2 ^ 10 * m + 180) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_180 : oddCount 180 10 = 3 ∧ acceleratedOrbit 10 180 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_180 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 180) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_180.1, data_10_180.2] + +/-- Complete interval computation for depth 10, residue 181. -/ +theorem bounds_10_181 : exactInterval 10 181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_181 (m : Nat) : + stoppingTime (2 ^ 10 * m + 181) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_181 : oddCount 181 10 = 3 ∧ acceleratedOrbit 10 181 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_181 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 181) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_181.1, data_10_181.2] + +/-- Complete interval computation for depth 10, residue 182. -/ +theorem bounds_10_182 : exactInterval 10 182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_182 (m : Nat) : + stoppingTime (2 ^ 10 * m + 182) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_182 : oddCount 182 10 = 7 ∧ acceleratedOrbit 10 182 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_182 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 182) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_182.1, data_10_182.2] + +/-- Complete interval computation for depth 10, residue 183. -/ +theorem bounds_10_183 : exactInterval 10 183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_183 (m : Nat) : + stoppingTime (2 ^ 10 * m + 183) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_183 : oddCount 183 10 = 7 ∧ acceleratedOrbit 10 183 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_183 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 183) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_183.1, data_10_183.2] + +end Collatz.Research.StoppingAtlas.Batch0012 From b4e45cca49d26bc87b6232388528102db9d5319c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:02 +0530 Subject: [PATCH 0013/1001] proof: certify atlas Batch0013 (10:184 to 10:198) --- Collatz/Research/StoppingAtlas/Batch0013.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0013.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0013.lean b/Collatz/Research/StoppingAtlas/Batch0013.lean new file mode 100644 index 00000000..a911791a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0013.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0013 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 184. -/ +theorem bounds_10_184 : exactInterval 10 184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_184 (m : Nat) : + stoppingTime (2 ^ 10 * m + 184) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_184 : oddCount 184 10 = 3 ∧ acceleratedOrbit 10 184 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_184 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 184) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_184.1, data_10_184.2] + +/-- Complete interval computation for depth 10, residue 185. -/ +theorem bounds_10_185 : exactInterval 10 185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_185 (m : Nat) : + stoppingTime (2 ^ 10 * m + 185) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_185 : oddCount 185 10 = 6 ∧ acceleratedOrbit 10 185 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_185 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 185) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_185.1, data_10_185.2] + +/-- Complete interval computation for depth 10, residue 186. -/ +theorem bounds_10_186 : exactInterval 10 186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_186 (m : Nat) : + stoppingTime (2 ^ 10 * m + 186) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_186 : oddCount 186 10 = 3 ∧ acceleratedOrbit 10 186 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_186 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 186) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_186.1, data_10_186.2] + +/-- Complete interval computation for depth 10, residue 187. -/ +theorem bounds_10_187 : exactInterval 10 187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_187 (m : Nat) : + stoppingTime (2 ^ 10 * m + 187) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_187 : oddCount 187 10 = 7 ∧ acceleratedOrbit 10 187 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_187 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 187) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_187.1, data_10_187.2] + +/-- Complete interval computation for depth 10, residue 188. -/ +theorem bounds_10_188 : exactInterval 10 188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_188 (m : Nat) : + stoppingTime (2 ^ 10 * m + 188) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_188 : oddCount 188 10 = 6 ∧ acceleratedOrbit 10 188 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_188 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 188) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_188.1, data_10_188.2] + +/-- Complete interval computation for depth 10, residue 189. -/ +theorem bounds_10_189 : exactInterval 10 189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_189 (m : Nat) : + stoppingTime (2 ^ 10 * m + 189) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_189 : oddCount 189 10 = 6 ∧ acceleratedOrbit 10 189 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_189 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 189) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_189.1, data_10_189.2] + +/-- Complete interval computation for depth 10, residue 190. -/ +theorem bounds_10_190 : exactInterval 10 190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_190 (m : Nat) : + stoppingTime (2 ^ 10 * m + 190) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_190 : oddCount 190 10 = 6 ∧ acceleratedOrbit 10 190 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_190 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 190) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_190.1, data_10_190.2] + +/-- Complete interval computation for depth 10, residue 191. -/ +theorem bounds_10_191 : exactInterval 10 191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_191 (m : Nat) : + stoppingTime (2 ^ 10 * m + 191) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_191 : oddCount 191 10 = 7 ∧ acceleratedOrbit 10 191 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_191 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 191) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_191.1, data_10_191.2] + +/-- Complete interval computation for depth 10, residue 192. -/ +theorem bounds_10_192 : exactInterval 10 192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_192 (m : Nat) : + stoppingTime (2 ^ 10 * m + 192) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_192 : oddCount 192 10 = 2 ∧ acceleratedOrbit 10 192 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_192 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 192) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_192.1, data_10_192.2] + +/-- Complete interval computation for depth 10, residue 193. -/ +theorem bounds_10_193 : exactInterval 10 193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_193 (m : Nat) : + stoppingTime (2 ^ 10 * m + 193) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_193 : oddCount 193 10 = 5 ∧ acceleratedOrbit 10 193 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_193 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 193) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_193.1, data_10_193.2] + +/-- Complete interval computation for depth 10, residue 194. -/ +theorem bounds_10_194 : exactInterval 10 194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_194 (m : Nat) : + stoppingTime (2 ^ 10 * m + 194) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_194 : oddCount 194 10 = 5 ∧ acceleratedOrbit 10 194 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_194 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 194) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_194.1, data_10_194.2] + +/-- Complete interval computation for depth 10, residue 195. -/ +theorem bounds_10_195 : exactInterval 10 195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_195 (m : Nat) : + stoppingTime (2 ^ 10 * m + 195) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_195 : oddCount 195 10 = 5 ∧ acceleratedOrbit 10 195 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_195 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 195) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_195.1, data_10_195.2] + +/-- Complete interval computation for depth 10, residue 196. -/ +theorem bounds_10_196 : exactInterval 10 196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_196 (m : Nat) : + stoppingTime (2 ^ 10 * m + 196) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_196 : oddCount 196 10 = 4 ∧ acceleratedOrbit 10 196 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_196 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 196) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_196.1, data_10_196.2] + +/-- Complete interval computation for depth 10, residue 197. -/ +theorem bounds_10_197 : exactInterval 10 197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_197 (m : Nat) : + stoppingTime (2 ^ 10 * m + 197) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_197 : oddCount 197 10 = 4 ∧ acceleratedOrbit 10 197 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_197 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 197) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_197.1, data_10_197.2] + +/-- Complete interval computation for depth 10, residue 198. -/ +theorem bounds_10_198 : exactInterval 10 198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_198 (m : Nat) : + stoppingTime (2 ^ 10 * m + 198) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_198 : oddCount 198 10 = 4 ∧ acceleratedOrbit 10 198 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_198 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 198) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_198.1, data_10_198.2] + +end Collatz.Research.StoppingAtlas.Batch0013 From 24a9d478ef83ccb02a5778c104164512eef09116 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:02 +0530 Subject: [PATCH 0014/1001] proof: certify atlas Batch0014 (10:199 to 10:214) --- Collatz/Research/StoppingAtlas/Batch0014.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0014.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0014.lean b/Collatz/Research/StoppingAtlas/Batch0014.lean new file mode 100644 index 00000000..73335e4d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0014.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0014 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 199. -/ +theorem bounds_10_199 : exactInterval 10 199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_199 (m : Nat) : + stoppingTime (2 ^ 10 * m + 199) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_199 : oddCount 199 10 = 6 ∧ acceleratedOrbit 10 199 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_199 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 199) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_199.1, data_10_199.2] + +/-- Complete interval computation for depth 10, residue 200. -/ +theorem bounds_10_200 : exactInterval 10 200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_200 (m : Nat) : + stoppingTime (2 ^ 10 * m + 200) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_200 : oddCount 200 10 = 4 ∧ acceleratedOrbit 10 200 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_200 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 200) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_200.1, data_10_200.2] + +/-- Complete interval computation for depth 10, residue 201. -/ +theorem bounds_10_201 : exactInterval 10 201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_201 (m : Nat) : + stoppingTime (2 ^ 10 * m + 201) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_201 : oddCount 201 10 = 4 ∧ acceleratedOrbit 10 201 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_201 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 201) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_201.1, data_10_201.2] + +/-- Complete interval computation for depth 10, residue 202. -/ +theorem bounds_10_202 : exactInterval 10 202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_202 (m : Nat) : + stoppingTime (2 ^ 10 * m + 202) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_202 : oddCount 202 10 = 4 ∧ acceleratedOrbit 10 202 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_202 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 202) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_202.1, data_10_202.2] + +/-- Complete interval computation for depth 10, residue 203. -/ +theorem bounds_10_203 : exactInterval 10 203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_203 (m : Nat) : + stoppingTime (2 ^ 10 * m + 203) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_203 : oddCount 203 10 = 5 ∧ acceleratedOrbit 10 203 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_203 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 203) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_203.1, data_10_203.2] + +/-- Complete interval computation for depth 10, residue 204. -/ +theorem bounds_10_204 : exactInterval 10 204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_204 (m : Nat) : + stoppingTime (2 ^ 10 * m + 204) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_204 : oddCount 204 10 = 4 ∧ acceleratedOrbit 10 204 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_204 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 204) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_204.1, data_10_204.2] + +/-- Complete interval computation for depth 10, residue 205. -/ +theorem bounds_10_205 : exactInterval 10 205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_205 (m : Nat) : + stoppingTime (2 ^ 10 * m + 205) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_205 : oddCount 205 10 = 4 ∧ acceleratedOrbit 10 205 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_205 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 205) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_205.1, data_10_205.2] + +/-- Complete interval computation for depth 10, residue 206. -/ +theorem bounds_10_206 : exactInterval 10 206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_206 (m : Nat) : + stoppingTime (2 ^ 10 * m + 206) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_206 : oddCount 206 10 = 7 ∧ acceleratedOrbit 10 206 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_206 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 206) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_206.1, data_10_206.2] + +/-- Complete interval computation for depth 10, residue 207. -/ +theorem bounds_10_207 : exactInterval 10 207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_207 (m : Nat) : + stoppingTime (2 ^ 10 * m + 207) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_207 : oddCount 207 10 = 7 ∧ acceleratedOrbit 10 207 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_207 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 207) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_207.1, data_10_207.2] + +/-- Complete interval computation for depth 10, residue 208. -/ +theorem bounds_10_208 : exactInterval 10 208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_208 (m : Nat) : + stoppingTime (2 ^ 10 * m + 208) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_208 : oddCount 208 10 = 2 ∧ acceleratedOrbit 10 208 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_208 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 208) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_208.1, data_10_208.2] + +/-- Complete interval computation for depth 10, residue 209. -/ +theorem bounds_10_209 : exactInterval 10 209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_209 (m : Nat) : + stoppingTime (2 ^ 10 * m + 209) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_209 : oddCount 209 10 = 6 ∧ acceleratedOrbit 10 209 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_209 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 209) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_209.1, data_10_209.2] + +/-- Complete interval computation for depth 10, residue 210. -/ +theorem bounds_10_210 : exactInterval 10 210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_210 (m : Nat) : + stoppingTime (2 ^ 10 * m + 210) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_210 : oddCount 210 10 = 6 ∧ acceleratedOrbit 10 210 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_210 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 210) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_210.1, data_10_210.2] + +/-- Complete interval computation for depth 10, residue 211. -/ +theorem bounds_10_211 : exactInterval 10 211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_211 (m : Nat) : + stoppingTime (2 ^ 10 * m + 211) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_211 : oddCount 211 10 = 6 ∧ acceleratedOrbit 10 211 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_211 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 211) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_211.1, data_10_211.2] + +/-- Complete interval computation for depth 10, residue 212. -/ +theorem bounds_10_212 : exactInterval 10 212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_212 (m : Nat) : + stoppingTime (2 ^ 10 * m + 212) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_212 : oddCount 212 10 = 2 ∧ acceleratedOrbit 10 212 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_212 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 212) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_212.1, data_10_212.2] + +/-- Complete interval computation for depth 10, residue 213. -/ +theorem bounds_10_213 : exactInterval 10 213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_213 (m : Nat) : + stoppingTime (2 ^ 10 * m + 213) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_213 : oddCount 213 10 = 2 ∧ acceleratedOrbit 10 213 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_213 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 213) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_213.1, data_10_213.2] + +/-- Complete interval computation for depth 10, residue 214. -/ +theorem bounds_10_214 : exactInterval 10 214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_214 (m : Nat) : + stoppingTime (2 ^ 10 * m + 214) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_214 : oddCount 214 10 = 6 ∧ acceleratedOrbit 10 214 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_214 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 214) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_214.1, data_10_214.2] + +end Collatz.Research.StoppingAtlas.Batch0014 From b06f482e10f6abb2767ecbe22b2f20aaf397f090 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:02 +0530 Subject: [PATCH 0015/1001] proof: certify atlas Batch0015 (10:215 to 10:229) --- Collatz/Research/StoppingAtlas/Batch0015.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0015.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0015.lean b/Collatz/Research/StoppingAtlas/Batch0015.lean new file mode 100644 index 00000000..6a4331a1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0015.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0015 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 215. -/ +theorem bounds_10_215 : exactInterval 10 215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_215 (m : Nat) : + stoppingTime (2 ^ 10 * m + 215) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_215 : oddCount 215 10 = 6 ∧ acceleratedOrbit 10 215 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_215 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 215) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_215.1, data_10_215.2] + +/-- Complete interval computation for depth 10, residue 216. -/ +theorem bounds_10_216 : exactInterval 10 216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_216 (m : Nat) : + stoppingTime (2 ^ 10 * m + 216) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_216 : oddCount 216 10 = 6 ∧ acceleratedOrbit 10 216 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_216 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 216) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_216.1, data_10_216.2] + +/-- Complete interval computation for depth 10, residue 217. -/ +theorem bounds_10_217 : exactInterval 10 217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_217 (m : Nat) : + stoppingTime (2 ^ 10 * m + 217) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_217 : oddCount 217 10 = 5 ∧ acceleratedOrbit 10 217 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_217 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 217) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_217.1, data_10_217.2] + +/-- Complete interval computation for depth 10, residue 218. -/ +theorem bounds_10_218 : exactInterval 10 218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_218 (m : Nat) : + stoppingTime (2 ^ 10 * m + 218) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_218 : oddCount 218 10 = 6 ∧ acceleratedOrbit 10 218 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_218 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 218) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_218.1, data_10_218.2] + +/-- Complete interval computation for depth 10, residue 219. -/ +theorem bounds_10_219 : exactInterval 10 219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_219 (m : Nat) : + stoppingTime (2 ^ 10 * m + 219) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_219 : oddCount 219 10 = 6 ∧ acceleratedOrbit 10 219 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_219 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 219) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_219.1, data_10_219.2] + +/-- Complete interval computation for depth 10, residue 220. -/ +theorem bounds_10_220 : exactInterval 10 220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_220 (m : Nat) : + stoppingTime (2 ^ 10 * m + 220) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_220 : oddCount 220 10 = 6 ∧ acceleratedOrbit 10 220 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_220 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 220) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_220.1, data_10_220.2] + +/-- Complete interval computation for depth 10, residue 221. -/ +theorem bounds_10_221 : exactInterval 10 221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_221 (m : Nat) : + stoppingTime (2 ^ 10 * m + 221) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_221 : oddCount 221 10 = 6 ∧ acceleratedOrbit 10 221 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_221 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 221) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_221.1, data_10_221.2] + +/-- Complete interval computation for depth 10, residue 222. -/ +theorem bounds_10_222 : exactInterval 10 222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_222 (m : Nat) : + stoppingTime (2 ^ 10 * m + 222) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_222 : oddCount 222 10 = 7 ∧ acceleratedOrbit 10 222 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_222 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 222) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_222.1, data_10_222.2] + +/-- Complete interval computation for depth 10, residue 223. -/ +theorem bounds_10_223 : exactInterval 10 223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_223 (m : Nat) : + stoppingTime (2 ^ 10 * m + 223) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_223 : oddCount 223 10 = 7 ∧ acceleratedOrbit 10 223 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_223 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 223) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_223.1, data_10_223.2] + +/-- Complete interval computation for depth 10, residue 224. -/ +theorem bounds_10_224 : exactInterval 10 224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_224 (m : Nat) : + stoppingTime (2 ^ 10 * m + 224) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_224 : oddCount 224 10 = 4 ∧ acceleratedOrbit 10 224 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_224 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 224) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_224.1, data_10_224.2] + +/-- Complete interval computation for depth 10, residue 225. -/ +theorem bounds_10_225 : exactInterval 10 225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_225 (m : Nat) : + stoppingTime (2 ^ 10 * m + 225) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_225 : oddCount 225 10 = 8 ∧ acceleratedOrbit 10 225 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_225 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 225) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_225.1, data_10_225.2] + +/-- Complete interval computation for depth 10, residue 226. -/ +theorem bounds_10_226 : exactInterval 10 226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_226 (m : Nat) : + stoppingTime (2 ^ 10 * m + 226) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_226 : oddCount 226 10 = 2 ∧ acceleratedOrbit 10 226 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_226 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 226) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_226.1, data_10_226.2] + +/-- Complete interval computation for depth 10, residue 227. -/ +theorem bounds_10_227 : exactInterval 10 227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_227 (m : Nat) : + stoppingTime (2 ^ 10 * m + 227) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_227 : oddCount 227 10 = 2 ∧ acceleratedOrbit 10 227 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_227 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 227) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_227.1, data_10_227.2] + +/-- Complete interval computation for depth 10, residue 228. -/ +theorem bounds_10_228 : exactInterval 10 228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_228 (m : Nat) : + stoppingTime (2 ^ 10 * m + 228) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_228 : oddCount 228 10 = 5 ∧ acceleratedOrbit 10 228 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_228 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 228) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_228.1, data_10_228.2] + +/-- Complete interval computation for depth 10, residue 229. -/ +theorem bounds_10_229 : exactInterval 10 229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_229 (m : Nat) : + stoppingTime (2 ^ 10 * m + 229) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_229 : oddCount 229 10 = 5 ∧ acceleratedOrbit 10 229 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_229 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 229) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_229.1, data_10_229.2] + +end Collatz.Research.StoppingAtlas.Batch0015 From 57e4e9d18859199cab6b2f827f5880144a704be6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:03 +0530 Subject: [PATCH 0016/1001] proof: certify atlas Batch0016 (10:230 to 10:244) --- Collatz/Research/StoppingAtlas/Batch0016.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0016.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0016.lean b/Collatz/Research/StoppingAtlas/Batch0016.lean new file mode 100644 index 00000000..79318e0a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0016.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0016 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 230. -/ +theorem bounds_10_230 : exactInterval 10 230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_230 (m : Nat) : + stoppingTime (2 ^ 10 * m + 230) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_230 : oddCount 230 10 = 5 ∧ acceleratedOrbit 10 230 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_230 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 230) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_230.1, data_10_230.2] + +/-- Complete interval computation for depth 10, residue 231. -/ +theorem bounds_10_231 : exactInterval 10 231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_231 (m : Nat) : + stoppingTime (2 ^ 10 * m + 231) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_231 : oddCount 231 10 = 7 ∧ acceleratedOrbit 10 231 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_231 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 231) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_231.1, data_10_231.2] + +/-- Complete interval computation for depth 10, residue 232. -/ +theorem bounds_10_232 : exactInterval 10 232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_232 (m : Nat) : + stoppingTime (2 ^ 10 * m + 232) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_232 : oddCount 232 10 = 4 ∧ acceleratedOrbit 10 232 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_232 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 232) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_232.1, data_10_232.2] + +/-- Complete interval computation for depth 10, residue 233. -/ +theorem bounds_10_233 : exactInterval 10 233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_233 (m : Nat) : + stoppingTime (2 ^ 10 * m + 233) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_233 : oddCount 233 10 = 6 ∧ acceleratedOrbit 10 233 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_233 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 233) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_233.1, data_10_233.2] + +/-- Complete interval computation for depth 10, residue 234. -/ +theorem bounds_10_234 : exactInterval 10 234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_234 (m : Nat) : + stoppingTime (2 ^ 10 * m + 234) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_234 : oddCount 234 10 = 4 ∧ acceleratedOrbit 10 234 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_234 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 234) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_234.1, data_10_234.2] + +/-- Complete interval computation for depth 10, residue 235. -/ +theorem bounds_10_235 : exactInterval 10 235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_235 (m : Nat) : + stoppingTime (2 ^ 10 * m + 235) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_235 : oddCount 235 10 = 7 ∧ acceleratedOrbit 10 235 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_235 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 235) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_235.1, data_10_235.2] + +/-- Complete interval computation for depth 10, residue 236. -/ +theorem bounds_10_236 : exactInterval 10 236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_236 (m : Nat) : + stoppingTime (2 ^ 10 * m + 236) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_236 : oddCount 236 10 = 4 ∧ acceleratedOrbit 10 236 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_236 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 236) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_236.1, data_10_236.2] + +/-- Complete interval computation for depth 10, residue 237. -/ +theorem bounds_10_237 : exactInterval 10 237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_237 (m : Nat) : + stoppingTime (2 ^ 10 * m + 237) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_237 : oddCount 237 10 = 4 ∧ acceleratedOrbit 10 237 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_237 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 237) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_237.1, data_10_237.2] + +/-- Complete interval computation for depth 10, residue 238. -/ +theorem bounds_10_238 : exactInterval 10 238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_238 (m : Nat) : + stoppingTime (2 ^ 10 * m + 238) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_238 : oddCount 238 10 = 4 ∧ acceleratedOrbit 10 238 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_238 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 238) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_238.1, data_10_238.2] + +/-- Complete interval computation for depth 10, residue 239. -/ +theorem bounds_10_239 : exactInterval 10 239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_239 (m : Nat) : + stoppingTime (2 ^ 10 * m + 239) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_239 : oddCount 239 10 = 9 ∧ acceleratedOrbit 10 239 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_239 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 239) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_239.1, data_10_239.2] + +/-- Complete interval computation for depth 10, residue 240. -/ +theorem bounds_10_240 : exactInterval 10 240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_240 (m : Nat) : + stoppingTime (2 ^ 10 * m + 240) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_240 : oddCount 240 10 = 4 ∧ acceleratedOrbit 10 240 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_240 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 240) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_240.1, data_10_240.2] + +/-- Complete interval computation for depth 10, residue 241. -/ +theorem bounds_10_241 : exactInterval 10 241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_241 (m : Nat) : + stoppingTime (2 ^ 10 * m + 241) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_241 : oddCount 241 10 = 4 ∧ acceleratedOrbit 10 241 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_241 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 241) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_241.1, data_10_241.2] + +/-- Complete interval computation for depth 10, residue 242. -/ +theorem bounds_10_242 : exactInterval 10 242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_242 (m : Nat) : + stoppingTime (2 ^ 10 * m + 242) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_242 : oddCount 242 10 = 6 ∧ acceleratedOrbit 10 242 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_242 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 242) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_242.1, data_10_242.2] + +/-- Complete interval computation for depth 10, residue 243. -/ +theorem bounds_10_243 : exactInterval 10 243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_243 (m : Nat) : + stoppingTime (2 ^ 10 * m + 243) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_243 : oddCount 243 10 = 6 ∧ acceleratedOrbit 10 243 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_243 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 243) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_243.1, data_10_243.2] + +/-- Complete interval computation for depth 10, residue 244. -/ +theorem bounds_10_244 : exactInterval 10 244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_244 (m : Nat) : + stoppingTime (2 ^ 10 * m + 244) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_244 : oddCount 244 10 = 4 ∧ acceleratedOrbit 10 244 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_244 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 244) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_244.1, data_10_244.2] + +end Collatz.Research.StoppingAtlas.Batch0016 From 79a2fb6334f17f86ef23f933fa200b557b24b72d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:03 +0530 Subject: [PATCH 0017/1001] proof: certify atlas Batch0017 (10:245 to 10:260) --- Collatz/Research/StoppingAtlas/Batch0017.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0017.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0017.lean b/Collatz/Research/StoppingAtlas/Batch0017.lean new file mode 100644 index 00000000..7edf50e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0017.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0017 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 245. -/ +theorem bounds_10_245 : exactInterval 10 245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_245 (m : Nat) : + stoppingTime (2 ^ 10 * m + 245) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_245 : oddCount 245 10 = 4 ∧ acceleratedOrbit 10 245 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_245 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 245) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_245.1, data_10_245.2] + +/-- Complete interval computation for depth 10, residue 246. -/ +theorem bounds_10_246 : exactInterval 10 246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_246 (m : Nat) : + stoppingTime (2 ^ 10 * m + 246) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_246 : oddCount 246 10 = 5 ∧ acceleratedOrbit 10 246 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_246 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 246) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_246.1, data_10_246.2] + +/-- Complete interval computation for depth 10, residue 247. -/ +theorem bounds_10_247 : exactInterval 10 247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_247 (m : Nat) : + stoppingTime (2 ^ 10 * m + 247) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_247 : oddCount 247 10 = 5 ∧ acceleratedOrbit 10 247 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_247 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 247) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_247.1, data_10_247.2] + +/-- Complete interval computation for depth 10, residue 248. -/ +theorem bounds_10_248 : exactInterval 10 248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_248 (m : Nat) : + stoppingTime (2 ^ 10 * m + 248) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_248 : oddCount 248 10 = 6 ∧ acceleratedOrbit 10 248 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_248 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 248) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_248.1, data_10_248.2] + +/-- Complete interval computation for depth 10, residue 249. -/ +theorem bounds_10_249 : exactInterval 10 249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_249 (m : Nat) : + stoppingTime (2 ^ 10 * m + 249) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_249 : oddCount 249 10 = 6 ∧ acceleratedOrbit 10 249 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_249 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 249) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_249.1, data_10_249.2] + +/-- Complete interval computation for depth 10, residue 250. -/ +theorem bounds_10_250 : exactInterval 10 250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_250 (m : Nat) : + stoppingTime (2 ^ 10 * m + 250) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_250 : oddCount 250 10 = 6 ∧ acceleratedOrbit 10 250 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_250 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 250) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_250.1, data_10_250.2] + +/-- Complete interval computation for depth 10, residue 251. -/ +theorem bounds_10_251 : exactInterval 10 251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_251 (m : Nat) : + stoppingTime (2 ^ 10 * m + 251) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_251 : oddCount 251 10 = 8 ∧ acceleratedOrbit 10 251 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_251 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 251) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_251.1, data_10_251.2] + +/-- Complete interval computation for depth 10, residue 252. -/ +theorem bounds_10_252 : exactInterval 10 252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_252 (m : Nat) : + stoppingTime (2 ^ 10 * m + 252) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_252 : oddCount 252 10 = 6 ∧ acceleratedOrbit 10 252 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_252 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 252) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_252.1, data_10_252.2] + +/-- Complete interval computation for depth 10, residue 253. -/ +theorem bounds_10_253 : exactInterval 10 253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_253 (m : Nat) : + stoppingTime (2 ^ 10 * m + 253) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_253 : oddCount 253 10 = 6 ∧ acceleratedOrbit 10 253 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_253 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 253) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_253.1, data_10_253.2] + +/-- Complete interval computation for depth 10, residue 254. -/ +theorem bounds_10_254 : exactInterval 10 254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_254 (m : Nat) : + stoppingTime (2 ^ 10 * m + 254) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_254 : oddCount 254 10 = 8 ∧ acceleratedOrbit 10 254 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_254 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 254) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_254.1, data_10_254.2] + +/-- Complete interval computation for depth 10, residue 255. -/ +theorem bounds_10_255 : exactInterval 10 255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_255 (m : Nat) : + stoppingTime (2 ^ 10 * m + 255) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_255 : oddCount 255 10 = 8 ∧ acceleratedOrbit 10 255 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_255 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 255) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_255.1, data_10_255.2] + +/-- Complete interval computation for depth 10, residue 256. -/ +theorem bounds_10_256 : exactInterval 10 256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_256 (m : Nat) : + stoppingTime (2 ^ 10 * m + 256) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_256 : oddCount 256 10 = 1 ∧ acceleratedOrbit 10 256 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_256 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 256) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_256.1, data_10_256.2] + +/-- Complete interval computation for depth 10, residue 257. -/ +theorem bounds_10_257 : exactInterval 10 257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_257 (m : Nat) : + stoppingTime (2 ^ 10 * m + 257) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_257 : oddCount 257 10 = 5 ∧ acceleratedOrbit 10 257 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_257 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 257) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_257.1, data_10_257.2] + +/-- Complete interval computation for depth 10, residue 258. -/ +theorem bounds_10_258 : exactInterval 10 258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_258 (m : Nat) : + stoppingTime (2 ^ 10 * m + 258) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_258 : oddCount 258 10 = 6 ∧ acceleratedOrbit 10 258 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_258 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 258) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_258.1, data_10_258.2] + +/-- Complete interval computation for depth 10, residue 259. -/ +theorem bounds_10_259 : exactInterval 10 259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_259 (m : Nat) : + stoppingTime (2 ^ 10 * m + 259) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_259 : oddCount 259 10 = 6 ∧ acceleratedOrbit 10 259 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_259 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 259) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_259.1, data_10_259.2] + +/-- Complete interval computation for depth 10, residue 260. -/ +theorem bounds_10_260 : exactInterval 10 260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_260 (m : Nat) : + stoppingTime (2 ^ 10 * m + 260) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_260 : oddCount 260 10 = 3 ∧ acceleratedOrbit 10 260 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_260 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 260) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_260.1, data_10_260.2] + +end Collatz.Research.StoppingAtlas.Batch0017 From 5428e2846692d9113b1497603e5c0a7eb55e8742 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:03 +0530 Subject: [PATCH 0018/1001] proof: certify atlas Batch0018 (10:261 to 10:275) --- Collatz/Research/StoppingAtlas/Batch0018.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0018.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0018.lean b/Collatz/Research/StoppingAtlas/Batch0018.lean new file mode 100644 index 00000000..9c40adcb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0018.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0018 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 261. -/ +theorem bounds_10_261 : exactInterval 10 261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_261 (m : Nat) : + stoppingTime (2 ^ 10 * m + 261) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_261 : oddCount 261 10 = 3 ∧ acceleratedOrbit 10 261 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_261 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 261) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_261.1, data_10_261.2] + +/-- Complete interval computation for depth 10, residue 262. -/ +theorem bounds_10_262 : exactInterval 10 262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_262 (m : Nat) : + stoppingTime (2 ^ 10 * m + 262) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_262 : oddCount 262 10 = 3 ∧ acceleratedOrbit 10 262 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_262 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 262) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_262.1, data_10_262.2] + +/-- Complete interval computation for depth 10, residue 263. -/ +theorem bounds_10_263 : exactInterval 10 263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_263 (m : Nat) : + stoppingTime (2 ^ 10 * m + 263) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_263 : oddCount 263 10 = 7 ∧ acceleratedOrbit 10 263 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_263 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 263) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_263.1, data_10_263.2] + +/-- Complete interval computation for depth 10, residue 264. -/ +theorem bounds_10_264 : exactInterval 10 264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_264 (m : Nat) : + stoppingTime (2 ^ 10 * m + 264) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_264 : oddCount 264 10 = 4 ∧ acceleratedOrbit 10 264 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_264 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 264) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_264.1, data_10_264.2] + +/-- Complete interval computation for depth 10, residue 265. -/ +theorem bounds_10_265 : exactInterval 10 265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_265 (m : Nat) : + stoppingTime (2 ^ 10 * m + 265) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_265 : oddCount 265 10 = 6 ∧ acceleratedOrbit 10 265 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_265 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 265) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_265.1, data_10_265.2] + +/-- Complete interval computation for depth 10, residue 266. -/ +theorem bounds_10_266 : exactInterval 10 266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_266 (m : Nat) : + stoppingTime (2 ^ 10 * m + 266) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_266 : oddCount 266 10 = 4 ∧ acceleratedOrbit 10 266 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_266 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 266) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_266.1, data_10_266.2] + +/-- Complete interval computation for depth 10, residue 267. -/ +theorem bounds_10_267 : exactInterval 10 267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_267 (m : Nat) : + stoppingTime (2 ^ 10 * m + 267) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_267 : oddCount 267 10 = 5 ∧ acceleratedOrbit 10 267 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_267 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 267) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_267.1, data_10_267.2] + +/-- Complete interval computation for depth 10, residue 268. -/ +theorem bounds_10_268 : exactInterval 10 268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_268 (m : Nat) : + stoppingTime (2 ^ 10 * m + 268) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_268 : oddCount 268 10 = 4 ∧ acceleratedOrbit 10 268 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_268 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 268) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_268.1, data_10_268.2] + +/-- Complete interval computation for depth 10, residue 269. -/ +theorem bounds_10_269 : exactInterval 10 269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_269 (m : Nat) : + stoppingTime (2 ^ 10 * m + 269) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_269 : oddCount 269 10 = 4 ∧ acceleratedOrbit 10 269 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_269 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 269) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_269.1, data_10_269.2] + +/-- Complete interval computation for depth 10, residue 270. -/ +theorem bounds_10_270 : exactInterval 10 270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_270 (m : Nat) : + stoppingTime (2 ^ 10 * m + 270) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_270 : oddCount 270 10 = 5 ∧ acceleratedOrbit 10 270 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_270 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 270) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_270.1, data_10_270.2] + +/-- Complete interval computation for depth 10, residue 271. -/ +theorem bounds_10_271 : exactInterval 10 271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_271 (m : Nat) : + stoppingTime (2 ^ 10 * m + 271) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_271 : oddCount 271 10 = 5 ∧ acceleratedOrbit 10 271 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_271 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 271) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_271.1, data_10_271.2] + +/-- Complete interval computation for depth 10, residue 272. -/ +theorem bounds_10_272 : exactInterval 10 272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_272 (m : Nat) : + stoppingTime (2 ^ 10 * m + 272) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_272 : oddCount 272 10 = 3 ∧ acceleratedOrbit 10 272 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_272 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 272) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_272.1, data_10_272.2] + +/-- Complete interval computation for depth 10, residue 273. -/ +theorem bounds_10_273 : exactInterval 10 273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_273 (m : Nat) : + stoppingTime (2 ^ 10 * m + 273) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_273 : oddCount 273 10 = 4 ∧ acceleratedOrbit 10 273 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_273 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 273) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_273.1, data_10_273.2] + +/-- Complete interval computation for depth 10, residue 274. -/ +theorem bounds_10_274 : exactInterval 10 274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_274 (m : Nat) : + stoppingTime (2 ^ 10 * m + 274) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_274 : oddCount 274 10 = 7 ∧ acceleratedOrbit 10 274 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_274 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 274) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_274.1, data_10_274.2] + +/-- Complete interval computation for depth 10, residue 275. -/ +theorem bounds_10_275 : exactInterval 10 275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_275 (m : Nat) : + stoppingTime (2 ^ 10 * m + 275) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_275 : oddCount 275 10 = 7 ∧ acceleratedOrbit 10 275 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_275 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 275) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_275.1, data_10_275.2] + +end Collatz.Research.StoppingAtlas.Batch0018 From 76f83714342f51760d3f8f64197c41fe934112a8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:04 +0530 Subject: [PATCH 0019/1001] proof: certify atlas Batch0019 (10:276 to 10:290) --- Collatz/Research/StoppingAtlas/Batch0019.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0019.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0019.lean b/Collatz/Research/StoppingAtlas/Batch0019.lean new file mode 100644 index 00000000..d24ec907 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0019.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0019 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 276. -/ +theorem bounds_10_276 : exactInterval 10 276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_276 (m : Nat) : + stoppingTime (2 ^ 10 * m + 276) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_276 : oddCount 276 10 = 3 ∧ acceleratedOrbit 10 276 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_276 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 276) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_276.1, data_10_276.2] + +/-- Complete interval computation for depth 10, residue 277. -/ +theorem bounds_10_277 : exactInterval 10 277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_277 (m : Nat) : + stoppingTime (2 ^ 10 * m + 277) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_277 : oddCount 277 10 = 3 ∧ acceleratedOrbit 10 277 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_277 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 277) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_277.1, data_10_277.2] + +/-- Complete interval computation for depth 10, residue 278. -/ +theorem bounds_10_278 : exactInterval 10 278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_278 (m : Nat) : + stoppingTime (2 ^ 10 * m + 278) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_278 : oddCount 278 10 = 5 ∧ acceleratedOrbit 10 278 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_278 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 278) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_278.1, data_10_278.2] + +/-- Complete interval computation for depth 10, residue 279. -/ +theorem bounds_10_279 : exactInterval 10 279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_279 (m : Nat) : + stoppingTime (2 ^ 10 * m + 279) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_279 : oddCount 279 10 = 5 ∧ acceleratedOrbit 10 279 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_279 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 279) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_279.1, data_10_279.2] + +/-- Complete interval computation for depth 10, residue 280. -/ +theorem bounds_10_280 : exactInterval 10 280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_280 (m : Nat) : + stoppingTime (2 ^ 10 * m + 280) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_280 : oddCount 280 10 = 3 ∧ acceleratedOrbit 10 280 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_280 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 280) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_280.1, data_10_280.2] + +/-- Complete interval computation for depth 10, residue 281. -/ +theorem bounds_10_281 : exactInterval 10 281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_281 (m : Nat) : + stoppingTime (2 ^ 10 * m + 281) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_281 : oddCount 281 10 = 6 ∧ acceleratedOrbit 10 281 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_281 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 281) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_281.1, data_10_281.2] + +/-- Complete interval computation for depth 10, residue 282. -/ +theorem bounds_10_282 : exactInterval 10 282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_282 (m : Nat) : + stoppingTime (2 ^ 10 * m + 282) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_282 : oddCount 282 10 = 3 ∧ acceleratedOrbit 10 282 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_282 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 282) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_282.1, data_10_282.2] + +/-- Complete interval computation for depth 10, residue 283. -/ +theorem bounds_10_283 : exactInterval 10 283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_283 (m : Nat) : + stoppingTime (2 ^ 10 * m + 283) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_283 : oddCount 283 10 = 8 ∧ acceleratedOrbit 10 283 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_283 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 283) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_283.1, data_10_283.2] + +/-- Complete interval computation for depth 10, residue 284. -/ +theorem bounds_10_284 : exactInterval 10 284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_284 (m : Nat) : + stoppingTime (2 ^ 10 * m + 284) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_284 : oddCount 284 10 = 6 ∧ acceleratedOrbit 10 284 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_284 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 284) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_284.1, data_10_284.2] + +/-- Complete interval computation for depth 10, residue 285. -/ +theorem bounds_10_285 : exactInterval 10 285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_285 (m : Nat) : + stoppingTime (2 ^ 10 * m + 285) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_285 : oddCount 285 10 = 6 ∧ acceleratedOrbit 10 285 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_285 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 285) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_285.1, data_10_285.2] + +/-- Complete interval computation for depth 10, residue 286. -/ +theorem bounds_10_286 : exactInterval 10 286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_286 (m : Nat) : + stoppingTime (2 ^ 10 * m + 286) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_286 : oddCount 286 10 = 6 ∧ acceleratedOrbit 10 286 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_286 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 286) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_286.1, data_10_286.2] + +/-- Complete interval computation for depth 10, residue 287. -/ +theorem bounds_10_287 : exactInterval 10 287 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_287 (m : Nat) : + stoppingTime (2 ^ 10 * m + 287) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_287 : oddCount 287 10 = 6 ∧ acceleratedOrbit 10 287 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_287 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 287) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_287.1, data_10_287.2] + +/-- Complete interval computation for depth 10, residue 288. -/ +theorem bounds_10_288 : exactInterval 10 288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_288 (m : Nat) : + stoppingTime (2 ^ 10 * m + 288) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_288 : oddCount 288 10 = 4 ∧ acceleratedOrbit 10 288 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_288 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 288) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_288.1, data_10_288.2] + +/-- Complete interval computation for depth 10, residue 289. -/ +theorem bounds_10_289 : exactInterval 10 289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_289 (m : Nat) : + stoppingTime (2 ^ 10 * m + 289) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_289 : oddCount 289 10 = 4 ∧ acceleratedOrbit 10 289 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_289 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 289) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_289.1, data_10_289.2] + +/-- Complete interval computation for depth 10, residue 290. -/ +theorem bounds_10_290 : exactInterval 10 290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_290 (m : Nat) : + stoppingTime (2 ^ 10 * m + 290) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_290 : oddCount 290 10 = 5 ∧ acceleratedOrbit 10 290 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_290 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 290) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_290.1, data_10_290.2] + +end Collatz.Research.StoppingAtlas.Batch0019 From 4a0a5f5916d48840a9b2f5ce0a9cea263212bc76 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:04 +0530 Subject: [PATCH 0020/1001] proof: certify atlas Batch0020 (10:291 to 10:306) --- Collatz/Research/StoppingAtlas/Batch0020.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0020.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0020.lean b/Collatz/Research/StoppingAtlas/Batch0020.lean new file mode 100644 index 00000000..e4c52093 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0020.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0020 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 291. -/ +theorem bounds_10_291 : exactInterval 10 291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_291 (m : Nat) : + stoppingTime (2 ^ 10 * m + 291) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_291 : oddCount 291 10 = 5 ∧ acceleratedOrbit 10 291 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_291 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 291) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_291.1, data_10_291.2] + +/-- Complete interval computation for depth 10, residue 292. -/ +theorem bounds_10_292 : exactInterval 10 292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_292 (m : Nat) : + stoppingTime (2 ^ 10 * m + 292) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_292 : oddCount 292 10 = 5 ∧ acceleratedOrbit 10 292 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_292 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 292) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_292.1, data_10_292.2] + +/-- Complete interval computation for depth 10, residue 293. -/ +theorem bounds_10_293 : exactInterval 10 293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_293 (m : Nat) : + stoppingTime (2 ^ 10 * m + 293) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_293 : oddCount 293 10 = 5 ∧ acceleratedOrbit 10 293 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_293 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 293) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_293.1, data_10_293.2] + +/-- Complete interval computation for depth 10, residue 294. -/ +theorem bounds_10_294 : exactInterval 10 294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_294 (m : Nat) : + stoppingTime (2 ^ 10 * m + 294) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_294 : oddCount 294 10 = 5 ∧ acceleratedOrbit 10 294 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_294 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 294) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_294.1, data_10_294.2] + +/-- Complete interval computation for depth 10, residue 295. -/ +theorem bounds_10_295 : exactInterval 10 295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_295 (m : Nat) : + stoppingTime (2 ^ 10 * m + 295) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_295 : oddCount 295 10 = 6 ∧ acceleratedOrbit 10 295 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_295 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 295) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_295.1, data_10_295.2] + +/-- Complete interval computation for depth 10, residue 296. -/ +theorem bounds_10_296 : exactInterval 10 296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_296 (m : Nat) : + stoppingTime (2 ^ 10 * m + 296) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_296 : oddCount 296 10 = 4 ∧ acceleratedOrbit 10 296 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_296 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 296) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_296.1, data_10_296.2] + +/-- Complete interval computation for depth 10, residue 297. -/ +theorem bounds_10_297 : exactInterval 10 297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_297 (m : Nat) : + stoppingTime (2 ^ 10 * m + 297) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_297 : oddCount 297 10 = 7 ∧ acceleratedOrbit 10 297 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_297 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 297) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_297.1, data_10_297.2] + +/-- Complete interval computation for depth 10, residue 298. -/ +theorem bounds_10_298 : exactInterval 10 298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_298 (m : Nat) : + stoppingTime (2 ^ 10 * m + 298) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_298 : oddCount 298 10 = 4 ∧ acceleratedOrbit 10 298 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_298 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 298) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_298.1, data_10_298.2] + +/-- Complete interval computation for depth 10, residue 299. -/ +theorem bounds_10_299 : exactInterval 10 299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_299 (m : Nat) : + stoppingTime (2 ^ 10 * m + 299) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_299 : oddCount 299 10 = 6 ∧ acceleratedOrbit 10 299 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_299 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 299) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_299.1, data_10_299.2] + +/-- Complete interval computation for depth 10, residue 300. -/ +theorem bounds_10_300 : exactInterval 10 300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_300 (m : Nat) : + stoppingTime (2 ^ 10 * m + 300) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_300 : oddCount 300 10 = 3 ∧ acceleratedOrbit 10 300 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_300 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 300) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_300.1, data_10_300.2] + +/-- Complete interval computation for depth 10, residue 301. -/ +theorem bounds_10_301 : exactInterval 10 301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_301 (m : Nat) : + stoppingTime (2 ^ 10 * m + 301) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_301 : oddCount 301 10 = 3 ∧ acceleratedOrbit 10 301 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_301 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 301) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_301.1, data_10_301.2] + +/-- Complete interval computation for depth 10, residue 302. -/ +theorem bounds_10_302 : exactInterval 10 302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_302 (m : Nat) : + stoppingTime (2 ^ 10 * m + 302) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_302 : oddCount 302 10 = 3 ∧ acceleratedOrbit 10 302 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_302 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 302) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_302.1, data_10_302.2] + +/-- Complete interval computation for depth 10, residue 303. -/ +theorem bounds_10_303 : exactInterval 10 303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_303 (m : Nat) : + stoppingTime (2 ^ 10 * m + 303) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_303 : oddCount 303 10 = 7 ∧ acceleratedOrbit 10 303 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_303 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 303) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_303.1, data_10_303.2] + +/-- Complete interval computation for depth 10, residue 304. -/ +theorem bounds_10_304 : exactInterval 10 304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_304 (m : Nat) : + stoppingTime (2 ^ 10 * m + 304) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_304 : oddCount 304 10 = 4 ∧ acceleratedOrbit 10 304 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_304 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 304) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_304.1, data_10_304.2] + +/-- Complete interval computation for depth 10, residue 305. -/ +theorem bounds_10_305 : exactInterval 10 305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_305 (m : Nat) : + stoppingTime (2 ^ 10 * m + 305) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_305 : oddCount 305 10 = 5 ∧ acceleratedOrbit 10 305 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_305 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 305) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_305.1, data_10_305.2] + +/-- Complete interval computation for depth 10, residue 306. -/ +theorem bounds_10_306 : exactInterval 10 306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_306 (m : Nat) : + stoppingTime (2 ^ 10 * m + 306) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_306 : oddCount 306 10 = 5 ∧ acceleratedOrbit 10 306 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_306 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 306) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_306.1, data_10_306.2] + +end Collatz.Research.StoppingAtlas.Batch0020 From 21694e30b78bb3ca69cba790c0a1fc37d02ec015 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:05 +0530 Subject: [PATCH 0021/1001] proof: certify atlas Batch0021 (10:307 to 10:321) --- Collatz/Research/StoppingAtlas/Batch0021.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0021.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0021.lean b/Collatz/Research/StoppingAtlas/Batch0021.lean new file mode 100644 index 00000000..d65b98eb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0021.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0021 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 307. -/ +theorem bounds_10_307 : exactInterval 10 307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_307 (m : Nat) : + stoppingTime (2 ^ 10 * m + 307) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_307 : oddCount 307 10 = 5 ∧ acceleratedOrbit 10 307 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_307 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 307) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_307.1, data_10_307.2] + +/-- Complete interval computation for depth 10, residue 308. -/ +theorem bounds_10_308 : exactInterval 10 308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_308 (m : Nat) : + stoppingTime (2 ^ 10 * m + 308) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_308 : oddCount 308 10 = 4 ∧ acceleratedOrbit 10 308 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_308 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 308) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_308.1, data_10_308.2] + +/-- Complete interval computation for depth 10, residue 309. -/ +theorem bounds_10_309 : exactInterval 10 309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_309 (m : Nat) : + stoppingTime (2 ^ 10 * m + 309) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_309 : oddCount 309 10 = 4 ∧ acceleratedOrbit 10 309 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_309 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 309) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_309.1, data_10_309.2] + +/-- Complete interval computation for depth 10, residue 310. -/ +theorem bounds_10_310 : exactInterval 10 310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_310 (m : Nat) : + stoppingTime (2 ^ 10 * m + 310) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_310 : oddCount 310 10 = 7 ∧ acceleratedOrbit 10 310 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_310 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 310) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_310.1, data_10_310.2] + +/-- Complete interval computation for depth 10, residue 311. -/ +theorem bounds_10_311 : exactInterval 10 311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_311 (m : Nat) : + stoppingTime (2 ^ 10 * m + 311) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_311 : oddCount 311 10 = 7 ∧ acceleratedOrbit 10 311 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_311 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 311) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_311.1, data_10_311.2] + +/-- Complete interval computation for depth 10, residue 312. -/ +theorem bounds_10_312 : exactInterval 10 312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_312 (m : Nat) : + stoppingTime (2 ^ 10 * m + 312) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_312 : oddCount 312 10 = 5 ∧ acceleratedOrbit 10 312 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_312 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 312) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_312.1, data_10_312.2] + +/-- Complete interval computation for depth 10, residue 313. -/ +theorem bounds_10_313 : exactInterval 10 313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_313 (m : Nat) : + stoppingTime (2 ^ 10 * m + 313) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_313 : oddCount 313 10 = 7 ∧ acceleratedOrbit 10 313 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_313 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 313) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_313.1, data_10_313.2] + +/-- Complete interval computation for depth 10, residue 314. -/ +theorem bounds_10_314 : exactInterval 10 314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_314 (m : Nat) : + stoppingTime (2 ^ 10 * m + 314) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_314 : oddCount 314 10 = 5 ∧ acceleratedOrbit 10 314 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_314 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 314) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_314.1, data_10_314.2] + +/-- Complete interval computation for depth 10, residue 315. -/ +theorem bounds_10_315 : exactInterval 10 315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_315 (m : Nat) : + stoppingTime (2 ^ 10 * m + 315) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_315 : oddCount 315 10 = 4 ∧ acceleratedOrbit 10 315 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_315 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 315) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_315.1, data_10_315.2] + +/-- Complete interval computation for depth 10, residue 316. -/ +theorem bounds_10_316 : exactInterval 10 316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_316 (m : Nat) : + stoppingTime (2 ^ 10 * m + 316) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_316 : oddCount 316 10 = 5 ∧ acceleratedOrbit 10 316 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_316 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 316) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_316.1, data_10_316.2] + +/-- Complete interval computation for depth 10, residue 317. -/ +theorem bounds_10_317 : exactInterval 10 317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_317 (m : Nat) : + stoppingTime (2 ^ 10 * m + 317) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_317 : oddCount 317 10 = 5 ∧ acceleratedOrbit 10 317 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_317 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 317) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_317.1, data_10_317.2] + +/-- Complete interval computation for depth 10, residue 318. -/ +theorem bounds_10_318 : exactInterval 10 318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_318 (m : Nat) : + stoppingTime (2 ^ 10 * m + 318) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_318 : oddCount 318 10 = 8 ∧ acceleratedOrbit 10 318 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_318 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 318) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_318.1, data_10_318.2] + +/-- Complete interval computation for depth 10, residue 319. -/ +theorem bounds_10_319 : exactInterval 10 319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_319 (m : Nat) : + stoppingTime (2 ^ 10 * m + 319) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_319 : oddCount 319 10 = 8 ∧ acceleratedOrbit 10 319 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_319 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 319) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_319.1, data_10_319.2] + +/-- Complete interval computation for depth 10, residue 320. -/ +theorem bounds_10_320 : exactInterval 10 320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_320 (m : Nat) : + stoppingTime (2 ^ 10 * m + 320) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_320 : oddCount 320 10 = 1 ∧ acceleratedOrbit 10 320 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_320 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 320) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_320.1, data_10_320.2] + +/-- Complete interval computation for depth 10, residue 321. -/ +theorem bounds_10_321 : exactInterval 10 321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_321 (m : Nat) : + stoppingTime (2 ^ 10 * m + 321) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_321 : oddCount 321 10 = 4 ∧ acceleratedOrbit 10 321 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_321 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 321) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_321.1, data_10_321.2] + +end Collatz.Research.StoppingAtlas.Batch0021 From 56e096f9275c9efaa7c82b979ed9a54946d2d0fa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:05 +0530 Subject: [PATCH 0022/1001] proof: certify atlas Batch0022 (10:322 to 10:336) --- Collatz/Research/StoppingAtlas/Batch0022.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0022.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0022.lean b/Collatz/Research/StoppingAtlas/Batch0022.lean new file mode 100644 index 00000000..37929565 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0022.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0022 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 322. -/ +theorem bounds_10_322 : exactInterval 10 322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_322 (m : Nat) : + stoppingTime (2 ^ 10 * m + 322) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_322 : oddCount 322 10 = 6 ∧ acceleratedOrbit 10 322 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_322 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 322) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_322.1, data_10_322.2] + +/-- Complete interval computation for depth 10, residue 323. -/ +theorem bounds_10_323 : exactInterval 10 323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_323 (m : Nat) : + stoppingTime (2 ^ 10 * m + 323) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_323 : oddCount 323 10 = 6 ∧ acceleratedOrbit 10 323 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_323 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 323) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_323.1, data_10_323.2] + +/-- Complete interval computation for depth 10, residue 324. -/ +theorem bounds_10_324 : exactInterval 10 324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_324 (m : Nat) : + stoppingTime (2 ^ 10 * m + 324) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_324 : oddCount 324 10 = 5 ∧ acceleratedOrbit 10 324 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_324 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 324) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_324.1, data_10_324.2] + +/-- Complete interval computation for depth 10, residue 325. -/ +theorem bounds_10_325 : exactInterval 10 325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_325 (m : Nat) : + stoppingTime (2 ^ 10 * m + 325) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_325 : oddCount 325 10 = 5 ∧ acceleratedOrbit 10 325 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_325 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 325) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_325.1, data_10_325.2] + +/-- Complete interval computation for depth 10, residue 326. -/ +theorem bounds_10_326 : exactInterval 10 326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_326 (m : Nat) : + stoppingTime (2 ^ 10 * m + 326) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_326 : oddCount 326 10 = 5 ∧ acceleratedOrbit 10 326 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_326 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 326) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_326.1, data_10_326.2] + +/-- Complete interval computation for depth 10, residue 327. -/ +theorem bounds_10_327 : exactInterval 10 327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_327 (m : Nat) : + stoppingTime (2 ^ 10 * m + 327) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_327 : oddCount 327 10 = 8 ∧ acceleratedOrbit 10 327 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_327 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 327) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_327.1, data_10_327.2] + +/-- Complete interval computation for depth 10, residue 328. -/ +theorem bounds_10_328 : exactInterval 10 328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_328 (m : Nat) : + stoppingTime (2 ^ 10 * m + 328) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_328 : oddCount 328 10 = 6 ∧ acceleratedOrbit 10 328 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_328 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 328) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_328.1, data_10_328.2] + +/-- Complete interval computation for depth 10, residue 329. -/ +theorem bounds_10_329 : exactInterval 10 329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_329 (m : Nat) : + stoppingTime (2 ^ 10 * m + 329) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_329 : oddCount 329 10 = 6 ∧ acceleratedOrbit 10 329 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_329 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 329) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_329.1, data_10_329.2] + +/-- Complete interval computation for depth 10, residue 330. -/ +theorem bounds_10_330 : exactInterval 10 330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_330 (m : Nat) : + stoppingTime (2 ^ 10 * m + 330) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_330 : oddCount 330 10 = 6 ∧ acceleratedOrbit 10 330 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_330 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 330) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_330.1, data_10_330.2] + +/-- Complete interval computation for depth 10, residue 331. -/ +theorem bounds_10_331 : exactInterval 10 331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_331 (m : Nat) : + stoppingTime (2 ^ 10 * m + 331) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_331 : oddCount 331 10 = 5 ∧ acceleratedOrbit 10 331 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_331 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 331) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_331.1, data_10_331.2] + +/-- Complete interval computation for depth 10, residue 332. -/ +theorem bounds_10_332 : exactInterval 10 332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_332 (m : Nat) : + stoppingTime (2 ^ 10 * m + 332) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_332 : oddCount 332 10 = 6 ∧ acceleratedOrbit 10 332 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_332 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 332) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_332.1, data_10_332.2] + +/-- Complete interval computation for depth 10, residue 333. -/ +theorem bounds_10_333 : exactInterval 10 333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_333 (m : Nat) : + stoppingTime (2 ^ 10 * m + 333) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_333 : oddCount 333 10 = 6 ∧ acceleratedOrbit 10 333 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_333 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 333) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_333.1, data_10_333.2] + +/-- Complete interval computation for depth 10, residue 334. -/ +theorem bounds_10_334 : exactInterval 10 334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_334 (m : Nat) : + stoppingTime (2 ^ 10 * m + 334) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_334 : oddCount 334 10 = 7 ∧ acceleratedOrbit 10 334 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_334 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 334) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_334.1, data_10_334.2] + +/-- Complete interval computation for depth 10, residue 335. -/ +theorem bounds_10_335 : exactInterval 10 335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_335 (m : Nat) : + stoppingTime (2 ^ 10 * m + 335) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_335 : oddCount 335 10 = 7 ∧ acceleratedOrbit 10 335 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_335 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 335) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_335.1, data_10_335.2] + +/-- Complete interval computation for depth 10, residue 336. -/ +theorem bounds_10_336 : exactInterval 10 336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_336 (m : Nat) : + stoppingTime (2 ^ 10 * m + 336) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_336 : oddCount 336 10 = 1 ∧ acceleratedOrbit 10 336 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_336 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 336) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_336.1, data_10_336.2] + +end Collatz.Research.StoppingAtlas.Batch0022 From 131d2a96a16cb6c8e201b5723ab16d478e49259f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:05 +0530 Subject: [PATCH 0023/1001] proof: certify atlas Batch0023 (10:337 to 10:352) --- Collatz/Research/StoppingAtlas/Batch0023.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0023.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0023.lean b/Collatz/Research/StoppingAtlas/Batch0023.lean new file mode 100644 index 00000000..17a6c270 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0023.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0023 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 337. -/ +theorem bounds_10_337 : exactInterval 10 337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_337 (m : Nat) : + stoppingTime (2 ^ 10 * m + 337) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_337 : oddCount 337 10 = 7 ∧ acceleratedOrbit 10 337 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_337 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 337) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_337.1, data_10_337.2] + +/-- Complete interval computation for depth 10, residue 338. -/ +theorem bounds_10_338 : exactInterval 10 338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_338 (m : Nat) : + stoppingTime (2 ^ 10 * m + 338) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_338 : oddCount 338 10 = 8 ∧ acceleratedOrbit 10 338 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_338 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 338) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_338.1, data_10_338.2] + +/-- Complete interval computation for depth 10, residue 339. -/ +theorem bounds_10_339 : exactInterval 10 339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_339 (m : Nat) : + stoppingTime (2 ^ 10 * m + 339) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_339 : oddCount 339 10 = 8 ∧ acceleratedOrbit 10 339 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_339 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 339) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_339.1, data_10_339.2] + +/-- Complete interval computation for depth 10, residue 340. -/ +theorem bounds_10_340 : exactInterval 10 340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_340 (m : Nat) : + stoppingTime (2 ^ 10 * m + 340) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_340 : oddCount 340 10 = 1 ∧ acceleratedOrbit 10 340 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_340 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 340) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_340.1, data_10_340.2] + +/-- Complete interval computation for depth 10, residue 341. -/ +theorem bounds_10_341 : exactInterval 10 341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_341 (m : Nat) : + stoppingTime (2 ^ 10 * m + 341) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_341 : oddCount 341 10 = 1 ∧ acceleratedOrbit 10 341 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_341 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 341) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_341.1, data_10_341.2] + +/-- Complete interval computation for depth 10, residue 342. -/ +theorem bounds_10_342 : exactInterval 10 342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_342 (m : Nat) : + stoppingTime (2 ^ 10 * m + 342) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_342 : oddCount 342 10 = 5 ∧ acceleratedOrbit 10 342 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_342 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 342) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_342.1, data_10_342.2] + +/-- Complete interval computation for depth 10, residue 343. -/ +theorem bounds_10_343 : exactInterval 10 343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_343 (m : Nat) : + stoppingTime (2 ^ 10 * m + 343) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_343 : oddCount 343 10 = 5 ∧ acceleratedOrbit 10 343 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_343 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 343) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_343.1, data_10_343.2] + +/-- Complete interval computation for depth 10, residue 344. -/ +theorem bounds_10_344 : exactInterval 10 344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_344 (m : Nat) : + stoppingTime (2 ^ 10 * m + 344) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_344 : oddCount 344 10 = 4 ∧ acceleratedOrbit 10 344 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_344 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 344) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_344.1, data_10_344.2] + +/-- Complete interval computation for depth 10, residue 345. -/ +theorem bounds_10_345 : exactInterval 10 345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_345 (m : Nat) : + stoppingTime (2 ^ 10 * m + 345) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_345 : oddCount 345 10 = 5 ∧ acceleratedOrbit 10 345 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_345 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 345) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_345.1, data_10_345.2] + +/-- Complete interval computation for depth 10, residue 346. -/ +theorem bounds_10_346 : exactInterval 10 346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_346 (m : Nat) : + stoppingTime (2 ^ 10 * m + 346) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_346 : oddCount 346 10 = 4 ∧ acceleratedOrbit 10 346 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_346 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 346) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_346.1, data_10_346.2] + +/-- Complete interval computation for depth 10, residue 347. -/ +theorem bounds_10_347 : exactInterval 10 347 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_347 (m : Nat) : + stoppingTime (2 ^ 10 * m + 347) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_347 : oddCount 347 10 = 6 ∧ acceleratedOrbit 10 347 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_347 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 347) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_347.1, data_10_347.2] + +/-- Complete interval computation for depth 10, residue 348. -/ +theorem bounds_10_348 : exactInterval 10 348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_348 (m : Nat) : + stoppingTime (2 ^ 10 * m + 348) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_348 : oddCount 348 10 = 4 ∧ acceleratedOrbit 10 348 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_348 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 348) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_348.1, data_10_348.2] + +/-- Complete interval computation for depth 10, residue 349. -/ +theorem bounds_10_349 : exactInterval 10 349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_349 (m : Nat) : + stoppingTime (2 ^ 10 * m + 349) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_349 : oddCount 349 10 = 4 ∧ acceleratedOrbit 10 349 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_349 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 349) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_349.1, data_10_349.2] + +/-- Complete interval computation for depth 10, residue 350. -/ +theorem bounds_10_350 : exactInterval 10 350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_350 (m : Nat) : + stoppingTime (2 ^ 10 * m + 350) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_350 : oddCount 350 10 = 6 ∧ acceleratedOrbit 10 350 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_350 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 350) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_350.1, data_10_350.2] + +/-- Complete interval computation for depth 10, residue 351. -/ +theorem bounds_10_351 : exactInterval 10 351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_351 (m : Nat) : + stoppingTime (2 ^ 10 * m + 351) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_351 : oddCount 351 10 = 6 ∧ acceleratedOrbit 10 351 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_351 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 351) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_351.1, data_10_351.2] + +/-- Complete interval computation for depth 10, residue 352. -/ +theorem bounds_10_352 : exactInterval 10 352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_352 (m : Nat) : + stoppingTime (2 ^ 10 * m + 352) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_352 : oddCount 352 10 = 3 ∧ acceleratedOrbit 10 352 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_352 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 352) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_352.1, data_10_352.2] + +end Collatz.Research.StoppingAtlas.Batch0023 From 92be686860251e06334cfcca46b1543ead77cf1f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:05 +0530 Subject: [PATCH 0024/1001] proof: certify atlas Batch0024 (10:353 to 10:367) --- Collatz/Research/StoppingAtlas/Batch0024.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0024.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0024.lean b/Collatz/Research/StoppingAtlas/Batch0024.lean new file mode 100644 index 00000000..a20faec1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0024.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0024 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 353. -/ +theorem bounds_10_353 : exactInterval 10 353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_353 (m : Nat) : + stoppingTime (2 ^ 10 * m + 353) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_353 : oddCount 353 10 = 6 ∧ acceleratedOrbit 10 353 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_353 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 353) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_353.1, data_10_353.2] + +/-- Complete interval computation for depth 10, residue 354. -/ +theorem bounds_10_354 : exactInterval 10 354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_354 (m : Nat) : + stoppingTime (2 ^ 10 * m + 354) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_354 : oddCount 354 10 = 4 ∧ acceleratedOrbit 10 354 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_354 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 354) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_354.1, data_10_354.2] + +/-- Complete interval computation for depth 10, residue 355. -/ +theorem bounds_10_355 : exactInterval 10 355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_355 (m : Nat) : + stoppingTime (2 ^ 10 * m + 355) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_355 : oddCount 355 10 = 4 ∧ acceleratedOrbit 10 355 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_355 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 355) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_355.1, data_10_355.2] + +/-- Complete interval computation for depth 10, residue 356. -/ +theorem bounds_10_356 : exactInterval 10 356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_356 (m : Nat) : + stoppingTime (2 ^ 10 * m + 356) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_356 : oddCount 356 10 = 4 ∧ acceleratedOrbit 10 356 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_356 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 356) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_356.1, data_10_356.2] + +/-- Complete interval computation for depth 10, residue 357. -/ +theorem bounds_10_357 : exactInterval 10 357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_357 (m : Nat) : + stoppingTime (2 ^ 10 * m + 357) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_357 : oddCount 357 10 = 4 ∧ acceleratedOrbit 10 357 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_357 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 357) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_357.1, data_10_357.2] + +/-- Complete interval computation for depth 10, residue 358. -/ +theorem bounds_10_358 : exactInterval 10 358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_358 (m : Nat) : + stoppingTime (2 ^ 10 * m + 358) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_358 : oddCount 358 10 = 4 ∧ acceleratedOrbit 10 358 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_358 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 358) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_358.1, data_10_358.2] + +/-- Complete interval computation for depth 10, residue 359. -/ +theorem bounds_10_359 : exactInterval 10 359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_359 (m : Nat) : + stoppingTime (2 ^ 10 * m + 359) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_359 : oddCount 359 10 = 8 ∧ acceleratedOrbit 10 359 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_359 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 359) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_359.1, data_10_359.2] + +/-- Complete interval computation for depth 10, residue 360. -/ +theorem bounds_10_360 : exactInterval 10 360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_360 (m : Nat) : + stoppingTime (2 ^ 10 * m + 360) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_360 : oddCount 360 10 = 3 ∧ acceleratedOrbit 10 360 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_360 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 360) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_360.1, data_10_360.2] + +/-- Complete interval computation for depth 10, residue 361. -/ +theorem bounds_10_361 : exactInterval 10 361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_361 (m : Nat) : + stoppingTime (2 ^ 10 * m + 361) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_361 : oddCount 361 10 = 5 ∧ acceleratedOrbit 10 361 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_361 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 361) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_361.1, data_10_361.2] + +/-- Complete interval computation for depth 10, residue 362. -/ +theorem bounds_10_362 : exactInterval 10 362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_362 (m : Nat) : + stoppingTime (2 ^ 10 * m + 362) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_362 : oddCount 362 10 = 3 ∧ acceleratedOrbit 10 362 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_362 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 362) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_362.1, data_10_362.2] + +/-- Complete interval computation for depth 10, residue 363. -/ +theorem bounds_10_363 : exactInterval 10 363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_363 (m : Nat) : + stoppingTime (2 ^ 10 * m + 363) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_363 : oddCount 363 10 = 6 ∧ acceleratedOrbit 10 363 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_363 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 363) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_363.1, data_10_363.2] + +/-- Complete interval computation for depth 10, residue 364. -/ +theorem bounds_10_364 : exactInterval 10 364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_364 (m : Nat) : + stoppingTime (2 ^ 10 * m + 364) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_364 : oddCount 364 10 = 6 ∧ acceleratedOrbit 10 364 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_364 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 364) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_364.1, data_10_364.2] + +/-- Complete interval computation for depth 10, residue 365. -/ +theorem bounds_10_365 : exactInterval 10 365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_365 (m : Nat) : + stoppingTime (2 ^ 10 * m + 365) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_365 : oddCount 365 10 = 6 ∧ acceleratedOrbit 10 365 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_365 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 365) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_365.1, data_10_365.2] + +/-- Complete interval computation for depth 10, residue 366. -/ +theorem bounds_10_366 : exactInterval 10 366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_366 (m : Nat) : + stoppingTime (2 ^ 10 * m + 366) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_366 : oddCount 366 10 = 6 ∧ acceleratedOrbit 10 366 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_366 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 366) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_366.1, data_10_366.2] + +/-- Complete interval computation for depth 10, residue 367. -/ +theorem bounds_10_367 : exactInterval 10 367 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_367 (m : Nat) : + stoppingTime (2 ^ 10 * m + 367) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_367 : oddCount 367 10 = 6 ∧ acceleratedOrbit 10 367 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_367 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 367) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_367.1, data_10_367.2] + +end Collatz.Research.StoppingAtlas.Batch0024 From 5a2f5bdac54426f4a4fd243754ab99186c10e6f5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:06 +0530 Subject: [PATCH 0025/1001] proof: certify atlas Batch0025 (10:368 to 10:383) --- Collatz/Research/StoppingAtlas/Batch0025.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0025.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0025.lean b/Collatz/Research/StoppingAtlas/Batch0025.lean new file mode 100644 index 00000000..a4ef87de --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0025.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0025 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 368. -/ +theorem bounds_10_368 : exactInterval 10 368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_368 (m : Nat) : + stoppingTime (2 ^ 10 * m + 368) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_368 : oddCount 368 10 = 3 ∧ acceleratedOrbit 10 368 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_368 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 368) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_368.1, data_10_368.2] + +/-- Complete interval computation for depth 10, residue 369. -/ +theorem bounds_10_369 : exactInterval 10 369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_369 (m : Nat) : + stoppingTime (2 ^ 10 * m + 369) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_369 : oddCount 369 10 = 3 ∧ acceleratedOrbit 10 369 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_369 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 369) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_369.1, data_10_369.2] + +/-- Complete interval computation for depth 10, residue 370. -/ +theorem bounds_10_370 : exactInterval 10 370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_370 (m : Nat) : + stoppingTime (2 ^ 10 * m + 370) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_370 : oddCount 370 10 = 5 ∧ acceleratedOrbit 10 370 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_370 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 370) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_370.1, data_10_370.2] + +/-- Complete interval computation for depth 10, residue 371. -/ +theorem bounds_10_371 : exactInterval 10 371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_371 (m : Nat) : + stoppingTime (2 ^ 10 * m + 371) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_371 : oddCount 371 10 = 5 ∧ acceleratedOrbit 10 371 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_371 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 371) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_371.1, data_10_371.2] + +/-- Complete interval computation for depth 10, residue 372. -/ +theorem bounds_10_372 : exactInterval 10 372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_372 (m : Nat) : + stoppingTime (2 ^ 10 * m + 372) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_372 : oddCount 372 10 = 3 ∧ acceleratedOrbit 10 372 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_372 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 372) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_372.1, data_10_372.2] + +/-- Complete interval computation for depth 10, residue 373. -/ +theorem bounds_10_373 : exactInterval 10 373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_373 (m : Nat) : + stoppingTime (2 ^ 10 * m + 373) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_373 : oddCount 373 10 = 3 ∧ acceleratedOrbit 10 373 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_373 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 373) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_373.1, data_10_373.2] + +/-- Complete interval computation for depth 10, residue 374. -/ +theorem bounds_10_374 : exactInterval 10 374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_374 (m : Nat) : + stoppingTime (2 ^ 10 * m + 374) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_374 : oddCount 374 10 = 6 ∧ acceleratedOrbit 10 374 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_374 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 374) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_374.1, data_10_374.2] + +/-- Complete interval computation for depth 10, residue 375. -/ +theorem bounds_10_375 : exactInterval 10 375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_375 (m : Nat) : + stoppingTime (2 ^ 10 * m + 375) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_375 : oddCount 375 10 = 6 ∧ acceleratedOrbit 10 375 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_375 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 375) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_375.1, data_10_375.2] + +/-- Complete interval computation for depth 10, residue 376. -/ +theorem bounds_10_376 : exactInterval 10 376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_376 (m : Nat) : + stoppingTime (2 ^ 10 * m + 376) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_376 : oddCount 376 10 = 5 ∧ acceleratedOrbit 10 376 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_376 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 376) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_376.1, data_10_376.2] + +/-- Complete interval computation for depth 10, residue 377. -/ +theorem bounds_10_377 : exactInterval 10 377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_377 (m : Nat) : + stoppingTime (2 ^ 10 * m + 377) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_377 : oddCount 377 10 = 8 ∧ acceleratedOrbit 10 377 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_377 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 377) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_377.1, data_10_377.2] + +/-- Complete interval computation for depth 10, residue 378. -/ +theorem bounds_10_378 : exactInterval 10 378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_378 (m : Nat) : + stoppingTime (2 ^ 10 * m + 378) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_378 : oddCount 378 10 = 5 ∧ acceleratedOrbit 10 378 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_378 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 378) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_378.1, data_10_378.2] + +/-- Complete interval computation for depth 10, residue 379. -/ +theorem bounds_10_379 : exactInterval 10 379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_379 (m : Nat) : + stoppingTime (2 ^ 10 * m + 379) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_379 : oddCount 379 10 = 6 ∧ acceleratedOrbit 10 379 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_379 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 379) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_379.1, data_10_379.2] + +/-- Complete interval computation for depth 10, residue 380. -/ +theorem bounds_10_380 : exactInterval 10 380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_380 (m : Nat) : + stoppingTime (2 ^ 10 * m + 380) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_380 : oddCount 380 10 = 5 ∧ acceleratedOrbit 10 380 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_380 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 380) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_380.1, data_10_380.2] + +/-- Complete interval computation for depth 10, residue 381. -/ +theorem bounds_10_381 : exactInterval 10 381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_381 (m : Nat) : + stoppingTime (2 ^ 10 * m + 381) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_381 : oddCount 381 10 = 5 ∧ acceleratedOrbit 10 381 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_381 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 381) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_381.1, data_10_381.2] + +/-- Complete interval computation for depth 10, residue 382. -/ +theorem bounds_10_382 : exactInterval 10 382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_382 (m : Nat) : + stoppingTime (2 ^ 10 * m + 382) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_382 : oddCount 382 10 = 7 ∧ acceleratedOrbit 10 382 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_382 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 382) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_382.1, data_10_382.2] + +/-- Complete interval computation for depth 10, residue 383. -/ +theorem bounds_10_383 : exactInterval 10 383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_383 (m : Nat) : + stoppingTime (2 ^ 10 * m + 383) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_383 : oddCount 383 10 = 7 ∧ acceleratedOrbit 10 383 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_383 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 383) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_383.1, data_10_383.2] + +end Collatz.Research.StoppingAtlas.Batch0025 From 92065b5f8cc802822b4328d4a948056d11e31b3e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:06 +0530 Subject: [PATCH 0026/1001] proof: certify atlas Batch0026 (10:384 to 10:398) --- Collatz/Research/StoppingAtlas/Batch0026.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0026.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0026.lean b/Collatz/Research/StoppingAtlas/Batch0026.lean new file mode 100644 index 00000000..00f1b909 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0026.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0026 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 384. -/ +theorem bounds_10_384 : exactInterval 10 384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_384 (m : Nat) : + stoppingTime (2 ^ 10 * m + 384) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_384 : oddCount 384 10 = 2 ∧ acceleratedOrbit 10 384 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_384 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 384) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_384.1, data_10_384.2] + +/-- Complete interval computation for depth 10, residue 385. -/ +theorem bounds_10_385 : exactInterval 10 385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_385 (m : Nat) : + stoppingTime (2 ^ 10 * m + 385) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_385 : oddCount 385 10 = 5 ∧ acceleratedOrbit 10 385 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_385 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 385) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_385.1, data_10_385.2] + +/-- Complete interval computation for depth 10, residue 386. -/ +theorem bounds_10_386 : exactInterval 10 386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_386 (m : Nat) : + stoppingTime (2 ^ 10 * m + 386) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_386 : oddCount 386 10 = 4 ∧ acceleratedOrbit 10 386 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_386 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 386) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_386.1, data_10_386.2] + +/-- Complete interval computation for depth 10, residue 387. -/ +theorem bounds_10_387 : exactInterval 10 387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_387 (m : Nat) : + stoppingTime (2 ^ 10 * m + 387) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_387 : oddCount 387 10 = 4 ∧ acceleratedOrbit 10 387 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_387 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 387) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_387.1, data_10_387.2] + +/-- Complete interval computation for depth 10, residue 388. -/ +theorem bounds_10_388 : exactInterval 10 388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_388 (m : Nat) : + stoppingTime (2 ^ 10 * m + 388) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_388 : oddCount 388 10 = 5 ∧ acceleratedOrbit 10 388 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_388 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 388) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_388.1, data_10_388.2] + +/-- Complete interval computation for depth 10, residue 389. -/ +theorem bounds_10_389 : exactInterval 10 389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_389 (m : Nat) : + stoppingTime (2 ^ 10 * m + 389) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_389 : oddCount 389 10 = 5 ∧ acceleratedOrbit 10 389 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_389 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 389) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_389.1, data_10_389.2] + +/-- Complete interval computation for depth 10, residue 390. -/ +theorem bounds_10_390 : exactInterval 10 390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_390 (m : Nat) : + stoppingTime (2 ^ 10 * m + 390) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_390 : oddCount 390 10 = 5 ∧ acceleratedOrbit 10 390 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_390 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 390) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_390.1, data_10_390.2] + +/-- Complete interval computation for depth 10, residue 391. -/ +theorem bounds_10_391 : exactInterval 10 391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_391 (m : Nat) : + stoppingTime (2 ^ 10 * m + 391) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_391 : oddCount 391 10 = 4 ∧ acceleratedOrbit 10 391 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_391 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 391) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_391.1, data_10_391.2] + +/-- Complete interval computation for depth 10, residue 392. -/ +theorem bounds_10_392 : exactInterval 10 392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_392 (m : Nat) : + stoppingTime (2 ^ 10 * m + 392) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_392 : oddCount 392 10 = 3 ∧ acceleratedOrbit 10 392 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_392 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 392) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_392.1, data_10_392.2] + +/-- Complete interval computation for depth 10, residue 393. -/ +theorem bounds_10_393 : exactInterval 10 393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_393 (m : Nat) : + stoppingTime (2 ^ 10 * m + 393) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_393 : oddCount 393 10 = 6 ∧ acceleratedOrbit 10 393 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_393 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 393) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_393.1, data_10_393.2] + +/-- Complete interval computation for depth 10, residue 394. -/ +theorem bounds_10_394 : exactInterval 10 394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_394 (m : Nat) : + stoppingTime (2 ^ 10 * m + 394) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_394 : oddCount 394 10 = 3 ∧ acceleratedOrbit 10 394 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_394 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 394) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_394.1, data_10_394.2] + +/-- Complete interval computation for depth 10, residue 395. -/ +theorem bounds_10_395 : exactInterval 10 395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_395 (m : Nat) : + stoppingTime (2 ^ 10 * m + 395) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_395 : oddCount 395 10 = 6 ∧ acceleratedOrbit 10 395 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_395 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 395) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_395.1, data_10_395.2] + +/-- Complete interval computation for depth 10, residue 396. -/ +theorem bounds_10_396 : exactInterval 10 396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_396 (m : Nat) : + stoppingTime (2 ^ 10 * m + 396) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_396 : oddCount 396 10 = 3 ∧ acceleratedOrbit 10 396 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_396 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 396) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_396.1, data_10_396.2] + +/-- Complete interval computation for depth 10, residue 397. -/ +theorem bounds_10_397 : exactInterval 10 397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_397 (m : Nat) : + stoppingTime (2 ^ 10 * m + 397) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_397 : oddCount 397 10 = 3 ∧ acceleratedOrbit 10 397 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_397 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 397) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_397.1, data_10_397.2] + +/-- Complete interval computation for depth 10, residue 398. -/ +theorem bounds_10_398 : exactInterval 10 398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_398 (m : Nat) : + stoppingTime (2 ^ 10 * m + 398) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_398 : oddCount 398 10 = 5 ∧ acceleratedOrbit 10 398 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_398 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 398) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_398.1, data_10_398.2] + +end Collatz.Research.StoppingAtlas.Batch0026 From a7e507afee0a55f49a5bcce6ecdf877e56b5a16f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:06 +0530 Subject: [PATCH 0027/1001] proof: certify atlas Batch0027 (10:399 to 10:413) --- Collatz/Research/StoppingAtlas/Batch0027.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0027.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0027.lean b/Collatz/Research/StoppingAtlas/Batch0027.lean new file mode 100644 index 00000000..de565064 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0027.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0027 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 399. -/ +theorem bounds_10_399 : exactInterval 10 399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_399 (m : Nat) : + stoppingTime (2 ^ 10 * m + 399) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_399 : oddCount 399 10 = 5 ∧ acceleratedOrbit 10 399 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_399 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 399) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_399.1, data_10_399.2] + +/-- Complete interval computation for depth 10, residue 400. -/ +theorem bounds_10_400 : exactInterval 10 400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_400 (m : Nat) : + stoppingTime (2 ^ 10 * m + 400) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_400 : oddCount 400 10 = 3 ∧ acceleratedOrbit 10 400 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_400 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 400) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_400.1, data_10_400.2] + +/-- Complete interval computation for depth 10, residue 401. -/ +theorem bounds_10_401 : exactInterval 10 401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_401 (m : Nat) : + stoppingTime (2 ^ 10 * m + 401) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_401 : oddCount 401 10 = 4 ∧ acceleratedOrbit 10 401 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_401 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 401) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_401.1, data_10_401.2] + +/-- Complete interval computation for depth 10, residue 402. -/ +theorem bounds_10_402 : exactInterval 10 402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_402 (m : Nat) : + stoppingTime (2 ^ 10 * m + 402) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_402 : oddCount 402 10 = 4 ∧ acceleratedOrbit 10 402 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_402 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 402) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_402.1, data_10_402.2] + +/-- Complete interval computation for depth 10, residue 403. -/ +theorem bounds_10_403 : exactInterval 10 403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_403 (m : Nat) : + stoppingTime (2 ^ 10 * m + 403) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_403 : oddCount 403 10 = 4 ∧ acceleratedOrbit 10 403 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_403 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 403) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_403.1, data_10_403.2] + +/-- Complete interval computation for depth 10, residue 404. -/ +theorem bounds_10_404 : exactInterval 10 404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_404 (m : Nat) : + stoppingTime (2 ^ 10 * m + 404) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_404 : oddCount 404 10 = 3 ∧ acceleratedOrbit 10 404 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_404 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 404) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_404.1, data_10_404.2] + +/-- Complete interval computation for depth 10, residue 405. -/ +theorem bounds_10_405 : exactInterval 10 405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_405 (m : Nat) : + stoppingTime (2 ^ 10 * m + 405) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_405 : oddCount 405 10 = 3 ∧ acceleratedOrbit 10 405 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_405 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 405) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_405.1, data_10_405.2] + +/-- Complete interval computation for depth 10, residue 406. -/ +theorem bounds_10_406 : exactInterval 10 406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_406 (m : Nat) : + stoppingTime (2 ^ 10 * m + 406) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_406 : oddCount 406 10 = 5 ∧ acceleratedOrbit 10 406 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_406 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 406) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_406.1, data_10_406.2] + +/-- Complete interval computation for depth 10, residue 407. -/ +theorem bounds_10_407 : exactInterval 10 407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_407 (m : Nat) : + stoppingTime (2 ^ 10 * m + 407) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_407 : oddCount 407 10 = 5 ∧ acceleratedOrbit 10 407 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_407 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 407) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_407.1, data_10_407.2] + +/-- Complete interval computation for depth 10, residue 408. -/ +theorem bounds_10_408 : exactInterval 10 408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_408 (m : Nat) : + stoppingTime (2 ^ 10 * m + 408) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_408 : oddCount 408 10 = 3 ∧ acceleratedOrbit 10 408 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_408 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 408) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_408.1, data_10_408.2] + +/-- Complete interval computation for depth 10, residue 409. -/ +theorem bounds_10_409 : exactInterval 10 409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_409 (m : Nat) : + stoppingTime (2 ^ 10 * m + 409) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_409 : oddCount 409 10 = 5 ∧ acceleratedOrbit 10 409 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_409 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 409) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_409.1, data_10_409.2] + +/-- Complete interval computation for depth 10, residue 410. -/ +theorem bounds_10_410 : exactInterval 10 410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_410 (m : Nat) : + stoppingTime (2 ^ 10 * m + 410) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_410 : oddCount 410 10 = 3 ∧ acceleratedOrbit 10 410 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_410 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 410) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_410.1, data_10_410.2] + +/-- Complete interval computation for depth 10, residue 411. -/ +theorem bounds_10_411 : exactInterval 10 411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_411 (m : Nat) : + stoppingTime (2 ^ 10 * m + 411) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_411 : oddCount 411 10 = 7 ∧ acceleratedOrbit 10 411 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_411 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 411) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_411.1, data_10_411.2] + +/-- Complete interval computation for depth 10, residue 412. -/ +theorem bounds_10_412 : exactInterval 10 412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_412 (m : Nat) : + stoppingTime (2 ^ 10 * m + 412) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_412 : oddCount 412 10 = 7 ∧ acceleratedOrbit 10 412 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_412 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 412) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_412.1, data_10_412.2] + +/-- Complete interval computation for depth 10, residue 413. -/ +theorem bounds_10_413 : exactInterval 10 413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_413 (m : Nat) : + stoppingTime (2 ^ 10 * m + 413) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_413 : oddCount 413 10 = 7 ∧ acceleratedOrbit 10 413 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_413 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 413) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_413.1, data_10_413.2] + +end Collatz.Research.StoppingAtlas.Batch0027 From 2e56656e40126dd99393cde36002147511922e66 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:07 +0530 Subject: [PATCH 0028/1001] proof: certify atlas Batch0028 (10:414 to 10:429) --- Collatz/Research/StoppingAtlas/Batch0028.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0028.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0028.lean b/Collatz/Research/StoppingAtlas/Batch0028.lean new file mode 100644 index 00000000..51929d48 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0028.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0028 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 414. -/ +theorem bounds_10_414 : exactInterval 10 414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_414 (m : Nat) : + stoppingTime (2 ^ 10 * m + 414) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_414 : oddCount 414 10 = 7 ∧ acceleratedOrbit 10 414 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_414 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 414) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_414.1, data_10_414.2] + +/-- Complete interval computation for depth 10, residue 415. -/ +theorem bounds_10_415 : exactInterval 10 415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_415 (m : Nat) : + stoppingTime (2 ^ 10 * m + 415) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_415 : oddCount 415 10 = 8 ∧ acceleratedOrbit 10 415 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_415 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 415) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_415.1, data_10_415.2] + +/-- Complete interval computation for depth 10, residue 416. -/ +theorem bounds_10_416 : exactInterval 10 416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_416 (m : Nat) : + stoppingTime (2 ^ 10 * m + 416) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_416 : oddCount 416 10 = 2 ∧ acceleratedOrbit 10 416 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_416 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 416) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_416.1, data_10_416.2] + +/-- Complete interval computation for depth 10, residue 417. -/ +theorem bounds_10_417 : exactInterval 10 417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_417 (m : Nat) : + stoppingTime (2 ^ 10 * m + 417) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_417 : oddCount 417 10 = 6 ∧ acceleratedOrbit 10 417 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_417 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 417) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_417.1, data_10_417.2] + +/-- Complete interval computation for depth 10, residue 418. -/ +theorem bounds_10_418 : exactInterval 10 418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_418 (m : Nat) : + stoppingTime (2 ^ 10 * m + 418) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_418 : oddCount 418 10 = 5 ∧ acceleratedOrbit 10 418 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_418 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 418) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_418.1, data_10_418.2] + +/-- Complete interval computation for depth 10, residue 419. -/ +theorem bounds_10_419 : exactInterval 10 419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_419 (m : Nat) : + stoppingTime (2 ^ 10 * m + 419) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_419 : oddCount 419 10 = 5 ∧ acceleratedOrbit 10 419 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_419 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 419) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_419.1, data_10_419.2] + +/-- Complete interval computation for depth 10, residue 420. -/ +theorem bounds_10_420 : exactInterval 10 420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_420 (m : Nat) : + stoppingTime (2 ^ 10 * m + 420) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_420 : oddCount 420 10 = 5 ∧ acceleratedOrbit 10 420 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_420 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 420) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_420.1, data_10_420.2] + +/-- Complete interval computation for depth 10, residue 421. -/ +theorem bounds_10_421 : exactInterval 10 421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_421 (m : Nat) : + stoppingTime (2 ^ 10 * m + 421) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_421 : oddCount 421 10 = 5 ∧ acceleratedOrbit 10 421 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_421 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 421) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_421.1, data_10_421.2] + +/-- Complete interval computation for depth 10, residue 422. -/ +theorem bounds_10_422 : exactInterval 10 422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_422 (m : Nat) : + stoppingTime (2 ^ 10 * m + 422) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_422 : oddCount 422 10 = 5 ∧ acceleratedOrbit 10 422 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_422 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 422) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_422.1, data_10_422.2] + +/-- Complete interval computation for depth 10, residue 423. -/ +theorem bounds_10_423 : exactInterval 10 423 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_423 (m : Nat) : + stoppingTime (2 ^ 10 * m + 423) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_423 : oddCount 423 10 = 6 ∧ acceleratedOrbit 10 423 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_423 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 423) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_423.1, data_10_423.2] + +/-- Complete interval computation for depth 10, residue 424. -/ +theorem bounds_10_424 : exactInterval 10 424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_424 (m : Nat) : + stoppingTime (2 ^ 10 * m + 424) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_424 : oddCount 424 10 = 2 ∧ acceleratedOrbit 10 424 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_424 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 424) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_424.1, data_10_424.2] + +/-- Complete interval computation for depth 10, residue 425. -/ +theorem bounds_10_425 : exactInterval 10 425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_425 (m : Nat) : + stoppingTime (2 ^ 10 * m + 425) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_425 : oddCount 425 10 = 7 ∧ acceleratedOrbit 10 425 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_425 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 425) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_425.1, data_10_425.2] + +/-- Complete interval computation for depth 10, residue 426. -/ +theorem bounds_10_426 : exactInterval 10 426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_426 (m : Nat) : + stoppingTime (2 ^ 10 * m + 426) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_426 : oddCount 426 10 = 2 ∧ acceleratedOrbit 10 426 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_426 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 426) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_426.1, data_10_426.2] + +/-- Complete interval computation for depth 10, residue 427. -/ +theorem bounds_10_427 : exactInterval 10 427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_427 (m : Nat) : + stoppingTime (2 ^ 10 * m + 427) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_427 : oddCount 427 10 = 7 ∧ acceleratedOrbit 10 427 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_427 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 427) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_427.1, data_10_427.2] + +/-- Complete interval computation for depth 10, residue 428. -/ +theorem bounds_10_428 : exactInterval 10 428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_428 (m : Nat) : + stoppingTime (2 ^ 10 * m + 428) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_428 : oddCount 428 10 = 5 ∧ acceleratedOrbit 10 428 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_428 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 428) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_428.1, data_10_428.2] + +/-- Complete interval computation for depth 10, residue 429. -/ +theorem bounds_10_429 : exactInterval 10 429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_429 (m : Nat) : + stoppingTime (2 ^ 10 * m + 429) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_429 : oddCount 429 10 = 5 ∧ acceleratedOrbit 10 429 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_429 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 429) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_429.1, data_10_429.2] + +end Collatz.Research.StoppingAtlas.Batch0028 From 2643c64c5351d152e867a21aa0dbddd448f29264 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:07 +0530 Subject: [PATCH 0029/1001] proof: certify atlas Batch0029 (10:430 to 10:444) --- Collatz/Research/StoppingAtlas/Batch0029.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0029.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0029.lean b/Collatz/Research/StoppingAtlas/Batch0029.lean new file mode 100644 index 00000000..8f129409 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0029.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0029 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 430. -/ +theorem bounds_10_430 : exactInterval 10 430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_430 (m : Nat) : + stoppingTime (2 ^ 10 * m + 430) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_430 : oddCount 430 10 = 5 ∧ acceleratedOrbit 10 430 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_430 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 430) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_430.1, data_10_430.2] + +/-- Complete interval computation for depth 10, residue 431. -/ +theorem bounds_10_431 : exactInterval 10 431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_431 (m : Nat) : + stoppingTime (2 ^ 10 * m + 431) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_431 : oddCount 431 10 = 6 ∧ acceleratedOrbit 10 431 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_431 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 431) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_431.1, data_10_431.2] + +/-- Complete interval computation for depth 10, residue 432. -/ +theorem bounds_10_432 : exactInterval 10 432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_432 (m : Nat) : + stoppingTime (2 ^ 10 * m + 432) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_432 : oddCount 432 10 = 5 ∧ acceleratedOrbit 10 432 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_432 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 432) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_432.1, data_10_432.2] + +/-- Complete interval computation for depth 10, residue 433. -/ +theorem bounds_10_433 : exactInterval 10 433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_433 (m : Nat) : + stoppingTime (2 ^ 10 * m + 433) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_433 : oddCount 433 10 = 4 ∧ acceleratedOrbit 10 433 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_433 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 433) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_433.1, data_10_433.2] + +/-- Complete interval computation for depth 10, residue 434. -/ +theorem bounds_10_434 : exactInterval 10 434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_434 (m : Nat) : + stoppingTime (2 ^ 10 * m + 434) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_434 : oddCount 434 10 = 4 ∧ acceleratedOrbit 10 434 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_434 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 434) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_434.1, data_10_434.2] + +/-- Complete interval computation for depth 10, residue 435. -/ +theorem bounds_10_435 : exactInterval 10 435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_435 (m : Nat) : + stoppingTime (2 ^ 10 * m + 435) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_435 : oddCount 435 10 = 4 ∧ acceleratedOrbit 10 435 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_435 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 435) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_435.1, data_10_435.2] + +/-- Complete interval computation for depth 10, residue 436. -/ +theorem bounds_10_436 : exactInterval 10 436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_436 (m : Nat) : + stoppingTime (2 ^ 10 * m + 436) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_436 : oddCount 436 10 = 5 ∧ acceleratedOrbit 10 436 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_436 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 436) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_436.1, data_10_436.2] + +/-- Complete interval computation for depth 10, residue 437. -/ +theorem bounds_10_437 : exactInterval 10 437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_437 (m : Nat) : + stoppingTime (2 ^ 10 * m + 437) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_437 : oddCount 437 10 = 5 ∧ acceleratedOrbit 10 437 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_437 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 437) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_437.1, data_10_437.2] + +/-- Complete interval computation for depth 10, residue 438. -/ +theorem bounds_10_438 : exactInterval 10 438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_438 (m : Nat) : + stoppingTime (2 ^ 10 * m + 438) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_438 : oddCount 438 10 = 6 ∧ acceleratedOrbit 10 438 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_438 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 438) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_438.1, data_10_438.2] + +/-- Complete interval computation for depth 10, residue 439. -/ +theorem bounds_10_439 : exactInterval 10 439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_439 (m : Nat) : + stoppingTime (2 ^ 10 * m + 439) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_439 : oddCount 439 10 = 6 ∧ acceleratedOrbit 10 439 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_439 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 439) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_439.1, data_10_439.2] + +/-- Complete interval computation for depth 10, residue 440. -/ +theorem bounds_10_440 : exactInterval 10 440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_440 (m : Nat) : + stoppingTime (2 ^ 10 * m + 440) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_440 : oddCount 440 10 = 5 ∧ acceleratedOrbit 10 440 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_440 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 440) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_440.1, data_10_440.2] + +/-- Complete interval computation for depth 10, residue 441. -/ +theorem bounds_10_441 : exactInterval 10 441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_441 (m : Nat) : + stoppingTime (2 ^ 10 * m + 441) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_441 : oddCount 441 10 = 4 ∧ acceleratedOrbit 10 441 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_441 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 441) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_441.1, data_10_441.2] + +/-- Complete interval computation for depth 10, residue 442. -/ +theorem bounds_10_442 : exactInterval 10 442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_442 (m : Nat) : + stoppingTime (2 ^ 10 * m + 442) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_442 : oddCount 442 10 = 5 ∧ acceleratedOrbit 10 442 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_442 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 442) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_442.1, data_10_442.2] + +/-- Complete interval computation for depth 10, residue 443. -/ +theorem bounds_10_443 : exactInterval 10 443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_443 (m : Nat) : + stoppingTime (2 ^ 10 * m + 443) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_443 : oddCount 443 10 = 6 ∧ acceleratedOrbit 10 443 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_443 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 443) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_443.1, data_10_443.2] + +/-- Complete interval computation for depth 10, residue 444. -/ +theorem bounds_10_444 : exactInterval 10 444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_444 (m : Nat) : + stoppingTime (2 ^ 10 * m + 444) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_444 : oddCount 444 10 = 6 ∧ acceleratedOrbit 10 444 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_444 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 444) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_444.1, data_10_444.2] + +end Collatz.Research.StoppingAtlas.Batch0029 From 0f5041c3c52b7aa66232e64060697b49ad906036 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:07 +0530 Subject: [PATCH 0030/1001] proof: certify atlas Batch0030 (10:445 to 10:459) --- Collatz/Research/StoppingAtlas/Batch0030.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0030.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0030.lean b/Collatz/Research/StoppingAtlas/Batch0030.lean new file mode 100644 index 00000000..0c943fbc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0030.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0030 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 445. -/ +theorem bounds_10_445 : exactInterval 10 445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_445 (m : Nat) : + stoppingTime (2 ^ 10 * m + 445) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_445 : oddCount 445 10 = 6 ∧ acceleratedOrbit 10 445 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_445 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 445) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_445.1, data_10_445.2] + +/-- Complete interval computation for depth 10, residue 446. -/ +theorem bounds_10_446 : exactInterval 10 446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_446 (m : Nat) : + stoppingTime (2 ^ 10 * m + 446) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_446 : oddCount 446 10 = 6 ∧ acceleratedOrbit 10 446 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_446 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 446) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_446.1, data_10_446.2] + +/-- Complete interval computation for depth 10, residue 447. -/ +theorem bounds_10_447 : exactInterval 10 447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_447 (m : Nat) : + stoppingTime (2 ^ 10 * m + 447) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_447 : oddCount 447 10 = 9 ∧ acceleratedOrbit 10 447 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_447 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 447) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_447.1, data_10_447.2] + +/-- Complete interval computation for depth 10, residue 448. -/ +theorem bounds_10_448 : exactInterval 10 448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_448 (m : Nat) : + stoppingTime (2 ^ 10 * m + 448) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_448 : oddCount 448 10 = 3 ∧ acceleratedOrbit 10 448 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_448 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 448) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_448.1, data_10_448.2] + +/-- Complete interval computation for depth 10, residue 449. -/ +theorem bounds_10_449 : exactInterval 10 449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_449 (m : Nat) : + stoppingTime (2 ^ 10 * m + 449) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_449 : oddCount 449 10 = 6 ∧ acceleratedOrbit 10 449 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_449 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 449) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_449.1, data_10_449.2] + +/-- Complete interval computation for depth 10, residue 450. -/ +theorem bounds_10_450 : exactInterval 10 450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_450 (m : Nat) : + stoppingTime (2 ^ 10 * m + 450) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_450 : oddCount 450 10 = 7 ∧ acceleratedOrbit 10 450 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_450 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 450) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_450.1, data_10_450.2] + +/-- Complete interval computation for depth 10, residue 451. -/ +theorem bounds_10_451 : exactInterval 10 451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_451 (m : Nat) : + stoppingTime (2 ^ 10 * m + 451) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_451 : oddCount 451 10 = 7 ∧ acceleratedOrbit 10 451 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_451 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 451) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_451.1, data_10_451.2] + +/-- Complete interval computation for depth 10, residue 452. -/ +theorem bounds_10_452 : exactInterval 10 452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_452 (m : Nat) : + stoppingTime (2 ^ 10 * m + 452) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_452 : oddCount 452 10 = 2 ∧ acceleratedOrbit 10 452 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_452 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 452) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_452.1, data_10_452.2] + +/-- Complete interval computation for depth 10, residue 453. -/ +theorem bounds_10_453 : exactInterval 10 453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_453 (m : Nat) : + stoppingTime (2 ^ 10 * m + 453) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_453 : oddCount 453 10 = 2 ∧ acceleratedOrbit 10 453 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_453 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 453) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_453.1, data_10_453.2] + +/-- Complete interval computation for depth 10, residue 454. -/ +theorem bounds_10_454 : exactInterval 10 454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_454 (m : Nat) : + stoppingTime (2 ^ 10 * m + 454) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_454 : oddCount 454 10 = 2 ∧ acceleratedOrbit 10 454 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_454 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 454) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_454.1, data_10_454.2] + +/-- Complete interval computation for depth 10, residue 455. -/ +theorem bounds_10_455 : exactInterval 10 455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_455 (m : Nat) : + stoppingTime (2 ^ 10 * m + 455) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_455 : oddCount 455 10 = 6 ∧ acceleratedOrbit 10 455 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_455 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 455) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_455.1, data_10_455.2] + +/-- Complete interval computation for depth 10, residue 456. -/ +theorem bounds_10_456 : exactInterval 10 456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_456 (m : Nat) : + stoppingTime (2 ^ 10 * m + 456) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_456 : oddCount 456 10 = 4 ∧ acceleratedOrbit 10 456 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_456 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 456) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_456.1, data_10_456.2] + +/-- Complete interval computation for depth 10, residue 457. -/ +theorem bounds_10_457 : exactInterval 10 457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_457 (m : Nat) : + stoppingTime (2 ^ 10 * m + 457) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_457 : oddCount 457 10 = 5 ∧ acceleratedOrbit 10 457 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_457 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 457) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_457.1, data_10_457.2] + +/-- Complete interval computation for depth 10, residue 458. -/ +theorem bounds_10_458 : exactInterval 10 458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_458 (m : Nat) : + stoppingTime (2 ^ 10 * m + 458) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_458 : oddCount 458 10 = 4 ∧ acceleratedOrbit 10 458 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_458 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 458) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_458.1, data_10_458.2] + +/-- Complete interval computation for depth 10, residue 459. -/ +theorem bounds_10_459 : exactInterval 10 459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_459 (m : Nat) : + stoppingTime (2 ^ 10 * m + 459) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_459 : oddCount 459 10 = 5 ∧ acceleratedOrbit 10 459 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_459 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 459) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_459.1, data_10_459.2] + +end Collatz.Research.StoppingAtlas.Batch0030 From 8b35a56deec999e9689916e30109906601239820 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:08 +0530 Subject: [PATCH 0031/1001] proof: certify atlas Batch0031 (10:460 to 10:475) --- Collatz/Research/StoppingAtlas/Batch0031.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0031.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0031.lean b/Collatz/Research/StoppingAtlas/Batch0031.lean new file mode 100644 index 00000000..cb8d2fc4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0031.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0031 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 460. -/ +theorem bounds_10_460 : exactInterval 10 460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_460 (m : Nat) : + stoppingTime (2 ^ 10 * m + 460) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_460 : oddCount 460 10 = 4 ∧ acceleratedOrbit 10 460 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_460 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 460) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_460.1, data_10_460.2] + +/-- Complete interval computation for depth 10, residue 461. -/ +theorem bounds_10_461 : exactInterval 10 461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_461 (m : Nat) : + stoppingTime (2 ^ 10 * m + 461) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_461 : oddCount 461 10 = 4 ∧ acceleratedOrbit 10 461 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_461 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 461) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_461.1, data_10_461.2] + +/-- Complete interval computation for depth 10, residue 462. -/ +theorem bounds_10_462 : exactInterval 10 462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_462 (m : Nat) : + stoppingTime (2 ^ 10 * m + 462) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_462 : oddCount 462 10 = 7 ∧ acceleratedOrbit 10 462 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_462 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 462) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_462.1, data_10_462.2] + +/-- Complete interval computation for depth 10, residue 463. -/ +theorem bounds_10_463 : exactInterval 10 463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_463 (m : Nat) : + stoppingTime (2 ^ 10 * m + 463) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_463 : oddCount 463 10 = 7 ∧ acceleratedOrbit 10 463 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_463 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 463) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_463.1, data_10_463.2] + +/-- Complete interval computation for depth 10, residue 464. -/ +theorem bounds_10_464 : exactInterval 10 464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_464 (m : Nat) : + stoppingTime (2 ^ 10 * m + 464) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_464 : oddCount 464 10 = 3 ∧ acceleratedOrbit 10 464 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_464 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 464) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_464.1, data_10_464.2] + +/-- Complete interval computation for depth 10, residue 465. -/ +theorem bounds_10_465 : exactInterval 10 465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_465 (m : Nat) : + stoppingTime (2 ^ 10 * m + 465) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_465 : oddCount 465 10 = 4 ∧ acceleratedOrbit 10 465 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_465 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 465) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_465.1, data_10_465.2] + +/-- Complete interval computation for depth 10, residue 466. -/ +theorem bounds_10_466 : exactInterval 10 466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_466 (m : Nat) : + stoppingTime (2 ^ 10 * m + 466) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_466 : oddCount 466 10 = 6 ∧ acceleratedOrbit 10 466 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_466 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 466) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_466.1, data_10_466.2] + +/-- Complete interval computation for depth 10, residue 467. -/ +theorem bounds_10_467 : exactInterval 10 467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_467 (m : Nat) : + stoppingTime (2 ^ 10 * m + 467) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_467 : oddCount 467 10 = 6 ∧ acceleratedOrbit 10 467 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_467 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 467) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_467.1, data_10_467.2] + +/-- Complete interval computation for depth 10, residue 468. -/ +theorem bounds_10_468 : exactInterval 10 468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_468 (m : Nat) : + stoppingTime (2 ^ 10 * m + 468) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_468 : oddCount 468 10 = 3 ∧ acceleratedOrbit 10 468 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_468 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 468) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_468.1, data_10_468.2] + +/-- Complete interval computation for depth 10, residue 469. -/ +theorem bounds_10_469 : exactInterval 10 469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_469 (m : Nat) : + stoppingTime (2 ^ 10 * m + 469) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_469 : oddCount 469 10 = 3 ∧ acceleratedOrbit 10 469 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_469 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 469) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_469.1, data_10_469.2] + +/-- Complete interval computation for depth 10, residue 470. -/ +theorem bounds_10_470 : exactInterval 10 470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_470 (m : Nat) : + stoppingTime (2 ^ 10 * m + 470) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_470 : oddCount 470 10 = 6 ∧ acceleratedOrbit 10 470 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_470 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 470) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_470.1, data_10_470.2] + +/-- Complete interval computation for depth 10, residue 471. -/ +theorem bounds_10_471 : exactInterval 10 471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_471 (m : Nat) : + stoppingTime (2 ^ 10 * m + 471) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_471 : oddCount 471 10 = 6 ∧ acceleratedOrbit 10 471 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_471 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 471) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_471.1, data_10_471.2] + +/-- Complete interval computation for depth 10, residue 472. -/ +theorem bounds_10_472 : exactInterval 10 472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_472 (m : Nat) : + stoppingTime (2 ^ 10 * m + 472) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_472 : oddCount 472 10 = 4 ∧ acceleratedOrbit 10 472 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_472 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 472) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_472.1, data_10_472.2] + +/-- Complete interval computation for depth 10, residue 473. -/ +theorem bounds_10_473 : exactInterval 10 473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_473 (m : Nat) : + stoppingTime (2 ^ 10 * m + 473) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_473 : oddCount 473 10 = 4 ∧ acceleratedOrbit 10 473 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_473 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 473) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_473.1, data_10_473.2] + +/-- Complete interval computation for depth 10, residue 474. -/ +theorem bounds_10_474 : exactInterval 10 474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_474 (m : Nat) : + stoppingTime (2 ^ 10 * m + 474) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_474 : oddCount 474 10 = 4 ∧ acceleratedOrbit 10 474 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_474 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 474) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_474.1, data_10_474.2] + +/-- Complete interval computation for depth 10, residue 475. -/ +theorem bounds_10_475 : exactInterval 10 475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_475 (m : Nat) : + stoppingTime (2 ^ 10 * m + 475) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_475 : oddCount 475 10 = 5 ∧ acceleratedOrbit 10 475 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_475 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 475) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_475.1, data_10_475.2] + +end Collatz.Research.StoppingAtlas.Batch0031 From 609f041ef85da0b90760087324319d3a969cf66c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:08 +0530 Subject: [PATCH 0032/1001] proof: certify atlas Batch0032 (10:476 to 10:490) --- Collatz/Research/StoppingAtlas/Batch0032.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0032.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0032.lean b/Collatz/Research/StoppingAtlas/Batch0032.lean new file mode 100644 index 00000000..cd6f248e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0032.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0032 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 476. -/ +theorem bounds_10_476 : exactInterval 10 476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_476 (m : Nat) : + stoppingTime (2 ^ 10 * m + 476) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_476 : oddCount 476 10 = 4 ∧ acceleratedOrbit 10 476 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_476 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 476) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_476.1, data_10_476.2] + +/-- Complete interval computation for depth 10, residue 477. -/ +theorem bounds_10_477 : exactInterval 10 477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_477 (m : Nat) : + stoppingTime (2 ^ 10 * m + 477) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_477 : oddCount 477 10 = 4 ∧ acceleratedOrbit 10 477 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_477 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 477) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_477.1, data_10_477.2] + +/-- Complete interval computation for depth 10, residue 478. -/ +theorem bounds_10_478 : exactInterval 10 478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_478 (m : Nat) : + stoppingTime (2 ^ 10 * m + 478) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_478 : oddCount 478 10 = 8 ∧ acceleratedOrbit 10 478 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_478 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 478) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_478.1, data_10_478.2] + +/-- Complete interval computation for depth 10, residue 479. -/ +theorem bounds_10_479 : exactInterval 10 479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_479 (m : Nat) : + stoppingTime (2 ^ 10 * m + 479) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_479 : oddCount 479 10 = 8 ∧ acceleratedOrbit 10 479 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_479 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 479) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_479.1, data_10_479.2] + +/-- Complete interval computation for depth 10, residue 480. -/ +theorem bounds_10_480 : exactInterval 10 480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_480 (m : Nat) : + stoppingTime (2 ^ 10 * m + 480) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_480 : oddCount 480 10 = 4 ∧ acceleratedOrbit 10 480 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_480 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 480) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_480.1, data_10_480.2] + +/-- Complete interval computation for depth 10, residue 481. -/ +theorem bounds_10_481 : exactInterval 10 481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_481 (m : Nat) : + stoppingTime (2 ^ 10 * m + 481) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_481 : oddCount 481 10 = 6 ∧ acceleratedOrbit 10 481 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_481 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 481) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_481.1, data_10_481.2] + +/-- Complete interval computation for depth 10, residue 482. -/ +theorem bounds_10_482 : exactInterval 10 482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_482 (m : Nat) : + stoppingTime (2 ^ 10 * m + 482) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_482 : oddCount 482 10 = 3 ∧ acceleratedOrbit 10 482 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_482 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 482) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_482.1, data_10_482.2] + +/-- Complete interval computation for depth 10, residue 483. -/ +theorem bounds_10_483 : exactInterval 10 483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_483 (m : Nat) : + stoppingTime (2 ^ 10 * m + 483) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_483 : oddCount 483 10 = 3 ∧ acceleratedOrbit 10 483 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_483 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 483) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_483.1, data_10_483.2] + +/-- Complete interval computation for depth 10, residue 484. -/ +theorem bounds_10_484 : exactInterval 10 484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_484 (m : Nat) : + stoppingTime (2 ^ 10 * m + 484) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_484 : oddCount 484 10 = 6 ∧ acceleratedOrbit 10 484 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_484 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 484) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_484.1, data_10_484.2] + +/-- Complete interval computation for depth 10, residue 485. -/ +theorem bounds_10_485 : exactInterval 10 485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_485 (m : Nat) : + stoppingTime (2 ^ 10 * m + 485) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_485 : oddCount 485 10 = 6 ∧ acceleratedOrbit 10 485 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_485 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 485) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_485.1, data_10_485.2] + +/-- Complete interval computation for depth 10, residue 486. -/ +theorem bounds_10_486 : exactInterval 10 486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_486 (m : Nat) : + stoppingTime (2 ^ 10 * m + 486) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_486 : oddCount 486 10 = 6 ∧ acceleratedOrbit 10 486 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_486 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 486) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_486.1, data_10_486.2] + +/-- Complete interval computation for depth 10, residue 487. -/ +theorem bounds_10_487 : exactInterval 10 487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_487 (m : Nat) : + stoppingTime (2 ^ 10 * m + 487) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_487 : oddCount 487 10 = 7 ∧ acceleratedOrbit 10 487 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_487 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 487) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_487.1, data_10_487.2] + +/-- Complete interval computation for depth 10, residue 488. -/ +theorem bounds_10_488 : exactInterval 10 488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_488 (m : Nat) : + stoppingTime (2 ^ 10 * m + 488) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_488 : oddCount 488 10 = 4 ∧ acceleratedOrbit 10 488 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_488 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 488) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_488.1, data_10_488.2] + +/-- Complete interval computation for depth 10, residue 489. -/ +theorem bounds_10_489 : exactInterval 10 489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_489 (m : Nat) : + stoppingTime (2 ^ 10 * m + 489) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_489 : oddCount 489 10 = 7 ∧ acceleratedOrbit 10 489 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_489 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 489) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_489.1, data_10_489.2] + +/-- Complete interval computation for depth 10, residue 490. -/ +theorem bounds_10_490 : exactInterval 10 490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_490 (m : Nat) : + stoppingTime (2 ^ 10 * m + 490) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_490 : oddCount 490 10 = 4 ∧ acceleratedOrbit 10 490 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_490 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 490) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_490.1, data_10_490.2] + +end Collatz.Research.StoppingAtlas.Batch0032 From 8fe531f546d4c9dad8e012e16912a4479e826a46 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:08 +0530 Subject: [PATCH 0033/1001] proof: certify atlas Batch0033 (10:491 to 10:505) --- Collatz/Research/StoppingAtlas/Batch0033.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0033.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0033.lean b/Collatz/Research/StoppingAtlas/Batch0033.lean new file mode 100644 index 00000000..90c66603 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0033.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0033 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 491. -/ +theorem bounds_10_491 : exactInterval 10 491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_491 (m : Nat) : + stoppingTime (2 ^ 10 * m + 491) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_491 : oddCount 491 10 = 8 ∧ acceleratedOrbit 10 491 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_491 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 491) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_491.1, data_10_491.2] + +/-- Complete interval computation for depth 10, residue 492. -/ +theorem bounds_10_492 : exactInterval 10 492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_492 (m : Nat) : + stoppingTime (2 ^ 10 * m + 492) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_492 : oddCount 492 10 = 5 ∧ acceleratedOrbit 10 492 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_492 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 492) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_492.1, data_10_492.2] + +/-- Complete interval computation for depth 10, residue 493. -/ +theorem bounds_10_493 : exactInterval 10 493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_493 (m : Nat) : + stoppingTime (2 ^ 10 * m + 493) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_493 : oddCount 493 10 = 5 ∧ acceleratedOrbit 10 493 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_493 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 493) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_493.1, data_10_493.2] + +/-- Complete interval computation for depth 10, residue 494. -/ +theorem bounds_10_494 : exactInterval 10 494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_494 (m : Nat) : + stoppingTime (2 ^ 10 * m + 494) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_494 : oddCount 494 10 = 5 ∧ acceleratedOrbit 10 494 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_494 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 494) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_494.1, data_10_494.2] + +/-- Complete interval computation for depth 10, residue 495. -/ +theorem bounds_10_495 : exactInterval 10 495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_495 (m : Nat) : + stoppingTime (2 ^ 10 * m + 495) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_495 : oddCount 495 10 = 8 ∧ acceleratedOrbit 10 495 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_495 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 495) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_495.1, data_10_495.2] + +/-- Complete interval computation for depth 10, residue 496. -/ +theorem bounds_10_496 : exactInterval 10 496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_496 (m : Nat) : + stoppingTime (2 ^ 10 * m + 496) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_496 : oddCount 496 10 = 5 ∧ acceleratedOrbit 10 496 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_496 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 496) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_496.1, data_10_496.2] + +/-- Complete interval computation for depth 10, residue 497. -/ +theorem bounds_10_497 : exactInterval 10 497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_497 (m : Nat) : + stoppingTime (2 ^ 10 * m + 497) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_497 : oddCount 497 10 = 4 ∧ acceleratedOrbit 10 497 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_497 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 497) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_497.1, data_10_497.2] + +/-- Complete interval computation for depth 10, residue 498. -/ +theorem bounds_10_498 : exactInterval 10 498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_498 (m : Nat) : + stoppingTime (2 ^ 10 * m + 498) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_498 : oddCount 498 10 = 5 ∧ acceleratedOrbit 10 498 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_498 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 498) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_498.1, data_10_498.2] + +/-- Complete interval computation for depth 10, residue 499. -/ +theorem bounds_10_499 : exactInterval 10 499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_499 (m : Nat) : + stoppingTime (2 ^ 10 * m + 499) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_499 : oddCount 499 10 = 5 ∧ acceleratedOrbit 10 499 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_499 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 499) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_499.1, data_10_499.2] + +/-- Complete interval computation for depth 10, residue 500. -/ +theorem bounds_10_500 : exactInterval 10 500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_500 (m : Nat) : + stoppingTime (2 ^ 10 * m + 500) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_500 : oddCount 500 10 = 5 ∧ acceleratedOrbit 10 500 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_500 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 500) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_500.1, data_10_500.2] + +/-- Complete interval computation for depth 10, residue 501. -/ +theorem bounds_10_501 : exactInterval 10 501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_501 (m : Nat) : + stoppingTime (2 ^ 10 * m + 501) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_501 : oddCount 501 10 = 5 ∧ acceleratedOrbit 10 501 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_501 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 501) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_501.1, data_10_501.2] + +/-- Complete interval computation for depth 10, residue 502. -/ +theorem bounds_10_502 : exactInterval 10 502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_502 (m : Nat) : + stoppingTime (2 ^ 10 * m + 502) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_502 : oddCount 502 10 = 7 ∧ acceleratedOrbit 10 502 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_502 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 502) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_502.1, data_10_502.2] + +/-- Complete interval computation for depth 10, residue 503. -/ +theorem bounds_10_503 : exactInterval 10 503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_503 (m : Nat) : + stoppingTime (2 ^ 10 * m + 503) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_503 : oddCount 503 10 = 7 ∧ acceleratedOrbit 10 503 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_503 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 503) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_503.1, data_10_503.2] + +/-- Complete interval computation for depth 10, residue 504. -/ +theorem bounds_10_504 : exactInterval 10 504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_504 (m : Nat) : + stoppingTime (2 ^ 10 * m + 504) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_504 : oddCount 504 10 = 6 ∧ acceleratedOrbit 10 504 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_504 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 504) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_504.1, data_10_504.2] + +/-- Complete interval computation for depth 10, residue 505. -/ +theorem bounds_10_505 : exactInterval 10 505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_505 (m : Nat) : + stoppingTime (2 ^ 10 * m + 505) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_505 : oddCount 505 10 = 6 ∧ acceleratedOrbit 10 505 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_505 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 505) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_505.1, data_10_505.2] + +end Collatz.Research.StoppingAtlas.Batch0033 From f843d4013391aa9b82512321471a78d88b173793 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:09 +0530 Subject: [PATCH 0034/1001] proof: certify atlas Batch0034 (10:506 to 10:521) --- Collatz/Research/StoppingAtlas/Batch0034.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0034.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0034.lean b/Collatz/Research/StoppingAtlas/Batch0034.lean new file mode 100644 index 00000000..cefff444 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0034.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0034 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 506. -/ +theorem bounds_10_506 : exactInterval 10 506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_506 (m : Nat) : + stoppingTime (2 ^ 10 * m + 506) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_506 : oddCount 506 10 = 6 ∧ acceleratedOrbit 10 506 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_506 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 506) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_506.1, data_10_506.2] + +/-- Complete interval computation for depth 10, residue 507. -/ +theorem bounds_10_507 : exactInterval 10 507 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_507 (m : Nat) : + stoppingTime (2 ^ 10 * m + 507) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_507 : oddCount 507 10 = 6 ∧ acceleratedOrbit 10 507 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_507 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 507) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_507.1, data_10_507.2] + +/-- Complete interval computation for depth 10, residue 508. -/ +theorem bounds_10_508 : exactInterval 10 508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_508 (m : Nat) : + stoppingTime (2 ^ 10 * m + 508) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_508 : oddCount 508 10 = 7 ∧ acceleratedOrbit 10 508 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_508 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 508) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_508.1, data_10_508.2] + +/-- Complete interval computation for depth 10, residue 509. -/ +theorem bounds_10_509 : exactInterval 10 509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_509 (m : Nat) : + stoppingTime (2 ^ 10 * m + 509) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_509 : oddCount 509 10 = 7 ∧ acceleratedOrbit 10 509 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_509 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 509) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_509.1, data_10_509.2] + +/-- Complete interval computation for depth 10, residue 510. -/ +theorem bounds_10_510 : exactInterval 10 510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_510 (m : Nat) : + stoppingTime (2 ^ 10 * m + 510) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_510 : oddCount 510 10 = 8 ∧ acceleratedOrbit 10 510 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_510 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 510) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_510.1, data_10_510.2] + +/-- Complete interval computation for depth 10, residue 511. -/ +theorem bounds_10_511 : exactInterval 10 511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_511 (m : Nat) : + stoppingTime (2 ^ 10 * m + 511) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_511 : oddCount 511 10 = 9 ∧ acceleratedOrbit 10 511 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_511 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 511) = 3 ^ 9 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_511.1, data_10_511.2] + +/-- Complete interval computation for depth 10, residue 512. -/ +theorem bounds_10_512 : exactInterval 10 512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_512 (m : Nat) : + stoppingTime (2 ^ 10 * m + 512) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_512 : oddCount 512 10 = 1 ∧ acceleratedOrbit 10 512 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_512 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 512) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_512.1, data_10_512.2] + +/-- Complete interval computation for depth 10, residue 513. -/ +theorem bounds_10_513 : exactInterval 10 513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_513 (m : Nat) : + stoppingTime (2 ^ 10 * m + 513) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_513 : oddCount 513 10 = 6 ∧ acceleratedOrbit 10 513 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_513 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 513) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_513.1, data_10_513.2] + +/-- Complete interval computation for depth 10, residue 514. -/ +theorem bounds_10_514 : exactInterval 10 514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_514 (m : Nat) : + stoppingTime (2 ^ 10 * m + 514) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_514 : oddCount 514 10 = 4 ∧ acceleratedOrbit 10 514 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_514 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 514) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_514.1, data_10_514.2] + +/-- Complete interval computation for depth 10, residue 515. -/ +theorem bounds_10_515 : exactInterval 10 515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_515 (m : Nat) : + stoppingTime (2 ^ 10 * m + 515) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_515 : oddCount 515 10 = 4 ∧ acceleratedOrbit 10 515 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_515 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 515) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_515.1, data_10_515.2] + +/-- Complete interval computation for depth 10, residue 516. -/ +theorem bounds_10_516 : exactInterval 10 516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_516 (m : Nat) : + stoppingTime (2 ^ 10 * m + 516) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_516 : oddCount 516 10 = 5 ∧ acceleratedOrbit 10 516 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_516 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 516) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_516.1, data_10_516.2] + +/-- Complete interval computation for depth 10, residue 517. -/ +theorem bounds_10_517 : exactInterval 10 517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_517 (m : Nat) : + stoppingTime (2 ^ 10 * m + 517) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_517 : oddCount 517 10 = 5 ∧ acceleratedOrbit 10 517 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_517 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 517) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_517.1, data_10_517.2] + +/-- Complete interval computation for depth 10, residue 518. -/ +theorem bounds_10_518 : exactInterval 10 518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_518 (m : Nat) : + stoppingTime (2 ^ 10 * m + 518) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_518 : oddCount 518 10 = 5 ∧ acceleratedOrbit 10 518 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_518 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 518) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_518.1, data_10_518.2] + +/-- Complete interval computation for depth 10, residue 519. -/ +theorem bounds_10_519 : exactInterval 10 519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_519 (m : Nat) : + stoppingTime (2 ^ 10 * m + 519) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_519 : oddCount 519 10 = 6 ∧ acceleratedOrbit 10 519 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_519 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 519) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_519.1, data_10_519.2] + +/-- Complete interval computation for depth 10, residue 520. -/ +theorem bounds_10_520 : exactInterval 10 520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_520 (m : Nat) : + stoppingTime (2 ^ 10 * m + 520) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_520 : oddCount 520 10 = 3 ∧ acceleratedOrbit 10 520 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_520 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 520) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_520.1, data_10_520.2] + +/-- Complete interval computation for depth 10, residue 521. -/ +theorem bounds_10_521 : exactInterval 10 521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_521 (m : Nat) : + stoppingTime (2 ^ 10 * m + 521) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_521 : oddCount 521 10 = 5 ∧ acceleratedOrbit 10 521 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_521 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 521) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_521.1, data_10_521.2] + +end Collatz.Research.StoppingAtlas.Batch0034 From 9400ac63393c47d59347b8574d0fb397fbe0ff5d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:09 +0530 Subject: [PATCH 0035/1001] proof: certify atlas Batch0035 (10:522 to 10:536) --- Collatz/Research/StoppingAtlas/Batch0035.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0035.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0035.lean b/Collatz/Research/StoppingAtlas/Batch0035.lean new file mode 100644 index 00000000..2c75574d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0035.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0035 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 522. -/ +theorem bounds_10_522 : exactInterval 10 522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_522 (m : Nat) : + stoppingTime (2 ^ 10 * m + 522) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_522 : oddCount 522 10 = 3 ∧ acceleratedOrbit 10 522 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_522 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 522) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_522.1, data_10_522.2] + +/-- Complete interval computation for depth 10, residue 523. -/ +theorem bounds_10_523 : exactInterval 10 523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_523 (m : Nat) : + stoppingTime (2 ^ 10 * m + 523) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_523 : oddCount 523 10 = 5 ∧ acceleratedOrbit 10 523 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_523 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 523) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_523.1, data_10_523.2] + +/-- Complete interval computation for depth 10, residue 524. -/ +theorem bounds_10_524 : exactInterval 10 524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_524 (m : Nat) : + stoppingTime (2 ^ 10 * m + 524) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_524 : oddCount 524 10 = 3 ∧ acceleratedOrbit 10 524 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_524 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 524) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_524.1, data_10_524.2] + +/-- Complete interval computation for depth 10, residue 525. -/ +theorem bounds_10_525 : exactInterval 10 525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_525 (m : Nat) : + stoppingTime (2 ^ 10 * m + 525) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_525 : oddCount 525 10 = 3 ∧ acceleratedOrbit 10 525 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_525 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 525) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_525.1, data_10_525.2] + +/-- Complete interval computation for depth 10, residue 526. -/ +theorem bounds_10_526 : exactInterval 10 526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_526 (m : Nat) : + stoppingTime (2 ^ 10 * m + 526) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_526 : oddCount 526 10 = 6 ∧ acceleratedOrbit 10 526 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_526 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 526) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_526.1, data_10_526.2] + +/-- Complete interval computation for depth 10, residue 527. -/ +theorem bounds_10_527 : exactInterval 10 527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_527 (m : Nat) : + stoppingTime (2 ^ 10 * m + 527) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_527 : oddCount 527 10 = 6 ∧ acceleratedOrbit 10 527 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_527 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 527) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_527.1, data_10_527.2] + +/-- Complete interval computation for depth 10, residue 528. -/ +theorem bounds_10_528 : exactInterval 10 528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_528 (m : Nat) : + stoppingTime (2 ^ 10 * m + 528) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_528 : oddCount 528 10 = 4 ∧ acceleratedOrbit 10 528 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_528 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 528) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_528.1, data_10_528.2] + +/-- Complete interval computation for depth 10, residue 529. -/ +theorem bounds_10_529 : exactInterval 10 529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_529 (m : Nat) : + stoppingTime (2 ^ 10 * m + 529) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_529 : oddCount 529 10 = 3 ∧ acceleratedOrbit 10 529 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_529 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 529) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_529.1, data_10_529.2] + +/-- Complete interval computation for depth 10, residue 530. -/ +theorem bounds_10_530 : exactInterval 10 530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_530 (m : Nat) : + stoppingTime (2 ^ 10 * m + 530) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_530 : oddCount 530 10 = 6 ∧ acceleratedOrbit 10 530 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_530 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 530) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_530.1, data_10_530.2] + +/-- Complete interval computation for depth 10, residue 531. -/ +theorem bounds_10_531 : exactInterval 10 531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_531 (m : Nat) : + stoppingTime (2 ^ 10 * m + 531) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_531 : oddCount 531 10 = 6 ∧ acceleratedOrbit 10 531 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_531 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 531) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_531.1, data_10_531.2] + +/-- Complete interval computation for depth 10, residue 532. -/ +theorem bounds_10_532 : exactInterval 10 532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_532 (m : Nat) : + stoppingTime (2 ^ 10 * m + 532) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_532 : oddCount 532 10 = 4 ∧ acceleratedOrbit 10 532 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_532 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 532) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_532.1, data_10_532.2] + +/-- Complete interval computation for depth 10, residue 533. -/ +theorem bounds_10_533 : exactInterval 10 533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_533 (m : Nat) : + stoppingTime (2 ^ 10 * m + 533) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_533 : oddCount 533 10 = 4 ∧ acceleratedOrbit 10 533 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_533 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 533) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_533.1, data_10_533.2] + +/-- Complete interval computation for depth 10, residue 534. -/ +theorem bounds_10_534 : exactInterval 10 534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_534 (m : Nat) : + stoppingTime (2 ^ 10 * m + 534) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_534 : oddCount 534 10 = 5 ∧ acceleratedOrbit 10 534 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_534 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 534) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_534.1, data_10_534.2] + +/-- Complete interval computation for depth 10, residue 535. -/ +theorem bounds_10_535 : exactInterval 10 535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_535 (m : Nat) : + stoppingTime (2 ^ 10 * m + 535) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_535 : oddCount 535 10 = 5 ∧ acceleratedOrbit 10 535 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_535 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 535) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_535.1, data_10_535.2] + +/-- Complete interval computation for depth 10, residue 536. -/ +theorem bounds_10_536 : exactInterval 10 536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_536 (m : Nat) : + stoppingTime (2 ^ 10 * m + 536) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_536 : oddCount 536 10 = 4 ∧ acceleratedOrbit 10 536 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_536 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 536) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_536.1, data_10_536.2] + +end Collatz.Research.StoppingAtlas.Batch0035 From f782b8ab52a535000b16f9c7934aba6cbf3eaaf1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:09 +0530 Subject: [PATCH 0036/1001] proof: certify atlas Batch0036 (10:537 to 10:551) --- Collatz/Research/StoppingAtlas/Batch0036.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0036.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0036.lean b/Collatz/Research/StoppingAtlas/Batch0036.lean new file mode 100644 index 00000000..0cf392e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0036.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0036 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 537. -/ +theorem bounds_10_537 : exactInterval 10 537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_537 (m : Nat) : + stoppingTime (2 ^ 10 * m + 537) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_537 : oddCount 537 10 = 5 ∧ acceleratedOrbit 10 537 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_537 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 537) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_537.1, data_10_537.2] + +/-- Complete interval computation for depth 10, residue 538. -/ +theorem bounds_10_538 : exactInterval 10 538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_538 (m : Nat) : + stoppingTime (2 ^ 10 * m + 538) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_538 : oddCount 538 10 = 4 ∧ acceleratedOrbit 10 538 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_538 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 538) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_538.1, data_10_538.2] + +/-- Complete interval computation for depth 10, residue 539. -/ +theorem bounds_10_539 : exactInterval 10 539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_539 (m : Nat) : + stoppingTime (2 ^ 10 * m + 539) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_539 : oddCount 539 10 = 7 ∧ acceleratedOrbit 10 539 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_539 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 539) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_539.1, data_10_539.2] + +/-- Complete interval computation for depth 10, residue 540. -/ +theorem bounds_10_540 : exactInterval 10 540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_540 (m : Nat) : + stoppingTime (2 ^ 10 * m + 540) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_540 : oddCount 540 10 = 4 ∧ acceleratedOrbit 10 540 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_540 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 540) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_540.1, data_10_540.2] + +/-- Complete interval computation for depth 10, residue 541. -/ +theorem bounds_10_541 : exactInterval 10 541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_541 (m : Nat) : + stoppingTime (2 ^ 10 * m + 541) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_541 : oddCount 541 10 = 4 ∧ acceleratedOrbit 10 541 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_541 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 541) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_541.1, data_10_541.2] + +/-- Complete interval computation for depth 10, residue 542. -/ +theorem bounds_10_542 : exactInterval 10 542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_542 (m : Nat) : + stoppingTime (2 ^ 10 * m + 542) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_542 : oddCount 542 10 = 4 ∧ acceleratedOrbit 10 542 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_542 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 542) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_542.1, data_10_542.2] + +/-- Complete interval computation for depth 10, residue 543. -/ +theorem bounds_10_543 : exactInterval 10 543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_543 (m : Nat) : + stoppingTime (2 ^ 10 * m + 543) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_543 : oddCount 543 10 = 7 ∧ acceleratedOrbit 10 543 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_543 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 543) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_543.1, data_10_543.2] + +/-- Complete interval computation for depth 10, residue 544. -/ +theorem bounds_10_544 : exactInterval 10 544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_544 (m : Nat) : + stoppingTime (2 ^ 10 * m + 544) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_544 : oddCount 544 10 = 2 ∧ acceleratedOrbit 10 544 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_544 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 544) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_544.1, data_10_544.2] + +/-- Complete interval computation for depth 10, residue 545. -/ +theorem bounds_10_545 : exactInterval 10 545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_545 (m : Nat) : + stoppingTime (2 ^ 10 * m + 545) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_545 : oddCount 545 10 = 5 ∧ acceleratedOrbit 10 545 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_545 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 545) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_545.1, data_10_545.2] + +/-- Complete interval computation for depth 10, residue 546. -/ +theorem bounds_10_546 : exactInterval 10 546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_546 (m : Nat) : + stoppingTime (2 ^ 10 * m + 546) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_546 : oddCount 546 10 = 4 ∧ acceleratedOrbit 10 546 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_546 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 546) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_546.1, data_10_546.2] + +/-- Complete interval computation for depth 10, residue 547. -/ +theorem bounds_10_547 : exactInterval 10 547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_547 (m : Nat) : + stoppingTime (2 ^ 10 * m + 547) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_547 : oddCount 547 10 = 4 ∧ acceleratedOrbit 10 547 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_547 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 547) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_547.1, data_10_547.2] + +/-- Complete interval computation for depth 10, residue 548. -/ +theorem bounds_10_548 : exactInterval 10 548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_548 (m : Nat) : + stoppingTime (2 ^ 10 * m + 548) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_548 : oddCount 548 10 = 6 ∧ acceleratedOrbit 10 548 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_548 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 548) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_548.1, data_10_548.2] + +/-- Complete interval computation for depth 10, residue 549. -/ +theorem bounds_10_549 : exactInterval 10 549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_549 (m : Nat) : + stoppingTime (2 ^ 10 * m + 549) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_549 : oddCount 549 10 = 6 ∧ acceleratedOrbit 10 549 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_549 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 549) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_549.1, data_10_549.2] + +/-- Complete interval computation for depth 10, residue 550. -/ +theorem bounds_10_550 : exactInterval 10 550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_550 (m : Nat) : + stoppingTime (2 ^ 10 * m + 550) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_550 : oddCount 550 10 = 6 ∧ acceleratedOrbit 10 550 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_550 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 550) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_550.1, data_10_550.2] + +/-- Complete interval computation for depth 10, residue 551. -/ +theorem bounds_10_551 : exactInterval 10 551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_551 (m : Nat) : + stoppingTime (2 ^ 10 * m + 551) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_551 : oddCount 551 10 = 5 ∧ acceleratedOrbit 10 551 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_551 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 551) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_551.1, data_10_551.2] + +end Collatz.Research.StoppingAtlas.Batch0036 From 644e11fdb561a1e9937f2a470ae2ab01196fe2c0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:10 +0530 Subject: [PATCH 0037/1001] proof: certify atlas Batch0037 (10:552 to 10:567) --- Collatz/Research/StoppingAtlas/Batch0037.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0037.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0037.lean b/Collatz/Research/StoppingAtlas/Batch0037.lean new file mode 100644 index 00000000..417ce4db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0037.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0037 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 552. -/ +theorem bounds_10_552 : exactInterval 10 552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_552 (m : Nat) : + stoppingTime (2 ^ 10 * m + 552) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_552 : oddCount 552 10 = 2 ∧ acceleratedOrbit 10 552 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_552 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 552) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_552.1, data_10_552.2] + +/-- Complete interval computation for depth 10, residue 553. -/ +theorem bounds_10_553 : exactInterval 10 553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_553 (m : Nat) : + stoppingTime (2 ^ 10 * m + 553) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_553 : oddCount 553 10 = 8 ∧ acceleratedOrbit 10 553 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_553 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 553) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_553.1, data_10_553.2] + +/-- Complete interval computation for depth 10, residue 554. -/ +theorem bounds_10_554 : exactInterval 10 554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_554 (m : Nat) : + stoppingTime (2 ^ 10 * m + 554) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_554 : oddCount 554 10 = 2 ∧ acceleratedOrbit 10 554 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_554 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 554) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_554.1, data_10_554.2] + +/-- Complete interval computation for depth 10, residue 555. -/ +theorem bounds_10_555 : exactInterval 10 555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_555 (m : Nat) : + stoppingTime (2 ^ 10 * m + 555) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_555 : oddCount 555 10 = 4 ∧ acceleratedOrbit 10 555 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_555 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 555) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_555.1, data_10_555.2] + +/-- Complete interval computation for depth 10, residue 556. -/ +theorem bounds_10_556 : exactInterval 10 556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_556 (m : Nat) : + stoppingTime (2 ^ 10 * m + 556) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_556 : oddCount 556 10 = 5 ∧ acceleratedOrbit 10 556 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_556 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 556) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_556.1, data_10_556.2] + +/-- Complete interval computation for depth 10, residue 557. -/ +theorem bounds_10_557 : exactInterval 10 557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_557 (m : Nat) : + stoppingTime (2 ^ 10 * m + 557) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_557 : oddCount 557 10 = 5 ∧ acceleratedOrbit 10 557 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_557 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 557) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_557.1, data_10_557.2] + +/-- Complete interval computation for depth 10, residue 558. -/ +theorem bounds_10_558 : exactInterval 10 558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_558 (m : Nat) : + stoppingTime (2 ^ 10 * m + 558) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_558 : oddCount 558 10 = 5 ∧ acceleratedOrbit 10 558 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_558 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 558) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_558.1, data_10_558.2] + +/-- Complete interval computation for depth 10, residue 559. -/ +theorem bounds_10_559 : exactInterval 10 559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_559 (m : Nat) : + stoppingTime (2 ^ 10 * m + 559) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_559 : oddCount 559 10 = 8 ∧ acceleratedOrbit 10 559 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_559 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 559) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_559.1, data_10_559.2] + +/-- Complete interval computation for depth 10, residue 560. -/ +theorem bounds_10_560 : exactInterval 10 560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_560 (m : Nat) : + stoppingTime (2 ^ 10 * m + 560) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_560 : oddCount 560 10 = 2 ∧ acceleratedOrbit 10 560 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_560 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 560) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_560.1, data_10_560.2] + +/-- Complete interval computation for depth 10, residue 561. -/ +theorem bounds_10_561 : exactInterval 10 561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_561 (m : Nat) : + stoppingTime (2 ^ 10 * m + 561) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_561 : oddCount 561 10 = 6 ∧ acceleratedOrbit 10 561 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_561 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 561) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_561.1, data_10_561.2] + +/-- Complete interval computation for depth 10, residue 562. -/ +theorem bounds_10_562 : exactInterval 10 562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_562 (m : Nat) : + stoppingTime (2 ^ 10 * m + 562) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_562 : oddCount 562 10 = 6 ∧ acceleratedOrbit 10 562 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_562 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 562) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_562.1, data_10_562.2] + +/-- Complete interval computation for depth 10, residue 563. -/ +theorem bounds_10_563 : exactInterval 10 563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_563 (m : Nat) : + stoppingTime (2 ^ 10 * m + 563) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_563 : oddCount 563 10 = 6 ∧ acceleratedOrbit 10 563 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_563 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 563) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_563.1, data_10_563.2] + +/-- Complete interval computation for depth 10, residue 564. -/ +theorem bounds_10_564 : exactInterval 10 564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_564 (m : Nat) : + stoppingTime (2 ^ 10 * m + 564) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_564 : oddCount 564 10 = 2 ∧ acceleratedOrbit 10 564 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_564 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 564) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_564.1, data_10_564.2] + +/-- Complete interval computation for depth 10, residue 565. -/ +theorem bounds_10_565 : exactInterval 10 565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_565 (m : Nat) : + stoppingTime (2 ^ 10 * m + 565) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_565 : oddCount 565 10 = 2 ∧ acceleratedOrbit 10 565 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_565 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 565) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_565.1, data_10_565.2] + +/-- Complete interval computation for depth 10, residue 566. -/ +theorem bounds_10_566 : exactInterval 10 566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_566 (m : Nat) : + stoppingTime (2 ^ 10 * m + 566) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_566 : oddCount 566 10 = 8 ∧ acceleratedOrbit 10 566 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_566 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 566) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_566.1, data_10_566.2] + +/-- Complete interval computation for depth 10, residue 567. -/ +theorem bounds_10_567 : exactInterval 10 567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_567 (m : Nat) : + stoppingTime (2 ^ 10 * m + 567) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_567 : oddCount 567 10 = 8 ∧ acceleratedOrbit 10 567 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_567 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 567) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_567.1, data_10_567.2] + +end Collatz.Research.StoppingAtlas.Batch0037 From e7b7d39fa0a5c1642b1da72035df3ff437da1b8e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:10 +0530 Subject: [PATCH 0038/1001] proof: certify atlas Batch0038 (10:568 to 10:582) --- Collatz/Research/StoppingAtlas/Batch0038.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0038.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0038.lean b/Collatz/Research/StoppingAtlas/Batch0038.lean new file mode 100644 index 00000000..1f89d189 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0038.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0038 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 568. -/ +theorem bounds_10_568 : exactInterval 10 568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_568 (m : Nat) : + stoppingTime (2 ^ 10 * m + 568) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_568 : oddCount 568 10 = 5 ∧ acceleratedOrbit 10 568 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_568 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 568) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_568.1, data_10_568.2] + +/-- Complete interval computation for depth 10, residue 569. -/ +theorem bounds_10_569 : exactInterval 10 569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_569 (m : Nat) : + stoppingTime (2 ^ 10 * m + 569) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_569 : oddCount 569 10 = 6 ∧ acceleratedOrbit 10 569 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_569 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 569) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_569.1, data_10_569.2] + +/-- Complete interval computation for depth 10, residue 570. -/ +theorem bounds_10_570 : exactInterval 10 570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_570 (m : Nat) : + stoppingTime (2 ^ 10 * m + 570) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_570 : oddCount 570 10 = 5 ∧ acceleratedOrbit 10 570 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_570 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 570) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_570.1, data_10_570.2] + +/-- Complete interval computation for depth 10, residue 571. -/ +theorem bounds_10_571 : exactInterval 10 571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_571 (m : Nat) : + stoppingTime (2 ^ 10 * m + 571) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_571 : oddCount 571 10 = 5 ∧ acceleratedOrbit 10 571 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_571 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 571) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_571.1, data_10_571.2] + +/-- Complete interval computation for depth 10, residue 572. -/ +theorem bounds_10_572 : exactInterval 10 572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_572 (m : Nat) : + stoppingTime (2 ^ 10 * m + 572) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_572 : oddCount 572 10 = 5 ∧ acceleratedOrbit 10 572 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_572 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 572) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_572.1, data_10_572.2] + +/-- Complete interval computation for depth 10, residue 573. -/ +theorem bounds_10_573 : exactInterval 10 573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_573 (m : Nat) : + stoppingTime (2 ^ 10 * m + 573) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_573 : oddCount 573 10 = 5 ∧ acceleratedOrbit 10 573 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_573 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 573) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_573.1, data_10_573.2] + +/-- Complete interval computation for depth 10, residue 574. -/ +theorem bounds_10_574 : exactInterval 10 574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_574 (m : Nat) : + stoppingTime (2 ^ 10 * m + 574) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_574 : oddCount 574 10 = 6 ∧ acceleratedOrbit 10 574 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_574 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 574) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_574.1, data_10_574.2] + +/-- Complete interval computation for depth 10, residue 575. -/ +theorem bounds_10_575 : exactInterval 10 575 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_575 (m : Nat) : + stoppingTime (2 ^ 10 * m + 575) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_575 : oddCount 575 10 = 6 ∧ acceleratedOrbit 10 575 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_575 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 575) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_575.1, data_10_575.2] + +/-- Complete interval computation for depth 10, residue 576. -/ +theorem bounds_10_576 : exactInterval 10 576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_576 (m : Nat) : + stoppingTime (2 ^ 10 * m + 576) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_576 : oddCount 576 10 = 3 ∧ acceleratedOrbit 10 576 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_576 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 576) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_576.1, data_10_576.2] + +/-- Complete interval computation for depth 10, residue 577. -/ +theorem bounds_10_577 : exactInterval 10 577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_577 (m : Nat) : + stoppingTime (2 ^ 10 * m + 577) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_577 : oddCount 577 10 = 4 ∧ acceleratedOrbit 10 577 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_577 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 577) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_577.1, data_10_577.2] + +/-- Complete interval computation for depth 10, residue 578. -/ +theorem bounds_10_578 : exactInterval 10 578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_578 (m : Nat) : + stoppingTime (2 ^ 10 * m + 578) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_578 : oddCount 578 10 = 4 ∧ acceleratedOrbit 10 578 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_578 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 578) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_578.1, data_10_578.2] + +/-- Complete interval computation for depth 10, residue 579. -/ +theorem bounds_10_579 : exactInterval 10 579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_579 (m : Nat) : + stoppingTime (2 ^ 10 * m + 579) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_579 : oddCount 579 10 = 4 ∧ acceleratedOrbit 10 579 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_579 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 579) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_579.1, data_10_579.2] + +/-- Complete interval computation for depth 10, residue 580. -/ +theorem bounds_10_580 : exactInterval 10 580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_580 (m : Nat) : + stoppingTime (2 ^ 10 * m + 580) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_580 : oddCount 580 10 = 4 ∧ acceleratedOrbit 10 580 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_580 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 580) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_580.1, data_10_580.2] + +/-- Complete interval computation for depth 10, residue 581. -/ +theorem bounds_10_581 : exactInterval 10 581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_581 (m : Nat) : + stoppingTime (2 ^ 10 * m + 581) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_581 : oddCount 581 10 = 4 ∧ acceleratedOrbit 10 581 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_581 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 581) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_581.1, data_10_581.2] + +/-- Complete interval computation for depth 10, residue 582. -/ +theorem bounds_10_582 : exactInterval 10 582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_582 (m : Nat) : + stoppingTime (2 ^ 10 * m + 582) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_582 : oddCount 582 10 = 4 ∧ acceleratedOrbit 10 582 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_582 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 582) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_582.1, data_10_582.2] + +end Collatz.Research.StoppingAtlas.Batch0038 From c292cca076440773c581cf866da2081b37d488c6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:10 +0530 Subject: [PATCH 0039/1001] proof: certify atlas Batch0039 (10:583 to 10:598) --- Collatz/Research/StoppingAtlas/Batch0039.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0039.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0039.lean b/Collatz/Research/StoppingAtlas/Batch0039.lean new file mode 100644 index 00000000..6c2e5568 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0039.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0039 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 583. -/ +theorem bounds_10_583 : exactInterval 10 583 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_583 (m : Nat) : + stoppingTime (2 ^ 10 * m + 583) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_583 : oddCount 583 10 = 6 ∧ acceleratedOrbit 10 583 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_583 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 583) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_583.1, data_10_583.2] + +/-- Complete interval computation for depth 10, residue 584. -/ +theorem bounds_10_584 : exactInterval 10 584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_584 (m : Nat) : + stoppingTime (2 ^ 10 * m + 584) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_584 : oddCount 584 10 = 4 ∧ acceleratedOrbit 10 584 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_584 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 584) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_584.1, data_10_584.2] + +/-- Complete interval computation for depth 10, residue 585. -/ +theorem bounds_10_585 : exactInterval 10 585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_585 (m : Nat) : + stoppingTime (2 ^ 10 * m + 585) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_585 : oddCount 585 10 = 6 ∧ acceleratedOrbit 10 585 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_585 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 585) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_585.1, data_10_585.2] + +/-- Complete interval computation for depth 10, residue 586. -/ +theorem bounds_10_586 : exactInterval 10 586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_586 (m : Nat) : + stoppingTime (2 ^ 10 * m + 586) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_586 : oddCount 586 10 = 4 ∧ acceleratedOrbit 10 586 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_586 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 586) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_586.1, data_10_586.2] + +/-- Complete interval computation for depth 10, residue 587. -/ +theorem bounds_10_587 : exactInterval 10 587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_587 (m : Nat) : + stoppingTime (2 ^ 10 * m + 587) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_587 : oddCount 587 10 = 4 ∧ acceleratedOrbit 10 587 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_587 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 587) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_587.1, data_10_587.2] + +/-- Complete interval computation for depth 10, residue 588. -/ +theorem bounds_10_588 : exactInterval 10 588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_588 (m : Nat) : + stoppingTime (2 ^ 10 * m + 588) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_588 : oddCount 588 10 = 4 ∧ acceleratedOrbit 10 588 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_588 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 588) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_588.1, data_10_588.2] + +/-- Complete interval computation for depth 10, residue 589. -/ +theorem bounds_10_589 : exactInterval 10 589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_589 (m : Nat) : + stoppingTime (2 ^ 10 * m + 589) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_589 : oddCount 589 10 = 4 ∧ acceleratedOrbit 10 589 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_589 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 589) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_589.1, data_10_589.2] + +/-- Complete interval computation for depth 10, residue 590. -/ +theorem bounds_10_590 : exactInterval 10 590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_590 (m : Nat) : + stoppingTime (2 ^ 10 * m + 590) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_590 : oddCount 590 10 = 6 ∧ acceleratedOrbit 10 590 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_590 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 590) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_590.1, data_10_590.2] + +/-- Complete interval computation for depth 10, residue 591. -/ +theorem bounds_10_591 : exactInterval 10 591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_591 (m : Nat) : + stoppingTime (2 ^ 10 * m + 591) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_591 : oddCount 591 10 = 6 ∧ acceleratedOrbit 10 591 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_591 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 591) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_591.1, data_10_591.2] + +/-- Complete interval computation for depth 10, residue 592. -/ +theorem bounds_10_592 : exactInterval 10 592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_592 (m : Nat) : + stoppingTime (2 ^ 10 * m + 592) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_592 : oddCount 592 10 = 3 ∧ acceleratedOrbit 10 592 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_592 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 592) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_592.1, data_10_592.2] + +/-- Complete interval computation for depth 10, residue 593. -/ +theorem bounds_10_593 : exactInterval 10 593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_593 (m : Nat) : + stoppingTime (2 ^ 10 * m + 593) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_593 : oddCount 593 10 = 6 ∧ acceleratedOrbit 10 593 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_593 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 593) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_593.1, data_10_593.2] + +/-- Complete interval computation for depth 10, residue 594. -/ +theorem bounds_10_594 : exactInterval 10 594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_594 (m : Nat) : + stoppingTime (2 ^ 10 * m + 594) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_594 : oddCount 594 10 = 6 ∧ acceleratedOrbit 10 594 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_594 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 594) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_594.1, data_10_594.2] + +/-- Complete interval computation for depth 10, residue 595. -/ +theorem bounds_10_595 : exactInterval 10 595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_595 (m : Nat) : + stoppingTime (2 ^ 10 * m + 595) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_595 : oddCount 595 10 = 6 ∧ acceleratedOrbit 10 595 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_595 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 595) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_595.1, data_10_595.2] + +/-- Complete interval computation for depth 10, residue 596. -/ +theorem bounds_10_596 : exactInterval 10 596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_596 (m : Nat) : + stoppingTime (2 ^ 10 * m + 596) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_596 : oddCount 596 10 = 3 ∧ acceleratedOrbit 10 596 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_596 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 596) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_596.1, data_10_596.2] + +/-- Complete interval computation for depth 10, residue 597. -/ +theorem bounds_10_597 : exactInterval 10 597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_597 (m : Nat) : + stoppingTime (2 ^ 10 * m + 597) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_597 : oddCount 597 10 = 3 ∧ acceleratedOrbit 10 597 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_597 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 597) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_597.1, data_10_597.2] + +/-- Complete interval computation for depth 10, residue 598. -/ +theorem bounds_10_598 : exactInterval 10 598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_598 (m : Nat) : + stoppingTime (2 ^ 10 * m + 598) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_598 : oddCount 598 10 = 5 ∧ acceleratedOrbit 10 598 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_598 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 598) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_598.1, data_10_598.2] + +end Collatz.Research.StoppingAtlas.Batch0039 From b0485e6c40f5b6d506b1f3f9f8f295604ee2ca49 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:11 +0530 Subject: [PATCH 0040/1001] proof: certify atlas Batch0040 (10:599 to 10:613) --- Collatz/Research/StoppingAtlas/Batch0040.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0040.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0040.lean b/Collatz/Research/StoppingAtlas/Batch0040.lean new file mode 100644 index 00000000..fd23d696 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0040.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0040 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 599. -/ +theorem bounds_10_599 : exactInterval 10 599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_599 (m : Nat) : + stoppingTime (2 ^ 10 * m + 599) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_599 : oddCount 599 10 = 5 ∧ acceleratedOrbit 10 599 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_599 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 599) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_599.1, data_10_599.2] + +/-- Complete interval computation for depth 10, residue 600. -/ +theorem bounds_10_600 : exactInterval 10 600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_600 (m : Nat) : + stoppingTime (2 ^ 10 * m + 600) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_600 : oddCount 600 10 = 3 ∧ acceleratedOrbit 10 600 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_600 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 600) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_600.1, data_10_600.2] + +/-- Complete interval computation for depth 10, residue 601. -/ +theorem bounds_10_601 : exactInterval 10 601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_601 (m : Nat) : + stoppingTime (2 ^ 10 * m + 601) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_601 : oddCount 601 10 = 6 ∧ acceleratedOrbit 10 601 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_601 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 601) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_601.1, data_10_601.2] + +/-- Complete interval computation for depth 10, residue 602. -/ +theorem bounds_10_602 : exactInterval 10 602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_602 (m : Nat) : + stoppingTime (2 ^ 10 * m + 602) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_602 : oddCount 602 10 = 3 ∧ acceleratedOrbit 10 602 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_602 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 602) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_602.1, data_10_602.2] + +/-- Complete interval computation for depth 10, residue 603. -/ +theorem bounds_10_603 : exactInterval 10 603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_603 (m : Nat) : + stoppingTime (2 ^ 10 * m + 603) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_603 : oddCount 603 10 = 7 ∧ acceleratedOrbit 10 603 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_603 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 603) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_603.1, data_10_603.2] + +/-- Complete interval computation for depth 10, residue 604. -/ +theorem bounds_10_604 : exactInterval 10 604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_604 (m : Nat) : + stoppingTime (2 ^ 10 * m + 604) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_604 : oddCount 604 10 = 3 ∧ acceleratedOrbit 10 604 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_604 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 604) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_604.1, data_10_604.2] + +/-- Complete interval computation for depth 10, residue 605. -/ +theorem bounds_10_605 : exactInterval 10 605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_605 (m : Nat) : + stoppingTime (2 ^ 10 * m + 605) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_605 : oddCount 605 10 = 3 ∧ acceleratedOrbit 10 605 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_605 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 605) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_605.1, data_10_605.2] + +/-- Complete interval computation for depth 10, residue 606. -/ +theorem bounds_10_606 : exactInterval 10 606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_606 (m : Nat) : + stoppingTime (2 ^ 10 * m + 606) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_606 : oddCount 606 10 = 6 ∧ acceleratedOrbit 10 606 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_606 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 606) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_606.1, data_10_606.2] + +/-- Complete interval computation for depth 10, residue 607. -/ +theorem bounds_10_607 : exactInterval 10 607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_607 (m : Nat) : + stoppingTime (2 ^ 10 * m + 607) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_607 : oddCount 607 10 = 6 ∧ acceleratedOrbit 10 607 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_607 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 607) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_607.1, data_10_607.2] + +/-- Complete interval computation for depth 10, residue 608. -/ +theorem bounds_10_608 : exactInterval 10 608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_608 (m : Nat) : + stoppingTime (2 ^ 10 * m + 608) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_608 : oddCount 608 10 = 3 ∧ acceleratedOrbit 10 608 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_608 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 608) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_608.1, data_10_608.2] + +/-- Complete interval computation for depth 10, residue 609. -/ +theorem bounds_10_609 : exactInterval 10 609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_609 (m : Nat) : + stoppingTime (2 ^ 10 * m + 609) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_609 : oddCount 609 10 = 5 ∧ acceleratedOrbit 10 609 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_609 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 609) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_609.1, data_10_609.2] + +/-- Complete interval computation for depth 10, residue 610. -/ +theorem bounds_10_610 : exactInterval 10 610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_610 (m : Nat) : + stoppingTime (2 ^ 10 * m + 610) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_610 : oddCount 610 10 = 4 ∧ acceleratedOrbit 10 610 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_610 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 610) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_610.1, data_10_610.2] + +/-- Complete interval computation for depth 10, residue 611. -/ +theorem bounds_10_611 : exactInterval 10 611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_611 (m : Nat) : + stoppingTime (2 ^ 10 * m + 611) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_611 : oddCount 611 10 = 4 ∧ acceleratedOrbit 10 611 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_611 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 611) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_611.1, data_10_611.2] + +/-- Complete interval computation for depth 10, residue 612. -/ +theorem bounds_10_612 : exactInterval 10 612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_612 (m : Nat) : + stoppingTime (2 ^ 10 * m + 612) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_612 : oddCount 612 10 = 4 ∧ acceleratedOrbit 10 612 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_612 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 612) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_612.1, data_10_612.2] + +/-- Complete interval computation for depth 10, residue 613. -/ +theorem bounds_10_613 : exactInterval 10 613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_613 (m : Nat) : + stoppingTime (2 ^ 10 * m + 613) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_613 : oddCount 613 10 = 4 ∧ acceleratedOrbit 10 613 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_613 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 613) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_613.1, data_10_613.2] + +end Collatz.Research.StoppingAtlas.Batch0040 From 02b3a898ad1f59f596cb9dd7dbecd26397fe3c0e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:11 +0530 Subject: [PATCH 0041/1001] proof: certify atlas Batch0041 (10:614 to 10:628) --- Collatz/Research/StoppingAtlas/Batch0041.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0041.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0041.lean b/Collatz/Research/StoppingAtlas/Batch0041.lean new file mode 100644 index 00000000..038218f9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0041.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0041 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 614. -/ +theorem bounds_10_614 : exactInterval 10 614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_614 (m : Nat) : + stoppingTime (2 ^ 10 * m + 614) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_614 : oddCount 614 10 = 4 ∧ acceleratedOrbit 10 614 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_614 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 614) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_614.1, data_10_614.2] + +/-- Complete interval computation for depth 10, residue 615. -/ +theorem bounds_10_615 : exactInterval 10 615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_615 (m : Nat) : + stoppingTime (2 ^ 10 * m + 615) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_615 : oddCount 615 10 = 7 ∧ acceleratedOrbit 10 615 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_615 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 615) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_615.1, data_10_615.2] + +/-- Complete interval computation for depth 10, residue 616. -/ +theorem bounds_10_616 : exactInterval 10 616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_616 (m : Nat) : + stoppingTime (2 ^ 10 * m + 616) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_616 : oddCount 616 10 = 3 ∧ acceleratedOrbit 10 616 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_616 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 616) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_616.1, data_10_616.2] + +/-- Complete interval computation for depth 10, residue 617. -/ +theorem bounds_10_617 : exactInterval 10 617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_617 (m : Nat) : + stoppingTime (2 ^ 10 * m + 617) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_617 : oddCount 617 10 = 7 ∧ acceleratedOrbit 10 617 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_617 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 617) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_617.1, data_10_617.2] + +/-- Complete interval computation for depth 10, residue 618. -/ +theorem bounds_10_618 : exactInterval 10 618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_618 (m : Nat) : + stoppingTime (2 ^ 10 * m + 618) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_618 : oddCount 618 10 = 3 ∧ acceleratedOrbit 10 618 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_618 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 618) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_618.1, data_10_618.2] + +/-- Complete interval computation for depth 10, residue 619. -/ +theorem bounds_10_619 : exactInterval 10 619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_619 (m : Nat) : + stoppingTime (2 ^ 10 * m + 619) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_619 : oddCount 619 10 = 6 ∧ acceleratedOrbit 10 619 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_619 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 619) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_619.1, data_10_619.2] + +/-- Complete interval computation for depth 10, residue 620. -/ +theorem bounds_10_620 : exactInterval 10 620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_620 (m : Nat) : + stoppingTime (2 ^ 10 * m + 620) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_620 : oddCount 620 10 = 6 ∧ acceleratedOrbit 10 620 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_620 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 620) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_620.1, data_10_620.2] + +/-- Complete interval computation for depth 10, residue 621. -/ +theorem bounds_10_621 : exactInterval 10 621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_621 (m : Nat) : + stoppingTime (2 ^ 10 * m + 621) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_621 : oddCount 621 10 = 6 ∧ acceleratedOrbit 10 621 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_621 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 621) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_621.1, data_10_621.2] + +/-- Complete interval computation for depth 10, residue 622. -/ +theorem bounds_10_622 : exactInterval 10 622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_622 (m : Nat) : + stoppingTime (2 ^ 10 * m + 622) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_622 : oddCount 622 10 = 6 ∧ acceleratedOrbit 10 622 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_622 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 622) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_622.1, data_10_622.2] + +/-- Complete interval computation for depth 10, residue 623. -/ +theorem bounds_10_623 : exactInterval 10 623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_623 (m : Nat) : + stoppingTime (2 ^ 10 * m + 623) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_623 : oddCount 623 10 = 7 ∧ acceleratedOrbit 10 623 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_623 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 623) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_623.1, data_10_623.2] + +/-- Complete interval computation for depth 10, residue 624. -/ +theorem bounds_10_624 : exactInterval 10 624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_624 (m : Nat) : + stoppingTime (2 ^ 10 * m + 624) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_624 : oddCount 624 10 = 5 ∧ acceleratedOrbit 10 624 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_624 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 624) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_624.1, data_10_624.2] + +/-- Complete interval computation for depth 10, residue 625. -/ +theorem bounds_10_625 : exactInterval 10 625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_625 (m : Nat) : + stoppingTime (2 ^ 10 * m + 625) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_625 : oddCount 625 10 = 3 ∧ acceleratedOrbit 10 625 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_625 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 625) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_625.1, data_10_625.2] + +/-- Complete interval computation for depth 10, residue 626. -/ +theorem bounds_10_626 : exactInterval 10 626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_626 (m : Nat) : + stoppingTime (2 ^ 10 * m + 626) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_626 : oddCount 626 10 = 6 ∧ acceleratedOrbit 10 626 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_626 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 626) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_626.1, data_10_626.2] + +/-- Complete interval computation for depth 10, residue 627. -/ +theorem bounds_10_627 : exactInterval 10 627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_627 (m : Nat) : + stoppingTime (2 ^ 10 * m + 627) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_627 : oddCount 627 10 = 6 ∧ acceleratedOrbit 10 627 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_627 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 627) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_627.1, data_10_627.2] + +/-- Complete interval computation for depth 10, residue 628. -/ +theorem bounds_10_628 : exactInterval 10 628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_628 (m : Nat) : + stoppingTime (2 ^ 10 * m + 628) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_628 : oddCount 628 10 = 5 ∧ acceleratedOrbit 10 628 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_628 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 628) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_628.1, data_10_628.2] + +end Collatz.Research.StoppingAtlas.Batch0041 From 6bea03c8fb349a203c689343b6c2d6f4619bcb57 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:11 +0530 Subject: [PATCH 0042/1001] proof: certify atlas Batch0042 (10:629 to 10:644) --- Collatz/Research/StoppingAtlas/Batch0042.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0042.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0042.lean b/Collatz/Research/StoppingAtlas/Batch0042.lean new file mode 100644 index 00000000..a8ac0945 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0042.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0042 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 629. -/ +theorem bounds_10_629 : exactInterval 10 629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_629 (m : Nat) : + stoppingTime (2 ^ 10 * m + 629) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_629 : oddCount 629 10 = 5 ∧ acceleratedOrbit 10 629 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_629 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 629) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_629.1, data_10_629.2] + +/-- Complete interval computation for depth 10, residue 630. -/ +theorem bounds_10_630 : exactInterval 10 630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_630 (m : Nat) : + stoppingTime (2 ^ 10 * m + 630) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_630 : oddCount 630 10 = 4 ∧ acceleratedOrbit 10 630 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_630 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 630) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_630.1, data_10_630.2] + +/-- Complete interval computation for depth 10, residue 631. -/ +theorem bounds_10_631 : exactInterval 10 631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_631 (m : Nat) : + stoppingTime (2 ^ 10 * m + 631) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_631 : oddCount 631 10 = 4 ∧ acceleratedOrbit 10 631 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_631 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 631) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_631.1, data_10_631.2] + +/-- Complete interval computation for depth 10, residue 632. -/ +theorem bounds_10_632 : exactInterval 10 632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_632 (m : Nat) : + stoppingTime (2 ^ 10 * m + 632) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_632 : oddCount 632 10 = 5 ∧ acceleratedOrbit 10 632 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_632 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 632) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_632.1, data_10_632.2] + +/-- Complete interval computation for depth 10, residue 633. -/ +theorem bounds_10_633 : exactInterval 10 633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_633 (m : Nat) : + stoppingTime (2 ^ 10 * m + 633) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_633 : oddCount 633 10 = 6 ∧ acceleratedOrbit 10 633 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_633 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 633) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_633.1, data_10_633.2] + +/-- Complete interval computation for depth 10, residue 634. -/ +theorem bounds_10_634 : exactInterval 10 634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_634 (m : Nat) : + stoppingTime (2 ^ 10 * m + 634) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_634 : oddCount 634 10 = 5 ∧ acceleratedOrbit 10 634 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_634 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 634) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_634.1, data_10_634.2] + +/-- Complete interval computation for depth 10, residue 635. -/ +theorem bounds_10_635 : exactInterval 10 635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_635 (m : Nat) : + stoppingTime (2 ^ 10 * m + 635) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_635 : oddCount 635 10 = 5 ∧ acceleratedOrbit 10 635 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_635 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 635) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_635.1, data_10_635.2] + +/-- Complete interval computation for depth 10, residue 636. -/ +theorem bounds_10_636 : exactInterval 10 636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_636 (m : Nat) : + stoppingTime (2 ^ 10 * m + 636) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_636 : oddCount 636 10 = 7 ∧ acceleratedOrbit 10 636 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_636 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 636) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_636.1, data_10_636.2] + +/-- Complete interval computation for depth 10, residue 637. -/ +theorem bounds_10_637 : exactInterval 10 637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_637 (m : Nat) : + stoppingTime (2 ^ 10 * m + 637) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_637 : oddCount 637 10 = 7 ∧ acceleratedOrbit 10 637 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_637 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 637) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_637.1, data_10_637.2] + +/-- Complete interval computation for depth 10, residue 638. -/ +theorem bounds_10_638 : exactInterval 10 638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_638 (m : Nat) : + stoppingTime (2 ^ 10 * m + 638) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_638 : oddCount 638 10 = 7 ∧ acceleratedOrbit 10 638 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_638 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 638) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_638.1, data_10_638.2] + +/-- Complete interval computation for depth 10, residue 639. -/ +theorem bounds_10_639 : exactInterval 10 639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_639 (m : Nat) : + stoppingTime (2 ^ 10 * m + 639) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_639 : oddCount 639 10 = 9 ∧ acceleratedOrbit 10 639 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_639 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 639) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_639.1, data_10_639.2] + +/-- Complete interval computation for depth 10, residue 640. -/ +theorem bounds_10_640 : exactInterval 10 640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_640 (m : Nat) : + stoppingTime (2 ^ 10 * m + 640) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_640 : oddCount 640 10 = 1 ∧ acceleratedOrbit 10 640 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_640 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 640) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_640.1, data_10_640.2] + +/-- Complete interval computation for depth 10, residue 641. -/ +theorem bounds_10_641 : exactInterval 10 641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_641 (m : Nat) : + stoppingTime (2 ^ 10 * m + 641) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_641 : oddCount 641 10 = 7 ∧ acceleratedOrbit 10 641 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_641 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 641) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_641.1, data_10_641.2] + +/-- Complete interval computation for depth 10, residue 642. -/ +theorem bounds_10_642 : exactInterval 10 642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_642 (m : Nat) : + stoppingTime (2 ^ 10 * m + 642) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_642 : oddCount 642 10 = 3 ∧ acceleratedOrbit 10 642 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_642 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 642) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_642.1, data_10_642.2] + +/-- Complete interval computation for depth 10, residue 643. -/ +theorem bounds_10_643 : exactInterval 10 643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_643 (m : Nat) : + stoppingTime (2 ^ 10 * m + 643) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_643 : oddCount 643 10 = 3 ∧ acceleratedOrbit 10 643 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_643 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 643) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_643.1, data_10_643.2] + +/-- Complete interval computation for depth 10, residue 644. -/ +theorem bounds_10_644 : exactInterval 10 644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_644 (m : Nat) : + stoppingTime (2 ^ 10 * m + 644) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_644 : oddCount 644 10 = 5 ∧ acceleratedOrbit 10 644 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_644 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 644) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_644.1, data_10_644.2] + +end Collatz.Research.StoppingAtlas.Batch0042 From 0331a726f0a6244415817d21f9d5901f9bdde7af Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:11 +0530 Subject: [PATCH 0043/1001] proof: certify atlas Batch0043 (10:645 to 10:659) --- Collatz/Research/StoppingAtlas/Batch0043.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0043.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0043.lean b/Collatz/Research/StoppingAtlas/Batch0043.lean new file mode 100644 index 00000000..b5ba2304 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0043.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0043 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 645. -/ +theorem bounds_10_645 : exactInterval 10 645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_645 (m : Nat) : + stoppingTime (2 ^ 10 * m + 645) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_645 : oddCount 645 10 = 5 ∧ acceleratedOrbit 10 645 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_645 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 645) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_645.1, data_10_645.2] + +/-- Complete interval computation for depth 10, residue 646. -/ +theorem bounds_10_646 : exactInterval 10 646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_646 (m : Nat) : + stoppingTime (2 ^ 10 * m + 646) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_646 : oddCount 646 10 = 5 ∧ acceleratedOrbit 10 646 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_646 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 646) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_646.1, data_10_646.2] + +/-- Complete interval computation for depth 10, residue 647. -/ +theorem bounds_10_647 : exactInterval 10 647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_647 (m : Nat) : + stoppingTime (2 ^ 10 * m + 647) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_647 : oddCount 647 10 = 5 ∧ acceleratedOrbit 10 647 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_647 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 647) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_647.1, data_10_647.2] + +/-- Complete interval computation for depth 10, residue 648. -/ +theorem bounds_10_648 : exactInterval 10 648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_648 (m : Nat) : + stoppingTime (2 ^ 10 * m + 648) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_648 : oddCount 648 10 = 4 ∧ acceleratedOrbit 10 648 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_648 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 648) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_648.1, data_10_648.2] + +/-- Complete interval computation for depth 10, residue 649. -/ +theorem bounds_10_649 : exactInterval 10 649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_649 (m : Nat) : + stoppingTime (2 ^ 10 * m + 649) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_649 : oddCount 649 10 = 7 ∧ acceleratedOrbit 10 649 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_649 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 649) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_649.1, data_10_649.2] + +/-- Complete interval computation for depth 10, residue 650. -/ +theorem bounds_10_650 : exactInterval 10 650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_650 (m : Nat) : + stoppingTime (2 ^ 10 * m + 650) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_650 : oddCount 650 10 = 4 ∧ acceleratedOrbit 10 650 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_650 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 650) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_650.1, data_10_650.2] + +/-- Complete interval computation for depth 10, residue 651. -/ +theorem bounds_10_651 : exactInterval 10 651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_651 (m : Nat) : + stoppingTime (2 ^ 10 * m + 651) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_651 : oddCount 651 10 = 5 ∧ acceleratedOrbit 10 651 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_651 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 651) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_651.1, data_10_651.2] + +/-- Complete interval computation for depth 10, residue 652. -/ +theorem bounds_10_652 : exactInterval 10 652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_652 (m : Nat) : + stoppingTime (2 ^ 10 * m + 652) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_652 : oddCount 652 10 = 4 ∧ acceleratedOrbit 10 652 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_652 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 652) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_652.1, data_10_652.2] + +/-- Complete interval computation for depth 10, residue 653. -/ +theorem bounds_10_653 : exactInterval 10 653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_653 (m : Nat) : + stoppingTime (2 ^ 10 * m + 653) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_653 : oddCount 653 10 = 4 ∧ acceleratedOrbit 10 653 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_653 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 653) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_653.1, data_10_653.2] + +/-- Complete interval computation for depth 10, residue 654. -/ +theorem bounds_10_654 : exactInterval 10 654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_654 (m : Nat) : + stoppingTime (2 ^ 10 * m + 654) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_654 : oddCount 654 10 = 7 ∧ acceleratedOrbit 10 654 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_654 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 654) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_654.1, data_10_654.2] + +/-- Complete interval computation for depth 10, residue 655. -/ +theorem bounds_10_655 : exactInterval 10 655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_655 (m : Nat) : + stoppingTime (2 ^ 10 * m + 655) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_655 : oddCount 655 10 = 7 ∧ acceleratedOrbit 10 655 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_655 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 655) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_655.1, data_10_655.2] + +/-- Complete interval computation for depth 10, residue 656. -/ +theorem bounds_10_656 : exactInterval 10 656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_656 (m : Nat) : + stoppingTime (2 ^ 10 * m + 656) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_656 : oddCount 656 10 = 5 ∧ acceleratedOrbit 10 656 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_656 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 656) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_656.1, data_10_656.2] + +/-- Complete interval computation for depth 10, residue 657. -/ +theorem bounds_10_657 : exactInterval 10 657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_657 (m : Nat) : + stoppingTime (2 ^ 10 * m + 657) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_657 : oddCount 657 10 = 5 ∧ acceleratedOrbit 10 657 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_657 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 657) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_657.1, data_10_657.2] + +/-- Complete interval computation for depth 10, residue 658. -/ +theorem bounds_10_658 : exactInterval 10 658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_658 (m : Nat) : + stoppingTime (2 ^ 10 * m + 658) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_658 : oddCount 658 10 = 5 ∧ acceleratedOrbit 10 658 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_658 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 658) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_658.1, data_10_658.2] + +/-- Complete interval computation for depth 10, residue 659. -/ +theorem bounds_10_659 : exactInterval 10 659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_659 (m : Nat) : + stoppingTime (2 ^ 10 * m + 659) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_659 : oddCount 659 10 = 5 ∧ acceleratedOrbit 10 659 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_659 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 659) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_659.1, data_10_659.2] + +end Collatz.Research.StoppingAtlas.Batch0043 From ed82b9896c92e0eeb1dc956025cd721d7c4e78dc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:12 +0530 Subject: [PATCH 0044/1001] proof: certify atlas Batch0044 (10:660 to 10:674) --- Collatz/Research/StoppingAtlas/Batch0044.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0044.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0044.lean b/Collatz/Research/StoppingAtlas/Batch0044.lean new file mode 100644 index 00000000..f3181b3a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0044.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0044 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 660. -/ +theorem bounds_10_660 : exactInterval 10 660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_660 (m : Nat) : + stoppingTime (2 ^ 10 * m + 660) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_660 : oddCount 660 10 = 5 ∧ acceleratedOrbit 10 660 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_660 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 660) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_660.1, data_10_660.2] + +/-- Complete interval computation for depth 10, residue 661. -/ +theorem bounds_10_661 : exactInterval 10 661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_661 (m : Nat) : + stoppingTime (2 ^ 10 * m + 661) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_661 : oddCount 661 10 = 5 ∧ acceleratedOrbit 10 661 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_661 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 661) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_661.1, data_10_661.2] + +/-- Complete interval computation for depth 10, residue 662. -/ +theorem bounds_10_662 : exactInterval 10 662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_662 (m : Nat) : + stoppingTime (2 ^ 10 * m + 662) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_662 : oddCount 662 10 = 4 ∧ acceleratedOrbit 10 662 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_662 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 662) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_662.1, data_10_662.2] + +/-- Complete interval computation for depth 10, residue 663. -/ +theorem bounds_10_663 : exactInterval 10 663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_663 (m : Nat) : + stoppingTime (2 ^ 10 * m + 663) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_663 : oddCount 663 10 = 4 ∧ acceleratedOrbit 10 663 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_663 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 663) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_663.1, data_10_663.2] + +/-- Complete interval computation for depth 10, residue 664. -/ +theorem bounds_10_664 : exactInterval 10 664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_664 (m : Nat) : + stoppingTime (2 ^ 10 * m + 664) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_664 : oddCount 664 10 = 5 ∧ acceleratedOrbit 10 664 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_664 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 664) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_664.1, data_10_664.2] + +/-- Complete interval computation for depth 10, residue 665. -/ +theorem bounds_10_665 : exactInterval 10 665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_665 (m : Nat) : + stoppingTime (2 ^ 10 * m + 665) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_665 : oddCount 665 10 = 6 ∧ acceleratedOrbit 10 665 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_665 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 665) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_665.1, data_10_665.2] + +/-- Complete interval computation for depth 10, residue 666. -/ +theorem bounds_10_666 : exactInterval 10 666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_666 (m : Nat) : + stoppingTime (2 ^ 10 * m + 666) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_666 : oddCount 666 10 = 5 ∧ acceleratedOrbit 10 666 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_666 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 666) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_666.1, data_10_666.2] + +/-- Complete interval computation for depth 10, residue 667. -/ +theorem bounds_10_667 : exactInterval 10 667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_667 (m : Nat) : + stoppingTime (2 ^ 10 * m + 667) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_667 : oddCount 667 10 = 8 ∧ acceleratedOrbit 10 667 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_667 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 667) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_667.1, data_10_667.2] + +/-- Complete interval computation for depth 10, residue 668. -/ +theorem bounds_10_668 : exactInterval 10 668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_668 (m : Nat) : + stoppingTime (2 ^ 10 * m + 668) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_668 : oddCount 668 10 = 6 ∧ acceleratedOrbit 10 668 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_668 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 668) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_668.1, data_10_668.2] + +/-- Complete interval computation for depth 10, residue 669. -/ +theorem bounds_10_669 : exactInterval 10 669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_669 (m : Nat) : + stoppingTime (2 ^ 10 * m + 669) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_669 : oddCount 669 10 = 6 ∧ acceleratedOrbit 10 669 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_669 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 669) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_669.1, data_10_669.2] + +/-- Complete interval computation for depth 10, residue 670. -/ +theorem bounds_10_670 : exactInterval 10 670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_670 (m : Nat) : + stoppingTime (2 ^ 10 * m + 670) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_670 : oddCount 670 10 = 6 ∧ acceleratedOrbit 10 670 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_670 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 670) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_670.1, data_10_670.2] + +/-- Complete interval computation for depth 10, residue 671. -/ +theorem bounds_10_671 : exactInterval 10 671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_671 (m : Nat) : + stoppingTime (2 ^ 10 * m + 671) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_671 : oddCount 671 10 = 8 ∧ acceleratedOrbit 10 671 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_671 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 671) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_671.1, data_10_671.2] + +/-- Complete interval computation for depth 10, residue 672. -/ +theorem bounds_10_672 : exactInterval 10 672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_672 (m : Nat) : + stoppingTime (2 ^ 10 * m + 672) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_672 : oddCount 672 10 = 1 ∧ acceleratedOrbit 10 672 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_672 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 672) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_672.1, data_10_672.2] + +/-- Complete interval computation for depth 10, residue 673. -/ +theorem bounds_10_673 : exactInterval 10 673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_673 (m : Nat) : + stoppingTime (2 ^ 10 * m + 673) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_673 : oddCount 673 10 = 6 ∧ acceleratedOrbit 10 673 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_673 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 673) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_673.1, data_10_673.2] + +/-- Complete interval computation for depth 10, residue 674. -/ +theorem bounds_10_674 : exactInterval 10 674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_674 (m : Nat) : + stoppingTime (2 ^ 10 * m + 674) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_674 : oddCount 674 10 = 6 ∧ acceleratedOrbit 10 674 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_674 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 674) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_674.1, data_10_674.2] + +end Collatz.Research.StoppingAtlas.Batch0044 From 59392643c015836598de6635c733458f7d710d31 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:12 +0530 Subject: [PATCH 0045/1001] proof: certify atlas Batch0045 (10:675 to 10:690) --- Collatz/Research/StoppingAtlas/Batch0045.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0045.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0045.lean b/Collatz/Research/StoppingAtlas/Batch0045.lean new file mode 100644 index 00000000..a94a14c2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0045.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0045 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 675. -/ +theorem bounds_10_675 : exactInterval 10 675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_675 (m : Nat) : + stoppingTime (2 ^ 10 * m + 675) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_675 : oddCount 675 10 = 6 ∧ acceleratedOrbit 10 675 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_675 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 675) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_675.1, data_10_675.2] + +/-- Complete interval computation for depth 10, residue 676. -/ +theorem bounds_10_676 : exactInterval 10 676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_676 (m : Nat) : + stoppingTime (2 ^ 10 * m + 676) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_676 : oddCount 676 10 = 7 ∧ acceleratedOrbit 10 676 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_676 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 676) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_676.1, data_10_676.2] + +/-- Complete interval computation for depth 10, residue 677. -/ +theorem bounds_10_677 : exactInterval 10 677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_677 (m : Nat) : + stoppingTime (2 ^ 10 * m + 677) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_677 : oddCount 677 10 = 7 ∧ acceleratedOrbit 10 677 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_677 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 677) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_677.1, data_10_677.2] + +/-- Complete interval computation for depth 10, residue 678. -/ +theorem bounds_10_678 : exactInterval 10 678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_678 (m : Nat) : + stoppingTime (2 ^ 10 * m + 678) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_678 : oddCount 678 10 = 7 ∧ acceleratedOrbit 10 678 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_678 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 678) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_678.1, data_10_678.2] + +/-- Complete interval computation for depth 10, residue 679. -/ +theorem bounds_10_679 : exactInterval 10 679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_679 (m : Nat) : + stoppingTime (2 ^ 10 * m + 679) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_679 : oddCount 679 10 = 7 ∧ acceleratedOrbit 10 679 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_679 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 679) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_679.1, data_10_679.2] + +/-- Complete interval computation for depth 10, residue 680. -/ +theorem bounds_10_680 : exactInterval 10 680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_680 (m : Nat) : + stoppingTime (2 ^ 10 * m + 680) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_680 : oddCount 680 10 = 1 ∧ acceleratedOrbit 10 680 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_680 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 680) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_680.1, data_10_680.2] + +/-- Complete interval computation for depth 10, residue 681. -/ +theorem bounds_10_681 : exactInterval 10 681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_681 (m : Nat) : + stoppingTime (2 ^ 10 * m + 681) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_681 : oddCount 681 10 = 9 ∧ acceleratedOrbit 10 681 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_681 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 681) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_681.1, data_10_681.2] + +/-- Complete interval computation for depth 10, residue 682. -/ +theorem bounds_10_682 : exactInterval 10 682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_682 (m : Nat) : + stoppingTime (2 ^ 10 * m + 682) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_682 : oddCount 682 10 = 1 ∧ acceleratedOrbit 10 682 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_682 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 682) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_682.1, data_10_682.2] + +/-- Complete interval computation for depth 10, residue 683. -/ +theorem bounds_10_683 : exactInterval 10 683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_683 (m : Nat) : + stoppingTime (2 ^ 10 * m + 683) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_683 : oddCount 683 10 = 6 ∧ acceleratedOrbit 10 683 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_683 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 683) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_683.1, data_10_683.2] + +/-- Complete interval computation for depth 10, residue 684. -/ +theorem bounds_10_684 : exactInterval 10 684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_684 (m : Nat) : + stoppingTime (2 ^ 10 * m + 684) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_684 : oddCount 684 10 = 5 ∧ acceleratedOrbit 10 684 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_684 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 684) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_684.1, data_10_684.2] + +/-- Complete interval computation for depth 10, residue 685. -/ +theorem bounds_10_685 : exactInterval 10 685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_685 (m : Nat) : + stoppingTime (2 ^ 10 * m + 685) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_685 : oddCount 685 10 = 5 ∧ acceleratedOrbit 10 685 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_685 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 685) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_685.1, data_10_685.2] + +/-- Complete interval computation for depth 10, residue 686. -/ +theorem bounds_10_686 : exactInterval 10 686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_686 (m : Nat) : + stoppingTime (2 ^ 10 * m + 686) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_686 : oddCount 686 10 = 5 ∧ acceleratedOrbit 10 686 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_686 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 686) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_686.1, data_10_686.2] + +/-- Complete interval computation for depth 10, residue 687. -/ +theorem bounds_10_687 : exactInterval 10 687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_687 (m : Nat) : + stoppingTime (2 ^ 10 * m + 687) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_687 : oddCount 687 10 = 6 ∧ acceleratedOrbit 10 687 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_687 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 687) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_687.1, data_10_687.2] + +/-- Complete interval computation for depth 10, residue 688. -/ +theorem bounds_10_688 : exactInterval 10 688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_688 (m : Nat) : + stoppingTime (2 ^ 10 * m + 688) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_688 : oddCount 688 10 = 4 ∧ acceleratedOrbit 10 688 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_688 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 688) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_688.1, data_10_688.2] + +/-- Complete interval computation for depth 10, residue 689. -/ +theorem bounds_10_689 : exactInterval 10 689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_689 (m : Nat) : + stoppingTime (2 ^ 10 * m + 689) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_689 : oddCount 689 10 = 4 ∧ acceleratedOrbit 10 689 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_689 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 689) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_689.1, data_10_689.2] + +/-- Complete interval computation for depth 10, residue 690. -/ +theorem bounds_10_690 : exactInterval 10 690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_690 (m : Nat) : + stoppingTime (2 ^ 10 * m + 690) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_690 : oddCount 690 10 = 4 ∧ acceleratedOrbit 10 690 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_690 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 690) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_690.1, data_10_690.2] + +end Collatz.Research.StoppingAtlas.Batch0045 From 34a9bb0f29187efbe74813043067a2e71f4a9d69 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:12 +0530 Subject: [PATCH 0046/1001] proof: certify atlas Batch0046 (10:691 to 10:705) --- Collatz/Research/StoppingAtlas/Batch0046.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0046.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0046.lean b/Collatz/Research/StoppingAtlas/Batch0046.lean new file mode 100644 index 00000000..a5c8112d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0046.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0046 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 691. -/ +theorem bounds_10_691 : exactInterval 10 691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_691 (m : Nat) : + stoppingTime (2 ^ 10 * m + 691) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_691 : oddCount 691 10 = 4 ∧ acceleratedOrbit 10 691 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_691 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 691) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_691.1, data_10_691.2] + +/-- Complete interval computation for depth 10, residue 692. -/ +theorem bounds_10_692 : exactInterval 10 692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_692 (m : Nat) : + stoppingTime (2 ^ 10 * m + 692) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_692 : oddCount 692 10 = 4 ∧ acceleratedOrbit 10 692 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_692 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 692) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_692.1, data_10_692.2] + +/-- Complete interval computation for depth 10, residue 693. -/ +theorem bounds_10_693 : exactInterval 10 693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_693 (m : Nat) : + stoppingTime (2 ^ 10 * m + 693) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_693 : oddCount 693 10 = 4 ∧ acceleratedOrbit 10 693 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_693 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 693) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_693.1, data_10_693.2] + +/-- Complete interval computation for depth 10, residue 694. -/ +theorem bounds_10_694 : exactInterval 10 694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_694 (m : Nat) : + stoppingTime (2 ^ 10 * m + 694) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_694 : oddCount 694 10 = 6 ∧ acceleratedOrbit 10 694 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_694 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 694) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_694.1, data_10_694.2] + +/-- Complete interval computation for depth 10, residue 695. -/ +theorem bounds_10_695 : exactInterval 10 695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_695 (m : Nat) : + stoppingTime (2 ^ 10 * m + 695) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_695 : oddCount 695 10 = 6 ∧ acceleratedOrbit 10 695 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_695 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 695) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_695.1, data_10_695.2] + +/-- Complete interval computation for depth 10, residue 696. -/ +theorem bounds_10_696 : exactInterval 10 696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_696 (m : Nat) : + stoppingTime (2 ^ 10 * m + 696) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_696 : oddCount 696 10 = 4 ∧ acceleratedOrbit 10 696 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_696 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 696) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_696.1, data_10_696.2] + +/-- Complete interval computation for depth 10, residue 697. -/ +theorem bounds_10_697 : exactInterval 10 697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_697 (m : Nat) : + stoppingTime (2 ^ 10 * m + 697) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_697 : oddCount 697 10 = 5 ∧ acceleratedOrbit 10 697 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_697 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 697) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_697.1, data_10_697.2] + +/-- Complete interval computation for depth 10, residue 698. -/ +theorem bounds_10_698 : exactInterval 10 698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_698 (m : Nat) : + stoppingTime (2 ^ 10 * m + 698) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_698 : oddCount 698 10 = 4 ∧ acceleratedOrbit 10 698 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_698 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 698) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_698.1, data_10_698.2] + +/-- Complete interval computation for depth 10, residue 699. -/ +theorem bounds_10_699 : exactInterval 10 699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_699 (m : Nat) : + stoppingTime (2 ^ 10 * m + 699) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_699 : oddCount 699 10 = 6 ∧ acceleratedOrbit 10 699 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_699 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 699) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_699.1, data_10_699.2] + +/-- Complete interval computation for depth 10, residue 700. -/ +theorem bounds_10_700 : exactInterval 10 700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_700 (m : Nat) : + stoppingTime (2 ^ 10 * m + 700) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_700 : oddCount 700 10 = 5 ∧ acceleratedOrbit 10 700 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_700 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 700) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_700.1, data_10_700.2] + +/-- Complete interval computation for depth 10, residue 701. -/ +theorem bounds_10_701 : exactInterval 10 701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_701 (m : Nat) : + stoppingTime (2 ^ 10 * m + 701) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_701 : oddCount 701 10 = 5 ∧ acceleratedOrbit 10 701 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_701 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 701) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_701.1, data_10_701.2] + +/-- Complete interval computation for depth 10, residue 702. -/ +theorem bounds_10_702 : exactInterval 10 702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_702 (m : Nat) : + stoppingTime (2 ^ 10 * m + 702) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_702 : oddCount 702 10 = 5 ∧ acceleratedOrbit 10 702 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_702 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 702) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_702.1, data_10_702.2] + +/-- Complete interval computation for depth 10, residue 703. -/ +theorem bounds_10_703 : exactInterval 10 703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_703 (m : Nat) : + stoppingTime (2 ^ 10 * m + 703) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_703 : oddCount 703 10 = 8 ∧ acceleratedOrbit 10 703 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_703 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 703) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_703.1, data_10_703.2] + +/-- Complete interval computation for depth 10, residue 704. -/ +theorem bounds_10_704 : exactInterval 10 704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_704 (m : Nat) : + stoppingTime (2 ^ 10 * m + 704) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_704 : oddCount 704 10 = 3 ∧ acceleratedOrbit 10 704 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_704 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 704) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_704.1, data_10_704.2] + +/-- Complete interval computation for depth 10, residue 705. -/ +theorem bounds_10_705 : exactInterval 10 705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_705 (m : Nat) : + stoppingTime (2 ^ 10 * m + 705) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_705 : oddCount 705 10 = 4 ∧ acceleratedOrbit 10 705 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_705 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 705) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_705.1, data_10_705.2] + +end Collatz.Research.StoppingAtlas.Batch0046 From c5a9f3bb65e723e6b5f487c5db1d12502d4d6945 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:13 +0530 Subject: [PATCH 0047/1001] proof: certify atlas Batch0047 (10:706 to 10:720) --- Collatz/Research/StoppingAtlas/Batch0047.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0047.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0047.lean b/Collatz/Research/StoppingAtlas/Batch0047.lean new file mode 100644 index 00000000..cec62d3c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0047.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0047 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 706. -/ +theorem bounds_10_706 : exactInterval 10 706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_706 (m : Nat) : + stoppingTime (2 ^ 10 * m + 706) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_706 : oddCount 706 10 = 6 ∧ acceleratedOrbit 10 706 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_706 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 706) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_706.1, data_10_706.2] + +/-- Complete interval computation for depth 10, residue 707. -/ +theorem bounds_10_707 : exactInterval 10 707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_707 (m : Nat) : + stoppingTime (2 ^ 10 * m + 707) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_707 : oddCount 707 10 = 6 ∧ acceleratedOrbit 10 707 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_707 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 707) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_707.1, data_10_707.2] + +/-- Complete interval computation for depth 10, residue 708. -/ +theorem bounds_10_708 : exactInterval 10 708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_708 (m : Nat) : + stoppingTime (2 ^ 10 * m + 708) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_708 : oddCount 708 10 = 3 ∧ acceleratedOrbit 10 708 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_708 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 708) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_708.1, data_10_708.2] + +/-- Complete interval computation for depth 10, residue 709. -/ +theorem bounds_10_709 : exactInterval 10 709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_709 (m : Nat) : + stoppingTime (2 ^ 10 * m + 709) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_709 : oddCount 709 10 = 3 ∧ acceleratedOrbit 10 709 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_709 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 709) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_709.1, data_10_709.2] + +/-- Complete interval computation for depth 10, residue 710. -/ +theorem bounds_10_710 : exactInterval 10 710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_710 (m : Nat) : + stoppingTime (2 ^ 10 * m + 710) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_710 : oddCount 710 10 = 3 ∧ acceleratedOrbit 10 710 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_710 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 710) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_710.1, data_10_710.2] + +/-- Complete interval computation for depth 10, residue 711. -/ +theorem bounds_10_711 : exactInterval 10 711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_711 (m : Nat) : + stoppingTime (2 ^ 10 * m + 711) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_711 : oddCount 711 10 = 5 ∧ acceleratedOrbit 10 711 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_711 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 711) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_711.1, data_10_711.2] + +/-- Complete interval computation for depth 10, residue 712. -/ +theorem bounds_10_712 : exactInterval 10 712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_712 (m : Nat) : + stoppingTime (2 ^ 10 * m + 712) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_712 : oddCount 712 10 = 3 ∧ acceleratedOrbit 10 712 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_712 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 712) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_712.1, data_10_712.2] + +/-- Complete interval computation for depth 10, residue 713. -/ +theorem bounds_10_713 : exactInterval 10 713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_713 (m : Nat) : + stoppingTime (2 ^ 10 * m + 713) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_713 : oddCount 713 10 = 5 ∧ acceleratedOrbit 10 713 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_713 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 713) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_713.1, data_10_713.2] + +/-- Complete interval computation for depth 10, residue 714. -/ +theorem bounds_10_714 : exactInterval 10 714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_714 (m : Nat) : + stoppingTime (2 ^ 10 * m + 714) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_714 : oddCount 714 10 = 3 ∧ acceleratedOrbit 10 714 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_714 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 714) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_714.1, data_10_714.2] + +/-- Complete interval computation for depth 10, residue 715. -/ +theorem bounds_10_715 : exactInterval 10 715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_715 (m : Nat) : + stoppingTime (2 ^ 10 * m + 715) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_715 : oddCount 715 10 = 6 ∧ acceleratedOrbit 10 715 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_715 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 715) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_715.1, data_10_715.2] + +/-- Complete interval computation for depth 10, residue 716. -/ +theorem bounds_10_716 : exactInterval 10 716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_716 (m : Nat) : + stoppingTime (2 ^ 10 * m + 716) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_716 : oddCount 716 10 = 3 ∧ acceleratedOrbit 10 716 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_716 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 716) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_716.1, data_10_716.2] + +/-- Complete interval computation for depth 10, residue 717. -/ +theorem bounds_10_717 : exactInterval 10 717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_717 (m : Nat) : + stoppingTime (2 ^ 10 * m + 717) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_717 : oddCount 717 10 = 3 ∧ acceleratedOrbit 10 717 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_717 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 717) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_717.1, data_10_717.2] + +/-- Complete interval computation for depth 10, residue 718. -/ +theorem bounds_10_718 : exactInterval 10 718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_718 (m : Nat) : + stoppingTime (2 ^ 10 * m + 718) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_718 : oddCount 718 10 = 8 ∧ acceleratedOrbit 10 718 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_718 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 718) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_718.1, data_10_718.2] + +/-- Complete interval computation for depth 10, residue 719. -/ +theorem bounds_10_719 : exactInterval 10 719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_719 (m : Nat) : + stoppingTime (2 ^ 10 * m + 719) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_719 : oddCount 719 10 = 8 ∧ acceleratedOrbit 10 719 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_719 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 719) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_719.1, data_10_719.2] + +/-- Complete interval computation for depth 10, residue 720. -/ +theorem bounds_10_720 : exactInterval 10 720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_720 (m : Nat) : + stoppingTime (2 ^ 10 * m + 720) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_720 : oddCount 720 10 = 3 ∧ acceleratedOrbit 10 720 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_720 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 720) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_720.1, data_10_720.2] + +end Collatz.Research.StoppingAtlas.Batch0047 From 41653a8735c26d25adf8f37b68367b89ce4150fc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:13 +0530 Subject: [PATCH 0048/1001] proof: certify atlas Batch0048 (10:721 to 10:736) --- Collatz/Research/StoppingAtlas/Batch0048.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0048.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0048.lean b/Collatz/Research/StoppingAtlas/Batch0048.lean new file mode 100644 index 00000000..14903cb6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0048.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0048 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 721. -/ +theorem bounds_10_721 : exactInterval 10 721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_721 (m : Nat) : + stoppingTime (2 ^ 10 * m + 721) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_721 : oddCount 721 10 = 5 ∧ acceleratedOrbit 10 721 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_721 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 721) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_721.1, data_10_721.2] + +/-- Complete interval computation for depth 10, residue 722. -/ +theorem bounds_10_722 : exactInterval 10 722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_722 (m : Nat) : + stoppingTime (2 ^ 10 * m + 722) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_722 : oddCount 722 10 = 5 ∧ acceleratedOrbit 10 722 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_722 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 722) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_722.1, data_10_722.2] + +/-- Complete interval computation for depth 10, residue 723. -/ +theorem bounds_10_723 : exactInterval 10 723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_723 (m : Nat) : + stoppingTime (2 ^ 10 * m + 723) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_723 : oddCount 723 10 = 5 ∧ acceleratedOrbit 10 723 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_723 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 723) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_723.1, data_10_723.2] + +/-- Complete interval computation for depth 10, residue 724. -/ +theorem bounds_10_724 : exactInterval 10 724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_724 (m : Nat) : + stoppingTime (2 ^ 10 * m + 724) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_724 : oddCount 724 10 = 3 ∧ acceleratedOrbit 10 724 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_724 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 724) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_724.1, data_10_724.2] + +/-- Complete interval computation for depth 10, residue 725. -/ +theorem bounds_10_725 : exactInterval 10 725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_725 (m : Nat) : + stoppingTime (2 ^ 10 * m + 725) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_725 : oddCount 725 10 = 3 ∧ acceleratedOrbit 10 725 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_725 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 725) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_725.1, data_10_725.2] + +/-- Complete interval computation for depth 10, residue 726. -/ +theorem bounds_10_726 : exactInterval 10 726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_726 (m : Nat) : + stoppingTime (2 ^ 10 * m + 726) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_726 : oddCount 726 10 = 5 ∧ acceleratedOrbit 10 726 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_726 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 726) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_726.1, data_10_726.2] + +/-- Complete interval computation for depth 10, residue 727. -/ +theorem bounds_10_727 : exactInterval 10 727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_727 (m : Nat) : + stoppingTime (2 ^ 10 * m + 727) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_727 : oddCount 727 10 = 5 ∧ acceleratedOrbit 10 727 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_727 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 727) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_727.1, data_10_727.2] + +/-- Complete interval computation for depth 10, residue 728. -/ +theorem bounds_10_728 : exactInterval 10 728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_728 (m : Nat) : + stoppingTime (2 ^ 10 * m + 728) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_728 : oddCount 728 10 = 5 ∧ acceleratedOrbit 10 728 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_728 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 728) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_728.1, data_10_728.2] + +/-- Complete interval computation for depth 10, residue 729. -/ +theorem bounds_10_729 : exactInterval 10 729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_729 (m : Nat) : + stoppingTime (2 ^ 10 * m + 729) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_729 : oddCount 729 10 = 4 ∧ acceleratedOrbit 10 729 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_729 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 729) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_729.1, data_10_729.2] + +/-- Complete interval computation for depth 10, residue 730. -/ +theorem bounds_10_730 : exactInterval 10 730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_730 (m : Nat) : + stoppingTime (2 ^ 10 * m + 730) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_730 : oddCount 730 10 = 5 ∧ acceleratedOrbit 10 730 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_730 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 730) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_730.1, data_10_730.2] + +/-- Complete interval computation for depth 10, residue 731. -/ +theorem bounds_10_731 : exactInterval 10 731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_731 (m : Nat) : + stoppingTime (2 ^ 10 * m + 731) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_731 : oddCount 731 10 = 7 ∧ acceleratedOrbit 10 731 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_731 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 731) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_731.1, data_10_731.2] + +/-- Complete interval computation for depth 10, residue 732. -/ +theorem bounds_10_732 : exactInterval 10 732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_732 (m : Nat) : + stoppingTime (2 ^ 10 * m + 732) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_732 : oddCount 732 10 = 5 ∧ acceleratedOrbit 10 732 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_732 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 732) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_732.1, data_10_732.2] + +/-- Complete interval computation for depth 10, residue 733. -/ +theorem bounds_10_733 : exactInterval 10 733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_733 (m : Nat) : + stoppingTime (2 ^ 10 * m + 733) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_733 : oddCount 733 10 = 5 ∧ acceleratedOrbit 10 733 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_733 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 733) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_733.1, data_10_733.2] + +/-- Complete interval computation for depth 10, residue 734. -/ +theorem bounds_10_734 : exactInterval 10 734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_734 (m : Nat) : + stoppingTime (2 ^ 10 * m + 734) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_734 : oddCount 734 10 = 6 ∧ acceleratedOrbit 10 734 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_734 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 734) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_734.1, data_10_734.2] + +/-- Complete interval computation for depth 10, residue 735. -/ +theorem bounds_10_735 : exactInterval 10 735 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_735 (m : Nat) : + stoppingTime (2 ^ 10 * m + 735) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_735 : oddCount 735 10 = 6 ∧ acceleratedOrbit 10 735 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_735 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 735) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_735.1, data_10_735.2] + +/-- Complete interval computation for depth 10, residue 736. -/ +theorem bounds_10_736 : exactInterval 10 736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_736 (m : Nat) : + stoppingTime (2 ^ 10 * m + 736) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_736 : oddCount 736 10 = 3 ∧ acceleratedOrbit 10 736 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_736 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 736) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_736.1, data_10_736.2] + +end Collatz.Research.StoppingAtlas.Batch0048 From e22223b6d665a0a292e89b304bc7c34411a0db3b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:13 +0530 Subject: [PATCH 0049/1001] proof: certify atlas Batch0049 (10:737 to 10:751) --- Collatz/Research/StoppingAtlas/Batch0049.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0049.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0049.lean b/Collatz/Research/StoppingAtlas/Batch0049.lean new file mode 100644 index 00000000..1a1201e7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0049.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0049 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 737. -/ +theorem bounds_10_737 : exactInterval 10 737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_737 (m : Nat) : + stoppingTime (2 ^ 10 * m + 737) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_737 : oddCount 737 10 = 7 ∧ acceleratedOrbit 10 737 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_737 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 737) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_737.1, data_10_737.2] + +/-- Complete interval computation for depth 10, residue 738. -/ +theorem bounds_10_738 : exactInterval 10 738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_738 (m : Nat) : + stoppingTime (2 ^ 10 * m + 738) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_738 : oddCount 738 10 = 3 ∧ acceleratedOrbit 10 738 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_738 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 738) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_738.1, data_10_738.2] + +/-- Complete interval computation for depth 10, residue 739. -/ +theorem bounds_10_739 : exactInterval 10 739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_739 (m : Nat) : + stoppingTime (2 ^ 10 * m + 739) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_739 : oddCount 739 10 = 3 ∧ acceleratedOrbit 10 739 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_739 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 739) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_739.1, data_10_739.2] + +/-- Complete interval computation for depth 10, residue 740. -/ +theorem bounds_10_740 : exactInterval 10 740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_740 (m : Nat) : + stoppingTime (2 ^ 10 * m + 740) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_740 : oddCount 740 10 = 4 ∧ acceleratedOrbit 10 740 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_740 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 740) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_740.1, data_10_740.2] + +/-- Complete interval computation for depth 10, residue 741. -/ +theorem bounds_10_741 : exactInterval 10 741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_741 (m : Nat) : + stoppingTime (2 ^ 10 * m + 741) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_741 : oddCount 741 10 = 4 ∧ acceleratedOrbit 10 741 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_741 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 741) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_741.1, data_10_741.2] + +/-- Complete interval computation for depth 10, residue 742. -/ +theorem bounds_10_742 : exactInterval 10 742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_742 (m : Nat) : + stoppingTime (2 ^ 10 * m + 742) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_742 : oddCount 742 10 = 4 ∧ acceleratedOrbit 10 742 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_742 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 742) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_742.1, data_10_742.2] + +/-- Complete interval computation for depth 10, residue 743. -/ +theorem bounds_10_743 : exactInterval 10 743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_743 (m : Nat) : + stoppingTime (2 ^ 10 * m + 743) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_743 : oddCount 743 10 = 8 ∧ acceleratedOrbit 10 743 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_743 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 743) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_743.1, data_10_743.2] + +/-- Complete interval computation for depth 10, residue 744. -/ +theorem bounds_10_744 : exactInterval 10 744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_744 (m : Nat) : + stoppingTime (2 ^ 10 * m + 744) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_744 : oddCount 744 10 = 3 ∧ acceleratedOrbit 10 744 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_744 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 744) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_744.1, data_10_744.2] + +/-- Complete interval computation for depth 10, residue 745. -/ +theorem bounds_10_745 : exactInterval 10 745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_745 (m : Nat) : + stoppingTime (2 ^ 10 * m + 745) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_745 : oddCount 745 10 = 7 ∧ acceleratedOrbit 10 745 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_745 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 745) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_745.1, data_10_745.2] + +/-- Complete interval computation for depth 10, residue 746. -/ +theorem bounds_10_746 : exactInterval 10 746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_746 (m : Nat) : + stoppingTime (2 ^ 10 * m + 746) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_746 : oddCount 746 10 = 3 ∧ acceleratedOrbit 10 746 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_746 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 746) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_746.1, data_10_746.2] + +/-- Complete interval computation for depth 10, residue 747. -/ +theorem bounds_10_747 : exactInterval 10 747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_747 (m : Nat) : + stoppingTime (2 ^ 10 * m + 747) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_747 : oddCount 747 10 = 6 ∧ acceleratedOrbit 10 747 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_747 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 747) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_747.1, data_10_747.2] + +/-- Complete interval computation for depth 10, residue 748. -/ +theorem bounds_10_748 : exactInterval 10 748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_748 (m : Nat) : + stoppingTime (2 ^ 10 * m + 748) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_748 : oddCount 748 10 = 5 ∧ acceleratedOrbit 10 748 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_748 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 748) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_748.1, data_10_748.2] + +/-- Complete interval computation for depth 10, residue 749. -/ +theorem bounds_10_749 : exactInterval 10 749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_749 (m : Nat) : + stoppingTime (2 ^ 10 * m + 749) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_749 : oddCount 749 10 = 5 ∧ acceleratedOrbit 10 749 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_749 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 749) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_749.1, data_10_749.2] + +/-- Complete interval computation for depth 10, residue 750. -/ +theorem bounds_10_750 : exactInterval 10 750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_750 (m : Nat) : + stoppingTime (2 ^ 10 * m + 750) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_750 : oddCount 750 10 = 5 ∧ acceleratedOrbit 10 750 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_750 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 750) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_750.1, data_10_750.2] + +/-- Complete interval computation for depth 10, residue 751. -/ +theorem bounds_10_751 : exactInterval 10 751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_751 (m : Nat) : + stoppingTime (2 ^ 10 * m + 751) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_751 : oddCount 751 10 = 8 ∧ acceleratedOrbit 10 751 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_751 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 751) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_751.1, data_10_751.2] + +end Collatz.Research.StoppingAtlas.Batch0049 From 6248c989870dbf6df380c29224efe1528dbbc6a9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:14 +0530 Subject: [PATCH 0050/1001] proof: certify atlas Batch0050 (10:752 to 10:767) --- Collatz/Research/StoppingAtlas/Batch0050.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0050.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0050.lean b/Collatz/Research/StoppingAtlas/Batch0050.lean new file mode 100644 index 00000000..05c39eb2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0050.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0050 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 752. -/ +theorem bounds_10_752 : exactInterval 10 752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_752 (m : Nat) : + stoppingTime (2 ^ 10 * m + 752) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_752 : oddCount 752 10 = 5 ∧ acceleratedOrbit 10 752 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_752 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 752) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_752.1, data_10_752.2] + +/-- Complete interval computation for depth 10, residue 753. -/ +theorem bounds_10_753 : exactInterval 10 753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_753 (m : Nat) : + stoppingTime (2 ^ 10 * m + 753) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_753 : oddCount 753 10 = 3 ∧ acceleratedOrbit 10 753 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_753 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 753) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_753.1, data_10_753.2] + +/-- Complete interval computation for depth 10, residue 754. -/ +theorem bounds_10_754 : exactInterval 10 754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_754 (m : Nat) : + stoppingTime (2 ^ 10 * m + 754) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_754 : oddCount 754 10 = 7 ∧ acceleratedOrbit 10 754 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_754 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 754) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_754.1, data_10_754.2] + +/-- Complete interval computation for depth 10, residue 755. -/ +theorem bounds_10_755 : exactInterval 10 755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_755 (m : Nat) : + stoppingTime (2 ^ 10 * m + 755) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_755 : oddCount 755 10 = 7 ∧ acceleratedOrbit 10 755 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_755 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 755) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_755.1, data_10_755.2] + +/-- Complete interval computation for depth 10, residue 756. -/ +theorem bounds_10_756 : exactInterval 10 756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_756 (m : Nat) : + stoppingTime (2 ^ 10 * m + 756) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_756 : oddCount 756 10 = 5 ∧ acceleratedOrbit 10 756 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_756 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 756) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_756.1, data_10_756.2] + +/-- Complete interval computation for depth 10, residue 757. -/ +theorem bounds_10_757 : exactInterval 10 757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_757 (m : Nat) : + stoppingTime (2 ^ 10 * m + 757) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_757 : oddCount 757 10 = 5 ∧ acceleratedOrbit 10 757 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_757 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 757) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_757.1, data_10_757.2] + +/-- Complete interval computation for depth 10, residue 758. -/ +theorem bounds_10_758 : exactInterval 10 758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_758 (m : Nat) : + stoppingTime (2 ^ 10 * m + 758) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_758 : oddCount 758 10 = 6 ∧ acceleratedOrbit 10 758 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_758 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 758) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_758.1, data_10_758.2] + +/-- Complete interval computation for depth 10, residue 759. -/ +theorem bounds_10_759 : exactInterval 10 759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_759 (m : Nat) : + stoppingTime (2 ^ 10 * m + 759) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_759 : oddCount 759 10 = 6 ∧ acceleratedOrbit 10 759 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_759 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 759) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_759.1, data_10_759.2] + +/-- Complete interval computation for depth 10, residue 760. -/ +theorem bounds_10_760 : exactInterval 10 760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_760 (m : Nat) : + stoppingTime (2 ^ 10 * m + 760) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_760 : oddCount 760 10 = 5 ∧ acceleratedOrbit 10 760 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_760 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 760) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_760.1, data_10_760.2] + +/-- Complete interval computation for depth 10, residue 761. -/ +theorem bounds_10_761 : exactInterval 10 761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_761 (m : Nat) : + stoppingTime (2 ^ 10 * m + 761) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_761 : oddCount 761 10 = 5 ∧ acceleratedOrbit 10 761 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_761 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 761) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_761.1, data_10_761.2] + +/-- Complete interval computation for depth 10, residue 762. -/ +theorem bounds_10_762 : exactInterval 10 762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_762 (m : Nat) : + stoppingTime (2 ^ 10 * m + 762) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_762 : oddCount 762 10 = 5 ∧ acceleratedOrbit 10 762 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_762 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 762) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_762.1, data_10_762.2] + +/-- Complete interval computation for depth 10, residue 763. -/ +theorem bounds_10_763 : exactInterval 10 763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_763 (m : Nat) : + stoppingTime (2 ^ 10 * m + 763) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_763 : oddCount 763 10 = 7 ∧ acceleratedOrbit 10 763 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_763 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 763) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_763.1, data_10_763.2] + +/-- Complete interval computation for depth 10, residue 764. -/ +theorem bounds_10_764 : exactInterval 10 764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_764 (m : Nat) : + stoppingTime (2 ^ 10 * m + 764) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_764 : oddCount 764 10 = 7 ∧ acceleratedOrbit 10 764 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_764 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 764) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_764.1, data_10_764.2] + +/-- Complete interval computation for depth 10, residue 765. -/ +theorem bounds_10_765 : exactInterval 10 765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_765 (m : Nat) : + stoppingTime (2 ^ 10 * m + 765) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_765 : oddCount 765 10 = 7 ∧ acceleratedOrbit 10 765 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_765 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 765) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_765.1, data_10_765.2] + +/-- Complete interval computation for depth 10, residue 766. -/ +theorem bounds_10_766 : exactInterval 10 766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_766 (m : Nat) : + stoppingTime (2 ^ 10 * m + 766) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_766 : oddCount 766 10 = 7 ∧ acceleratedOrbit 10 766 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_766 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 766) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_766.1, data_10_766.2] + +/-- Complete interval computation for depth 10, residue 767. -/ +theorem bounds_10_767 : exactInterval 10 767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_767 (m : Nat) : + stoppingTime (2 ^ 10 * m + 767) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_767 : oddCount 767 10 = 9 ∧ acceleratedOrbit 10 767 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_767 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 767) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_767.1, data_10_767.2] + +end Collatz.Research.StoppingAtlas.Batch0050 From c2b89cd6cfb238c353d285b50989eb9634428da0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:14 +0530 Subject: [PATCH 0051/1001] proof: certify atlas Batch0051 (10:768 to 10:782) --- Collatz/Research/StoppingAtlas/Batch0051.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0051.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0051.lean b/Collatz/Research/StoppingAtlas/Batch0051.lean new file mode 100644 index 00000000..5e6b2b88 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0051.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0051 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 768. -/ +theorem bounds_10_768 : exactInterval 10 768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_768 (m : Nat) : + stoppingTime (2 ^ 10 * m + 768) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_768 : oddCount 768 10 = 2 ∧ acceleratedOrbit 10 768 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_768 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 768) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_768.1, data_10_768.2] + +/-- Complete interval computation for depth 10, residue 769. -/ +theorem bounds_10_769 : exactInterval 10 769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_769 (m : Nat) : + stoppingTime (2 ^ 10 * m + 769) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_769 : oddCount 769 10 = 4 ∧ acceleratedOrbit 10 769 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_769 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 769) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_769.1, data_10_769.2] + +/-- Complete interval computation for depth 10, residue 770. -/ +theorem bounds_10_770 : exactInterval 10 770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_770 (m : Nat) : + stoppingTime (2 ^ 10 * m + 770) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_770 : oddCount 770 10 = 5 ∧ acceleratedOrbit 10 770 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_770 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 770) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_770.1, data_10_770.2] + +/-- Complete interval computation for depth 10, residue 771. -/ +theorem bounds_10_771 : exactInterval 10 771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_771 (m : Nat) : + stoppingTime (2 ^ 10 * m + 771) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_771 : oddCount 771 10 = 5 ∧ acceleratedOrbit 10 771 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_771 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 771) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_771.1, data_10_771.2] + +/-- Complete interval computation for depth 10, residue 772. -/ +theorem bounds_10_772 : exactInterval 10 772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_772 (m : Nat) : + stoppingTime (2 ^ 10 * m + 772) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_772 : oddCount 772 10 = 4 ∧ acceleratedOrbit 10 772 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_772 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 772) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_772.1, data_10_772.2] + +/-- Complete interval computation for depth 10, residue 773. -/ +theorem bounds_10_773 : exactInterval 10 773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_773 (m : Nat) : + stoppingTime (2 ^ 10 * m + 773) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_773 : oddCount 773 10 = 4 ∧ acceleratedOrbit 10 773 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_773 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 773) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_773.1, data_10_773.2] + +/-- Complete interval computation for depth 10, residue 774. -/ +theorem bounds_10_774 : exactInterval 10 774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_774 (m : Nat) : + stoppingTime (2 ^ 10 * m + 774) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_774 : oddCount 774 10 = 4 ∧ acceleratedOrbit 10 774 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_774 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 774) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_774.1, data_10_774.2] + +/-- Complete interval computation for depth 10, residue 775. -/ +theorem bounds_10_775 : exactInterval 10 775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_775 (m : Nat) : + stoppingTime (2 ^ 10 * m + 775) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_775 : oddCount 775 10 = 6 ∧ acceleratedOrbit 10 775 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_775 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 775) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_775.1, data_10_775.2] + +/-- Complete interval computation for depth 10, residue 776. -/ +theorem bounds_10_776 : exactInterval 10 776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_776 (m : Nat) : + stoppingTime (2 ^ 10 * m + 776) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_776 : oddCount 776 10 = 5 ∧ acceleratedOrbit 10 776 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_776 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 776) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_776.1, data_10_776.2] + +/-- Complete interval computation for depth 10, residue 777. -/ +theorem bounds_10_777 : exactInterval 10 777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_777 (m : Nat) : + stoppingTime (2 ^ 10 * m + 777) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_777 : oddCount 777 10 = 7 ∧ acceleratedOrbit 10 777 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_777 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 777) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_777.1, data_10_777.2] + +/-- Complete interval computation for depth 10, residue 778. -/ +theorem bounds_10_778 : exactInterval 10 778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_778 (m : Nat) : + stoppingTime (2 ^ 10 * m + 778) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_778 : oddCount 778 10 = 5 ∧ acceleratedOrbit 10 778 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_778 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 778) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_778.1, data_10_778.2] + +/-- Complete interval computation for depth 10, residue 779. -/ +theorem bounds_10_779 : exactInterval 10 779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_779 (m : Nat) : + stoppingTime (2 ^ 10 * m + 779) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_779 : oddCount 779 10 = 6 ∧ acceleratedOrbit 10 779 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_779 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 779) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_779.1, data_10_779.2] + +/-- Complete interval computation for depth 10, residue 780. -/ +theorem bounds_10_780 : exactInterval 10 780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_780 (m : Nat) : + stoppingTime (2 ^ 10 * m + 780) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_780 : oddCount 780 10 = 5 ∧ acceleratedOrbit 10 780 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_780 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 780) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_780.1, data_10_780.2] + +/-- Complete interval computation for depth 10, residue 781. -/ +theorem bounds_10_781 : exactInterval 10 781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_781 (m : Nat) : + stoppingTime (2 ^ 10 * m + 781) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_781 : oddCount 781 10 = 5 ∧ acceleratedOrbit 10 781 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_781 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 781) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_781.1, data_10_781.2] + +/-- Complete interval computation for depth 10, residue 782. -/ +theorem bounds_10_782 : exactInterval 10 782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_782 (m : Nat) : + stoppingTime (2 ^ 10 * m + 782) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_782 : oddCount 782 10 = 4 ∧ acceleratedOrbit 10 782 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_782 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 782) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_782.1, data_10_782.2] + +end Collatz.Research.StoppingAtlas.Batch0051 From 87221e6284e1142682df2569dac116cf87eecaee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:15 +0530 Subject: [PATCH 0052/1001] proof: certify atlas Batch0052 (10:783 to 10:797) --- Collatz/Research/StoppingAtlas/Batch0052.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0052.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0052.lean b/Collatz/Research/StoppingAtlas/Batch0052.lean new file mode 100644 index 00000000..84572fa0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0052.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0052 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 783. -/ +theorem bounds_10_783 : exactInterval 10 783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_783 (m : Nat) : + stoppingTime (2 ^ 10 * m + 783) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_783 : oddCount 783 10 = 4 ∧ acceleratedOrbit 10 783 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_783 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 783) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_783.1, data_10_783.2] + +/-- Complete interval computation for depth 10, residue 784. -/ +theorem bounds_10_784 : exactInterval 10 784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_784 (m : Nat) : + stoppingTime (2 ^ 10 * m + 784) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_784 : oddCount 784 10 = 2 ∧ acceleratedOrbit 10 784 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_784 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 784) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_784.1, data_10_784.2] + +/-- Complete interval computation for depth 10, residue 785. -/ +theorem bounds_10_785 : exactInterval 10 785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_785 (m : Nat) : + stoppingTime (2 ^ 10 * m + 785) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_785 : oddCount 785 10 = 5 ∧ acceleratedOrbit 10 785 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_785 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 785) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_785.1, data_10_785.2] + +/-- Complete interval computation for depth 10, residue 786. -/ +theorem bounds_10_786 : exactInterval 10 786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_786 (m : Nat) : + stoppingTime (2 ^ 10 * m + 786) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_786 : oddCount 786 10 = 6 ∧ acceleratedOrbit 10 786 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_786 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 786) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_786.1, data_10_786.2] + +/-- Complete interval computation for depth 10, residue 787. -/ +theorem bounds_10_787 : exactInterval 10 787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_787 (m : Nat) : + stoppingTime (2 ^ 10 * m + 787) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_787 : oddCount 787 10 = 6 ∧ acceleratedOrbit 10 787 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_787 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 787) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_787.1, data_10_787.2] + +/-- Complete interval computation for depth 10, residue 788. -/ +theorem bounds_10_788 : exactInterval 10 788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_788 (m : Nat) : + stoppingTime (2 ^ 10 * m + 788) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_788 : oddCount 788 10 = 2 ∧ acceleratedOrbit 10 788 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_788 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 788) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_788.1, data_10_788.2] + +/-- Complete interval computation for depth 10, residue 789. -/ +theorem bounds_10_789 : exactInterval 10 789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_789 (m : Nat) : + stoppingTime (2 ^ 10 * m + 789) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_789 : oddCount 789 10 = 2 ∧ acceleratedOrbit 10 789 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_789 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 789) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_789.1, data_10_789.2] + +/-- Complete interval computation for depth 10, residue 790. -/ +theorem bounds_10_790 : exactInterval 10 790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_790 (m : Nat) : + stoppingTime (2 ^ 10 * m + 790) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_790 : oddCount 790 10 = 6 ∧ acceleratedOrbit 10 790 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_790 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 790) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_790.1, data_10_790.2] + +/-- Complete interval computation for depth 10, residue 791. -/ +theorem bounds_10_791 : exactInterval 10 791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_791 (m : Nat) : + stoppingTime (2 ^ 10 * m + 791) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_791 : oddCount 791 10 = 6 ∧ acceleratedOrbit 10 791 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_791 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 791) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_791.1, data_10_791.2] + +/-- Complete interval computation for depth 10, residue 792. -/ +theorem bounds_10_792 : exactInterval 10 792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_792 (m : Nat) : + stoppingTime (2 ^ 10 * m + 792) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_792 : oddCount 792 10 = 2 ∧ acceleratedOrbit 10 792 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_792 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 792) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_792.1, data_10_792.2] + +/-- Complete interval computation for depth 10, residue 793. -/ +theorem bounds_10_793 : exactInterval 10 793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_793 (m : Nat) : + stoppingTime (2 ^ 10 * m + 793) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_793 : oddCount 793 10 = 7 ∧ acceleratedOrbit 10 793 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_793 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 793) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_793.1, data_10_793.2] + +/-- Complete interval computation for depth 10, residue 794. -/ +theorem bounds_10_794 : exactInterval 10 794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_794 (m : Nat) : + stoppingTime (2 ^ 10 * m + 794) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_794 : oddCount 794 10 = 2 ∧ acceleratedOrbit 10 794 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_794 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 794) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_794.1, data_10_794.2] + +/-- Complete interval computation for depth 10, residue 795. -/ +theorem bounds_10_795 : exactInterval 10 795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_795 (m : Nat) : + stoppingTime (2 ^ 10 * m + 795) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_795 : oddCount 795 10 = 9 ∧ acceleratedOrbit 10 795 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_795 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 795) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_795.1, data_10_795.2] + +/-- Complete interval computation for depth 10, residue 796. -/ +theorem bounds_10_796 : exactInterval 10 796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_796 (m : Nat) : + stoppingTime (2 ^ 10 * m + 796) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_796 : oddCount 796 10 = 5 ∧ acceleratedOrbit 10 796 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_796 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 796) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_796.1, data_10_796.2] + +/-- Complete interval computation for depth 10, residue 797. -/ +theorem bounds_10_797 : exactInterval 10 797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_797 (m : Nat) : + stoppingTime (2 ^ 10 * m + 797) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_797 : oddCount 797 10 = 5 ∧ acceleratedOrbit 10 797 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_797 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 797) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_797.1, data_10_797.2] + +end Collatz.Research.StoppingAtlas.Batch0052 From f3331a58c57aff0e2c5cffdc58009e8250da25d7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:15 +0530 Subject: [PATCH 0053/1001] proof: certify atlas Batch0053 (10:798 to 10:813) --- Collatz/Research/StoppingAtlas/Batch0053.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0053.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0053.lean b/Collatz/Research/StoppingAtlas/Batch0053.lean new file mode 100644 index 00000000..83f6139c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0053.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0053 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 798. -/ +theorem bounds_10_798 : exactInterval 10 798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_798 (m : Nat) : + stoppingTime (2 ^ 10 * m + 798) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_798 : oddCount 798 10 = 5 ∧ acceleratedOrbit 10 798 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_798 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 798) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_798.1, data_10_798.2] + +/-- Complete interval computation for depth 10, residue 799. -/ +theorem bounds_10_799 : exactInterval 10 799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_799 (m : Nat) : + stoppingTime (2 ^ 10 * m + 799) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_799 : oddCount 799 10 = 7 ∧ acceleratedOrbit 10 799 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_799 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 799) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_799.1, data_10_799.2] + +/-- Complete interval computation for depth 10, residue 800. -/ +theorem bounds_10_800 : exactInterval 10 800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_800 (m : Nat) : + stoppingTime (2 ^ 10 * m + 800) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_800 : oddCount 800 10 = 3 ∧ acceleratedOrbit 10 800 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_800 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 800) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_800.1, data_10_800.2] + +/-- Complete interval computation for depth 10, residue 801. -/ +theorem bounds_10_801 : exactInterval 10 801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_801 (m : Nat) : + stoppingTime (2 ^ 10 * m + 801) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_801 : oddCount 801 10 = 5 ∧ acceleratedOrbit 10 801 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_801 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 801) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_801.1, data_10_801.2] + +/-- Complete interval computation for depth 10, residue 802. -/ +theorem bounds_10_802 : exactInterval 10 802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_802 (m : Nat) : + stoppingTime (2 ^ 10 * m + 802) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_802 : oddCount 802 10 = 4 ∧ acceleratedOrbit 10 802 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_802 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 802) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_802.1, data_10_802.2] + +/-- Complete interval computation for depth 10, residue 803. -/ +theorem bounds_10_803 : exactInterval 10 803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_803 (m : Nat) : + stoppingTime (2 ^ 10 * m + 803) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_803 : oddCount 803 10 = 4 ∧ acceleratedOrbit 10 803 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_803 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 803) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_803.1, data_10_803.2] + +/-- Complete interval computation for depth 10, residue 804. -/ +theorem bounds_10_804 : exactInterval 10 804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_804 (m : Nat) : + stoppingTime (2 ^ 10 * m + 804) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_804 : oddCount 804 10 = 4 ∧ acceleratedOrbit 10 804 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_804 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 804) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_804.1, data_10_804.2] + +/-- Complete interval computation for depth 10, residue 805. -/ +theorem bounds_10_805 : exactInterval 10 805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_805 (m : Nat) : + stoppingTime (2 ^ 10 * m + 805) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_805 : oddCount 805 10 = 4 ∧ acceleratedOrbit 10 805 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_805 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 805) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_805.1, data_10_805.2] + +/-- Complete interval computation for depth 10, residue 806. -/ +theorem bounds_10_806 : exactInterval 10 806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_806 (m : Nat) : + stoppingTime (2 ^ 10 * m + 806) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_806 : oddCount 806 10 = 4 ∧ acceleratedOrbit 10 806 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_806 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 806) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_806.1, data_10_806.2] + +/-- Complete interval computation for depth 10, residue 807. -/ +theorem bounds_10_807 : exactInterval 10 807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_807 (m : Nat) : + stoppingTime (2 ^ 10 * m + 807) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_807 : oddCount 807 10 = 7 ∧ acceleratedOrbit 10 807 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_807 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 807) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_807.1, data_10_807.2] + +/-- Complete interval computation for depth 10, residue 808. -/ +theorem bounds_10_808 : exactInterval 10 808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_808 (m : Nat) : + stoppingTime (2 ^ 10 * m + 808) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_808 : oddCount 808 10 = 3 ∧ acceleratedOrbit 10 808 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_808 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 808) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_808.1, data_10_808.2] + +/-- Complete interval computation for depth 10, residue 809. -/ +theorem bounds_10_809 : exactInterval 10 809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_809 (m : Nat) : + stoppingTime (2 ^ 10 * m + 809) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_809 : oddCount 809 10 = 6 ∧ acceleratedOrbit 10 809 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_809 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 809) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_809.1, data_10_809.2] + +/-- Complete interval computation for depth 10, residue 810. -/ +theorem bounds_10_810 : exactInterval 10 810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_810 (m : Nat) : + stoppingTime (2 ^ 10 * m + 810) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_810 : oddCount 810 10 = 3 ∧ acceleratedOrbit 10 810 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_810 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 810) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_810.1, data_10_810.2] + +/-- Complete interval computation for depth 10, residue 811. -/ +theorem bounds_10_811 : exactInterval 10 811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_811 (m : Nat) : + stoppingTime (2 ^ 10 * m + 811) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_811 : oddCount 811 10 = 5 ∧ acceleratedOrbit 10 811 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_811 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 811) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_811.1, data_10_811.2] + +/-- Complete interval computation for depth 10, residue 812. -/ +theorem bounds_10_812 : exactInterval 10 812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_812 (m : Nat) : + stoppingTime (2 ^ 10 * m + 812) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_812 : oddCount 812 10 = 4 ∧ acceleratedOrbit 10 812 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_812 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 812) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_812.1, data_10_812.2] + +/-- Complete interval computation for depth 10, residue 813. -/ +theorem bounds_10_813 : exactInterval 10 813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_813 (m : Nat) : + stoppingTime (2 ^ 10 * m + 813) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_813 : oddCount 813 10 = 4 ∧ acceleratedOrbit 10 813 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_813 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 813) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_813.1, data_10_813.2] + +end Collatz.Research.StoppingAtlas.Batch0053 From f24bfd13e94a412b11f679ed7d659afc8fcbe6d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:16 +0530 Subject: [PATCH 0054/1001] proof: certify atlas Batch0054 (10:814 to 10:828) --- Collatz/Research/StoppingAtlas/Batch0054.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0054.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0054.lean b/Collatz/Research/StoppingAtlas/Batch0054.lean new file mode 100644 index 00000000..849a2354 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0054.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0054 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 814. -/ +theorem bounds_10_814 : exactInterval 10 814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_814 (m : Nat) : + stoppingTime (2 ^ 10 * m + 814) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_814 : oddCount 814 10 = 4 ∧ acceleratedOrbit 10 814 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_814 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 814) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_814.1, data_10_814.2] + +/-- Complete interval computation for depth 10, residue 815. -/ +theorem bounds_10_815 : exactInterval 10 815 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_815 (m : Nat) : + stoppingTime (2 ^ 10 * m + 815) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_815 : oddCount 815 10 = 6 ∧ acceleratedOrbit 10 815 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_815 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 815) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_815.1, data_10_815.2] + +/-- Complete interval computation for depth 10, residue 816. -/ +theorem bounds_10_816 : exactInterval 10 816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_816 (m : Nat) : + stoppingTime (2 ^ 10 * m + 816) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_816 : oddCount 816 10 = 3 ∧ acceleratedOrbit 10 816 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_816 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 816) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_816.1, data_10_816.2] + +/-- Complete interval computation for depth 10, residue 817. -/ +theorem bounds_10_817 : exactInterval 10 817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_817 (m : Nat) : + stoppingTime (2 ^ 10 * m + 817) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_817 : oddCount 817 10 = 4 ∧ acceleratedOrbit 10 817 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_817 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 817) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_817.1, data_10_817.2] + +/-- Complete interval computation for depth 10, residue 818. -/ +theorem bounds_10_818 : exactInterval 10 818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_818 (m : Nat) : + stoppingTime (2 ^ 10 * m + 818) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_818 : oddCount 818 10 = 4 ∧ acceleratedOrbit 10 818 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_818 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 818) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_818.1, data_10_818.2] + +/-- Complete interval computation for depth 10, residue 819. -/ +theorem bounds_10_819 : exactInterval 10 819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_819 (m : Nat) : + stoppingTime (2 ^ 10 * m + 819) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_819 : oddCount 819 10 = 4 ∧ acceleratedOrbit 10 819 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_819 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 819) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_819.1, data_10_819.2] + +/-- Complete interval computation for depth 10, residue 820. -/ +theorem bounds_10_820 : exactInterval 10 820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_820 (m : Nat) : + stoppingTime (2 ^ 10 * m + 820) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_820 : oddCount 820 10 = 3 ∧ acceleratedOrbit 10 820 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_820 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 820) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_820.1, data_10_820.2] + +/-- Complete interval computation for depth 10, residue 821. -/ +theorem bounds_10_821 : exactInterval 10 821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_821 (m : Nat) : + stoppingTime (2 ^ 10 * m + 821) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_821 : oddCount 821 10 = 3 ∧ acceleratedOrbit 10 821 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_821 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 821) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_821.1, data_10_821.2] + +/-- Complete interval computation for depth 10, residue 822. -/ +theorem bounds_10_822 : exactInterval 10 822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_822 (m : Nat) : + stoppingTime (2 ^ 10 * m + 822) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_822 : oddCount 822 10 = 6 ∧ acceleratedOrbit 10 822 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_822 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 822) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_822.1, data_10_822.2] + +/-- Complete interval computation for depth 10, residue 823. -/ +theorem bounds_10_823 : exactInterval 10 823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_823 (m : Nat) : + stoppingTime (2 ^ 10 * m + 823) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_823 : oddCount 823 10 = 6 ∧ acceleratedOrbit 10 823 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_823 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 823) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_823.1, data_10_823.2] + +/-- Complete interval computation for depth 10, residue 824. -/ +theorem bounds_10_824 : exactInterval 10 824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_824 (m : Nat) : + stoppingTime (2 ^ 10 * m + 824) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_824 : oddCount 824 10 = 6 ∧ acceleratedOrbit 10 824 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_824 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 824) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_824.1, data_10_824.2] + +/-- Complete interval computation for depth 10, residue 825. -/ +theorem bounds_10_825 : exactInterval 10 825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_825 (m : Nat) : + stoppingTime (2 ^ 10 * m + 825) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_825 : oddCount 825 10 = 6 ∧ acceleratedOrbit 10 825 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_825 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 825) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_825.1, data_10_825.2] + +/-- Complete interval computation for depth 10, residue 826. -/ +theorem bounds_10_826 : exactInterval 10 826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_826 (m : Nat) : + stoppingTime (2 ^ 10 * m + 826) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_826 : oddCount 826 10 = 6 ∧ acceleratedOrbit 10 826 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_826 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 826) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_826.1, data_10_826.2] + +/-- Complete interval computation for depth 10, residue 827. -/ +theorem bounds_10_827 : exactInterval 10 827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_827 (m : Nat) : + stoppingTime (2 ^ 10 * m + 827) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_827 : oddCount 827 10 = 5 ∧ acceleratedOrbit 10 827 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_827 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 827) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_827.1, data_10_827.2] + +/-- Complete interval computation for depth 10, residue 828. -/ +theorem bounds_10_828 : exactInterval 10 828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_828 (m : Nat) : + stoppingTime (2 ^ 10 * m + 828) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_828 : oddCount 828 10 = 6 ∧ acceleratedOrbit 10 828 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_828 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 828) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_828.1, data_10_828.2] + +end Collatz.Research.StoppingAtlas.Batch0054 From 6e397d5aae62557c1831b8e6dd5c2f72327d3e45 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:16 +0530 Subject: [PATCH 0055/1001] proof: certify atlas Batch0055 (10:829 to 10:843) --- Collatz/Research/StoppingAtlas/Batch0055.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0055.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0055.lean b/Collatz/Research/StoppingAtlas/Batch0055.lean new file mode 100644 index 00000000..2209686a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0055.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0055 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 829. -/ +theorem bounds_10_829 : exactInterval 10 829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_829 (m : Nat) : + stoppingTime (2 ^ 10 * m + 829) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_829 : oddCount 829 10 = 6 ∧ acceleratedOrbit 10 829 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_829 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 829) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_829.1, data_10_829.2] + +/-- Complete interval computation for depth 10, residue 830. -/ +theorem bounds_10_830 : exactInterval 10 830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_830 (m : Nat) : + stoppingTime (2 ^ 10 * m + 830) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_830 : oddCount 830 10 = 7 ∧ acceleratedOrbit 10 830 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_830 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 830) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_830.1, data_10_830.2] + +/-- Complete interval computation for depth 10, residue 831. -/ +theorem bounds_10_831 : exactInterval 10 831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_831 (m : Nat) : + stoppingTime (2 ^ 10 * m + 831) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_831 : oddCount 831 10 = 7 ∧ acceleratedOrbit 10 831 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_831 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 831) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_831.1, data_10_831.2] + +/-- Complete interval computation for depth 10, residue 832. -/ +theorem bounds_10_832 : exactInterval 10 832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_832 (m : Nat) : + stoppingTime (2 ^ 10 * m + 832) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_832 : oddCount 832 10 = 2 ∧ acceleratedOrbit 10 832 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_832 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 832) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_832.1, data_10_832.2] + +/-- Complete interval computation for depth 10, residue 833. -/ +theorem bounds_10_833 : exactInterval 10 833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_833 (m : Nat) : + stoppingTime (2 ^ 10 * m + 833) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_833 : oddCount 833 10 = 3 ∧ acceleratedOrbit 10 833 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_833 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 833) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_833.1, data_10_833.2] + +/-- Complete interval computation for depth 10, residue 834. -/ +theorem bounds_10_834 : exactInterval 10 834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_834 (m : Nat) : + stoppingTime (2 ^ 10 * m + 834) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_834 : oddCount 834 10 = 5 ∧ acceleratedOrbit 10 834 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_834 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 834) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_834.1, data_10_834.2] + +/-- Complete interval computation for depth 10, residue 835. -/ +theorem bounds_10_835 : exactInterval 10 835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_835 (m : Nat) : + stoppingTime (2 ^ 10 * m + 835) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_835 : oddCount 835 10 = 5 ∧ acceleratedOrbit 10 835 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_835 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 835) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_835.1, data_10_835.2] + +/-- Complete interval computation for depth 10, residue 836. -/ +theorem bounds_10_836 : exactInterval 10 836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_836 (m : Nat) : + stoppingTime (2 ^ 10 * m + 836) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_836 : oddCount 836 10 = 4 ∧ acceleratedOrbit 10 836 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_836 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 836) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_836.1, data_10_836.2] + +/-- Complete interval computation for depth 10, residue 837. -/ +theorem bounds_10_837 : exactInterval 10 837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_837 (m : Nat) : + stoppingTime (2 ^ 10 * m + 837) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_837 : oddCount 837 10 = 4 ∧ acceleratedOrbit 10 837 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_837 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 837) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_837.1, data_10_837.2] + +/-- Complete interval computation for depth 10, residue 838. -/ +theorem bounds_10_838 : exactInterval 10 838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_838 (m : Nat) : + stoppingTime (2 ^ 10 * m + 838) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_838 : oddCount 838 10 = 4 ∧ acceleratedOrbit 10 838 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_838 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 838) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_838.1, data_10_838.2] + +/-- Complete interval computation for depth 10, residue 839. -/ +theorem bounds_10_839 : exactInterval 10 839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_839 (m : Nat) : + stoppingTime (2 ^ 10 * m + 839) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_839 : oddCount 839 10 = 7 ∧ acceleratedOrbit 10 839 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_839 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 839) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_839.1, data_10_839.2] + +/-- Complete interval computation for depth 10, residue 840. -/ +theorem bounds_10_840 : exactInterval 10 840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_840 (m : Nat) : + stoppingTime (2 ^ 10 * m + 840) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_840 : oddCount 840 10 = 5 ∧ acceleratedOrbit 10 840 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_840 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 840) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_840.1, data_10_840.2] + +/-- Complete interval computation for depth 10, residue 841. -/ +theorem bounds_10_841 : exactInterval 10 841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_841 (m : Nat) : + stoppingTime (2 ^ 10 * m + 841) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_841 : oddCount 841 10 = 5 ∧ acceleratedOrbit 10 841 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_841 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 841) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_841.1, data_10_841.2] + +/-- Complete interval computation for depth 10, residue 842. -/ +theorem bounds_10_842 : exactInterval 10 842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_842 (m : Nat) : + stoppingTime (2 ^ 10 * m + 842) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_842 : oddCount 842 10 = 5 ∧ acceleratedOrbit 10 842 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_842 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 842) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_842.1, data_10_842.2] + +/-- Complete interval computation for depth 10, residue 843. -/ +theorem bounds_10_843 : exactInterval 10 843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_843 (m : Nat) : + stoppingTime (2 ^ 10 * m + 843) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_843 : oddCount 843 10 = 4 ∧ acceleratedOrbit 10 843 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_843 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 843) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_843.1, data_10_843.2] + +end Collatz.Research.StoppingAtlas.Batch0055 From 6fd17d1060e9031cc5031b78c8c14c20e48003c3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:16 +0530 Subject: [PATCH 0056/1001] proof: certify atlas Batch0056 (10:844 to 10:859) --- Collatz/Research/StoppingAtlas/Batch0056.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0056.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0056.lean b/Collatz/Research/StoppingAtlas/Batch0056.lean new file mode 100644 index 00000000..8829508d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0056.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0056 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 844. -/ +theorem bounds_10_844 : exactInterval 10 844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_844 (m : Nat) : + stoppingTime (2 ^ 10 * m + 844) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_844 : oddCount 844 10 = 5 ∧ acceleratedOrbit 10 844 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_844 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 844) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_844.1, data_10_844.2] + +/-- Complete interval computation for depth 10, residue 845. -/ +theorem bounds_10_845 : exactInterval 10 845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_845 (m : Nat) : + stoppingTime (2 ^ 10 * m + 845) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_845 : oddCount 845 10 = 5 ∧ acceleratedOrbit 10 845 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_845 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 845) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_845.1, data_10_845.2] + +/-- Complete interval computation for depth 10, residue 846. -/ +theorem bounds_10_846 : exactInterval 10 846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_846 (m : Nat) : + stoppingTime (2 ^ 10 * m + 846) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_846 : oddCount 846 10 = 6 ∧ acceleratedOrbit 10 846 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_846 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 846) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_846.1, data_10_846.2] + +/-- Complete interval computation for depth 10, residue 847. -/ +theorem bounds_10_847 : exactInterval 10 847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_847 (m : Nat) : + stoppingTime (2 ^ 10 * m + 847) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_847 : oddCount 847 10 = 6 ∧ acceleratedOrbit 10 847 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_847 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 847) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_847.1, data_10_847.2] + +/-- Complete interval computation for depth 10, residue 848. -/ +theorem bounds_10_848 : exactInterval 10 848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_848 (m : Nat) : + stoppingTime (2 ^ 10 * m + 848) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_848 : oddCount 848 10 = 2 ∧ acceleratedOrbit 10 848 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_848 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 848) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_848.1, data_10_848.2] + +/-- Complete interval computation for depth 10, residue 849. -/ +theorem bounds_10_849 : exactInterval 10 849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_849 (m : Nat) : + stoppingTime (2 ^ 10 * m + 849) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_849 : oddCount 849 10 = 6 ∧ acceleratedOrbit 10 849 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_849 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 849) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_849.1, data_10_849.2] + +/-- Complete interval computation for depth 10, residue 850. -/ +theorem bounds_10_850 : exactInterval 10 850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_850 (m : Nat) : + stoppingTime (2 ^ 10 * m + 850) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_850 : oddCount 850 10 = 7 ∧ acceleratedOrbit 10 850 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_850 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 850) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_850.1, data_10_850.2] + +/-- Complete interval computation for depth 10, residue 851. -/ +theorem bounds_10_851 : exactInterval 10 851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_851 (m : Nat) : + stoppingTime (2 ^ 10 * m + 851) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_851 : oddCount 851 10 = 7 ∧ acceleratedOrbit 10 851 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_851 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 851) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_851.1, data_10_851.2] + +/-- Complete interval computation for depth 10, residue 852. -/ +theorem bounds_10_852 : exactInterval 10 852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_852 (m : Nat) : + stoppingTime (2 ^ 10 * m + 852) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_852 : oddCount 852 10 = 2 ∧ acceleratedOrbit 10 852 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_852 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 852) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_852.1, data_10_852.2] + +/-- Complete interval computation for depth 10, residue 853. -/ +theorem bounds_10_853 : exactInterval 10 853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_853 (m : Nat) : + stoppingTime (2 ^ 10 * m + 853) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_853 : oddCount 853 10 = 2 ∧ acceleratedOrbit 10 853 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_853 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 853) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_853.1, data_10_853.2] + +/-- Complete interval computation for depth 10, residue 854. -/ +theorem bounds_10_854 : exactInterval 10 854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_854 (m : Nat) : + stoppingTime (2 ^ 10 * m + 854) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_854 : oddCount 854 10 = 6 ∧ acceleratedOrbit 10 854 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_854 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 854) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_854.1, data_10_854.2] + +/-- Complete interval computation for depth 10, residue 855. -/ +theorem bounds_10_855 : exactInterval 10 855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_855 (m : Nat) : + stoppingTime (2 ^ 10 * m + 855) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_855 : oddCount 855 10 = 6 ∧ acceleratedOrbit 10 855 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_855 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 855) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_855.1, data_10_855.2] + +/-- Complete interval computation for depth 10, residue 856. -/ +theorem bounds_10_856 : exactInterval 10 856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_856 (m : Nat) : + stoppingTime (2 ^ 10 * m + 856) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_856 : oddCount 856 10 = 5 ∧ acceleratedOrbit 10 856 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_856 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 856) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_856.1, data_10_856.2] + +/-- Complete interval computation for depth 10, residue 857. -/ +theorem bounds_10_857 : exactInterval 10 857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_857 (m : Nat) : + stoppingTime (2 ^ 10 * m + 857) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_857 : oddCount 857 10 = 4 ∧ acceleratedOrbit 10 857 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_857 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 857) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_857.1, data_10_857.2] + +/-- Complete interval computation for depth 10, residue 858. -/ +theorem bounds_10_858 : exactInterval 10 858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_858 (m : Nat) : + stoppingTime (2 ^ 10 * m + 858) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_858 : oddCount 858 10 = 5 ∧ acceleratedOrbit 10 858 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_858 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 858) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_858.1, data_10_858.2] + +/-- Complete interval computation for depth 10, residue 859. -/ +theorem bounds_10_859 : exactInterval 10 859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_859 (m : Nat) : + stoppingTime (2 ^ 10 * m + 859) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_859 : oddCount 859 10 = 7 ∧ acceleratedOrbit 10 859 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_859 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 859) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_859.1, data_10_859.2] + +end Collatz.Research.StoppingAtlas.Batch0056 From fbb3a2a7d1f0f65637f8d8d92cf8171227f56c93 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:17 +0530 Subject: [PATCH 0057/1001] proof: certify atlas Batch0057 (10:860 to 10:874) --- Collatz/Research/StoppingAtlas/Batch0057.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0057.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0057.lean b/Collatz/Research/StoppingAtlas/Batch0057.lean new file mode 100644 index 00000000..dd476830 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0057.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0057 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 860. -/ +theorem bounds_10_860 : exactInterval 10 860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_860 (m : Nat) : + stoppingTime (2 ^ 10 * m + 860) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_860 : oddCount 860 10 = 5 ∧ acceleratedOrbit 10 860 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_860 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 860) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_860.1, data_10_860.2] + +/-- Complete interval computation for depth 10, residue 861. -/ +theorem bounds_10_861 : exactInterval 10 861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_861 (m : Nat) : + stoppingTime (2 ^ 10 * m + 861) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_861 : oddCount 861 10 = 5 ∧ acceleratedOrbit 10 861 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_861 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 861) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_861.1, data_10_861.2] + +/-- Complete interval computation for depth 10, residue 862. -/ +theorem bounds_10_862 : exactInterval 10 862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_862 (m : Nat) : + stoppingTime (2 ^ 10 * m + 862) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_862 : oddCount 862 10 = 5 ∧ acceleratedOrbit 10 862 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_862 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 862) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_862.1, data_10_862.2] + +/-- Complete interval computation for depth 10, residue 863. -/ +theorem bounds_10_863 : exactInterval 10 863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_863 (m : Nat) : + stoppingTime (2 ^ 10 * m + 863) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_863 : oddCount 863 10 = 5 ∧ acceleratedOrbit 10 863 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_863 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 863) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_863.1, data_10_863.2] + +/-- Complete interval computation for depth 10, residue 864. -/ +theorem bounds_10_864 : exactInterval 10 864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_864 (m : Nat) : + stoppingTime (2 ^ 10 * m + 864) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_864 : oddCount 864 10 = 4 ∧ acceleratedOrbit 10 864 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_864 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 864) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_864.1, data_10_864.2] + +/-- Complete interval computation for depth 10, residue 865. -/ +theorem bounds_10_865 : exactInterval 10 865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_865 (m : Nat) : + stoppingTime (2 ^ 10 * m + 865) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_865 : oddCount 865 10 = 7 ∧ acceleratedOrbit 10 865 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_865 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 865) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_865.1, data_10_865.2] + +/-- Complete interval computation for depth 10, residue 866. -/ +theorem bounds_10_866 : exactInterval 10 866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_866 (m : Nat) : + stoppingTime (2 ^ 10 * m + 866) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_866 : oddCount 866 10 = 3 ∧ acceleratedOrbit 10 866 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_866 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 866) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_866.1, data_10_866.2] + +/-- Complete interval computation for depth 10, residue 867. -/ +theorem bounds_10_867 : exactInterval 10 867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_867 (m : Nat) : + stoppingTime (2 ^ 10 * m + 867) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_867 : oddCount 867 10 = 3 ∧ acceleratedOrbit 10 867 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_867 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 867) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_867.1, data_10_867.2] + +/-- Complete interval computation for depth 10, residue 868. -/ +theorem bounds_10_868 : exactInterval 10 868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_868 (m : Nat) : + stoppingTime (2 ^ 10 * m + 868) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_868 : oddCount 868 10 = 3 ∧ acceleratedOrbit 10 868 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_868 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 868) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_868.1, data_10_868.2] + +/-- Complete interval computation for depth 10, residue 869. -/ +theorem bounds_10_869 : exactInterval 10 869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_869 (m : Nat) : + stoppingTime (2 ^ 10 * m + 869) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_869 : oddCount 869 10 = 3 ∧ acceleratedOrbit 10 869 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_869 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 869) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_869.1, data_10_869.2] + +/-- Complete interval computation for depth 10, residue 870. -/ +theorem bounds_10_870 : exactInterval 10 870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_870 (m : Nat) : + stoppingTime (2 ^ 10 * m + 870) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_870 : oddCount 870 10 = 3 ∧ acceleratedOrbit 10 870 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_870 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 870) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_870.1, data_10_870.2] + +/-- Complete interval computation for depth 10, residue 871. -/ +theorem bounds_10_871 : exactInterval 10 871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_871 (m : Nat) : + stoppingTime (2 ^ 10 * m + 871) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_871 : oddCount 871 10 = 9 ∧ acceleratedOrbit 10 871 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_871 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 871) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_871.1, data_10_871.2] + +/-- Complete interval computation for depth 10, residue 872. -/ +theorem bounds_10_872 : exactInterval 10 872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_872 (m : Nat) : + stoppingTime (2 ^ 10 * m + 872) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_872 : oddCount 872 10 = 4 ∧ acceleratedOrbit 10 872 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_872 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 872) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_872.1, data_10_872.2] + +/-- Complete interval computation for depth 10, residue 873. -/ +theorem bounds_10_873 : exactInterval 10 873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_873 (m : Nat) : + stoppingTime (2 ^ 10 * m + 873) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_873 : oddCount 873 10 = 6 ∧ acceleratedOrbit 10 873 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_873 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 873) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_873.1, data_10_873.2] + +/-- Complete interval computation for depth 10, residue 874. -/ +theorem bounds_10_874 : exactInterval 10 874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_874 (m : Nat) : + stoppingTime (2 ^ 10 * m + 874) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_874 : oddCount 874 10 = 4 ∧ acceleratedOrbit 10 874 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_874 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 874) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_874.1, data_10_874.2] + +end Collatz.Research.StoppingAtlas.Batch0057 From df3f44f43800dab2eb5851bb2ed08e31805eb253 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:17 +0530 Subject: [PATCH 0058/1001] proof: certify atlas Batch0058 (10:875 to 10:889) --- Collatz/Research/StoppingAtlas/Batch0058.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0058.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0058.lean b/Collatz/Research/StoppingAtlas/Batch0058.lean new file mode 100644 index 00000000..5d6b79cc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0058.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0058 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 875. -/ +theorem bounds_10_875 : exactInterval 10 875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_875 (m : Nat) : + stoppingTime (2 ^ 10 * m + 875) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_875 : oddCount 875 10 = 5 ∧ acceleratedOrbit 10 875 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_875 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 875) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_875.1, data_10_875.2] + +/-- Complete interval computation for depth 10, residue 876. -/ +theorem bounds_10_876 : exactInterval 10 876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_876 (m : Nat) : + stoppingTime (2 ^ 10 * m + 876) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_876 : oddCount 876 10 = 5 ∧ acceleratedOrbit 10 876 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_876 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 876) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_876.1, data_10_876.2] + +/-- Complete interval computation for depth 10, residue 877. -/ +theorem bounds_10_877 : exactInterval 10 877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_877 (m : Nat) : + stoppingTime (2 ^ 10 * m + 877) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_877 : oddCount 877 10 = 5 ∧ acceleratedOrbit 10 877 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_877 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 877) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_877.1, data_10_877.2] + +/-- Complete interval computation for depth 10, residue 878. -/ +theorem bounds_10_878 : exactInterval 10 878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_878 (m : Nat) : + stoppingTime (2 ^ 10 * m + 878) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_878 : oddCount 878 10 = 5 ∧ acceleratedOrbit 10 878 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_878 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 878) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_878.1, data_10_878.2] + +/-- Complete interval computation for depth 10, residue 879. -/ +theorem bounds_10_879 : exactInterval 10 879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_879 (m : Nat) : + stoppingTime (2 ^ 10 * m + 879) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_879 : oddCount 879 10 = 7 ∧ acceleratedOrbit 10 879 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_879 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 879) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_879.1, data_10_879.2] + +/-- Complete interval computation for depth 10, residue 880. -/ +theorem bounds_10_880 : exactInterval 10 880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_880 (m : Nat) : + stoppingTime (2 ^ 10 * m + 880) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_880 : oddCount 880 10 = 4 ∧ acceleratedOrbit 10 880 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_880 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 880) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_880.1, data_10_880.2] + +/-- Complete interval computation for depth 10, residue 881. -/ +theorem bounds_10_881 : exactInterval 10 881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_881 (m : Nat) : + stoppingTime (2 ^ 10 * m + 881) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_881 : oddCount 881 10 = 4 ∧ acceleratedOrbit 10 881 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_881 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 881) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_881.1, data_10_881.2] + +/-- Complete interval computation for depth 10, residue 882. -/ +theorem bounds_10_882 : exactInterval 10 882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_882 (m : Nat) : + stoppingTime (2 ^ 10 * m + 882) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_882 : oddCount 882 10 = 4 ∧ acceleratedOrbit 10 882 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_882 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 882) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_882.1, data_10_882.2] + +/-- Complete interval computation for depth 10, residue 883. -/ +theorem bounds_10_883 : exactInterval 10 883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_883 (m : Nat) : + stoppingTime (2 ^ 10 * m + 883) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_883 : oddCount 883 10 = 4 ∧ acceleratedOrbit 10 883 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_883 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 883) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_883.1, data_10_883.2] + +/-- Complete interval computation for depth 10, residue 884. -/ +theorem bounds_10_884 : exactInterval 10 884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_884 (m : Nat) : + stoppingTime (2 ^ 10 * m + 884) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_884 : oddCount 884 10 = 4 ∧ acceleratedOrbit 10 884 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_884 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 884) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_884.1, data_10_884.2] + +/-- Complete interval computation for depth 10, residue 885. -/ +theorem bounds_10_885 : exactInterval 10 885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_885 (m : Nat) : + stoppingTime (2 ^ 10 * m + 885) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_885 : oddCount 885 10 = 4 ∧ acceleratedOrbit 10 885 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_885 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 885) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_885.1, data_10_885.2] + +/-- Complete interval computation for depth 10, residue 886. -/ +theorem bounds_10_886 : exactInterval 10 886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_886 (m : Nat) : + stoppingTime (2 ^ 10 * m + 886) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_886 : oddCount 886 10 = 5 ∧ acceleratedOrbit 10 886 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_886 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 886) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_886.1, data_10_886.2] + +/-- Complete interval computation for depth 10, residue 887. -/ +theorem bounds_10_887 : exactInterval 10 887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_887 (m : Nat) : + stoppingTime (2 ^ 10 * m + 887) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_887 : oddCount 887 10 = 5 ∧ acceleratedOrbit 10 887 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_887 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 887) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_887.1, data_10_887.2] + +/-- Complete interval computation for depth 10, residue 888. -/ +theorem bounds_10_888 : exactInterval 10 888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_888 (m : Nat) : + stoppingTime (2 ^ 10 * m + 888) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_888 : oddCount 888 10 = 6 ∧ acceleratedOrbit 10 888 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_888 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 888) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_888.1, data_10_888.2] + +/-- Complete interval computation for depth 10, residue 889. -/ +theorem bounds_10_889 : exactInterval 10 889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_889 (m : Nat) : + stoppingTime (2 ^ 10 * m + 889) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_889 : oddCount 889 10 = 7 ∧ acceleratedOrbit 10 889 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_889 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 889) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_889.1, data_10_889.2] + +end Collatz.Research.StoppingAtlas.Batch0058 From 4d961417921af9d86c40f49e3cfcebe4d0919315 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:17 +0530 Subject: [PATCH 0059/1001] proof: certify atlas Batch0059 (10:890 to 10:905) --- Collatz/Research/StoppingAtlas/Batch0059.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0059.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0059.lean b/Collatz/Research/StoppingAtlas/Batch0059.lean new file mode 100644 index 00000000..29e2163d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0059.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0059 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 890. -/ +theorem bounds_10_890 : exactInterval 10 890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_890 (m : Nat) : + stoppingTime (2 ^ 10 * m + 890) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_890 : oddCount 890 10 = 6 ∧ acceleratedOrbit 10 890 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_890 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 890) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_890.1, data_10_890.2] + +/-- Complete interval computation for depth 10, residue 891. -/ +theorem bounds_10_891 : exactInterval 10 891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_891 (m : Nat) : + stoppingTime (2 ^ 10 * m + 891) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_891 : oddCount 891 10 = 7 ∧ acceleratedOrbit 10 891 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_891 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 891) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_891.1, data_10_891.2] + +/-- Complete interval computation for depth 10, residue 892. -/ +theorem bounds_10_892 : exactInterval 10 892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_892 (m : Nat) : + stoppingTime (2 ^ 10 * m + 892) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_892 : oddCount 892 10 = 6 ∧ acceleratedOrbit 10 892 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_892 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 892) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_892.1, data_10_892.2] + +/-- Complete interval computation for depth 10, residue 893. -/ +theorem bounds_10_893 : exactInterval 10 893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_893 (m : Nat) : + stoppingTime (2 ^ 10 * m + 893) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_893 : oddCount 893 10 = 6 ∧ acceleratedOrbit 10 893 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_893 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 893) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_893.1, data_10_893.2] + +/-- Complete interval computation for depth 10, residue 894. -/ +theorem bounds_10_894 : exactInterval 10 894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_894 (m : Nat) : + stoppingTime (2 ^ 10 * m + 894) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_894 : oddCount 894 10 = 8 ∧ acceleratedOrbit 10 894 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_894 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 894) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_894.1, data_10_894.2] + +/-- Complete interval computation for depth 10, residue 895. -/ +theorem bounds_10_895 : exactInterval 10 895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_895 (m : Nat) : + stoppingTime (2 ^ 10 * m + 895) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_895 : oddCount 895 10 = 8 ∧ acceleratedOrbit 10 895 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_895 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 895) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_895.1, data_10_895.2] + +/-- Complete interval computation for depth 10, residue 896. -/ +theorem bounds_10_896 : exactInterval 10 896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_896 (m : Nat) : + stoppingTime (2 ^ 10 * m + 896) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_896 : oddCount 896 10 = 3 ∧ acceleratedOrbit 10 896 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_896 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 896) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_896.1, data_10_896.2] + +/-- Complete interval computation for depth 10, residue 897. -/ +theorem bounds_10_897 : exactInterval 10 897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_897 (m : Nat) : + stoppingTime (2 ^ 10 * m + 897) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_897 : oddCount 897 10 = 6 ∧ acceleratedOrbit 10 897 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_897 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 897) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_897.1, data_10_897.2] + +/-- Complete interval computation for depth 10, residue 898. -/ +theorem bounds_10_898 : exactInterval 10 898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_898 (m : Nat) : + stoppingTime (2 ^ 10 * m + 898) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_898 : oddCount 898 10 = 5 ∧ acceleratedOrbit 10 898 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_898 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 898) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_898.1, data_10_898.2] + +/-- Complete interval computation for depth 10, residue 899. -/ +theorem bounds_10_899 : exactInterval 10 899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_899 (m : Nat) : + stoppingTime (2 ^ 10 * m + 899) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_899 : oddCount 899 10 = 5 ∧ acceleratedOrbit 10 899 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_899 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 899) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_899.1, data_10_899.2] + +/-- Complete interval computation for depth 10, residue 900. -/ +theorem bounds_10_900 : exactInterval 10 900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_900 (m : Nat) : + stoppingTime (2 ^ 10 * m + 900) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_900 : oddCount 900 10 = 6 ∧ acceleratedOrbit 10 900 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_900 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 900) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_900.1, data_10_900.2] + +/-- Complete interval computation for depth 10, residue 901. -/ +theorem bounds_10_901 : exactInterval 10 901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_901 (m : Nat) : + stoppingTime (2 ^ 10 * m + 901) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_901 : oddCount 901 10 = 6 ∧ acceleratedOrbit 10 901 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_901 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 901) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_901.1, data_10_901.2] + +/-- Complete interval computation for depth 10, residue 902. -/ +theorem bounds_10_902 : exactInterval 10 902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_902 (m : Nat) : + stoppingTime (2 ^ 10 * m + 902) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_902 : oddCount 902 10 = 6 ∧ acceleratedOrbit 10 902 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_902 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 902) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_902.1, data_10_902.2] + +/-- Complete interval computation for depth 10, residue 903. -/ +theorem bounds_10_903 : exactInterval 10 903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_903 (m : Nat) : + stoppingTime (2 ^ 10 * m + 903) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_903 : oddCount 903 10 = 5 ∧ acceleratedOrbit 10 903 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_903 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 903) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_903.1, data_10_903.2] + +/-- Complete interval computation for depth 10, residue 904. -/ +theorem bounds_10_904 : exactInterval 10 904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_904 (m : Nat) : + stoppingTime (2 ^ 10 * m + 904) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_904 : oddCount 904 10 = 2 ∧ acceleratedOrbit 10 904 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_904 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 904) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_904.1, data_10_904.2] + +/-- Complete interval computation for depth 10, residue 905. -/ +theorem bounds_10_905 : exactInterval 10 905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_905 (m : Nat) : + stoppingTime (2 ^ 10 * m + 905) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_905 : oddCount 905 10 = 7 ∧ acceleratedOrbit 10 905 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_905 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 905) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_905.1, data_10_905.2] + +end Collatz.Research.StoppingAtlas.Batch0059 From e5a752862d04749adee3a6345e7f5d3c3293b0bc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:17 +0530 Subject: [PATCH 0060/1001] proof: certify atlas Batch0060 (10:906 to 10:920) --- Collatz/Research/StoppingAtlas/Batch0060.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0060.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0060.lean b/Collatz/Research/StoppingAtlas/Batch0060.lean new file mode 100644 index 00000000..c26dd44a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0060.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0060 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 906. -/ +theorem bounds_10_906 : exactInterval 10 906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_906 (m : Nat) : + stoppingTime (2 ^ 10 * m + 906) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_906 : oddCount 906 10 = 2 ∧ acceleratedOrbit 10 906 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_906 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 906) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_906.1, data_10_906.2] + +/-- Complete interval computation for depth 10, residue 907. -/ +theorem bounds_10_907 : exactInterval 10 907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_907 (m : Nat) : + stoppingTime (2 ^ 10 * m + 907) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_907 : oddCount 907 10 = 7 ∧ acceleratedOrbit 10 907 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_907 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 907) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_907.1, data_10_907.2] + +/-- Complete interval computation for depth 10, residue 908. -/ +theorem bounds_10_908 : exactInterval 10 908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_908 (m : Nat) : + stoppingTime (2 ^ 10 * m + 908) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_908 : oddCount 908 10 = 2 ∧ acceleratedOrbit 10 908 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_908 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 908) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_908.1, data_10_908.2] + +/-- Complete interval computation for depth 10, residue 909. -/ +theorem bounds_10_909 : exactInterval 10 909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_909 (m : Nat) : + stoppingTime (2 ^ 10 * m + 909) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_909 : oddCount 909 10 = 2 ∧ acceleratedOrbit 10 909 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_909 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 909) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_909.1, data_10_909.2] + +/-- Complete interval computation for depth 10, residue 910. -/ +theorem bounds_10_910 : exactInterval 10 910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_910 (m : Nat) : + stoppingTime (2 ^ 10 * m + 910) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_910 : oddCount 910 10 = 6 ∧ acceleratedOrbit 10 910 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_910 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 910) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_910.1, data_10_910.2] + +/-- Complete interval computation for depth 10, residue 911. -/ +theorem bounds_10_911 : exactInterval 10 911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_911 (m : Nat) : + stoppingTime (2 ^ 10 * m + 911) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_911 : oddCount 911 10 = 6 ∧ acceleratedOrbit 10 911 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_911 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 911) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_911.1, data_10_911.2] + +/-- Complete interval computation for depth 10, residue 912. -/ +theorem bounds_10_912 : exactInterval 10 912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_912 (m : Nat) : + stoppingTime (2 ^ 10 * m + 912) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_912 : oddCount 912 10 = 4 ∧ acceleratedOrbit 10 912 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_912 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 912) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_912.1, data_10_912.2] + +/-- Complete interval computation for depth 10, residue 913. -/ +theorem bounds_10_913 : exactInterval 10 913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_913 (m : Nat) : + stoppingTime (2 ^ 10 * m + 913) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_913 : oddCount 913 10 = 5 ∧ acceleratedOrbit 10 913 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_913 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 913) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_913.1, data_10_913.2] + +/-- Complete interval computation for depth 10, residue 914. -/ +theorem bounds_10_914 : exactInterval 10 914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_914 (m : Nat) : + stoppingTime (2 ^ 10 * m + 914) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_914 : oddCount 914 10 = 5 ∧ acceleratedOrbit 10 914 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_914 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 914) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_914.1, data_10_914.2] + +/-- Complete interval computation for depth 10, residue 915. -/ +theorem bounds_10_915 : exactInterval 10 915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_915 (m : Nat) : + stoppingTime (2 ^ 10 * m + 915) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_915 : oddCount 915 10 = 5 ∧ acceleratedOrbit 10 915 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_915 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 915) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_915.1, data_10_915.2] + +/-- Complete interval computation for depth 10, residue 916. -/ +theorem bounds_10_916 : exactInterval 10 916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_916 (m : Nat) : + stoppingTime (2 ^ 10 * m + 916) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_916 : oddCount 916 10 = 4 ∧ acceleratedOrbit 10 916 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_916 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 916) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_916.1, data_10_916.2] + +/-- Complete interval computation for depth 10, residue 917. -/ +theorem bounds_10_917 : exactInterval 10 917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_917 (m : Nat) : + stoppingTime (2 ^ 10 * m + 917) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_917 : oddCount 917 10 = 4 ∧ acceleratedOrbit 10 917 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_917 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 917) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_917.1, data_10_917.2] + +/-- Complete interval computation for depth 10, residue 918. -/ +theorem bounds_10_918 : exactInterval 10 918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_918 (m : Nat) : + stoppingTime (2 ^ 10 * m + 918) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_918 : oddCount 918 10 = 4 ∧ acceleratedOrbit 10 918 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_918 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 918) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_918.1, data_10_918.2] + +/-- Complete interval computation for depth 10, residue 919. -/ +theorem bounds_10_919 : exactInterval 10 919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_919 (m : Nat) : + stoppingTime (2 ^ 10 * m + 919) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_919 : oddCount 919 10 = 4 ∧ acceleratedOrbit 10 919 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_919 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 919) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_919.1, data_10_919.2] + +/-- Complete interval computation for depth 10, residue 920. -/ +theorem bounds_10_920 : exactInterval 10 920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_920 (m : Nat) : + stoppingTime (2 ^ 10 * m + 920) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_920 : oddCount 920 10 = 4 ∧ acceleratedOrbit 10 920 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_920 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 920) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_920.1, data_10_920.2] + +end Collatz.Research.StoppingAtlas.Batch0060 From 4644c9ef8943eaade26b8950576ba9c935ec24ca Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:18 +0530 Subject: [PATCH 0061/1001] proof: certify atlas Batch0061 (10:921 to 10:935) --- Collatz/Research/StoppingAtlas/Batch0061.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0061.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0061.lean b/Collatz/Research/StoppingAtlas/Batch0061.lean new file mode 100644 index 00000000..39c8c773 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0061.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0061 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 921. -/ +theorem bounds_10_921 : exactInterval 10 921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_921 (m : Nat) : + stoppingTime (2 ^ 10 * m + 921) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_921 : oddCount 921 10 = 4 ∧ acceleratedOrbit 10 921 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_921 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 921) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_921.1, data_10_921.2] + +/-- Complete interval computation for depth 10, residue 922. -/ +theorem bounds_10_922 : exactInterval 10 922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_922 (m : Nat) : + stoppingTime (2 ^ 10 * m + 922) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_922 : oddCount 922 10 = 4 ∧ acceleratedOrbit 10 922 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_922 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 922) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_922.1, data_10_922.2] + +/-- Complete interval computation for depth 10, residue 923. -/ +theorem bounds_10_923 : exactInterval 10 923 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_923 (m : Nat) : + stoppingTime (2 ^ 10 * m + 923) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_923 : oddCount 923 10 = 6 ∧ acceleratedOrbit 10 923 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_923 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 923) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_923.1, data_10_923.2] + +/-- Complete interval computation for depth 10, residue 924. -/ +theorem bounds_10_924 : exactInterval 10 924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_924 (m : Nat) : + stoppingTime (2 ^ 10 * m + 924) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_924 : oddCount 924 10 = 6 ∧ acceleratedOrbit 10 924 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_924 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 924) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_924.1, data_10_924.2] + +/-- Complete interval computation for depth 10, residue 925. -/ +theorem bounds_10_925 : exactInterval 10 925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_925 (m : Nat) : + stoppingTime (2 ^ 10 * m + 925) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_925 : oddCount 925 10 = 6 ∧ acceleratedOrbit 10 925 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_925 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 925) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_925.1, data_10_925.2] + +/-- Complete interval computation for depth 10, residue 926. -/ +theorem bounds_10_926 : exactInterval 10 926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_926 (m : Nat) : + stoppingTime (2 ^ 10 * m + 926) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_926 : oddCount 926 10 = 6 ∧ acceleratedOrbit 10 926 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_926 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 926) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_926.1, data_10_926.2] + +/-- Complete interval computation for depth 10, residue 927. -/ +theorem bounds_10_927 : exactInterval 10 927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_927 (m : Nat) : + stoppingTime (2 ^ 10 * m + 927) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_927 : oddCount 927 10 = 7 ∧ acceleratedOrbit 10 927 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_927 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 927) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_927.1, data_10_927.2] + +/-- Complete interval computation for depth 10, residue 928. -/ +theorem bounds_10_928 : exactInterval 10 928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_928 (m : Nat) : + stoppingTime (2 ^ 10 * m + 928) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_928 : oddCount 928 10 = 3 ∧ acceleratedOrbit 10 928 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_928 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 928) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_928.1, data_10_928.2] + +/-- Complete interval computation for depth 10, residue 929. -/ +theorem bounds_10_929 : exactInterval 10 929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_929 (m : Nat) : + stoppingTime (2 ^ 10 * m + 929) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_929 : oddCount 929 10 = 5 ∧ acceleratedOrbit 10 929 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_929 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 929) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_929.1, data_10_929.2] + +/-- Complete interval computation for depth 10, residue 930. -/ +theorem bounds_10_930 : exactInterval 10 930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_930 (m : Nat) : + stoppingTime (2 ^ 10 * m + 930) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_930 : oddCount 930 10 = 4 ∧ acceleratedOrbit 10 930 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_930 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 930) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_930.1, data_10_930.2] + +/-- Complete interval computation for depth 10, residue 931. -/ +theorem bounds_10_931 : exactInterval 10 931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_931 (m : Nat) : + stoppingTime (2 ^ 10 * m + 931) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_931 : oddCount 931 10 = 4 ∧ acceleratedOrbit 10 931 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_931 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 931) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_931.1, data_10_931.2] + +/-- Complete interval computation for depth 10, residue 932. -/ +theorem bounds_10_932 : exactInterval 10 932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_932 (m : Nat) : + stoppingTime (2 ^ 10 * m + 932) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_932 : oddCount 932 10 = 6 ∧ acceleratedOrbit 10 932 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_932 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 932) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_932.1, data_10_932.2] + +/-- Complete interval computation for depth 10, residue 933. -/ +theorem bounds_10_933 : exactInterval 10 933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_933 (m : Nat) : + stoppingTime (2 ^ 10 * m + 933) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_933 : oddCount 933 10 = 6 ∧ acceleratedOrbit 10 933 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_933 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 933) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_933.1, data_10_933.2] + +/-- Complete interval computation for depth 10, residue 934. -/ +theorem bounds_10_934 : exactInterval 10 934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_934 (m : Nat) : + stoppingTime (2 ^ 10 * m + 934) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_934 : oddCount 934 10 = 6 ∧ acceleratedOrbit 10 934 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_934 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 934) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_934.1, data_10_934.2] + +/-- Complete interval computation for depth 10, residue 935. -/ +theorem bounds_10_935 : exactInterval 10 935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_935 (m : Nat) : + stoppingTime (2 ^ 10 * m + 935) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_935 : oddCount 935 10 = 7 ∧ acceleratedOrbit 10 935 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_935 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 935) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_935.1, data_10_935.2] + +end Collatz.Research.StoppingAtlas.Batch0061 From e821ef3d203791431340da49c4a5cfdfd390eaa6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:18 +0530 Subject: [PATCH 0062/1001] proof: certify atlas Batch0062 (10:936 to 10:951) --- Collatz/Research/StoppingAtlas/Batch0062.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0062.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0062.lean b/Collatz/Research/StoppingAtlas/Batch0062.lean new file mode 100644 index 00000000..484e1299 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0062.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0062 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 936. -/ +theorem bounds_10_936 : exactInterval 10 936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_936 (m : Nat) : + stoppingTime (2 ^ 10 * m + 936) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_936 : oddCount 936 10 = 3 ∧ acceleratedOrbit 10 936 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_936 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 936) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_936.1, data_10_936.2] + +/-- Complete interval computation for depth 10, residue 937. -/ +theorem bounds_10_937 : exactInterval 10 937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_937 (m : Nat) : + stoppingTime (2 ^ 10 * m + 937) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_937 : oddCount 937 10 = 8 ∧ acceleratedOrbit 10 937 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_937 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 937) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_937.1, data_10_937.2] + +/-- Complete interval computation for depth 10, residue 938. -/ +theorem bounds_10_938 : exactInterval 10 938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_938 (m : Nat) : + stoppingTime (2 ^ 10 * m + 938) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_938 : oddCount 938 10 = 3 ∧ acceleratedOrbit 10 938 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_938 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 938) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_938.1, data_10_938.2] + +/-- Complete interval computation for depth 10, residue 939. -/ +theorem bounds_10_939 : exactInterval 10 939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_939 (m : Nat) : + stoppingTime (2 ^ 10 * m + 939) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_939 : oddCount 939 10 = 6 ∧ acceleratedOrbit 10 939 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_939 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 939) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_939.1, data_10_939.2] + +/-- Complete interval computation for depth 10, residue 940. -/ +theorem bounds_10_940 : exactInterval 10 940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_940 (m : Nat) : + stoppingTime (2 ^ 10 * m + 940) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_940 : oddCount 940 10 = 6 ∧ acceleratedOrbit 10 940 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_940 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 940) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_940.1, data_10_940.2] + +/-- Complete interval computation for depth 10, residue 941. -/ +theorem bounds_10_941 : exactInterval 10 941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_941 (m : Nat) : + stoppingTime (2 ^ 10 * m + 941) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_941 : oddCount 941 10 = 6 ∧ acceleratedOrbit 10 941 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_941 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 941) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_941.1, data_10_941.2] + +/-- Complete interval computation for depth 10, residue 942. -/ +theorem bounds_10_942 : exactInterval 10 942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_942 (m : Nat) : + stoppingTime (2 ^ 10 * m + 942) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_942 : oddCount 942 10 = 6 ∧ acceleratedOrbit 10 942 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_942 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 942) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_942.1, data_10_942.2] + +/-- Complete interval computation for depth 10, residue 943. -/ +theorem bounds_10_943 : exactInterval 10 943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_943 (m : Nat) : + stoppingTime (2 ^ 10 * m + 943) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_943 : oddCount 943 10 = 5 ∧ acceleratedOrbit 10 943 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_943 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 943) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_943.1, data_10_943.2] + +/-- Complete interval computation for depth 10, residue 944. -/ +theorem bounds_10_944 : exactInterval 10 944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_944 (m : Nat) : + stoppingTime (2 ^ 10 * m + 944) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_944 : oddCount 944 10 = 4 ∧ acceleratedOrbit 10 944 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_944 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 944) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_944.1, data_10_944.2] + +/-- Complete interval computation for depth 10, residue 945. -/ +theorem bounds_10_945 : exactInterval 10 945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_945 (m : Nat) : + stoppingTime (2 ^ 10 * m + 945) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_945 : oddCount 945 10 = 3 ∧ acceleratedOrbit 10 945 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_945 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 945) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_945.1, data_10_945.2] + +/-- Complete interval computation for depth 10, residue 946. -/ +theorem bounds_10_946 : exactInterval 10 946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_946 (m : Nat) : + stoppingTime (2 ^ 10 * m + 946) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_946 : oddCount 946 10 = 3 ∧ acceleratedOrbit 10 946 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_946 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 946) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_946.1, data_10_946.2] + +/-- Complete interval computation for depth 10, residue 947. -/ +theorem bounds_10_947 : exactInterval 10 947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_947 (m : Nat) : + stoppingTime (2 ^ 10 * m + 947) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_947 : oddCount 947 10 = 3 ∧ acceleratedOrbit 10 947 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_947 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 947) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_947.1, data_10_947.2] + +/-- Complete interval computation for depth 10, residue 948. -/ +theorem bounds_10_948 : exactInterval 10 948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_948 (m : Nat) : + stoppingTime (2 ^ 10 * m + 948) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_948 : oddCount 948 10 = 4 ∧ acceleratedOrbit 10 948 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_948 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 948) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_948.1, data_10_948.2] + +/-- Complete interval computation for depth 10, residue 949. -/ +theorem bounds_10_949 : exactInterval 10 949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_949 (m : Nat) : + stoppingTime (2 ^ 10 * m + 949) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_949 : oddCount 949 10 = 4 ∧ acceleratedOrbit 10 949 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_949 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 949) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_949.1, data_10_949.2] + +/-- Complete interval computation for depth 10, residue 950. -/ +theorem bounds_10_950 : exactInterval 10 950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_950 (m : Nat) : + stoppingTime (2 ^ 10 * m + 950) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_950 : oddCount 950 10 = 5 ∧ acceleratedOrbit 10 950 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_950 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 950) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_950.1, data_10_950.2] + +/-- Complete interval computation for depth 10, residue 951. -/ +theorem bounds_10_951 : exactInterval 10 951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_951 (m : Nat) : + stoppingTime (2 ^ 10 * m + 951) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_951 : oddCount 951 10 = 5 ∧ acceleratedOrbit 10 951 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_951 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 951) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_951.1, data_10_951.2] + +end Collatz.Research.StoppingAtlas.Batch0062 From bf170b65bf0a3cfb2911d1424aa26cdfa8f623fa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:18 +0530 Subject: [PATCH 0063/1001] proof: certify atlas Batch0063 (10:952 to 10:966) --- Collatz/Research/StoppingAtlas/Batch0063.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0063.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0063.lean b/Collatz/Research/StoppingAtlas/Batch0063.lean new file mode 100644 index 00000000..417c55b9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0063.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0063 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 952. -/ +theorem bounds_10_952 : exactInterval 10 952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_952 (m : Nat) : + stoppingTime (2 ^ 10 * m + 952) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_952 : oddCount 952 10 = 4 ∧ acceleratedOrbit 10 952 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_952 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 952) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_952.1, data_10_952.2] + +/-- Complete interval computation for depth 10, residue 953. -/ +theorem bounds_10_953 : exactInterval 10 953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_953 (m : Nat) : + stoppingTime (2 ^ 10 * m + 953) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_953 : oddCount 953 10 = 5 ∧ acceleratedOrbit 10 953 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_953 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 953) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_953.1, data_10_953.2] + +/-- Complete interval computation for depth 10, residue 954. -/ +theorem bounds_10_954 : exactInterval 10 954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_954 (m : Nat) : + stoppingTime (2 ^ 10 * m + 954) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_954 : oddCount 954 10 = 4 ∧ acceleratedOrbit 10 954 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_954 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 954) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_954.1, data_10_954.2] + +/-- Complete interval computation for depth 10, residue 955. -/ +theorem bounds_10_955 : exactInterval 10 955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_955 (m : Nat) : + stoppingTime (2 ^ 10 * m + 955) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_955 : oddCount 955 10 = 5 ∧ acceleratedOrbit 10 955 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_955 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 955) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_955.1, data_10_955.2] + +/-- Complete interval computation for depth 10, residue 956. -/ +theorem bounds_10_956 : exactInterval 10 956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_956 (m : Nat) : + stoppingTime (2 ^ 10 * m + 956) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_956 : oddCount 956 10 = 7 ∧ acceleratedOrbit 10 956 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_956 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 956) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_956.1, data_10_956.2] + +/-- Complete interval computation for depth 10, residue 957. -/ +theorem bounds_10_957 : exactInterval 10 957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_957 (m : Nat) : + stoppingTime (2 ^ 10 * m + 957) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_957 : oddCount 957 10 = 7 ∧ acceleratedOrbit 10 957 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_957 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 957) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_957.1, data_10_957.2] + +/-- Complete interval computation for depth 10, residue 958. -/ +theorem bounds_10_958 : exactInterval 10 958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_958 (m : Nat) : + stoppingTime (2 ^ 10 * m + 958) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_958 : oddCount 958 10 = 7 ∧ acceleratedOrbit 10 958 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_958 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 958) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_958.1, data_10_958.2] + +/-- Complete interval computation for depth 10, residue 959. -/ +theorem bounds_10_959 : exactInterval 10 959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_959 (m : Nat) : + stoppingTime (2 ^ 10 * m + 959) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_959 : oddCount 959 10 = 8 ∧ acceleratedOrbit 10 959 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_959 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 959) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_959.1, data_10_959.2] + +/-- Complete interval computation for depth 10, residue 960. -/ +theorem bounds_10_960 : exactInterval 10 960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_960 (m : Nat) : + stoppingTime (2 ^ 10 * m + 960) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_960 : oddCount 960 10 = 4 ∧ acceleratedOrbit 10 960 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_960 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 960) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_960.1, data_10_960.2] + +/-- Complete interval computation for depth 10, residue 961. -/ +theorem bounds_10_961 : exactInterval 10 961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_961 (m : Nat) : + stoppingTime (2 ^ 10 * m + 961) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_961 : oddCount 961 10 = 5 ∧ acceleratedOrbit 10 961 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_961 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 961) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_961.1, data_10_961.2] + +/-- Complete interval computation for depth 10, residue 962. -/ +theorem bounds_10_962 : exactInterval 10 962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_962 (m : Nat) : + stoppingTime (2 ^ 10 * m + 962) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_962 : oddCount 962 10 = 6 ∧ acceleratedOrbit 10 962 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_962 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 962) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_962.1, data_10_962.2] + +/-- Complete interval computation for depth 10, residue 963. -/ +theorem bounds_10_963 : exactInterval 10 963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_963 (m : Nat) : + stoppingTime (2 ^ 10 * m + 963) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_963 : oddCount 963 10 = 6 ∧ acceleratedOrbit 10 963 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_963 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 963) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_963.1, data_10_963.2] + +/-- Complete interval computation for depth 10, residue 964. -/ +theorem bounds_10_964 : exactInterval 10 964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_964 (m : Nat) : + stoppingTime (2 ^ 10 * m + 964) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_964 : oddCount 964 10 = 3 ∧ acceleratedOrbit 10 964 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_964 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 964) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_964.1, data_10_964.2] + +/-- Complete interval computation for depth 10, residue 965. -/ +theorem bounds_10_965 : exactInterval 10 965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_965 (m : Nat) : + stoppingTime (2 ^ 10 * m + 965) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_965 : oddCount 965 10 = 3 ∧ acceleratedOrbit 10 965 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_965 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 965) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_965.1, data_10_965.2] + +/-- Complete interval computation for depth 10, residue 966. -/ +theorem bounds_10_966 : exactInterval 10 966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_966 (m : Nat) : + stoppingTime (2 ^ 10 * m + 966) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_966 : oddCount 966 10 = 3 ∧ acceleratedOrbit 10 966 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_966 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 966) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_966.1, data_10_966.2] + +end Collatz.Research.StoppingAtlas.Batch0063 From bf1a428123762a1299e7688b48834fe6e9322c62 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:19 +0530 Subject: [PATCH 0064/1001] proof: certify atlas Batch0064 (10:967 to 10:982) --- Collatz/Research/StoppingAtlas/Batch0064.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0064.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0064.lean b/Collatz/Research/StoppingAtlas/Batch0064.lean new file mode 100644 index 00000000..2a25b33e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0064.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0064 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 967. -/ +theorem bounds_10_967 : exactInterval 10 967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_967 (m : Nat) : + stoppingTime (2 ^ 10 * m + 967) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_967 : oddCount 967 10 = 7 ∧ acceleratedOrbit 10 967 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_967 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 967) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_967.1, data_10_967.2] + +/-- Complete interval computation for depth 10, residue 968. -/ +theorem bounds_10_968 : exactInterval 10 968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_968 (m : Nat) : + stoppingTime (2 ^ 10 * m + 968) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_968 : oddCount 968 10 = 5 ∧ acceleratedOrbit 10 968 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_968 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 968) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_968.1, data_10_968.2] + +/-- Complete interval computation for depth 10, residue 969. -/ +theorem bounds_10_969 : exactInterval 10 969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_969 (m : Nat) : + stoppingTime (2 ^ 10 * m + 969) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_969 : oddCount 969 10 = 6 ∧ acceleratedOrbit 10 969 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_969 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 969) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_969.1, data_10_969.2] + +/-- Complete interval computation for depth 10, residue 970. -/ +theorem bounds_10_970 : exactInterval 10 970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_970 (m : Nat) : + stoppingTime (2 ^ 10 * m + 970) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_970 : oddCount 970 10 = 5 ∧ acceleratedOrbit 10 970 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_970 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 970) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_970.1, data_10_970.2] + +/-- Complete interval computation for depth 10, residue 971. -/ +theorem bounds_10_971 : exactInterval 10 971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_971 (m : Nat) : + stoppingTime (2 ^ 10 * m + 971) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_971 : oddCount 971 10 = 4 ∧ acceleratedOrbit 10 971 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_971 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 971) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_971.1, data_10_971.2] + +/-- Complete interval computation for depth 10, residue 972. -/ +theorem bounds_10_972 : exactInterval 10 972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_972 (m : Nat) : + stoppingTime (2 ^ 10 * m + 972) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_972 : oddCount 972 10 = 5 ∧ acceleratedOrbit 10 972 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_972 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 972) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_972.1, data_10_972.2] + +/-- Complete interval computation for depth 10, residue 973. -/ +theorem bounds_10_973 : exactInterval 10 973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_973 (m : Nat) : + stoppingTime (2 ^ 10 * m + 973) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_973 : oddCount 973 10 = 5 ∧ acceleratedOrbit 10 973 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_973 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 973) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_973.1, data_10_973.2] + +/-- Complete interval computation for depth 10, residue 974. -/ +theorem bounds_10_974 : exactInterval 10 974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_974 (m : Nat) : + stoppingTime (2 ^ 10 * m + 974) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_974 : oddCount 974 10 = 6 ∧ acceleratedOrbit 10 974 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_974 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 974) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_974.1, data_10_974.2] + +/-- Complete interval computation for depth 10, residue 975. -/ +theorem bounds_10_975 : exactInterval 10 975 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_975 (m : Nat) : + stoppingTime (2 ^ 10 * m + 975) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_975 : oddCount 975 10 = 6 ∧ acceleratedOrbit 10 975 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_975 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 975) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_975.1, data_10_975.2] + +/-- Complete interval computation for depth 10, residue 976. -/ +theorem bounds_10_976 : exactInterval 10 976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_976 (m : Nat) : + stoppingTime (2 ^ 10 * m + 976) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_976 : oddCount 976 10 = 4 ∧ acceleratedOrbit 10 976 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_976 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 976) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_976.1, data_10_976.2] + +/-- Complete interval computation for depth 10, residue 977. -/ +theorem bounds_10_977 : exactInterval 10 977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_977 (m : Nat) : + stoppingTime (2 ^ 10 * m + 977) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_977 : oddCount 977 10 = 5 ∧ acceleratedOrbit 10 977 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_977 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 977) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_977.1, data_10_977.2] + +/-- Complete interval computation for depth 10, residue 978. -/ +theorem bounds_10_978 : exactInterval 10 978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_978 (m : Nat) : + stoppingTime (2 ^ 10 * m + 978) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_978 : oddCount 978 10 = 7 ∧ acceleratedOrbit 10 978 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_978 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 978) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_978.1, data_10_978.2] + +/-- Complete interval computation for depth 10, residue 979. -/ +theorem bounds_10_979 : exactInterval 10 979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_979 (m : Nat) : + stoppingTime (2 ^ 10 * m + 979) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_979 : oddCount 979 10 = 7 ∧ acceleratedOrbit 10 979 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_979 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 979) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_979.1, data_10_979.2] + +/-- Complete interval computation for depth 10, residue 980. -/ +theorem bounds_10_980 : exactInterval 10 980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_980 (m : Nat) : + stoppingTime (2 ^ 10 * m + 980) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_980 : oddCount 980 10 = 4 ∧ acceleratedOrbit 10 980 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_980 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 980) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_980.1, data_10_980.2] + +/-- Complete interval computation for depth 10, residue 981. -/ +theorem bounds_10_981 : exactInterval 10 981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_981 (m : Nat) : + stoppingTime (2 ^ 10 * m + 981) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_981 : oddCount 981 10 = 4 ∧ acceleratedOrbit 10 981 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_981 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 981) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_981.1, data_10_981.2] + +/-- Complete interval computation for depth 10, residue 982. -/ +theorem bounds_10_982 : exactInterval 10 982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_982 (m : Nat) : + stoppingTime (2 ^ 10 * m + 982) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_982 : oddCount 982 10 = 7 ∧ acceleratedOrbit 10 982 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_982 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 982) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_982.1, data_10_982.2] + +end Collatz.Research.StoppingAtlas.Batch0064 From 3b536048c7c79a80c742c4e30e35642636214890 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:19 +0530 Subject: [PATCH 0065/1001] proof: certify atlas Batch0065 (10:983 to 10:997) --- Collatz/Research/StoppingAtlas/Batch0065.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0065.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0065.lean b/Collatz/Research/StoppingAtlas/Batch0065.lean new file mode 100644 index 00000000..a00d96e2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0065.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0065 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 983. -/ +theorem bounds_10_983 : exactInterval 10 983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_983 (m : Nat) : + stoppingTime (2 ^ 10 * m + 983) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_983 : oddCount 983 10 = 7 ∧ acceleratedOrbit 10 983 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_983 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 983) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_983.1, data_10_983.2] + +/-- Complete interval computation for depth 10, residue 984. -/ +theorem bounds_10_984 : exactInterval 10 984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_984 (m : Nat) : + stoppingTime (2 ^ 10 * m + 984) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_984 : oddCount 984 10 = 5 ∧ acceleratedOrbit 10 984 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_984 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 984) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_984.1, data_10_984.2] + +/-- Complete interval computation for depth 10, residue 985. -/ +theorem bounds_10_985 : exactInterval 10 985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_985 (m : Nat) : + stoppingTime (2 ^ 10 * m + 985) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_985 : oddCount 985 10 = 3 ∧ acceleratedOrbit 10 985 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_985 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 985) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_985.1, data_10_985.2] + +/-- Complete interval computation for depth 10, residue 986. -/ +theorem bounds_10_986 : exactInterval 10 986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_986 (m : Nat) : + stoppingTime (2 ^ 10 * m + 986) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_986 : oddCount 986 10 = 5 ∧ acceleratedOrbit 10 986 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_986 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 986) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_986.1, data_10_986.2] + +/-- Complete interval computation for depth 10, residue 987. -/ +theorem bounds_10_987 : exactInterval 10 987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_987 (m : Nat) : + stoppingTime (2 ^ 10 * m + 987) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_987 : oddCount 987 10 = 6 ∧ acceleratedOrbit 10 987 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_987 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 987) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_987.1, data_10_987.2] + +/-- Complete interval computation for depth 10, residue 988. -/ +theorem bounds_10_988 : exactInterval 10 988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_988 (m : Nat) : + stoppingTime (2 ^ 10 * m + 988) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_988 : oddCount 988 10 = 5 ∧ acceleratedOrbit 10 988 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_988 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 988) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_988.1, data_10_988.2] + +/-- Complete interval computation for depth 10, residue 989. -/ +theorem bounds_10_989 : exactInterval 10 989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_989 (m : Nat) : + stoppingTime (2 ^ 10 * m + 989) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_989 : oddCount 989 10 = 5 ∧ acceleratedOrbit 10 989 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_989 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 989) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_989.1, data_10_989.2] + +/-- Complete interval computation for depth 10, residue 990. -/ +theorem bounds_10_990 : exactInterval 10 990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_990 (m : Nat) : + stoppingTime (2 ^ 10 * m + 990) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_990 : oddCount 990 10 = 7 ∧ acceleratedOrbit 10 990 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_990 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 990) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_990.1, data_10_990.2] + +/-- Complete interval computation for depth 10, residue 991. -/ +theorem bounds_10_991 : exactInterval 10 991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_991 (m : Nat) : + stoppingTime (2 ^ 10 * m + 991) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_991 : oddCount 991 10 = 7 ∧ acceleratedOrbit 10 991 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_991 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 991) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_991.1, data_10_991.2] + +/-- Complete interval computation for depth 10, residue 992. -/ +theorem bounds_10_992 : exactInterval 10 992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_992 (m : Nat) : + stoppingTime (2 ^ 10 * m + 992) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_992 : oddCount 992 10 = 5 ∧ acceleratedOrbit 10 992 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_992 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 992) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_992.1, data_10_992.2] + +/-- Complete interval computation for depth 10, residue 993. -/ +theorem bounds_10_993 : exactInterval 10 993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_993 (m : Nat) : + stoppingTime (2 ^ 10 * m + 993) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_993 : oddCount 993 10 = 7 ∧ acceleratedOrbit 10 993 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_993 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 993) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_993.1, data_10_993.2] + +/-- Complete interval computation for depth 10, residue 994. -/ +theorem bounds_10_994 : exactInterval 10 994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_994 (m : Nat) : + stoppingTime (2 ^ 10 * m + 994) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_994 : oddCount 994 10 = 4 ∧ acceleratedOrbit 10 994 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_994 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 994) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_994.1, data_10_994.2] + +/-- Complete interval computation for depth 10, residue 995. -/ +theorem bounds_10_995 : exactInterval 10 995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_995 (m : Nat) : + stoppingTime (2 ^ 10 * m + 995) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_995 : oddCount 995 10 = 4 ∧ acceleratedOrbit 10 995 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_995 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 995) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_995.1, data_10_995.2] + +/-- Complete interval computation for depth 10, residue 996. -/ +theorem bounds_10_996 : exactInterval 10 996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_996 (m : Nat) : + stoppingTime (2 ^ 10 * m + 996) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_996 : oddCount 996 10 = 5 ∧ acceleratedOrbit 10 996 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_996 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 996) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_996.1, data_10_996.2] + +/-- Complete interval computation for depth 10, residue 997. -/ +theorem bounds_10_997 : exactInterval 10 997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_997 (m : Nat) : + stoppingTime (2 ^ 10 * m + 997) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_997 : oddCount 997 10 = 5 ∧ acceleratedOrbit 10 997 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_997 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 997) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_997.1, data_10_997.2] + +end Collatz.Research.StoppingAtlas.Batch0065 From 2a100a189921f8b987a3035cc4ecc40164ce1823 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:20 +0530 Subject: [PATCH 0066/1001] proof: certify atlas Batch0066 (10:998 to 10:1012) --- Collatz/Research/StoppingAtlas/Batch0066.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0066.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0066.lean b/Collatz/Research/StoppingAtlas/Batch0066.lean new file mode 100644 index 00000000..167f45e7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0066.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0066 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 998. -/ +theorem bounds_10_998 : exactInterval 10 998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_998 (m : Nat) : + stoppingTime (2 ^ 10 * m + 998) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_998 : oddCount 998 10 = 5 ∧ acceleratedOrbit 10 998 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_998 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 998) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_998.1, data_10_998.2] + +/-- Complete interval computation for depth 10, residue 999. -/ +theorem bounds_10_999 : exactInterval 10 999 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_999 (m : Nat) : + stoppingTime (2 ^ 10 * m + 999) 10 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_999 : oddCount 999 10 = 6 ∧ acceleratedOrbit 10 999 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_999 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 999) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_999.1, data_10_999.2] + +/-- Complete interval computation for depth 10, residue 1000. -/ +theorem bounds_10_1000 : exactInterval 10 1000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1000 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1000) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1000 : oddCount 1000 10 = 5 ∧ acceleratedOrbit 10 1000 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1000 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1000) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1000.1, data_10_1000.2] + +/-- Complete interval computation for depth 10, residue 1001. -/ +theorem bounds_10_1001 : exactInterval 10 1001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1001 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1001) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1001 : oddCount 1001 10 = 8 ∧ acceleratedOrbit 10 1001 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1001 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1001) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1001.1, data_10_1001.2] + +/-- Complete interval computation for depth 10, residue 1002. -/ +theorem bounds_10_1002 : exactInterval 10 1002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1002 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1002) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1002 : oddCount 1002 10 = 5 ∧ acceleratedOrbit 10 1002 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1002 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1002) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1002.1, data_10_1002.2] + +/-- Complete interval computation for depth 10, residue 1003. -/ +theorem bounds_10_1003 : exactInterval 10 1003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1003 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1003) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1003 : oddCount 1003 10 = 7 ∧ acceleratedOrbit 10 1003 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1003 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1003) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1003.1, data_10_1003.2] + +/-- Complete interval computation for depth 10, residue 1004. -/ +theorem bounds_10_1004 : exactInterval 10 1004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1004 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1004) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1004 : oddCount 1004 10 = 6 ∧ acceleratedOrbit 10 1004 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1004 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1004) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1004.1, data_10_1004.2] + +/-- Complete interval computation for depth 10, residue 1005. -/ +theorem bounds_10_1005 : exactInterval 10 1005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1005 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1005) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1005 : oddCount 1005 10 = 6 ∧ acceleratedOrbit 10 1005 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1005 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1005) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1005.1, data_10_1005.2] + +/-- Complete interval computation for depth 10, residue 1006. -/ +theorem bounds_10_1006 : exactInterval 10 1006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1006 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1006) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1006 : oddCount 1006 10 = 6 ∧ acceleratedOrbit 10 1006 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1006 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1006) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1006.1, data_10_1006.2] + +/-- Complete interval computation for depth 10, residue 1007. -/ +theorem bounds_10_1007 : exactInterval 10 1007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1007 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1007) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1007 : oddCount 1007 10 = 7 ∧ acceleratedOrbit 10 1007 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1007 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1007) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1007.1, data_10_1007.2] + +/-- Complete interval computation for depth 10, residue 1008. -/ +theorem bounds_10_1008 : exactInterval 10 1008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1008 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1008) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1008 : oddCount 1008 10 = 6 ∧ acceleratedOrbit 10 1008 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1008 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1008) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1008.1, data_10_1008.2] + +/-- Complete interval computation for depth 10, residue 1009. -/ +theorem bounds_10_1009 : exactInterval 10 1009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1009 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1009) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1009 : oddCount 1009 10 = 5 ∧ acceleratedOrbit 10 1009 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1009 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1009) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1009.1, data_10_1009.2] + +/-- Complete interval computation for depth 10, residue 1010. -/ +theorem bounds_10_1010 : exactInterval 10 1010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1010 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1010) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1010 : oddCount 1010 10 = 6 ∧ acceleratedOrbit 10 1010 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1010 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1010) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1010.1, data_10_1010.2] + +/-- Complete interval computation for depth 10, residue 1011. -/ +theorem bounds_10_1011 : exactInterval 10 1011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1011 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1011) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1011 : oddCount 1011 10 = 6 ∧ acceleratedOrbit 10 1011 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1011 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1011) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1011.1, data_10_1011.2] + +/-- Complete interval computation for depth 10, residue 1012. -/ +theorem bounds_10_1012 : exactInterval 10 1012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1012 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1012) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1012 : oddCount 1012 10 = 6 ∧ acceleratedOrbit 10 1012 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1012 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1012) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1012.1, data_10_1012.2] + +end Collatz.Research.StoppingAtlas.Batch0066 From 8591402029b458756a1189272e8a0d1ed4ed3341 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:20 +0530 Subject: [PATCH 0067/1001] proof: certify atlas Batch0067 (10:1013 to 11:4) --- Collatz/Research/StoppingAtlas/Batch0067.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0067.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0067.lean b/Collatz/Research/StoppingAtlas/Batch0067.lean new file mode 100644 index 00000000..8773b3f2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0067.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0067 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 10, residue 1013. -/ +theorem bounds_10_1013 : exactInterval 10 1013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1013 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1013) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1013 : oddCount 1013 10 = 6 ∧ acceleratedOrbit 10 1013 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1013 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1013) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1013.1, data_10_1013.2] + +/-- Complete interval computation for depth 10, residue 1014. -/ +theorem bounds_10_1014 : exactInterval 10 1014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1014 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1014) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1014 : oddCount 1014 10 = 6 ∧ acceleratedOrbit 10 1014 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1014 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1014) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1014.1, data_10_1014.2] + +/-- Complete interval computation for depth 10, residue 1015. -/ +theorem bounds_10_1015 : exactInterval 10 1015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1015 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1015) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1015 : oddCount 1015 10 = 6 ∧ acceleratedOrbit 10 1015 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1015 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1015) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1015.1, data_10_1015.2] + +/-- Complete interval computation for depth 10, residue 1016. -/ +theorem bounds_10_1016 : exactInterval 10 1016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1016 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1016) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1016 : oddCount 1016 10 = 7 ∧ acceleratedOrbit 10 1016 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1016 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1016) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1016.1, data_10_1016.2] + +/-- Complete interval computation for depth 10, residue 1017. -/ +theorem bounds_10_1017 : exactInterval 10 1017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1017 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1017) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1017 : oddCount 1017 10 = 7 ∧ acceleratedOrbit 10 1017 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1017 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1017) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1017.1, data_10_1017.2] + +/-- Complete interval computation for depth 10, residue 1018. -/ +theorem bounds_10_1018 : exactInterval 10 1018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1018 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1018) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1018 : oddCount 1018 10 = 7 ∧ acceleratedOrbit 10 1018 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1018 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1018) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1018.1, data_10_1018.2] + +/-- Complete interval computation for depth 10, residue 1019. -/ +theorem bounds_10_1019 : exactInterval 10 1019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1019 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1019) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1019 : oddCount 1019 10 = 7 ∧ acceleratedOrbit 10 1019 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1019 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1019) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1019.1, data_10_1019.2] + +/-- Complete interval computation for depth 10, residue 1020. -/ +theorem bounds_10_1020 : exactInterval 10 1020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1020 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1020) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1020 : oddCount 1020 10 = 8 ∧ acceleratedOrbit 10 1020 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1020 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1020) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1020.1, data_10_1020.2] + +/-- Complete interval computation for depth 10, residue 1021. -/ +theorem bounds_10_1021 : exactInterval 10 1021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1021 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1021) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1021 : oddCount 1021 10 = 8 ∧ acceleratedOrbit 10 1021 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1021 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1021) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1021.1, data_10_1021.2] + +/-- Complete interval computation for depth 10, residue 1022. -/ +theorem bounds_10_1022 : exactInterval 10 1022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1022 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1022) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1022 : oddCount 1022 10 = 9 ∧ acceleratedOrbit 10 1022 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1022 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1022) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1022.1, data_10_1022.2] + +/-- Complete interval computation for depth 10, residue 1023. -/ +theorem bounds_10_1023 : exactInterval 10 1023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_10_1023 (m : Nat) : + stoppingTime (2 ^ 10 * m + 1023) 10 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_10_1023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_10_1023 : oddCount 1023 10 = 10 ∧ acceleratedOrbit 10 1023 = 59048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_10_1023 (m : Nat) : + acceleratedOrbit 10 (2 ^ 10 * m + 1023) = 3 ^ 10 * m + 59048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_10_1023.1, data_10_1023.2] + +/-- Complete interval computation for depth 11, residue 0. -/ +theorem bounds_11_0 : exactInterval 11 0 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_0 (m : Nat) : + stoppingTime (2 ^ 11 * m + 0) 11 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_0 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_0 : oddCount 0 11 = 0 ∧ acceleratedOrbit 11 0 = 0 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_0 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 0) = 3 ^ 0 * m + 0 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_0.1, data_11_0.2] + +/-- Complete interval computation for depth 11, residue 1. -/ +theorem bounds_11_1 : exactInterval 11 1 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1) 11 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1 : oddCount 1 11 = 6 ∧ acceleratedOrbit 11 1 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1.1, data_11_1.2] + +/-- Complete interval computation for depth 11, residue 2. -/ +theorem bounds_11_2 : exactInterval 11 2 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2 : oddCount 2 11 = 5 ∧ acceleratedOrbit 11 2 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2.1, data_11_2.2] + +/-- Complete interval computation for depth 11, residue 3. -/ +theorem bounds_11_3 : exactInterval 11 3 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_3 (m : Nat) : + stoppingTime (2 ^ 11 * m + 3) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_3 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_3 : oddCount 3 11 = 5 ∧ acceleratedOrbit 11 3 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_3 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 3) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_3.1, data_11_3.2] + +/-- Complete interval computation for depth 11, residue 4. -/ +theorem bounds_11_4 : exactInterval 11 4 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_4 (m : Nat) : + stoppingTime (2 ^ 11 * m + 4) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_4 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_4 : oddCount 4 11 = 5 ∧ acceleratedOrbit 11 4 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_4 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 4) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_4.1, data_11_4.2] + +end Collatz.Research.StoppingAtlas.Batch0067 From ddddd2ade26519f95118287d0c15acf3e65e2d04 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:20 +0530 Subject: [PATCH 0068/1001] proof: certify atlas Batch0068 (11:5 to 11:19) --- Collatz/Research/StoppingAtlas/Batch0068.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0068.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0068.lean b/Collatz/Research/StoppingAtlas/Batch0068.lean new file mode 100644 index 00000000..081ac211 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0068.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0068 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 5. -/ +theorem bounds_11_5 : exactInterval 11 5 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_5 (m : Nat) : + stoppingTime (2 ^ 11 * m + 5) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_5 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_5 : oddCount 5 11 = 5 ∧ acceleratedOrbit 11 5 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_5 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 5) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_5.1, data_11_5.2] + +/-- Complete interval computation for depth 11, residue 6. -/ +theorem bounds_11_6 : exactInterval 11 6 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_6 (m : Nat) : + stoppingTime (2 ^ 11 * m + 6) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_6 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_6 : oddCount 6 11 = 5 ∧ acceleratedOrbit 11 6 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_6 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 6) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_6.1, data_11_6.2] + +/-- Complete interval computation for depth 11, residue 7. -/ +theorem bounds_11_7 : exactInterval 11 7 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_7 (m : Nat) : + stoppingTime (2 ^ 11 * m + 7) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_7 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_7 : oddCount 7 11 = 5 ∧ acceleratedOrbit 11 7 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_7 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 7) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_7.1, data_11_7.2] + +/-- Complete interval computation for depth 11, residue 8. -/ +theorem bounds_11_8 : exactInterval 11 8 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_8 (m : Nat) : + stoppingTime (2 ^ 11 * m + 8) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_8 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_8 : oddCount 8 11 = 4 ∧ acceleratedOrbit 11 8 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_8 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 8) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_8.1, data_11_8.2] + +/-- Complete interval computation for depth 11, residue 9. -/ +theorem bounds_11_9 : exactInterval 11 9 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_9 (m : Nat) : + stoppingTime (2 ^ 11 * m + 9) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_9 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_9 : oddCount 9 11 = 6 ∧ acceleratedOrbit 11 9 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_9 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 9) = 3 ^ 6 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_9.1, data_11_9.2] + +/-- Complete interval computation for depth 11, residue 10. -/ +theorem bounds_11_10 : exactInterval 11 10 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_10 (m : Nat) : + stoppingTime (2 ^ 11 * m + 10) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_10 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_10 : oddCount 10 11 = 4 ∧ acceleratedOrbit 11 10 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_10 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 10) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_10.1, data_11_10.2] + +/-- Complete interval computation for depth 11, residue 11. -/ +theorem bounds_11_11 : exactInterval 11 11 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_11 (m : Nat) : + stoppingTime (2 ^ 11 * m + 11) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_11 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_11 : oddCount 11 11 = 5 ∧ acceleratedOrbit 11 11 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_11 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 11) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_11.1, data_11_11.2] + +/-- Complete interval computation for depth 11, residue 12. -/ +theorem bounds_11_12 : exactInterval 11 12 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_12 (m : Nat) : + stoppingTime (2 ^ 11 * m + 12) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_12 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_12 : oddCount 12 11 = 4 ∧ acceleratedOrbit 11 12 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_12 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 12) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_12.1, data_11_12.2] + +/-- Complete interval computation for depth 11, residue 13. -/ +theorem bounds_11_13 : exactInterval 11 13 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_13 (m : Nat) : + stoppingTime (2 ^ 11 * m + 13) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_13 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_13 : oddCount 13 11 = 4 ∧ acceleratedOrbit 11 13 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_13 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 13) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_13.1, data_11_13.2] + +/-- Complete interval computation for depth 11, residue 14. -/ +theorem bounds_11_14 : exactInterval 11 14 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_14 (m : Nat) : + stoppingTime (2 ^ 11 * m + 14) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_14 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_14 : oddCount 14 11 = 5 ∧ acceleratedOrbit 11 14 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_14 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 14) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_14.1, data_11_14.2] + +/-- Complete interval computation for depth 11, residue 15. -/ +theorem bounds_11_15 : exactInterval 11 15 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_15 (m : Nat) : + stoppingTime (2 ^ 11 * m + 15) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_15 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_15 : oddCount 15 11 = 5 ∧ acceleratedOrbit 11 15 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_15 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 15) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_15.1, data_11_15.2] + +/-- Complete interval computation for depth 11, residue 16. -/ +theorem bounds_11_16 : exactInterval 11 16 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_16 (m : Nat) : + stoppingTime (2 ^ 11 * m + 16) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_16 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_16 : oddCount 16 11 = 4 ∧ acceleratedOrbit 11 16 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_16 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 16) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_16.1, data_11_16.2] + +/-- Complete interval computation for depth 11, residue 17. -/ +theorem bounds_11_17 : exactInterval 11 17 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_17 (m : Nat) : + stoppingTime (2 ^ 11 * m + 17) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_17 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_17 : oddCount 17 11 = 4 ∧ acceleratedOrbit 11 17 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_17 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 17) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_17.1, data_11_17.2] + +/-- Complete interval computation for depth 11, residue 18. -/ +theorem bounds_11_18 : exactInterval 11 18 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_18 (m : Nat) : + stoppingTime (2 ^ 11 * m + 18) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_18 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_18 : oddCount 18 11 = 6 ∧ acceleratedOrbit 11 18 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_18 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 18) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_18.1, data_11_18.2] + +/-- Complete interval computation for depth 11, residue 19. -/ +theorem bounds_11_19 : exactInterval 11 19 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_19 (m : Nat) : + stoppingTime (2 ^ 11 * m + 19) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_19 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_19 : oddCount 19 11 = 6 ∧ acceleratedOrbit 11 19 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_19 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 19) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_19.1, data_11_19.2] + +end Collatz.Research.StoppingAtlas.Batch0068 From b37c40f3c1b99235bbd568e797d7688d85f47bea Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:21 +0530 Subject: [PATCH 0069/1001] proof: certify atlas Batch0069 (11:20 to 11:34) --- Collatz/Research/StoppingAtlas/Batch0069.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0069.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0069.lean b/Collatz/Research/StoppingAtlas/Batch0069.lean new file mode 100644 index 00000000..9bba1043 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0069.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0069 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 20. -/ +theorem bounds_11_20 : exactInterval 11 20 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_20 (m : Nat) : + stoppingTime (2 ^ 11 * m + 20) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_20 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_20 : oddCount 20 11 = 4 ∧ acceleratedOrbit 11 20 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_20 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 20) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_20.1, data_11_20.2] + +/-- Complete interval computation for depth 11, residue 21. -/ +theorem bounds_11_21 : exactInterval 11 21 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_21 (m : Nat) : + stoppingTime (2 ^ 11 * m + 21) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_21 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_21 : oddCount 21 11 = 4 ∧ acceleratedOrbit 11 21 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_21 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 21) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_21.1, data_11_21.2] + +/-- Complete interval computation for depth 11, residue 22. -/ +theorem bounds_11_22 : exactInterval 11 22 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_22 (m : Nat) : + stoppingTime (2 ^ 11 * m + 22) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_22 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_22 : oddCount 22 11 = 4 ∧ acceleratedOrbit 11 22 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_22 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 22) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_22.1, data_11_22.2] + +/-- Complete interval computation for depth 11, residue 23. -/ +theorem bounds_11_23 : exactInterval 11 23 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_23 (m : Nat) : + stoppingTime (2 ^ 11 * m + 23) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_23 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_23 : oddCount 23 11 = 4 ∧ acceleratedOrbit 11 23 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_23 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 23) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_23.1, data_11_23.2] + +/-- Complete interval computation for depth 11, residue 24. -/ +theorem bounds_11_24 : exactInterval 11 24 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_24 (m : Nat) : + stoppingTime (2 ^ 11 * m + 24) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_24 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_24 : oddCount 24 11 = 4 ∧ acceleratedOrbit 11 24 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_24 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 24) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_24.1, data_11_24.2] + +/-- Complete interval computation for depth 11, residue 25. -/ +theorem bounds_11_25 : exactInterval 11 25 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_25 (m : Nat) : + stoppingTime (2 ^ 11 * m + 25) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_25 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_25 : oddCount 25 11 = 6 ∧ acceleratedOrbit 11 25 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_25 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 25) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_25.1, data_11_25.2] + +/-- Complete interval computation for depth 11, residue 26. -/ +theorem bounds_11_26 : exactInterval 11 26 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_26 (m : Nat) : + stoppingTime (2 ^ 11 * m + 26) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_26 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_26 : oddCount 26 11 = 4 ∧ acceleratedOrbit 11 26 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_26 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 26) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_26.1, data_11_26.2] + +/-- Complete interval computation for depth 11, residue 27. -/ +theorem bounds_11_27 : exactInterval 11 27 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_27 (m : Nat) : + stoppingTime (2 ^ 11 * m + 27) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_27 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_27 : oddCount 27 11 = 8 ∧ acceleratedOrbit 11 27 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_27 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 27) = 3 ^ 8 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_27.1, data_11_27.2] + +/-- Complete interval computation for depth 11, residue 28. -/ +theorem bounds_11_28 : exactInterval 11 28 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_28 (m : Nat) : + stoppingTime (2 ^ 11 * m + 28) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_28 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_28 : oddCount 28 11 = 5 ∧ acceleratedOrbit 11 28 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_28 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 28) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_28.1, data_11_28.2] + +/-- Complete interval computation for depth 11, residue 29. -/ +theorem bounds_11_29 : exactInterval 11 29 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_29 (m : Nat) : + stoppingTime (2 ^ 11 * m + 29) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_29 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_29 : oddCount 29 11 = 5 ∧ acceleratedOrbit 11 29 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_29 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 29) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_29.1, data_11_29.2] + +/-- Complete interval computation for depth 11, residue 30. -/ +theorem bounds_11_30 : exactInterval 11 30 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_30 (m : Nat) : + stoppingTime (2 ^ 11 * m + 30) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_30 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_30 : oddCount 30 11 = 5 ∧ acceleratedOrbit 11 30 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_30 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 30) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_30.1, data_11_30.2] + +/-- Complete interval computation for depth 11, residue 31. -/ +theorem bounds_11_31 : exactInterval 11 31 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_31 (m : Nat) : + stoppingTime (2 ^ 11 * m + 31) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_31 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_31 : oddCount 31 11 = 8 ∧ acceleratedOrbit 11 31 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_31 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 31) = 3 ^ 8 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_31.1, data_11_31.2] + +/-- Complete interval computation for depth 11, residue 32. -/ +theorem bounds_11_32 : exactInterval 11 32 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_32 (m : Nat) : + stoppingTime (2 ^ 11 * m + 32) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_32 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_32 : oddCount 32 11 = 3 ∧ acceleratedOrbit 11 32 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_32 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 32) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_32.1, data_11_32.2] + +/-- Complete interval computation for depth 11, residue 33. -/ +theorem bounds_11_33 : exactInterval 11 33 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_33 (m : Nat) : + stoppingTime (2 ^ 11 * m + 33) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_33 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_33 : oddCount 33 11 = 6 ∧ acceleratedOrbit 11 33 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_33 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 33) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_33.1, data_11_33.2] + +/-- Complete interval computation for depth 11, residue 34. -/ +theorem bounds_11_34 : exactInterval 11 34 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_34 (m : Nat) : + stoppingTime (2 ^ 11 * m + 34) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_34 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_34 : oddCount 34 11 = 4 ∧ acceleratedOrbit 11 34 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_34 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 34) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_34.1, data_11_34.2] + +end Collatz.Research.StoppingAtlas.Batch0069 From 8fbf43ae2ff1996cc1ae4fa16db46657ead6f2d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:21 +0530 Subject: [PATCH 0070/1001] proof: certify atlas Batch0070 (11:35 to 11:50) --- Collatz/Research/StoppingAtlas/Batch0070.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0070.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0070.lean b/Collatz/Research/StoppingAtlas/Batch0070.lean new file mode 100644 index 00000000..3b92f01e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0070.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0070 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 35. -/ +theorem bounds_11_35 : exactInterval 11 35 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_35 (m : Nat) : + stoppingTime (2 ^ 11 * m + 35) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_35 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_35 : oddCount 35 11 = 4 ∧ acceleratedOrbit 11 35 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_35 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 35) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_35.1, data_11_35.2] + +/-- Complete interval computation for depth 11, residue 36. -/ +theorem bounds_11_36 : exactInterval 11 36 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_36 (m : Nat) : + stoppingTime (2 ^ 11 * m + 36) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_36 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_36 : oddCount 36 11 = 5 ∧ acceleratedOrbit 11 36 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_36 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 36) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_36.1, data_11_36.2] + +/-- Complete interval computation for depth 11, residue 37. -/ +theorem bounds_11_37 : exactInterval 11 37 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_37 (m : Nat) : + stoppingTime (2 ^ 11 * m + 37) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_37 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_37 : oddCount 37 11 = 5 ∧ acceleratedOrbit 11 37 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_37 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 37) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_37.1, data_11_37.2] + +/-- Complete interval computation for depth 11, residue 38. -/ +theorem bounds_11_38 : exactInterval 11 38 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_38 (m : Nat) : + stoppingTime (2 ^ 11 * m + 38) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_38 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_38 : oddCount 38 11 = 5 ∧ acceleratedOrbit 11 38 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_38 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 38) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_38.1, data_11_38.2] + +/-- Complete interval computation for depth 11, residue 39. -/ +theorem bounds_11_39 : exactInterval 11 39 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_39 (m : Nat) : + stoppingTime (2 ^ 11 * m + 39) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_39 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_39 : oddCount 39 11 = 7 ∧ acceleratedOrbit 11 39 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_39 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 39) = 3 ^ 7 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_39.1, data_11_39.2] + +/-- Complete interval computation for depth 11, residue 40. -/ +theorem bounds_11_40 : exactInterval 11 40 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_40 (m : Nat) : + stoppingTime (2 ^ 11 * m + 40) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_40 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_40 : oddCount 40 11 = 3 ∧ acceleratedOrbit 11 40 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_40 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 40) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_40.1, data_11_40.2] + +/-- Complete interval computation for depth 11, residue 41. -/ +theorem bounds_11_41 : exactInterval 11 41 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_41 (m : Nat) : + stoppingTime (2 ^ 11 * m + 41) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_41 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_41 : oddCount 41 11 = 8 ∧ acceleratedOrbit 11 41 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_41 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 41) = 3 ^ 8 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_41.1, data_11_41.2] + +/-- Complete interval computation for depth 11, residue 42. -/ +theorem bounds_11_42 : exactInterval 11 42 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_42 (m : Nat) : + stoppingTime (2 ^ 11 * m + 42) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_42 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_42 : oddCount 42 11 = 3 ∧ acceleratedOrbit 11 42 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_42 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 42) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_42.1, data_11_42.2] + +/-- Complete interval computation for depth 11, residue 43. -/ +theorem bounds_11_43 : exactInterval 11 43 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_43 (m : Nat) : + stoppingTime (2 ^ 11 * m + 43) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_43 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_43 : oddCount 43 11 = 6 ∧ acceleratedOrbit 11 43 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_43 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 43) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_43.1, data_11_43.2] + +/-- Complete interval computation for depth 11, residue 44. -/ +theorem bounds_11_44 : exactInterval 11 44 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_44 (m : Nat) : + stoppingTime (2 ^ 11 * m + 44) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_44 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_44 : oddCount 44 11 = 4 ∧ acceleratedOrbit 11 44 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_44 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 44) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_44.1, data_11_44.2] + +/-- Complete interval computation for depth 11, residue 45. -/ +theorem bounds_11_45 : exactInterval 11 45 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_45 (m : Nat) : + stoppingTime (2 ^ 11 * m + 45) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_45 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_45 : oddCount 45 11 = 4 ∧ acceleratedOrbit 11 45 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_45 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 45) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_45.1, data_11_45.2] + +/-- Complete interval computation for depth 11, residue 46. -/ +theorem bounds_11_46 : exactInterval 11 46 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_46 (m : Nat) : + stoppingTime (2 ^ 11 * m + 46) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_46 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_46 : oddCount 46 11 = 4 ∧ acceleratedOrbit 11 46 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_46 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 46) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_46.1, data_11_46.2] + +/-- Complete interval computation for depth 11, residue 47. -/ +theorem bounds_11_47 : exactInterval 11 47 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_47 (m : Nat) : + stoppingTime (2 ^ 11 * m + 47) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_47 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_47 : oddCount 47 11 = 8 ∧ acceleratedOrbit 11 47 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_47 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 47) = 3 ^ 8 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_47.1, data_11_47.2] + +/-- Complete interval computation for depth 11, residue 48. -/ +theorem bounds_11_48 : exactInterval 11 48 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_48 (m : Nat) : + stoppingTime (2 ^ 11 * m + 48) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_48 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_48 : oddCount 48 11 = 3 ∧ acceleratedOrbit 11 48 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_48 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 48) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_48.1, data_11_48.2] + +/-- Complete interval computation for depth 11, residue 49. -/ +theorem bounds_11_49 : exactInterval 11 49 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_49 (m : Nat) : + stoppingTime (2 ^ 11 * m + 49) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_49 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_49 : oddCount 49 11 = 6 ∧ acceleratedOrbit 11 49 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_49 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 49) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_49.1, data_11_49.2] + +/-- Complete interval computation for depth 11, residue 50. -/ +theorem bounds_11_50 : exactInterval 11 50 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_50 (m : Nat) : + stoppingTime (2 ^ 11 * m + 50) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_50 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_50 : oddCount 50 11 = 6 ∧ acceleratedOrbit 11 50 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_50 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 50) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_50.1, data_11_50.2] + +end Collatz.Research.StoppingAtlas.Batch0070 From bb37a1a3e65d2e9187a87b74892a4576b8d81b81 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:21 +0530 Subject: [PATCH 0071/1001] proof: certify atlas Batch0071 (11:51 to 11:65) --- Collatz/Research/StoppingAtlas/Batch0071.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0071.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0071.lean b/Collatz/Research/StoppingAtlas/Batch0071.lean new file mode 100644 index 00000000..9daee993 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0071.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0071 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 51. -/ +theorem bounds_11_51 : exactInterval 11 51 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_51 (m : Nat) : + stoppingTime (2 ^ 11 * m + 51) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_51 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_51 : oddCount 51 11 = 6 ∧ acceleratedOrbit 11 51 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_51 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 51) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_51.1, data_11_51.2] + +/-- Complete interval computation for depth 11, residue 52. -/ +theorem bounds_11_52 : exactInterval 11 52 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_52 (m : Nat) : + stoppingTime (2 ^ 11 * m + 52) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_52 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_52 : oddCount 52 11 = 3 ∧ acceleratedOrbit 11 52 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_52 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 52) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_52.1, data_11_52.2] + +/-- Complete interval computation for depth 11, residue 53. -/ +theorem bounds_11_53 : exactInterval 11 53 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_53 (m : Nat) : + stoppingTime (2 ^ 11 * m + 53) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_53 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_53 : oddCount 53 11 = 3 ∧ acceleratedOrbit 11 53 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_53 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 53) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_53.1, data_11_53.2] + +/-- Complete interval computation for depth 11, residue 54. -/ +theorem bounds_11_54 : exactInterval 11 54 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_54 (m : Nat) : + stoppingTime (2 ^ 11 * m + 54) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_54 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_54 : oddCount 54 11 = 8 ∧ acceleratedOrbit 11 54 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_54 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 54) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_54.1, data_11_54.2] + +/-- Complete interval computation for depth 11, residue 55. -/ +theorem bounds_11_55 : exactInterval 11 55 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_55 (m : Nat) : + stoppingTime (2 ^ 11 * m + 55) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_55 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_55 : oddCount 55 11 = 8 ∧ acceleratedOrbit 11 55 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_55 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 55) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_55.1, data_11_55.2] + +/-- Complete interval computation for depth 11, residue 56. -/ +theorem bounds_11_56 : exactInterval 11 56 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_56 (m : Nat) : + stoppingTime (2 ^ 11 * m + 56) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_56 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_56 : oddCount 56 11 = 5 ∧ acceleratedOrbit 11 56 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_56 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 56) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_56.1, data_11_56.2] + +/-- Complete interval computation for depth 11, residue 57. -/ +theorem bounds_11_57 : exactInterval 11 57 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_57 (m : Nat) : + stoppingTime (2 ^ 11 * m + 57) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_57 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_57 : oddCount 57 11 = 5 ∧ acceleratedOrbit 11 57 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_57 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 57) = 3 ^ 5 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_57.1, data_11_57.2] + +/-- Complete interval computation for depth 11, residue 58. -/ +theorem bounds_11_58 : exactInterval 11 58 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_58 (m : Nat) : + stoppingTime (2 ^ 11 * m + 58) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_58 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_58 : oddCount 58 11 = 5 ∧ acceleratedOrbit 11 58 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_58 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 58) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_58.1, data_11_58.2] + +/-- Complete interval computation for depth 11, residue 59. -/ +theorem bounds_11_59 : exactInterval 11 59 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_59 (m : Nat) : + stoppingTime (2 ^ 11 * m + 59) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_59 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_59 : oddCount 59 11 = 6 ∧ acceleratedOrbit 11 59 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_59 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 59) = 3 ^ 6 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_59.1, data_11_59.2] + +/-- Complete interval computation for depth 11, residue 60. -/ +theorem bounds_11_60 : exactInterval 11 60 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_60 (m : Nat) : + stoppingTime (2 ^ 11 * m + 60) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_60 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_60 : oddCount 60 11 = 5 ∧ acceleratedOrbit 11 60 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_60 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 60) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_60.1, data_11_60.2] + +/-- Complete interval computation for depth 11, residue 61. -/ +theorem bounds_11_61 : exactInterval 11 61 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_61 (m : Nat) : + stoppingTime (2 ^ 11 * m + 61) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_61 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_61 : oddCount 61 11 = 5 ∧ acceleratedOrbit 11 61 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_61 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 61) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_61.1, data_11_61.2] + +/-- Complete interval computation for depth 11, residue 62. -/ +theorem bounds_11_62 : exactInterval 11 62 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_62 (m : Nat) : + stoppingTime (2 ^ 11 * m + 62) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_62 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_62 : oddCount 62 11 = 8 ∧ acceleratedOrbit 11 62 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_62 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 62) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_62.1, data_11_62.2] + +/-- Complete interval computation for depth 11, residue 63. -/ +theorem bounds_11_63 : exactInterval 11 63 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_63 (m : Nat) : + stoppingTime (2 ^ 11 * m + 63) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_63 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_63 : oddCount 63 11 = 8 ∧ acceleratedOrbit 11 63 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_63 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 63) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_63.1, data_11_63.2] + +/-- Complete interval computation for depth 11, residue 64. -/ +theorem bounds_11_64 : exactInterval 11 64 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_64 (m : Nat) : + stoppingTime (2 ^ 11 * m + 64) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_64 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_64 : oddCount 64 11 = 3 ∧ acceleratedOrbit 11 64 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_64 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 64) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_64.1, data_11_64.2] + +/-- Complete interval computation for depth 11, residue 65. -/ +theorem bounds_11_65 : exactInterval 11 65 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_65 (m : Nat) : + stoppingTime (2 ^ 11 * m + 65) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_65 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_65 : oddCount 65 11 = 6 ∧ acceleratedOrbit 11 65 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_65 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 65) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_65.1, data_11_65.2] + +end Collatz.Research.StoppingAtlas.Batch0071 From c7a06d17d992a186adfeb799d2b36d5e06b40d7b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:22 +0530 Subject: [PATCH 0072/1001] proof: certify atlas Batch0072 (11:66 to 11:80) --- Collatz/Research/StoppingAtlas/Batch0072.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0072.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0072.lean b/Collatz/Research/StoppingAtlas/Batch0072.lean new file mode 100644 index 00000000..fd5fba82 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0072.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0072 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 66. -/ +theorem bounds_11_66 : exactInterval 11 66 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_66 (m : Nat) : + stoppingTime (2 ^ 11 * m + 66) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_66 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_66 : oddCount 66 11 = 6 ∧ acceleratedOrbit 11 66 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_66 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 66) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_66.1, data_11_66.2] + +/-- Complete interval computation for depth 11, residue 67. -/ +theorem bounds_11_67 : exactInterval 11 67 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_67 (m : Nat) : + stoppingTime (2 ^ 11 * m + 67) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_67 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_67 : oddCount 67 11 = 6 ∧ acceleratedOrbit 11 67 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_67 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 67) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_67.1, data_11_67.2] + +/-- Complete interval computation for depth 11, residue 68. -/ +theorem bounds_11_68 : exactInterval 11 68 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_68 (m : Nat) : + stoppingTime (2 ^ 11 * m + 68) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_68 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_68 : oddCount 68 11 = 3 ∧ acceleratedOrbit 11 68 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_68 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 68) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_68.1, data_11_68.2] + +/-- Complete interval computation for depth 11, residue 69. -/ +theorem bounds_11_69 : exactInterval 11 69 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_69 (m : Nat) : + stoppingTime (2 ^ 11 * m + 69) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_69 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_69 : oddCount 69 11 = 3 ∧ acceleratedOrbit 11 69 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_69 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 69) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_69.1, data_11_69.2] + +/-- Complete interval computation for depth 11, residue 70. -/ +theorem bounds_11_70 : exactInterval 11 70 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_70 (m : Nat) : + stoppingTime (2 ^ 11 * m + 70) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_70 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_70 : oddCount 70 11 = 3 ∧ acceleratedOrbit 11 70 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_70 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 70) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_70.1, data_11_70.2] + +/-- Complete interval computation for depth 11, residue 71. -/ +theorem bounds_11_71 : exactInterval 11 71 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_71 (m : Nat) : + stoppingTime (2 ^ 11 * m + 71) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_71 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_71 : oddCount 71 11 = 8 ∧ acceleratedOrbit 11 71 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_71 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 71) = 3 ^ 8 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_71.1, data_11_71.2] + +/-- Complete interval computation for depth 11, residue 72. -/ +theorem bounds_11_72 : exactInterval 11 72 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_72 (m : Nat) : + stoppingTime (2 ^ 11 * m + 72) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_72 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_72 : oddCount 72 11 = 5 ∧ acceleratedOrbit 11 72 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_72 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 72) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_72.1, data_11_72.2] + +/-- Complete interval computation for depth 11, residue 73. -/ +theorem bounds_11_73 : exactInterval 11 73 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_73 (m : Nat) : + stoppingTime (2 ^ 11 * m + 73) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_73 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_73 : oddCount 73 11 = 8 ∧ acceleratedOrbit 11 73 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_73 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 73) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_73.1, data_11_73.2] + +/-- Complete interval computation for depth 11, residue 74. -/ +theorem bounds_11_74 : exactInterval 11 74 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_74 (m : Nat) : + stoppingTime (2 ^ 11 * m + 74) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_74 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_74 : oddCount 74 11 = 5 ∧ acceleratedOrbit 11 74 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_74 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 74) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_74.1, data_11_74.2] + +/-- Complete interval computation for depth 11, residue 75. -/ +theorem bounds_11_75 : exactInterval 11 75 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_75 (m : Nat) : + stoppingTime (2 ^ 11 * m + 75) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_75 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_75 : oddCount 75 11 = 3 ∧ acceleratedOrbit 11 75 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_75 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 75) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_75.1, data_11_75.2] + +/-- Complete interval computation for depth 11, residue 76. -/ +theorem bounds_11_76 : exactInterval 11 76 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_76 (m : Nat) : + stoppingTime (2 ^ 11 * m + 76) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_76 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_76 : oddCount 76 11 = 5 ∧ acceleratedOrbit 11 76 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_76 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 76) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_76.1, data_11_76.2] + +/-- Complete interval computation for depth 11, residue 77. -/ +theorem bounds_11_77 : exactInterval 11 77 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_77 (m : Nat) : + stoppingTime (2 ^ 11 * m + 77) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_77 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_77 : oddCount 77 11 = 5 ∧ acceleratedOrbit 11 77 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_77 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 77) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_77.1, data_11_77.2] + +/-- Complete interval computation for depth 11, residue 78. -/ +theorem bounds_11_78 : exactInterval 11 78 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_78 (m : Nat) : + stoppingTime (2 ^ 11 * m + 78) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_78 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_78 : oddCount 78 11 = 6 ∧ acceleratedOrbit 11 78 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_78 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 78) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_78.1, data_11_78.2] + +/-- Complete interval computation for depth 11, residue 79. -/ +theorem bounds_11_79 : exactInterval 11 79 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_79 (m : Nat) : + stoppingTime (2 ^ 11 * m + 79) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_79 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_79 : oddCount 79 11 = 6 ∧ acceleratedOrbit 11 79 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_79 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 79) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_79.1, data_11_79.2] + +/-- Complete interval computation for depth 11, residue 80. -/ +theorem bounds_11_80 : exactInterval 11 80 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_80 (m : Nat) : + stoppingTime (2 ^ 11 * m + 80) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_80 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_80 : oddCount 80 11 = 3 ∧ acceleratedOrbit 11 80 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_80 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 80) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_80.1, data_11_80.2] + +end Collatz.Research.StoppingAtlas.Batch0072 From 856aa3586a6cc6b2866ee7385ad5e465cef1d1a9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:22 +0530 Subject: [PATCH 0073/1001] proof: certify atlas Batch0073 (11:81 to 11:96) --- Collatz/Research/StoppingAtlas/Batch0073.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0073.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0073.lean b/Collatz/Research/StoppingAtlas/Batch0073.lean new file mode 100644 index 00000000..36f55e28 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0073.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0073 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 81. -/ +theorem bounds_11_81 : exactInterval 11 81 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_81 (m : Nat) : + stoppingTime (2 ^ 11 * m + 81) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_81 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_81 : oddCount 81 11 = 5 ∧ acceleratedOrbit 11 81 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_81 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 81) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_81.1, data_11_81.2] + +/-- Complete interval computation for depth 11, residue 82. -/ +theorem bounds_11_82 : exactInterval 11 82 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_82 (m : Nat) : + stoppingTime (2 ^ 11 * m + 82) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_82 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_82 : oddCount 82 11 = 7 ∧ acceleratedOrbit 11 82 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_82 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 82) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_82.1, data_11_82.2] + +/-- Complete interval computation for depth 11, residue 83. -/ +theorem bounds_11_83 : exactInterval 11 83 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_83 (m : Nat) : + stoppingTime (2 ^ 11 * m + 83) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_83 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_83 : oddCount 83 11 = 7 ∧ acceleratedOrbit 11 83 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_83 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 83) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_83.1, data_11_83.2] + +/-- Complete interval computation for depth 11, residue 84. -/ +theorem bounds_11_84 : exactInterval 11 84 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_84 (m : Nat) : + stoppingTime (2 ^ 11 * m + 84) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_84 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_84 : oddCount 84 11 = 3 ∧ acceleratedOrbit 11 84 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_84 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 84) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_84.1, data_11_84.2] + +/-- Complete interval computation for depth 11, residue 85. -/ +theorem bounds_11_85 : exactInterval 11 85 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_85 (m : Nat) : + stoppingTime (2 ^ 11 * m + 85) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_85 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_85 : oddCount 85 11 = 3 ∧ acceleratedOrbit 11 85 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_85 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 85) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_85.1, data_11_85.2] + +/-- Complete interval computation for depth 11, residue 86. -/ +theorem bounds_11_86 : exactInterval 11 86 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_86 (m : Nat) : + stoppingTime (2 ^ 11 * m + 86) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_86 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_86 : oddCount 86 11 = 5 ∧ acceleratedOrbit 11 86 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_86 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 86) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_86.1, data_11_86.2] + +/-- Complete interval computation for depth 11, residue 87. -/ +theorem bounds_11_87 : exactInterval 11 87 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_87 (m : Nat) : + stoppingTime (2 ^ 11 * m + 87) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_87 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_87 : oddCount 87 11 = 5 ∧ acceleratedOrbit 11 87 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_87 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 87) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_87.1, data_11_87.2] + +/-- Complete interval computation for depth 11, residue 88. -/ +theorem bounds_11_88 : exactInterval 11 88 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_88 (m : Nat) : + stoppingTime (2 ^ 11 * m + 88) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_88 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_88 : oddCount 88 11 = 4 ∧ acceleratedOrbit 11 88 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_88 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 88) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_88.1, data_11_88.2] + +/-- Complete interval computation for depth 11, residue 89. -/ +theorem bounds_11_89 : exactInterval 11 89 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_89 (m : Nat) : + stoppingTime (2 ^ 11 * m + 89) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_89 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_89 : oddCount 89 11 = 5 ∧ acceleratedOrbit 11 89 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_89 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 89) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_89.1, data_11_89.2] + +/-- Complete interval computation for depth 11, residue 90. -/ +theorem bounds_11_90 : exactInterval 11 90 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_90 (m : Nat) : + stoppingTime (2 ^ 11 * m + 90) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_90 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_90 : oddCount 90 11 = 4 ∧ acceleratedOrbit 11 90 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_90 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 90) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_90.1, data_11_90.2] + +/-- Complete interval computation for depth 11, residue 91. -/ +theorem bounds_11_91 : exactInterval 11 91 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_91 (m : Nat) : + stoppingTime (2 ^ 11 * m + 91) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_91 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_91 : oddCount 91 11 = 9 ∧ acceleratedOrbit 11 91 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_91 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 91) = 3 ^ 9 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_91.1, data_11_91.2] + +/-- Complete interval computation for depth 11, residue 92. -/ +theorem bounds_11_92 : exactInterval 11 92 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_92 (m : Nat) : + stoppingTime (2 ^ 11 * m + 92) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_92 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_92 : oddCount 92 11 = 4 ∧ acceleratedOrbit 11 92 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_92 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 92) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_92.1, data_11_92.2] + +/-- Complete interval computation for depth 11, residue 93. -/ +theorem bounds_11_93 : exactInterval 11 93 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_93 (m : Nat) : + stoppingTime (2 ^ 11 * m + 93) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_93 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_93 : oddCount 93 11 = 4 ∧ acceleratedOrbit 11 93 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_93 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 93) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_93.1, data_11_93.2] + +/-- Complete interval computation for depth 11, residue 94. -/ +theorem bounds_11_94 : exactInterval 11 94 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_94 (m : Nat) : + stoppingTime (2 ^ 11 * m + 94) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_94 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_94 : oddCount 94 11 = 7 ∧ acceleratedOrbit 11 94 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_94 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 94) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_94.1, data_11_94.2] + +/-- Complete interval computation for depth 11, residue 95. -/ +theorem bounds_11_95 : exactInterval 11 95 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_95 (m : Nat) : + stoppingTime (2 ^ 11 * m + 95) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_95 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_95 : oddCount 95 11 = 7 ∧ acceleratedOrbit 11 95 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_95 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 95) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_95.1, data_11_95.2] + +/-- Complete interval computation for depth 11, residue 96. -/ +theorem bounds_11_96 : exactInterval 11 96 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_96 (m : Nat) : + stoppingTime (2 ^ 11 * m + 96) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_96 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_96 : oddCount 96 11 = 3 ∧ acceleratedOrbit 11 96 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_96 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 96) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_96.1, data_11_96.2] + +end Collatz.Research.StoppingAtlas.Batch0073 From b403db64843ca210c0f98b0b630120724883be1a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:22 +0530 Subject: [PATCH 0074/1001] proof: certify atlas Batch0074 (11:97 to 11:111) --- Collatz/Research/StoppingAtlas/Batch0074.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0074.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0074.lean b/Collatz/Research/StoppingAtlas/Batch0074.lean new file mode 100644 index 00000000..aaa3f1e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0074.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0074 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 97. -/ +theorem bounds_11_97 : exactInterval 11 97 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_97 (m : Nat) : + stoppingTime (2 ^ 11 * m + 97) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_97 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_97 : oddCount 97 11 = 7 ∧ acceleratedOrbit 11 97 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_97 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 97) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_97.1, data_11_97.2] + +/-- Complete interval computation for depth 11, residue 98. -/ +theorem bounds_11_98 : exactInterval 11 98 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_98 (m : Nat) : + stoppingTime (2 ^ 11 * m + 98) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_98 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_98 : oddCount 98 11 = 5 ∧ acceleratedOrbit 11 98 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_98 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 98) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_98.1, data_11_98.2] + +/-- Complete interval computation for depth 11, residue 99. -/ +theorem bounds_11_99 : exactInterval 11 99 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_99 (m : Nat) : + stoppingTime (2 ^ 11 * m + 99) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_99 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_99 : oddCount 99 11 = 5 ∧ acceleratedOrbit 11 99 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_99 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 99) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_99.1, data_11_99.2] + +/-- Complete interval computation for depth 11, residue 100. -/ +theorem bounds_11_100 : exactInterval 11 100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_100 (m : Nat) : + stoppingTime (2 ^ 11 * m + 100) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_100 : oddCount 100 11 = 5 ∧ acceleratedOrbit 11 100 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_100 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 100) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_100.1, data_11_100.2] + +/-- Complete interval computation for depth 11, residue 101. -/ +theorem bounds_11_101 : exactInterval 11 101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_101 (m : Nat) : + stoppingTime (2 ^ 11 * m + 101) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_101 : oddCount 101 11 = 5 ∧ acceleratedOrbit 11 101 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_101 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 101) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_101.1, data_11_101.2] + +/-- Complete interval computation for depth 11, residue 102. -/ +theorem bounds_11_102 : exactInterval 11 102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_102 (m : Nat) : + stoppingTime (2 ^ 11 * m + 102) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_102 : oddCount 102 11 = 5 ∧ acceleratedOrbit 11 102 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_102 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 102) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_102.1, data_11_102.2] + +/-- Complete interval computation for depth 11, residue 103. -/ +theorem bounds_11_103 : exactInterval 11 103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_103 (m : Nat) : + stoppingTime (2 ^ 11 * m + 103) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_103 : oddCount 103 11 = 8 ∧ acceleratedOrbit 11 103 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_103 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 103) = 3 ^ 8 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_103.1, data_11_103.2] + +/-- Complete interval computation for depth 11, residue 104. -/ +theorem bounds_11_104 : exactInterval 11 104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_104 (m : Nat) : + stoppingTime (2 ^ 11 * m + 104) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_104 : oddCount 104 11 = 3 ∧ acceleratedOrbit 11 104 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_104 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 104) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_104.1, data_11_104.2] + +/-- Complete interval computation for depth 11, residue 105. -/ +theorem bounds_11_105 : exactInterval 11 105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_105 (m : Nat) : + stoppingTime (2 ^ 11 * m + 105) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_105 : oddCount 105 11 = 6 ∧ acceleratedOrbit 11 105 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_105 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 105) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_105.1, data_11_105.2] + +/-- Complete interval computation for depth 11, residue 106. -/ +theorem bounds_11_106 : exactInterval 11 106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_106 (m : Nat) : + stoppingTime (2 ^ 11 * m + 106) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_106 : oddCount 106 11 = 3 ∧ acceleratedOrbit 11 106 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_106 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 106) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_106.1, data_11_106.2] + +/-- Complete interval computation for depth 11, residue 107. -/ +theorem bounds_11_107 : exactInterval 11 107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_107 (m : Nat) : + stoppingTime (2 ^ 11 * m + 107) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_107 : oddCount 107 11 = 8 ∧ acceleratedOrbit 11 107 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_107 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 107) = 3 ^ 8 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_107.1, data_11_107.2] + +/-- Complete interval computation for depth 11, residue 108. -/ +theorem bounds_11_108 : exactInterval 11 108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_108 (m : Nat) : + stoppingTime (2 ^ 11 * m + 108) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_108 : oddCount 108 11 = 7 ∧ acceleratedOrbit 11 108 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_108 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 108) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_108.1, data_11_108.2] + +/-- Complete interval computation for depth 11, residue 109. -/ +theorem bounds_11_109 : exactInterval 11 109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_109 (m : Nat) : + stoppingTime (2 ^ 11 * m + 109) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_109 : oddCount 109 11 = 7 ∧ acceleratedOrbit 11 109 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_109 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 109) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_109.1, data_11_109.2] + +/-- Complete interval computation for depth 11, residue 110. -/ +theorem bounds_11_110 : exactInterval 11 110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_110 (m : Nat) : + stoppingTime (2 ^ 11 * m + 110) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_110 : oddCount 110 11 = 7 ∧ acceleratedOrbit 11 110 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_110 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 110) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_110.1, data_11_110.2] + +/-- Complete interval computation for depth 11, residue 111. -/ +theorem bounds_11_111 : exactInterval 11 111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_111 (m : Nat) : + stoppingTime (2 ^ 11 * m + 111) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_111 : oddCount 111 11 = 9 ∧ acceleratedOrbit 11 111 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_111 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 111) = 3 ^ 9 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_111.1, data_11_111.2] + +end Collatz.Research.StoppingAtlas.Batch0074 From fda56969a1314d849ef4ef6a21b88b4f031de895 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:22 +0530 Subject: [PATCH 0075/1001] proof: certify atlas Batch0075 (11:112 to 11:127) --- Collatz/Research/StoppingAtlas/Batch0075.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0075.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0075.lean b/Collatz/Research/StoppingAtlas/Batch0075.lean new file mode 100644 index 00000000..16ae2848 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0075.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0075 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 112. -/ +theorem bounds_11_112 : exactInterval 11 112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_112 (m : Nat) : + stoppingTime (2 ^ 11 * m + 112) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_112 : oddCount 112 11 = 4 ∧ acceleratedOrbit 11 112 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_112 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 112) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_112.1, data_11_112.2] + +/-- Complete interval computation for depth 11, residue 113. -/ +theorem bounds_11_113 : exactInterval 11 113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_113 (m : Nat) : + stoppingTime (2 ^ 11 * m + 113) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_113 : oddCount 113 11 = 3 ∧ acceleratedOrbit 11 113 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_113 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 113) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_113.1, data_11_113.2] + +/-- Complete interval computation for depth 11, residue 114. -/ +theorem bounds_11_114 : exactInterval 11 114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_114 (m : Nat) : + stoppingTime (2 ^ 11 * m + 114) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_114 : oddCount 114 11 = 5 ∧ acceleratedOrbit 11 114 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_114 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 114) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_114.1, data_11_114.2] + +/-- Complete interval computation for depth 11, residue 115. -/ +theorem bounds_11_115 : exactInterval 11 115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_115 (m : Nat) : + stoppingTime (2 ^ 11 * m + 115) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_115 : oddCount 115 11 = 5 ∧ acceleratedOrbit 11 115 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_115 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 115) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_115.1, data_11_115.2] + +/-- Complete interval computation for depth 11, residue 116. -/ +theorem bounds_11_116 : exactInterval 11 116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_116 (m : Nat) : + stoppingTime (2 ^ 11 * m + 116) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_116 : oddCount 116 11 = 4 ∧ acceleratedOrbit 11 116 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_116 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 116) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_116.1, data_11_116.2] + +/-- Complete interval computation for depth 11, residue 117. -/ +theorem bounds_11_117 : exactInterval 11 117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_117 (m : Nat) : + stoppingTime (2 ^ 11 * m + 117) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_117 : oddCount 117 11 = 4 ∧ acceleratedOrbit 11 117 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_117 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 117) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_117.1, data_11_117.2] + +/-- Complete interval computation for depth 11, residue 118. -/ +theorem bounds_11_118 : exactInterval 11 118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_118 (m : Nat) : + stoppingTime (2 ^ 11 * m + 118) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_118 : oddCount 118 11 = 6 ∧ acceleratedOrbit 11 118 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_118 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 118) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_118.1, data_11_118.2] + +/-- Complete interval computation for depth 11, residue 119. -/ +theorem bounds_11_119 : exactInterval 11 119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_119 (m : Nat) : + stoppingTime (2 ^ 11 * m + 119) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_119 : oddCount 119 11 = 6 ∧ acceleratedOrbit 11 119 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_119 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 119) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_119.1, data_11_119.2] + +/-- Complete interval computation for depth 11, residue 120. -/ +theorem bounds_11_120 : exactInterval 11 120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_120 (m : Nat) : + stoppingTime (2 ^ 11 * m + 120) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_120 : oddCount 120 11 = 4 ∧ acceleratedOrbit 11 120 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_120 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 120) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_120.1, data_11_120.2] + +/-- Complete interval computation for depth 11, residue 121. -/ +theorem bounds_11_121 : exactInterval 11 121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_121 (m : Nat) : + stoppingTime (2 ^ 11 * m + 121) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_121 : oddCount 121 11 = 8 ∧ acceleratedOrbit 11 121 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_121 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 121) = 3 ^ 8 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_121.1, data_11_121.2] + +/-- Complete interval computation for depth 11, residue 122. -/ +theorem bounds_11_122 : exactInterval 11 122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_122 (m : Nat) : + stoppingTime (2 ^ 11 * m + 122) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_122 : oddCount 122 11 = 4 ∧ acceleratedOrbit 11 122 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_122 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 122) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_122.1, data_11_122.2] + +/-- Complete interval computation for depth 11, residue 123. -/ +theorem bounds_11_123 : exactInterval 11 123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_123 (m : Nat) : + stoppingTime (2 ^ 11 * m + 123) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_123 : oddCount 123 11 = 7 ∧ acceleratedOrbit 11 123 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_123 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 123) = 3 ^ 7 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_123.1, data_11_123.2] + +/-- Complete interval computation for depth 11, residue 124. -/ +theorem bounds_11_124 : exactInterval 11 124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_124 (m : Nat) : + stoppingTime (2 ^ 11 * m + 124) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_124 : oddCount 124 11 = 7 ∧ acceleratedOrbit 11 124 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_124 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 124) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_124.1, data_11_124.2] + +/-- Complete interval computation for depth 11, residue 125. -/ +theorem bounds_11_125 : exactInterval 11 125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_125 (m : Nat) : + stoppingTime (2 ^ 11 * m + 125) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_125 : oddCount 125 11 = 7 ∧ acceleratedOrbit 11 125 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_125 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 125) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_125.1, data_11_125.2] + +/-- Complete interval computation for depth 11, residue 126. -/ +theorem bounds_11_126 : exactInterval 11 126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_126 (m : Nat) : + stoppingTime (2 ^ 11 * m + 126) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_126 : oddCount 126 11 = 7 ∧ acceleratedOrbit 11 126 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_126 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 126) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_126.1, data_11_126.2] + +/-- Complete interval computation for depth 11, residue 127. -/ +theorem bounds_11_127 : exactInterval 11 127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_127 (m : Nat) : + stoppingTime (2 ^ 11 * m + 127) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_127 : oddCount 127 11 = 8 ∧ acceleratedOrbit 11 127 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_127 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 127) = 3 ^ 8 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_127.1, data_11_127.2] + +end Collatz.Research.StoppingAtlas.Batch0075 From 53c9e6733041b953f49851b2a20d93c90f4e115b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:23 +0530 Subject: [PATCH 0076/1001] proof: certify atlas Batch0076 (11:128 to 11:142) --- Collatz/Research/StoppingAtlas/Batch0076.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0076.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0076.lean b/Collatz/Research/StoppingAtlas/Batch0076.lean new file mode 100644 index 00000000..135edac0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0076.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0076 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 128. -/ +theorem bounds_11_128 : exactInterval 11 128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_128 (m : Nat) : + stoppingTime (2 ^ 11 * m + 128) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_128 : oddCount 128 11 = 2 ∧ acceleratedOrbit 11 128 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_128 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 128) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_128.1, data_11_128.2] + +/-- Complete interval computation for depth 11, residue 129. -/ +theorem bounds_11_129 : exactInterval 11 129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_129 (m : Nat) : + stoppingTime (2 ^ 11 * m + 129) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_129 : oddCount 129 11 = 6 ∧ acceleratedOrbit 11 129 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_129 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 129) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_129.1, data_11_129.2] + +/-- Complete interval computation for depth 11, residue 130. -/ +theorem bounds_11_130 : exactInterval 11 130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_130 (m : Nat) : + stoppingTime (2 ^ 11 * m + 130) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_130 : oddCount 130 11 = 5 ∧ acceleratedOrbit 11 130 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_130 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 130) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_130.1, data_11_130.2] + +/-- Complete interval computation for depth 11, residue 131. -/ +theorem bounds_11_131 : exactInterval 11 131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_131 (m : Nat) : + stoppingTime (2 ^ 11 * m + 131) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_131 : oddCount 131 11 = 5 ∧ acceleratedOrbit 11 131 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_131 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 131) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_131.1, data_11_131.2] + +/-- Complete interval computation for depth 11, residue 132. -/ +theorem bounds_11_132 : exactInterval 11 132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_132 (m : Nat) : + stoppingTime (2 ^ 11 * m + 132) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_132 : oddCount 132 11 = 5 ∧ acceleratedOrbit 11 132 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_132 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 132) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_132.1, data_11_132.2] + +/-- Complete interval computation for depth 11, residue 133. -/ +theorem bounds_11_133 : exactInterval 11 133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_133 (m : Nat) : + stoppingTime (2 ^ 11 * m + 133) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_133 : oddCount 133 11 = 5 ∧ acceleratedOrbit 11 133 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_133 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 133) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_133.1, data_11_133.2] + +/-- Complete interval computation for depth 11, residue 134. -/ +theorem bounds_11_134 : exactInterval 11 134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_134 (m : Nat) : + stoppingTime (2 ^ 11 * m + 134) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_134 : oddCount 134 11 = 5 ∧ acceleratedOrbit 11 134 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_134 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 134) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_134.1, data_11_134.2] + +/-- Complete interval computation for depth 11, residue 135. -/ +theorem bounds_11_135 : exactInterval 11 135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_135 (m : Nat) : + stoppingTime (2 ^ 11 * m + 135) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_135 : oddCount 135 11 = 6 ∧ acceleratedOrbit 11 135 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_135 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 135) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_135.1, data_11_135.2] + +/-- Complete interval computation for depth 11, residue 136. -/ +theorem bounds_11_136 : exactInterval 11 136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_136 (m : Nat) : + stoppingTime (2 ^ 11 * m + 136) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_136 : oddCount 136 11 = 3 ∧ acceleratedOrbit 11 136 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_136 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 136) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_136.1, data_11_136.2] + +/-- Complete interval computation for depth 11, residue 137. -/ +theorem bounds_11_137 : exactInterval 11 137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_137 (m : Nat) : + stoppingTime (2 ^ 11 * m + 137) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_137 : oddCount 137 11 = 8 ∧ acceleratedOrbit 11 137 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_137 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 137) = 3 ^ 8 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_137.1, data_11_137.2] + +/-- Complete interval computation for depth 11, residue 138. -/ +theorem bounds_11_138 : exactInterval 11 138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_138 (m : Nat) : + stoppingTime (2 ^ 11 * m + 138) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_138 : oddCount 138 11 = 3 ∧ acceleratedOrbit 11 138 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_138 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 138) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_138.1, data_11_138.2] + +/-- Complete interval computation for depth 11, residue 139. -/ +theorem bounds_11_139 : exactInterval 11 139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_139 (m : Nat) : + stoppingTime (2 ^ 11 * m + 139) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_139 : oddCount 139 11 = 7 ∧ acceleratedOrbit 11 139 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_139 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 139) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_139.1, data_11_139.2] + +/-- Complete interval computation for depth 11, residue 140. -/ +theorem bounds_11_140 : exactInterval 11 140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_140 (m : Nat) : + stoppingTime (2 ^ 11 * m + 140) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_140 : oddCount 140 11 = 3 ∧ acceleratedOrbit 11 140 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_140 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 140) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_140.1, data_11_140.2] + +/-- Complete interval computation for depth 11, residue 141. -/ +theorem bounds_11_141 : exactInterval 11 141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_141 (m : Nat) : + stoppingTime (2 ^ 11 * m + 141) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_141 : oddCount 141 11 = 3 ∧ acceleratedOrbit 11 141 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_141 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 141) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_141.1, data_11_141.2] + +/-- Complete interval computation for depth 11, residue 142. -/ +theorem bounds_11_142 : exactInterval 11 142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_142 (m : Nat) : + stoppingTime (2 ^ 11 * m + 142) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_142 : oddCount 142 11 = 7 ∧ acceleratedOrbit 11 142 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_142 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 142) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_142.1, data_11_142.2] + +end Collatz.Research.StoppingAtlas.Batch0076 From e093e539555bf40acdc716e01202b0babd9f4e82 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:23 +0530 Subject: [PATCH 0077/1001] proof: certify atlas Batch0077 (11:143 to 11:157) --- Collatz/Research/StoppingAtlas/Batch0077.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0077.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0077.lean b/Collatz/Research/StoppingAtlas/Batch0077.lean new file mode 100644 index 00000000..6df42ccc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0077.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0077 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 143. -/ +theorem bounds_11_143 : exactInterval 11 143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_143 (m : Nat) : + stoppingTime (2 ^ 11 * m + 143) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_143 : oddCount 143 11 = 7 ∧ acceleratedOrbit 11 143 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_143 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 143) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_143.1, data_11_143.2] + +/-- Complete interval computation for depth 11, residue 144. -/ +theorem bounds_11_144 : exactInterval 11 144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_144 (m : Nat) : + stoppingTime (2 ^ 11 * m + 144) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_144 : oddCount 144 11 = 5 ∧ acceleratedOrbit 11 144 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_144 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 144) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_144.1, data_11_144.2] + +/-- Complete interval computation for depth 11, residue 145. -/ +theorem bounds_11_145 : exactInterval 11 145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_145 (m : Nat) : + stoppingTime (2 ^ 11 * m + 145) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_145 : oddCount 145 11 = 7 ∧ acceleratedOrbit 11 145 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_145 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 145) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_145.1, data_11_145.2] + +/-- Complete interval computation for depth 11, residue 146. -/ +theorem bounds_11_146 : exactInterval 11 146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_146 (m : Nat) : + stoppingTime (2 ^ 11 * m + 146) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_146 : oddCount 146 11 = 7 ∧ acceleratedOrbit 11 146 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_146 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 146) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_146.1, data_11_146.2] + +/-- Complete interval computation for depth 11, residue 147. -/ +theorem bounds_11_147 : exactInterval 11 147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_147 (m : Nat) : + stoppingTime (2 ^ 11 * m + 147) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_147 : oddCount 147 11 = 7 ∧ acceleratedOrbit 11 147 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_147 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 147) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_147.1, data_11_147.2] + +/-- Complete interval computation for depth 11, residue 148. -/ +theorem bounds_11_148 : exactInterval 11 148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_148 (m : Nat) : + stoppingTime (2 ^ 11 * m + 148) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_148 : oddCount 148 11 = 5 ∧ acceleratedOrbit 11 148 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_148 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 148) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_148.1, data_11_148.2] + +/-- Complete interval computation for depth 11, residue 149. -/ +theorem bounds_11_149 : exactInterval 11 149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_149 (m : Nat) : + stoppingTime (2 ^ 11 * m + 149) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_149 : oddCount 149 11 = 5 ∧ acceleratedOrbit 11 149 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_149 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 149) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_149.1, data_11_149.2] + +/-- Complete interval computation for depth 11, residue 150. -/ +theorem bounds_11_150 : exactInterval 11 150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_150 (m : Nat) : + stoppingTime (2 ^ 11 * m + 150) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_150 : oddCount 150 11 = 3 ∧ acceleratedOrbit 11 150 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_150 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 150) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_150.1, data_11_150.2] + +/-- Complete interval computation for depth 11, residue 151. -/ +theorem bounds_11_151 : exactInterval 11 151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_151 (m : Nat) : + stoppingTime (2 ^ 11 * m + 151) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_151 : oddCount 151 11 = 3 ∧ acceleratedOrbit 11 151 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_151 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 151) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_151.1, data_11_151.2] + +/-- Complete interval computation for depth 11, residue 152. -/ +theorem bounds_11_152 : exactInterval 11 152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_152 (m : Nat) : + stoppingTime (2 ^ 11 * m + 152) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_152 : oddCount 152 11 = 5 ∧ acceleratedOrbit 11 152 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_152 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 152) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_152.1, data_11_152.2] + +/-- Complete interval computation for depth 11, residue 153. -/ +theorem bounds_11_153 : exactInterval 11 153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_153 (m : Nat) : + stoppingTime (2 ^ 11 * m + 153) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_153 : oddCount 153 11 = 6 ∧ acceleratedOrbit 11 153 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_153 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 153) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_153.1, data_11_153.2] + +/-- Complete interval computation for depth 11, residue 154. -/ +theorem bounds_11_154 : exactInterval 11 154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_154 (m : Nat) : + stoppingTime (2 ^ 11 * m + 154) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_154 : oddCount 154 11 = 5 ∧ acceleratedOrbit 11 154 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_154 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 154) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_154.1, data_11_154.2] + +/-- Complete interval computation for depth 11, residue 155. -/ +theorem bounds_11_155 : exactInterval 11 155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_155 (m : Nat) : + stoppingTime (2 ^ 11 * m + 155) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_155 : oddCount 155 11 = 7 ∧ acceleratedOrbit 11 155 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_155 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 155) = 3 ^ 7 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_155.1, data_11_155.2] + +/-- Complete interval computation for depth 11, residue 156. -/ +theorem bounds_11_156 : exactInterval 11 156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_156 (m : Nat) : + stoppingTime (2 ^ 11 * m + 156) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_156 : oddCount 156 11 = 5 ∧ acceleratedOrbit 11 156 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_156 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 156) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_156.1, data_11_156.2] + +/-- Complete interval computation for depth 11, residue 157. -/ +theorem bounds_11_157 : exactInterval 11 157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_157 (m : Nat) : + stoppingTime (2 ^ 11 * m + 157) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_157 : oddCount 157 11 = 5 ∧ acceleratedOrbit 11 157 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_157 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 157) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_157.1, data_11_157.2] + +end Collatz.Research.StoppingAtlas.Batch0077 From 9d2598d3005b25711515a57249e61bc7c15e6e54 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:23 +0530 Subject: [PATCH 0078/1001] proof: certify atlas Batch0078 (11:158 to 11:173) --- Collatz/Research/StoppingAtlas/Batch0078.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0078.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0078.lean b/Collatz/Research/StoppingAtlas/Batch0078.lean new file mode 100644 index 00000000..468cc6d6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0078.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0078 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 158. -/ +theorem bounds_11_158 : exactInterval 11 158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_158 (m : Nat) : + stoppingTime (2 ^ 11 * m + 158) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_158 : oddCount 158 11 = 5 ∧ acceleratedOrbit 11 158 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_158 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 158) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_158.1, data_11_158.2] + +/-- Complete interval computation for depth 11, residue 159. -/ +theorem bounds_11_159 : exactInterval 11 159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_159 (m : Nat) : + stoppingTime (2 ^ 11 * m + 159) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_159 : oddCount 159 11 = 10 ∧ acceleratedOrbit 11 159 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_159 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 159) = 3 ^ 10 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_159.1, data_11_159.2] + +/-- Complete interval computation for depth 11, residue 160. -/ +theorem bounds_11_160 : exactInterval 11 160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_160 (m : Nat) : + stoppingTime (2 ^ 11 * m + 160) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_160 : oddCount 160 11 = 2 ∧ acceleratedOrbit 11 160 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_160 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 160) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_160.1, data_11_160.2] + +/-- Complete interval computation for depth 11, residue 161. -/ +theorem bounds_11_161 : exactInterval 11 161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_161 (m : Nat) : + stoppingTime (2 ^ 11 * m + 161) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_161 : oddCount 161 11 = 7 ∧ acceleratedOrbit 11 161 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_161 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 161) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_161.1, data_11_161.2] + +/-- Complete interval computation for depth 11, residue 162. -/ +theorem bounds_11_162 : exactInterval 11 162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_162 (m : Nat) : + stoppingTime (2 ^ 11 * m + 162) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_162 : oddCount 162 11 = 5 ∧ acceleratedOrbit 11 162 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_162 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 162) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_162.1, data_11_162.2] + +/-- Complete interval computation for depth 11, residue 163. -/ +theorem bounds_11_163 : exactInterval 11 163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_163 (m : Nat) : + stoppingTime (2 ^ 11 * m + 163) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_163 : oddCount 163 11 = 5 ∧ acceleratedOrbit 11 163 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_163 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 163) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_163.1, data_11_163.2] + +/-- Complete interval computation for depth 11, residue 164. -/ +theorem bounds_11_164 : exactInterval 11 164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_164 (m : Nat) : + stoppingTime (2 ^ 11 * m + 164) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_164 : oddCount 164 11 = 7 ∧ acceleratedOrbit 11 164 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_164 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 164) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_164.1, data_11_164.2] + +/-- Complete interval computation for depth 11, residue 165. -/ +theorem bounds_11_165 : exactInterval 11 165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_165 (m : Nat) : + stoppingTime (2 ^ 11 * m + 165) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_165 : oddCount 165 11 = 7 ∧ acceleratedOrbit 11 165 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_165 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 165) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_165.1, data_11_165.2] + +/-- Complete interval computation for depth 11, residue 166. -/ +theorem bounds_11_166 : exactInterval 11 166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_166 (m : Nat) : + stoppingTime (2 ^ 11 * m + 166) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_166 : oddCount 166 11 = 7 ∧ acceleratedOrbit 11 166 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_166 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 166) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_166.1, data_11_166.2] + +/-- Complete interval computation for depth 11, residue 167. -/ +theorem bounds_11_167 : exactInterval 11 167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_167 (m : Nat) : + stoppingTime (2 ^ 11 * m + 167) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_167 : oddCount 167 11 = 9 ∧ acceleratedOrbit 11 167 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_167 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 167) = 3 ^ 9 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_167.1, data_11_167.2] + +/-- Complete interval computation for depth 11, residue 168. -/ +theorem bounds_11_168 : exactInterval 11 168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_168 (m : Nat) : + stoppingTime (2 ^ 11 * m + 168) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_168 : oddCount 168 11 = 2 ∧ acceleratedOrbit 11 168 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_168 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 168) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_168.1, data_11_168.2] + +/-- Complete interval computation for depth 11, residue 169. -/ +theorem bounds_11_169 : exactInterval 11 169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_169 (m : Nat) : + stoppingTime (2 ^ 11 * m + 169) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_169 : oddCount 169 11 = 9 ∧ acceleratedOrbit 11 169 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_169 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 169) = 3 ^ 9 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_169.1, data_11_169.2] + +/-- Complete interval computation for depth 11, residue 170. -/ +theorem bounds_11_170 : exactInterval 11 170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_170 (m : Nat) : + stoppingTime (2 ^ 11 * m + 170) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_170 : oddCount 170 11 = 2 ∧ acceleratedOrbit 11 170 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_170 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 170) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_170.1, data_11_170.2] + +/-- Complete interval computation for depth 11, residue 171. -/ +theorem bounds_11_171 : exactInterval 11 171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_171 (m : Nat) : + stoppingTime (2 ^ 11 * m + 171) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_171 : oddCount 171 11 = 6 ∧ acceleratedOrbit 11 171 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_171 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 171) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_171.1, data_11_171.2] + +/-- Complete interval computation for depth 11, residue 172. -/ +theorem bounds_11_172 : exactInterval 11 172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_172 (m : Nat) : + stoppingTime (2 ^ 11 * m + 172) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_172 : oddCount 172 11 = 4 ∧ acceleratedOrbit 11 172 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_172 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 172) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_172.1, data_11_172.2] + +/-- Complete interval computation for depth 11, residue 173. -/ +theorem bounds_11_173 : exactInterval 11 173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_173 (m : Nat) : + stoppingTime (2 ^ 11 * m + 173) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_173 : oddCount 173 11 = 4 ∧ acceleratedOrbit 11 173 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_173 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 173) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_173.1, data_11_173.2] + +end Collatz.Research.StoppingAtlas.Batch0078 From 571216c8730435f6cd91b3a2b0c3b9e1aceb462e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:24 +0530 Subject: [PATCH 0079/1001] proof: certify atlas Batch0079 (11:174 to 11:188) --- Collatz/Research/StoppingAtlas/Batch0079.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0079.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0079.lean b/Collatz/Research/StoppingAtlas/Batch0079.lean new file mode 100644 index 00000000..4894795b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0079.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0079 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 174. -/ +theorem bounds_11_174 : exactInterval 11 174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_174 (m : Nat) : + stoppingTime (2 ^ 11 * m + 174) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_174 : oddCount 174 11 = 4 ∧ acceleratedOrbit 11 174 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_174 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 174) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_174.1, data_11_174.2] + +/-- Complete interval computation for depth 11, residue 175. -/ +theorem bounds_11_175 : exactInterval 11 175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_175 (m : Nat) : + stoppingTime (2 ^ 11 * m + 175) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_175 : oddCount 175 11 = 8 ∧ acceleratedOrbit 11 175 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_175 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 175) = 3 ^ 8 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_175.1, data_11_175.2] + +/-- Complete interval computation for depth 11, residue 176. -/ +theorem bounds_11_176 : exactInterval 11 176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_176 (m : Nat) : + stoppingTime (2 ^ 11 * m + 176) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_176 : oddCount 176 11 = 4 ∧ acceleratedOrbit 11 176 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_176 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 176) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_176.1, data_11_176.2] + +/-- Complete interval computation for depth 11, residue 177. -/ +theorem bounds_11_177 : exactInterval 11 177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_177 (m : Nat) : + stoppingTime (2 ^ 11 * m + 177) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_177 : oddCount 177 11 = 5 ∧ acceleratedOrbit 11 177 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_177 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 177) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_177.1, data_11_177.2] + +/-- Complete interval computation for depth 11, residue 178. -/ +theorem bounds_11_178 : exactInterval 11 178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_178 (m : Nat) : + stoppingTime (2 ^ 11 * m + 178) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_178 : oddCount 178 11 = 5 ∧ acceleratedOrbit 11 178 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_178 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 178) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_178.1, data_11_178.2] + +/-- Complete interval computation for depth 11, residue 179. -/ +theorem bounds_11_179 : exactInterval 11 179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_179 (m : Nat) : + stoppingTime (2 ^ 11 * m + 179) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_179 : oddCount 179 11 = 5 ∧ acceleratedOrbit 11 179 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_179 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 179) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_179.1, data_11_179.2] + +/-- Complete interval computation for depth 11, residue 180. -/ +theorem bounds_11_180 : exactInterval 11 180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_180 (m : Nat) : + stoppingTime (2 ^ 11 * m + 180) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_180 : oddCount 180 11 = 4 ∧ acceleratedOrbit 11 180 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_180 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 180) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_180.1, data_11_180.2] + +/-- Complete interval computation for depth 11, residue 181. -/ +theorem bounds_11_181 : exactInterval 11 181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_181 (m : Nat) : + stoppingTime (2 ^ 11 * m + 181) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_181 : oddCount 181 11 = 4 ∧ acceleratedOrbit 11 181 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_181 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 181) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_181.1, data_11_181.2] + +/-- Complete interval computation for depth 11, residue 182. -/ +theorem bounds_11_182 : exactInterval 11 182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_182 (m : Nat) : + stoppingTime (2 ^ 11 * m + 182) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_182 : oddCount 182 11 = 8 ∧ acceleratedOrbit 11 182 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_182 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 182) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_182.1, data_11_182.2] + +/-- Complete interval computation for depth 11, residue 183. -/ +theorem bounds_11_183 : exactInterval 11 183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_183 (m : Nat) : + stoppingTime (2 ^ 11 * m + 183) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_183 : oddCount 183 11 = 8 ∧ acceleratedOrbit 11 183 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_183 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 183) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_183.1, data_11_183.2] + +/-- Complete interval computation for depth 11, residue 184. -/ +theorem bounds_11_184 : exactInterval 11 184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_184 (m : Nat) : + stoppingTime (2 ^ 11 * m + 184) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_184 : oddCount 184 11 = 4 ∧ acceleratedOrbit 11 184 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_184 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 184) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_184.1, data_11_184.2] + +/-- Complete interval computation for depth 11, residue 185. -/ +theorem bounds_11_185 : exactInterval 11 185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_185 (m : Nat) : + stoppingTime (2 ^ 11 * m + 185) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_185 : oddCount 185 11 = 6 ∧ acceleratedOrbit 11 185 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_185 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 185) = 3 ^ 6 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_185.1, data_11_185.2] + +/-- Complete interval computation for depth 11, residue 186. -/ +theorem bounds_11_186 : exactInterval 11 186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_186 (m : Nat) : + stoppingTime (2 ^ 11 * m + 186) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_186 : oddCount 186 11 = 4 ∧ acceleratedOrbit 11 186 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_186 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 186) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_186.1, data_11_186.2] + +/-- Complete interval computation for depth 11, residue 187. -/ +theorem bounds_11_187 : exactInterval 11 187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_187 (m : Nat) : + stoppingTime (2 ^ 11 * m + 187) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_187 : oddCount 187 11 = 7 ∧ acceleratedOrbit 11 187 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_187 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 187) = 3 ^ 7 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_187.1, data_11_187.2] + +/-- Complete interval computation for depth 11, residue 188. -/ +theorem bounds_11_188 : exactInterval 11 188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_188 (m : Nat) : + stoppingTime (2 ^ 11 * m + 188) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_188 : oddCount 188 11 = 7 ∧ acceleratedOrbit 11 188 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_188 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 188) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_188.1, data_11_188.2] + +end Collatz.Research.StoppingAtlas.Batch0079 From 84afc7a0285fee0262654c6947ba5406d9ab79fb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:24 +0530 Subject: [PATCH 0080/1001] proof: certify atlas Batch0080 (11:189 to 11:203) --- Collatz/Research/StoppingAtlas/Batch0080.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0080.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0080.lean b/Collatz/Research/StoppingAtlas/Batch0080.lean new file mode 100644 index 00000000..0b661fb9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0080.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0080 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 189. -/ +theorem bounds_11_189 : exactInterval 11 189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_189 (m : Nat) : + stoppingTime (2 ^ 11 * m + 189) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_189 : oddCount 189 11 = 7 ∧ acceleratedOrbit 11 189 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_189 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 189) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_189.1, data_11_189.2] + +/-- Complete interval computation for depth 11, residue 190. -/ +theorem bounds_11_190 : exactInterval 11 190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_190 (m : Nat) : + stoppingTime (2 ^ 11 * m + 190) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_190 : oddCount 190 11 = 7 ∧ acceleratedOrbit 11 190 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_190 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 190) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_190.1, data_11_190.2] + +/-- Complete interval computation for depth 11, residue 191. -/ +theorem bounds_11_191 : exactInterval 11 191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_191 (m : Nat) : + stoppingTime (2 ^ 11 * m + 191) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_191 : oddCount 191 11 = 7 ∧ acceleratedOrbit 11 191 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_191 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 191) = 3 ^ 7 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_191.1, data_11_191.2] + +/-- Complete interval computation for depth 11, residue 192. -/ +theorem bounds_11_192 : exactInterval 11 192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_192 (m : Nat) : + stoppingTime (2 ^ 11 * m + 192) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_192 : oddCount 192 11 = 2 ∧ acceleratedOrbit 11 192 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_192 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 192) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_192.1, data_11_192.2] + +/-- Complete interval computation for depth 11, residue 193. -/ +theorem bounds_11_193 : exactInterval 11 193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_193 (m : Nat) : + stoppingTime (2 ^ 11 * m + 193) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_193 : oddCount 193 11 = 6 ∧ acceleratedOrbit 11 193 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_193 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 193) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_193.1, data_11_193.2] + +/-- Complete interval computation for depth 11, residue 194. -/ +theorem bounds_11_194 : exactInterval 11 194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_194 (m : Nat) : + stoppingTime (2 ^ 11 * m + 194) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_194 : oddCount 194 11 = 6 ∧ acceleratedOrbit 11 194 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_194 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 194) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_194.1, data_11_194.2] + +/-- Complete interval computation for depth 11, residue 195. -/ +theorem bounds_11_195 : exactInterval 11 195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_195 (m : Nat) : + stoppingTime (2 ^ 11 * m + 195) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_195 : oddCount 195 11 = 6 ∧ acceleratedOrbit 11 195 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_195 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 195) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_195.1, data_11_195.2] + +/-- Complete interval computation for depth 11, residue 196. -/ +theorem bounds_11_196 : exactInterval 11 196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_196 (m : Nat) : + stoppingTime (2 ^ 11 * m + 196) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_196 : oddCount 196 11 = 5 ∧ acceleratedOrbit 11 196 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_196 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 196) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_196.1, data_11_196.2] + +/-- Complete interval computation for depth 11, residue 197. -/ +theorem bounds_11_197 : exactInterval 11 197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_197 (m : Nat) : + stoppingTime (2 ^ 11 * m + 197) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_197 : oddCount 197 11 = 5 ∧ acceleratedOrbit 11 197 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_197 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 197) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_197.1, data_11_197.2] + +/-- Complete interval computation for depth 11, residue 198. -/ +theorem bounds_11_198 : exactInterval 11 198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_198 (m : Nat) : + stoppingTime (2 ^ 11 * m + 198) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_198 : oddCount 198 11 = 5 ∧ acceleratedOrbit 11 198 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_198 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 198) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_198.1, data_11_198.2] + +/-- Complete interval computation for depth 11, residue 199. -/ +theorem bounds_11_199 : exactInterval 11 199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_199 (m : Nat) : + stoppingTime (2 ^ 11 * m + 199) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_199 : oddCount 199 11 = 7 ∧ acceleratedOrbit 11 199 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_199 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 199) = 3 ^ 7 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_199.1, data_11_199.2] + +/-- Complete interval computation for depth 11, residue 200. -/ +theorem bounds_11_200 : exactInterval 11 200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_200 (m : Nat) : + stoppingTime (2 ^ 11 * m + 200) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_200 : oddCount 200 11 = 5 ∧ acceleratedOrbit 11 200 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_200 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 200) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_200.1, data_11_200.2] + +/-- Complete interval computation for depth 11, residue 201. -/ +theorem bounds_11_201 : exactInterval 11 201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_201 (m : Nat) : + stoppingTime (2 ^ 11 * m + 201) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_201 : oddCount 201 11 = 4 ∧ acceleratedOrbit 11 201 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_201 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 201) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_201.1, data_11_201.2] + +/-- Complete interval computation for depth 11, residue 202. -/ +theorem bounds_11_202 : exactInterval 11 202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_202 (m : Nat) : + stoppingTime (2 ^ 11 * m + 202) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_202 : oddCount 202 11 = 5 ∧ acceleratedOrbit 11 202 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_202 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 202) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_202.1, data_11_202.2] + +/-- Complete interval computation for depth 11, residue 203. -/ +theorem bounds_11_203 : exactInterval 11 203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_203 (m : Nat) : + stoppingTime (2 ^ 11 * m + 203) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_203 : oddCount 203 11 = 6 ∧ acceleratedOrbit 11 203 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_203 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 203) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_203.1, data_11_203.2] + +end Collatz.Research.StoppingAtlas.Batch0080 From 1ebc94214bc362db23f19af0b0e5690bd81ea981 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:24 +0530 Subject: [PATCH 0081/1001] proof: certify atlas Batch0081 (11:204 to 11:219) --- Collatz/Research/StoppingAtlas/Batch0081.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0081.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0081.lean b/Collatz/Research/StoppingAtlas/Batch0081.lean new file mode 100644 index 00000000..3b4de94a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0081.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0081 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 204. -/ +theorem bounds_11_204 : exactInterval 11 204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_204 (m : Nat) : + stoppingTime (2 ^ 11 * m + 204) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_204 : oddCount 204 11 = 5 ∧ acceleratedOrbit 11 204 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_204 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 204) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_204.1, data_11_204.2] + +/-- Complete interval computation for depth 11, residue 205. -/ +theorem bounds_11_205 : exactInterval 11 205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_205 (m : Nat) : + stoppingTime (2 ^ 11 * m + 205) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_205 : oddCount 205 11 = 5 ∧ acceleratedOrbit 11 205 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_205 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 205) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_205.1, data_11_205.2] + +/-- Complete interval computation for depth 11, residue 206. -/ +theorem bounds_11_206 : exactInterval 11 206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_206 (m : Nat) : + stoppingTime (2 ^ 11 * m + 206) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_206 : oddCount 206 11 = 8 ∧ acceleratedOrbit 11 206 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_206 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 206) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_206.1, data_11_206.2] + +/-- Complete interval computation for depth 11, residue 207. -/ +theorem bounds_11_207 : exactInterval 11 207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_207 (m : Nat) : + stoppingTime (2 ^ 11 * m + 207) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_207 : oddCount 207 11 = 8 ∧ acceleratedOrbit 11 207 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_207 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 207) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_207.1, data_11_207.2] + +/-- Complete interval computation for depth 11, residue 208. -/ +theorem bounds_11_208 : exactInterval 11 208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_208 (m : Nat) : + stoppingTime (2 ^ 11 * m + 208) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_208 : oddCount 208 11 = 2 ∧ acceleratedOrbit 11 208 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_208 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 208) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_208.1, data_11_208.2] + +/-- Complete interval computation for depth 11, residue 209. -/ +theorem bounds_11_209 : exactInterval 11 209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_209 (m : Nat) : + stoppingTime (2 ^ 11 * m + 209) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_209 : oddCount 209 11 = 6 ∧ acceleratedOrbit 11 209 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_209 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 209) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_209.1, data_11_209.2] + +/-- Complete interval computation for depth 11, residue 210. -/ +theorem bounds_11_210 : exactInterval 11 210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_210 (m : Nat) : + stoppingTime (2 ^ 11 * m + 210) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_210 : oddCount 210 11 = 6 ∧ acceleratedOrbit 11 210 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_210 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 210) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_210.1, data_11_210.2] + +/-- Complete interval computation for depth 11, residue 211. -/ +theorem bounds_11_211 : exactInterval 11 211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_211 (m : Nat) : + stoppingTime (2 ^ 11 * m + 211) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_211 : oddCount 211 11 = 6 ∧ acceleratedOrbit 11 211 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_211 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 211) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_211.1, data_11_211.2] + +/-- Complete interval computation for depth 11, residue 212. -/ +theorem bounds_11_212 : exactInterval 11 212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_212 (m : Nat) : + stoppingTime (2 ^ 11 * m + 212) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_212 : oddCount 212 11 = 2 ∧ acceleratedOrbit 11 212 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_212 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 212) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_212.1, data_11_212.2] + +/-- Complete interval computation for depth 11, residue 213. -/ +theorem bounds_11_213 : exactInterval 11 213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_213 (m : Nat) : + stoppingTime (2 ^ 11 * m + 213) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_213 : oddCount 213 11 = 2 ∧ acceleratedOrbit 11 213 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_213 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 213) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_213.1, data_11_213.2] + +/-- Complete interval computation for depth 11, residue 214. -/ +theorem bounds_11_214 : exactInterval 11 214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_214 (m : Nat) : + stoppingTime (2 ^ 11 * m + 214) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_214 : oddCount 214 11 = 7 ∧ acceleratedOrbit 11 214 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_214 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 214) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_214.1, data_11_214.2] + +/-- Complete interval computation for depth 11, residue 215. -/ +theorem bounds_11_215 : exactInterval 11 215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_215 (m : Nat) : + stoppingTime (2 ^ 11 * m + 215) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_215 : oddCount 215 11 = 7 ∧ acceleratedOrbit 11 215 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_215 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 215) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_215.1, data_11_215.2] + +/-- Complete interval computation for depth 11, residue 216. -/ +theorem bounds_11_216 : exactInterval 11 216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_216 (m : Nat) : + stoppingTime (2 ^ 11 * m + 216) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_216 : oddCount 216 11 = 7 ∧ acceleratedOrbit 11 216 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_216 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 216) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_216.1, data_11_216.2] + +/-- Complete interval computation for depth 11, residue 217. -/ +theorem bounds_11_217 : exactInterval 11 217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_217 (m : Nat) : + stoppingTime (2 ^ 11 * m + 217) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_217 : oddCount 217 11 = 6 ∧ acceleratedOrbit 11 217 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_217 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 217) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_217.1, data_11_217.2] + +/-- Complete interval computation for depth 11, residue 218. -/ +theorem bounds_11_218 : exactInterval 11 218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_218 (m : Nat) : + stoppingTime (2 ^ 11 * m + 218) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_218 : oddCount 218 11 = 7 ∧ acceleratedOrbit 11 218 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_218 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 218) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_218.1, data_11_218.2] + +/-- Complete interval computation for depth 11, residue 219. -/ +theorem bounds_11_219 : exactInterval 11 219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_219 (m : Nat) : + stoppingTime (2 ^ 11 * m + 219) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_219 : oddCount 219 11 = 7 ∧ acceleratedOrbit 11 219 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_219 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 219) = 3 ^ 7 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_219.1, data_11_219.2] + +end Collatz.Research.StoppingAtlas.Batch0081 From 421ebf5a1851e6f5a61f5a429379ddad211c6439 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:25 +0530 Subject: [PATCH 0082/1001] proof: certify atlas Batch0082 (11:220 to 11:234) --- Collatz/Research/StoppingAtlas/Batch0082.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0082.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0082.lean b/Collatz/Research/StoppingAtlas/Batch0082.lean new file mode 100644 index 00000000..fd150a09 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0082.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0082 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 220. -/ +theorem bounds_11_220 : exactInterval 11 220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_220 (m : Nat) : + stoppingTime (2 ^ 11 * m + 220) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_220 : oddCount 220 11 = 7 ∧ acceleratedOrbit 11 220 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_220 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 220) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_220.1, data_11_220.2] + +/-- Complete interval computation for depth 11, residue 221. -/ +theorem bounds_11_221 : exactInterval 11 221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_221 (m : Nat) : + stoppingTime (2 ^ 11 * m + 221) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_221 : oddCount 221 11 = 7 ∧ acceleratedOrbit 11 221 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_221 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 221) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_221.1, data_11_221.2] + +/-- Complete interval computation for depth 11, residue 222. -/ +theorem bounds_11_222 : exactInterval 11 222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_222 (m : Nat) : + stoppingTime (2 ^ 11 * m + 222) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_222 : oddCount 222 11 = 8 ∧ acceleratedOrbit 11 222 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_222 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 222) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_222.1, data_11_222.2] + +/-- Complete interval computation for depth 11, residue 223. -/ +theorem bounds_11_223 : exactInterval 11 223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_223 (m : Nat) : + stoppingTime (2 ^ 11 * m + 223) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_223 : oddCount 223 11 = 8 ∧ acceleratedOrbit 11 223 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_223 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 223) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_223.1, data_11_223.2] + +/-- Complete interval computation for depth 11, residue 224. -/ +theorem bounds_11_224 : exactInterval 11 224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_224 (m : Nat) : + stoppingTime (2 ^ 11 * m + 224) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_224 : oddCount 224 11 = 4 ∧ acceleratedOrbit 11 224 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_224 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 224) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_224.1, data_11_224.2] + +/-- Complete interval computation for depth 11, residue 225. -/ +theorem bounds_11_225 : exactInterval 11 225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_225 (m : Nat) : + stoppingTime (2 ^ 11 * m + 225) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_225 : oddCount 225 11 = 9 ∧ acceleratedOrbit 11 225 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_225 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 225) = 3 ^ 9 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_225.1, data_11_225.2] + +/-- Complete interval computation for depth 11, residue 226. -/ +theorem bounds_11_226 : exactInterval 11 226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_226 (m : Nat) : + stoppingTime (2 ^ 11 * m + 226) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_226 : oddCount 226 11 = 2 ∧ acceleratedOrbit 11 226 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_226 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 226) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_226.1, data_11_226.2] + +/-- Complete interval computation for depth 11, residue 227. -/ +theorem bounds_11_227 : exactInterval 11 227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_227 (m : Nat) : + stoppingTime (2 ^ 11 * m + 227) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_227 : oddCount 227 11 = 2 ∧ acceleratedOrbit 11 227 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_227 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 227) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_227.1, data_11_227.2] + +/-- Complete interval computation for depth 11, residue 228. -/ +theorem bounds_11_228 : exactInterval 11 228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_228 (m : Nat) : + stoppingTime (2 ^ 11 * m + 228) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_228 : oddCount 228 11 = 5 ∧ acceleratedOrbit 11 228 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_228 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 228) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_228.1, data_11_228.2] + +/-- Complete interval computation for depth 11, residue 229. -/ +theorem bounds_11_229 : exactInterval 11 229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_229 (m : Nat) : + stoppingTime (2 ^ 11 * m + 229) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_229 : oddCount 229 11 = 5 ∧ acceleratedOrbit 11 229 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_229 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 229) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_229.1, data_11_229.2] + +/-- Complete interval computation for depth 11, residue 230. -/ +theorem bounds_11_230 : exactInterval 11 230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_230 (m : Nat) : + stoppingTime (2 ^ 11 * m + 230) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_230 : oddCount 230 11 = 5 ∧ acceleratedOrbit 11 230 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_230 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 230) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_230.1, data_11_230.2] + +/-- Complete interval computation for depth 11, residue 231. -/ +theorem bounds_11_231 : exactInterval 11 231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_231 (m : Nat) : + stoppingTime (2 ^ 11 * m + 231) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_231 : oddCount 231 11 = 7 ∧ acceleratedOrbit 11 231 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_231 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 231) = 3 ^ 7 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_231.1, data_11_231.2] + +/-- Complete interval computation for depth 11, residue 232. -/ +theorem bounds_11_232 : exactInterval 11 232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_232 (m : Nat) : + stoppingTime (2 ^ 11 * m + 232) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_232 : oddCount 232 11 = 4 ∧ acceleratedOrbit 11 232 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_232 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 232) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_232.1, data_11_232.2] + +/-- Complete interval computation for depth 11, residue 233. -/ +theorem bounds_11_233 : exactInterval 11 233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_233 (m : Nat) : + stoppingTime (2 ^ 11 * m + 233) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_233 : oddCount 233 11 = 7 ∧ acceleratedOrbit 11 233 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_233 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 233) = 3 ^ 7 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_233.1, data_11_233.2] + +/-- Complete interval computation for depth 11, residue 234. -/ +theorem bounds_11_234 : exactInterval 11 234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_234 (m : Nat) : + stoppingTime (2 ^ 11 * m + 234) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_234 : oddCount 234 11 = 4 ∧ acceleratedOrbit 11 234 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_234 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 234) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_234.1, data_11_234.2] + +end Collatz.Research.StoppingAtlas.Batch0082 From de9921815b9900f50159568fdf07adee934b27d1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:25 +0530 Subject: [PATCH 0083/1001] proof: certify atlas Batch0083 (11:235 to 11:249) --- Collatz/Research/StoppingAtlas/Batch0083.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0083.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0083.lean b/Collatz/Research/StoppingAtlas/Batch0083.lean new file mode 100644 index 00000000..ec41e85d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0083.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0083 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 235. -/ +theorem bounds_11_235 : exactInterval 11 235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_235 (m : Nat) : + stoppingTime (2 ^ 11 * m + 235) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_235 : oddCount 235 11 = 7 ∧ acceleratedOrbit 11 235 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_235 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 235) = 3 ^ 7 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_235.1, data_11_235.2] + +/-- Complete interval computation for depth 11, residue 236. -/ +theorem bounds_11_236 : exactInterval 11 236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_236 (m : Nat) : + stoppingTime (2 ^ 11 * m + 236) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_236 : oddCount 236 11 = 5 ∧ acceleratedOrbit 11 236 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_236 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 236) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_236.1, data_11_236.2] + +/-- Complete interval computation for depth 11, residue 237. -/ +theorem bounds_11_237 : exactInterval 11 237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_237 (m : Nat) : + stoppingTime (2 ^ 11 * m + 237) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_237 : oddCount 237 11 = 5 ∧ acceleratedOrbit 11 237 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_237 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 237) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_237.1, data_11_237.2] + +/-- Complete interval computation for depth 11, residue 238. -/ +theorem bounds_11_238 : exactInterval 11 238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_238 (m : Nat) : + stoppingTime (2 ^ 11 * m + 238) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_238 : oddCount 238 11 = 5 ∧ acceleratedOrbit 11 238 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_238 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 238) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_238.1, data_11_238.2] + +/-- Complete interval computation for depth 11, residue 239. -/ +theorem bounds_11_239 : exactInterval 11 239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_239 (m : Nat) : + stoppingTime (2 ^ 11 * m + 239) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_239 : oddCount 239 11 = 9 ∧ acceleratedOrbit 11 239 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_239 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 239) = 3 ^ 9 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_239.1, data_11_239.2] + +/-- Complete interval computation for depth 11, residue 240. -/ +theorem bounds_11_240 : exactInterval 11 240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_240 (m : Nat) : + stoppingTime (2 ^ 11 * m + 240) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_240 : oddCount 240 11 = 4 ∧ acceleratedOrbit 11 240 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_240 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 240) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_240.1, data_11_240.2] + +/-- Complete interval computation for depth 11, residue 241. -/ +theorem bounds_11_241 : exactInterval 11 241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_241 (m : Nat) : + stoppingTime (2 ^ 11 * m + 241) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_241 : oddCount 241 11 = 4 ∧ acceleratedOrbit 11 241 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_241 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 241) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_241.1, data_11_241.2] + +/-- Complete interval computation for depth 11, residue 242. -/ +theorem bounds_11_242 : exactInterval 11 242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_242 (m : Nat) : + stoppingTime (2 ^ 11 * m + 242) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_242 : oddCount 242 11 = 7 ∧ acceleratedOrbit 11 242 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_242 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 242) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_242.1, data_11_242.2] + +/-- Complete interval computation for depth 11, residue 243. -/ +theorem bounds_11_243 : exactInterval 11 243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_243 (m : Nat) : + stoppingTime (2 ^ 11 * m + 243) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_243 : oddCount 243 11 = 7 ∧ acceleratedOrbit 11 243 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_243 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 243) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_243.1, data_11_243.2] + +/-- Complete interval computation for depth 11, residue 244. -/ +theorem bounds_11_244 : exactInterval 11 244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_244 (m : Nat) : + stoppingTime (2 ^ 11 * m + 244) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_244 : oddCount 244 11 = 4 ∧ acceleratedOrbit 11 244 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_244 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 244) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_244.1, data_11_244.2] + +/-- Complete interval computation for depth 11, residue 245. -/ +theorem bounds_11_245 : exactInterval 11 245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_245 (m : Nat) : + stoppingTime (2 ^ 11 * m + 245) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_245 : oddCount 245 11 = 4 ∧ acceleratedOrbit 11 245 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_245 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 245) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_245.1, data_11_245.2] + +/-- Complete interval computation for depth 11, residue 246. -/ +theorem bounds_11_246 : exactInterval 11 246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_246 (m : Nat) : + stoppingTime (2 ^ 11 * m + 246) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_246 : oddCount 246 11 = 6 ∧ acceleratedOrbit 11 246 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_246 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 246) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_246.1, data_11_246.2] + +/-- Complete interval computation for depth 11, residue 247. -/ +theorem bounds_11_247 : exactInterval 11 247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_247 (m : Nat) : + stoppingTime (2 ^ 11 * m + 247) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_247 : oddCount 247 11 = 6 ∧ acceleratedOrbit 11 247 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_247 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 247) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_247.1, data_11_247.2] + +/-- Complete interval computation for depth 11, residue 248. -/ +theorem bounds_11_248 : exactInterval 11 248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_248 (m : Nat) : + stoppingTime (2 ^ 11 * m + 248) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_248 : oddCount 248 11 = 6 ∧ acceleratedOrbit 11 248 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_248 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 248) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_248.1, data_11_248.2] + +/-- Complete interval computation for depth 11, residue 249. -/ +theorem bounds_11_249 : exactInterval 11 249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_249 (m : Nat) : + stoppingTime (2 ^ 11 * m + 249) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_249 : oddCount 249 11 = 7 ∧ acceleratedOrbit 11 249 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_249 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 249) = 3 ^ 7 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_249.1, data_11_249.2] + +end Collatz.Research.StoppingAtlas.Batch0083 From e8435183b1049ecf66d6a558351497623b3f817e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:26 +0530 Subject: [PATCH 0084/1001] proof: certify atlas Batch0084 (11:250 to 11:265) --- Collatz/Research/StoppingAtlas/Batch0084.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0084.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0084.lean b/Collatz/Research/StoppingAtlas/Batch0084.lean new file mode 100644 index 00000000..35ad94ba --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0084.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0084 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 250. -/ +theorem bounds_11_250 : exactInterval 11 250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_250 (m : Nat) : + stoppingTime (2 ^ 11 * m + 250) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_250 : oddCount 250 11 = 6 ∧ acceleratedOrbit 11 250 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_250 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 250) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_250.1, data_11_250.2] + +/-- Complete interval computation for depth 11, residue 251. -/ +theorem bounds_11_251 : exactInterval 11 251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_251 (m : Nat) : + stoppingTime (2 ^ 11 * m + 251) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_251 : oddCount 251 11 = 9 ∧ acceleratedOrbit 11 251 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_251 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 251) = 3 ^ 9 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_251.1, data_11_251.2] + +/-- Complete interval computation for depth 11, residue 252. -/ +theorem bounds_11_252 : exactInterval 11 252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_252 (m : Nat) : + stoppingTime (2 ^ 11 * m + 252) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_252 : oddCount 252 11 = 6 ∧ acceleratedOrbit 11 252 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_252 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 252) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_252.1, data_11_252.2] + +/-- Complete interval computation for depth 11, residue 253. -/ +theorem bounds_11_253 : exactInterval 11 253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_253 (m : Nat) : + stoppingTime (2 ^ 11 * m + 253) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_253 : oddCount 253 11 = 6 ∧ acceleratedOrbit 11 253 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_253 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 253) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_253.1, data_11_253.2] + +/-- Complete interval computation for depth 11, residue 254. -/ +theorem bounds_11_254 : exactInterval 11 254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_254 (m : Nat) : + stoppingTime (2 ^ 11 * m + 254) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_254 : oddCount 254 11 = 8 ∧ acceleratedOrbit 11 254 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_254 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 254) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_254.1, data_11_254.2] + +/-- Complete interval computation for depth 11, residue 255. -/ +theorem bounds_11_255 : exactInterval 11 255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_255 (m : Nat) : + stoppingTime (2 ^ 11 * m + 255) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_255 : oddCount 255 11 = 8 ∧ acceleratedOrbit 11 255 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_255 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 255) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_255.1, data_11_255.2] + +/-- Complete interval computation for depth 11, residue 256. -/ +theorem bounds_11_256 : exactInterval 11 256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_256 (m : Nat) : + stoppingTime (2 ^ 11 * m + 256) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_256 : oddCount 256 11 = 2 ∧ acceleratedOrbit 11 256 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_256 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 256) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_256.1, data_11_256.2] + +/-- Complete interval computation for depth 11, residue 257. -/ +theorem bounds_11_257 : exactInterval 11 257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_257 (m : Nat) : + stoppingTime (2 ^ 11 * m + 257) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_257 : oddCount 257 11 = 5 ∧ acceleratedOrbit 11 257 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_257 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 257) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_257.1, data_11_257.2] + +/-- Complete interval computation for depth 11, residue 258. -/ +theorem bounds_11_258 : exactInterval 11 258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_258 (m : Nat) : + stoppingTime (2 ^ 11 * m + 258) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_258 : oddCount 258 11 = 6 ∧ acceleratedOrbit 11 258 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_258 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 258) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_258.1, data_11_258.2] + +/-- Complete interval computation for depth 11, residue 259. -/ +theorem bounds_11_259 : exactInterval 11 259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_259 (m : Nat) : + stoppingTime (2 ^ 11 * m + 259) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_259 : oddCount 259 11 = 6 ∧ acceleratedOrbit 11 259 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_259 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 259) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_259.1, data_11_259.2] + +/-- Complete interval computation for depth 11, residue 260. -/ +theorem bounds_11_260 : exactInterval 11 260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_260 (m : Nat) : + stoppingTime (2 ^ 11 * m + 260) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_260 : oddCount 260 11 = 4 ∧ acceleratedOrbit 11 260 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_260 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 260) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_260.1, data_11_260.2] + +/-- Complete interval computation for depth 11, residue 261. -/ +theorem bounds_11_261 : exactInterval 11 261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_261 (m : Nat) : + stoppingTime (2 ^ 11 * m + 261) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_261 : oddCount 261 11 = 4 ∧ acceleratedOrbit 11 261 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_261 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 261) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_261.1, data_11_261.2] + +/-- Complete interval computation for depth 11, residue 262. -/ +theorem bounds_11_262 : exactInterval 11 262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_262 (m : Nat) : + stoppingTime (2 ^ 11 * m + 262) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_262 : oddCount 262 11 = 4 ∧ acceleratedOrbit 11 262 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_262 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 262) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_262.1, data_11_262.2] + +/-- Complete interval computation for depth 11, residue 263. -/ +theorem bounds_11_263 : exactInterval 11 263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_263 (m : Nat) : + stoppingTime (2 ^ 11 * m + 263) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_263 : oddCount 263 11 = 7 ∧ acceleratedOrbit 11 263 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_263 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 263) = 3 ^ 7 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_263.1, data_11_263.2] + +/-- Complete interval computation for depth 11, residue 264. -/ +theorem bounds_11_264 : exactInterval 11 264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_264 (m : Nat) : + stoppingTime (2 ^ 11 * m + 264) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_264 : oddCount 264 11 = 4 ∧ acceleratedOrbit 11 264 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_264 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 264) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_264.1, data_11_264.2] + +/-- Complete interval computation for depth 11, residue 265. -/ +theorem bounds_11_265 : exactInterval 11 265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_265 (m : Nat) : + stoppingTime (2 ^ 11 * m + 265) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_265 : oddCount 265 11 = 6 ∧ acceleratedOrbit 11 265 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_265 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 265) = 3 ^ 6 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_265.1, data_11_265.2] + +end Collatz.Research.StoppingAtlas.Batch0084 From e78b9e75a4fbbd4974575947a6e6370f3843d726 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:26 +0530 Subject: [PATCH 0085/1001] proof: certify atlas Batch0085 (11:266 to 11:280) --- Collatz/Research/StoppingAtlas/Batch0085.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0085.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0085.lean b/Collatz/Research/StoppingAtlas/Batch0085.lean new file mode 100644 index 00000000..9b20febd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0085.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0085 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 266. -/ +theorem bounds_11_266 : exactInterval 11 266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_266 (m : Nat) : + stoppingTime (2 ^ 11 * m + 266) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_266 : oddCount 266 11 = 4 ∧ acceleratedOrbit 11 266 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_266 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 266) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_266.1, data_11_266.2] + +/-- Complete interval computation for depth 11, residue 267. -/ +theorem bounds_11_267 : exactInterval 11 267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_267 (m : Nat) : + stoppingTime (2 ^ 11 * m + 267) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_267 : oddCount 267 11 = 5 ∧ acceleratedOrbit 11 267 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_267 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 267) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_267.1, data_11_267.2] + +/-- Complete interval computation for depth 11, residue 268. -/ +theorem bounds_11_268 : exactInterval 11 268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_268 (m : Nat) : + stoppingTime (2 ^ 11 * m + 268) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_268 : oddCount 268 11 = 4 ∧ acceleratedOrbit 11 268 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_268 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 268) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_268.1, data_11_268.2] + +/-- Complete interval computation for depth 11, residue 269. -/ +theorem bounds_11_269 : exactInterval 11 269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_269 (m : Nat) : + stoppingTime (2 ^ 11 * m + 269) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_269 : oddCount 269 11 = 4 ∧ acceleratedOrbit 11 269 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_269 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 269) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_269.1, data_11_269.2] + +/-- Complete interval computation for depth 11, residue 270. -/ +theorem bounds_11_270 : exactInterval 11 270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_270 (m : Nat) : + stoppingTime (2 ^ 11 * m + 270) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_270 : oddCount 270 11 = 6 ∧ acceleratedOrbit 11 270 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_270 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 270) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_270.1, data_11_270.2] + +/-- Complete interval computation for depth 11, residue 271. -/ +theorem bounds_11_271 : exactInterval 11 271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_271 (m : Nat) : + stoppingTime (2 ^ 11 * m + 271) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_271 : oddCount 271 11 = 6 ∧ acceleratedOrbit 11 271 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_271 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 271) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_271.1, data_11_271.2] + +/-- Complete interval computation for depth 11, residue 272. -/ +theorem bounds_11_272 : exactInterval 11 272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_272 (m : Nat) : + stoppingTime (2 ^ 11 * m + 272) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_272 : oddCount 272 11 = 3 ∧ acceleratedOrbit 11 272 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_272 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 272) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_272.1, data_11_272.2] + +/-- Complete interval computation for depth 11, residue 273. -/ +theorem bounds_11_273 : exactInterval 11 273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_273 (m : Nat) : + stoppingTime (2 ^ 11 * m + 273) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_273 : oddCount 273 11 = 4 ∧ acceleratedOrbit 11 273 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_273 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 273) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_273.1, data_11_273.2] + +/-- Complete interval computation for depth 11, residue 274. -/ +theorem bounds_11_274 : exactInterval 11 274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_274 (m : Nat) : + stoppingTime (2 ^ 11 * m + 274) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_274 : oddCount 274 11 = 8 ∧ acceleratedOrbit 11 274 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_274 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 274) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_274.1, data_11_274.2] + +/-- Complete interval computation for depth 11, residue 275. -/ +theorem bounds_11_275 : exactInterval 11 275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_275 (m : Nat) : + stoppingTime (2 ^ 11 * m + 275) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_275 : oddCount 275 11 = 8 ∧ acceleratedOrbit 11 275 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_275 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 275) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_275.1, data_11_275.2] + +/-- Complete interval computation for depth 11, residue 276. -/ +theorem bounds_11_276 : exactInterval 11 276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_276 (m : Nat) : + stoppingTime (2 ^ 11 * m + 276) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_276 : oddCount 276 11 = 3 ∧ acceleratedOrbit 11 276 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_276 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 276) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_276.1, data_11_276.2] + +/-- Complete interval computation for depth 11, residue 277. -/ +theorem bounds_11_277 : exactInterval 11 277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_277 (m : Nat) : + stoppingTime (2 ^ 11 * m + 277) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_277 : oddCount 277 11 = 3 ∧ acceleratedOrbit 11 277 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_277 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 277) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_277.1, data_11_277.2] + +/-- Complete interval computation for depth 11, residue 278. -/ +theorem bounds_11_278 : exactInterval 11 278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_278 (m : Nat) : + stoppingTime (2 ^ 11 * m + 278) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_278 : oddCount 278 11 = 6 ∧ acceleratedOrbit 11 278 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_278 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 278) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_278.1, data_11_278.2] + +/-- Complete interval computation for depth 11, residue 279. -/ +theorem bounds_11_279 : exactInterval 11 279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_279 (m : Nat) : + stoppingTime (2 ^ 11 * m + 279) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_279 : oddCount 279 11 = 6 ∧ acceleratedOrbit 11 279 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_279 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 279) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_279.1, data_11_279.2] + +/-- Complete interval computation for depth 11, residue 280. -/ +theorem bounds_11_280 : exactInterval 11 280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_280 (m : Nat) : + stoppingTime (2 ^ 11 * m + 280) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_280 : oddCount 280 11 = 3 ∧ acceleratedOrbit 11 280 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_280 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 280) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_280.1, data_11_280.2] + +end Collatz.Research.StoppingAtlas.Batch0085 From 2b88c341348214d116ecdbb59589ab375e855d50 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:26 +0530 Subject: [PATCH 0086/1001] proof: certify atlas Batch0086 (11:281 to 11:295) --- Collatz/Research/StoppingAtlas/Batch0086.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0086.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0086.lean b/Collatz/Research/StoppingAtlas/Batch0086.lean new file mode 100644 index 00000000..b312317a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0086.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0086 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 281. -/ +theorem bounds_11_281 : exactInterval 11 281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_281 (m : Nat) : + stoppingTime (2 ^ 11 * m + 281) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_281 : oddCount 281 11 = 6 ∧ acceleratedOrbit 11 281 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_281 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 281) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_281.1, data_11_281.2] + +/-- Complete interval computation for depth 11, residue 282. -/ +theorem bounds_11_282 : exactInterval 11 282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_282 (m : Nat) : + stoppingTime (2 ^ 11 * m + 282) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_282 : oddCount 282 11 = 3 ∧ acceleratedOrbit 11 282 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_282 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 282) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_282.1, data_11_282.2] + +/-- Complete interval computation for depth 11, residue 283. -/ +theorem bounds_11_283 : exactInterval 11 283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_283 (m : Nat) : + stoppingTime (2 ^ 11 * m + 283) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_283 : oddCount 283 11 = 8 ∧ acceleratedOrbit 11 283 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_283 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 283) = 3 ^ 8 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_283.1, data_11_283.2] + +/-- Complete interval computation for depth 11, residue 284. -/ +theorem bounds_11_284 : exactInterval 11 284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_284 (m : Nat) : + stoppingTime (2 ^ 11 * m + 284) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_284 : oddCount 284 11 = 6 ∧ acceleratedOrbit 11 284 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_284 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 284) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_284.1, data_11_284.2] + +/-- Complete interval computation for depth 11, residue 285. -/ +theorem bounds_11_285 : exactInterval 11 285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_285 (m : Nat) : + stoppingTime (2 ^ 11 * m + 285) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_285 : oddCount 285 11 = 6 ∧ acceleratedOrbit 11 285 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_285 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 285) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_285.1, data_11_285.2] + +/-- Complete interval computation for depth 11, residue 286. -/ +theorem bounds_11_286 : exactInterval 11 286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_286 (m : Nat) : + stoppingTime (2 ^ 11 * m + 286) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_286 : oddCount 286 11 = 6 ∧ acceleratedOrbit 11 286 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_286 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 286) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_286.1, data_11_286.2] + +/-- Complete interval computation for depth 11, residue 287. -/ +theorem bounds_11_287 : exactInterval 11 287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_287 (m : Nat) : + stoppingTime (2 ^ 11 * m + 287) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_287 : oddCount 287 11 = 7 ∧ acceleratedOrbit 11 287 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_287 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 287) = 3 ^ 7 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_287.1, data_11_287.2] + +/-- Complete interval computation for depth 11, residue 288. -/ +theorem bounds_11_288 : exactInterval 11 288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_288 (m : Nat) : + stoppingTime (2 ^ 11 * m + 288) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_288 : oddCount 288 11 = 4 ∧ acceleratedOrbit 11 288 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_288 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 288) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_288.1, data_11_288.2] + +/-- Complete interval computation for depth 11, residue 289. -/ +theorem bounds_11_289 : exactInterval 11 289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_289 (m : Nat) : + stoppingTime (2 ^ 11 * m + 289) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_289 : oddCount 289 11 = 5 ∧ acceleratedOrbit 11 289 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_289 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 289) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_289.1, data_11_289.2] + +/-- Complete interval computation for depth 11, residue 290. -/ +theorem bounds_11_290 : exactInterval 11 290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_290 (m : Nat) : + stoppingTime (2 ^ 11 * m + 290) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_290 : oddCount 290 11 = 6 ∧ acceleratedOrbit 11 290 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_290 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 290) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_290.1, data_11_290.2] + +/-- Complete interval computation for depth 11, residue 291. -/ +theorem bounds_11_291 : exactInterval 11 291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_291 (m : Nat) : + stoppingTime (2 ^ 11 * m + 291) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_291 : oddCount 291 11 = 6 ∧ acceleratedOrbit 11 291 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_291 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 291) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_291.1, data_11_291.2] + +/-- Complete interval computation for depth 11, residue 292. -/ +theorem bounds_11_292 : exactInterval 11 292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_292 (m : Nat) : + stoppingTime (2 ^ 11 * m + 292) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_292 : oddCount 292 11 = 6 ∧ acceleratedOrbit 11 292 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_292 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 292) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_292.1, data_11_292.2] + +/-- Complete interval computation for depth 11, residue 293. -/ +theorem bounds_11_293 : exactInterval 11 293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_293 (m : Nat) : + stoppingTime (2 ^ 11 * m + 293) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_293 : oddCount 293 11 = 6 ∧ acceleratedOrbit 11 293 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_293 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 293) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_293.1, data_11_293.2] + +/-- Complete interval computation for depth 11, residue 294. -/ +theorem bounds_11_294 : exactInterval 11 294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_294 (m : Nat) : + stoppingTime (2 ^ 11 * m + 294) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_294 : oddCount 294 11 = 6 ∧ acceleratedOrbit 11 294 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_294 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 294) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_294.1, data_11_294.2] + +/-- Complete interval computation for depth 11, residue 295. -/ +theorem bounds_11_295 : exactInterval 11 295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_295 (m : Nat) : + stoppingTime (2 ^ 11 * m + 295) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_295 : oddCount 295 11 = 7 ∧ acceleratedOrbit 11 295 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_295 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 295) = 3 ^ 7 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_295.1, data_11_295.2] + +end Collatz.Research.StoppingAtlas.Batch0086 From af340a3903f492eb796012aff62e160b6d1b22f5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:26 +0530 Subject: [PATCH 0087/1001] proof: certify atlas Batch0087 (11:296 to 11:311) --- Collatz/Research/StoppingAtlas/Batch0087.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0087.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0087.lean b/Collatz/Research/StoppingAtlas/Batch0087.lean new file mode 100644 index 00000000..6339b0ee --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0087.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0087 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 296. -/ +theorem bounds_11_296 : exactInterval 11 296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_296 (m : Nat) : + stoppingTime (2 ^ 11 * m + 296) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_296 : oddCount 296 11 = 4 ∧ acceleratedOrbit 11 296 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_296 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 296) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_296.1, data_11_296.2] + +/-- Complete interval computation for depth 11, residue 297. -/ +theorem bounds_11_297 : exactInterval 11 297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_297 (m : Nat) : + stoppingTime (2 ^ 11 * m + 297) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_297 : oddCount 297 11 = 7 ∧ acceleratedOrbit 11 297 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_297 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 297) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_297.1, data_11_297.2] + +/-- Complete interval computation for depth 11, residue 298. -/ +theorem bounds_11_298 : exactInterval 11 298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_298 (m : Nat) : + stoppingTime (2 ^ 11 * m + 298) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_298 : oddCount 298 11 = 4 ∧ acceleratedOrbit 11 298 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_298 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 298) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_298.1, data_11_298.2] + +/-- Complete interval computation for depth 11, residue 299. -/ +theorem bounds_11_299 : exactInterval 11 299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_299 (m : Nat) : + stoppingTime (2 ^ 11 * m + 299) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_299 : oddCount 299 11 = 7 ∧ acceleratedOrbit 11 299 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_299 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 299) = 3 ^ 7 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_299.1, data_11_299.2] + +/-- Complete interval computation for depth 11, residue 300. -/ +theorem bounds_11_300 : exactInterval 11 300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_300 (m : Nat) : + stoppingTime (2 ^ 11 * m + 300) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_300 : oddCount 300 11 = 3 ∧ acceleratedOrbit 11 300 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_300 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 300) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_300.1, data_11_300.2] + +/-- Complete interval computation for depth 11, residue 301. -/ +theorem bounds_11_301 : exactInterval 11 301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_301 (m : Nat) : + stoppingTime (2 ^ 11 * m + 301) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_301 : oddCount 301 11 = 3 ∧ acceleratedOrbit 11 301 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_301 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 301) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_301.1, data_11_301.2] + +/-- Complete interval computation for depth 11, residue 302. -/ +theorem bounds_11_302 : exactInterval 11 302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_302 (m : Nat) : + stoppingTime (2 ^ 11 * m + 302) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_302 : oddCount 302 11 = 3 ∧ acceleratedOrbit 11 302 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_302 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 302) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_302.1, data_11_302.2] + +/-- Complete interval computation for depth 11, residue 303. -/ +theorem bounds_11_303 : exactInterval 11 303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_303 (m : Nat) : + stoppingTime (2 ^ 11 * m + 303) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_303 : oddCount 303 11 = 7 ∧ acceleratedOrbit 11 303 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_303 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 303) = 3 ^ 7 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_303.1, data_11_303.2] + +/-- Complete interval computation for depth 11, residue 304. -/ +theorem bounds_11_304 : exactInterval 11 304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_304 (m : Nat) : + stoppingTime (2 ^ 11 * m + 304) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_304 : oddCount 304 11 = 4 ∧ acceleratedOrbit 11 304 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_304 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 304) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_304.1, data_11_304.2] + +/-- Complete interval computation for depth 11, residue 305. -/ +theorem bounds_11_305 : exactInterval 11 305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_305 (m : Nat) : + stoppingTime (2 ^ 11 * m + 305) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_305 : oddCount 305 11 = 5 ∧ acceleratedOrbit 11 305 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_305 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 305) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_305.1, data_11_305.2] + +/-- Complete interval computation for depth 11, residue 306. -/ +theorem bounds_11_306 : exactInterval 11 306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_306 (m : Nat) : + stoppingTime (2 ^ 11 * m + 306) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_306 : oddCount 306 11 = 5 ∧ acceleratedOrbit 11 306 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_306 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 306) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_306.1, data_11_306.2] + +/-- Complete interval computation for depth 11, residue 307. -/ +theorem bounds_11_307 : exactInterval 11 307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_307 (m : Nat) : + stoppingTime (2 ^ 11 * m + 307) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_307 : oddCount 307 11 = 5 ∧ acceleratedOrbit 11 307 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_307 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 307) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_307.1, data_11_307.2] + +/-- Complete interval computation for depth 11, residue 308. -/ +theorem bounds_11_308 : exactInterval 11 308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_308 (m : Nat) : + stoppingTime (2 ^ 11 * m + 308) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_308 : oddCount 308 11 = 4 ∧ acceleratedOrbit 11 308 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_308 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 308) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_308.1, data_11_308.2] + +/-- Complete interval computation for depth 11, residue 309. -/ +theorem bounds_11_309 : exactInterval 11 309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_309 (m : Nat) : + stoppingTime (2 ^ 11 * m + 309) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_309 : oddCount 309 11 = 4 ∧ acceleratedOrbit 11 309 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_309 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 309) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_309.1, data_11_309.2] + +/-- Complete interval computation for depth 11, residue 310. -/ +theorem bounds_11_310 : exactInterval 11 310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_310 (m : Nat) : + stoppingTime (2 ^ 11 * m + 310) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_310 : oddCount 310 11 = 7 ∧ acceleratedOrbit 11 310 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_310 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 310) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_310.1, data_11_310.2] + +/-- Complete interval computation for depth 11, residue 311. -/ +theorem bounds_11_311 : exactInterval 11 311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_311 (m : Nat) : + stoppingTime (2 ^ 11 * m + 311) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_311 : oddCount 311 11 = 7 ∧ acceleratedOrbit 11 311 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_311 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 311) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_311.1, data_11_311.2] + +end Collatz.Research.StoppingAtlas.Batch0087 From 1d619b249f8c7a85e1e4aa4952c4a534fb4340f1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:27 +0530 Subject: [PATCH 0088/1001] proof: certify atlas Batch0088 (11:312 to 11:326) --- Collatz/Research/StoppingAtlas/Batch0088.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0088.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0088.lean b/Collatz/Research/StoppingAtlas/Batch0088.lean new file mode 100644 index 00000000..1538daa0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0088.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0088 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 312. -/ +theorem bounds_11_312 : exactInterval 11 312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_312 (m : Nat) : + stoppingTime (2 ^ 11 * m + 312) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_312 : oddCount 312 11 = 5 ∧ acceleratedOrbit 11 312 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_312 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 312) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_312.1, data_11_312.2] + +/-- Complete interval computation for depth 11, residue 313. -/ +theorem bounds_11_313 : exactInterval 11 313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_313 (m : Nat) : + stoppingTime (2 ^ 11 * m + 313) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_313 : oddCount 313 11 = 7 ∧ acceleratedOrbit 11 313 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_313 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 313) = 3 ^ 7 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_313.1, data_11_313.2] + +/-- Complete interval computation for depth 11, residue 314. -/ +theorem bounds_11_314 : exactInterval 11 314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_314 (m : Nat) : + stoppingTime (2 ^ 11 * m + 314) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_314 : oddCount 314 11 = 5 ∧ acceleratedOrbit 11 314 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_314 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 314) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_314.1, data_11_314.2] + +/-- Complete interval computation for depth 11, residue 315. -/ +theorem bounds_11_315 : exactInterval 11 315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_315 (m : Nat) : + stoppingTime (2 ^ 11 * m + 315) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_315 : oddCount 315 11 = 5 ∧ acceleratedOrbit 11 315 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_315 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 315) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_315.1, data_11_315.2] + +/-- Complete interval computation for depth 11, residue 316. -/ +theorem bounds_11_316 : exactInterval 11 316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_316 (m : Nat) : + stoppingTime (2 ^ 11 * m + 316) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_316 : oddCount 316 11 = 5 ∧ acceleratedOrbit 11 316 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_316 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 316) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_316.1, data_11_316.2] + +/-- Complete interval computation for depth 11, residue 317. -/ +theorem bounds_11_317 : exactInterval 11 317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_317 (m : Nat) : + stoppingTime (2 ^ 11 * m + 317) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_317 : oddCount 317 11 = 5 ∧ acceleratedOrbit 11 317 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_317 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 317) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_317.1, data_11_317.2] + +/-- Complete interval computation for depth 11, residue 318. -/ +theorem bounds_11_318 : exactInterval 11 318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_318 (m : Nat) : + stoppingTime (2 ^ 11 * m + 318) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_318 : oddCount 318 11 = 9 ∧ acceleratedOrbit 11 318 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_318 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 318) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_318.1, data_11_318.2] + +/-- Complete interval computation for depth 11, residue 319. -/ +theorem bounds_11_319 : exactInterval 11 319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_319 (m : Nat) : + stoppingTime (2 ^ 11 * m + 319) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_319 : oddCount 319 11 = 9 ∧ acceleratedOrbit 11 319 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_319 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 319) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_319.1, data_11_319.2] + +/-- Complete interval computation for depth 11, residue 320. -/ +theorem bounds_11_320 : exactInterval 11 320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_320 (m : Nat) : + stoppingTime (2 ^ 11 * m + 320) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_320 : oddCount 320 11 = 2 ∧ acceleratedOrbit 11 320 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_320 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 320) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_320.1, data_11_320.2] + +/-- Complete interval computation for depth 11, residue 321. -/ +theorem bounds_11_321 : exactInterval 11 321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_321 (m : Nat) : + stoppingTime (2 ^ 11 * m + 321) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_321 : oddCount 321 11 = 4 ∧ acceleratedOrbit 11 321 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_321 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 321) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_321.1, data_11_321.2] + +/-- Complete interval computation for depth 11, residue 322. -/ +theorem bounds_11_322 : exactInterval 11 322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_322 (m : Nat) : + stoppingTime (2 ^ 11 * m + 322) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_322 : oddCount 322 11 = 7 ∧ acceleratedOrbit 11 322 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_322 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 322) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_322.1, data_11_322.2] + +/-- Complete interval computation for depth 11, residue 323. -/ +theorem bounds_11_323 : exactInterval 11 323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_323 (m : Nat) : + stoppingTime (2 ^ 11 * m + 323) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_323 : oddCount 323 11 = 7 ∧ acceleratedOrbit 11 323 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_323 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 323) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_323.1, data_11_323.2] + +/-- Complete interval computation for depth 11, residue 324. -/ +theorem bounds_11_324 : exactInterval 11 324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_324 (m : Nat) : + stoppingTime (2 ^ 11 * m + 324) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_324 : oddCount 324 11 = 5 ∧ acceleratedOrbit 11 324 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_324 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 324) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_324.1, data_11_324.2] + +/-- Complete interval computation for depth 11, residue 325. -/ +theorem bounds_11_325 : exactInterval 11 325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_325 (m : Nat) : + stoppingTime (2 ^ 11 * m + 325) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_325 : oddCount 325 11 = 5 ∧ acceleratedOrbit 11 325 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_325 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 325) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_325.1, data_11_325.2] + +/-- Complete interval computation for depth 11, residue 326. -/ +theorem bounds_11_326 : exactInterval 11 326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_326 (m : Nat) : + stoppingTime (2 ^ 11 * m + 326) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_326 : oddCount 326 11 = 5 ∧ acceleratedOrbit 11 326 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_326 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 326) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_326.1, data_11_326.2] + +end Collatz.Research.StoppingAtlas.Batch0088 From bf406ad3ac9846c7d9479eae83248dfb5b3c932f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:27 +0530 Subject: [PATCH 0089/1001] proof: certify atlas Batch0089 (11:327 to 11:342) --- Collatz/Research/StoppingAtlas/Batch0089.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0089.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0089.lean b/Collatz/Research/StoppingAtlas/Batch0089.lean new file mode 100644 index 00000000..2ab0c1d0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0089.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0089 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 327. -/ +theorem bounds_11_327 : exactInterval 11 327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_327 (m : Nat) : + stoppingTime (2 ^ 11 * m + 327) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_327 : oddCount 327 11 = 9 ∧ acceleratedOrbit 11 327 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_327 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 327) = 3 ^ 9 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_327.1, data_11_327.2] + +/-- Complete interval computation for depth 11, residue 328. -/ +theorem bounds_11_328 : exactInterval 11 328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_328 (m : Nat) : + stoppingTime (2 ^ 11 * m + 328) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_328 : oddCount 328 11 = 6 ∧ acceleratedOrbit 11 328 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_328 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 328) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_328.1, data_11_328.2] + +/-- Complete interval computation for depth 11, residue 329. -/ +theorem bounds_11_329 : exactInterval 11 329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_329 (m : Nat) : + stoppingTime (2 ^ 11 * m + 329) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_329 : oddCount 329 11 = 6 ∧ acceleratedOrbit 11 329 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_329 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 329) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_329.1, data_11_329.2] + +/-- Complete interval computation for depth 11, residue 330. -/ +theorem bounds_11_330 : exactInterval 11 330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_330 (m : Nat) : + stoppingTime (2 ^ 11 * m + 330) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_330 : oddCount 330 11 = 6 ∧ acceleratedOrbit 11 330 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_330 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 330) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_330.1, data_11_330.2] + +/-- Complete interval computation for depth 11, residue 331. -/ +theorem bounds_11_331 : exactInterval 11 331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_331 (m : Nat) : + stoppingTime (2 ^ 11 * m + 331) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_331 : oddCount 331 11 = 5 ∧ acceleratedOrbit 11 331 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_331 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 331) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_331.1, data_11_331.2] + +/-- Complete interval computation for depth 11, residue 332. -/ +theorem bounds_11_332 : exactInterval 11 332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_332 (m : Nat) : + stoppingTime (2 ^ 11 * m + 332) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_332 : oddCount 332 11 = 6 ∧ acceleratedOrbit 11 332 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_332 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 332) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_332.1, data_11_332.2] + +/-- Complete interval computation for depth 11, residue 333. -/ +theorem bounds_11_333 : exactInterval 11 333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_333 (m : Nat) : + stoppingTime (2 ^ 11 * m + 333) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_333 : oddCount 333 11 = 6 ∧ acceleratedOrbit 11 333 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_333 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 333) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_333.1, data_11_333.2] + +/-- Complete interval computation for depth 11, residue 334. -/ +theorem bounds_11_334 : exactInterval 11 334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_334 (m : Nat) : + stoppingTime (2 ^ 11 * m + 334) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_334 : oddCount 334 11 = 8 ∧ acceleratedOrbit 11 334 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_334 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 334) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_334.1, data_11_334.2] + +/-- Complete interval computation for depth 11, residue 335. -/ +theorem bounds_11_335 : exactInterval 11 335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_335 (m : Nat) : + stoppingTime (2 ^ 11 * m + 335) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_335 : oddCount 335 11 = 8 ∧ acceleratedOrbit 11 335 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_335 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 335) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_335.1, data_11_335.2] + +/-- Complete interval computation for depth 11, residue 336. -/ +theorem bounds_11_336 : exactInterval 11 336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_336 (m : Nat) : + stoppingTime (2 ^ 11 * m + 336) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_336 : oddCount 336 11 = 2 ∧ acceleratedOrbit 11 336 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_336 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 336) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_336.1, data_11_336.2] + +/-- Complete interval computation for depth 11, residue 337. -/ +theorem bounds_11_337 : exactInterval 11 337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_337 (m : Nat) : + stoppingTime (2 ^ 11 * m + 337) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_337 : oddCount 337 11 = 7 ∧ acceleratedOrbit 11 337 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_337 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 337) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_337.1, data_11_337.2] + +/-- Complete interval computation for depth 11, residue 338. -/ +theorem bounds_11_338 : exactInterval 11 338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_338 (m : Nat) : + stoppingTime (2 ^ 11 * m + 338) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_338 : oddCount 338 11 = 8 ∧ acceleratedOrbit 11 338 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_338 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 338) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_338.1, data_11_338.2] + +/-- Complete interval computation for depth 11, residue 339. -/ +theorem bounds_11_339 : exactInterval 11 339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_339 (m : Nat) : + stoppingTime (2 ^ 11 * m + 339) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_339 : oddCount 339 11 = 8 ∧ acceleratedOrbit 11 339 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_339 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 339) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_339.1, data_11_339.2] + +/-- Complete interval computation for depth 11, residue 340. -/ +theorem bounds_11_340 : exactInterval 11 340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_340 (m : Nat) : + stoppingTime (2 ^ 11 * m + 340) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_340 : oddCount 340 11 = 2 ∧ acceleratedOrbit 11 340 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_340 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 340) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_340.1, data_11_340.2] + +/-- Complete interval computation for depth 11, residue 341. -/ +theorem bounds_11_341 : exactInterval 11 341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_341 (m : Nat) : + stoppingTime (2 ^ 11 * m + 341) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_341 : oddCount 341 11 = 2 ∧ acceleratedOrbit 11 341 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_341 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 341) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_341.1, data_11_341.2] + +/-- Complete interval computation for depth 11, residue 342. -/ +theorem bounds_11_342 : exactInterval 11 342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_342 (m : Nat) : + stoppingTime (2 ^ 11 * m + 342) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_342 : oddCount 342 11 = 5 ∧ acceleratedOrbit 11 342 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_342 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 342) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_342.1, data_11_342.2] + +end Collatz.Research.StoppingAtlas.Batch0089 From 1fcfe8d1c4f6852f79bb7a00bdec4351bf6fc2cc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:27 +0530 Subject: [PATCH 0090/1001] proof: certify atlas Batch0090 (11:343 to 11:357) --- Collatz/Research/StoppingAtlas/Batch0090.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0090.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0090.lean b/Collatz/Research/StoppingAtlas/Batch0090.lean new file mode 100644 index 00000000..64aceab8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0090.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0090 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 343. -/ +theorem bounds_11_343 : exactInterval 11 343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_343 (m : Nat) : + stoppingTime (2 ^ 11 * m + 343) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_343 : oddCount 343 11 = 5 ∧ acceleratedOrbit 11 343 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_343 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 343) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_343.1, data_11_343.2] + +/-- Complete interval computation for depth 11, residue 344. -/ +theorem bounds_11_344 : exactInterval 11 344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_344 (m : Nat) : + stoppingTime (2 ^ 11 * m + 344) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_344 : oddCount 344 11 = 4 ∧ acceleratedOrbit 11 344 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_344 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 344) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_344.1, data_11_344.2] + +/-- Complete interval computation for depth 11, residue 345. -/ +theorem bounds_11_345 : exactInterval 11 345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_345 (m : Nat) : + stoppingTime (2 ^ 11 * m + 345) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_345 : oddCount 345 11 = 6 ∧ acceleratedOrbit 11 345 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_345 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 345) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_345.1, data_11_345.2] + +/-- Complete interval computation for depth 11, residue 346. -/ +theorem bounds_11_346 : exactInterval 11 346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_346 (m : Nat) : + stoppingTime (2 ^ 11 * m + 346) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_346 : oddCount 346 11 = 4 ∧ acceleratedOrbit 11 346 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_346 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 346) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_346.1, data_11_346.2] + +/-- Complete interval computation for depth 11, residue 347. -/ +theorem bounds_11_347 : exactInterval 11 347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_347 (m : Nat) : + stoppingTime (2 ^ 11 * m + 347) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_347 : oddCount 347 11 = 6 ∧ acceleratedOrbit 11 347 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_347 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 347) = 3 ^ 6 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_347.1, data_11_347.2] + +/-- Complete interval computation for depth 11, residue 348. -/ +theorem bounds_11_348 : exactInterval 11 348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_348 (m : Nat) : + stoppingTime (2 ^ 11 * m + 348) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_348 : oddCount 348 11 = 4 ∧ acceleratedOrbit 11 348 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_348 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 348) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_348.1, data_11_348.2] + +/-- Complete interval computation for depth 11, residue 349. -/ +theorem bounds_11_349 : exactInterval 11 349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_349 (m : Nat) : + stoppingTime (2 ^ 11 * m + 349) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_349 : oddCount 349 11 = 4 ∧ acceleratedOrbit 11 349 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_349 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 349) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_349.1, data_11_349.2] + +/-- Complete interval computation for depth 11, residue 350. -/ +theorem bounds_11_350 : exactInterval 11 350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_350 (m : Nat) : + stoppingTime (2 ^ 11 * m + 350) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_350 : oddCount 350 11 = 7 ∧ acceleratedOrbit 11 350 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_350 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 350) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_350.1, data_11_350.2] + +/-- Complete interval computation for depth 11, residue 351. -/ +theorem bounds_11_351 : exactInterval 11 351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_351 (m : Nat) : + stoppingTime (2 ^ 11 * m + 351) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_351 : oddCount 351 11 = 7 ∧ acceleratedOrbit 11 351 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_351 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 351) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_351.1, data_11_351.2] + +/-- Complete interval computation for depth 11, residue 352. -/ +theorem bounds_11_352 : exactInterval 11 352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_352 (m : Nat) : + stoppingTime (2 ^ 11 * m + 352) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_352 : oddCount 352 11 = 3 ∧ acceleratedOrbit 11 352 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_352 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 352) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_352.1, data_11_352.2] + +/-- Complete interval computation for depth 11, residue 353. -/ +theorem bounds_11_353 : exactInterval 11 353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_353 (m : Nat) : + stoppingTime (2 ^ 11 * m + 353) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_353 : oddCount 353 11 = 7 ∧ acceleratedOrbit 11 353 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_353 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 353) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_353.1, data_11_353.2] + +/-- Complete interval computation for depth 11, residue 354. -/ +theorem bounds_11_354 : exactInterval 11 354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_354 (m : Nat) : + stoppingTime (2 ^ 11 * m + 354) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_354 : oddCount 354 11 = 5 ∧ acceleratedOrbit 11 354 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_354 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 354) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_354.1, data_11_354.2] + +/-- Complete interval computation for depth 11, residue 355. -/ +theorem bounds_11_355 : exactInterval 11 355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_355 (m : Nat) : + stoppingTime (2 ^ 11 * m + 355) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_355 : oddCount 355 11 = 5 ∧ acceleratedOrbit 11 355 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_355 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 355) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_355.1, data_11_355.2] + +/-- Complete interval computation for depth 11, residue 356. -/ +theorem bounds_11_356 : exactInterval 11 356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_356 (m : Nat) : + stoppingTime (2 ^ 11 * m + 356) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_356 : oddCount 356 11 = 5 ∧ acceleratedOrbit 11 356 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_356 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 356) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_356.1, data_11_356.2] + +/-- Complete interval computation for depth 11, residue 357. -/ +theorem bounds_11_357 : exactInterval 11 357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_357 (m : Nat) : + stoppingTime (2 ^ 11 * m + 357) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_357 : oddCount 357 11 = 5 ∧ acceleratedOrbit 11 357 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_357 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 357) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_357.1, data_11_357.2] + +end Collatz.Research.StoppingAtlas.Batch0090 From 7d0d225ced8a5328eff007355966266c1c9abb6e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:27 +0530 Subject: [PATCH 0091/1001] proof: certify atlas Batch0091 (11:358 to 11:372) --- Collatz/Research/StoppingAtlas/Batch0091.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0091.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0091.lean b/Collatz/Research/StoppingAtlas/Batch0091.lean new file mode 100644 index 00000000..95151524 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0091.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0091 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 358. -/ +theorem bounds_11_358 : exactInterval 11 358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_358 (m : Nat) : + stoppingTime (2 ^ 11 * m + 358) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_358 : oddCount 358 11 = 5 ∧ acceleratedOrbit 11 358 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_358 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 358) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_358.1, data_11_358.2] + +/-- Complete interval computation for depth 11, residue 359. -/ +theorem bounds_11_359 : exactInterval 11 359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_359 (m : Nat) : + stoppingTime (2 ^ 11 * m + 359) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_359 : oddCount 359 11 = 8 ∧ acceleratedOrbit 11 359 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_359 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 359) = 3 ^ 8 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_359.1, data_11_359.2] + +/-- Complete interval computation for depth 11, residue 360. -/ +theorem bounds_11_360 : exactInterval 11 360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_360 (m : Nat) : + stoppingTime (2 ^ 11 * m + 360) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_360 : oddCount 360 11 = 3 ∧ acceleratedOrbit 11 360 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_360 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 360) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_360.1, data_11_360.2] + +/-- Complete interval computation for depth 11, residue 361. -/ +theorem bounds_11_361 : exactInterval 11 361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_361 (m : Nat) : + stoppingTime (2 ^ 11 * m + 361) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_361 : oddCount 361 11 = 5 ∧ acceleratedOrbit 11 361 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_361 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 361) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_361.1, data_11_361.2] + +/-- Complete interval computation for depth 11, residue 362. -/ +theorem bounds_11_362 : exactInterval 11 362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_362 (m : Nat) : + stoppingTime (2 ^ 11 * m + 362) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_362 : oddCount 362 11 = 3 ∧ acceleratedOrbit 11 362 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_362 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 362) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_362.1, data_11_362.2] + +/-- Complete interval computation for depth 11, residue 363. -/ +theorem bounds_11_363 : exactInterval 11 363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_363 (m : Nat) : + stoppingTime (2 ^ 11 * m + 363) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_363 : oddCount 363 11 = 6 ∧ acceleratedOrbit 11 363 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_363 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 363) = 3 ^ 6 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_363.1, data_11_363.2] + +/-- Complete interval computation for depth 11, residue 364. -/ +theorem bounds_11_364 : exactInterval 11 364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_364 (m : Nat) : + stoppingTime (2 ^ 11 * m + 364) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_364 : oddCount 364 11 = 7 ∧ acceleratedOrbit 11 364 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_364 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 364) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_364.1, data_11_364.2] + +/-- Complete interval computation for depth 11, residue 365. -/ +theorem bounds_11_365 : exactInterval 11 365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_365 (m : Nat) : + stoppingTime (2 ^ 11 * m + 365) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_365 : oddCount 365 11 = 7 ∧ acceleratedOrbit 11 365 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_365 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 365) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_365.1, data_11_365.2] + +/-- Complete interval computation for depth 11, residue 366. -/ +theorem bounds_11_366 : exactInterval 11 366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_366 (m : Nat) : + stoppingTime (2 ^ 11 * m + 366) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_366 : oddCount 366 11 = 7 ∧ acceleratedOrbit 11 366 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_366 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 366) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_366.1, data_11_366.2] + +/-- Complete interval computation for depth 11, residue 367. -/ +theorem bounds_11_367 : exactInterval 11 367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_367 (m : Nat) : + stoppingTime (2 ^ 11 * m + 367) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_367 : oddCount 367 11 = 6 ∧ acceleratedOrbit 11 367 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_367 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 367) = 3 ^ 6 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_367.1, data_11_367.2] + +/-- Complete interval computation for depth 11, residue 368. -/ +theorem bounds_11_368 : exactInterval 11 368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_368 (m : Nat) : + stoppingTime (2 ^ 11 * m + 368) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_368 : oddCount 368 11 = 3 ∧ acceleratedOrbit 11 368 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_368 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 368) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_368.1, data_11_368.2] + +/-- Complete interval computation for depth 11, residue 369. -/ +theorem bounds_11_369 : exactInterval 11 369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_369 (m : Nat) : + stoppingTime (2 ^ 11 * m + 369) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_369 : oddCount 369 11 = 3 ∧ acceleratedOrbit 11 369 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_369 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 369) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_369.1, data_11_369.2] + +/-- Complete interval computation for depth 11, residue 370. -/ +theorem bounds_11_370 : exactInterval 11 370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_370 (m : Nat) : + stoppingTime (2 ^ 11 * m + 370) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_370 : oddCount 370 11 = 6 ∧ acceleratedOrbit 11 370 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_370 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 370) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_370.1, data_11_370.2] + +/-- Complete interval computation for depth 11, residue 371. -/ +theorem bounds_11_371 : exactInterval 11 371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_371 (m : Nat) : + stoppingTime (2 ^ 11 * m + 371) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_371 : oddCount 371 11 = 6 ∧ acceleratedOrbit 11 371 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_371 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 371) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_371.1, data_11_371.2] + +/-- Complete interval computation for depth 11, residue 372. -/ +theorem bounds_11_372 : exactInterval 11 372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_372 (m : Nat) : + stoppingTime (2 ^ 11 * m + 372) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_372 : oddCount 372 11 = 3 ∧ acceleratedOrbit 11 372 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_372 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 372) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_372.1, data_11_372.2] + +end Collatz.Research.StoppingAtlas.Batch0091 From e068dfc623ac0c5c747fcb1b225c8e9b51eaa882 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:28 +0530 Subject: [PATCH 0092/1001] proof: certify atlas Batch0092 (11:373 to 11:388) --- Collatz/Research/StoppingAtlas/Batch0092.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0092.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0092.lean b/Collatz/Research/StoppingAtlas/Batch0092.lean new file mode 100644 index 00000000..d7afd41c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0092.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0092 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 373. -/ +theorem bounds_11_373 : exactInterval 11 373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_373 (m : Nat) : + stoppingTime (2 ^ 11 * m + 373) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_373 : oddCount 373 11 = 3 ∧ acceleratedOrbit 11 373 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_373 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 373) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_373.1, data_11_373.2] + +/-- Complete interval computation for depth 11, residue 374. -/ +theorem bounds_11_374 : exactInterval 11 374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_374 (m : Nat) : + stoppingTime (2 ^ 11 * m + 374) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_374 : oddCount 374 11 = 7 ∧ acceleratedOrbit 11 374 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_374 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 374) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_374.1, data_11_374.2] + +/-- Complete interval computation for depth 11, residue 375. -/ +theorem bounds_11_375 : exactInterval 11 375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_375 (m : Nat) : + stoppingTime (2 ^ 11 * m + 375) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_375 : oddCount 375 11 = 7 ∧ acceleratedOrbit 11 375 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_375 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 375) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_375.1, data_11_375.2] + +/-- Complete interval computation for depth 11, residue 376. -/ +theorem bounds_11_376 : exactInterval 11 376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_376 (m : Nat) : + stoppingTime (2 ^ 11 * m + 376) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_376 : oddCount 376 11 = 6 ∧ acceleratedOrbit 11 376 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_376 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 376) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_376.1, data_11_376.2] + +/-- Complete interval computation for depth 11, residue 377. -/ +theorem bounds_11_377 : exactInterval 11 377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_377 (m : Nat) : + stoppingTime (2 ^ 11 * m + 377) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_377 : oddCount 377 11 = 9 ∧ acceleratedOrbit 11 377 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_377 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 377) = 3 ^ 9 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_377.1, data_11_377.2] + +/-- Complete interval computation for depth 11, residue 378. -/ +theorem bounds_11_378 : exactInterval 11 378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_378 (m : Nat) : + stoppingTime (2 ^ 11 * m + 378) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_378 : oddCount 378 11 = 6 ∧ acceleratedOrbit 11 378 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_378 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 378) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_378.1, data_11_378.2] + +/-- Complete interval computation for depth 11, residue 379. -/ +theorem bounds_11_379 : exactInterval 11 379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_379 (m : Nat) : + stoppingTime (2 ^ 11 * m + 379) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_379 : oddCount 379 11 = 7 ∧ acceleratedOrbit 11 379 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_379 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 379) = 3 ^ 7 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_379.1, data_11_379.2] + +/-- Complete interval computation for depth 11, residue 380. -/ +theorem bounds_11_380 : exactInterval 11 380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_380 (m : Nat) : + stoppingTime (2 ^ 11 * m + 380) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_380 : oddCount 380 11 = 6 ∧ acceleratedOrbit 11 380 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_380 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 380) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_380.1, data_11_380.2] + +/-- Complete interval computation for depth 11, residue 381. -/ +theorem bounds_11_381 : exactInterval 11 381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_381 (m : Nat) : + stoppingTime (2 ^ 11 * m + 381) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_381 : oddCount 381 11 = 6 ∧ acceleratedOrbit 11 381 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_381 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 381) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_381.1, data_11_381.2] + +/-- Complete interval computation for depth 11, residue 382. -/ +theorem bounds_11_382 : exactInterval 11 382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_382 (m : Nat) : + stoppingTime (2 ^ 11 * m + 382) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_382 : oddCount 382 11 = 7 ∧ acceleratedOrbit 11 382 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_382 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 382) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_382.1, data_11_382.2] + +/-- Complete interval computation for depth 11, residue 383. -/ +theorem bounds_11_383 : exactInterval 11 383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_383 (m : Nat) : + stoppingTime (2 ^ 11 * m + 383) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_383 : oddCount 383 11 = 7 ∧ acceleratedOrbit 11 383 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_383 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 383) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_383.1, data_11_383.2] + +/-- Complete interval computation for depth 11, residue 384. -/ +theorem bounds_11_384 : exactInterval 11 384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_384 (m : Nat) : + stoppingTime (2 ^ 11 * m + 384) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_384 : oddCount 384 11 = 2 ∧ acceleratedOrbit 11 384 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_384 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 384) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_384.1, data_11_384.2] + +/-- Complete interval computation for depth 11, residue 385. -/ +theorem bounds_11_385 : exactInterval 11 385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_385 (m : Nat) : + stoppingTime (2 ^ 11 * m + 385) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_385 : oddCount 385 11 = 5 ∧ acceleratedOrbit 11 385 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_385 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 385) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_385.1, data_11_385.2] + +/-- Complete interval computation for depth 11, residue 386. -/ +theorem bounds_11_386 : exactInterval 11 386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_386 (m : Nat) : + stoppingTime (2 ^ 11 * m + 386) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_386 : oddCount 386 11 = 5 ∧ acceleratedOrbit 11 386 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_386 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 386) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_386.1, data_11_386.2] + +/-- Complete interval computation for depth 11, residue 387. -/ +theorem bounds_11_387 : exactInterval 11 387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_387 (m : Nat) : + stoppingTime (2 ^ 11 * m + 387) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_387 : oddCount 387 11 = 5 ∧ acceleratedOrbit 11 387 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_387 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 387) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_387.1, data_11_387.2] + +/-- Complete interval computation for depth 11, residue 388. -/ +theorem bounds_11_388 : exactInterval 11 388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_388 (m : Nat) : + stoppingTime (2 ^ 11 * m + 388) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_388 : oddCount 388 11 = 5 ∧ acceleratedOrbit 11 388 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_388 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 388) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_388.1, data_11_388.2] + +end Collatz.Research.StoppingAtlas.Batch0092 From f91f265dd83a87decc31d06c7f91338f3fa45458 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:28 +0530 Subject: [PATCH 0093/1001] proof: certify atlas Batch0093 (11:389 to 11:403) --- Collatz/Research/StoppingAtlas/Batch0093.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0093.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0093.lean b/Collatz/Research/StoppingAtlas/Batch0093.lean new file mode 100644 index 00000000..8282a1fa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0093.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0093 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 389. -/ +theorem bounds_11_389 : exactInterval 11 389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_389 (m : Nat) : + stoppingTime (2 ^ 11 * m + 389) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_389 : oddCount 389 11 = 5 ∧ acceleratedOrbit 11 389 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_389 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 389) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_389.1, data_11_389.2] + +/-- Complete interval computation for depth 11, residue 390. -/ +theorem bounds_11_390 : exactInterval 11 390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_390 (m : Nat) : + stoppingTime (2 ^ 11 * m + 390) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_390 : oddCount 390 11 = 5 ∧ acceleratedOrbit 11 390 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_390 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 390) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_390.1, data_11_390.2] + +/-- Complete interval computation for depth 11, residue 391. -/ +theorem bounds_11_391 : exactInterval 11 391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_391 (m : Nat) : + stoppingTime (2 ^ 11 * m + 391) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_391 : oddCount 391 11 = 5 ∧ acceleratedOrbit 11 391 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_391 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 391) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_391.1, data_11_391.2] + +/-- Complete interval computation for depth 11, residue 392. -/ +theorem bounds_11_392 : exactInterval 11 392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_392 (m : Nat) : + stoppingTime (2 ^ 11 * m + 392) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_392 : oddCount 392 11 = 4 ∧ acceleratedOrbit 11 392 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_392 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 392) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_392.1, data_11_392.2] + +/-- Complete interval computation for depth 11, residue 393. -/ +theorem bounds_11_393 : exactInterval 11 393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_393 (m : Nat) : + stoppingTime (2 ^ 11 * m + 393) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_393 : oddCount 393 11 = 7 ∧ acceleratedOrbit 11 393 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_393 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 393) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_393.1, data_11_393.2] + +/-- Complete interval computation for depth 11, residue 394. -/ +theorem bounds_11_394 : exactInterval 11 394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_394 (m : Nat) : + stoppingTime (2 ^ 11 * m + 394) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_394 : oddCount 394 11 = 4 ∧ acceleratedOrbit 11 394 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_394 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 394) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_394.1, data_11_394.2] + +/-- Complete interval computation for depth 11, residue 395. -/ +theorem bounds_11_395 : exactInterval 11 395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_395 (m : Nat) : + stoppingTime (2 ^ 11 * m + 395) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_395 : oddCount 395 11 = 7 ∧ acceleratedOrbit 11 395 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_395 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 395) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_395.1, data_11_395.2] + +/-- Complete interval computation for depth 11, residue 396. -/ +theorem bounds_11_396 : exactInterval 11 396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_396 (m : Nat) : + stoppingTime (2 ^ 11 * m + 396) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_396 : oddCount 396 11 = 4 ∧ acceleratedOrbit 11 396 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_396 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 396) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_396.1, data_11_396.2] + +/-- Complete interval computation for depth 11, residue 397. -/ +theorem bounds_11_397 : exactInterval 11 397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_397 (m : Nat) : + stoppingTime (2 ^ 11 * m + 397) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_397 : oddCount 397 11 = 4 ∧ acceleratedOrbit 11 397 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_397 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 397) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_397.1, data_11_397.2] + +/-- Complete interval computation for depth 11, residue 398. -/ +theorem bounds_11_398 : exactInterval 11 398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_398 (m : Nat) : + stoppingTime (2 ^ 11 * m + 398) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_398 : oddCount 398 11 = 6 ∧ acceleratedOrbit 11 398 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_398 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 398) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_398.1, data_11_398.2] + +/-- Complete interval computation for depth 11, residue 399. -/ +theorem bounds_11_399 : exactInterval 11 399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_399 (m : Nat) : + stoppingTime (2 ^ 11 * m + 399) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_399 : oddCount 399 11 = 6 ∧ acceleratedOrbit 11 399 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_399 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 399) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_399.1, data_11_399.2] + +/-- Complete interval computation for depth 11, residue 400. -/ +theorem bounds_11_400 : exactInterval 11 400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_400 (m : Nat) : + stoppingTime (2 ^ 11 * m + 400) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_400 : oddCount 400 11 = 4 ∧ acceleratedOrbit 11 400 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_400 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 400) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_400.1, data_11_400.2] + +/-- Complete interval computation for depth 11, residue 401. -/ +theorem bounds_11_401 : exactInterval 11 401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_401 (m : Nat) : + stoppingTime (2 ^ 11 * m + 401) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_401 : oddCount 401 11 = 4 ∧ acceleratedOrbit 11 401 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_401 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 401) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_401.1, data_11_401.2] + +/-- Complete interval computation for depth 11, residue 402. -/ +theorem bounds_11_402 : exactInterval 11 402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_402 (m : Nat) : + stoppingTime (2 ^ 11 * m + 402) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_402 : oddCount 402 11 = 4 ∧ acceleratedOrbit 11 402 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_402 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 402) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_402.1, data_11_402.2] + +/-- Complete interval computation for depth 11, residue 403. -/ +theorem bounds_11_403 : exactInterval 11 403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_403 (m : Nat) : + stoppingTime (2 ^ 11 * m + 403) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_403 : oddCount 403 11 = 4 ∧ acceleratedOrbit 11 403 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_403 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 403) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_403.1, data_11_403.2] + +end Collatz.Research.StoppingAtlas.Batch0093 From 81d695bf35b795f2540576bc8e18f1099d5b02bc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:29 +0530 Subject: [PATCH 0094/1001] proof: certify atlas Batch0094 (11:404 to 11:418) --- Collatz/Research/StoppingAtlas/Batch0094.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0094.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0094.lean b/Collatz/Research/StoppingAtlas/Batch0094.lean new file mode 100644 index 00000000..709d65bf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0094.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0094 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 404. -/ +theorem bounds_11_404 : exactInterval 11 404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_404 (m : Nat) : + stoppingTime (2 ^ 11 * m + 404) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_404 : oddCount 404 11 = 4 ∧ acceleratedOrbit 11 404 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_404 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 404) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_404.1, data_11_404.2] + +/-- Complete interval computation for depth 11, residue 405. -/ +theorem bounds_11_405 : exactInterval 11 405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_405 (m : Nat) : + stoppingTime (2 ^ 11 * m + 405) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_405 : oddCount 405 11 = 4 ∧ acceleratedOrbit 11 405 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_405 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 405) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_405.1, data_11_405.2] + +/-- Complete interval computation for depth 11, residue 406. -/ +theorem bounds_11_406 : exactInterval 11 406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_406 (m : Nat) : + stoppingTime (2 ^ 11 * m + 406) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_406 : oddCount 406 11 = 5 ∧ acceleratedOrbit 11 406 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_406 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 406) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_406.1, data_11_406.2] + +/-- Complete interval computation for depth 11, residue 407. -/ +theorem bounds_11_407 : exactInterval 11 407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_407 (m : Nat) : + stoppingTime (2 ^ 11 * m + 407) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_407 : oddCount 407 11 = 5 ∧ acceleratedOrbit 11 407 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_407 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 407) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_407.1, data_11_407.2] + +/-- Complete interval computation for depth 11, residue 408. -/ +theorem bounds_11_408 : exactInterval 11 408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_408 (m : Nat) : + stoppingTime (2 ^ 11 * m + 408) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_408 : oddCount 408 11 = 4 ∧ acceleratedOrbit 11 408 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_408 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 408) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_408.1, data_11_408.2] + +/-- Complete interval computation for depth 11, residue 409. -/ +theorem bounds_11_409 : exactInterval 11 409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_409 (m : Nat) : + stoppingTime (2 ^ 11 * m + 409) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_409 : oddCount 409 11 = 5 ∧ acceleratedOrbit 11 409 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_409 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 409) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_409.1, data_11_409.2] + +/-- Complete interval computation for depth 11, residue 410. -/ +theorem bounds_11_410 : exactInterval 11 410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_410 (m : Nat) : + stoppingTime (2 ^ 11 * m + 410) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_410 : oddCount 410 11 = 4 ∧ acceleratedOrbit 11 410 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_410 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 410) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_410.1, data_11_410.2] + +/-- Complete interval computation for depth 11, residue 411. -/ +theorem bounds_11_411 : exactInterval 11 411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_411 (m : Nat) : + stoppingTime (2 ^ 11 * m + 411) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_411 : oddCount 411 11 = 8 ∧ acceleratedOrbit 11 411 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_411 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 411) = 3 ^ 8 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_411.1, data_11_411.2] + +/-- Complete interval computation for depth 11, residue 412. -/ +theorem bounds_11_412 : exactInterval 11 412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_412 (m : Nat) : + stoppingTime (2 ^ 11 * m + 412) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_412 : oddCount 412 11 = 7 ∧ acceleratedOrbit 11 412 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_412 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 412) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_412.1, data_11_412.2] + +/-- Complete interval computation for depth 11, residue 413. -/ +theorem bounds_11_413 : exactInterval 11 413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_413 (m : Nat) : + stoppingTime (2 ^ 11 * m + 413) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_413 : oddCount 413 11 = 7 ∧ acceleratedOrbit 11 413 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_413 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 413) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_413.1, data_11_413.2] + +/-- Complete interval computation for depth 11, residue 414. -/ +theorem bounds_11_414 : exactInterval 11 414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_414 (m : Nat) : + stoppingTime (2 ^ 11 * m + 414) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_414 : oddCount 414 11 = 7 ∧ acceleratedOrbit 11 414 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_414 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 414) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_414.1, data_11_414.2] + +/-- Complete interval computation for depth 11, residue 415. -/ +theorem bounds_11_415 : exactInterval 11 415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_415 (m : Nat) : + stoppingTime (2 ^ 11 * m + 415) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_415 : oddCount 415 11 = 8 ∧ acceleratedOrbit 11 415 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_415 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 415) = 3 ^ 8 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_415.1, data_11_415.2] + +/-- Complete interval computation for depth 11, residue 416. -/ +theorem bounds_11_416 : exactInterval 11 416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_416 (m : Nat) : + stoppingTime (2 ^ 11 * m + 416) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_416 : oddCount 416 11 = 2 ∧ acceleratedOrbit 11 416 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_416 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 416) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_416.1, data_11_416.2] + +/-- Complete interval computation for depth 11, residue 417. -/ +theorem bounds_11_417 : exactInterval 11 417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_417 (m : Nat) : + stoppingTime (2 ^ 11 * m + 417) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_417 : oddCount 417 11 = 7 ∧ acceleratedOrbit 11 417 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_417 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 417) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_417.1, data_11_417.2] + +/-- Complete interval computation for depth 11, residue 418. -/ +theorem bounds_11_418 : exactInterval 11 418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_418 (m : Nat) : + stoppingTime (2 ^ 11 * m + 418) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_418 : oddCount 418 11 = 6 ∧ acceleratedOrbit 11 418 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_418 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 418) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_418.1, data_11_418.2] + +end Collatz.Research.StoppingAtlas.Batch0094 From 96b2f4dc02d5f83c726d6f403370762368fd3eb4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:29 +0530 Subject: [PATCH 0095/1001] proof: certify atlas Batch0095 (11:419 to 11:434) --- Collatz/Research/StoppingAtlas/Batch0095.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0095.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0095.lean b/Collatz/Research/StoppingAtlas/Batch0095.lean new file mode 100644 index 00000000..e9475c49 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0095.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0095 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 419. -/ +theorem bounds_11_419 : exactInterval 11 419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_419 (m : Nat) : + stoppingTime (2 ^ 11 * m + 419) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_419 : oddCount 419 11 = 6 ∧ acceleratedOrbit 11 419 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_419 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 419) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_419.1, data_11_419.2] + +/-- Complete interval computation for depth 11, residue 420. -/ +theorem bounds_11_420 : exactInterval 11 420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_420 (m : Nat) : + stoppingTime (2 ^ 11 * m + 420) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_420 : oddCount 420 11 = 6 ∧ acceleratedOrbit 11 420 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_420 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 420) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_420.1, data_11_420.2] + +/-- Complete interval computation for depth 11, residue 421. -/ +theorem bounds_11_421 : exactInterval 11 421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_421 (m : Nat) : + stoppingTime (2 ^ 11 * m + 421) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_421 : oddCount 421 11 = 6 ∧ acceleratedOrbit 11 421 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_421 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 421) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_421.1, data_11_421.2] + +/-- Complete interval computation for depth 11, residue 422. -/ +theorem bounds_11_422 : exactInterval 11 422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_422 (m : Nat) : + stoppingTime (2 ^ 11 * m + 422) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_422 : oddCount 422 11 = 6 ∧ acceleratedOrbit 11 422 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_422 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 422) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_422.1, data_11_422.2] + +/-- Complete interval computation for depth 11, residue 423. -/ +theorem bounds_11_423 : exactInterval 11 423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_423 (m : Nat) : + stoppingTime (2 ^ 11 * m + 423) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_423 : oddCount 423 11 = 6 ∧ acceleratedOrbit 11 423 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_423 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 423) = 3 ^ 6 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_423.1, data_11_423.2] + +/-- Complete interval computation for depth 11, residue 424. -/ +theorem bounds_11_424 : exactInterval 11 424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_424 (m : Nat) : + stoppingTime (2 ^ 11 * m + 424) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_424 : oddCount 424 11 = 2 ∧ acceleratedOrbit 11 424 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_424 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 424) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_424.1, data_11_424.2] + +/-- Complete interval computation for depth 11, residue 425. -/ +theorem bounds_11_425 : exactInterval 11 425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_425 (m : Nat) : + stoppingTime (2 ^ 11 * m + 425) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_425 : oddCount 425 11 = 8 ∧ acceleratedOrbit 11 425 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_425 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 425) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_425.1, data_11_425.2] + +/-- Complete interval computation for depth 11, residue 426. -/ +theorem bounds_11_426 : exactInterval 11 426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_426 (m : Nat) : + stoppingTime (2 ^ 11 * m + 426) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_426 : oddCount 426 11 = 2 ∧ acceleratedOrbit 11 426 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_426 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 426) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_426.1, data_11_426.2] + +/-- Complete interval computation for depth 11, residue 427. -/ +theorem bounds_11_427 : exactInterval 11 427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_427 (m : Nat) : + stoppingTime (2 ^ 11 * m + 427) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_427 : oddCount 427 11 = 8 ∧ acceleratedOrbit 11 427 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_427 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 427) = 3 ^ 8 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_427.1, data_11_427.2] + +/-- Complete interval computation for depth 11, residue 428. -/ +theorem bounds_11_428 : exactInterval 11 428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_428 (m : Nat) : + stoppingTime (2 ^ 11 * m + 428) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_428 : oddCount 428 11 = 6 ∧ acceleratedOrbit 11 428 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_428 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 428) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_428.1, data_11_428.2] + +/-- Complete interval computation for depth 11, residue 429. -/ +theorem bounds_11_429 : exactInterval 11 429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_429 (m : Nat) : + stoppingTime (2 ^ 11 * m + 429) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_429 : oddCount 429 11 = 6 ∧ acceleratedOrbit 11 429 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_429 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 429) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_429.1, data_11_429.2] + +/-- Complete interval computation for depth 11, residue 430. -/ +theorem bounds_11_430 : exactInterval 11 430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_430 (m : Nat) : + stoppingTime (2 ^ 11 * m + 430) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_430 : oddCount 430 11 = 6 ∧ acceleratedOrbit 11 430 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_430 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 430) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_430.1, data_11_430.2] + +/-- Complete interval computation for depth 11, residue 431. -/ +theorem bounds_11_431 : exactInterval 11 431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_431 (m : Nat) : + stoppingTime (2 ^ 11 * m + 431) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_431 : oddCount 431 11 = 6 ∧ acceleratedOrbit 11 431 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_431 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 431) = 3 ^ 6 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_431.1, data_11_431.2] + +/-- Complete interval computation for depth 11, residue 432. -/ +theorem bounds_11_432 : exactInterval 11 432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_432 (m : Nat) : + stoppingTime (2 ^ 11 * m + 432) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_432 : oddCount 432 11 = 6 ∧ acceleratedOrbit 11 432 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_432 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 432) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_432.1, data_11_432.2] + +/-- Complete interval computation for depth 11, residue 433. -/ +theorem bounds_11_433 : exactInterval 11 433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_433 (m : Nat) : + stoppingTime (2 ^ 11 * m + 433) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_433 : oddCount 433 11 = 5 ∧ acceleratedOrbit 11 433 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_433 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 433) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_433.1, data_11_433.2] + +/-- Complete interval computation for depth 11, residue 434. -/ +theorem bounds_11_434 : exactInterval 11 434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_434 (m : Nat) : + stoppingTime (2 ^ 11 * m + 434) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_434 : oddCount 434 11 = 5 ∧ acceleratedOrbit 11 434 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_434 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 434) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_434.1, data_11_434.2] + +end Collatz.Research.StoppingAtlas.Batch0095 From 2a6d5f0a985bd0c9d970778a2f7f17d6ce826b10 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:29 +0530 Subject: [PATCH 0096/1001] proof: certify atlas Batch0096 (11:435 to 11:449) --- Collatz/Research/StoppingAtlas/Batch0096.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0096.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0096.lean b/Collatz/Research/StoppingAtlas/Batch0096.lean new file mode 100644 index 00000000..e6ec9327 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0096.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0096 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 435. -/ +theorem bounds_11_435 : exactInterval 11 435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_435 (m : Nat) : + stoppingTime (2 ^ 11 * m + 435) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_435 : oddCount 435 11 = 5 ∧ acceleratedOrbit 11 435 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_435 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 435) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_435.1, data_11_435.2] + +/-- Complete interval computation for depth 11, residue 436. -/ +theorem bounds_11_436 : exactInterval 11 436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_436 (m : Nat) : + stoppingTime (2 ^ 11 * m + 436) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_436 : oddCount 436 11 = 6 ∧ acceleratedOrbit 11 436 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_436 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 436) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_436.1, data_11_436.2] + +/-- Complete interval computation for depth 11, residue 437. -/ +theorem bounds_11_437 : exactInterval 11 437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_437 (m : Nat) : + stoppingTime (2 ^ 11 * m + 437) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_437 : oddCount 437 11 = 6 ∧ acceleratedOrbit 11 437 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_437 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 437) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_437.1, data_11_437.2] + +/-- Complete interval computation for depth 11, residue 438. -/ +theorem bounds_11_438 : exactInterval 11 438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_438 (m : Nat) : + stoppingTime (2 ^ 11 * m + 438) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_438 : oddCount 438 11 = 6 ∧ acceleratedOrbit 11 438 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_438 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 438) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_438.1, data_11_438.2] + +/-- Complete interval computation for depth 11, residue 439. -/ +theorem bounds_11_439 : exactInterval 11 439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_439 (m : Nat) : + stoppingTime (2 ^ 11 * m + 439) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_439 : oddCount 439 11 = 6 ∧ acceleratedOrbit 11 439 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_439 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 439) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_439.1, data_11_439.2] + +/-- Complete interval computation for depth 11, residue 440. -/ +theorem bounds_11_440 : exactInterval 11 440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_440 (m : Nat) : + stoppingTime (2 ^ 11 * m + 440) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_440 : oddCount 440 11 = 6 ∧ acceleratedOrbit 11 440 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_440 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 440) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_440.1, data_11_440.2] + +/-- Complete interval computation for depth 11, residue 441. -/ +theorem bounds_11_441 : exactInterval 11 441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_441 (m : Nat) : + stoppingTime (2 ^ 11 * m + 441) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_441 : oddCount 441 11 = 5 ∧ acceleratedOrbit 11 441 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_441 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 441) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_441.1, data_11_441.2] + +/-- Complete interval computation for depth 11, residue 442. -/ +theorem bounds_11_442 : exactInterval 11 442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_442 (m : Nat) : + stoppingTime (2 ^ 11 * m + 442) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_442 : oddCount 442 11 = 6 ∧ acceleratedOrbit 11 442 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_442 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 442) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_442.1, data_11_442.2] + +/-- Complete interval computation for depth 11, residue 443. -/ +theorem bounds_11_443 : exactInterval 11 443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_443 (m : Nat) : + stoppingTime (2 ^ 11 * m + 443) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_443 : oddCount 443 11 = 7 ∧ acceleratedOrbit 11 443 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_443 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 443) = 3 ^ 7 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_443.1, data_11_443.2] + +/-- Complete interval computation for depth 11, residue 444. -/ +theorem bounds_11_444 : exactInterval 11 444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_444 (m : Nat) : + stoppingTime (2 ^ 11 * m + 444) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_444 : oddCount 444 11 = 7 ∧ acceleratedOrbit 11 444 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_444 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 444) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_444.1, data_11_444.2] + +/-- Complete interval computation for depth 11, residue 445. -/ +theorem bounds_11_445 : exactInterval 11 445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_445 (m : Nat) : + stoppingTime (2 ^ 11 * m + 445) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_445 : oddCount 445 11 = 7 ∧ acceleratedOrbit 11 445 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_445 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 445) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_445.1, data_11_445.2] + +/-- Complete interval computation for depth 11, residue 446. -/ +theorem bounds_11_446 : exactInterval 11 446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_446 (m : Nat) : + stoppingTime (2 ^ 11 * m + 446) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_446 : oddCount 446 11 = 7 ∧ acceleratedOrbit 11 446 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_446 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 446) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_446.1, data_11_446.2] + +/-- Complete interval computation for depth 11, residue 447. -/ +theorem bounds_11_447 : exactInterval 11 447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_447 (m : Nat) : + stoppingTime (2 ^ 11 * m + 447) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_447 : oddCount 447 11 = 9 ∧ acceleratedOrbit 11 447 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_447 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 447) = 3 ^ 9 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_447.1, data_11_447.2] + +/-- Complete interval computation for depth 11, residue 448. -/ +theorem bounds_11_448 : exactInterval 11 448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_448 (m : Nat) : + stoppingTime (2 ^ 11 * m + 448) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_448 : oddCount 448 11 = 4 ∧ acceleratedOrbit 11 448 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_448 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 448) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_448.1, data_11_448.2] + +/-- Complete interval computation for depth 11, residue 449. -/ +theorem bounds_11_449 : exactInterval 11 449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_449 (m : Nat) : + stoppingTime (2 ^ 11 * m + 449) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_449 : oddCount 449 11 = 7 ∧ acceleratedOrbit 11 449 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_449 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 449) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_449.1, data_11_449.2] + +end Collatz.Research.StoppingAtlas.Batch0096 From 87de5e8df21228cb91a9cfd004213e059937e691 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:29 +0530 Subject: [PATCH 0097/1001] proof: certify atlas Batch0097 (11:450 to 11:464) --- Collatz/Research/StoppingAtlas/Batch0097.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0097.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0097.lean b/Collatz/Research/StoppingAtlas/Batch0097.lean new file mode 100644 index 00000000..36ace415 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0097.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0097 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 450. -/ +theorem bounds_11_450 : exactInterval 11 450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_450 (m : Nat) : + stoppingTime (2 ^ 11 * m + 450) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_450 : oddCount 450 11 = 8 ∧ acceleratedOrbit 11 450 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_450 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 450) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_450.1, data_11_450.2] + +/-- Complete interval computation for depth 11, residue 451. -/ +theorem bounds_11_451 : exactInterval 11 451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_451 (m : Nat) : + stoppingTime (2 ^ 11 * m + 451) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_451 : oddCount 451 11 = 8 ∧ acceleratedOrbit 11 451 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_451 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 451) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_451.1, data_11_451.2] + +/-- Complete interval computation for depth 11, residue 452. -/ +theorem bounds_11_452 : exactInterval 11 452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_452 (m : Nat) : + stoppingTime (2 ^ 11 * m + 452) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_452 : oddCount 452 11 = 2 ∧ acceleratedOrbit 11 452 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_452 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 452) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_452.1, data_11_452.2] + +/-- Complete interval computation for depth 11, residue 453. -/ +theorem bounds_11_453 : exactInterval 11 453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_453 (m : Nat) : + stoppingTime (2 ^ 11 * m + 453) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_453 : oddCount 453 11 = 2 ∧ acceleratedOrbit 11 453 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_453 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 453) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_453.1, data_11_453.2] + +/-- Complete interval computation for depth 11, residue 454. -/ +theorem bounds_11_454 : exactInterval 11 454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_454 (m : Nat) : + stoppingTime (2 ^ 11 * m + 454) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_454 : oddCount 454 11 = 2 ∧ acceleratedOrbit 11 454 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_454 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 454) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_454.1, data_11_454.2] + +/-- Complete interval computation for depth 11, residue 455. -/ +theorem bounds_11_455 : exactInterval 11 455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_455 (m : Nat) : + stoppingTime (2 ^ 11 * m + 455) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_455 : oddCount 455 11 = 7 ∧ acceleratedOrbit 11 455 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_455 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 455) = 3 ^ 7 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_455.1, data_11_455.2] + +/-- Complete interval computation for depth 11, residue 456. -/ +theorem bounds_11_456 : exactInterval 11 456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_456 (m : Nat) : + stoppingTime (2 ^ 11 * m + 456) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_456 : oddCount 456 11 = 5 ∧ acceleratedOrbit 11 456 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_456 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 456) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_456.1, data_11_456.2] + +/-- Complete interval computation for depth 11, residue 457. -/ +theorem bounds_11_457 : exactInterval 11 457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_457 (m : Nat) : + stoppingTime (2 ^ 11 * m + 457) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_457 : oddCount 457 11 = 6 ∧ acceleratedOrbit 11 457 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_457 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 457) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_457.1, data_11_457.2] + +/-- Complete interval computation for depth 11, residue 458. -/ +theorem bounds_11_458 : exactInterval 11 458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_458 (m : Nat) : + stoppingTime (2 ^ 11 * m + 458) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_458 : oddCount 458 11 = 5 ∧ acceleratedOrbit 11 458 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_458 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 458) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_458.1, data_11_458.2] + +/-- Complete interval computation for depth 11, residue 459. -/ +theorem bounds_11_459 : exactInterval 11 459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_459 (m : Nat) : + stoppingTime (2 ^ 11 * m + 459) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_459 : oddCount 459 11 = 5 ∧ acceleratedOrbit 11 459 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_459 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 459) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_459.1, data_11_459.2] + +/-- Complete interval computation for depth 11, residue 460. -/ +theorem bounds_11_460 : exactInterval 11 460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_460 (m : Nat) : + stoppingTime (2 ^ 11 * m + 460) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_460 : oddCount 460 11 = 5 ∧ acceleratedOrbit 11 460 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_460 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 460) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_460.1, data_11_460.2] + +/-- Complete interval computation for depth 11, residue 461. -/ +theorem bounds_11_461 : exactInterval 11 461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_461 (m : Nat) : + stoppingTime (2 ^ 11 * m + 461) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_461 : oddCount 461 11 = 5 ∧ acceleratedOrbit 11 461 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_461 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 461) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_461.1, data_11_461.2] + +/-- Complete interval computation for depth 11, residue 462. -/ +theorem bounds_11_462 : exactInterval 11 462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_462 (m : Nat) : + stoppingTime (2 ^ 11 * m + 462) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_462 : oddCount 462 11 = 7 ∧ acceleratedOrbit 11 462 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_462 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 462) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_462.1, data_11_462.2] + +/-- Complete interval computation for depth 11, residue 463. -/ +theorem bounds_11_463 : exactInterval 11 463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_463 (m : Nat) : + stoppingTime (2 ^ 11 * m + 463) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_463 : oddCount 463 11 = 7 ∧ acceleratedOrbit 11 463 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_463 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 463) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_463.1, data_11_463.2] + +/-- Complete interval computation for depth 11, residue 464. -/ +theorem bounds_11_464 : exactInterval 11 464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_464 (m : Nat) : + stoppingTime (2 ^ 11 * m + 464) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_464 : oddCount 464 11 = 4 ∧ acceleratedOrbit 11 464 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_464 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 464) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_464.1, data_11_464.2] + +end Collatz.Research.StoppingAtlas.Batch0097 From 22139b2a4134d5eb4435e3cbbd3257e32c2db042 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:30 +0530 Subject: [PATCH 0098/1001] proof: certify atlas Batch0098 (11:465 to 11:480) --- Collatz/Research/StoppingAtlas/Batch0098.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0098.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0098.lean b/Collatz/Research/StoppingAtlas/Batch0098.lean new file mode 100644 index 00000000..6cec2426 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0098.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0098 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 465. -/ +theorem bounds_11_465 : exactInterval 11 465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_465 (m : Nat) : + stoppingTime (2 ^ 11 * m + 465) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_465 : oddCount 465 11 = 5 ∧ acceleratedOrbit 11 465 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_465 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 465) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_465.1, data_11_465.2] + +/-- Complete interval computation for depth 11, residue 466. -/ +theorem bounds_11_466 : exactInterval 11 466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_466 (m : Nat) : + stoppingTime (2 ^ 11 * m + 466) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_466 : oddCount 466 11 = 6 ∧ acceleratedOrbit 11 466 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_466 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 466) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_466.1, data_11_466.2] + +/-- Complete interval computation for depth 11, residue 467. -/ +theorem bounds_11_467 : exactInterval 11 467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_467 (m : Nat) : + stoppingTime (2 ^ 11 * m + 467) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_467 : oddCount 467 11 = 6 ∧ acceleratedOrbit 11 467 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_467 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 467) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_467.1, data_11_467.2] + +/-- Complete interval computation for depth 11, residue 468. -/ +theorem bounds_11_468 : exactInterval 11 468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_468 (m : Nat) : + stoppingTime (2 ^ 11 * m + 468) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_468 : oddCount 468 11 = 4 ∧ acceleratedOrbit 11 468 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_468 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 468) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_468.1, data_11_468.2] + +/-- Complete interval computation for depth 11, residue 469. -/ +theorem bounds_11_469 : exactInterval 11 469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_469 (m : Nat) : + stoppingTime (2 ^ 11 * m + 469) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_469 : oddCount 469 11 = 4 ∧ acceleratedOrbit 11 469 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_469 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 469) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_469.1, data_11_469.2] + +/-- Complete interval computation for depth 11, residue 470. -/ +theorem bounds_11_470 : exactInterval 11 470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_470 (m : Nat) : + stoppingTime (2 ^ 11 * m + 470) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_470 : oddCount 470 11 = 7 ∧ acceleratedOrbit 11 470 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_470 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 470) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_470.1, data_11_470.2] + +/-- Complete interval computation for depth 11, residue 471. -/ +theorem bounds_11_471 : exactInterval 11 471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_471 (m : Nat) : + stoppingTime (2 ^ 11 * m + 471) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_471 : oddCount 471 11 = 7 ∧ acceleratedOrbit 11 471 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_471 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 471) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_471.1, data_11_471.2] + +/-- Complete interval computation for depth 11, residue 472. -/ +theorem bounds_11_472 : exactInterval 11 472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_472 (m : Nat) : + stoppingTime (2 ^ 11 * m + 472) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_472 : oddCount 472 11 = 4 ∧ acceleratedOrbit 11 472 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_472 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 472) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_472.1, data_11_472.2] + +/-- Complete interval computation for depth 11, residue 473. -/ +theorem bounds_11_473 : exactInterval 11 473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_473 (m : Nat) : + stoppingTime (2 ^ 11 * m + 473) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_473 : oddCount 473 11 = 4 ∧ acceleratedOrbit 11 473 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_473 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 473) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_473.1, data_11_473.2] + +/-- Complete interval computation for depth 11, residue 474. -/ +theorem bounds_11_474 : exactInterval 11 474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_474 (m : Nat) : + stoppingTime (2 ^ 11 * m + 474) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_474 : oddCount 474 11 = 4 ∧ acceleratedOrbit 11 474 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_474 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 474) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_474.1, data_11_474.2] + +/-- Complete interval computation for depth 11, residue 475. -/ +theorem bounds_11_475 : exactInterval 11 475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_475 (m : Nat) : + stoppingTime (2 ^ 11 * m + 475) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_475 : oddCount 475 11 = 6 ∧ acceleratedOrbit 11 475 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_475 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 475) = 3 ^ 6 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_475.1, data_11_475.2] + +/-- Complete interval computation for depth 11, residue 476. -/ +theorem bounds_11_476 : exactInterval 11 476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_476 (m : Nat) : + stoppingTime (2 ^ 11 * m + 476) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_476 : oddCount 476 11 = 4 ∧ acceleratedOrbit 11 476 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_476 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 476) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_476.1, data_11_476.2] + +/-- Complete interval computation for depth 11, residue 477. -/ +theorem bounds_11_477 : exactInterval 11 477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_477 (m : Nat) : + stoppingTime (2 ^ 11 * m + 477) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_477 : oddCount 477 11 = 4 ∧ acceleratedOrbit 11 477 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_477 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 477) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_477.1, data_11_477.2] + +/-- Complete interval computation for depth 11, residue 478. -/ +theorem bounds_11_478 : exactInterval 11 478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_478 (m : Nat) : + stoppingTime (2 ^ 11 * m + 478) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_478 : oddCount 478 11 = 9 ∧ acceleratedOrbit 11 478 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_478 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 478) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_478.1, data_11_478.2] + +/-- Complete interval computation for depth 11, residue 479. -/ +theorem bounds_11_479 : exactInterval 11 479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_479 (m : Nat) : + stoppingTime (2 ^ 11 * m + 479) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_479 : oddCount 479 11 = 9 ∧ acceleratedOrbit 11 479 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_479 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 479) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_479.1, data_11_479.2] + +/-- Complete interval computation for depth 11, residue 480. -/ +theorem bounds_11_480 : exactInterval 11 480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_480 (m : Nat) : + stoppingTime (2 ^ 11 * m + 480) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_480 : oddCount 480 11 = 4 ∧ acceleratedOrbit 11 480 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_480 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 480) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_480.1, data_11_480.2] + +end Collatz.Research.StoppingAtlas.Batch0098 From c13e2e8ad99e6b56536af642ca86cf70f28d1fca Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:30 +0530 Subject: [PATCH 0099/1001] proof: certify atlas Batch0099 (11:481 to 11:495) --- Collatz/Research/StoppingAtlas/Batch0099.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0099.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0099.lean b/Collatz/Research/StoppingAtlas/Batch0099.lean new file mode 100644 index 00000000..b315cbf5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0099.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0099 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 481. -/ +theorem bounds_11_481 : exactInterval 11 481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_481 (m : Nat) : + stoppingTime (2 ^ 11 * m + 481) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_481 : oddCount 481 11 = 6 ∧ acceleratedOrbit 11 481 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_481 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 481) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_481.1, data_11_481.2] + +/-- Complete interval computation for depth 11, residue 482. -/ +theorem bounds_11_482 : exactInterval 11 482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_482 (m : Nat) : + stoppingTime (2 ^ 11 * m + 482) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_482 : oddCount 482 11 = 4 ∧ acceleratedOrbit 11 482 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_482 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 482) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_482.1, data_11_482.2] + +/-- Complete interval computation for depth 11, residue 483. -/ +theorem bounds_11_483 : exactInterval 11 483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_483 (m : Nat) : + stoppingTime (2 ^ 11 * m + 483) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_483 : oddCount 483 11 = 4 ∧ acceleratedOrbit 11 483 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_483 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 483) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_483.1, data_11_483.2] + +/-- Complete interval computation for depth 11, residue 484. -/ +theorem bounds_11_484 : exactInterval 11 484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_484 (m : Nat) : + stoppingTime (2 ^ 11 * m + 484) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_484 : oddCount 484 11 = 6 ∧ acceleratedOrbit 11 484 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_484 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 484) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_484.1, data_11_484.2] + +/-- Complete interval computation for depth 11, residue 485. -/ +theorem bounds_11_485 : exactInterval 11 485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_485 (m : Nat) : + stoppingTime (2 ^ 11 * m + 485) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_485 : oddCount 485 11 = 6 ∧ acceleratedOrbit 11 485 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_485 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 485) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_485.1, data_11_485.2] + +/-- Complete interval computation for depth 11, residue 486. -/ +theorem bounds_11_486 : exactInterval 11 486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_486 (m : Nat) : + stoppingTime (2 ^ 11 * m + 486) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_486 : oddCount 486 11 = 6 ∧ acceleratedOrbit 11 486 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_486 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 486) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_486.1, data_11_486.2] + +/-- Complete interval computation for depth 11, residue 487. -/ +theorem bounds_11_487 : exactInterval 11 487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_487 (m : Nat) : + stoppingTime (2 ^ 11 * m + 487) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_487 : oddCount 487 11 = 8 ∧ acceleratedOrbit 11 487 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_487 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 487) = 3 ^ 8 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_487.1, data_11_487.2] + +/-- Complete interval computation for depth 11, residue 488. -/ +theorem bounds_11_488 : exactInterval 11 488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_488 (m : Nat) : + stoppingTime (2 ^ 11 * m + 488) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_488 : oddCount 488 11 = 4 ∧ acceleratedOrbit 11 488 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_488 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 488) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_488.1, data_11_488.2] + +/-- Complete interval computation for depth 11, residue 489. -/ +theorem bounds_11_489 : exactInterval 11 489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_489 (m : Nat) : + stoppingTime (2 ^ 11 * m + 489) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_489 : oddCount 489 11 = 7 ∧ acceleratedOrbit 11 489 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_489 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 489) = 3 ^ 7 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_489.1, data_11_489.2] + +/-- Complete interval computation for depth 11, residue 490. -/ +theorem bounds_11_490 : exactInterval 11 490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_490 (m : Nat) : + stoppingTime (2 ^ 11 * m + 490) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_490 : oddCount 490 11 = 4 ∧ acceleratedOrbit 11 490 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_490 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 490) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_490.1, data_11_490.2] + +/-- Complete interval computation for depth 11, residue 491. -/ +theorem bounds_11_491 : exactInterval 11 491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_491 (m : Nat) : + stoppingTime (2 ^ 11 * m + 491) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_491 : oddCount 491 11 = 8 ∧ acceleratedOrbit 11 491 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_491 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 491) = 3 ^ 8 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_491.1, data_11_491.2] + +/-- Complete interval computation for depth 11, residue 492. -/ +theorem bounds_11_492 : exactInterval 11 492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_492 (m : Nat) : + stoppingTime (2 ^ 11 * m + 492) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_492 : oddCount 492 11 = 5 ∧ acceleratedOrbit 11 492 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_492 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 492) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_492.1, data_11_492.2] + +/-- Complete interval computation for depth 11, residue 493. -/ +theorem bounds_11_493 : exactInterval 11 493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_493 (m : Nat) : + stoppingTime (2 ^ 11 * m + 493) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_493 : oddCount 493 11 = 5 ∧ acceleratedOrbit 11 493 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_493 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 493) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_493.1, data_11_493.2] + +/-- Complete interval computation for depth 11, residue 494. -/ +theorem bounds_11_494 : exactInterval 11 494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_494 (m : Nat) : + stoppingTime (2 ^ 11 * m + 494) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_494 : oddCount 494 11 = 5 ∧ acceleratedOrbit 11 494 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_494 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 494) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_494.1, data_11_494.2] + +/-- Complete interval computation for depth 11, residue 495. -/ +theorem bounds_11_495 : exactInterval 11 495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_495 (m : Nat) : + stoppingTime (2 ^ 11 * m + 495) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_495 : oddCount 495 11 = 9 ∧ acceleratedOrbit 11 495 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_495 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 495) = 3 ^ 9 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_495.1, data_11_495.2] + +end Collatz.Research.StoppingAtlas.Batch0099 From 55bd2cc32668c1f5e551d18bccd82bb03a52ea9e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:31 +0530 Subject: [PATCH 0100/1001] proof: certify atlas Batch0100 (11:496 to 11:511) --- Collatz/Research/StoppingAtlas/Batch0100.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0100.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0100.lean b/Collatz/Research/StoppingAtlas/Batch0100.lean new file mode 100644 index 00000000..26b695ac --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0100.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0100 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 496. -/ +theorem bounds_11_496 : exactInterval 11 496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_496 (m : Nat) : + stoppingTime (2 ^ 11 * m + 496) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_496 : oddCount 496 11 = 6 ∧ acceleratedOrbit 11 496 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_496 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 496) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_496.1, data_11_496.2] + +/-- Complete interval computation for depth 11, residue 497. -/ +theorem bounds_11_497 : exactInterval 11 497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_497 (m : Nat) : + stoppingTime (2 ^ 11 * m + 497) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_497 : oddCount 497 11 = 4 ∧ acceleratedOrbit 11 497 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_497 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 497) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_497.1, data_11_497.2] + +/-- Complete interval computation for depth 11, residue 498. -/ +theorem bounds_11_498 : exactInterval 11 498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_498 (m : Nat) : + stoppingTime (2 ^ 11 * m + 498) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_498 : oddCount 498 11 = 6 ∧ acceleratedOrbit 11 498 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_498 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 498) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_498.1, data_11_498.2] + +/-- Complete interval computation for depth 11, residue 499. -/ +theorem bounds_11_499 : exactInterval 11 499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_499 (m : Nat) : + stoppingTime (2 ^ 11 * m + 499) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_499 : oddCount 499 11 = 6 ∧ acceleratedOrbit 11 499 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_499 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 499) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_499.1, data_11_499.2] + +/-- Complete interval computation for depth 11, residue 500. -/ +theorem bounds_11_500 : exactInterval 11 500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_500 (m : Nat) : + stoppingTime (2 ^ 11 * m + 500) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_500 : oddCount 500 11 = 6 ∧ acceleratedOrbit 11 500 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_500 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 500) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_500.1, data_11_500.2] + +/-- Complete interval computation for depth 11, residue 501. -/ +theorem bounds_11_501 : exactInterval 11 501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_501 (m : Nat) : + stoppingTime (2 ^ 11 * m + 501) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_501 : oddCount 501 11 = 6 ∧ acceleratedOrbit 11 501 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_501 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 501) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_501.1, data_11_501.2] + +/-- Complete interval computation for depth 11, residue 502. -/ +theorem bounds_11_502 : exactInterval 11 502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_502 (m : Nat) : + stoppingTime (2 ^ 11 * m + 502) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_502 : oddCount 502 11 = 8 ∧ acceleratedOrbit 11 502 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_502 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 502) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_502.1, data_11_502.2] + +/-- Complete interval computation for depth 11, residue 503. -/ +theorem bounds_11_503 : exactInterval 11 503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_503 (m : Nat) : + stoppingTime (2 ^ 11 * m + 503) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_503 : oddCount 503 11 = 8 ∧ acceleratedOrbit 11 503 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_503 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 503) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_503.1, data_11_503.2] + +/-- Complete interval computation for depth 11, residue 504. -/ +theorem bounds_11_504 : exactInterval 11 504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_504 (m : Nat) : + stoppingTime (2 ^ 11 * m + 504) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_504 : oddCount 504 11 = 6 ∧ acceleratedOrbit 11 504 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_504 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 504) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_504.1, data_11_504.2] + +/-- Complete interval computation for depth 11, residue 505. -/ +theorem bounds_11_505 : exactInterval 11 505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_505 (m : Nat) : + stoppingTime (2 ^ 11 * m + 505) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_505 : oddCount 505 11 = 7 ∧ acceleratedOrbit 11 505 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_505 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 505) = 3 ^ 7 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_505.1, data_11_505.2] + +/-- Complete interval computation for depth 11, residue 506. -/ +theorem bounds_11_506 : exactInterval 11 506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_506 (m : Nat) : + stoppingTime (2 ^ 11 * m + 506) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_506 : oddCount 506 11 = 6 ∧ acceleratedOrbit 11 506 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_506 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 506) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_506.1, data_11_506.2] + +/-- Complete interval computation for depth 11, residue 507. -/ +theorem bounds_11_507 : exactInterval 11 507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_507 (m : Nat) : + stoppingTime (2 ^ 11 * m + 507) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_507 : oddCount 507 11 = 6 ∧ acceleratedOrbit 11 507 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_507 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 507) = 3 ^ 6 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_507.1, data_11_507.2] + +/-- Complete interval computation for depth 11, residue 508. -/ +theorem bounds_11_508 : exactInterval 11 508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_508 (m : Nat) : + stoppingTime (2 ^ 11 * m + 508) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_508 : oddCount 508 11 = 8 ∧ acceleratedOrbit 11 508 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_508 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 508) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_508.1, data_11_508.2] + +/-- Complete interval computation for depth 11, residue 509. -/ +theorem bounds_11_509 : exactInterval 11 509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_509 (m : Nat) : + stoppingTime (2 ^ 11 * m + 509) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_509 : oddCount 509 11 = 8 ∧ acceleratedOrbit 11 509 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_509 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 509) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_509.1, data_11_509.2] + +/-- Complete interval computation for depth 11, residue 510. -/ +theorem bounds_11_510 : exactInterval 11 510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_510 (m : Nat) : + stoppingTime (2 ^ 11 * m + 510) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_510 : oddCount 510 11 = 8 ∧ acceleratedOrbit 11 510 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_510 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 510) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_510.1, data_11_510.2] + +/-- Complete interval computation for depth 11, residue 511. -/ +theorem bounds_11_511 : exactInterval 11 511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_511 (m : Nat) : + stoppingTime (2 ^ 11 * m + 511) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_511 : oddCount 511 11 = 10 ∧ acceleratedOrbit 11 511 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_511 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 511) = 3 ^ 10 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_511.1, data_11_511.2] + +end Collatz.Research.StoppingAtlas.Batch0100 From 4b4ecf4196bd956aeac58e81a2f8314e2e913d5d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:31 +0530 Subject: [PATCH 0101/1001] proof: certify atlas Batch0101 (11:512 to 11:526) --- Collatz/Research/StoppingAtlas/Batch0101.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0101.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0101.lean b/Collatz/Research/StoppingAtlas/Batch0101.lean new file mode 100644 index 00000000..272dfacf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0101.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0101 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 512. -/ +theorem bounds_11_512 : exactInterval 11 512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_512 (m : Nat) : + stoppingTime (2 ^ 11 * m + 512) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_512 : oddCount 512 11 = 1 ∧ acceleratedOrbit 11 512 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_512 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 512) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_512.1, data_11_512.2] + +/-- Complete interval computation for depth 11, residue 513. -/ +theorem bounds_11_513 : exactInterval 11 513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_513 (m : Nat) : + stoppingTime (2 ^ 11 * m + 513) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_513 : oddCount 513 11 = 6 ∧ acceleratedOrbit 11 513 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_513 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 513) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_513.1, data_11_513.2] + +/-- Complete interval computation for depth 11, residue 514. -/ +theorem bounds_11_514 : exactInterval 11 514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_514 (m : Nat) : + stoppingTime (2 ^ 11 * m + 514) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_514 : oddCount 514 11 = 5 ∧ acceleratedOrbit 11 514 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_514 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 514) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_514.1, data_11_514.2] + +/-- Complete interval computation for depth 11, residue 515. -/ +theorem bounds_11_515 : exactInterval 11 515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_515 (m : Nat) : + stoppingTime (2 ^ 11 * m + 515) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_515 : oddCount 515 11 = 5 ∧ acceleratedOrbit 11 515 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_515 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 515) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_515.1, data_11_515.2] + +/-- Complete interval computation for depth 11, residue 516. -/ +theorem bounds_11_516 : exactInterval 11 516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_516 (m : Nat) : + stoppingTime (2 ^ 11 * m + 516) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_516 : oddCount 516 11 = 6 ∧ acceleratedOrbit 11 516 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_516 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 516) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_516.1, data_11_516.2] + +/-- Complete interval computation for depth 11, residue 517. -/ +theorem bounds_11_517 : exactInterval 11 517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_517 (m : Nat) : + stoppingTime (2 ^ 11 * m + 517) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_517 : oddCount 517 11 = 6 ∧ acceleratedOrbit 11 517 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_517 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 517) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_517.1, data_11_517.2] + +/-- Complete interval computation for depth 11, residue 518. -/ +theorem bounds_11_518 : exactInterval 11 518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_518 (m : Nat) : + stoppingTime (2 ^ 11 * m + 518) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_518 : oddCount 518 11 = 6 ∧ acceleratedOrbit 11 518 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_518 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 518) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_518.1, data_11_518.2] + +/-- Complete interval computation for depth 11, residue 519. -/ +theorem bounds_11_519 : exactInterval 11 519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_519 (m : Nat) : + stoppingTime (2 ^ 11 * m + 519) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_519 : oddCount 519 11 = 7 ∧ acceleratedOrbit 11 519 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_519 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 519) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_519.1, data_11_519.2] + +/-- Complete interval computation for depth 11, residue 520. -/ +theorem bounds_11_520 : exactInterval 11 520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_520 (m : Nat) : + stoppingTime (2 ^ 11 * m + 520) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_520 : oddCount 520 11 = 3 ∧ acceleratedOrbit 11 520 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_520 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 520) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_520.1, data_11_520.2] + +/-- Complete interval computation for depth 11, residue 521. -/ +theorem bounds_11_521 : exactInterval 11 521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_521 (m : Nat) : + stoppingTime (2 ^ 11 * m + 521) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_521 : oddCount 521 11 = 5 ∧ acceleratedOrbit 11 521 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_521 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 521) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_521.1, data_11_521.2] + +/-- Complete interval computation for depth 11, residue 522. -/ +theorem bounds_11_522 : exactInterval 11 522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_522 (m : Nat) : + stoppingTime (2 ^ 11 * m + 522) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_522 : oddCount 522 11 = 3 ∧ acceleratedOrbit 11 522 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_522 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 522) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_522.1, data_11_522.2] + +/-- Complete interval computation for depth 11, residue 523. -/ +theorem bounds_11_523 : exactInterval 11 523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_523 (m : Nat) : + stoppingTime (2 ^ 11 * m + 523) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_523 : oddCount 523 11 = 6 ∧ acceleratedOrbit 11 523 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_523 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 523) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_523.1, data_11_523.2] + +/-- Complete interval computation for depth 11, residue 524. -/ +theorem bounds_11_524 : exactInterval 11 524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_524 (m : Nat) : + stoppingTime (2 ^ 11 * m + 524) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_524 : oddCount 524 11 = 3 ∧ acceleratedOrbit 11 524 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_524 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 524) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_524.1, data_11_524.2] + +/-- Complete interval computation for depth 11, residue 525. -/ +theorem bounds_11_525 : exactInterval 11 525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_525 (m : Nat) : + stoppingTime (2 ^ 11 * m + 525) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_525 : oddCount 525 11 = 3 ∧ acceleratedOrbit 11 525 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_525 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 525) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_525.1, data_11_525.2] + +/-- Complete interval computation for depth 11, residue 526. -/ +theorem bounds_11_526 : exactInterval 11 526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_526 (m : Nat) : + stoppingTime (2 ^ 11 * m + 526) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_526 : oddCount 526 11 = 7 ∧ acceleratedOrbit 11 526 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_526 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 526) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_526.1, data_11_526.2] + +end Collatz.Research.StoppingAtlas.Batch0101 From c092df9febfb92bd1a030adaed2c40ffffad7737 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:31 +0530 Subject: [PATCH 0102/1001] proof: certify atlas Batch0102 (11:527 to 11:541) --- Collatz/Research/StoppingAtlas/Batch0102.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0102.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0102.lean b/Collatz/Research/StoppingAtlas/Batch0102.lean new file mode 100644 index 00000000..1d9a9878 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0102.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0102 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 527. -/ +theorem bounds_11_527 : exactInterval 11 527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_527 (m : Nat) : + stoppingTime (2 ^ 11 * m + 527) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_527 : oddCount 527 11 = 7 ∧ acceleratedOrbit 11 527 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_527 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 527) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_527.1, data_11_527.2] + +/-- Complete interval computation for depth 11, residue 528. -/ +theorem bounds_11_528 : exactInterval 11 528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_528 (m : Nat) : + stoppingTime (2 ^ 11 * m + 528) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_528 : oddCount 528 11 = 4 ∧ acceleratedOrbit 11 528 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_528 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 528) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_528.1, data_11_528.2] + +/-- Complete interval computation for depth 11, residue 529. -/ +theorem bounds_11_529 : exactInterval 11 529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_529 (m : Nat) : + stoppingTime (2 ^ 11 * m + 529) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_529 : oddCount 529 11 = 3 ∧ acceleratedOrbit 11 529 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_529 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 529) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_529.1, data_11_529.2] + +/-- Complete interval computation for depth 11, residue 530. -/ +theorem bounds_11_530 : exactInterval 11 530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_530 (m : Nat) : + stoppingTime (2 ^ 11 * m + 530) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_530 : oddCount 530 11 = 6 ∧ acceleratedOrbit 11 530 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_530 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 530) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_530.1, data_11_530.2] + +/-- Complete interval computation for depth 11, residue 531. -/ +theorem bounds_11_531 : exactInterval 11 531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_531 (m : Nat) : + stoppingTime (2 ^ 11 * m + 531) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_531 : oddCount 531 11 = 6 ∧ acceleratedOrbit 11 531 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_531 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 531) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_531.1, data_11_531.2] + +/-- Complete interval computation for depth 11, residue 532. -/ +theorem bounds_11_532 : exactInterval 11 532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_532 (m : Nat) : + stoppingTime (2 ^ 11 * m + 532) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_532 : oddCount 532 11 = 4 ∧ acceleratedOrbit 11 532 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_532 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 532) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_532.1, data_11_532.2] + +/-- Complete interval computation for depth 11, residue 533. -/ +theorem bounds_11_533 : exactInterval 11 533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_533 (m : Nat) : + stoppingTime (2 ^ 11 * m + 533) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_533 : oddCount 533 11 = 4 ∧ acceleratedOrbit 11 533 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_533 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 533) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_533.1, data_11_533.2] + +/-- Complete interval computation for depth 11, residue 534. -/ +theorem bounds_11_534 : exactInterval 11 534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_534 (m : Nat) : + stoppingTime (2 ^ 11 * m + 534) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_534 : oddCount 534 11 = 5 ∧ acceleratedOrbit 11 534 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_534 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 534) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_534.1, data_11_534.2] + +/-- Complete interval computation for depth 11, residue 535. -/ +theorem bounds_11_535 : exactInterval 11 535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_535 (m : Nat) : + stoppingTime (2 ^ 11 * m + 535) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_535 : oddCount 535 11 = 5 ∧ acceleratedOrbit 11 535 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_535 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 535) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_535.1, data_11_535.2] + +/-- Complete interval computation for depth 11, residue 536. -/ +theorem bounds_11_536 : exactInterval 11 536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_536 (m : Nat) : + stoppingTime (2 ^ 11 * m + 536) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_536 : oddCount 536 11 = 4 ∧ acceleratedOrbit 11 536 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_536 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 536) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_536.1, data_11_536.2] + +/-- Complete interval computation for depth 11, residue 537. -/ +theorem bounds_11_537 : exactInterval 11 537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_537 (m : Nat) : + stoppingTime (2 ^ 11 * m + 537) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_537 : oddCount 537 11 = 5 ∧ acceleratedOrbit 11 537 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_537 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 537) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_537.1, data_11_537.2] + +/-- Complete interval computation for depth 11, residue 538. -/ +theorem bounds_11_538 : exactInterval 11 538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_538 (m : Nat) : + stoppingTime (2 ^ 11 * m + 538) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_538 : oddCount 538 11 = 4 ∧ acceleratedOrbit 11 538 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_538 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 538) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_538.1, data_11_538.2] + +/-- Complete interval computation for depth 11, residue 539. -/ +theorem bounds_11_539 : exactInterval 11 539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_539 (m : Nat) : + stoppingTime (2 ^ 11 * m + 539) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_539 : oddCount 539 11 = 7 ∧ acceleratedOrbit 11 539 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_539 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 539) = 3 ^ 7 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_539.1, data_11_539.2] + +/-- Complete interval computation for depth 11, residue 540. -/ +theorem bounds_11_540 : exactInterval 11 540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_540 (m : Nat) : + stoppingTime (2 ^ 11 * m + 540) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_540 : oddCount 540 11 = 5 ∧ acceleratedOrbit 11 540 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_540 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 540) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_540.1, data_11_540.2] + +/-- Complete interval computation for depth 11, residue 541. -/ +theorem bounds_11_541 : exactInterval 11 541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_541 (m : Nat) : + stoppingTime (2 ^ 11 * m + 541) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_541 : oddCount 541 11 = 5 ∧ acceleratedOrbit 11 541 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_541 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 541) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_541.1, data_11_541.2] + +end Collatz.Research.StoppingAtlas.Batch0102 From ac42126067a62a2ff789fa06802e33cea217b4d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:31 +0530 Subject: [PATCH 0103/1001] proof: certify atlas Batch0103 (11:542 to 11:557) --- Collatz/Research/StoppingAtlas/Batch0103.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0103.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0103.lean b/Collatz/Research/StoppingAtlas/Batch0103.lean new file mode 100644 index 00000000..59781617 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0103.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0103 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 542. -/ +theorem bounds_11_542 : exactInterval 11 542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_542 (m : Nat) : + stoppingTime (2 ^ 11 * m + 542) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_542 : oddCount 542 11 = 5 ∧ acceleratedOrbit 11 542 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_542 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 542) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_542.1, data_11_542.2] + +/-- Complete interval computation for depth 11, residue 543. -/ +theorem bounds_11_543 : exactInterval 11 543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_543 (m : Nat) : + stoppingTime (2 ^ 11 * m + 543) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_543 : oddCount 543 11 = 7 ∧ acceleratedOrbit 11 543 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_543 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 543) = 3 ^ 7 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_543.1, data_11_543.2] + +/-- Complete interval computation for depth 11, residue 544. -/ +theorem bounds_11_544 : exactInterval 11 544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_544 (m : Nat) : + stoppingTime (2 ^ 11 * m + 544) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_544 : oddCount 544 11 = 3 ∧ acceleratedOrbit 11 544 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_544 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 544) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_544.1, data_11_544.2] + +/-- Complete interval computation for depth 11, residue 545. -/ +theorem bounds_11_545 : exactInterval 11 545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_545 (m : Nat) : + stoppingTime (2 ^ 11 * m + 545) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_545 : oddCount 545 11 = 5 ∧ acceleratedOrbit 11 545 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_545 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 545) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_545.1, data_11_545.2] + +/-- Complete interval computation for depth 11, residue 546. -/ +theorem bounds_11_546 : exactInterval 11 546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_546 (m : Nat) : + stoppingTime (2 ^ 11 * m + 546) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_546 : oddCount 546 11 = 4 ∧ acceleratedOrbit 11 546 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_546 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 546) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_546.1, data_11_546.2] + +/-- Complete interval computation for depth 11, residue 547. -/ +theorem bounds_11_547 : exactInterval 11 547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_547 (m : Nat) : + stoppingTime (2 ^ 11 * m + 547) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_547 : oddCount 547 11 = 4 ∧ acceleratedOrbit 11 547 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_547 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 547) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_547.1, data_11_547.2] + +/-- Complete interval computation for depth 11, residue 548. -/ +theorem bounds_11_548 : exactInterval 11 548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_548 (m : Nat) : + stoppingTime (2 ^ 11 * m + 548) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_548 : oddCount 548 11 = 7 ∧ acceleratedOrbit 11 548 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_548 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 548) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_548.1, data_11_548.2] + +/-- Complete interval computation for depth 11, residue 549. -/ +theorem bounds_11_549 : exactInterval 11 549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_549 (m : Nat) : + stoppingTime (2 ^ 11 * m + 549) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_549 : oddCount 549 11 = 7 ∧ acceleratedOrbit 11 549 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_549 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 549) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_549.1, data_11_549.2] + +/-- Complete interval computation for depth 11, residue 550. -/ +theorem bounds_11_550 : exactInterval 11 550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_550 (m : Nat) : + stoppingTime (2 ^ 11 * m + 550) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_550 : oddCount 550 11 = 7 ∧ acceleratedOrbit 11 550 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_550 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 550) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_550.1, data_11_550.2] + +/-- Complete interval computation for depth 11, residue 551. -/ +theorem bounds_11_551 : exactInterval 11 551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_551 (m : Nat) : + stoppingTime (2 ^ 11 * m + 551) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_551 : oddCount 551 11 = 6 ∧ acceleratedOrbit 11 551 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_551 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 551) = 3 ^ 6 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_551.1, data_11_551.2] + +/-- Complete interval computation for depth 11, residue 552. -/ +theorem bounds_11_552 : exactInterval 11 552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_552 (m : Nat) : + stoppingTime (2 ^ 11 * m + 552) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_552 : oddCount 552 11 = 3 ∧ acceleratedOrbit 11 552 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_552 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 552) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_552.1, data_11_552.2] + +/-- Complete interval computation for depth 11, residue 553. -/ +theorem bounds_11_553 : exactInterval 11 553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_553 (m : Nat) : + stoppingTime (2 ^ 11 * m + 553) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_553 : oddCount 553 11 = 8 ∧ acceleratedOrbit 11 553 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_553 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 553) = 3 ^ 8 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_553.1, data_11_553.2] + +/-- Complete interval computation for depth 11, residue 554. -/ +theorem bounds_11_554 : exactInterval 11 554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_554 (m : Nat) : + stoppingTime (2 ^ 11 * m + 554) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_554 : oddCount 554 11 = 3 ∧ acceleratedOrbit 11 554 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_554 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 554) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_554.1, data_11_554.2] + +/-- Complete interval computation for depth 11, residue 555. -/ +theorem bounds_11_555 : exactInterval 11 555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_555 (m : Nat) : + stoppingTime (2 ^ 11 * m + 555) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_555 : oddCount 555 11 = 4 ∧ acceleratedOrbit 11 555 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_555 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 555) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_555.1, data_11_555.2] + +/-- Complete interval computation for depth 11, residue 556. -/ +theorem bounds_11_556 : exactInterval 11 556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_556 (m : Nat) : + stoppingTime (2 ^ 11 * m + 556) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_556 : oddCount 556 11 = 5 ∧ acceleratedOrbit 11 556 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_556 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 556) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_556.1, data_11_556.2] + +/-- Complete interval computation for depth 11, residue 557. -/ +theorem bounds_11_557 : exactInterval 11 557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_557 (m : Nat) : + stoppingTime (2 ^ 11 * m + 557) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_557 : oddCount 557 11 = 5 ∧ acceleratedOrbit 11 557 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_557 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 557) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_557.1, data_11_557.2] + +end Collatz.Research.StoppingAtlas.Batch0103 From af08711a5a030e6074c3dcfdf91db66c64e0b55f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:32 +0530 Subject: [PATCH 0104/1001] proof: certify atlas Batch0104 (11:558 to 11:572) --- Collatz/Research/StoppingAtlas/Batch0104.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0104.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0104.lean b/Collatz/Research/StoppingAtlas/Batch0104.lean new file mode 100644 index 00000000..9683faa9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0104.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0104 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 558. -/ +theorem bounds_11_558 : exactInterval 11 558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_558 (m : Nat) : + stoppingTime (2 ^ 11 * m + 558) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_558 : oddCount 558 11 = 5 ∧ acceleratedOrbit 11 558 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_558 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 558) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_558.1, data_11_558.2] + +/-- Complete interval computation for depth 11, residue 559. -/ +theorem bounds_11_559 : exactInterval 11 559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_559 (m : Nat) : + stoppingTime (2 ^ 11 * m + 559) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_559 : oddCount 559 11 = 8 ∧ acceleratedOrbit 11 559 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_559 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 559) = 3 ^ 8 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_559.1, data_11_559.2] + +/-- Complete interval computation for depth 11, residue 560. -/ +theorem bounds_11_560 : exactInterval 11 560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_560 (m : Nat) : + stoppingTime (2 ^ 11 * m + 560) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_560 : oddCount 560 11 = 3 ∧ acceleratedOrbit 11 560 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_560 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 560) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_560.1, data_11_560.2] + +/-- Complete interval computation for depth 11, residue 561. -/ +theorem bounds_11_561 : exactInterval 11 561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_561 (m : Nat) : + stoppingTime (2 ^ 11 * m + 561) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_561 : oddCount 561 11 = 6 ∧ acceleratedOrbit 11 561 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_561 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 561) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_561.1, data_11_561.2] + +/-- Complete interval computation for depth 11, residue 562. -/ +theorem bounds_11_562 : exactInterval 11 562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_562 (m : Nat) : + stoppingTime (2 ^ 11 * m + 562) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_562 : oddCount 562 11 = 6 ∧ acceleratedOrbit 11 562 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_562 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 562) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_562.1, data_11_562.2] + +/-- Complete interval computation for depth 11, residue 563. -/ +theorem bounds_11_563 : exactInterval 11 563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_563 (m : Nat) : + stoppingTime (2 ^ 11 * m + 563) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_563 : oddCount 563 11 = 6 ∧ acceleratedOrbit 11 563 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_563 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 563) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_563.1, data_11_563.2] + +/-- Complete interval computation for depth 11, residue 564. -/ +theorem bounds_11_564 : exactInterval 11 564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_564 (m : Nat) : + stoppingTime (2 ^ 11 * m + 564) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_564 : oddCount 564 11 = 3 ∧ acceleratedOrbit 11 564 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_564 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 564) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_564.1, data_11_564.2] + +/-- Complete interval computation for depth 11, residue 565. -/ +theorem bounds_11_565 : exactInterval 11 565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_565 (m : Nat) : + stoppingTime (2 ^ 11 * m + 565) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_565 : oddCount 565 11 = 3 ∧ acceleratedOrbit 11 565 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_565 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 565) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_565.1, data_11_565.2] + +/-- Complete interval computation for depth 11, residue 566. -/ +theorem bounds_11_566 : exactInterval 11 566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_566 (m : Nat) : + stoppingTime (2 ^ 11 * m + 566) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_566 : oddCount 566 11 = 8 ∧ acceleratedOrbit 11 566 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_566 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 566) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_566.1, data_11_566.2] + +/-- Complete interval computation for depth 11, residue 567. -/ +theorem bounds_11_567 : exactInterval 11 567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_567 (m : Nat) : + stoppingTime (2 ^ 11 * m + 567) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_567 : oddCount 567 11 = 8 ∧ acceleratedOrbit 11 567 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_567 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 567) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_567.1, data_11_567.2] + +/-- Complete interval computation for depth 11, residue 568. -/ +theorem bounds_11_568 : exactInterval 11 568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_568 (m : Nat) : + stoppingTime (2 ^ 11 * m + 568) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_568 : oddCount 568 11 = 6 ∧ acceleratedOrbit 11 568 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_568 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 568) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_568.1, data_11_568.2] + +/-- Complete interval computation for depth 11, residue 569. -/ +theorem bounds_11_569 : exactInterval 11 569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_569 (m : Nat) : + stoppingTime (2 ^ 11 * m + 569) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_569 : oddCount 569 11 = 7 ∧ acceleratedOrbit 11 569 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_569 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 569) = 3 ^ 7 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_569.1, data_11_569.2] + +/-- Complete interval computation for depth 11, residue 570. -/ +theorem bounds_11_570 : exactInterval 11 570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_570 (m : Nat) : + stoppingTime (2 ^ 11 * m + 570) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_570 : oddCount 570 11 = 6 ∧ acceleratedOrbit 11 570 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_570 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 570) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_570.1, data_11_570.2] + +/-- Complete interval computation for depth 11, residue 571. -/ +theorem bounds_11_571 : exactInterval 11 571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_571 (m : Nat) : + stoppingTime (2 ^ 11 * m + 571) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_571 : oddCount 571 11 = 5 ∧ acceleratedOrbit 11 571 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_571 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 571) = 3 ^ 5 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_571.1, data_11_571.2] + +/-- Complete interval computation for depth 11, residue 572. -/ +theorem bounds_11_572 : exactInterval 11 572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_572 (m : Nat) : + stoppingTime (2 ^ 11 * m + 572) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_572 : oddCount 572 11 = 6 ∧ acceleratedOrbit 11 572 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_572 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 572) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_572.1, data_11_572.2] + +end Collatz.Research.StoppingAtlas.Batch0104 From a850f6c76f63cd651f085f0d1aa73b0a9cf5330c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:32 +0530 Subject: [PATCH 0105/1001] proof: certify atlas Batch0105 (11:573 to 11:587) --- Collatz/Research/StoppingAtlas/Batch0105.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0105.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0105.lean b/Collatz/Research/StoppingAtlas/Batch0105.lean new file mode 100644 index 00000000..01d8a923 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0105.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0105 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 573. -/ +theorem bounds_11_573 : exactInterval 11 573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_573 (m : Nat) : + stoppingTime (2 ^ 11 * m + 573) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_573 : oddCount 573 11 = 6 ∧ acceleratedOrbit 11 573 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_573 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 573) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_573.1, data_11_573.2] + +/-- Complete interval computation for depth 11, residue 574. -/ +theorem bounds_11_574 : exactInterval 11 574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_574 (m : Nat) : + stoppingTime (2 ^ 11 * m + 574) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_574 : oddCount 574 11 = 6 ∧ acceleratedOrbit 11 574 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_574 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 574) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_574.1, data_11_574.2] + +/-- Complete interval computation for depth 11, residue 575. -/ +theorem bounds_11_575 : exactInterval 11 575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_575 (m : Nat) : + stoppingTime (2 ^ 11 * m + 575) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_575 : oddCount 575 11 = 6 ∧ acceleratedOrbit 11 575 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_575 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 575) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_575.1, data_11_575.2] + +/-- Complete interval computation for depth 11, residue 576. -/ +theorem bounds_11_576 : exactInterval 11 576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_576 (m : Nat) : + stoppingTime (2 ^ 11 * m + 576) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_576 : oddCount 576 11 = 4 ∧ acceleratedOrbit 11 576 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_576 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 576) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_576.1, data_11_576.2] + +/-- Complete interval computation for depth 11, residue 577. -/ +theorem bounds_11_577 : exactInterval 11 577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_577 (m : Nat) : + stoppingTime (2 ^ 11 * m + 577) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_577 : oddCount 577 11 = 4 ∧ acceleratedOrbit 11 577 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_577 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 577) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_577.1, data_11_577.2] + +/-- Complete interval computation for depth 11, residue 578. -/ +theorem bounds_11_578 : exactInterval 11 578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_578 (m : Nat) : + stoppingTime (2 ^ 11 * m + 578) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_578 : oddCount 578 11 = 4 ∧ acceleratedOrbit 11 578 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_578 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 578) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_578.1, data_11_578.2] + +/-- Complete interval computation for depth 11, residue 579. -/ +theorem bounds_11_579 : exactInterval 11 579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_579 (m : Nat) : + stoppingTime (2 ^ 11 * m + 579) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_579 : oddCount 579 11 = 4 ∧ acceleratedOrbit 11 579 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_579 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 579) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_579.1, data_11_579.2] + +/-- Complete interval computation for depth 11, residue 580. -/ +theorem bounds_11_580 : exactInterval 11 580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_580 (m : Nat) : + stoppingTime (2 ^ 11 * m + 580) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_580 : oddCount 580 11 = 5 ∧ acceleratedOrbit 11 580 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_580 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 580) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_580.1, data_11_580.2] + +/-- Complete interval computation for depth 11, residue 581. -/ +theorem bounds_11_581 : exactInterval 11 581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_581 (m : Nat) : + stoppingTime (2 ^ 11 * m + 581) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_581 : oddCount 581 11 = 5 ∧ acceleratedOrbit 11 581 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_581 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 581) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_581.1, data_11_581.2] + +/-- Complete interval computation for depth 11, residue 582. -/ +theorem bounds_11_582 : exactInterval 11 582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_582 (m : Nat) : + stoppingTime (2 ^ 11 * m + 582) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_582 : oddCount 582 11 = 5 ∧ acceleratedOrbit 11 582 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_582 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 582) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_582.1, data_11_582.2] + +/-- Complete interval computation for depth 11, residue 583. -/ +theorem bounds_11_583 : exactInterval 11 583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_583 (m : Nat) : + stoppingTime (2 ^ 11 * m + 583) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_583 : oddCount 583 11 = 6 ∧ acceleratedOrbit 11 583 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_583 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 583) = 3 ^ 6 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_583.1, data_11_583.2] + +/-- Complete interval computation for depth 11, residue 584. -/ +theorem bounds_11_584 : exactInterval 11 584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_584 (m : Nat) : + stoppingTime (2 ^ 11 * m + 584) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_584 : oddCount 584 11 = 5 ∧ acceleratedOrbit 11 584 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_584 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 584) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_584.1, data_11_584.2] + +/-- Complete interval computation for depth 11, residue 585. -/ +theorem bounds_11_585 : exactInterval 11 585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_585 (m : Nat) : + stoppingTime (2 ^ 11 * m + 585) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_585 : oddCount 585 11 = 6 ∧ acceleratedOrbit 11 585 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_585 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 585) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_585.1, data_11_585.2] + +/-- Complete interval computation for depth 11, residue 586. -/ +theorem bounds_11_586 : exactInterval 11 586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_586 (m : Nat) : + stoppingTime (2 ^ 11 * m + 586) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_586 : oddCount 586 11 = 5 ∧ acceleratedOrbit 11 586 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_586 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 586) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_586.1, data_11_586.2] + +/-- Complete interval computation for depth 11, residue 587. -/ +theorem bounds_11_587 : exactInterval 11 587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_587 (m : Nat) : + stoppingTime (2 ^ 11 * m + 587) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_587 : oddCount 587 11 = 5 ∧ acceleratedOrbit 11 587 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_587 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 587) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_587.1, data_11_587.2] + +end Collatz.Research.StoppingAtlas.Batch0105 From 59d6a105e199f542ec7e3c2d73f44bbe7098058f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:33 +0530 Subject: [PATCH 0106/1001] proof: certify atlas Batch0106 (11:588 to 11:603) --- Collatz/Research/StoppingAtlas/Batch0106.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0106.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0106.lean b/Collatz/Research/StoppingAtlas/Batch0106.lean new file mode 100644 index 00000000..bf00bfc1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0106.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0106 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 588. -/ +theorem bounds_11_588 : exactInterval 11 588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_588 (m : Nat) : + stoppingTime (2 ^ 11 * m + 588) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_588 : oddCount 588 11 = 5 ∧ acceleratedOrbit 11 588 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_588 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 588) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_588.1, data_11_588.2] + +/-- Complete interval computation for depth 11, residue 589. -/ +theorem bounds_11_589 : exactInterval 11 589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_589 (m : Nat) : + stoppingTime (2 ^ 11 * m + 589) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_589 : oddCount 589 11 = 5 ∧ acceleratedOrbit 11 589 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_589 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 589) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_589.1, data_11_589.2] + +/-- Complete interval computation for depth 11, residue 590. -/ +theorem bounds_11_590 : exactInterval 11 590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_590 (m : Nat) : + stoppingTime (2 ^ 11 * m + 590) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_590 : oddCount 590 11 = 6 ∧ acceleratedOrbit 11 590 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_590 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 590) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_590.1, data_11_590.2] + +/-- Complete interval computation for depth 11, residue 591. -/ +theorem bounds_11_591 : exactInterval 11 591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_591 (m : Nat) : + stoppingTime (2 ^ 11 * m + 591) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_591 : oddCount 591 11 = 6 ∧ acceleratedOrbit 11 591 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_591 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 591) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_591.1, data_11_591.2] + +/-- Complete interval computation for depth 11, residue 592. -/ +theorem bounds_11_592 : exactInterval 11 592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_592 (m : Nat) : + stoppingTime (2 ^ 11 * m + 592) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_592 : oddCount 592 11 = 4 ∧ acceleratedOrbit 11 592 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_592 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 592) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_592.1, data_11_592.2] + +/-- Complete interval computation for depth 11, residue 593. -/ +theorem bounds_11_593 : exactInterval 11 593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_593 (m : Nat) : + stoppingTime (2 ^ 11 * m + 593) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_593 : oddCount 593 11 = 7 ∧ acceleratedOrbit 11 593 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_593 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 593) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_593.1, data_11_593.2] + +/-- Complete interval computation for depth 11, residue 594. -/ +theorem bounds_11_594 : exactInterval 11 594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_594 (m : Nat) : + stoppingTime (2 ^ 11 * m + 594) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_594 : oddCount 594 11 = 7 ∧ acceleratedOrbit 11 594 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_594 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 594) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_594.1, data_11_594.2] + +/-- Complete interval computation for depth 11, residue 595. -/ +theorem bounds_11_595 : exactInterval 11 595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_595 (m : Nat) : + stoppingTime (2 ^ 11 * m + 595) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_595 : oddCount 595 11 = 7 ∧ acceleratedOrbit 11 595 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_595 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 595) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_595.1, data_11_595.2] + +/-- Complete interval computation for depth 11, residue 596. -/ +theorem bounds_11_596 : exactInterval 11 596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_596 (m : Nat) : + stoppingTime (2 ^ 11 * m + 596) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_596 : oddCount 596 11 = 4 ∧ acceleratedOrbit 11 596 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_596 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 596) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_596.1, data_11_596.2] + +/-- Complete interval computation for depth 11, residue 597. -/ +theorem bounds_11_597 : exactInterval 11 597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_597 (m : Nat) : + stoppingTime (2 ^ 11 * m + 597) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_597 : oddCount 597 11 = 4 ∧ acceleratedOrbit 11 597 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_597 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 597) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_597.1, data_11_597.2] + +/-- Complete interval computation for depth 11, residue 598. -/ +theorem bounds_11_598 : exactInterval 11 598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_598 (m : Nat) : + stoppingTime (2 ^ 11 * m + 598) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_598 : oddCount 598 11 = 6 ∧ acceleratedOrbit 11 598 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_598 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 598) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_598.1, data_11_598.2] + +/-- Complete interval computation for depth 11, residue 599. -/ +theorem bounds_11_599 : exactInterval 11 599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_599 (m : Nat) : + stoppingTime (2 ^ 11 * m + 599) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_599 : oddCount 599 11 = 6 ∧ acceleratedOrbit 11 599 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_599 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 599) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_599.1, data_11_599.2] + +/-- Complete interval computation for depth 11, residue 600. -/ +theorem bounds_11_600 : exactInterval 11 600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_600 (m : Nat) : + stoppingTime (2 ^ 11 * m + 600) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_600 : oddCount 600 11 = 3 ∧ acceleratedOrbit 11 600 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_600 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 600) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_600.1, data_11_600.2] + +/-- Complete interval computation for depth 11, residue 601. -/ +theorem bounds_11_601 : exactInterval 11 601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_601 (m : Nat) : + stoppingTime (2 ^ 11 * m + 601) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_601 : oddCount 601 11 = 7 ∧ acceleratedOrbit 11 601 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_601 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 601) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_601.1, data_11_601.2] + +/-- Complete interval computation for depth 11, residue 602. -/ +theorem bounds_11_602 : exactInterval 11 602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_602 (m : Nat) : + stoppingTime (2 ^ 11 * m + 602) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_602 : oddCount 602 11 = 3 ∧ acceleratedOrbit 11 602 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_602 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 602) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_602.1, data_11_602.2] + +/-- Complete interval computation for depth 11, residue 603. -/ +theorem bounds_11_603 : exactInterval 11 603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_603 (m : Nat) : + stoppingTime (2 ^ 11 * m + 603) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_603 : oddCount 603 11 = 8 ∧ acceleratedOrbit 11 603 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_603 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 603) = 3 ^ 8 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_603.1, data_11_603.2] + +end Collatz.Research.StoppingAtlas.Batch0106 From 379f5ecaefc3434b3422126e0367181daaa0fbae Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:33 +0530 Subject: [PATCH 0107/1001] proof: certify atlas Batch0107 (11:604 to 11:618) --- Collatz/Research/StoppingAtlas/Batch0107.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0107.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0107.lean b/Collatz/Research/StoppingAtlas/Batch0107.lean new file mode 100644 index 00000000..67dfddd3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0107.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0107 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 604. -/ +theorem bounds_11_604 : exactInterval 11 604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_604 (m : Nat) : + stoppingTime (2 ^ 11 * m + 604) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_604 : oddCount 604 11 = 3 ∧ acceleratedOrbit 11 604 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_604 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 604) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_604.1, data_11_604.2] + +/-- Complete interval computation for depth 11, residue 605. -/ +theorem bounds_11_605 : exactInterval 11 605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_605 (m : Nat) : + stoppingTime (2 ^ 11 * m + 605) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_605 : oddCount 605 11 = 3 ∧ acceleratedOrbit 11 605 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_605 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 605) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_605.1, data_11_605.2] + +/-- Complete interval computation for depth 11, residue 606. -/ +theorem bounds_11_606 : exactInterval 11 606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_606 (m : Nat) : + stoppingTime (2 ^ 11 * m + 606) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_606 : oddCount 606 11 = 7 ∧ acceleratedOrbit 11 606 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_606 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 606) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_606.1, data_11_606.2] + +/-- Complete interval computation for depth 11, residue 607. -/ +theorem bounds_11_607 : exactInterval 11 607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_607 (m : Nat) : + stoppingTime (2 ^ 11 * m + 607) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_607 : oddCount 607 11 = 7 ∧ acceleratedOrbit 11 607 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_607 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 607) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_607.1, data_11_607.2] + +/-- Complete interval computation for depth 11, residue 608. -/ +theorem bounds_11_608 : exactInterval 11 608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_608 (m : Nat) : + stoppingTime (2 ^ 11 * m + 608) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_608 : oddCount 608 11 = 4 ∧ acceleratedOrbit 11 608 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_608 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 608) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_608.1, data_11_608.2] + +/-- Complete interval computation for depth 11, residue 609. -/ +theorem bounds_11_609 : exactInterval 11 609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_609 (m : Nat) : + stoppingTime (2 ^ 11 * m + 609) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_609 : oddCount 609 11 = 6 ∧ acceleratedOrbit 11 609 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_609 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 609) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_609.1, data_11_609.2] + +/-- Complete interval computation for depth 11, residue 610. -/ +theorem bounds_11_610 : exactInterval 11 610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_610 (m : Nat) : + stoppingTime (2 ^ 11 * m + 610) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_610 : oddCount 610 11 = 5 ∧ acceleratedOrbit 11 610 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_610 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 610) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_610.1, data_11_610.2] + +/-- Complete interval computation for depth 11, residue 611. -/ +theorem bounds_11_611 : exactInterval 11 611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_611 (m : Nat) : + stoppingTime (2 ^ 11 * m + 611) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_611 : oddCount 611 11 = 5 ∧ acceleratedOrbit 11 611 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_611 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 611) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_611.1, data_11_611.2] + +/-- Complete interval computation for depth 11, residue 612. -/ +theorem bounds_11_612 : exactInterval 11 612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_612 (m : Nat) : + stoppingTime (2 ^ 11 * m + 612) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_612 : oddCount 612 11 = 5 ∧ acceleratedOrbit 11 612 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_612 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 612) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_612.1, data_11_612.2] + +/-- Complete interval computation for depth 11, residue 613. -/ +theorem bounds_11_613 : exactInterval 11 613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_613 (m : Nat) : + stoppingTime (2 ^ 11 * m + 613) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_613 : oddCount 613 11 = 5 ∧ acceleratedOrbit 11 613 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_613 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 613) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_613.1, data_11_613.2] + +/-- Complete interval computation for depth 11, residue 614. -/ +theorem bounds_11_614 : exactInterval 11 614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_614 (m : Nat) : + stoppingTime (2 ^ 11 * m + 614) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_614 : oddCount 614 11 = 5 ∧ acceleratedOrbit 11 614 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_614 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 614) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_614.1, data_11_614.2] + +/-- Complete interval computation for depth 11, residue 615. -/ +theorem bounds_11_615 : exactInterval 11 615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_615 (m : Nat) : + stoppingTime (2 ^ 11 * m + 615) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_615 : oddCount 615 11 = 7 ∧ acceleratedOrbit 11 615 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_615 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 615) = 3 ^ 7 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_615.1, data_11_615.2] + +/-- Complete interval computation for depth 11, residue 616. -/ +theorem bounds_11_616 : exactInterval 11 616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_616 (m : Nat) : + stoppingTime (2 ^ 11 * m + 616) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_616 : oddCount 616 11 = 4 ∧ acceleratedOrbit 11 616 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_616 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 616) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_616.1, data_11_616.2] + +/-- Complete interval computation for depth 11, residue 617. -/ +theorem bounds_11_617 : exactInterval 11 617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_617 (m : Nat) : + stoppingTime (2 ^ 11 * m + 617) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_617 : oddCount 617 11 = 7 ∧ acceleratedOrbit 11 617 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_617 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 617) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_617.1, data_11_617.2] + +/-- Complete interval computation for depth 11, residue 618. -/ +theorem bounds_11_618 : exactInterval 11 618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_618 (m : Nat) : + stoppingTime (2 ^ 11 * m + 618) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_618 : oddCount 618 11 = 4 ∧ acceleratedOrbit 11 618 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_618 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 618) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_618.1, data_11_618.2] + +end Collatz.Research.StoppingAtlas.Batch0107 From c1e55e74188996f68b8e4d2ca103380da69885fe Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:33 +0530 Subject: [PATCH 0108/1001] proof: certify atlas Batch0108 (11:619 to 11:633) --- Collatz/Research/StoppingAtlas/Batch0108.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0108.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0108.lean b/Collatz/Research/StoppingAtlas/Batch0108.lean new file mode 100644 index 00000000..14f41adf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0108.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0108 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 619. -/ +theorem bounds_11_619 : exactInterval 11 619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_619 (m : Nat) : + stoppingTime (2 ^ 11 * m + 619) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_619 : oddCount 619 11 = 6 ∧ acceleratedOrbit 11 619 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_619 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 619) = 3 ^ 6 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_619.1, data_11_619.2] + +/-- Complete interval computation for depth 11, residue 620. -/ +theorem bounds_11_620 : exactInterval 11 620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_620 (m : Nat) : + stoppingTime (2 ^ 11 * m + 620) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_620 : oddCount 620 11 = 7 ∧ acceleratedOrbit 11 620 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_620 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 620) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_620.1, data_11_620.2] + +/-- Complete interval computation for depth 11, residue 621. -/ +theorem bounds_11_621 : exactInterval 11 621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_621 (m : Nat) : + stoppingTime (2 ^ 11 * m + 621) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_621 : oddCount 621 11 = 7 ∧ acceleratedOrbit 11 621 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_621 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 621) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_621.1, data_11_621.2] + +/-- Complete interval computation for depth 11, residue 622. -/ +theorem bounds_11_622 : exactInterval 11 622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_622 (m : Nat) : + stoppingTime (2 ^ 11 * m + 622) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_622 : oddCount 622 11 = 7 ∧ acceleratedOrbit 11 622 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_622 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 622) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_622.1, data_11_622.2] + +/-- Complete interval computation for depth 11, residue 623. -/ +theorem bounds_11_623 : exactInterval 11 623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_623 (m : Nat) : + stoppingTime (2 ^ 11 * m + 623) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_623 : oddCount 623 11 = 8 ∧ acceleratedOrbit 11 623 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_623 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 623) = 3 ^ 8 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_623.1, data_11_623.2] + +/-- Complete interval computation for depth 11, residue 624. -/ +theorem bounds_11_624 : exactInterval 11 624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_624 (m : Nat) : + stoppingTime (2 ^ 11 * m + 624) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_624 : oddCount 624 11 = 5 ∧ acceleratedOrbit 11 624 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_624 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 624) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_624.1, data_11_624.2] + +/-- Complete interval computation for depth 11, residue 625. -/ +theorem bounds_11_625 : exactInterval 11 625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_625 (m : Nat) : + stoppingTime (2 ^ 11 * m + 625) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_625 : oddCount 625 11 = 4 ∧ acceleratedOrbit 11 625 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_625 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 625) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_625.1, data_11_625.2] + +/-- Complete interval computation for depth 11, residue 626. -/ +theorem bounds_11_626 : exactInterval 11 626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_626 (m : Nat) : + stoppingTime (2 ^ 11 * m + 626) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_626 : oddCount 626 11 = 7 ∧ acceleratedOrbit 11 626 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_626 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 626) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_626.1, data_11_626.2] + +/-- Complete interval computation for depth 11, residue 627. -/ +theorem bounds_11_627 : exactInterval 11 627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_627 (m : Nat) : + stoppingTime (2 ^ 11 * m + 627) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_627 : oddCount 627 11 = 7 ∧ acceleratedOrbit 11 627 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_627 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 627) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_627.1, data_11_627.2] + +/-- Complete interval computation for depth 11, residue 628. -/ +theorem bounds_11_628 : exactInterval 11 628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_628 (m : Nat) : + stoppingTime (2 ^ 11 * m + 628) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_628 : oddCount 628 11 = 5 ∧ acceleratedOrbit 11 628 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_628 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 628) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_628.1, data_11_628.2] + +/-- Complete interval computation for depth 11, residue 629. -/ +theorem bounds_11_629 : exactInterval 11 629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_629 (m : Nat) : + stoppingTime (2 ^ 11 * m + 629) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_629 : oddCount 629 11 = 5 ∧ acceleratedOrbit 11 629 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_629 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 629) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_629.1, data_11_629.2] + +/-- Complete interval computation for depth 11, residue 630. -/ +theorem bounds_11_630 : exactInterval 11 630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_630 (m : Nat) : + stoppingTime (2 ^ 11 * m + 630) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_630 : oddCount 630 11 = 4 ∧ acceleratedOrbit 11 630 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_630 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 630) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_630.1, data_11_630.2] + +/-- Complete interval computation for depth 11, residue 631. -/ +theorem bounds_11_631 : exactInterval 11 631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_631 (m : Nat) : + stoppingTime (2 ^ 11 * m + 631) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_631 : oddCount 631 11 = 4 ∧ acceleratedOrbit 11 631 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_631 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 631) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_631.1, data_11_631.2] + +/-- Complete interval computation for depth 11, residue 632. -/ +theorem bounds_11_632 : exactInterval 11 632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_632 (m : Nat) : + stoppingTime (2 ^ 11 * m + 632) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_632 : oddCount 632 11 = 5 ∧ acceleratedOrbit 11 632 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_632 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 632) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_632.1, data_11_632.2] + +/-- Complete interval computation for depth 11, residue 633. -/ +theorem bounds_11_633 : exactInterval 11 633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_633 (m : Nat) : + stoppingTime (2 ^ 11 * m + 633) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_633 : oddCount 633 11 = 6 ∧ acceleratedOrbit 11 633 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_633 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 633) = 3 ^ 6 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_633.1, data_11_633.2] + +end Collatz.Research.StoppingAtlas.Batch0108 From f579fa21c68e54d4936c2866a39e264af48f9c57 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:33 +0530 Subject: [PATCH 0109/1001] proof: certify atlas Batch0109 (11:634 to 11:649) --- Collatz/Research/StoppingAtlas/Batch0109.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0109.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0109.lean b/Collatz/Research/StoppingAtlas/Batch0109.lean new file mode 100644 index 00000000..fb669338 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0109.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0109 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 634. -/ +theorem bounds_11_634 : exactInterval 11 634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_634 (m : Nat) : + stoppingTime (2 ^ 11 * m + 634) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_634 : oddCount 634 11 = 5 ∧ acceleratedOrbit 11 634 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_634 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 634) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_634.1, data_11_634.2] + +/-- Complete interval computation for depth 11, residue 635. -/ +theorem bounds_11_635 : exactInterval 11 635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_635 (m : Nat) : + stoppingTime (2 ^ 11 * m + 635) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_635 : oddCount 635 11 = 6 ∧ acceleratedOrbit 11 635 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_635 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 635) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_635.1, data_11_635.2] + +/-- Complete interval computation for depth 11, residue 636. -/ +theorem bounds_11_636 : exactInterval 11 636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_636 (m : Nat) : + stoppingTime (2 ^ 11 * m + 636) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_636 : oddCount 636 11 = 8 ∧ acceleratedOrbit 11 636 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_636 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 636) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_636.1, data_11_636.2] + +/-- Complete interval computation for depth 11, residue 637. -/ +theorem bounds_11_637 : exactInterval 11 637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_637 (m : Nat) : + stoppingTime (2 ^ 11 * m + 637) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_637 : oddCount 637 11 = 8 ∧ acceleratedOrbit 11 637 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_637 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 637) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_637.1, data_11_637.2] + +/-- Complete interval computation for depth 11, residue 638. -/ +theorem bounds_11_638 : exactInterval 11 638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_638 (m : Nat) : + stoppingTime (2 ^ 11 * m + 638) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_638 : oddCount 638 11 = 8 ∧ acceleratedOrbit 11 638 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_638 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 638) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_638.1, data_11_638.2] + +/-- Complete interval computation for depth 11, residue 639. -/ +theorem bounds_11_639 : exactInterval 11 639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_639 (m : Nat) : + stoppingTime (2 ^ 11 * m + 639) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_639 : oddCount 639 11 = 9 ∧ acceleratedOrbit 11 639 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_639 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 639) = 3 ^ 9 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_639.1, data_11_639.2] + +/-- Complete interval computation for depth 11, residue 640. -/ +theorem bounds_11_640 : exactInterval 11 640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_640 (m : Nat) : + stoppingTime (2 ^ 11 * m + 640) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_640 : oddCount 640 11 = 1 ∧ acceleratedOrbit 11 640 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_640 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 640) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_640.1, data_11_640.2] + +/-- Complete interval computation for depth 11, residue 641. -/ +theorem bounds_11_641 : exactInterval 11 641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_641 (m : Nat) : + stoppingTime (2 ^ 11 * m + 641) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_641 : oddCount 641 11 = 7 ∧ acceleratedOrbit 11 641 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_641 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 641) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_641.1, data_11_641.2] + +/-- Complete interval computation for depth 11, residue 642. -/ +theorem bounds_11_642 : exactInterval 11 642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_642 (m : Nat) : + stoppingTime (2 ^ 11 * m + 642) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_642 : oddCount 642 11 = 4 ∧ acceleratedOrbit 11 642 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_642 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 642) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_642.1, data_11_642.2] + +/-- Complete interval computation for depth 11, residue 643. -/ +theorem bounds_11_643 : exactInterval 11 643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_643 (m : Nat) : + stoppingTime (2 ^ 11 * m + 643) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_643 : oddCount 643 11 = 4 ∧ acceleratedOrbit 11 643 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_643 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 643) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_643.1, data_11_643.2] + +/-- Complete interval computation for depth 11, residue 644. -/ +theorem bounds_11_644 : exactInterval 11 644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_644 (m : Nat) : + stoppingTime (2 ^ 11 * m + 644) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_644 : oddCount 644 11 = 6 ∧ acceleratedOrbit 11 644 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_644 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 644) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_644.1, data_11_644.2] + +/-- Complete interval computation for depth 11, residue 645. -/ +theorem bounds_11_645 : exactInterval 11 645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_645 (m : Nat) : + stoppingTime (2 ^ 11 * m + 645) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_645 : oddCount 645 11 = 6 ∧ acceleratedOrbit 11 645 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_645 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 645) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_645.1, data_11_645.2] + +/-- Complete interval computation for depth 11, residue 646. -/ +theorem bounds_11_646 : exactInterval 11 646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_646 (m : Nat) : + stoppingTime (2 ^ 11 * m + 646) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_646 : oddCount 646 11 = 6 ∧ acceleratedOrbit 11 646 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_646 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 646) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_646.1, data_11_646.2] + +/-- Complete interval computation for depth 11, residue 647. -/ +theorem bounds_11_647 : exactInterval 11 647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_647 (m : Nat) : + stoppingTime (2 ^ 11 * m + 647) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_647 : oddCount 647 11 = 5 ∧ acceleratedOrbit 11 647 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_647 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 647) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_647.1, data_11_647.2] + +/-- Complete interval computation for depth 11, residue 648. -/ +theorem bounds_11_648 : exactInterval 11 648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_648 (m : Nat) : + stoppingTime (2 ^ 11 * m + 648) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_648 : oddCount 648 11 = 5 ∧ acceleratedOrbit 11 648 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_648 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 648) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_648.1, data_11_648.2] + +/-- Complete interval computation for depth 11, residue 649. -/ +theorem bounds_11_649 : exactInterval 11 649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_649 (m : Nat) : + stoppingTime (2 ^ 11 * m + 649) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_649 : oddCount 649 11 = 7 ∧ acceleratedOrbit 11 649 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_649 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 649) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_649.1, data_11_649.2] + +end Collatz.Research.StoppingAtlas.Batch0109 From 8584ffaf0298baa694688141a43bbc1a0617f6c9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:34 +0530 Subject: [PATCH 0110/1001] proof: certify atlas Batch0110 (11:650 to 11:664) --- Collatz/Research/StoppingAtlas/Batch0110.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0110.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0110.lean b/Collatz/Research/StoppingAtlas/Batch0110.lean new file mode 100644 index 00000000..b8a542c0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0110.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0110 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 650. -/ +theorem bounds_11_650 : exactInterval 11 650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_650 (m : Nat) : + stoppingTime (2 ^ 11 * m + 650) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_650 : oddCount 650 11 = 5 ∧ acceleratedOrbit 11 650 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_650 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 650) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_650.1, data_11_650.2] + +/-- Complete interval computation for depth 11, residue 651. -/ +theorem bounds_11_651 : exactInterval 11 651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_651 (m : Nat) : + stoppingTime (2 ^ 11 * m + 651) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_651 : oddCount 651 11 = 6 ∧ acceleratedOrbit 11 651 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_651 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 651) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_651.1, data_11_651.2] + +/-- Complete interval computation for depth 11, residue 652. -/ +theorem bounds_11_652 : exactInterval 11 652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_652 (m : Nat) : + stoppingTime (2 ^ 11 * m + 652) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_652 : oddCount 652 11 = 5 ∧ acceleratedOrbit 11 652 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_652 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 652) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_652.1, data_11_652.2] + +/-- Complete interval computation for depth 11, residue 653. -/ +theorem bounds_11_653 : exactInterval 11 653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_653 (m : Nat) : + stoppingTime (2 ^ 11 * m + 653) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_653 : oddCount 653 11 = 5 ∧ acceleratedOrbit 11 653 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_653 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 653) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_653.1, data_11_653.2] + +/-- Complete interval computation for depth 11, residue 654. -/ +theorem bounds_11_654 : exactInterval 11 654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_654 (m : Nat) : + stoppingTime (2 ^ 11 * m + 654) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_654 : oddCount 654 11 = 8 ∧ acceleratedOrbit 11 654 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_654 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 654) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_654.1, data_11_654.2] + +/-- Complete interval computation for depth 11, residue 655. -/ +theorem bounds_11_655 : exactInterval 11 655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_655 (m : Nat) : + stoppingTime (2 ^ 11 * m + 655) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_655 : oddCount 655 11 = 8 ∧ acceleratedOrbit 11 655 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_655 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 655) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_655.1, data_11_655.2] + +/-- Complete interval computation for depth 11, residue 656. -/ +theorem bounds_11_656 : exactInterval 11 656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_656 (m : Nat) : + stoppingTime (2 ^ 11 * m + 656) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_656 : oddCount 656 11 = 6 ∧ acceleratedOrbit 11 656 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_656 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 656) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_656.1, data_11_656.2] + +/-- Complete interval computation for depth 11, residue 657. -/ +theorem bounds_11_657 : exactInterval 11 657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_657 (m : Nat) : + stoppingTime (2 ^ 11 * m + 657) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_657 : oddCount 657 11 = 6 ∧ acceleratedOrbit 11 657 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_657 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 657) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_657.1, data_11_657.2] + +/-- Complete interval computation for depth 11, residue 658. -/ +theorem bounds_11_658 : exactInterval 11 658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_658 (m : Nat) : + stoppingTime (2 ^ 11 * m + 658) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_658 : oddCount 658 11 = 6 ∧ acceleratedOrbit 11 658 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_658 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 658) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_658.1, data_11_658.2] + +/-- Complete interval computation for depth 11, residue 659. -/ +theorem bounds_11_659 : exactInterval 11 659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_659 (m : Nat) : + stoppingTime (2 ^ 11 * m + 659) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_659 : oddCount 659 11 = 6 ∧ acceleratedOrbit 11 659 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_659 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 659) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_659.1, data_11_659.2] + +/-- Complete interval computation for depth 11, residue 660. -/ +theorem bounds_11_660 : exactInterval 11 660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_660 (m : Nat) : + stoppingTime (2 ^ 11 * m + 660) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_660 : oddCount 660 11 = 6 ∧ acceleratedOrbit 11 660 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_660 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 660) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_660.1, data_11_660.2] + +/-- Complete interval computation for depth 11, residue 661. -/ +theorem bounds_11_661 : exactInterval 11 661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_661 (m : Nat) : + stoppingTime (2 ^ 11 * m + 661) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_661 : oddCount 661 11 = 6 ∧ acceleratedOrbit 11 661 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_661 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 661) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_661.1, data_11_661.2] + +/-- Complete interval computation for depth 11, residue 662. -/ +theorem bounds_11_662 : exactInterval 11 662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_662 (m : Nat) : + stoppingTime (2 ^ 11 * m + 662) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_662 : oddCount 662 11 = 5 ∧ acceleratedOrbit 11 662 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_662 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 662) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_662.1, data_11_662.2] + +/-- Complete interval computation for depth 11, residue 663. -/ +theorem bounds_11_663 : exactInterval 11 663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_663 (m : Nat) : + stoppingTime (2 ^ 11 * m + 663) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_663 : oddCount 663 11 = 5 ∧ acceleratedOrbit 11 663 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_663 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 663) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_663.1, data_11_663.2] + +/-- Complete interval computation for depth 11, residue 664. -/ +theorem bounds_11_664 : exactInterval 11 664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_664 (m : Nat) : + stoppingTime (2 ^ 11 * m + 664) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_664 : oddCount 664 11 = 6 ∧ acceleratedOrbit 11 664 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_664 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 664) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_664.1, data_11_664.2] + +end Collatz.Research.StoppingAtlas.Batch0110 From d3814275a82e7cd8d13039c714220d4bae2786fa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:34 +0530 Subject: [PATCH 0111/1001] proof: certify atlas Batch0111 (11:665 to 11:679) --- Collatz/Research/StoppingAtlas/Batch0111.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0111.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0111.lean b/Collatz/Research/StoppingAtlas/Batch0111.lean new file mode 100644 index 00000000..b5ed45c3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0111.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0111 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 665. -/ +theorem bounds_11_665 : exactInterval 11 665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_665 (m : Nat) : + stoppingTime (2 ^ 11 * m + 665) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_665 : oddCount 665 11 = 6 ∧ acceleratedOrbit 11 665 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_665 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 665) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_665.1, data_11_665.2] + +/-- Complete interval computation for depth 11, residue 666. -/ +theorem bounds_11_666 : exactInterval 11 666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_666 (m : Nat) : + stoppingTime (2 ^ 11 * m + 666) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_666 : oddCount 666 11 = 6 ∧ acceleratedOrbit 11 666 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_666 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 666) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_666.1, data_11_666.2] + +/-- Complete interval computation for depth 11, residue 667. -/ +theorem bounds_11_667 : exactInterval 11 667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_667 (m : Nat) : + stoppingTime (2 ^ 11 * m + 667) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_667 : oddCount 667 11 = 9 ∧ acceleratedOrbit 11 667 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_667 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 667) = 3 ^ 9 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_667.1, data_11_667.2] + +/-- Complete interval computation for depth 11, residue 668. -/ +theorem bounds_11_668 : exactInterval 11 668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_668 (m : Nat) : + stoppingTime (2 ^ 11 * m + 668) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_668 : oddCount 668 11 = 7 ∧ acceleratedOrbit 11 668 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_668 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 668) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_668.1, data_11_668.2] + +/-- Complete interval computation for depth 11, residue 669. -/ +theorem bounds_11_669 : exactInterval 11 669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_669 (m : Nat) : + stoppingTime (2 ^ 11 * m + 669) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_669 : oddCount 669 11 = 7 ∧ acceleratedOrbit 11 669 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_669 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 669) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_669.1, data_11_669.2] + +/-- Complete interval computation for depth 11, residue 670. -/ +theorem bounds_11_670 : exactInterval 11 670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_670 (m : Nat) : + stoppingTime (2 ^ 11 * m + 670) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_670 : oddCount 670 11 = 7 ∧ acceleratedOrbit 11 670 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_670 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 670) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_670.1, data_11_670.2] + +/-- Complete interval computation for depth 11, residue 671. -/ +theorem bounds_11_671 : exactInterval 11 671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_671 (m : Nat) : + stoppingTime (2 ^ 11 * m + 671) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_671 : oddCount 671 11 = 8 ∧ acceleratedOrbit 11 671 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_671 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 671) = 3 ^ 8 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_671.1, data_11_671.2] + +/-- Complete interval computation for depth 11, residue 672. -/ +theorem bounds_11_672 : exactInterval 11 672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_672 (m : Nat) : + stoppingTime (2 ^ 11 * m + 672) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_672 : oddCount 672 11 = 1 ∧ acceleratedOrbit 11 672 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_672 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 672) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_672.1, data_11_672.2] + +/-- Complete interval computation for depth 11, residue 673. -/ +theorem bounds_11_673 : exactInterval 11 673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_673 (m : Nat) : + stoppingTime (2 ^ 11 * m + 673) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_673 : oddCount 673 11 = 7 ∧ acceleratedOrbit 11 673 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_673 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 673) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_673.1, data_11_673.2] + +/-- Complete interval computation for depth 11, residue 674. -/ +theorem bounds_11_674 : exactInterval 11 674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_674 (m : Nat) : + stoppingTime (2 ^ 11 * m + 674) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_674 : oddCount 674 11 = 7 ∧ acceleratedOrbit 11 674 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_674 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 674) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_674.1, data_11_674.2] + +/-- Complete interval computation for depth 11, residue 675. -/ +theorem bounds_11_675 : exactInterval 11 675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_675 (m : Nat) : + stoppingTime (2 ^ 11 * m + 675) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_675 : oddCount 675 11 = 7 ∧ acceleratedOrbit 11 675 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_675 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 675) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_675.1, data_11_675.2] + +/-- Complete interval computation for depth 11, residue 676. -/ +theorem bounds_11_676 : exactInterval 11 676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_676 (m : Nat) : + stoppingTime (2 ^ 11 * m + 676) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_676 : oddCount 676 11 = 8 ∧ acceleratedOrbit 11 676 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_676 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 676) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_676.1, data_11_676.2] + +/-- Complete interval computation for depth 11, residue 677. -/ +theorem bounds_11_677 : exactInterval 11 677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_677 (m : Nat) : + stoppingTime (2 ^ 11 * m + 677) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_677 : oddCount 677 11 = 8 ∧ acceleratedOrbit 11 677 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_677 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 677) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_677.1, data_11_677.2] + +/-- Complete interval computation for depth 11, residue 678. -/ +theorem bounds_11_678 : exactInterval 11 678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_678 (m : Nat) : + stoppingTime (2 ^ 11 * m + 678) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_678 : oddCount 678 11 = 8 ∧ acceleratedOrbit 11 678 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_678 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 678) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_678.1, data_11_678.2] + +/-- Complete interval computation for depth 11, residue 679. -/ +theorem bounds_11_679 : exactInterval 11 679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_679 (m : Nat) : + stoppingTime (2 ^ 11 * m + 679) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_679 : oddCount 679 11 = 8 ∧ acceleratedOrbit 11 679 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_679 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 679) = 3 ^ 8 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_679.1, data_11_679.2] + +end Collatz.Research.StoppingAtlas.Batch0111 From 3c5a39049c4b71f061a3e024548e899d622384a3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:35 +0530 Subject: [PATCH 0112/1001] proof: certify atlas Batch0112 (11:680 to 11:695) --- Collatz/Research/StoppingAtlas/Batch0112.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0112.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0112.lean b/Collatz/Research/StoppingAtlas/Batch0112.lean new file mode 100644 index 00000000..9dcd074a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0112.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0112 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 680. -/ +theorem bounds_11_680 : exactInterval 11 680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_680 (m : Nat) : + stoppingTime (2 ^ 11 * m + 680) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_680 : oddCount 680 11 = 1 ∧ acceleratedOrbit 11 680 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_680 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 680) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_680.1, data_11_680.2] + +/-- Complete interval computation for depth 11, residue 681. -/ +theorem bounds_11_681 : exactInterval 11 681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_681 (m : Nat) : + stoppingTime (2 ^ 11 * m + 681) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_681 : oddCount 681 11 = 10 ∧ acceleratedOrbit 11 681 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_681 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 681) = 3 ^ 10 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_681.1, data_11_681.2] + +/-- Complete interval computation for depth 11, residue 682. -/ +theorem bounds_11_682 : exactInterval 11 682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_682 (m : Nat) : + stoppingTime (2 ^ 11 * m + 682) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_682 : oddCount 682 11 = 1 ∧ acceleratedOrbit 11 682 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_682 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 682) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_682.1, data_11_682.2] + +/-- Complete interval computation for depth 11, residue 683. -/ +theorem bounds_11_683 : exactInterval 11 683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_683 (m : Nat) : + stoppingTime (2 ^ 11 * m + 683) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_683 : oddCount 683 11 = 6 ∧ acceleratedOrbit 11 683 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_683 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 683) = 3 ^ 6 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_683.1, data_11_683.2] + +/-- Complete interval computation for depth 11, residue 684. -/ +theorem bounds_11_684 : exactInterval 11 684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_684 (m : Nat) : + stoppingTime (2 ^ 11 * m + 684) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_684 : oddCount 684 11 = 5 ∧ acceleratedOrbit 11 684 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_684 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 684) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_684.1, data_11_684.2] + +/-- Complete interval computation for depth 11, residue 685. -/ +theorem bounds_11_685 : exactInterval 11 685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_685 (m : Nat) : + stoppingTime (2 ^ 11 * m + 685) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_685 : oddCount 685 11 = 5 ∧ acceleratedOrbit 11 685 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_685 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 685) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_685.1, data_11_685.2] + +/-- Complete interval computation for depth 11, residue 686. -/ +theorem bounds_11_686 : exactInterval 11 686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_686 (m : Nat) : + stoppingTime (2 ^ 11 * m + 686) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_686 : oddCount 686 11 = 5 ∧ acceleratedOrbit 11 686 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_686 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 686) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_686.1, data_11_686.2] + +/-- Complete interval computation for depth 11, residue 687. -/ +theorem bounds_11_687 : exactInterval 11 687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_687 (m : Nat) : + stoppingTime (2 ^ 11 * m + 687) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_687 : oddCount 687 11 = 6 ∧ acceleratedOrbit 11 687 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_687 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 687) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_687.1, data_11_687.2] + +/-- Complete interval computation for depth 11, residue 688. -/ +theorem bounds_11_688 : exactInterval 11 688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_688 (m : Nat) : + stoppingTime (2 ^ 11 * m + 688) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_688 : oddCount 688 11 = 4 ∧ acceleratedOrbit 11 688 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_688 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 688) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_688.1, data_11_688.2] + +/-- Complete interval computation for depth 11, residue 689. -/ +theorem bounds_11_689 : exactInterval 11 689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_689 (m : Nat) : + stoppingTime (2 ^ 11 * m + 689) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_689 : oddCount 689 11 = 5 ∧ acceleratedOrbit 11 689 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_689 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 689) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_689.1, data_11_689.2] + +/-- Complete interval computation for depth 11, residue 690. -/ +theorem bounds_11_690 : exactInterval 11 690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_690 (m : Nat) : + stoppingTime (2 ^ 11 * m + 690) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_690 : oddCount 690 11 = 5 ∧ acceleratedOrbit 11 690 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_690 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 690) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_690.1, data_11_690.2] + +/-- Complete interval computation for depth 11, residue 691. -/ +theorem bounds_11_691 : exactInterval 11 691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_691 (m : Nat) : + stoppingTime (2 ^ 11 * m + 691) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_691 : oddCount 691 11 = 5 ∧ acceleratedOrbit 11 691 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_691 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 691) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_691.1, data_11_691.2] + +/-- Complete interval computation for depth 11, residue 692. -/ +theorem bounds_11_692 : exactInterval 11 692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_692 (m : Nat) : + stoppingTime (2 ^ 11 * m + 692) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_692 : oddCount 692 11 = 4 ∧ acceleratedOrbit 11 692 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_692 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 692) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_692.1, data_11_692.2] + +/-- Complete interval computation for depth 11, residue 693. -/ +theorem bounds_11_693 : exactInterval 11 693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_693 (m : Nat) : + stoppingTime (2 ^ 11 * m + 693) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_693 : oddCount 693 11 = 4 ∧ acceleratedOrbit 11 693 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_693 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 693) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_693.1, data_11_693.2] + +/-- Complete interval computation for depth 11, residue 694. -/ +theorem bounds_11_694 : exactInterval 11 694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_694 (m : Nat) : + stoppingTime (2 ^ 11 * m + 694) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_694 : oddCount 694 11 = 6 ∧ acceleratedOrbit 11 694 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_694 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 694) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_694.1, data_11_694.2] + +/-- Complete interval computation for depth 11, residue 695. -/ +theorem bounds_11_695 : exactInterval 11 695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_695 (m : Nat) : + stoppingTime (2 ^ 11 * m + 695) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_695 : oddCount 695 11 = 6 ∧ acceleratedOrbit 11 695 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_695 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 695) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_695.1, data_11_695.2] + +end Collatz.Research.StoppingAtlas.Batch0112 From 7cf1fbe5a0f30d22b1f9757a4f751bfacdb8666d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:35 +0530 Subject: [PATCH 0113/1001] proof: certify atlas Batch0113 (11:696 to 11:710) --- Collatz/Research/StoppingAtlas/Batch0113.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0113.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0113.lean b/Collatz/Research/StoppingAtlas/Batch0113.lean new file mode 100644 index 00000000..8c8ee0f9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0113.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0113 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 696. -/ +theorem bounds_11_696 : exactInterval 11 696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_696 (m : Nat) : + stoppingTime (2 ^ 11 * m + 696) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_696 : oddCount 696 11 = 4 ∧ acceleratedOrbit 11 696 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_696 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 696) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_696.1, data_11_696.2] + +/-- Complete interval computation for depth 11, residue 697. -/ +theorem bounds_11_697 : exactInterval 11 697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_697 (m : Nat) : + stoppingTime (2 ^ 11 * m + 697) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_697 : oddCount 697 11 = 5 ∧ acceleratedOrbit 11 697 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_697 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 697) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_697.1, data_11_697.2] + +/-- Complete interval computation for depth 11, residue 698. -/ +theorem bounds_11_698 : exactInterval 11 698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_698 (m : Nat) : + stoppingTime (2 ^ 11 * m + 698) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_698 : oddCount 698 11 = 4 ∧ acceleratedOrbit 11 698 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_698 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 698) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_698.1, data_11_698.2] + +/-- Complete interval computation for depth 11, residue 699. -/ +theorem bounds_11_699 : exactInterval 11 699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_699 (m : Nat) : + stoppingTime (2 ^ 11 * m + 699) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_699 : oddCount 699 11 = 7 ∧ acceleratedOrbit 11 699 = 749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_699 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 699) = 3 ^ 7 * m + 749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_699.1, data_11_699.2] + +/-- Complete interval computation for depth 11, residue 700. -/ +theorem bounds_11_700 : exactInterval 11 700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_700 (m : Nat) : + stoppingTime (2 ^ 11 * m + 700) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_700 : oddCount 700 11 = 6 ∧ acceleratedOrbit 11 700 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_700 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 700) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_700.1, data_11_700.2] + +/-- Complete interval computation for depth 11, residue 701. -/ +theorem bounds_11_701 : exactInterval 11 701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_701 (m : Nat) : + stoppingTime (2 ^ 11 * m + 701) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_701 : oddCount 701 11 = 6 ∧ acceleratedOrbit 11 701 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_701 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 701) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_701.1, data_11_701.2] + +/-- Complete interval computation for depth 11, residue 702. -/ +theorem bounds_11_702 : exactInterval 11 702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_702 (m : Nat) : + stoppingTime (2 ^ 11 * m + 702) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_702 : oddCount 702 11 = 6 ∧ acceleratedOrbit 11 702 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_702 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 702) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_702.1, data_11_702.2] + +/-- Complete interval computation for depth 11, residue 703. -/ +theorem bounds_11_703 : exactInterval 11 703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_703 (m : Nat) : + stoppingTime (2 ^ 11 * m + 703) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_703 : oddCount 703 11 = 9 ∧ acceleratedOrbit 11 703 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_703 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 703) = 3 ^ 9 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_703.1, data_11_703.2] + +/-- Complete interval computation for depth 11, residue 704. -/ +theorem bounds_11_704 : exactInterval 11 704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_704 (m : Nat) : + stoppingTime (2 ^ 11 * m + 704) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_704 : oddCount 704 11 = 3 ∧ acceleratedOrbit 11 704 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_704 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 704) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_704.1, data_11_704.2] + +/-- Complete interval computation for depth 11, residue 705. -/ +theorem bounds_11_705 : exactInterval 11 705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_705 (m : Nat) : + stoppingTime (2 ^ 11 * m + 705) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_705 : oddCount 705 11 = 4 ∧ acceleratedOrbit 11 705 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_705 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 705) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_705.1, data_11_705.2] + +/-- Complete interval computation for depth 11, residue 706. -/ +theorem bounds_11_706 : exactInterval 11 706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_706 (m : Nat) : + stoppingTime (2 ^ 11 * m + 706) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_706 : oddCount 706 11 = 6 ∧ acceleratedOrbit 11 706 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_706 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 706) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_706.1, data_11_706.2] + +/-- Complete interval computation for depth 11, residue 707. -/ +theorem bounds_11_707 : exactInterval 11 707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_707 (m : Nat) : + stoppingTime (2 ^ 11 * m + 707) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_707 : oddCount 707 11 = 6 ∧ acceleratedOrbit 11 707 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_707 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 707) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_707.1, data_11_707.2] + +/-- Complete interval computation for depth 11, residue 708. -/ +theorem bounds_11_708 : exactInterval 11 708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_708 (m : Nat) : + stoppingTime (2 ^ 11 * m + 708) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_708 : oddCount 708 11 = 4 ∧ acceleratedOrbit 11 708 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_708 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 708) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_708.1, data_11_708.2] + +/-- Complete interval computation for depth 11, residue 709. -/ +theorem bounds_11_709 : exactInterval 11 709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_709 (m : Nat) : + stoppingTime (2 ^ 11 * m + 709) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_709 : oddCount 709 11 = 4 ∧ acceleratedOrbit 11 709 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_709 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 709) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_709.1, data_11_709.2] + +/-- Complete interval computation for depth 11, residue 710. -/ +theorem bounds_11_710 : exactInterval 11 710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_710 (m : Nat) : + stoppingTime (2 ^ 11 * m + 710) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_710 : oddCount 710 11 = 4 ∧ acceleratedOrbit 11 710 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_710 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 710) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_710.1, data_11_710.2] + +end Collatz.Research.StoppingAtlas.Batch0113 From 0e579a63531eb4eb972c50432bbb21d5392a6e02 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:35 +0530 Subject: [PATCH 0114/1001] proof: certify atlas Batch0114 (11:711 to 11:726) --- Collatz/Research/StoppingAtlas/Batch0114.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0114.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0114.lean b/Collatz/Research/StoppingAtlas/Batch0114.lean new file mode 100644 index 00000000..ead79dd4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0114.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0114 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 711. -/ +theorem bounds_11_711 : exactInterval 11 711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_711 (m : Nat) : + stoppingTime (2 ^ 11 * m + 711) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_711 : oddCount 711 11 = 6 ∧ acceleratedOrbit 11 711 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_711 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 711) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_711.1, data_11_711.2] + +/-- Complete interval computation for depth 11, residue 712. -/ +theorem bounds_11_712 : exactInterval 11 712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_712 (m : Nat) : + stoppingTime (2 ^ 11 * m + 712) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_712 : oddCount 712 11 = 4 ∧ acceleratedOrbit 11 712 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_712 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 712) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_712.1, data_11_712.2] + +/-- Complete interval computation for depth 11, residue 713. -/ +theorem bounds_11_713 : exactInterval 11 713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_713 (m : Nat) : + stoppingTime (2 ^ 11 * m + 713) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_713 : oddCount 713 11 = 5 ∧ acceleratedOrbit 11 713 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_713 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 713) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_713.1, data_11_713.2] + +/-- Complete interval computation for depth 11, residue 714. -/ +theorem bounds_11_714 : exactInterval 11 714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_714 (m : Nat) : + stoppingTime (2 ^ 11 * m + 714) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_714 : oddCount 714 11 = 4 ∧ acceleratedOrbit 11 714 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_714 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 714) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_714.1, data_11_714.2] + +/-- Complete interval computation for depth 11, residue 715. -/ +theorem bounds_11_715 : exactInterval 11 715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_715 (m : Nat) : + stoppingTime (2 ^ 11 * m + 715) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_715 : oddCount 715 11 = 6 ∧ acceleratedOrbit 11 715 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_715 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 715) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_715.1, data_11_715.2] + +/-- Complete interval computation for depth 11, residue 716. -/ +theorem bounds_11_716 : exactInterval 11 716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_716 (m : Nat) : + stoppingTime (2 ^ 11 * m + 716) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_716 : oddCount 716 11 = 4 ∧ acceleratedOrbit 11 716 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_716 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 716) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_716.1, data_11_716.2] + +/-- Complete interval computation for depth 11, residue 717. -/ +theorem bounds_11_717 : exactInterval 11 717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_717 (m : Nat) : + stoppingTime (2 ^ 11 * m + 717) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_717 : oddCount 717 11 = 4 ∧ acceleratedOrbit 11 717 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_717 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 717) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_717.1, data_11_717.2] + +/-- Complete interval computation for depth 11, residue 718. -/ +theorem bounds_11_718 : exactInterval 11 718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_718 (m : Nat) : + stoppingTime (2 ^ 11 * m + 718) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_718 : oddCount 718 11 = 8 ∧ acceleratedOrbit 11 718 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_718 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 718) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_718.1, data_11_718.2] + +/-- Complete interval computation for depth 11, residue 719. -/ +theorem bounds_11_719 : exactInterval 11 719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_719 (m : Nat) : + stoppingTime (2 ^ 11 * m + 719) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_719 : oddCount 719 11 = 8 ∧ acceleratedOrbit 11 719 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_719 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 719) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_719.1, data_11_719.2] + +/-- Complete interval computation for depth 11, residue 720. -/ +theorem bounds_11_720 : exactInterval 11 720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_720 (m : Nat) : + stoppingTime (2 ^ 11 * m + 720) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_720 : oddCount 720 11 = 3 ∧ acceleratedOrbit 11 720 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_720 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 720) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_720.1, data_11_720.2] + +/-- Complete interval computation for depth 11, residue 721. -/ +theorem bounds_11_721 : exactInterval 11 721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_721 (m : Nat) : + stoppingTime (2 ^ 11 * m + 721) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_721 : oddCount 721 11 = 5 ∧ acceleratedOrbit 11 721 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_721 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 721) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_721.1, data_11_721.2] + +/-- Complete interval computation for depth 11, residue 722. -/ +theorem bounds_11_722 : exactInterval 11 722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_722 (m : Nat) : + stoppingTime (2 ^ 11 * m + 722) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_722 : oddCount 722 11 = 5 ∧ acceleratedOrbit 11 722 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_722 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 722) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_722.1, data_11_722.2] + +/-- Complete interval computation for depth 11, residue 723. -/ +theorem bounds_11_723 : exactInterval 11 723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_723 (m : Nat) : + stoppingTime (2 ^ 11 * m + 723) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_723 : oddCount 723 11 = 5 ∧ acceleratedOrbit 11 723 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_723 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 723) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_723.1, data_11_723.2] + +/-- Complete interval computation for depth 11, residue 724. -/ +theorem bounds_11_724 : exactInterval 11 724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_724 (m : Nat) : + stoppingTime (2 ^ 11 * m + 724) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_724 : oddCount 724 11 = 3 ∧ acceleratedOrbit 11 724 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_724 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 724) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_724.1, data_11_724.2] + +/-- Complete interval computation for depth 11, residue 725. -/ +theorem bounds_11_725 : exactInterval 11 725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_725 (m : Nat) : + stoppingTime (2 ^ 11 * m + 725) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_725 : oddCount 725 11 = 3 ∧ acceleratedOrbit 11 725 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_725 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 725) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_725.1, data_11_725.2] + +/-- Complete interval computation for depth 11, residue 726. -/ +theorem bounds_11_726 : exactInterval 11 726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_726 (m : Nat) : + stoppingTime (2 ^ 11 * m + 726) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_726 : oddCount 726 11 = 6 ∧ acceleratedOrbit 11 726 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_726 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 726) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_726.1, data_11_726.2] + +end Collatz.Research.StoppingAtlas.Batch0114 From 61d6ecbc5065aae8f7ead9ab65810905f7c18f43 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:35 +0530 Subject: [PATCH 0115/1001] proof: certify atlas Batch0115 (11:727 to 11:741) --- Collatz/Research/StoppingAtlas/Batch0115.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0115.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0115.lean b/Collatz/Research/StoppingAtlas/Batch0115.lean new file mode 100644 index 00000000..698fefef --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0115.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0115 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 727. -/ +theorem bounds_11_727 : exactInterval 11 727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_727 (m : Nat) : + stoppingTime (2 ^ 11 * m + 727) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_727 : oddCount 727 11 = 6 ∧ acceleratedOrbit 11 727 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_727 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 727) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_727.1, data_11_727.2] + +/-- Complete interval computation for depth 11, residue 728. -/ +theorem bounds_11_728 : exactInterval 11 728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_728 (m : Nat) : + stoppingTime (2 ^ 11 * m + 728) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_728 : oddCount 728 11 = 6 ∧ acceleratedOrbit 11 728 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_728 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 728) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_728.1, data_11_728.2] + +/-- Complete interval computation for depth 11, residue 729. -/ +theorem bounds_11_729 : exactInterval 11 729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_729 (m : Nat) : + stoppingTime (2 ^ 11 * m + 729) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_729 : oddCount 729 11 = 4 ∧ acceleratedOrbit 11 729 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_729 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 729) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_729.1, data_11_729.2] + +/-- Complete interval computation for depth 11, residue 730. -/ +theorem bounds_11_730 : exactInterval 11 730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_730 (m : Nat) : + stoppingTime (2 ^ 11 * m + 730) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_730 : oddCount 730 11 = 6 ∧ acceleratedOrbit 11 730 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_730 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 730) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_730.1, data_11_730.2] + +/-- Complete interval computation for depth 11, residue 731. -/ +theorem bounds_11_731 : exactInterval 11 731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_731 (m : Nat) : + stoppingTime (2 ^ 11 * m + 731) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_731 : oddCount 731 11 = 8 ∧ acceleratedOrbit 11 731 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_731 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 731) = 3 ^ 8 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_731.1, data_11_731.2] + +/-- Complete interval computation for depth 11, residue 732. -/ +theorem bounds_11_732 : exactInterval 11 732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_732 (m : Nat) : + stoppingTime (2 ^ 11 * m + 732) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_732 : oddCount 732 11 = 6 ∧ acceleratedOrbit 11 732 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_732 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 732) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_732.1, data_11_732.2] + +/-- Complete interval computation for depth 11, residue 733. -/ +theorem bounds_11_733 : exactInterval 11 733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_733 (m : Nat) : + stoppingTime (2 ^ 11 * m + 733) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_733 : oddCount 733 11 = 6 ∧ acceleratedOrbit 11 733 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_733 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 733) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_733.1, data_11_733.2] + +/-- Complete interval computation for depth 11, residue 734. -/ +theorem bounds_11_734 : exactInterval 11 734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_734 (m : Nat) : + stoppingTime (2 ^ 11 * m + 734) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_734 : oddCount 734 11 = 6 ∧ acceleratedOrbit 11 734 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_734 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 734) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_734.1, data_11_734.2] + +/-- Complete interval computation for depth 11, residue 735. -/ +theorem bounds_11_735 : exactInterval 11 735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_735 (m : Nat) : + stoppingTime (2 ^ 11 * m + 735) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_735 : oddCount 735 11 = 6 ∧ acceleratedOrbit 11 735 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_735 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 735) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_735.1, data_11_735.2] + +/-- Complete interval computation for depth 11, residue 736. -/ +theorem bounds_11_736 : exactInterval 11 736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_736 (m : Nat) : + stoppingTime (2 ^ 11 * m + 736) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_736 : oddCount 736 11 = 3 ∧ acceleratedOrbit 11 736 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_736 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 736) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_736.1, data_11_736.2] + +/-- Complete interval computation for depth 11, residue 737. -/ +theorem bounds_11_737 : exactInterval 11 737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_737 (m : Nat) : + stoppingTime (2 ^ 11 * m + 737) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_737 : oddCount 737 11 = 8 ∧ acceleratedOrbit 11 737 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_737 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 737) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_737.1, data_11_737.2] + +/-- Complete interval computation for depth 11, residue 738. -/ +theorem bounds_11_738 : exactInterval 11 738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_738 (m : Nat) : + stoppingTime (2 ^ 11 * m + 738) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_738 : oddCount 738 11 = 3 ∧ acceleratedOrbit 11 738 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_738 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 738) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_738.1, data_11_738.2] + +/-- Complete interval computation for depth 11, residue 739. -/ +theorem bounds_11_739 : exactInterval 11 739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_739 (m : Nat) : + stoppingTime (2 ^ 11 * m + 739) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_739 : oddCount 739 11 = 3 ∧ acceleratedOrbit 11 739 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_739 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 739) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_739.1, data_11_739.2] + +/-- Complete interval computation for depth 11, residue 740. -/ +theorem bounds_11_740 : exactInterval 11 740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_740 (m : Nat) : + stoppingTime (2 ^ 11 * m + 740) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_740 : oddCount 740 11 = 5 ∧ acceleratedOrbit 11 740 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_740 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 740) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_740.1, data_11_740.2] + +/-- Complete interval computation for depth 11, residue 741. -/ +theorem bounds_11_741 : exactInterval 11 741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_741 (m : Nat) : + stoppingTime (2 ^ 11 * m + 741) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_741 : oddCount 741 11 = 5 ∧ acceleratedOrbit 11 741 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_741 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 741) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_741.1, data_11_741.2] + +end Collatz.Research.StoppingAtlas.Batch0115 From 56e6924e998c8c1bbc001bf4235ffd2922161334 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:36 +0530 Subject: [PATCH 0116/1001] proof: certify atlas Batch0116 (11:742 to 11:756) --- Collatz/Research/StoppingAtlas/Batch0116.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0116.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0116.lean b/Collatz/Research/StoppingAtlas/Batch0116.lean new file mode 100644 index 00000000..d2db117a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0116.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0116 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 742. -/ +theorem bounds_11_742 : exactInterval 11 742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_742 (m : Nat) : + stoppingTime (2 ^ 11 * m + 742) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_742 : oddCount 742 11 = 5 ∧ acceleratedOrbit 11 742 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_742 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 742) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_742.1, data_11_742.2] + +/-- Complete interval computation for depth 11, residue 743. -/ +theorem bounds_11_743 : exactInterval 11 743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_743 (m : Nat) : + stoppingTime (2 ^ 11 * m + 743) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_743 : oddCount 743 11 = 9 ∧ acceleratedOrbit 11 743 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_743 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 743) = 3 ^ 9 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_743.1, data_11_743.2] + +/-- Complete interval computation for depth 11, residue 744. -/ +theorem bounds_11_744 : exactInterval 11 744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_744 (m : Nat) : + stoppingTime (2 ^ 11 * m + 744) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_744 : oddCount 744 11 = 3 ∧ acceleratedOrbit 11 744 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_744 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 744) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_744.1, data_11_744.2] + +/-- Complete interval computation for depth 11, residue 745. -/ +theorem bounds_11_745 : exactInterval 11 745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_745 (m : Nat) : + stoppingTime (2 ^ 11 * m + 745) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_745 : oddCount 745 11 = 8 ∧ acceleratedOrbit 11 745 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_745 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 745) = 3 ^ 8 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_745.1, data_11_745.2] + +/-- Complete interval computation for depth 11, residue 746. -/ +theorem bounds_11_746 : exactInterval 11 746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_746 (m : Nat) : + stoppingTime (2 ^ 11 * m + 746) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_746 : oddCount 746 11 = 3 ∧ acceleratedOrbit 11 746 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_746 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 746) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_746.1, data_11_746.2] + +/-- Complete interval computation for depth 11, residue 747. -/ +theorem bounds_11_747 : exactInterval 11 747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_747 (m : Nat) : + stoppingTime (2 ^ 11 * m + 747) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_747 : oddCount 747 11 = 7 ∧ acceleratedOrbit 11 747 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_747 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 747) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_747.1, data_11_747.2] + +/-- Complete interval computation for depth 11, residue 748. -/ +theorem bounds_11_748 : exactInterval 11 748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_748 (m : Nat) : + stoppingTime (2 ^ 11 * m + 748) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_748 : oddCount 748 11 = 6 ∧ acceleratedOrbit 11 748 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_748 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 748) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_748.1, data_11_748.2] + +/-- Complete interval computation for depth 11, residue 749. -/ +theorem bounds_11_749 : exactInterval 11 749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_749 (m : Nat) : + stoppingTime (2 ^ 11 * m + 749) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_749 : oddCount 749 11 = 6 ∧ acceleratedOrbit 11 749 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_749 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 749) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_749.1, data_11_749.2] + +/-- Complete interval computation for depth 11, residue 750. -/ +theorem bounds_11_750 : exactInterval 11 750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_750 (m : Nat) : + stoppingTime (2 ^ 11 * m + 750) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_750 : oddCount 750 11 = 6 ∧ acceleratedOrbit 11 750 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_750 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 750) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_750.1, data_11_750.2] + +/-- Complete interval computation for depth 11, residue 751. -/ +theorem bounds_11_751 : exactInterval 11 751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_751 (m : Nat) : + stoppingTime (2 ^ 11 * m + 751) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_751 : oddCount 751 11 = 9 ∧ acceleratedOrbit 11 751 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_751 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 751) = 3 ^ 9 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_751.1, data_11_751.2] + +/-- Complete interval computation for depth 11, residue 752. -/ +theorem bounds_11_752 : exactInterval 11 752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_752 (m : Nat) : + stoppingTime (2 ^ 11 * m + 752) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_752 : oddCount 752 11 = 5 ∧ acceleratedOrbit 11 752 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_752 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 752) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_752.1, data_11_752.2] + +/-- Complete interval computation for depth 11, residue 753. -/ +theorem bounds_11_753 : exactInterval 11 753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_753 (m : Nat) : + stoppingTime (2 ^ 11 * m + 753) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_753 : oddCount 753 11 = 3 ∧ acceleratedOrbit 11 753 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_753 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 753) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_753.1, data_11_753.2] + +/-- Complete interval computation for depth 11, residue 754. -/ +theorem bounds_11_754 : exactInterval 11 754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_754 (m : Nat) : + stoppingTime (2 ^ 11 * m + 754) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_754 : oddCount 754 11 = 8 ∧ acceleratedOrbit 11 754 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_754 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 754) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_754.1, data_11_754.2] + +/-- Complete interval computation for depth 11, residue 755. -/ +theorem bounds_11_755 : exactInterval 11 755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_755 (m : Nat) : + stoppingTime (2 ^ 11 * m + 755) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_755 : oddCount 755 11 = 8 ∧ acceleratedOrbit 11 755 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_755 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 755) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_755.1, data_11_755.2] + +/-- Complete interval computation for depth 11, residue 756. -/ +theorem bounds_11_756 : exactInterval 11 756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_756 (m : Nat) : + stoppingTime (2 ^ 11 * m + 756) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_756 : oddCount 756 11 = 5 ∧ acceleratedOrbit 11 756 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_756 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 756) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_756.1, data_11_756.2] + +end Collatz.Research.StoppingAtlas.Batch0116 From 5c39ae1b8dc9949c6a8274e931531d64f99799f0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:36 +0530 Subject: [PATCH 0117/1001] proof: certify atlas Batch0117 (11:757 to 11:772) --- Collatz/Research/StoppingAtlas/Batch0117.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0117.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0117.lean b/Collatz/Research/StoppingAtlas/Batch0117.lean new file mode 100644 index 00000000..fbabf289 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0117.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0117 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 757. -/ +theorem bounds_11_757 : exactInterval 11 757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_757 (m : Nat) : + stoppingTime (2 ^ 11 * m + 757) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_757 : oddCount 757 11 = 5 ∧ acceleratedOrbit 11 757 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_757 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 757) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_757.1, data_11_757.2] + +/-- Complete interval computation for depth 11, residue 758. -/ +theorem bounds_11_758 : exactInterval 11 758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_758 (m : Nat) : + stoppingTime (2 ^ 11 * m + 758) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_758 : oddCount 758 11 = 6 ∧ acceleratedOrbit 11 758 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_758 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 758) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_758.1, data_11_758.2] + +/-- Complete interval computation for depth 11, residue 759. -/ +theorem bounds_11_759 : exactInterval 11 759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_759 (m : Nat) : + stoppingTime (2 ^ 11 * m + 759) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_759 : oddCount 759 11 = 6 ∧ acceleratedOrbit 11 759 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_759 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 759) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_759.1, data_11_759.2] + +/-- Complete interval computation for depth 11, residue 760. -/ +theorem bounds_11_760 : exactInterval 11 760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_760 (m : Nat) : + stoppingTime (2 ^ 11 * m + 760) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_760 : oddCount 760 11 = 5 ∧ acceleratedOrbit 11 760 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_760 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 760) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_760.1, data_11_760.2] + +/-- Complete interval computation for depth 11, residue 761. -/ +theorem bounds_11_761 : exactInterval 11 761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_761 (m : Nat) : + stoppingTime (2 ^ 11 * m + 761) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_761 : oddCount 761 11 = 6 ∧ acceleratedOrbit 11 761 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_761 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 761) = 3 ^ 6 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_761.1, data_11_761.2] + +/-- Complete interval computation for depth 11, residue 762. -/ +theorem bounds_11_762 : exactInterval 11 762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_762 (m : Nat) : + stoppingTime (2 ^ 11 * m + 762) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_762 : oddCount 762 11 = 5 ∧ acceleratedOrbit 11 762 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_762 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 762) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_762.1, data_11_762.2] + +/-- Complete interval computation for depth 11, residue 763. -/ +theorem bounds_11_763 : exactInterval 11 763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_763 (m : Nat) : + stoppingTime (2 ^ 11 * m + 763) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_763 : oddCount 763 11 = 8 ∧ acceleratedOrbit 11 763 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_763 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 763) = 3 ^ 8 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_763.1, data_11_763.2] + +/-- Complete interval computation for depth 11, residue 764. -/ +theorem bounds_11_764 : exactInterval 11 764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_764 (m : Nat) : + stoppingTime (2 ^ 11 * m + 764) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_764 : oddCount 764 11 = 7 ∧ acceleratedOrbit 11 764 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_764 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 764) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_764.1, data_11_764.2] + +/-- Complete interval computation for depth 11, residue 765. -/ +theorem bounds_11_765 : exactInterval 11 765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_765 (m : Nat) : + stoppingTime (2 ^ 11 * m + 765) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_765 : oddCount 765 11 = 7 ∧ acceleratedOrbit 11 765 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_765 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 765) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_765.1, data_11_765.2] + +/-- Complete interval computation for depth 11, residue 766. -/ +theorem bounds_11_766 : exactInterval 11 766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_766 (m : Nat) : + stoppingTime (2 ^ 11 * m + 766) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_766 : oddCount 766 11 = 7 ∧ acceleratedOrbit 11 766 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_766 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 766) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_766.1, data_11_766.2] + +/-- Complete interval computation for depth 11, residue 767. -/ +theorem bounds_11_767 : exactInterval 11 767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_767 (m : Nat) : + stoppingTime (2 ^ 11 * m + 767) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_767 : oddCount 767 11 = 9 ∧ acceleratedOrbit 11 767 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_767 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 767) = 3 ^ 9 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_767.1, data_11_767.2] + +/-- Complete interval computation for depth 11, residue 768. -/ +theorem bounds_11_768 : exactInterval 11 768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_768 (m : Nat) : + stoppingTime (2 ^ 11 * m + 768) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_768 : oddCount 768 11 = 2 ∧ acceleratedOrbit 11 768 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_768 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 768) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_768.1, data_11_768.2] + +/-- Complete interval computation for depth 11, residue 769. -/ +theorem bounds_11_769 : exactInterval 11 769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_769 (m : Nat) : + stoppingTime (2 ^ 11 * m + 769) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_769 : oddCount 769 11 = 5 ∧ acceleratedOrbit 11 769 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_769 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 769) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_769.1, data_11_769.2] + +/-- Complete interval computation for depth 11, residue 770. -/ +theorem bounds_11_770 : exactInterval 11 770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_770 (m : Nat) : + stoppingTime (2 ^ 11 * m + 770) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_770 : oddCount 770 11 = 5 ∧ acceleratedOrbit 11 770 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_770 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 770) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_770.1, data_11_770.2] + +/-- Complete interval computation for depth 11, residue 771. -/ +theorem bounds_11_771 : exactInterval 11 771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_771 (m : Nat) : + stoppingTime (2 ^ 11 * m + 771) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_771 : oddCount 771 11 = 5 ∧ acceleratedOrbit 11 771 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_771 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 771) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_771.1, data_11_771.2] + +/-- Complete interval computation for depth 11, residue 772. -/ +theorem bounds_11_772 : exactInterval 11 772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_772 (m : Nat) : + stoppingTime (2 ^ 11 * m + 772) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_772 : oddCount 772 11 = 4 ∧ acceleratedOrbit 11 772 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_772 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 772) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_772.1, data_11_772.2] + +end Collatz.Research.StoppingAtlas.Batch0117 From d3fcd2ca9ef072f56b28bcbcb8d83600ac52e652 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:36 +0530 Subject: [PATCH 0118/1001] proof: certify atlas Batch0118 (11:773 to 11:787) --- Collatz/Research/StoppingAtlas/Batch0118.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0118.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0118.lean b/Collatz/Research/StoppingAtlas/Batch0118.lean new file mode 100644 index 00000000..862a78b2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0118.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0118 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 773. -/ +theorem bounds_11_773 : exactInterval 11 773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_773 (m : Nat) : + stoppingTime (2 ^ 11 * m + 773) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_773 : oddCount 773 11 = 4 ∧ acceleratedOrbit 11 773 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_773 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 773) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_773.1, data_11_773.2] + +/-- Complete interval computation for depth 11, residue 774. -/ +theorem bounds_11_774 : exactInterval 11 774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_774 (m : Nat) : + stoppingTime (2 ^ 11 * m + 774) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_774 : oddCount 774 11 = 4 ∧ acceleratedOrbit 11 774 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_774 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 774) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_774.1, data_11_774.2] + +/-- Complete interval computation for depth 11, residue 775. -/ +theorem bounds_11_775 : exactInterval 11 775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_775 (m : Nat) : + stoppingTime (2 ^ 11 * m + 775) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_775 : oddCount 775 11 = 7 ∧ acceleratedOrbit 11 775 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_775 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 775) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_775.1, data_11_775.2] + +/-- Complete interval computation for depth 11, residue 776. -/ +theorem bounds_11_776 : exactInterval 11 776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_776 (m : Nat) : + stoppingTime (2 ^ 11 * m + 776) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_776 : oddCount 776 11 = 5 ∧ acceleratedOrbit 11 776 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_776 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 776) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_776.1, data_11_776.2] + +/-- Complete interval computation for depth 11, residue 777. -/ +theorem bounds_11_777 : exactInterval 11 777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_777 (m : Nat) : + stoppingTime (2 ^ 11 * m + 777) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_777 : oddCount 777 11 = 7 ∧ acceleratedOrbit 11 777 = 832 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_777 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 777) = 3 ^ 7 * m + 832 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_777.1, data_11_777.2] + +/-- Complete interval computation for depth 11, residue 778. -/ +theorem bounds_11_778 : exactInterval 11 778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_778 (m : Nat) : + stoppingTime (2 ^ 11 * m + 778) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_778 : oddCount 778 11 = 5 ∧ acceleratedOrbit 11 778 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_778 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 778) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_778.1, data_11_778.2] + +/-- Complete interval computation for depth 11, residue 779. -/ +theorem bounds_11_779 : exactInterval 11 779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_779 (m : Nat) : + stoppingTime (2 ^ 11 * m + 779) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_779 : oddCount 779 11 = 7 ∧ acceleratedOrbit 11 779 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_779 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 779) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_779.1, data_11_779.2] + +/-- Complete interval computation for depth 11, residue 780. -/ +theorem bounds_11_780 : exactInterval 11 780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_780 (m : Nat) : + stoppingTime (2 ^ 11 * m + 780) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_780 : oddCount 780 11 = 5 ∧ acceleratedOrbit 11 780 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_780 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 780) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_780.1, data_11_780.2] + +/-- Complete interval computation for depth 11, residue 781. -/ +theorem bounds_11_781 : exactInterval 11 781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_781 (m : Nat) : + stoppingTime (2 ^ 11 * m + 781) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_781 : oddCount 781 11 = 5 ∧ acceleratedOrbit 11 781 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_781 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 781) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_781.1, data_11_781.2] + +/-- Complete interval computation for depth 11, residue 782. -/ +theorem bounds_11_782 : exactInterval 11 782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_782 (m : Nat) : + stoppingTime (2 ^ 11 * m + 782) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_782 : oddCount 782 11 = 4 ∧ acceleratedOrbit 11 782 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_782 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 782) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_782.1, data_11_782.2] + +/-- Complete interval computation for depth 11, residue 783. -/ +theorem bounds_11_783 : exactInterval 11 783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_783 (m : Nat) : + stoppingTime (2 ^ 11 * m + 783) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_783 : oddCount 783 11 = 4 ∧ acceleratedOrbit 11 783 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_783 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 783) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_783.1, data_11_783.2] + +/-- Complete interval computation for depth 11, residue 784. -/ +theorem bounds_11_784 : exactInterval 11 784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_784 (m : Nat) : + stoppingTime (2 ^ 11 * m + 784) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_784 : oddCount 784 11 = 3 ∧ acceleratedOrbit 11 784 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_784 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 784) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_784.1, data_11_784.2] + +/-- Complete interval computation for depth 11, residue 785. -/ +theorem bounds_11_785 : exactInterval 11 785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_785 (m : Nat) : + stoppingTime (2 ^ 11 * m + 785) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_785 : oddCount 785 11 = 5 ∧ acceleratedOrbit 11 785 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_785 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 785) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_785.1, data_11_785.2] + +/-- Complete interval computation for depth 11, residue 786. -/ +theorem bounds_11_786 : exactInterval 11 786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_786 (m : Nat) : + stoppingTime (2 ^ 11 * m + 786) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_786 : oddCount 786 11 = 6 ∧ acceleratedOrbit 11 786 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_786 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 786) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_786.1, data_11_786.2] + +/-- Complete interval computation for depth 11, residue 787. -/ +theorem bounds_11_787 : exactInterval 11 787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_787 (m : Nat) : + stoppingTime (2 ^ 11 * m + 787) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_787 : oddCount 787 11 = 6 ∧ acceleratedOrbit 11 787 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_787 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 787) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_787.1, data_11_787.2] + +end Collatz.Research.StoppingAtlas.Batch0118 From eaa8c71e60d0c0f802f75e88299feee41f1de297 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:37 +0530 Subject: [PATCH 0119/1001] proof: certify atlas Batch0119 (11:788 to 11:802) --- Collatz/Research/StoppingAtlas/Batch0119.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0119.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0119.lean b/Collatz/Research/StoppingAtlas/Batch0119.lean new file mode 100644 index 00000000..b7ff6cce --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0119.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0119 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 788. -/ +theorem bounds_11_788 : exactInterval 11 788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_788 (m : Nat) : + stoppingTime (2 ^ 11 * m + 788) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_788 : oddCount 788 11 = 3 ∧ acceleratedOrbit 11 788 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_788 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 788) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_788.1, data_11_788.2] + +/-- Complete interval computation for depth 11, residue 789. -/ +theorem bounds_11_789 : exactInterval 11 789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_789 (m : Nat) : + stoppingTime (2 ^ 11 * m + 789) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_789 : oddCount 789 11 = 3 ∧ acceleratedOrbit 11 789 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_789 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 789) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_789.1, data_11_789.2] + +/-- Complete interval computation for depth 11, residue 790. -/ +theorem bounds_11_790 : exactInterval 11 790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_790 (m : Nat) : + stoppingTime (2 ^ 11 * m + 790) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_790 : oddCount 790 11 = 6 ∧ acceleratedOrbit 11 790 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_790 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 790) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_790.1, data_11_790.2] + +/-- Complete interval computation for depth 11, residue 791. -/ +theorem bounds_11_791 : exactInterval 11 791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_791 (m : Nat) : + stoppingTime (2 ^ 11 * m + 791) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_791 : oddCount 791 11 = 6 ∧ acceleratedOrbit 11 791 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_791 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 791) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_791.1, data_11_791.2] + +/-- Complete interval computation for depth 11, residue 792. -/ +theorem bounds_11_792 : exactInterval 11 792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_792 (m : Nat) : + stoppingTime (2 ^ 11 * m + 792) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_792 : oddCount 792 11 = 3 ∧ acceleratedOrbit 11 792 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_792 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 792) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_792.1, data_11_792.2] + +/-- Complete interval computation for depth 11, residue 793. -/ +theorem bounds_11_793 : exactInterval 11 793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_793 (m : Nat) : + stoppingTime (2 ^ 11 * m + 793) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_793 : oddCount 793 11 = 7 ∧ acceleratedOrbit 11 793 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_793 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 793) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_793.1, data_11_793.2] + +/-- Complete interval computation for depth 11, residue 794. -/ +theorem bounds_11_794 : exactInterval 11 794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_794 (m : Nat) : + stoppingTime (2 ^ 11 * m + 794) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_794 : oddCount 794 11 = 3 ∧ acceleratedOrbit 11 794 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_794 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 794) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_794.1, data_11_794.2] + +/-- Complete interval computation for depth 11, residue 795. -/ +theorem bounds_11_795 : exactInterval 11 795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_795 (m : Nat) : + stoppingTime (2 ^ 11 * m + 795) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_795 : oddCount 795 11 = 9 ∧ acceleratedOrbit 11 795 = 7654 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_795 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 795) = 3 ^ 9 * m + 7654 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_795.1, data_11_795.2] + +/-- Complete interval computation for depth 11, residue 796. -/ +theorem bounds_11_796 : exactInterval 11 796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_796 (m : Nat) : + stoppingTime (2 ^ 11 * m + 796) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_796 : oddCount 796 11 = 5 ∧ acceleratedOrbit 11 796 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_796 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 796) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_796.1, data_11_796.2] + +/-- Complete interval computation for depth 11, residue 797. -/ +theorem bounds_11_797 : exactInterval 11 797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_797 (m : Nat) : + stoppingTime (2 ^ 11 * m + 797) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_797 : oddCount 797 11 = 5 ∧ acceleratedOrbit 11 797 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_797 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 797) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_797.1, data_11_797.2] + +/-- Complete interval computation for depth 11, residue 798. -/ +theorem bounds_11_798 : exactInterval 11 798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_798 (m : Nat) : + stoppingTime (2 ^ 11 * m + 798) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_798 : oddCount 798 11 = 5 ∧ acceleratedOrbit 11 798 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_798 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 798) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_798.1, data_11_798.2] + +/-- Complete interval computation for depth 11, residue 799. -/ +theorem bounds_11_799 : exactInterval 11 799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_799 (m : Nat) : + stoppingTime (2 ^ 11 * m + 799) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_799 : oddCount 799 11 = 8 ∧ acceleratedOrbit 11 799 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_799 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 799) = 3 ^ 8 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_799.1, data_11_799.2] + +/-- Complete interval computation for depth 11, residue 800. -/ +theorem bounds_11_800 : exactInterval 11 800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_800 (m : Nat) : + stoppingTime (2 ^ 11 * m + 800) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_800 : oddCount 800 11 = 3 ∧ acceleratedOrbit 11 800 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_800 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 800) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_800.1, data_11_800.2] + +/-- Complete interval computation for depth 11, residue 801. -/ +theorem bounds_11_801 : exactInterval 11 801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_801 (m : Nat) : + stoppingTime (2 ^ 11 * m + 801) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_801 : oddCount 801 11 = 6 ∧ acceleratedOrbit 11 801 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_801 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 801) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_801.1, data_11_801.2] + +/-- Complete interval computation for depth 11, residue 802. -/ +theorem bounds_11_802 : exactInterval 11 802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_802 (m : Nat) : + stoppingTime (2 ^ 11 * m + 802) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_802 : oddCount 802 11 = 4 ∧ acceleratedOrbit 11 802 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_802 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 802) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_802.1, data_11_802.2] + +end Collatz.Research.StoppingAtlas.Batch0119 From c2de7d1fd50589b8077728f3b567a341f12aa34e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:37 +0530 Subject: [PATCH 0120/1001] proof: certify atlas Batch0120 (11:803 to 11:818) --- Collatz/Research/StoppingAtlas/Batch0120.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0120.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0120.lean b/Collatz/Research/StoppingAtlas/Batch0120.lean new file mode 100644 index 00000000..2c2565f8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0120.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0120 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 803. -/ +theorem bounds_11_803 : exactInterval 11 803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_803 (m : Nat) : + stoppingTime (2 ^ 11 * m + 803) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_803 : oddCount 803 11 = 4 ∧ acceleratedOrbit 11 803 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_803 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 803) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_803.1, data_11_803.2] + +/-- Complete interval computation for depth 11, residue 804. -/ +theorem bounds_11_804 : exactInterval 11 804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_804 (m : Nat) : + stoppingTime (2 ^ 11 * m + 804) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_804 : oddCount 804 11 = 4 ∧ acceleratedOrbit 11 804 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_804 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 804) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_804.1, data_11_804.2] + +/-- Complete interval computation for depth 11, residue 805. -/ +theorem bounds_11_805 : exactInterval 11 805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_805 (m : Nat) : + stoppingTime (2 ^ 11 * m + 805) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_805 : oddCount 805 11 = 4 ∧ acceleratedOrbit 11 805 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_805 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 805) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_805.1, data_11_805.2] + +/-- Complete interval computation for depth 11, residue 806. -/ +theorem bounds_11_806 : exactInterval 11 806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_806 (m : Nat) : + stoppingTime (2 ^ 11 * m + 806) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_806 : oddCount 806 11 = 4 ∧ acceleratedOrbit 11 806 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_806 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 806) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_806.1, data_11_806.2] + +/-- Complete interval computation for depth 11, residue 807. -/ +theorem bounds_11_807 : exactInterval 11 807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_807 (m : Nat) : + stoppingTime (2 ^ 11 * m + 807) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_807 : oddCount 807 11 = 8 ∧ acceleratedOrbit 11 807 = 2591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_807 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 807) = 3 ^ 8 * m + 2591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_807.1, data_11_807.2] + +/-- Complete interval computation for depth 11, residue 808. -/ +theorem bounds_11_808 : exactInterval 11 808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_808 (m : Nat) : + stoppingTime (2 ^ 11 * m + 808) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_808 : oddCount 808 11 = 3 ∧ acceleratedOrbit 11 808 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_808 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 808) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_808.1, data_11_808.2] + +/-- Complete interval computation for depth 11, residue 809. -/ +theorem bounds_11_809 : exactInterval 11 809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_809 (m : Nat) : + stoppingTime (2 ^ 11 * m + 809) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_809 : oddCount 809 11 = 7 ∧ acceleratedOrbit 11 809 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_809 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 809) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_809.1, data_11_809.2] + +/-- Complete interval computation for depth 11, residue 810. -/ +theorem bounds_11_810 : exactInterval 11 810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_810 (m : Nat) : + stoppingTime (2 ^ 11 * m + 810) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_810 : oddCount 810 11 = 3 ∧ acceleratedOrbit 11 810 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_810 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 810) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_810.1, data_11_810.2] + +/-- Complete interval computation for depth 11, residue 811. -/ +theorem bounds_11_811 : exactInterval 11 811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_811 (m : Nat) : + stoppingTime (2 ^ 11 * m + 811) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_811 : oddCount 811 11 = 6 ∧ acceleratedOrbit 11 811 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_811 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 811) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_811.1, data_11_811.2] + +/-- Complete interval computation for depth 11, residue 812. -/ +theorem bounds_11_812 : exactInterval 11 812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_812 (m : Nat) : + stoppingTime (2 ^ 11 * m + 812) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_812 : oddCount 812 11 = 5 ∧ acceleratedOrbit 11 812 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_812 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 812) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_812.1, data_11_812.2] + +/-- Complete interval computation for depth 11, residue 813. -/ +theorem bounds_11_813 : exactInterval 11 813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_813 (m : Nat) : + stoppingTime (2 ^ 11 * m + 813) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_813 : oddCount 813 11 = 5 ∧ acceleratedOrbit 11 813 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_813 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 813) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_813.1, data_11_813.2] + +/-- Complete interval computation for depth 11, residue 814. -/ +theorem bounds_11_814 : exactInterval 11 814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_814 (m : Nat) : + stoppingTime (2 ^ 11 * m + 814) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_814 : oddCount 814 11 = 5 ∧ acceleratedOrbit 11 814 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_814 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 814) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_814.1, data_11_814.2] + +/-- Complete interval computation for depth 11, residue 815. -/ +theorem bounds_11_815 : exactInterval 11 815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_815 (m : Nat) : + stoppingTime (2 ^ 11 * m + 815) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_815 : oddCount 815 11 = 7 ∧ acceleratedOrbit 11 815 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_815 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 815) = 3 ^ 7 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_815.1, data_11_815.2] + +/-- Complete interval computation for depth 11, residue 816. -/ +theorem bounds_11_816 : exactInterval 11 816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_816 (m : Nat) : + stoppingTime (2 ^ 11 * m + 816) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_816 : oddCount 816 11 = 3 ∧ acceleratedOrbit 11 816 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_816 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 816) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_816.1, data_11_816.2] + +/-- Complete interval computation for depth 11, residue 817. -/ +theorem bounds_11_817 : exactInterval 11 817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_817 (m : Nat) : + stoppingTime (2 ^ 11 * m + 817) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_817 : oddCount 817 11 = 5 ∧ acceleratedOrbit 11 817 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_817 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 817) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_817.1, data_11_817.2] + +/-- Complete interval computation for depth 11, residue 818. -/ +theorem bounds_11_818 : exactInterval 11 818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_818 (m : Nat) : + stoppingTime (2 ^ 11 * m + 818) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_818 : oddCount 818 11 = 5 ∧ acceleratedOrbit 11 818 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_818 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 818) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_818.1, data_11_818.2] + +end Collatz.Research.StoppingAtlas.Batch0120 From 92bb737f63a2160464292c75b5e050a81be30f45 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:37 +0530 Subject: [PATCH 0121/1001] proof: certify atlas Batch0121 (11:819 to 11:833) --- Collatz/Research/StoppingAtlas/Batch0121.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0121.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0121.lean b/Collatz/Research/StoppingAtlas/Batch0121.lean new file mode 100644 index 00000000..fac7b572 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0121.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0121 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 819. -/ +theorem bounds_11_819 : exactInterval 11 819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_819 (m : Nat) : + stoppingTime (2 ^ 11 * m + 819) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_819 : oddCount 819 11 = 5 ∧ acceleratedOrbit 11 819 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_819 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 819) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_819.1, data_11_819.2] + +/-- Complete interval computation for depth 11, residue 820. -/ +theorem bounds_11_820 : exactInterval 11 820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_820 (m : Nat) : + stoppingTime (2 ^ 11 * m + 820) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_820 : oddCount 820 11 = 3 ∧ acceleratedOrbit 11 820 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_820 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 820) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_820.1, data_11_820.2] + +/-- Complete interval computation for depth 11, residue 821. -/ +theorem bounds_11_821 : exactInterval 11 821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_821 (m : Nat) : + stoppingTime (2 ^ 11 * m + 821) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_821 : oddCount 821 11 = 3 ∧ acceleratedOrbit 11 821 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_821 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 821) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_821.1, data_11_821.2] + +/-- Complete interval computation for depth 11, residue 822. -/ +theorem bounds_11_822 : exactInterval 11 822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_822 (m : Nat) : + stoppingTime (2 ^ 11 * m + 822) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_822 : oddCount 822 11 = 7 ∧ acceleratedOrbit 11 822 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_822 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 822) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_822.1, data_11_822.2] + +/-- Complete interval computation for depth 11, residue 823. -/ +theorem bounds_11_823 : exactInterval 11 823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_823 (m : Nat) : + stoppingTime (2 ^ 11 * m + 823) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_823 : oddCount 823 11 = 7 ∧ acceleratedOrbit 11 823 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_823 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 823) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_823.1, data_11_823.2] + +/-- Complete interval computation for depth 11, residue 824. -/ +theorem bounds_11_824 : exactInterval 11 824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_824 (m : Nat) : + stoppingTime (2 ^ 11 * m + 824) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_824 : oddCount 824 11 = 7 ∧ acceleratedOrbit 11 824 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_824 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 824) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_824.1, data_11_824.2] + +/-- Complete interval computation for depth 11, residue 825. -/ +theorem bounds_11_825 : exactInterval 11 825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_825 (m : Nat) : + stoppingTime (2 ^ 11 * m + 825) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_825 : oddCount 825 11 = 7 ∧ acceleratedOrbit 11 825 = 884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_825 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 825) = 3 ^ 7 * m + 884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_825.1, data_11_825.2] + +/-- Complete interval computation for depth 11, residue 826. -/ +theorem bounds_11_826 : exactInterval 11 826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_826 (m : Nat) : + stoppingTime (2 ^ 11 * m + 826) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_826 : oddCount 826 11 = 7 ∧ acceleratedOrbit 11 826 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_826 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 826) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_826.1, data_11_826.2] + +/-- Complete interval computation for depth 11, residue 827. -/ +theorem bounds_11_827 : exactInterval 11 827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_827 (m : Nat) : + stoppingTime (2 ^ 11 * m + 827) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_827 : oddCount 827 11 = 6 ∧ acceleratedOrbit 11 827 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_827 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 827) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_827.1, data_11_827.2] + +/-- Complete interval computation for depth 11, residue 828. -/ +theorem bounds_11_828 : exactInterval 11 828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_828 (m : Nat) : + stoppingTime (2 ^ 11 * m + 828) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_828 : oddCount 828 11 = 7 ∧ acceleratedOrbit 11 828 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_828 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 828) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_828.1, data_11_828.2] + +/-- Complete interval computation for depth 11, residue 829. -/ +theorem bounds_11_829 : exactInterval 11 829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_829 (m : Nat) : + stoppingTime (2 ^ 11 * m + 829) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_829 : oddCount 829 11 = 7 ∧ acceleratedOrbit 11 829 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_829 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 829) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_829.1, data_11_829.2] + +/-- Complete interval computation for depth 11, residue 830. -/ +theorem bounds_11_830 : exactInterval 11 830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_830 (m : Nat) : + stoppingTime (2 ^ 11 * m + 830) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_830 : oddCount 830 11 = 8 ∧ acceleratedOrbit 11 830 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_830 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 830) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_830.1, data_11_830.2] + +/-- Complete interval computation for depth 11, residue 831. -/ +theorem bounds_11_831 : exactInterval 11 831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_831 (m : Nat) : + stoppingTime (2 ^ 11 * m + 831) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_831 : oddCount 831 11 = 8 ∧ acceleratedOrbit 11 831 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_831 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 831) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_831.1, data_11_831.2] + +/-- Complete interval computation for depth 11, residue 832. -/ +theorem bounds_11_832 : exactInterval 11 832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_832 (m : Nat) : + stoppingTime (2 ^ 11 * m + 832) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_832 : oddCount 832 11 = 2 ∧ acceleratedOrbit 11 832 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_832 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 832) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_832.1, data_11_832.2] + +/-- Complete interval computation for depth 11, residue 833. -/ +theorem bounds_11_833 : exactInterval 11 833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_833 (m : Nat) : + stoppingTime (2 ^ 11 * m + 833) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_833 : oddCount 833 11 = 3 ∧ acceleratedOrbit 11 833 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_833 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 833) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_833.1, data_11_833.2] + +end Collatz.Research.StoppingAtlas.Batch0121 From 2134e9a988db27324f81bab96653eff677a9fbcc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:38 +0530 Subject: [PATCH 0122/1001] proof: certify atlas Batch0122 (11:834 to 11:848) --- Collatz/Research/StoppingAtlas/Batch0122.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0122.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0122.lean b/Collatz/Research/StoppingAtlas/Batch0122.lean new file mode 100644 index 00000000..5667cc4a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0122.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0122 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 834. -/ +theorem bounds_11_834 : exactInterval 11 834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_834 (m : Nat) : + stoppingTime (2 ^ 11 * m + 834) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_834 : oddCount 834 11 = 6 ∧ acceleratedOrbit 11 834 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_834 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 834) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_834.1, data_11_834.2] + +/-- Complete interval computation for depth 11, residue 835. -/ +theorem bounds_11_835 : exactInterval 11 835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_835 (m : Nat) : + stoppingTime (2 ^ 11 * m + 835) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_835 : oddCount 835 11 = 6 ∧ acceleratedOrbit 11 835 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_835 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 835) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_835.1, data_11_835.2] + +/-- Complete interval computation for depth 11, residue 836. -/ +theorem bounds_11_836 : exactInterval 11 836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_836 (m : Nat) : + stoppingTime (2 ^ 11 * m + 836) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_836 : oddCount 836 11 = 5 ∧ acceleratedOrbit 11 836 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_836 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 836) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_836.1, data_11_836.2] + +/-- Complete interval computation for depth 11, residue 837. -/ +theorem bounds_11_837 : exactInterval 11 837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_837 (m : Nat) : + stoppingTime (2 ^ 11 * m + 837) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_837 : oddCount 837 11 = 5 ∧ acceleratedOrbit 11 837 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_837 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 837) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_837.1, data_11_837.2] + +/-- Complete interval computation for depth 11, residue 838. -/ +theorem bounds_11_838 : exactInterval 11 838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_838 (m : Nat) : + stoppingTime (2 ^ 11 * m + 838) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_838 : oddCount 838 11 = 5 ∧ acceleratedOrbit 11 838 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_838 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 838) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_838.1, data_11_838.2] + +/-- Complete interval computation for depth 11, residue 839. -/ +theorem bounds_11_839 : exactInterval 11 839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_839 (m : Nat) : + stoppingTime (2 ^ 11 * m + 839) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_839 : oddCount 839 11 = 8 ∧ acceleratedOrbit 11 839 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_839 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 839) = 3 ^ 8 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_839.1, data_11_839.2] + +/-- Complete interval computation for depth 11, residue 840. -/ +theorem bounds_11_840 : exactInterval 11 840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_840 (m : Nat) : + stoppingTime (2 ^ 11 * m + 840) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_840 : oddCount 840 11 = 5 ∧ acceleratedOrbit 11 840 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_840 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 840) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_840.1, data_11_840.2] + +/-- Complete interval computation for depth 11, residue 841. -/ +theorem bounds_11_841 : exactInterval 11 841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_841 (m : Nat) : + stoppingTime (2 ^ 11 * m + 841) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_841 : oddCount 841 11 = 5 ∧ acceleratedOrbit 11 841 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_841 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 841) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_841.1, data_11_841.2] + +/-- Complete interval computation for depth 11, residue 842. -/ +theorem bounds_11_842 : exactInterval 11 842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_842 (m : Nat) : + stoppingTime (2 ^ 11 * m + 842) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_842 : oddCount 842 11 = 5 ∧ acceleratedOrbit 11 842 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_842 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 842) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_842.1, data_11_842.2] + +/-- Complete interval computation for depth 11, residue 843. -/ +theorem bounds_11_843 : exactInterval 11 843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_843 (m : Nat) : + stoppingTime (2 ^ 11 * m + 843) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_843 : oddCount 843 11 = 5 ∧ acceleratedOrbit 11 843 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_843 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 843) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_843.1, data_11_843.2] + +/-- Complete interval computation for depth 11, residue 844. -/ +theorem bounds_11_844 : exactInterval 11 844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_844 (m : Nat) : + stoppingTime (2 ^ 11 * m + 844) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_844 : oddCount 844 11 = 5 ∧ acceleratedOrbit 11 844 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_844 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 844) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_844.1, data_11_844.2] + +/-- Complete interval computation for depth 11, residue 845. -/ +theorem bounds_11_845 : exactInterval 11 845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_845 (m : Nat) : + stoppingTime (2 ^ 11 * m + 845) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_845 : oddCount 845 11 = 5 ∧ acceleratedOrbit 11 845 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_845 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 845) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_845.1, data_11_845.2] + +/-- Complete interval computation for depth 11, residue 846. -/ +theorem bounds_11_846 : exactInterval 11 846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_846 (m : Nat) : + stoppingTime (2 ^ 11 * m + 846) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_846 : oddCount 846 11 = 6 ∧ acceleratedOrbit 11 846 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_846 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 846) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_846.1, data_11_846.2] + +/-- Complete interval computation for depth 11, residue 847. -/ +theorem bounds_11_847 : exactInterval 11 847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_847 (m : Nat) : + stoppingTime (2 ^ 11 * m + 847) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_847 : oddCount 847 11 = 6 ∧ acceleratedOrbit 11 847 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_847 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 847) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_847.1, data_11_847.2] + +/-- Complete interval computation for depth 11, residue 848. -/ +theorem bounds_11_848 : exactInterval 11 848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_848 (m : Nat) : + stoppingTime (2 ^ 11 * m + 848) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_848 : oddCount 848 11 = 2 ∧ acceleratedOrbit 11 848 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_848 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 848) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_848.1, data_11_848.2] + +end Collatz.Research.StoppingAtlas.Batch0122 From 72cfc4dbb172490b3ff8f6f3d821c2ae72e2fb8f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:38 +0530 Subject: [PATCH 0123/1001] proof: certify atlas Batch0123 (11:849 to 11:864) --- Collatz/Research/StoppingAtlas/Batch0123.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0123.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0123.lean b/Collatz/Research/StoppingAtlas/Batch0123.lean new file mode 100644 index 00000000..f2dccad8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0123.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0123 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 849. -/ +theorem bounds_11_849 : exactInterval 11 849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_849 (m : Nat) : + stoppingTime (2 ^ 11 * m + 849) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_849 : oddCount 849 11 = 7 ∧ acceleratedOrbit 11 849 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_849 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 849) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_849.1, data_11_849.2] + +/-- Complete interval computation for depth 11, residue 850. -/ +theorem bounds_11_850 : exactInterval 11 850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_850 (m : Nat) : + stoppingTime (2 ^ 11 * m + 850) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_850 : oddCount 850 11 = 7 ∧ acceleratedOrbit 11 850 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_850 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 850) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_850.1, data_11_850.2] + +/-- Complete interval computation for depth 11, residue 851. -/ +theorem bounds_11_851 : exactInterval 11 851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_851 (m : Nat) : + stoppingTime (2 ^ 11 * m + 851) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_851 : oddCount 851 11 = 7 ∧ acceleratedOrbit 11 851 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_851 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 851) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_851.1, data_11_851.2] + +/-- Complete interval computation for depth 11, residue 852. -/ +theorem bounds_11_852 : exactInterval 11 852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_852 (m : Nat) : + stoppingTime (2 ^ 11 * m + 852) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_852 : oddCount 852 11 = 2 ∧ acceleratedOrbit 11 852 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_852 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 852) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_852.1, data_11_852.2] + +/-- Complete interval computation for depth 11, residue 853. -/ +theorem bounds_11_853 : exactInterval 11 853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_853 (m : Nat) : + stoppingTime (2 ^ 11 * m + 853) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_853 : oddCount 853 11 = 2 ∧ acceleratedOrbit 11 853 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_853 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 853) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_853.1, data_11_853.2] + +/-- Complete interval computation for depth 11, residue 854. -/ +theorem bounds_11_854 : exactInterval 11 854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_854 (m : Nat) : + stoppingTime (2 ^ 11 * m + 854) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_854 : oddCount 854 11 = 7 ∧ acceleratedOrbit 11 854 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_854 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 854) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_854.1, data_11_854.2] + +/-- Complete interval computation for depth 11, residue 855. -/ +theorem bounds_11_855 : exactInterval 11 855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_855 (m : Nat) : + stoppingTime (2 ^ 11 * m + 855) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_855 : oddCount 855 11 = 7 ∧ acceleratedOrbit 11 855 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_855 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 855) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_855.1, data_11_855.2] + +/-- Complete interval computation for depth 11, residue 856. -/ +theorem bounds_11_856 : exactInterval 11 856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_856 (m : Nat) : + stoppingTime (2 ^ 11 * m + 856) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_856 : oddCount 856 11 = 5 ∧ acceleratedOrbit 11 856 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_856 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 856) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_856.1, data_11_856.2] + +/-- Complete interval computation for depth 11, residue 857. -/ +theorem bounds_11_857 : exactInterval 11 857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_857 (m : Nat) : + stoppingTime (2 ^ 11 * m + 857) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_857 : oddCount 857 11 = 4 ∧ acceleratedOrbit 11 857 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_857 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 857) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_857.1, data_11_857.2] + +/-- Complete interval computation for depth 11, residue 858. -/ +theorem bounds_11_858 : exactInterval 11 858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_858 (m : Nat) : + stoppingTime (2 ^ 11 * m + 858) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_858 : oddCount 858 11 = 5 ∧ acceleratedOrbit 11 858 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_858 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 858) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_858.1, data_11_858.2] + +/-- Complete interval computation for depth 11, residue 859. -/ +theorem bounds_11_859 : exactInterval 11 859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_859 (m : Nat) : + stoppingTime (2 ^ 11 * m + 859) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_859 : oddCount 859 11 = 7 ∧ acceleratedOrbit 11 859 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_859 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 859) = 3 ^ 7 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_859.1, data_11_859.2] + +/-- Complete interval computation for depth 11, residue 860. -/ +theorem bounds_11_860 : exactInterval 11 860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_860 (m : Nat) : + stoppingTime (2 ^ 11 * m + 860) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_860 : oddCount 860 11 = 5 ∧ acceleratedOrbit 11 860 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_860 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 860) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_860.1, data_11_860.2] + +/-- Complete interval computation for depth 11, residue 861. -/ +theorem bounds_11_861 : exactInterval 11 861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_861 (m : Nat) : + stoppingTime (2 ^ 11 * m + 861) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_861 : oddCount 861 11 = 5 ∧ acceleratedOrbit 11 861 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_861 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 861) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_861.1, data_11_861.2] + +/-- Complete interval computation for depth 11, residue 862. -/ +theorem bounds_11_862 : exactInterval 11 862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_862 (m : Nat) : + stoppingTime (2 ^ 11 * m + 862) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_862 : oddCount 862 11 = 6 ∧ acceleratedOrbit 11 862 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_862 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 862) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_862.1, data_11_862.2] + +/-- Complete interval computation for depth 11, residue 863. -/ +theorem bounds_11_863 : exactInterval 11 863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_863 (m : Nat) : + stoppingTime (2 ^ 11 * m + 863) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_863 : oddCount 863 11 = 6 ∧ acceleratedOrbit 11 863 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_863 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 863) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_863.1, data_11_863.2] + +/-- Complete interval computation for depth 11, residue 864. -/ +theorem bounds_11_864 : exactInterval 11 864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_864 (m : Nat) : + stoppingTime (2 ^ 11 * m + 864) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_864 : oddCount 864 11 = 5 ∧ acceleratedOrbit 11 864 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_864 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 864) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_864.1, data_11_864.2] + +end Collatz.Research.StoppingAtlas.Batch0123 From 1699f21312cd56ba39aa4fbfc467e05c3eeeba76 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:38 +0530 Subject: [PATCH 0124/1001] proof: certify atlas Batch0124 (11:865 to 11:879) --- Collatz/Research/StoppingAtlas/Batch0124.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0124.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0124.lean b/Collatz/Research/StoppingAtlas/Batch0124.lean new file mode 100644 index 00000000..f3d16617 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0124.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0124 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 865. -/ +theorem bounds_11_865 : exactInterval 11 865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_865 (m : Nat) : + stoppingTime (2 ^ 11 * m + 865) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_865 : oddCount 865 11 = 8 ∧ acceleratedOrbit 11 865 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_865 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 865) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_865.1, data_11_865.2] + +/-- Complete interval computation for depth 11, residue 866. -/ +theorem bounds_11_866 : exactInterval 11 866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_866 (m : Nat) : + stoppingTime (2 ^ 11 * m + 866) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_866 : oddCount 866 11 = 4 ∧ acceleratedOrbit 11 866 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_866 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 866) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_866.1, data_11_866.2] + +/-- Complete interval computation for depth 11, residue 867. -/ +theorem bounds_11_867 : exactInterval 11 867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_867 (m : Nat) : + stoppingTime (2 ^ 11 * m + 867) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_867 : oddCount 867 11 = 4 ∧ acceleratedOrbit 11 867 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_867 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 867) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_867.1, data_11_867.2] + +/-- Complete interval computation for depth 11, residue 868. -/ +theorem bounds_11_868 : exactInterval 11 868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_868 (m : Nat) : + stoppingTime (2 ^ 11 * m + 868) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_868 : oddCount 868 11 = 4 ∧ acceleratedOrbit 11 868 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_868 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 868) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_868.1, data_11_868.2] + +/-- Complete interval computation for depth 11, residue 869. -/ +theorem bounds_11_869 : exactInterval 11 869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_869 (m : Nat) : + stoppingTime (2 ^ 11 * m + 869) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_869 : oddCount 869 11 = 4 ∧ acceleratedOrbit 11 869 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_869 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 869) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_869.1, data_11_869.2] + +/-- Complete interval computation for depth 11, residue 870. -/ +theorem bounds_11_870 : exactInterval 11 870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_870 (m : Nat) : + stoppingTime (2 ^ 11 * m + 870) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_870 : oddCount 870 11 = 4 ∧ acceleratedOrbit 11 870 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_870 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 870) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_870.1, data_11_870.2] + +/-- Complete interval computation for depth 11, residue 871. -/ +theorem bounds_11_871 : exactInterval 11 871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_871 (m : Nat) : + stoppingTime (2 ^ 11 * m + 871) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_871 : oddCount 871 11 = 9 ∧ acceleratedOrbit 11 871 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_871 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 871) = 3 ^ 9 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_871.1, data_11_871.2] + +/-- Complete interval computation for depth 11, residue 872. -/ +theorem bounds_11_872 : exactInterval 11 872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_872 (m : Nat) : + stoppingTime (2 ^ 11 * m + 872) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_872 : oddCount 872 11 = 5 ∧ acceleratedOrbit 11 872 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_872 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 872) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_872.1, data_11_872.2] + +/-- Complete interval computation for depth 11, residue 873. -/ +theorem bounds_11_873 : exactInterval 11 873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_873 (m : Nat) : + stoppingTime (2 ^ 11 * m + 873) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_873 : oddCount 873 11 = 7 ∧ acceleratedOrbit 11 873 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_873 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 873) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_873.1, data_11_873.2] + +/-- Complete interval computation for depth 11, residue 874. -/ +theorem bounds_11_874 : exactInterval 11 874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_874 (m : Nat) : + stoppingTime (2 ^ 11 * m + 874) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_874 : oddCount 874 11 = 5 ∧ acceleratedOrbit 11 874 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_874 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 874) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_874.1, data_11_874.2] + +/-- Complete interval computation for depth 11, residue 875. -/ +theorem bounds_11_875 : exactInterval 11 875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_875 (m : Nat) : + stoppingTime (2 ^ 11 * m + 875) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_875 : oddCount 875 11 = 5 ∧ acceleratedOrbit 11 875 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_875 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 875) = 3 ^ 5 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_875.1, data_11_875.2] + +/-- Complete interval computation for depth 11, residue 876. -/ +theorem bounds_11_876 : exactInterval 11 876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_876 (m : Nat) : + stoppingTime (2 ^ 11 * m + 876) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_876 : oddCount 876 11 = 6 ∧ acceleratedOrbit 11 876 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_876 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 876) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_876.1, data_11_876.2] + +/-- Complete interval computation for depth 11, residue 877. -/ +theorem bounds_11_877 : exactInterval 11 877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_877 (m : Nat) : + stoppingTime (2 ^ 11 * m + 877) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_877 : oddCount 877 11 = 6 ∧ acceleratedOrbit 11 877 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_877 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 877) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_877.1, data_11_877.2] + +/-- Complete interval computation for depth 11, residue 878. -/ +theorem bounds_11_878 : exactInterval 11 878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_878 (m : Nat) : + stoppingTime (2 ^ 11 * m + 878) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_878 : oddCount 878 11 = 6 ∧ acceleratedOrbit 11 878 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_878 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 878) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_878.1, data_11_878.2] + +/-- Complete interval computation for depth 11, residue 879. -/ +theorem bounds_11_879 : exactInterval 11 879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_879 (m : Nat) : + stoppingTime (2 ^ 11 * m + 879) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_879 : oddCount 879 11 = 7 ∧ acceleratedOrbit 11 879 = 940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_879 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 879) = 3 ^ 7 * m + 940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_879.1, data_11_879.2] + +end Collatz.Research.StoppingAtlas.Batch0124 From b599ecbcd8703e61ebf13bc0685da28ecf7dbed6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:39 +0530 Subject: [PATCH 0125/1001] proof: certify atlas Batch0125 (11:880 to 11:895) --- Collatz/Research/StoppingAtlas/Batch0125.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0125.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0125.lean b/Collatz/Research/StoppingAtlas/Batch0125.lean new file mode 100644 index 00000000..9855404a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0125.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0125 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 880. -/ +theorem bounds_11_880 : exactInterval 11 880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_880 (m : Nat) : + stoppingTime (2 ^ 11 * m + 880) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_880 : oddCount 880 11 = 5 ∧ acceleratedOrbit 11 880 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_880 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 880) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_880.1, data_11_880.2] + +/-- Complete interval computation for depth 11, residue 881. -/ +theorem bounds_11_881 : exactInterval 11 881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_881 (m : Nat) : + stoppingTime (2 ^ 11 * m + 881) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_881 : oddCount 881 11 = 5 ∧ acceleratedOrbit 11 881 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_881 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 881) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_881.1, data_11_881.2] + +/-- Complete interval computation for depth 11, residue 882. -/ +theorem bounds_11_882 : exactInterval 11 882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_882 (m : Nat) : + stoppingTime (2 ^ 11 * m + 882) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_882 : oddCount 882 11 = 4 ∧ acceleratedOrbit 11 882 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_882 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 882) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_882.1, data_11_882.2] + +/-- Complete interval computation for depth 11, residue 883. -/ +theorem bounds_11_883 : exactInterval 11 883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_883 (m : Nat) : + stoppingTime (2 ^ 11 * m + 883) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_883 : oddCount 883 11 = 4 ∧ acceleratedOrbit 11 883 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_883 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 883) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_883.1, data_11_883.2] + +/-- Complete interval computation for depth 11, residue 884. -/ +theorem bounds_11_884 : exactInterval 11 884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_884 (m : Nat) : + stoppingTime (2 ^ 11 * m + 884) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_884 : oddCount 884 11 = 5 ∧ acceleratedOrbit 11 884 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_884 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 884) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_884.1, data_11_884.2] + +/-- Complete interval computation for depth 11, residue 885. -/ +theorem bounds_11_885 : exactInterval 11 885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_885 (m : Nat) : + stoppingTime (2 ^ 11 * m + 885) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_885 : oddCount 885 11 = 5 ∧ acceleratedOrbit 11 885 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_885 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 885) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_885.1, data_11_885.2] + +/-- Complete interval computation for depth 11, residue 886. -/ +theorem bounds_11_886 : exactInterval 11 886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_886 (m : Nat) : + stoppingTime (2 ^ 11 * m + 886) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_886 : oddCount 886 11 = 6 ∧ acceleratedOrbit 11 886 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_886 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 886) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_886.1, data_11_886.2] + +/-- Complete interval computation for depth 11, residue 887. -/ +theorem bounds_11_887 : exactInterval 11 887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_887 (m : Nat) : + stoppingTime (2 ^ 11 * m + 887) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_887 : oddCount 887 11 = 6 ∧ acceleratedOrbit 11 887 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_887 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 887) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_887.1, data_11_887.2] + +/-- Complete interval computation for depth 11, residue 888. -/ +theorem bounds_11_888 : exactInterval 11 888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_888 (m : Nat) : + stoppingTime (2 ^ 11 * m + 888) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_888 : oddCount 888 11 = 6 ∧ acceleratedOrbit 11 888 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_888 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 888) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_888.1, data_11_888.2] + +/-- Complete interval computation for depth 11, residue 889. -/ +theorem bounds_11_889 : exactInterval 11 889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_889 (m : Nat) : + stoppingTime (2 ^ 11 * m + 889) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_889 : oddCount 889 11 = 8 ∧ acceleratedOrbit 11 889 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_889 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 889) = 3 ^ 8 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_889.1, data_11_889.2] + +/-- Complete interval computation for depth 11, residue 890. -/ +theorem bounds_11_890 : exactInterval 11 890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_890 (m : Nat) : + stoppingTime (2 ^ 11 * m + 890) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_890 : oddCount 890 11 = 6 ∧ acceleratedOrbit 11 890 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_890 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 890) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_890.1, data_11_890.2] + +/-- Complete interval computation for depth 11, residue 891. -/ +theorem bounds_11_891 : exactInterval 11 891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_891 (m : Nat) : + stoppingTime (2 ^ 11 * m + 891) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_891 : oddCount 891 11 = 8 ∧ acceleratedOrbit 11 891 = 2861 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_891 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 891) = 3 ^ 8 * m + 2861 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_891.1, data_11_891.2] + +/-- Complete interval computation for depth 11, residue 892. -/ +theorem bounds_11_892 : exactInterval 11 892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_892 (m : Nat) : + stoppingTime (2 ^ 11 * m + 892) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_892 : oddCount 892 11 = 6 ∧ acceleratedOrbit 11 892 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_892 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 892) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_892.1, data_11_892.2] + +/-- Complete interval computation for depth 11, residue 893. -/ +theorem bounds_11_893 : exactInterval 11 893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_893 (m : Nat) : + stoppingTime (2 ^ 11 * m + 893) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_893 : oddCount 893 11 = 6 ∧ acceleratedOrbit 11 893 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_893 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 893) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_893.1, data_11_893.2] + +/-- Complete interval computation for depth 11, residue 894. -/ +theorem bounds_11_894 : exactInterval 11 894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_894 (m : Nat) : + stoppingTime (2 ^ 11 * m + 894) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_894 : oddCount 894 11 = 9 ∧ acceleratedOrbit 11 894 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_894 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 894) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_894.1, data_11_894.2] + +/-- Complete interval computation for depth 11, residue 895. -/ +theorem bounds_11_895 : exactInterval 11 895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_895 (m : Nat) : + stoppingTime (2 ^ 11 * m + 895) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_895 : oddCount 895 11 = 9 ∧ acceleratedOrbit 11 895 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_895 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 895) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_895.1, data_11_895.2] + +end Collatz.Research.StoppingAtlas.Batch0125 From d1a24ad937a23593176e01cca453920b04f0f8b7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:39 +0530 Subject: [PATCH 0126/1001] proof: certify atlas Batch0126 (11:896 to 11:910) --- Collatz/Research/StoppingAtlas/Batch0126.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0126.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0126.lean b/Collatz/Research/StoppingAtlas/Batch0126.lean new file mode 100644 index 00000000..34715869 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0126.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0126 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 896. -/ +theorem bounds_11_896 : exactInterval 11 896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_896 (m : Nat) : + stoppingTime (2 ^ 11 * m + 896) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_896 : oddCount 896 11 = 3 ∧ acceleratedOrbit 11 896 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_896 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 896) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_896.1, data_11_896.2] + +/-- Complete interval computation for depth 11, residue 897. -/ +theorem bounds_11_897 : exactInterval 11 897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_897 (m : Nat) : + stoppingTime (2 ^ 11 * m + 897) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_897 : oddCount 897 11 = 7 ∧ acceleratedOrbit 11 897 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_897 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 897) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_897.1, data_11_897.2] + +/-- Complete interval computation for depth 11, residue 898. -/ +theorem bounds_11_898 : exactInterval 11 898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_898 (m : Nat) : + stoppingTime (2 ^ 11 * m + 898) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_898 : oddCount 898 11 = 6 ∧ acceleratedOrbit 11 898 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_898 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 898) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_898.1, data_11_898.2] + +/-- Complete interval computation for depth 11, residue 899. -/ +theorem bounds_11_899 : exactInterval 11 899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_899 (m : Nat) : + stoppingTime (2 ^ 11 * m + 899) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_899 : oddCount 899 11 = 6 ∧ acceleratedOrbit 11 899 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_899 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 899) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_899.1, data_11_899.2] + +/-- Complete interval computation for depth 11, residue 900. -/ +theorem bounds_11_900 : exactInterval 11 900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_900 (m : Nat) : + stoppingTime (2 ^ 11 * m + 900) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_900 : oddCount 900 11 = 7 ∧ acceleratedOrbit 11 900 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_900 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 900) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_900.1, data_11_900.2] + +/-- Complete interval computation for depth 11, residue 901. -/ +theorem bounds_11_901 : exactInterval 11 901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_901 (m : Nat) : + stoppingTime (2 ^ 11 * m + 901) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_901 : oddCount 901 11 = 7 ∧ acceleratedOrbit 11 901 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_901 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 901) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_901.1, data_11_901.2] + +/-- Complete interval computation for depth 11, residue 902. -/ +theorem bounds_11_902 : exactInterval 11 902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_902 (m : Nat) : + stoppingTime (2 ^ 11 * m + 902) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_902 : oddCount 902 11 = 7 ∧ acceleratedOrbit 11 902 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_902 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 902) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_902.1, data_11_902.2] + +/-- Complete interval computation for depth 11, residue 903. -/ +theorem bounds_11_903 : exactInterval 11 903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_903 (m : Nat) : + stoppingTime (2 ^ 11 * m + 903) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_903 : oddCount 903 11 = 6 ∧ acceleratedOrbit 11 903 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_903 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 903) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_903.1, data_11_903.2] + +/-- Complete interval computation for depth 11, residue 904. -/ +theorem bounds_11_904 : exactInterval 11 904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_904 (m : Nat) : + stoppingTime (2 ^ 11 * m + 904) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_904 : oddCount 904 11 = 2 ∧ acceleratedOrbit 11 904 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_904 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 904) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_904.1, data_11_904.2] + +/-- Complete interval computation for depth 11, residue 905. -/ +theorem bounds_11_905 : exactInterval 11 905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_905 (m : Nat) : + stoppingTime (2 ^ 11 * m + 905) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_905 : oddCount 905 11 = 8 ∧ acceleratedOrbit 11 905 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_905 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 905) = 3 ^ 8 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_905.1, data_11_905.2] + +/-- Complete interval computation for depth 11, residue 906. -/ +theorem bounds_11_906 : exactInterval 11 906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_906 (m : Nat) : + stoppingTime (2 ^ 11 * m + 906) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_906 : oddCount 906 11 = 2 ∧ acceleratedOrbit 11 906 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_906 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 906) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_906.1, data_11_906.2] + +/-- Complete interval computation for depth 11, residue 907. -/ +theorem bounds_11_907 : exactInterval 11 907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_907 (m : Nat) : + stoppingTime (2 ^ 11 * m + 907) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_907 : oddCount 907 11 = 8 ∧ acceleratedOrbit 11 907 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_907 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 907) = 3 ^ 8 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_907.1, data_11_907.2] + +/-- Complete interval computation for depth 11, residue 908. -/ +theorem bounds_11_908 : exactInterval 11 908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_908 (m : Nat) : + stoppingTime (2 ^ 11 * m + 908) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_908 : oddCount 908 11 = 2 ∧ acceleratedOrbit 11 908 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_908 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 908) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_908.1, data_11_908.2] + +/-- Complete interval computation for depth 11, residue 909. -/ +theorem bounds_11_909 : exactInterval 11 909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_909 (m : Nat) : + stoppingTime (2 ^ 11 * m + 909) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_909 : oddCount 909 11 = 2 ∧ acceleratedOrbit 11 909 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_909 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 909) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_909.1, data_11_909.2] + +/-- Complete interval computation for depth 11, residue 910. -/ +theorem bounds_11_910 : exactInterval 11 910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_910 (m : Nat) : + stoppingTime (2 ^ 11 * m + 910) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_910 : oddCount 910 11 = 6 ∧ acceleratedOrbit 11 910 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_910 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 910) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_910.1, data_11_910.2] + +end Collatz.Research.StoppingAtlas.Batch0126 From 565687e0d516bc2000636ec4b3af2d2645caf638 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:39 +0530 Subject: [PATCH 0127/1001] proof: certify atlas Batch0127 (11:911 to 11:925) --- Collatz/Research/StoppingAtlas/Batch0127.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0127.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0127.lean b/Collatz/Research/StoppingAtlas/Batch0127.lean new file mode 100644 index 00000000..3e94d9bc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0127.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0127 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 911. -/ +theorem bounds_11_911 : exactInterval 11 911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_911 (m : Nat) : + stoppingTime (2 ^ 11 * m + 911) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_911 : oddCount 911 11 = 6 ∧ acceleratedOrbit 11 911 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_911 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 911) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_911.1, data_11_911.2] + +/-- Complete interval computation for depth 11, residue 912. -/ +theorem bounds_11_912 : exactInterval 11 912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_912 (m : Nat) : + stoppingTime (2 ^ 11 * m + 912) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_912 : oddCount 912 11 = 4 ∧ acceleratedOrbit 11 912 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_912 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 912) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_912.1, data_11_912.2] + +/-- Complete interval computation for depth 11, residue 913. -/ +theorem bounds_11_913 : exactInterval 11 913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_913 (m : Nat) : + stoppingTime (2 ^ 11 * m + 913) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_913 : oddCount 913 11 = 5 ∧ acceleratedOrbit 11 913 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_913 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 913) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_913.1, data_11_913.2] + +/-- Complete interval computation for depth 11, residue 914. -/ +theorem bounds_11_914 : exactInterval 11 914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_914 (m : Nat) : + stoppingTime (2 ^ 11 * m + 914) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_914 : oddCount 914 11 = 5 ∧ acceleratedOrbit 11 914 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_914 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 914) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_914.1, data_11_914.2] + +/-- Complete interval computation for depth 11, residue 915. -/ +theorem bounds_11_915 : exactInterval 11 915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_915 (m : Nat) : + stoppingTime (2 ^ 11 * m + 915) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_915 : oddCount 915 11 = 5 ∧ acceleratedOrbit 11 915 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_915 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 915) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_915.1, data_11_915.2] + +/-- Complete interval computation for depth 11, residue 916. -/ +theorem bounds_11_916 : exactInterval 11 916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_916 (m : Nat) : + stoppingTime (2 ^ 11 * m + 916) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_916 : oddCount 916 11 = 4 ∧ acceleratedOrbit 11 916 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_916 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 916) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_916.1, data_11_916.2] + +/-- Complete interval computation for depth 11, residue 917. -/ +theorem bounds_11_917 : exactInterval 11 917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_917 (m : Nat) : + stoppingTime (2 ^ 11 * m + 917) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_917 : oddCount 917 11 = 4 ∧ acceleratedOrbit 11 917 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_917 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 917) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_917.1, data_11_917.2] + +/-- Complete interval computation for depth 11, residue 918. -/ +theorem bounds_11_918 : exactInterval 11 918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_918 (m : Nat) : + stoppingTime (2 ^ 11 * m + 918) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_918 : oddCount 918 11 = 5 ∧ acceleratedOrbit 11 918 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_918 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 918) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_918.1, data_11_918.2] + +/-- Complete interval computation for depth 11, residue 919. -/ +theorem bounds_11_919 : exactInterval 11 919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_919 (m : Nat) : + stoppingTime (2 ^ 11 * m + 919) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_919 : oddCount 919 11 = 5 ∧ acceleratedOrbit 11 919 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_919 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 919) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_919.1, data_11_919.2] + +/-- Complete interval computation for depth 11, residue 920. -/ +theorem bounds_11_920 : exactInterval 11 920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_920 (m : Nat) : + stoppingTime (2 ^ 11 * m + 920) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_920 : oddCount 920 11 = 4 ∧ acceleratedOrbit 11 920 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_920 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 920) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_920.1, data_11_920.2] + +/-- Complete interval computation for depth 11, residue 921. -/ +theorem bounds_11_921 : exactInterval 11 921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_921 (m : Nat) : + stoppingTime (2 ^ 11 * m + 921) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_921 : oddCount 921 11 = 5 ∧ acceleratedOrbit 11 921 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_921 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 921) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_921.1, data_11_921.2] + +/-- Complete interval computation for depth 11, residue 922. -/ +theorem bounds_11_922 : exactInterval 11 922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_922 (m : Nat) : + stoppingTime (2 ^ 11 * m + 922) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_922 : oddCount 922 11 = 4 ∧ acceleratedOrbit 11 922 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_922 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 922) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_922.1, data_11_922.2] + +/-- Complete interval computation for depth 11, residue 923. -/ +theorem bounds_11_923 : exactInterval 11 923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_923 (m : Nat) : + stoppingTime (2 ^ 11 * m + 923) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_923 : oddCount 923 11 = 6 ∧ acceleratedOrbit 11 923 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_923 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 923) = 3 ^ 6 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_923.1, data_11_923.2] + +/-- Complete interval computation for depth 11, residue 924. -/ +theorem bounds_11_924 : exactInterval 11 924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_924 (m : Nat) : + stoppingTime (2 ^ 11 * m + 924) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_924 : oddCount 924 11 = 7 ∧ acceleratedOrbit 11 924 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_924 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 924) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_924.1, data_11_924.2] + +/-- Complete interval computation for depth 11, residue 925. -/ +theorem bounds_11_925 : exactInterval 11 925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_925 (m : Nat) : + stoppingTime (2 ^ 11 * m + 925) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_925 : oddCount 925 11 = 7 ∧ acceleratedOrbit 11 925 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_925 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 925) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_925.1, data_11_925.2] + +end Collatz.Research.StoppingAtlas.Batch0127 From 47b12dd55d68bf8fd8eff262a95e892faffa6f44 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:40 +0530 Subject: [PATCH 0128/1001] proof: certify atlas Batch0128 (11:926 to 11:941) --- Collatz/Research/StoppingAtlas/Batch0128.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0128.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0128.lean b/Collatz/Research/StoppingAtlas/Batch0128.lean new file mode 100644 index 00000000..d9383f08 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0128.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0128 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 926. -/ +theorem bounds_11_926 : exactInterval 11 926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_926 (m : Nat) : + stoppingTime (2 ^ 11 * m + 926) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_926 : oddCount 926 11 = 7 ∧ acceleratedOrbit 11 926 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_926 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 926) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_926.1, data_11_926.2] + +/-- Complete interval computation for depth 11, residue 927. -/ +theorem bounds_11_927 : exactInterval 11 927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_927 (m : Nat) : + stoppingTime (2 ^ 11 * m + 927) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_927 : oddCount 927 11 = 7 ∧ acceleratedOrbit 11 927 = 991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_927 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 927) = 3 ^ 7 * m + 991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_927.1, data_11_927.2] + +/-- Complete interval computation for depth 11, residue 928. -/ +theorem bounds_11_928 : exactInterval 11 928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_928 (m : Nat) : + stoppingTime (2 ^ 11 * m + 928) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_928 : oddCount 928 11 = 3 ∧ acceleratedOrbit 11 928 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_928 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 928) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_928.1, data_11_928.2] + +/-- Complete interval computation for depth 11, residue 929. -/ +theorem bounds_11_929 : exactInterval 11 929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_929 (m : Nat) : + stoppingTime (2 ^ 11 * m + 929) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_929 : oddCount 929 11 = 6 ∧ acceleratedOrbit 11 929 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_929 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 929) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_929.1, data_11_929.2] + +/-- Complete interval computation for depth 11, residue 930. -/ +theorem bounds_11_930 : exactInterval 11 930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_930 (m : Nat) : + stoppingTime (2 ^ 11 * m + 930) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_930 : oddCount 930 11 = 4 ∧ acceleratedOrbit 11 930 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_930 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 930) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_930.1, data_11_930.2] + +/-- Complete interval computation for depth 11, residue 931. -/ +theorem bounds_11_931 : exactInterval 11 931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_931 (m : Nat) : + stoppingTime (2 ^ 11 * m + 931) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_931 : oddCount 931 11 = 4 ∧ acceleratedOrbit 11 931 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_931 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 931) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_931.1, data_11_931.2] + +/-- Complete interval computation for depth 11, residue 932. -/ +theorem bounds_11_932 : exactInterval 11 932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_932 (m : Nat) : + stoppingTime (2 ^ 11 * m + 932) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_932 : oddCount 932 11 = 6 ∧ acceleratedOrbit 11 932 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_932 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 932) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_932.1, data_11_932.2] + +/-- Complete interval computation for depth 11, residue 933. -/ +theorem bounds_11_933 : exactInterval 11 933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_933 (m : Nat) : + stoppingTime (2 ^ 11 * m + 933) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_933 : oddCount 933 11 = 6 ∧ acceleratedOrbit 11 933 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_933 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 933) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_933.1, data_11_933.2] + +/-- Complete interval computation for depth 11, residue 934. -/ +theorem bounds_11_934 : exactInterval 11 934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_934 (m : Nat) : + stoppingTime (2 ^ 11 * m + 934) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_934 : oddCount 934 11 = 6 ∧ acceleratedOrbit 11 934 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_934 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 934) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_934.1, data_11_934.2] + +/-- Complete interval computation for depth 11, residue 935. -/ +theorem bounds_11_935 : exactInterval 11 935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_935 (m : Nat) : + stoppingTime (2 ^ 11 * m + 935) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_935 : oddCount 935 11 = 7 ∧ acceleratedOrbit 11 935 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_935 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 935) = 3 ^ 7 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_935.1, data_11_935.2] + +/-- Complete interval computation for depth 11, residue 936. -/ +theorem bounds_11_936 : exactInterval 11 936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_936 (m : Nat) : + stoppingTime (2 ^ 11 * m + 936) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_936 : oddCount 936 11 = 3 ∧ acceleratedOrbit 11 936 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_936 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 936) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_936.1, data_11_936.2] + +/-- Complete interval computation for depth 11, residue 937. -/ +theorem bounds_11_937 : exactInterval 11 937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_937 (m : Nat) : + stoppingTime (2 ^ 11 * m + 937) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_937 : oddCount 937 11 = 8 ∧ acceleratedOrbit 11 937 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_937 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 937) = 3 ^ 8 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_937.1, data_11_937.2] + +/-- Complete interval computation for depth 11, residue 938. -/ +theorem bounds_11_938 : exactInterval 11 938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_938 (m : Nat) : + stoppingTime (2 ^ 11 * m + 938) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_938 : oddCount 938 11 = 3 ∧ acceleratedOrbit 11 938 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_938 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 938) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_938.1, data_11_938.2] + +/-- Complete interval computation for depth 11, residue 939. -/ +theorem bounds_11_939 : exactInterval 11 939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_939 (m : Nat) : + stoppingTime (2 ^ 11 * m + 939) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_939 : oddCount 939 11 = 6 ∧ acceleratedOrbit 11 939 = 335 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_939 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 939) = 3 ^ 6 * m + 335 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_939.1, data_11_939.2] + +/-- Complete interval computation for depth 11, residue 940. -/ +theorem bounds_11_940 : exactInterval 11 940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_940 (m : Nat) : + stoppingTime (2 ^ 11 * m + 940) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_940 : oddCount 940 11 = 6 ∧ acceleratedOrbit 11 940 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_940 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 940) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_940.1, data_11_940.2] + +/-- Complete interval computation for depth 11, residue 941. -/ +theorem bounds_11_941 : exactInterval 11 941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_941 (m : Nat) : + stoppingTime (2 ^ 11 * m + 941) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_941 : oddCount 941 11 = 6 ∧ acceleratedOrbit 11 941 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_941 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 941) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_941.1, data_11_941.2] + +end Collatz.Research.StoppingAtlas.Batch0128 From 5ac36450674c22c8a418a2907bcc30e2723f1034 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:40 +0530 Subject: [PATCH 0129/1001] proof: certify atlas Batch0129 (11:942 to 11:956) --- Collatz/Research/StoppingAtlas/Batch0129.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0129.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0129.lean b/Collatz/Research/StoppingAtlas/Batch0129.lean new file mode 100644 index 00000000..df6b4e08 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0129.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0129 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 942. -/ +theorem bounds_11_942 : exactInterval 11 942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_942 (m : Nat) : + stoppingTime (2 ^ 11 * m + 942) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_942 : oddCount 942 11 = 6 ∧ acceleratedOrbit 11 942 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_942 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 942) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_942.1, data_11_942.2] + +/-- Complete interval computation for depth 11, residue 943. -/ +theorem bounds_11_943 : exactInterval 11 943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_943 (m : Nat) : + stoppingTime (2 ^ 11 * m + 943) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_943 : oddCount 943 11 = 5 ∧ acceleratedOrbit 11 943 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_943 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 943) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_943.1, data_11_943.2] + +/-- Complete interval computation for depth 11, residue 944. -/ +theorem bounds_11_944 : exactInterval 11 944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_944 (m : Nat) : + stoppingTime (2 ^ 11 * m + 944) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_944 : oddCount 944 11 = 4 ∧ acceleratedOrbit 11 944 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_944 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 944) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_944.1, data_11_944.2] + +/-- Complete interval computation for depth 11, residue 945. -/ +theorem bounds_11_945 : exactInterval 11 945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_945 (m : Nat) : + stoppingTime (2 ^ 11 * m + 945) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_945 : oddCount 945 11 = 4 ∧ acceleratedOrbit 11 945 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_945 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 945) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_945.1, data_11_945.2] + +/-- Complete interval computation for depth 11, residue 946. -/ +theorem bounds_11_946 : exactInterval 11 946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_946 (m : Nat) : + stoppingTime (2 ^ 11 * m + 946) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_946 : oddCount 946 11 = 4 ∧ acceleratedOrbit 11 946 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_946 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 946) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_946.1, data_11_946.2] + +/-- Complete interval computation for depth 11, residue 947. -/ +theorem bounds_11_947 : exactInterval 11 947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_947 (m : Nat) : + stoppingTime (2 ^ 11 * m + 947) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_947 : oddCount 947 11 = 4 ∧ acceleratedOrbit 11 947 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_947 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 947) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_947.1, data_11_947.2] + +/-- Complete interval computation for depth 11, residue 948. -/ +theorem bounds_11_948 : exactInterval 11 948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_948 (m : Nat) : + stoppingTime (2 ^ 11 * m + 948) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_948 : oddCount 948 11 = 4 ∧ acceleratedOrbit 11 948 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_948 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 948) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_948.1, data_11_948.2] + +/-- Complete interval computation for depth 11, residue 949. -/ +theorem bounds_11_949 : exactInterval 11 949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_949 (m : Nat) : + stoppingTime (2 ^ 11 * m + 949) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_949 : oddCount 949 11 = 4 ∧ acceleratedOrbit 11 949 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_949 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 949) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_949.1, data_11_949.2] + +/-- Complete interval computation for depth 11, residue 950. -/ +theorem bounds_11_950 : exactInterval 11 950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_950 (m : Nat) : + stoppingTime (2 ^ 11 * m + 950) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_950 : oddCount 950 11 = 5 ∧ acceleratedOrbit 11 950 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_950 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 950) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_950.1, data_11_950.2] + +/-- Complete interval computation for depth 11, residue 951. -/ +theorem bounds_11_951 : exactInterval 11 951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_951 (m : Nat) : + stoppingTime (2 ^ 11 * m + 951) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_951 : oddCount 951 11 = 5 ∧ acceleratedOrbit 11 951 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_951 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 951) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_951.1, data_11_951.2] + +/-- Complete interval computation for depth 11, residue 952. -/ +theorem bounds_11_952 : exactInterval 11 952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_952 (m : Nat) : + stoppingTime (2 ^ 11 * m + 952) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_952 : oddCount 952 11 = 4 ∧ acceleratedOrbit 11 952 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_952 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 952) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_952.1, data_11_952.2] + +/-- Complete interval computation for depth 11, residue 953. -/ +theorem bounds_11_953 : exactInterval 11 953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_953 (m : Nat) : + stoppingTime (2 ^ 11 * m + 953) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_953 : oddCount 953 11 = 6 ∧ acceleratedOrbit 11 953 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_953 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 953) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_953.1, data_11_953.2] + +/-- Complete interval computation for depth 11, residue 954. -/ +theorem bounds_11_954 : exactInterval 11 954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_954 (m : Nat) : + stoppingTime (2 ^ 11 * m + 954) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_954 : oddCount 954 11 = 4 ∧ acceleratedOrbit 11 954 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_954 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 954) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_954.1, data_11_954.2] + +/-- Complete interval computation for depth 11, residue 955. -/ +theorem bounds_11_955 : exactInterval 11 955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_955 (m : Nat) : + stoppingTime (2 ^ 11 * m + 955) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_955 : oddCount 955 11 = 6 ∧ acceleratedOrbit 11 955 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_955 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 955) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_955.1, data_11_955.2] + +/-- Complete interval computation for depth 11, residue 956. -/ +theorem bounds_11_956 : exactInterval 11 956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_956 (m : Nat) : + stoppingTime (2 ^ 11 * m + 956) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_956 : oddCount 956 11 = 8 ∧ acceleratedOrbit 11 956 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_956 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 956) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_956.1, data_11_956.2] + +end Collatz.Research.StoppingAtlas.Batch0129 From 395a6ae7c066ed73938387989c22d31d0e42b1e6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:40 +0530 Subject: [PATCH 0130/1001] proof: certify atlas Batch0130 (11:957 to 11:971) --- Collatz/Research/StoppingAtlas/Batch0130.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0130.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0130.lean b/Collatz/Research/StoppingAtlas/Batch0130.lean new file mode 100644 index 00000000..c9e6e5f9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0130.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0130 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 957. -/ +theorem bounds_11_957 : exactInterval 11 957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_957 (m : Nat) : + stoppingTime (2 ^ 11 * m + 957) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_957 : oddCount 957 11 = 8 ∧ acceleratedOrbit 11 957 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_957 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 957) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_957.1, data_11_957.2] + +/-- Complete interval computation for depth 11, residue 958. -/ +theorem bounds_11_958 : exactInterval 11 958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_958 (m : Nat) : + stoppingTime (2 ^ 11 * m + 958) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_958 : oddCount 958 11 = 8 ∧ acceleratedOrbit 11 958 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_958 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 958) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_958.1, data_11_958.2] + +/-- Complete interval computation for depth 11, residue 959. -/ +theorem bounds_11_959 : exactInterval 11 959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_959 (m : Nat) : + stoppingTime (2 ^ 11 * m + 959) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_959 : oddCount 959 11 = 9 ∧ acceleratedOrbit 11 959 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_959 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 959) = 3 ^ 9 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_959.1, data_11_959.2] + +/-- Complete interval computation for depth 11, residue 960. -/ +theorem bounds_11_960 : exactInterval 11 960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_960 (m : Nat) : + stoppingTime (2 ^ 11 * m + 960) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_960 : oddCount 960 11 = 4 ∧ acceleratedOrbit 11 960 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_960 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 960) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_960.1, data_11_960.2] + +/-- Complete interval computation for depth 11, residue 961. -/ +theorem bounds_11_961 : exactInterval 11 961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_961 (m : Nat) : + stoppingTime (2 ^ 11 * m + 961) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_961 : oddCount 961 11 = 6 ∧ acceleratedOrbit 11 961 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_961 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 961) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_961.1, data_11_961.2] + +/-- Complete interval computation for depth 11, residue 962. -/ +theorem bounds_11_962 : exactInterval 11 962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_962 (m : Nat) : + stoppingTime (2 ^ 11 * m + 962) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_962 : oddCount 962 11 = 6 ∧ acceleratedOrbit 11 962 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_962 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 962) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_962.1, data_11_962.2] + +/-- Complete interval computation for depth 11, residue 963. -/ +theorem bounds_11_963 : exactInterval 11 963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_963 (m : Nat) : + stoppingTime (2 ^ 11 * m + 963) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_963 : oddCount 963 11 = 6 ∧ acceleratedOrbit 11 963 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_963 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 963) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_963.1, data_11_963.2] + +/-- Complete interval computation for depth 11, residue 964. -/ +theorem bounds_11_964 : exactInterval 11 964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_964 (m : Nat) : + stoppingTime (2 ^ 11 * m + 964) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_964 : oddCount 964 11 = 3 ∧ acceleratedOrbit 11 964 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_964 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 964) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_964.1, data_11_964.2] + +/-- Complete interval computation for depth 11, residue 965. -/ +theorem bounds_11_965 : exactInterval 11 965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_965 (m : Nat) : + stoppingTime (2 ^ 11 * m + 965) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_965 : oddCount 965 11 = 3 ∧ acceleratedOrbit 11 965 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_965 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 965) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_965.1, data_11_965.2] + +/-- Complete interval computation for depth 11, residue 966. -/ +theorem bounds_11_966 : exactInterval 11 966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_966 (m : Nat) : + stoppingTime (2 ^ 11 * m + 966) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_966 : oddCount 966 11 = 3 ∧ acceleratedOrbit 11 966 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_966 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 966) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_966.1, data_11_966.2] + +/-- Complete interval computation for depth 11, residue 967. -/ +theorem bounds_11_967 : exactInterval 11 967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_967 (m : Nat) : + stoppingTime (2 ^ 11 * m + 967) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_967 : oddCount 967 11 = 8 ∧ acceleratedOrbit 11 967 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_967 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 967) = 3 ^ 8 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_967.1, data_11_967.2] + +/-- Complete interval computation for depth 11, residue 968. -/ +theorem bounds_11_968 : exactInterval 11 968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_968 (m : Nat) : + stoppingTime (2 ^ 11 * m + 968) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_968 : oddCount 968 11 = 6 ∧ acceleratedOrbit 11 968 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_968 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 968) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_968.1, data_11_968.2] + +/-- Complete interval computation for depth 11, residue 969. -/ +theorem bounds_11_969 : exactInterval 11 969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_969 (m : Nat) : + stoppingTime (2 ^ 11 * m + 969) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_969 : oddCount 969 11 = 6 ∧ acceleratedOrbit 11 969 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_969 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 969) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_969.1, data_11_969.2] + +/-- Complete interval computation for depth 11, residue 970. -/ +theorem bounds_11_970 : exactInterval 11 970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_970 (m : Nat) : + stoppingTime (2 ^ 11 * m + 970) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_970 : oddCount 970 11 = 6 ∧ acceleratedOrbit 11 970 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_970 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 970) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_970.1, data_11_970.2] + +/-- Complete interval computation for depth 11, residue 971. -/ +theorem bounds_11_971 : exactInterval 11 971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_971 (m : Nat) : + stoppingTime (2 ^ 11 * m + 971) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_971 : oddCount 971 11 = 5 ∧ acceleratedOrbit 11 971 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_971 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 971) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_971.1, data_11_971.2] + +end Collatz.Research.StoppingAtlas.Batch0130 From 4a69ec4e3728e20b50ae5112360f1645a193508e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:41 +0530 Subject: [PATCH 0131/1001] proof: certify atlas Batch0131 (11:972 to 11:987) --- Collatz/Research/StoppingAtlas/Batch0131.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0131.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0131.lean b/Collatz/Research/StoppingAtlas/Batch0131.lean new file mode 100644 index 00000000..077efc80 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0131.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0131 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 972. -/ +theorem bounds_11_972 : exactInterval 11 972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_972 (m : Nat) : + stoppingTime (2 ^ 11 * m + 972) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_972 : oddCount 972 11 = 6 ∧ acceleratedOrbit 11 972 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_972 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 972) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_972.1, data_11_972.2] + +/-- Complete interval computation for depth 11, residue 973. -/ +theorem bounds_11_973 : exactInterval 11 973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_973 (m : Nat) : + stoppingTime (2 ^ 11 * m + 973) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_973 : oddCount 973 11 = 6 ∧ acceleratedOrbit 11 973 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_973 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 973) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_973.1, data_11_973.2] + +/-- Complete interval computation for depth 11, residue 974. -/ +theorem bounds_11_974 : exactInterval 11 974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_974 (m : Nat) : + stoppingTime (2 ^ 11 * m + 974) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_974 : oddCount 974 11 = 7 ∧ acceleratedOrbit 11 974 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_974 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 974) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_974.1, data_11_974.2] + +/-- Complete interval computation for depth 11, residue 975. -/ +theorem bounds_11_975 : exactInterval 11 975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_975 (m : Nat) : + stoppingTime (2 ^ 11 * m + 975) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_975 : oddCount 975 11 = 7 ∧ acceleratedOrbit 11 975 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_975 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 975) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_975.1, data_11_975.2] + +/-- Complete interval computation for depth 11, residue 976. -/ +theorem bounds_11_976 : exactInterval 11 976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_976 (m : Nat) : + stoppingTime (2 ^ 11 * m + 976) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_976 : oddCount 976 11 = 4 ∧ acceleratedOrbit 11 976 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_976 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 976) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_976.1, data_11_976.2] + +/-- Complete interval computation for depth 11, residue 977. -/ +theorem bounds_11_977 : exactInterval 11 977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_977 (m : Nat) : + stoppingTime (2 ^ 11 * m + 977) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_977 : oddCount 977 11 = 6 ∧ acceleratedOrbit 11 977 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_977 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 977) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_977.1, data_11_977.2] + +/-- Complete interval computation for depth 11, residue 978. -/ +theorem bounds_11_978 : exactInterval 11 978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_978 (m : Nat) : + stoppingTime (2 ^ 11 * m + 978) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_978 : oddCount 978 11 = 7 ∧ acceleratedOrbit 11 978 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_978 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 978) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_978.1, data_11_978.2] + +/-- Complete interval computation for depth 11, residue 979. -/ +theorem bounds_11_979 : exactInterval 11 979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_979 (m : Nat) : + stoppingTime (2 ^ 11 * m + 979) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_979 : oddCount 979 11 = 7 ∧ acceleratedOrbit 11 979 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_979 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 979) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_979.1, data_11_979.2] + +/-- Complete interval computation for depth 11, residue 980. -/ +theorem bounds_11_980 : exactInterval 11 980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_980 (m : Nat) : + stoppingTime (2 ^ 11 * m + 980) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_980 : oddCount 980 11 = 4 ∧ acceleratedOrbit 11 980 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_980 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 980) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_980.1, data_11_980.2] + +/-- Complete interval computation for depth 11, residue 981. -/ +theorem bounds_11_981 : exactInterval 11 981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_981 (m : Nat) : + stoppingTime (2 ^ 11 * m + 981) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_981 : oddCount 981 11 = 4 ∧ acceleratedOrbit 11 981 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_981 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 981) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_981.1, data_11_981.2] + +/-- Complete interval computation for depth 11, residue 982. -/ +theorem bounds_11_982 : exactInterval 11 982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_982 (m : Nat) : + stoppingTime (2 ^ 11 * m + 982) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_982 : oddCount 982 11 = 8 ∧ acceleratedOrbit 11 982 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_982 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 982) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_982.1, data_11_982.2] + +/-- Complete interval computation for depth 11, residue 983. -/ +theorem bounds_11_983 : exactInterval 11 983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_983 (m : Nat) : + stoppingTime (2 ^ 11 * m + 983) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_983 : oddCount 983 11 = 8 ∧ acceleratedOrbit 11 983 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_983 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 983) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_983.1, data_11_983.2] + +/-- Complete interval computation for depth 11, residue 984. -/ +theorem bounds_11_984 : exactInterval 11 984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_984 (m : Nat) : + stoppingTime (2 ^ 11 * m + 984) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_984 : oddCount 984 11 = 5 ∧ acceleratedOrbit 11 984 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_984 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 984) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_984.1, data_11_984.2] + +/-- Complete interval computation for depth 11, residue 985. -/ +theorem bounds_11_985 : exactInterval 11 985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_985 (m : Nat) : + stoppingTime (2 ^ 11 * m + 985) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_985 : oddCount 985 11 = 3 ∧ acceleratedOrbit 11 985 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_985 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 985) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_985.1, data_11_985.2] + +/-- Complete interval computation for depth 11, residue 986. -/ +theorem bounds_11_986 : exactInterval 11 986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_986 (m : Nat) : + stoppingTime (2 ^ 11 * m + 986) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_986 : oddCount 986 11 = 5 ∧ acceleratedOrbit 11 986 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_986 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 986) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_986.1, data_11_986.2] + +/-- Complete interval computation for depth 11, residue 987. -/ +theorem bounds_11_987 : exactInterval 11 987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_987 (m : Nat) : + stoppingTime (2 ^ 11 * m + 987) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_987 : oddCount 987 11 = 6 ∧ acceleratedOrbit 11 987 = 352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_987 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 987) = 3 ^ 6 * m + 352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_987.1, data_11_987.2] + +end Collatz.Research.StoppingAtlas.Batch0131 From 439174d1815fcdb3182f4909db5e7419c93cb2fd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:41 +0530 Subject: [PATCH 0132/1001] proof: certify atlas Batch0132 (11:988 to 11:1002) --- Collatz/Research/StoppingAtlas/Batch0132.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0132.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0132.lean b/Collatz/Research/StoppingAtlas/Batch0132.lean new file mode 100644 index 00000000..3c6ef9f7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0132.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0132 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 988. -/ +theorem bounds_11_988 : exactInterval 11 988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_988 (m : Nat) : + stoppingTime (2 ^ 11 * m + 988) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_988 : oddCount 988 11 = 5 ∧ acceleratedOrbit 11 988 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_988 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 988) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_988.1, data_11_988.2] + +/-- Complete interval computation for depth 11, residue 989. -/ +theorem bounds_11_989 : exactInterval 11 989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_989 (m : Nat) : + stoppingTime (2 ^ 11 * m + 989) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_989 : oddCount 989 11 = 5 ∧ acceleratedOrbit 11 989 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_989 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 989) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_989.1, data_11_989.2] + +/-- Complete interval computation for depth 11, residue 990. -/ +theorem bounds_11_990 : exactInterval 11 990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_990 (m : Nat) : + stoppingTime (2 ^ 11 * m + 990) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_990 : oddCount 990 11 = 8 ∧ acceleratedOrbit 11 990 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_990 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 990) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_990.1, data_11_990.2] + +/-- Complete interval computation for depth 11, residue 991. -/ +theorem bounds_11_991 : exactInterval 11 991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_991 (m : Nat) : + stoppingTime (2 ^ 11 * m + 991) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_991 : oddCount 991 11 = 8 ∧ acceleratedOrbit 11 991 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_991 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 991) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_991.1, data_11_991.2] + +/-- Complete interval computation for depth 11, residue 992. -/ +theorem bounds_11_992 : exactInterval 11 992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_992 (m : Nat) : + stoppingTime (2 ^ 11 * m + 992) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_992 : oddCount 992 11 = 5 ∧ acceleratedOrbit 11 992 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_992 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 992) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_992.1, data_11_992.2] + +/-- Complete interval computation for depth 11, residue 993. -/ +theorem bounds_11_993 : exactInterval 11 993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_993 (m : Nat) : + stoppingTime (2 ^ 11 * m + 993) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_993 : oddCount 993 11 = 7 ∧ acceleratedOrbit 11 993 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_993 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 993) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_993.1, data_11_993.2] + +/-- Complete interval computation for depth 11, residue 994. -/ +theorem bounds_11_994 : exactInterval 11 994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_994 (m : Nat) : + stoppingTime (2 ^ 11 * m + 994) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_994 : oddCount 994 11 = 4 ∧ acceleratedOrbit 11 994 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_994 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 994) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_994.1, data_11_994.2] + +/-- Complete interval computation for depth 11, residue 995. -/ +theorem bounds_11_995 : exactInterval 11 995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_995 (m : Nat) : + stoppingTime (2 ^ 11 * m + 995) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_995 : oddCount 995 11 = 4 ∧ acceleratedOrbit 11 995 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_995 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 995) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_995.1, data_11_995.2] + +/-- Complete interval computation for depth 11, residue 996. -/ +theorem bounds_11_996 : exactInterval 11 996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_996 (m : Nat) : + stoppingTime (2 ^ 11 * m + 996) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_996 : oddCount 996 11 = 5 ∧ acceleratedOrbit 11 996 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_996 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 996) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_996.1, data_11_996.2] + +/-- Complete interval computation for depth 11, residue 997. -/ +theorem bounds_11_997 : exactInterval 11 997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_997 (m : Nat) : + stoppingTime (2 ^ 11 * m + 997) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_997 : oddCount 997 11 = 5 ∧ acceleratedOrbit 11 997 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_997 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 997) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_997.1, data_11_997.2] + +/-- Complete interval computation for depth 11, residue 998. -/ +theorem bounds_11_998 : exactInterval 11 998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_998 (m : Nat) : + stoppingTime (2 ^ 11 * m + 998) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_998 : oddCount 998 11 = 5 ∧ acceleratedOrbit 11 998 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_998 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 998) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_998.1, data_11_998.2] + +/-- Complete interval computation for depth 11, residue 999. -/ +theorem bounds_11_999 : exactInterval 11 999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_999 (m : Nat) : + stoppingTime (2 ^ 11 * m + 999) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_999 : oddCount 999 11 = 6 ∧ acceleratedOrbit 11 999 = 356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_999 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 999) = 3 ^ 6 * m + 356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_999.1, data_11_999.2] + +/-- Complete interval computation for depth 11, residue 1000. -/ +theorem bounds_11_1000 : exactInterval 11 1000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1000 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1000) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1000 : oddCount 1000 11 = 5 ∧ acceleratedOrbit 11 1000 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1000 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1000) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1000.1, data_11_1000.2] + +/-- Complete interval computation for depth 11, residue 1001. -/ +theorem bounds_11_1001 : exactInterval 11 1001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1001 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1001) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1001 : oddCount 1001 11 = 9 ∧ acceleratedOrbit 11 1001 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1001 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1001) = 3 ^ 9 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1001.1, data_11_1001.2] + +/-- Complete interval computation for depth 11, residue 1002. -/ +theorem bounds_11_1002 : exactInterval 11 1002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1002 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1002) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1002 : oddCount 1002 11 = 5 ∧ acceleratedOrbit 11 1002 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1002 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1002) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1002.1, data_11_1002.2] + +end Collatz.Research.StoppingAtlas.Batch0132 From d44d64fc6237cc54fec6ae41391f06ee50296468 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:41 +0530 Subject: [PATCH 0133/1001] proof: certify atlas Batch0133 (11:1003 to 11:1017) --- Collatz/Research/StoppingAtlas/Batch0133.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0133.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0133.lean b/Collatz/Research/StoppingAtlas/Batch0133.lean new file mode 100644 index 00000000..0b09713c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0133.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0133 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1003. -/ +theorem bounds_11_1003 : exactInterval 11 1003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1003 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1003) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1003 : oddCount 1003 11 = 7 ∧ acceleratedOrbit 11 1003 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1003 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1003) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1003.1, data_11_1003.2] + +/-- Complete interval computation for depth 11, residue 1004. -/ +theorem bounds_11_1004 : exactInterval 11 1004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1004 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1004) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1004 : oddCount 1004 11 = 7 ∧ acceleratedOrbit 11 1004 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1004 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1004) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1004.1, data_11_1004.2] + +/-- Complete interval computation for depth 11, residue 1005. -/ +theorem bounds_11_1005 : exactInterval 11 1005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1005 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1005) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1005 : oddCount 1005 11 = 7 ∧ acceleratedOrbit 11 1005 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1005 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1005) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1005.1, data_11_1005.2] + +/-- Complete interval computation for depth 11, residue 1006. -/ +theorem bounds_11_1006 : exactInterval 11 1006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1006 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1006) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1006 : oddCount 1006 11 = 7 ∧ acceleratedOrbit 11 1006 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1006 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1006) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1006.1, data_11_1006.2] + +/-- Complete interval computation for depth 11, residue 1007. -/ +theorem bounds_11_1007 : exactInterval 11 1007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1007 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1007) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1007 : oddCount 1007 11 = 8 ∧ acceleratedOrbit 11 1007 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1007 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1007) = 3 ^ 8 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1007.1, data_11_1007.2] + +/-- Complete interval computation for depth 11, residue 1008. -/ +theorem bounds_11_1008 : exactInterval 11 1008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1008 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1008) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1008 : oddCount 1008 11 = 6 ∧ acceleratedOrbit 11 1008 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1008 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1008) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1008.1, data_11_1008.2] + +/-- Complete interval computation for depth 11, residue 1009. -/ +theorem bounds_11_1009 : exactInterval 11 1009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1009 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1009) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1009 : oddCount 1009 11 = 5 ∧ acceleratedOrbit 11 1009 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1009 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1009) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1009.1, data_11_1009.2] + +/-- Complete interval computation for depth 11, residue 1010. -/ +theorem bounds_11_1010 : exactInterval 11 1010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1010 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1010) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1010 : oddCount 1010 11 = 6 ∧ acceleratedOrbit 11 1010 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1010 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1010) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1010.1, data_11_1010.2] + +/-- Complete interval computation for depth 11, residue 1011. -/ +theorem bounds_11_1011 : exactInterval 11 1011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1011 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1011) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1011 : oddCount 1011 11 = 6 ∧ acceleratedOrbit 11 1011 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1011 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1011) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1011.1, data_11_1011.2] + +/-- Complete interval computation for depth 11, residue 1012. -/ +theorem bounds_11_1012 : exactInterval 11 1012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1012 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1012) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1012 : oddCount 1012 11 = 6 ∧ acceleratedOrbit 11 1012 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1012 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1012) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1012.1, data_11_1012.2] + +/-- Complete interval computation for depth 11, residue 1013. -/ +theorem bounds_11_1013 : exactInterval 11 1013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1013 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1013) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1013 : oddCount 1013 11 = 6 ∧ acceleratedOrbit 11 1013 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1013 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1013) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1013.1, data_11_1013.2] + +/-- Complete interval computation for depth 11, residue 1014. -/ +theorem bounds_11_1014 : exactInterval 11 1014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1014 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1014) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1014 : oddCount 1014 11 = 6 ∧ acceleratedOrbit 11 1014 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1014 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1014) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1014.1, data_11_1014.2] + +/-- Complete interval computation for depth 11, residue 1015. -/ +theorem bounds_11_1015 : exactInterval 11 1015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1015 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1015) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1015 : oddCount 1015 11 = 6 ∧ acceleratedOrbit 11 1015 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1015 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1015) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1015.1, data_11_1015.2] + +/-- Complete interval computation for depth 11, residue 1016. -/ +theorem bounds_11_1016 : exactInterval 11 1016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1016 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1016) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1016 : oddCount 1016 11 = 7 ∧ acceleratedOrbit 11 1016 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1016 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1016) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1016.1, data_11_1016.2] + +/-- Complete interval computation for depth 11, residue 1017. -/ +theorem bounds_11_1017 : exactInterval 11 1017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1017 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1017) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1017 : oddCount 1017 11 = 8 ∧ acceleratedOrbit 11 1017 = 3266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1017 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1017) = 3 ^ 8 * m + 3266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1017.1, data_11_1017.2] + +end Collatz.Research.StoppingAtlas.Batch0133 From 39e60a22b4c3b0556c737636439bc65ed4385c65 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:42 +0530 Subject: [PATCH 0134/1001] proof: certify atlas Batch0134 (11:1018 to 11:1033) --- Collatz/Research/StoppingAtlas/Batch0134.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0134.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0134.lean b/Collatz/Research/StoppingAtlas/Batch0134.lean new file mode 100644 index 00000000..16b40ceb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0134.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0134 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1018. -/ +theorem bounds_11_1018 : exactInterval 11 1018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1018 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1018) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1018 : oddCount 1018 11 = 7 ∧ acceleratedOrbit 11 1018 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1018 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1018) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1018.1, data_11_1018.2] + +/-- Complete interval computation for depth 11, residue 1019. -/ +theorem bounds_11_1019 : exactInterval 11 1019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1019 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1019) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1019 : oddCount 1019 11 = 7 ∧ acceleratedOrbit 11 1019 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1019 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1019) = 3 ^ 7 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1019.1, data_11_1019.2] + +/-- Complete interval computation for depth 11, residue 1020. -/ +theorem bounds_11_1020 : exactInterval 11 1020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1020 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1020) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1020 : oddCount 1020 11 = 8 ∧ acceleratedOrbit 11 1020 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1020 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1020) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1020.1, data_11_1020.2] + +/-- Complete interval computation for depth 11, residue 1021. -/ +theorem bounds_11_1021 : exactInterval 11 1021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1021 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1021) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1021 : oddCount 1021 11 = 8 ∧ acceleratedOrbit 11 1021 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1021 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1021) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1021.1, data_11_1021.2] + +/-- Complete interval computation for depth 11, residue 1022. -/ +theorem bounds_11_1022 : exactInterval 11 1022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1022 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1022) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1022 : oddCount 1022 11 = 9 ∧ acceleratedOrbit 11 1022 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1022 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1022) = 3 ^ 9 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1022.1, data_11_1022.2] + +/-- Complete interval computation for depth 11, residue 1023. -/ +theorem bounds_11_1023 : exactInterval 11 1023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1023 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1023) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1023 : oddCount 1023 11 = 10 ∧ acceleratedOrbit 11 1023 = 29524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1023 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1023) = 3 ^ 10 * m + 29524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1023.1, data_11_1023.2] + +/-- Complete interval computation for depth 11, residue 1024. -/ +theorem bounds_11_1024 : exactInterval 11 1024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1024 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1024) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1024 : oddCount 1024 11 = 1 ∧ acceleratedOrbit 11 1024 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1024 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1024) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1024.1, data_11_1024.2] + +/-- Complete interval computation for depth 11, residue 1025. -/ +theorem bounds_11_1025 : exactInterval 11 1025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1025 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1025) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1025 : oddCount 1025 11 = 5 ∧ acceleratedOrbit 11 1025 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1025 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1025) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1025.1, data_11_1025.2] + +/-- Complete interval computation for depth 11, residue 1026. -/ +theorem bounds_11_1026 : exactInterval 11 1026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1026 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1026) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1026 : oddCount 1026 11 = 6 ∧ acceleratedOrbit 11 1026 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1026 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1026) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1026.1, data_11_1026.2] + +/-- Complete interval computation for depth 11, residue 1027. -/ +theorem bounds_11_1027 : exactInterval 11 1027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1027 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1027) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1027 : oddCount 1027 11 = 6 ∧ acceleratedOrbit 11 1027 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1027 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1027) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1027.1, data_11_1027.2] + +/-- Complete interval computation for depth 11, residue 1028. -/ +theorem bounds_11_1028 : exactInterval 11 1028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1028 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1028) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1028 : oddCount 1028 11 = 4 ∧ acceleratedOrbit 11 1028 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1028 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1028) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1028.1, data_11_1028.2] + +/-- Complete interval computation for depth 11, residue 1029. -/ +theorem bounds_11_1029 : exactInterval 11 1029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1029 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1029) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1029 : oddCount 1029 11 = 4 ∧ acceleratedOrbit 11 1029 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1029 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1029) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1029.1, data_11_1029.2] + +/-- Complete interval computation for depth 11, residue 1030. -/ +theorem bounds_11_1030 : exactInterval 11 1030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1030 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1030) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1030 : oddCount 1030 11 = 4 ∧ acceleratedOrbit 11 1030 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1030 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1030) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1030.1, data_11_1030.2] + +/-- Complete interval computation for depth 11, residue 1031. -/ +theorem bounds_11_1031 : exactInterval 11 1031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1031 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1031) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1031 : oddCount 1031 11 = 6 ∧ acceleratedOrbit 11 1031 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1031 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1031) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1031.1, data_11_1031.2] + +/-- Complete interval computation for depth 11, residue 1032. -/ +theorem bounds_11_1032 : exactInterval 11 1032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1032 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1032) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1032 : oddCount 1032 11 = 5 ∧ acceleratedOrbit 11 1032 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1032 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1032) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1032.1, data_11_1032.2] + +/-- Complete interval computation for depth 11, residue 1033. -/ +theorem bounds_11_1033 : exactInterval 11 1033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1033 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1033) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1033 : oddCount 1033 11 = 7 ∧ acceleratedOrbit 11 1033 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1033 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1033) = 3 ^ 7 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1033.1, data_11_1033.2] + +end Collatz.Research.StoppingAtlas.Batch0134 From 58cd9e7643d00721a46202f2db8aedbffc43a7f2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:42 +0530 Subject: [PATCH 0135/1001] proof: certify atlas Batch0135 (11:1034 to 11:1048) --- Collatz/Research/StoppingAtlas/Batch0135.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0135.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0135.lean b/Collatz/Research/StoppingAtlas/Batch0135.lean new file mode 100644 index 00000000..e3cf7ca2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0135.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0135 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1034. -/ +theorem bounds_11_1034 : exactInterval 11 1034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1034 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1034) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1034 : oddCount 1034 11 = 5 ∧ acceleratedOrbit 11 1034 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1034 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1034) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1034.1, data_11_1034.2] + +/-- Complete interval computation for depth 11, residue 1035. -/ +theorem bounds_11_1035 : exactInterval 11 1035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1035 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1035) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1035 : oddCount 1035 11 = 4 ∧ acceleratedOrbit 11 1035 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1035 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1035) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1035.1, data_11_1035.2] + +/-- Complete interval computation for depth 11, residue 1036. -/ +theorem bounds_11_1036 : exactInterval 11 1036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1036 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1036) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1036 : oddCount 1036 11 = 5 ∧ acceleratedOrbit 11 1036 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1036 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1036) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1036.1, data_11_1036.2] + +/-- Complete interval computation for depth 11, residue 1037. -/ +theorem bounds_11_1037 : exactInterval 11 1037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1037 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1037) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1037 : oddCount 1037 11 = 5 ∧ acceleratedOrbit 11 1037 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1037 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1037) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1037.1, data_11_1037.2] + +/-- Complete interval computation for depth 11, residue 1038. -/ +theorem bounds_11_1038 : exactInterval 11 1038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1038 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1038) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1038 : oddCount 1038 11 = 6 ∧ acceleratedOrbit 11 1038 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1038 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1038) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1038.1, data_11_1038.2] + +/-- Complete interval computation for depth 11, residue 1039. -/ +theorem bounds_11_1039 : exactInterval 11 1039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1039 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1039) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1039 : oddCount 1039 11 = 6 ∧ acceleratedOrbit 11 1039 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1039 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1039) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1039.1, data_11_1039.2] + +/-- Complete interval computation for depth 11, residue 1040. -/ +theorem bounds_11_1040 : exactInterval 11 1040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1040 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1040) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1040 : oddCount 1040 11 = 3 ∧ acceleratedOrbit 11 1040 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1040 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1040) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1040.1, data_11_1040.2] + +/-- Complete interval computation for depth 11, residue 1041. -/ +theorem bounds_11_1041 : exactInterval 11 1041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1041 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1041) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1041 : oddCount 1041 11 = 5 ∧ acceleratedOrbit 11 1041 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1041 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1041) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1041.1, data_11_1041.2] + +/-- Complete interval computation for depth 11, residue 1042. -/ +theorem bounds_11_1042 : exactInterval 11 1042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1042 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1042) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1042 : oddCount 1042 11 = 5 ∧ acceleratedOrbit 11 1042 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1042 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1042) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1042.1, data_11_1042.2] + +/-- Complete interval computation for depth 11, residue 1043. -/ +theorem bounds_11_1043 : exactInterval 11 1043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1043 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1043) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1043 : oddCount 1043 11 = 5 ∧ acceleratedOrbit 11 1043 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1043 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1043) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1043.1, data_11_1043.2] + +/-- Complete interval computation for depth 11, residue 1044. -/ +theorem bounds_11_1044 : exactInterval 11 1044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1044 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1044) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1044 : oddCount 1044 11 = 3 ∧ acceleratedOrbit 11 1044 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1044 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1044) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1044.1, data_11_1044.2] + +/-- Complete interval computation for depth 11, residue 1045. -/ +theorem bounds_11_1045 : exactInterval 11 1045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1045 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1045) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1045 : oddCount 1045 11 = 3 ∧ acceleratedOrbit 11 1045 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1045 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1045) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1045.1, data_11_1045.2] + +/-- Complete interval computation for depth 11, residue 1046. -/ +theorem bounds_11_1046 : exactInterval 11 1046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1046 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1046) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1046 : oddCount 1046 11 = 5 ∧ acceleratedOrbit 11 1046 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1046 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1046) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1046.1, data_11_1046.2] + +/-- Complete interval computation for depth 11, residue 1047. -/ +theorem bounds_11_1047 : exactInterval 11 1047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1047 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1047) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1047 : oddCount 1047 11 = 5 ∧ acceleratedOrbit 11 1047 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1047 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1047) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1047.1, data_11_1047.2] + +/-- Complete interval computation for depth 11, residue 1048. -/ +theorem bounds_11_1048 : exactInterval 11 1048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1048 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1048) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1048 : oddCount 1048 11 = 3 ∧ acceleratedOrbit 11 1048 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1048 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1048) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1048.1, data_11_1048.2] + +end Collatz.Research.StoppingAtlas.Batch0135 From 93ed515395ad1ea6aa8e4d501159e247e977c132 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:43 +0530 Subject: [PATCH 0136/1001] proof: certify atlas Batch0136 (11:1049 to 11:1063) --- Collatz/Research/StoppingAtlas/Batch0136.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0136.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0136.lean b/Collatz/Research/StoppingAtlas/Batch0136.lean new file mode 100644 index 00000000..c7ba96e6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0136.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0136 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1049. -/ +theorem bounds_11_1049 : exactInterval 11 1049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1049 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1049) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1049 : oddCount 1049 11 = 7 ∧ acceleratedOrbit 11 1049 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1049 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1049) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1049.1, data_11_1049.2] + +/-- Complete interval computation for depth 11, residue 1050. -/ +theorem bounds_11_1050 : exactInterval 11 1050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1050 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1050) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1050 : oddCount 1050 11 = 3 ∧ acceleratedOrbit 11 1050 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1050 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1050) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1050.1, data_11_1050.2] + +/-- Complete interval computation for depth 11, residue 1051. -/ +theorem bounds_11_1051 : exactInterval 11 1051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1051 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1051) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1051 : oddCount 1051 11 = 9 ∧ acceleratedOrbit 11 1051 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1051 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1051) = 3 ^ 9 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1051.1, data_11_1051.2] + +/-- Complete interval computation for depth 11, residue 1052. -/ +theorem bounds_11_1052 : exactInterval 11 1052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1052 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1052) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1052 : oddCount 1052 11 = 6 ∧ acceleratedOrbit 11 1052 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1052 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1052) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1052.1, data_11_1052.2] + +/-- Complete interval computation for depth 11, residue 1053. -/ +theorem bounds_11_1053 : exactInterval 11 1053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1053 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1053) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1053 : oddCount 1053 11 = 6 ∧ acceleratedOrbit 11 1053 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1053 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1053) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1053.1, data_11_1053.2] + +/-- Complete interval computation for depth 11, residue 1054. -/ +theorem bounds_11_1054 : exactInterval 11 1054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1054 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1054) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1054 : oddCount 1054 11 = 6 ∧ acceleratedOrbit 11 1054 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1054 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1054) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1054.1, data_11_1054.2] + +/-- Complete interval computation for depth 11, residue 1055. -/ +theorem bounds_11_1055 : exactInterval 11 1055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1055 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1055) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1055 : oddCount 1055 11 = 9 ∧ acceleratedOrbit 11 1055 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1055 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1055) = 3 ^ 9 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1055.1, data_11_1055.2] + +/-- Complete interval computation for depth 11, residue 1056. -/ +theorem bounds_11_1056 : exactInterval 11 1056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1056 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1056) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1056 : oddCount 1056 11 = 4 ∧ acceleratedOrbit 11 1056 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1056 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1056) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1056.1, data_11_1056.2] + +/-- Complete interval computation for depth 11, residue 1057. -/ +theorem bounds_11_1057 : exactInterval 11 1057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1057 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1057) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1057 : oddCount 1057 11 = 7 ∧ acceleratedOrbit 11 1057 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1057 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1057) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1057.1, data_11_1057.2] + +/-- Complete interval computation for depth 11, residue 1058. -/ +theorem bounds_11_1058 : exactInterval 11 1058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1058 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1058) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1058 : oddCount 1058 11 = 3 ∧ acceleratedOrbit 11 1058 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1058 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1058) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1058.1, data_11_1058.2] + +/-- Complete interval computation for depth 11, residue 1059. -/ +theorem bounds_11_1059 : exactInterval 11 1059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1059 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1059) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1059 : oddCount 1059 11 = 3 ∧ acceleratedOrbit 11 1059 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1059 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1059) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1059.1, data_11_1059.2] + +/-- Complete interval computation for depth 11, residue 1060. -/ +theorem bounds_11_1060 : exactInterval 11 1060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1060 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1060) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1060 : oddCount 1060 11 = 6 ∧ acceleratedOrbit 11 1060 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1060 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1060) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1060.1, data_11_1060.2] + +/-- Complete interval computation for depth 11, residue 1061. -/ +theorem bounds_11_1061 : exactInterval 11 1061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1061 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1061) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1061 : oddCount 1061 11 = 6 ∧ acceleratedOrbit 11 1061 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1061 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1061) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1061.1, data_11_1061.2] + +/-- Complete interval computation for depth 11, residue 1062. -/ +theorem bounds_11_1062 : exactInterval 11 1062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1062 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1062) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1062 : oddCount 1062 11 = 6 ∧ acceleratedOrbit 11 1062 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1062 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1062) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1062.1, data_11_1062.2] + +/-- Complete interval computation for depth 11, residue 1063. -/ +theorem bounds_11_1063 : exactInterval 11 1063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1063 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1063) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1063 : oddCount 1063 11 = 6 ∧ acceleratedOrbit 11 1063 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1063 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1063) = 3 ^ 6 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1063.1, data_11_1063.2] + +end Collatz.Research.StoppingAtlas.Batch0136 From 727d6df98c36fc52caeaa8c6f82a78b9a02241ea Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:43 +0530 Subject: [PATCH 0137/1001] proof: certify atlas Batch0137 (11:1064 to 11:1079) --- Collatz/Research/StoppingAtlas/Batch0137.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0137.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0137.lean b/Collatz/Research/StoppingAtlas/Batch0137.lean new file mode 100644 index 00000000..9ee4d389 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0137.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0137 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1064. -/ +theorem bounds_11_1064 : exactInterval 11 1064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1064 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1064) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1064 : oddCount 1064 11 = 4 ∧ acceleratedOrbit 11 1064 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1064 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1064) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1064.1, data_11_1064.2] + +/-- Complete interval computation for depth 11, residue 1065. -/ +theorem bounds_11_1065 : exactInterval 11 1065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1065 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1065) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1065 : oddCount 1065 11 = 7 ∧ acceleratedOrbit 11 1065 = 1139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1065 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1065) = 3 ^ 7 * m + 1139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1065.1, data_11_1065.2] + +/-- Complete interval computation for depth 11, residue 1066. -/ +theorem bounds_11_1066 : exactInterval 11 1066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1066 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1066) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1066 : oddCount 1066 11 = 4 ∧ acceleratedOrbit 11 1066 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1066 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1066) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1066.1, data_11_1066.2] + +/-- Complete interval computation for depth 11, residue 1067. -/ +theorem bounds_11_1067 : exactInterval 11 1067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1067 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1067) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1067 : oddCount 1067 11 = 5 ∧ acceleratedOrbit 11 1067 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1067 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1067) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1067.1, data_11_1067.2] + +/-- Complete interval computation for depth 11, residue 1068. -/ +theorem bounds_11_1068 : exactInterval 11 1068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1068 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1068) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1068 : oddCount 1068 11 = 5 ∧ acceleratedOrbit 11 1068 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1068 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1068) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1068.1, data_11_1068.2] + +/-- Complete interval computation for depth 11, residue 1069. -/ +theorem bounds_11_1069 : exactInterval 11 1069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1069 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1069) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1069 : oddCount 1069 11 = 5 ∧ acceleratedOrbit 11 1069 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1069 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1069) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1069.1, data_11_1069.2] + +/-- Complete interval computation for depth 11, residue 1070. -/ +theorem bounds_11_1070 : exactInterval 11 1070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1070 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1070) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1070 : oddCount 1070 11 = 5 ∧ acceleratedOrbit 11 1070 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1070 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1070) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1070.1, data_11_1070.2] + +/-- Complete interval computation for depth 11, residue 1071. -/ +theorem bounds_11_1071 : exactInterval 11 1071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1071 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1071) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1071 : oddCount 1071 11 = 7 ∧ acceleratedOrbit 11 1071 = 1145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1071 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1071) = 3 ^ 7 * m + 1145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1071.1, data_11_1071.2] + +/-- Complete interval computation for depth 11, residue 1072. -/ +theorem bounds_11_1072 : exactInterval 11 1072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1072 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1072) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1072 : oddCount 1072 11 = 4 ∧ acceleratedOrbit 11 1072 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1072 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1072) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1072.1, data_11_1072.2] + +/-- Complete interval computation for depth 11, residue 1073. -/ +theorem bounds_11_1073 : exactInterval 11 1073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1073 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1073) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1073 : oddCount 1073 11 = 5 ∧ acceleratedOrbit 11 1073 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1073 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1073) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1073.1, data_11_1073.2] + +/-- Complete interval computation for depth 11, residue 1074. -/ +theorem bounds_11_1074 : exactInterval 11 1074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1074 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1074) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1074 : oddCount 1074 11 = 5 ∧ acceleratedOrbit 11 1074 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1074 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1074) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1074.1, data_11_1074.2] + +/-- Complete interval computation for depth 11, residue 1075. -/ +theorem bounds_11_1075 : exactInterval 11 1075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1075 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1075) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1075 : oddCount 1075 11 = 5 ∧ acceleratedOrbit 11 1075 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1075 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1075) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1075.1, data_11_1075.2] + +/-- Complete interval computation for depth 11, residue 1076. -/ +theorem bounds_11_1076 : exactInterval 11 1076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1076 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1076) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1076 : oddCount 1076 11 = 4 ∧ acceleratedOrbit 11 1076 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1076 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1076) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1076.1, data_11_1076.2] + +/-- Complete interval computation for depth 11, residue 1077. -/ +theorem bounds_11_1077 : exactInterval 11 1077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1077 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1077) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1077 : oddCount 1077 11 = 4 ∧ acceleratedOrbit 11 1077 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1077 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1077) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1077.1, data_11_1077.2] + +/-- Complete interval computation for depth 11, residue 1078. -/ +theorem bounds_11_1078 : exactInterval 11 1078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1078 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1078) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1078 : oddCount 1078 11 = 7 ∧ acceleratedOrbit 11 1078 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1078 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1078) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1078.1, data_11_1078.2] + +/-- Complete interval computation for depth 11, residue 1079. -/ +theorem bounds_11_1079 : exactInterval 11 1079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1079 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1079) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1079 : oddCount 1079 11 = 7 ∧ acceleratedOrbit 11 1079 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1079 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1079) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1079.1, data_11_1079.2] + +end Collatz.Research.StoppingAtlas.Batch0137 From 4588d11eaa774a3324faa21ecdf08f524b3a0a17 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:43 +0530 Subject: [PATCH 0138/1001] proof: certify atlas Batch0138 (11:1080 to 11:1094) --- Collatz/Research/StoppingAtlas/Batch0138.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0138.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0138.lean b/Collatz/Research/StoppingAtlas/Batch0138.lean new file mode 100644 index 00000000..67b0a049 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0138.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0138 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1080. -/ +theorem bounds_11_1080 : exactInterval 11 1080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1080 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1080) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1080 : oddCount 1080 11 = 4 ∧ acceleratedOrbit 11 1080 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1080 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1080) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1080.1, data_11_1080.2] + +/-- Complete interval computation for depth 11, residue 1081. -/ +theorem bounds_11_1081 : exactInterval 11 1081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1081 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1081) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1081 : oddCount 1081 11 = 6 ∧ acceleratedOrbit 11 1081 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1081 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1081) = 3 ^ 6 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1081.1, data_11_1081.2] + +/-- Complete interval computation for depth 11, residue 1082. -/ +theorem bounds_11_1082 : exactInterval 11 1082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1082 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1082) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1082 : oddCount 1082 11 = 4 ∧ acceleratedOrbit 11 1082 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1082 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1082) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1082.1, data_11_1082.2] + +/-- Complete interval computation for depth 11, residue 1083. -/ +theorem bounds_11_1083 : exactInterval 11 1083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1083 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1083) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1083 : oddCount 1083 11 = 7 ∧ acceleratedOrbit 11 1083 = 1160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1083 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1083) = 3 ^ 7 * m + 1160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1083.1, data_11_1083.2] + +/-- Complete interval computation for depth 11, residue 1084. -/ +theorem bounds_11_1084 : exactInterval 11 1084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1084 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1084) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1084 : oddCount 1084 11 = 4 ∧ acceleratedOrbit 11 1084 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1084 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1084) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1084.1, data_11_1084.2] + +/-- Complete interval computation for depth 11, residue 1085. -/ +theorem bounds_11_1085 : exactInterval 11 1085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1085 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1085) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1085 : oddCount 1085 11 = 4 ∧ acceleratedOrbit 11 1085 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1085 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1085) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1085.1, data_11_1085.2] + +/-- Complete interval computation for depth 11, residue 1086. -/ +theorem bounds_11_1086 : exactInterval 11 1086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1086 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1086) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1086 : oddCount 1086 11 = 7 ∧ acceleratedOrbit 11 1086 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1086 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1086) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1086.1, data_11_1086.2] + +/-- Complete interval computation for depth 11, residue 1087. -/ +theorem bounds_11_1087 : exactInterval 11 1087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1087 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1087) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1087 : oddCount 1087 11 = 7 ∧ acceleratedOrbit 11 1087 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1087 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1087) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1087.1, data_11_1087.2] + +/-- Complete interval computation for depth 11, residue 1088. -/ +theorem bounds_11_1088 : exactInterval 11 1088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1088 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1088) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1088 : oddCount 1088 11 = 2 ∧ acceleratedOrbit 11 1088 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1088 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1088) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1088.1, data_11_1088.2] + +/-- Complete interval computation for depth 11, residue 1089. -/ +theorem bounds_11_1089 : exactInterval 11 1089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1089 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1089) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1089 : oddCount 1089 11 = 5 ∧ acceleratedOrbit 11 1089 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1089 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1089) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1089.1, data_11_1089.2] + +/-- Complete interval computation for depth 11, residue 1090. -/ +theorem bounds_11_1090 : exactInterval 11 1090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1090 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1090) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1090 : oddCount 1090 11 = 5 ∧ acceleratedOrbit 11 1090 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1090 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1090) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1090.1, data_11_1090.2] + +/-- Complete interval computation for depth 11, residue 1091. -/ +theorem bounds_11_1091 : exactInterval 11 1091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1091 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1091) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1091 : oddCount 1091 11 = 5 ∧ acceleratedOrbit 11 1091 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1091 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1091) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1091.1, data_11_1091.2] + +/-- Complete interval computation for depth 11, residue 1092. -/ +theorem bounds_11_1092 : exactInterval 11 1092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1092 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1092) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1092 : oddCount 1092 11 = 4 ∧ acceleratedOrbit 11 1092 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1092 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1092) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1092.1, data_11_1092.2] + +/-- Complete interval computation for depth 11, residue 1093. -/ +theorem bounds_11_1093 : exactInterval 11 1093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1093 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1093) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1093 : oddCount 1093 11 = 4 ∧ acceleratedOrbit 11 1093 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1093 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1093) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1093.1, data_11_1093.2] + +/-- Complete interval computation for depth 11, residue 1094. -/ +theorem bounds_11_1094 : exactInterval 11 1094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1094 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1094) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1094 : oddCount 1094 11 = 4 ∧ acceleratedOrbit 11 1094 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1094 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1094) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1094.1, data_11_1094.2] + +end Collatz.Research.StoppingAtlas.Batch0138 From 4007940fdd344a04c1aa8e7550bf0df3ae57131c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:43 +0530 Subject: [PATCH 0139/1001] proof: certify atlas Batch0139 (11:1095 to 11:1110) --- Collatz/Research/StoppingAtlas/Batch0139.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0139.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0139.lean b/Collatz/Research/StoppingAtlas/Batch0139.lean new file mode 100644 index 00000000..a1dfcf91 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0139.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0139 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1095. -/ +theorem bounds_11_1095 : exactInterval 11 1095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1095 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1095) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1095 : oddCount 1095 11 = 7 ∧ acceleratedOrbit 11 1095 = 1171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1095 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1095) = 3 ^ 7 * m + 1171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1095.1, data_11_1095.2] + +/-- Complete interval computation for depth 11, residue 1096. -/ +theorem bounds_11_1096 : exactInterval 11 1096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1096 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1096) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1096 : oddCount 1096 11 = 6 ∧ acceleratedOrbit 11 1096 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1096 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1096) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1096.1, data_11_1096.2] + +/-- Complete interval computation for depth 11, residue 1097. -/ +theorem bounds_11_1097 : exactInterval 11 1097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1097 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1097) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1097 : oddCount 1097 11 = 7 ∧ acceleratedOrbit 11 1097 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1097 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1097) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1097.1, data_11_1097.2] + +/-- Complete interval computation for depth 11, residue 1098. -/ +theorem bounds_11_1098 : exactInterval 11 1098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1098 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1098) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1098 : oddCount 1098 11 = 6 ∧ acceleratedOrbit 11 1098 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1098 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1098) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1098.1, data_11_1098.2] + +/-- Complete interval computation for depth 11, residue 1099. -/ +theorem bounds_11_1099 : exactInterval 11 1099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1099 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1099) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1099 : oddCount 1099 11 = 4 ∧ acceleratedOrbit 11 1099 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1099 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1099) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1099.1, data_11_1099.2] + +/-- Complete interval computation for depth 11, residue 1100. -/ +theorem bounds_11_1100 : exactInterval 11 1100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1100 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1100) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1100 : oddCount 1100 11 = 6 ∧ acceleratedOrbit 11 1100 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1100 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1100) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1100.1, data_11_1100.2] + +/-- Complete interval computation for depth 11, residue 1101. -/ +theorem bounds_11_1101 : exactInterval 11 1101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1101 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1101) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1101 : oddCount 1101 11 = 6 ∧ acceleratedOrbit 11 1101 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1101 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1101) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1101.1, data_11_1101.2] + +/-- Complete interval computation for depth 11, residue 1102. -/ +theorem bounds_11_1102 : exactInterval 11 1102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1102 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1102) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1102 : oddCount 1102 11 = 5 ∧ acceleratedOrbit 11 1102 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1102 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1102) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1102.1, data_11_1102.2] + +/-- Complete interval computation for depth 11, residue 1103. -/ +theorem bounds_11_1103 : exactInterval 11 1103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1103 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1103) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1103 : oddCount 1103 11 = 5 ∧ acceleratedOrbit 11 1103 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1103 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1103) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1103.1, data_11_1103.2] + +/-- Complete interval computation for depth 11, residue 1104. -/ +theorem bounds_11_1104 : exactInterval 11 1104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1104 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1104) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1104 : oddCount 1104 11 = 2 ∧ acceleratedOrbit 11 1104 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1104 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1104) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1104.1, data_11_1104.2] + +/-- Complete interval computation for depth 11, residue 1105. -/ +theorem bounds_11_1105 : exactInterval 11 1105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1105 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1105) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1105 : oddCount 1105 11 = 6 ∧ acceleratedOrbit 11 1105 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1105 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1105) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1105.1, data_11_1105.2] + +/-- Complete interval computation for depth 11, residue 1106. -/ +theorem bounds_11_1106 : exactInterval 11 1106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1106 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1106) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1106 : oddCount 1106 11 = 8 ∧ acceleratedOrbit 11 1106 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1106 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1106) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1106.1, data_11_1106.2] + +/-- Complete interval computation for depth 11, residue 1107. -/ +theorem bounds_11_1107 : exactInterval 11 1107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1107 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1107) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1107 : oddCount 1107 11 = 8 ∧ acceleratedOrbit 11 1107 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1107 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1107) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1107.1, data_11_1107.2] + +/-- Complete interval computation for depth 11, residue 1108. -/ +theorem bounds_11_1108 : exactInterval 11 1108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1108 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1108) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1108 : oddCount 1108 11 = 2 ∧ acceleratedOrbit 11 1108 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1108 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1108) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1108.1, data_11_1108.2] + +/-- Complete interval computation for depth 11, residue 1109. -/ +theorem bounds_11_1109 : exactInterval 11 1109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1109 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1109) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1109 : oddCount 1109 11 = 2 ∧ acceleratedOrbit 11 1109 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1109 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1109) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1109.1, data_11_1109.2] + +/-- Complete interval computation for depth 11, residue 1110. -/ +theorem bounds_11_1110 : exactInterval 11 1110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1110 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1110) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1110 : oddCount 1110 11 = 4 ∧ acceleratedOrbit 11 1110 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1110 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1110) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1110.1, data_11_1110.2] + +end Collatz.Research.StoppingAtlas.Batch0139 From c82c55eb09d0d62bd125e2094334cee15b772330 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:44 +0530 Subject: [PATCH 0140/1001] proof: certify atlas Batch0140 (11:1111 to 11:1125) --- Collatz/Research/StoppingAtlas/Batch0140.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0140.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0140.lean b/Collatz/Research/StoppingAtlas/Batch0140.lean new file mode 100644 index 00000000..5e65c9b8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0140.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0140 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1111. -/ +theorem bounds_11_1111 : exactInterval 11 1111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1111 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1111) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1111 : oddCount 1111 11 = 4 ∧ acceleratedOrbit 11 1111 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1111 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1111) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1111.1, data_11_1111.2] + +/-- Complete interval computation for depth 11, residue 1112. -/ +theorem bounds_11_1112 : exactInterval 11 1112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1112 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1112) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1112 : oddCount 1112 11 = 5 ∧ acceleratedOrbit 11 1112 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1112 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1112) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1112.1, data_11_1112.2] + +/-- Complete interval computation for depth 11, residue 1113. -/ +theorem bounds_11_1113 : exactInterval 11 1113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1113 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1113) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1113 : oddCount 1113 11 = 6 ∧ acceleratedOrbit 11 1113 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1113 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1113) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1113.1, data_11_1113.2] + +/-- Complete interval computation for depth 11, residue 1114. -/ +theorem bounds_11_1114 : exactInterval 11 1114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1114 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1114) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1114 : oddCount 1114 11 = 5 ∧ acceleratedOrbit 11 1114 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1114 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1114) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1114.1, data_11_1114.2] + +/-- Complete interval computation for depth 11, residue 1115. -/ +theorem bounds_11_1115 : exactInterval 11 1115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1115 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1115) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1115 : oddCount 1115 11 = 8 ∧ acceleratedOrbit 11 1115 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1115 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1115) = 3 ^ 8 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1115.1, data_11_1115.2] + +/-- Complete interval computation for depth 11, residue 1116. -/ +theorem bounds_11_1116 : exactInterval 11 1116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1116 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1116) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1116 : oddCount 1116 11 = 5 ∧ acceleratedOrbit 11 1116 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1116 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1116) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1116.1, data_11_1116.2] + +/-- Complete interval computation for depth 11, residue 1117. -/ +theorem bounds_11_1117 : exactInterval 11 1117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1117 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1117) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1117 : oddCount 1117 11 = 5 ∧ acceleratedOrbit 11 1117 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1117 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1117) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1117.1, data_11_1117.2] + +/-- Complete interval computation for depth 11, residue 1118. -/ +theorem bounds_11_1118 : exactInterval 11 1118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1118 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1118) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1118 : oddCount 1118 11 = 8 ∧ acceleratedOrbit 11 1118 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1118 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1118) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1118.1, data_11_1118.2] + +/-- Complete interval computation for depth 11, residue 1119. -/ +theorem bounds_11_1119 : exactInterval 11 1119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1119 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1119) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1119 : oddCount 1119 11 = 8 ∧ acceleratedOrbit 11 1119 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1119 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1119) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1119.1, data_11_1119.2] + +/-- Complete interval computation for depth 11, residue 1120. -/ +theorem bounds_11_1120 : exactInterval 11 1120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1120 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1120) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1120 : oddCount 1120 11 = 2 ∧ acceleratedOrbit 11 1120 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1120 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1120) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1120.1, data_11_1120.2] + +/-- Complete interval computation for depth 11, residue 1121. -/ +theorem bounds_11_1121 : exactInterval 11 1121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1121 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1121) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1121 : oddCount 1121 11 = 6 ∧ acceleratedOrbit 11 1121 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1121 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1121) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1121.1, data_11_1121.2] + +/-- Complete interval computation for depth 11, residue 1122. -/ +theorem bounds_11_1122 : exactInterval 11 1122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1122 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1122) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1122 : oddCount 1122 11 = 6 ∧ acceleratedOrbit 11 1122 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1122 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1122) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1122.1, data_11_1122.2] + +/-- Complete interval computation for depth 11, residue 1123. -/ +theorem bounds_11_1123 : exactInterval 11 1123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1123 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1123) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1123 : oddCount 1123 11 = 6 ∧ acceleratedOrbit 11 1123 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1123 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1123) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1123.1, data_11_1123.2] + +/-- Complete interval computation for depth 11, residue 1124. -/ +theorem bounds_11_1124 : exactInterval 11 1124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1124 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1124) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1124 : oddCount 1124 11 = 6 ∧ acceleratedOrbit 11 1124 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1124 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1124) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1124.1, data_11_1124.2] + +/-- Complete interval computation for depth 11, residue 1125. -/ +theorem bounds_11_1125 : exactInterval 11 1125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1125 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1125) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1125 : oddCount 1125 11 = 6 ∧ acceleratedOrbit 11 1125 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1125 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1125) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1125.1, data_11_1125.2] + +end Collatz.Research.StoppingAtlas.Batch0140 From 9721f79463bb6aacd8fc445570675e0a16de26c9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:44 +0530 Subject: [PATCH 0141/1001] proof: certify atlas Batch0141 (11:1126 to 11:1140) --- Collatz/Research/StoppingAtlas/Batch0141.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0141.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0141.lean b/Collatz/Research/StoppingAtlas/Batch0141.lean new file mode 100644 index 00000000..d0c074b9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0141.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0141 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1126. -/ +theorem bounds_11_1126 : exactInterval 11 1126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1126 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1126) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1126 : oddCount 1126 11 = 6 ∧ acceleratedOrbit 11 1126 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1126 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1126) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1126.1, data_11_1126.2] + +/-- Complete interval computation for depth 11, residue 1127. -/ +theorem bounds_11_1127 : exactInterval 11 1127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1127 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1127) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1127 : oddCount 1127 11 = 9 ∧ acceleratedOrbit 11 1127 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1127 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1127) = 3 ^ 9 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1127.1, data_11_1127.2] + +/-- Complete interval computation for depth 11, residue 1128. -/ +theorem bounds_11_1128 : exactInterval 11 1128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1128 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1128) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1128 : oddCount 1128 11 = 2 ∧ acceleratedOrbit 11 1128 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1128 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1128) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1128.1, data_11_1128.2] + +/-- Complete interval computation for depth 11, residue 1129. -/ +theorem bounds_11_1129 : exactInterval 11 1129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1129 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1129) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1129 : oddCount 1129 11 = 7 ∧ acceleratedOrbit 11 1129 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1129 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1129) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1129.1, data_11_1129.2] + +/-- Complete interval computation for depth 11, residue 1130. -/ +theorem bounds_11_1130 : exactInterval 11 1130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1130 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1130) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1130 : oddCount 1130 11 = 2 ∧ acceleratedOrbit 11 1130 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1130 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1130) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1130.1, data_11_1130.2] + +/-- Complete interval computation for depth 11, residue 1131. -/ +theorem bounds_11_1131 : exactInterval 11 1131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1131 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1131) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1131 : oddCount 1131 11 = 7 ∧ acceleratedOrbit 11 1131 = 1210 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1131 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1131) = 3 ^ 7 * m + 1210 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1131.1, data_11_1131.2] + +/-- Complete interval computation for depth 11, residue 1132. -/ +theorem bounds_11_1132 : exactInterval 11 1132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1132 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1132) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1132 : oddCount 1132 11 = 8 ∧ acceleratedOrbit 11 1132 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1132 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1132) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1132.1, data_11_1132.2] + +/-- Complete interval computation for depth 11, residue 1133. -/ +theorem bounds_11_1133 : exactInterval 11 1133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1133 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1133) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1133 : oddCount 1133 11 = 8 ∧ acceleratedOrbit 11 1133 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1133 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1133) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1133.1, data_11_1133.2] + +/-- Complete interval computation for depth 11, residue 1134. -/ +theorem bounds_11_1134 : exactInterval 11 1134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1134 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1134) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1134 : oddCount 1134 11 = 8 ∧ acceleratedOrbit 11 1134 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1134 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1134) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1134.1, data_11_1134.2] + +/-- Complete interval computation for depth 11, residue 1135. -/ +theorem bounds_11_1135 : exactInterval 11 1135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1135 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1135) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1135 : oddCount 1135 11 = 8 ∧ acceleratedOrbit 11 1135 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1135 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1135) = 3 ^ 8 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1135.1, data_11_1135.2] + +/-- Complete interval computation for depth 11, residue 1136. -/ +theorem bounds_11_1136 : exactInterval 11 1136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1136 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1136) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1136 : oddCount 1136 11 = 5 ∧ acceleratedOrbit 11 1136 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1136 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1136) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1136.1, data_11_1136.2] + +/-- Complete interval computation for depth 11, residue 1137. -/ +theorem bounds_11_1137 : exactInterval 11 1137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1137 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1137) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1137 : oddCount 1137 11 = 2 ∧ acceleratedOrbit 11 1137 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1137 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1137) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1137.1, data_11_1137.2] + +/-- Complete interval computation for depth 11, residue 1138. -/ +theorem bounds_11_1138 : exactInterval 11 1138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1138 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1138) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1138 : oddCount 1138 11 = 6 ∧ acceleratedOrbit 11 1138 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1138 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1138) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1138.1, data_11_1138.2] + +/-- Complete interval computation for depth 11, residue 1139. -/ +theorem bounds_11_1139 : exactInterval 11 1139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1139 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1139) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1139 : oddCount 1139 11 = 6 ∧ acceleratedOrbit 11 1139 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1139 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1139) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1139.1, data_11_1139.2] + +/-- Complete interval computation for depth 11, residue 1140. -/ +theorem bounds_11_1140 : exactInterval 11 1140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1140 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1140) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1140 : oddCount 1140 11 = 5 ∧ acceleratedOrbit 11 1140 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1140 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1140) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1140.1, data_11_1140.2] + +end Collatz.Research.StoppingAtlas.Batch0141 From e607d111a86071758828f1f18fd6fa28e15b4810 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:44 +0530 Subject: [PATCH 0142/1001] proof: certify atlas Batch0142 (11:1141 to 11:1156) --- Collatz/Research/StoppingAtlas/Batch0142.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0142.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0142.lean b/Collatz/Research/StoppingAtlas/Batch0142.lean new file mode 100644 index 00000000..74122cec --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0142.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0142 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1141. -/ +theorem bounds_11_1141 : exactInterval 11 1141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1141 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1141) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1141 : oddCount 1141 11 = 5 ∧ acceleratedOrbit 11 1141 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1141 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1141) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1141.1, data_11_1141.2] + +/-- Complete interval computation for depth 11, residue 1142. -/ +theorem bounds_11_1142 : exactInterval 11 1142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1142 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1142) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1142 : oddCount 1142 11 = 5 ∧ acceleratedOrbit 11 1142 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1142 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1142) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1142.1, data_11_1142.2] + +/-- Complete interval computation for depth 11, residue 1143. -/ +theorem bounds_11_1143 : exactInterval 11 1143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1143 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1143) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1143 : oddCount 1143 11 = 5 ∧ acceleratedOrbit 11 1143 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1143 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1143) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1143.1, data_11_1143.2] + +/-- Complete interval computation for depth 11, residue 1144. -/ +theorem bounds_11_1144 : exactInterval 11 1144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1144 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1144) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1144 : oddCount 1144 11 = 5 ∧ acceleratedOrbit 11 1144 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1144 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1144) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1144.1, data_11_1144.2] + +/-- Complete interval computation for depth 11, residue 1145. -/ +theorem bounds_11_1145 : exactInterval 11 1145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1145 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1145) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1145 : oddCount 1145 11 = 7 ∧ acceleratedOrbit 11 1145 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1145 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1145) = 3 ^ 7 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1145.1, data_11_1145.2] + +/-- Complete interval computation for depth 11, residue 1146. -/ +theorem bounds_11_1146 : exactInterval 11 1146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1146 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1146) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1146 : oddCount 1146 11 = 5 ∧ acceleratedOrbit 11 1146 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1146 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1146) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1146.1, data_11_1146.2] + +/-- Complete interval computation for depth 11, residue 1147. -/ +theorem bounds_11_1147 : exactInterval 11 1147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1147 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1147) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1147 : oddCount 1147 11 = 6 ∧ acceleratedOrbit 11 1147 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1147 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1147) = 3 ^ 6 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1147.1, data_11_1147.2] + +/-- Complete interval computation for depth 11, residue 1148. -/ +theorem bounds_11_1148 : exactInterval 11 1148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1148 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1148) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1148 : oddCount 1148 11 = 6 ∧ acceleratedOrbit 11 1148 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1148 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1148) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1148.1, data_11_1148.2] + +/-- Complete interval computation for depth 11, residue 1149. -/ +theorem bounds_11_1149 : exactInterval 11 1149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1149 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1149) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1149 : oddCount 1149 11 = 6 ∧ acceleratedOrbit 11 1149 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1149 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1149) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1149.1, data_11_1149.2] + +/-- Complete interval computation for depth 11, residue 1150. -/ +theorem bounds_11_1150 : exactInterval 11 1150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1150 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1150) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1150 : oddCount 1150 11 = 6 ∧ acceleratedOrbit 11 1150 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1150 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1150) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1150.1, data_11_1150.2] + +/-- Complete interval computation for depth 11, residue 1151. -/ +theorem bounds_11_1151 : exactInterval 11 1151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1151 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1151) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1151 : oddCount 1151 11 = 9 ∧ acceleratedOrbit 11 1151 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1151 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1151) = 3 ^ 9 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1151.1, data_11_1151.2] + +/-- Complete interval computation for depth 11, residue 1152. -/ +theorem bounds_11_1152 : exactInterval 11 1152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1152 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1152) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1152 : oddCount 1152 11 = 3 ∧ acceleratedOrbit 11 1152 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1152 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1152) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1152.1, data_11_1152.2] + +/-- Complete interval computation for depth 11, residue 1153. -/ +theorem bounds_11_1153 : exactInterval 11 1153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1153 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1153) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1153 : oddCount 1153 11 = 7 ∧ acceleratedOrbit 11 1153 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1153 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1153) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1153.1, data_11_1153.2] + +/-- Complete interval computation for depth 11, residue 1154. -/ +theorem bounds_11_1154 : exactInterval 11 1154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1154 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1154) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1154 : oddCount 1154 11 = 4 ∧ acceleratedOrbit 11 1154 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1154 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1154) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1154.1, data_11_1154.2] + +/-- Complete interval computation for depth 11, residue 1155. -/ +theorem bounds_11_1155 : exactInterval 11 1155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1155 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1155) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1155 : oddCount 1155 11 = 4 ∧ acceleratedOrbit 11 1155 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1155 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1155) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1155.1, data_11_1155.2] + +/-- Complete interval computation for depth 11, residue 1156. -/ +theorem bounds_11_1156 : exactInterval 11 1156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1156 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1156) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1156 : oddCount 1156 11 = 4 ∧ acceleratedOrbit 11 1156 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1156 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1156) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1156.1, data_11_1156.2] + +end Collatz.Research.StoppingAtlas.Batch0142 From cdea0b572796e4133e307f1841da7770b87e04f5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:44 +0530 Subject: [PATCH 0143/1001] proof: certify atlas Batch0143 (11:1157 to 11:1171) --- Collatz/Research/StoppingAtlas/Batch0143.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0143.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0143.lean b/Collatz/Research/StoppingAtlas/Batch0143.lean new file mode 100644 index 00000000..12298c10 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0143.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0143 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1157. -/ +theorem bounds_11_1157 : exactInterval 11 1157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1157 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1157) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1157 : oddCount 1157 11 = 4 ∧ acceleratedOrbit 11 1157 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1157 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1157) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1157.1, data_11_1157.2] + +/-- Complete interval computation for depth 11, residue 1158. -/ +theorem bounds_11_1158 : exactInterval 11 1158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1158 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1158) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1158 : oddCount 1158 11 = 4 ∧ acceleratedOrbit 11 1158 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1158 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1158) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1158.1, data_11_1158.2] + +/-- Complete interval computation for depth 11, residue 1159. -/ +theorem bounds_11_1159 : exactInterval 11 1159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1159 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1159) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1159 : oddCount 1159 11 = 7 ∧ acceleratedOrbit 11 1159 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1159 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1159) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1159.1, data_11_1159.2] + +/-- Complete interval computation for depth 11, residue 1160. -/ +theorem bounds_11_1160 : exactInterval 11 1160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1160 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1160) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1160 : oddCount 1160 11 = 4 ∧ acceleratedOrbit 11 1160 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1160 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1160) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1160.1, data_11_1160.2] + +/-- Complete interval computation for depth 11, residue 1161. -/ +theorem bounds_11_1161 : exactInterval 11 1161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1161 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1161) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1161 : oddCount 1161 11 = 9 ∧ acceleratedOrbit 11 1161 = 11177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1161 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1161) = 3 ^ 9 * m + 11177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1161.1, data_11_1161.2] + +/-- Complete interval computation for depth 11, residue 1162. -/ +theorem bounds_11_1162 : exactInterval 11 1162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1162 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1162) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1162 : oddCount 1162 11 = 4 ∧ acceleratedOrbit 11 1162 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1162 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1162) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1162.1, data_11_1162.2] + +/-- Complete interval computation for depth 11, residue 1163. -/ +theorem bounds_11_1163 : exactInterval 11 1163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1163 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1163) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1163 : oddCount 1163 11 = 6 ∧ acceleratedOrbit 11 1163 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1163 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1163) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1163.1, data_11_1163.2] + +/-- Complete interval computation for depth 11, residue 1164. -/ +theorem bounds_11_1164 : exactInterval 11 1164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1164 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1164) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1164 : oddCount 1164 11 = 4 ∧ acceleratedOrbit 11 1164 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1164 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1164) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1164.1, data_11_1164.2] + +/-- Complete interval computation for depth 11, residue 1165. -/ +theorem bounds_11_1165 : exactInterval 11 1165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1165 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1165) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1165 : oddCount 1165 11 = 4 ∧ acceleratedOrbit 11 1165 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1165 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1165) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1165.1, data_11_1165.2] + +/-- Complete interval computation for depth 11, residue 1166. -/ +theorem bounds_11_1166 : exactInterval 11 1166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1166 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1166) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1166 : oddCount 1166 11 = 6 ∧ acceleratedOrbit 11 1166 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1166 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1166) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1166.1, data_11_1166.2] + +/-- Complete interval computation for depth 11, residue 1167. -/ +theorem bounds_11_1167 : exactInterval 11 1167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1167 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1167) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1167 : oddCount 1167 11 = 6 ∧ acceleratedOrbit 11 1167 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1167 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1167) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1167.1, data_11_1167.2] + +/-- Complete interval computation for depth 11, residue 1168. -/ +theorem bounds_11_1168 : exactInterval 11 1168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1168 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1168) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1168 : oddCount 1168 11 = 4 ∧ acceleratedOrbit 11 1168 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1168 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1168) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1168.1, data_11_1168.2] + +/-- Complete interval computation for depth 11, residue 1169. -/ +theorem bounds_11_1169 : exactInterval 11 1169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1169 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1169) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1169 : oddCount 1169 11 = 6 ∧ acceleratedOrbit 11 1169 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1169 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1169) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1169.1, data_11_1169.2] + +/-- Complete interval computation for depth 11, residue 1170. -/ +theorem bounds_11_1170 : exactInterval 11 1170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1170 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1170) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1170 : oddCount 1170 11 = 6 ∧ acceleratedOrbit 11 1170 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1170 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1170) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1170.1, data_11_1170.2] + +/-- Complete interval computation for depth 11, residue 1171. -/ +theorem bounds_11_1171 : exactInterval 11 1171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1171 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1171) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1171 : oddCount 1171 11 = 6 ∧ acceleratedOrbit 11 1171 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1171 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1171) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1171.1, data_11_1171.2] + +end Collatz.Research.StoppingAtlas.Batch0143 From 975c961bcdc319d078e074d8498fc7eb96732007 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:45 +0530 Subject: [PATCH 0144/1001] proof: certify atlas Batch0144 (11:1172 to 11:1186) --- Collatz/Research/StoppingAtlas/Batch0144.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0144.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0144.lean b/Collatz/Research/StoppingAtlas/Batch0144.lean new file mode 100644 index 00000000..d8fbb3c7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0144.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0144 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1172. -/ +theorem bounds_11_1172 : exactInterval 11 1172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1172 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1172) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1172 : oddCount 1172 11 = 4 ∧ acceleratedOrbit 11 1172 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1172 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1172) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1172.1, data_11_1172.2] + +/-- Complete interval computation for depth 11, residue 1173. -/ +theorem bounds_11_1173 : exactInterval 11 1173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1173 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1173) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1173 : oddCount 1173 11 = 4 ∧ acceleratedOrbit 11 1173 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1173 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1173) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1173.1, data_11_1173.2] + +/-- Complete interval computation for depth 11, residue 1174. -/ +theorem bounds_11_1174 : exactInterval 11 1174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1174 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1174) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1174 : oddCount 1174 11 = 4 ∧ acceleratedOrbit 11 1174 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1174 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1174) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1174.1, data_11_1174.2] + +/-- Complete interval computation for depth 11, residue 1175. -/ +theorem bounds_11_1175 : exactInterval 11 1175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1175 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1175) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1175 : oddCount 1175 11 = 4 ∧ acceleratedOrbit 11 1175 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1175 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1175) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1175.1, data_11_1175.2] + +/-- Complete interval computation for depth 11, residue 1176. -/ +theorem bounds_11_1176 : exactInterval 11 1176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1176 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1176) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1176 : oddCount 1176 11 = 4 ∧ acceleratedOrbit 11 1176 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1176 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1176) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1176.1, data_11_1176.2] + +/-- Complete interval computation for depth 11, residue 1177. -/ +theorem bounds_11_1177 : exactInterval 11 1177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1177 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1177) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1177 : oddCount 1177 11 = 5 ∧ acceleratedOrbit 11 1177 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1177 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1177) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1177.1, data_11_1177.2] + +/-- Complete interval computation for depth 11, residue 1178. -/ +theorem bounds_11_1178 : exactInterval 11 1178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1178 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1178) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1178 : oddCount 1178 11 = 4 ∧ acceleratedOrbit 11 1178 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1178 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1178) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1178.1, data_11_1178.2] + +/-- Complete interval computation for depth 11, residue 1179. -/ +theorem bounds_11_1179 : exactInterval 11 1179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1179 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1179) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1179 : oddCount 1179 11 = 8 ∧ acceleratedOrbit 11 1179 = 3782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1179 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1179) = 3 ^ 8 * m + 3782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1179.1, data_11_1179.2] + +/-- Complete interval computation for depth 11, residue 1180. -/ +theorem bounds_11_1180 : exactInterval 11 1180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1180 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1180) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1180 : oddCount 1180 11 = 6 ∧ acceleratedOrbit 11 1180 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1180 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1180) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1180.1, data_11_1180.2] + +/-- Complete interval computation for depth 11, residue 1181. -/ +theorem bounds_11_1181 : exactInterval 11 1181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1181 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1181) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1181 : oddCount 1181 11 = 6 ∧ acceleratedOrbit 11 1181 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1181 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1181) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1181.1, data_11_1181.2] + +/-- Complete interval computation for depth 11, residue 1182. -/ +theorem bounds_11_1182 : exactInterval 11 1182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1182 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1182) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1182 : oddCount 1182 11 = 6 ∧ acceleratedOrbit 11 1182 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1182 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1182) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1182.1, data_11_1182.2] + +/-- Complete interval computation for depth 11, residue 1183. -/ +theorem bounds_11_1183 : exactInterval 11 1183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1183 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1183) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1183 : oddCount 1183 11 = 9 ∧ acceleratedOrbit 11 1183 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1183 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1183) = 3 ^ 9 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1183.1, data_11_1183.2] + +/-- Complete interval computation for depth 11, residue 1184. -/ +theorem bounds_11_1184 : exactInterval 11 1184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1184 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1184) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1184 : oddCount 1184 11 = 3 ∧ acceleratedOrbit 11 1184 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1184 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1184) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1184.1, data_11_1184.2] + +/-- Complete interval computation for depth 11, residue 1185. -/ +theorem bounds_11_1185 : exactInterval 11 1185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1185 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1185) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1185 : oddCount 1185 11 = 8 ∧ acceleratedOrbit 11 1185 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1185 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1185) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1185.1, data_11_1185.2] + +/-- Complete interval computation for depth 11, residue 1186. -/ +theorem bounds_11_1186 : exactInterval 11 1186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1186 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1186) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1186 : oddCount 1186 11 = 6 ∧ acceleratedOrbit 11 1186 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1186 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1186) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1186.1, data_11_1186.2] + +end Collatz.Research.StoppingAtlas.Batch0144 From 82b2c143b5ac8e8e5c78cc0a6690223649d017fe Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:45 +0530 Subject: [PATCH 0145/1001] proof: certify atlas Batch0145 (11:1187 to 11:1202) --- Collatz/Research/StoppingAtlas/Batch0145.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0145.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0145.lean b/Collatz/Research/StoppingAtlas/Batch0145.lean new file mode 100644 index 00000000..16e6befd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0145.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0145 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1187. -/ +theorem bounds_11_1187 : exactInterval 11 1187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1187 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1187) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1187 : oddCount 1187 11 = 6 ∧ acceleratedOrbit 11 1187 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1187 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1187) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1187.1, data_11_1187.2] + +/-- Complete interval computation for depth 11, residue 1188. -/ +theorem bounds_11_1188 : exactInterval 11 1188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1188 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1188) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1188 : oddCount 1188 11 = 6 ∧ acceleratedOrbit 11 1188 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1188 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1188) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1188.1, data_11_1188.2] + +/-- Complete interval computation for depth 11, residue 1189. -/ +theorem bounds_11_1189 : exactInterval 11 1189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1189 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1189) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1189 : oddCount 1189 11 = 6 ∧ acceleratedOrbit 11 1189 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1189 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1189) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1189.1, data_11_1189.2] + +/-- Complete interval computation for depth 11, residue 1190. -/ +theorem bounds_11_1190 : exactInterval 11 1190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1190 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1190) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1190 : oddCount 1190 11 = 6 ∧ acceleratedOrbit 11 1190 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1190 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1190) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1190.1, data_11_1190.2] + +/-- Complete interval computation for depth 11, residue 1191. -/ +theorem bounds_11_1191 : exactInterval 11 1191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1191 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1191) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1191 : oddCount 1191 11 = 8 ∧ acceleratedOrbit 11 1191 = 3820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1191 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1191) = 3 ^ 8 * m + 3820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1191.1, data_11_1191.2] + +/-- Complete interval computation for depth 11, residue 1192. -/ +theorem bounds_11_1192 : exactInterval 11 1192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1192 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1192) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1192 : oddCount 1192 11 = 3 ∧ acceleratedOrbit 11 1192 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1192 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1192) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1192.1, data_11_1192.2] + +/-- Complete interval computation for depth 11, residue 1193. -/ +theorem bounds_11_1193 : exactInterval 11 1193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1193 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1193) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1193 : oddCount 1193 11 = 8 ∧ acceleratedOrbit 11 1193 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1193 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1193) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1193.1, data_11_1193.2] + +/-- Complete interval computation for depth 11, residue 1194. -/ +theorem bounds_11_1194 : exactInterval 11 1194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1194 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1194) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1194 : oddCount 1194 11 = 3 ∧ acceleratedOrbit 11 1194 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1194 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1194) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1194.1, data_11_1194.2] + +/-- Complete interval computation for depth 11, residue 1195. -/ +theorem bounds_11_1195 : exactInterval 11 1195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1195 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1195) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1195 : oddCount 1195 11 = 5 ∧ acceleratedOrbit 11 1195 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1195 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1195) = 3 ^ 5 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1195.1, data_11_1195.2] + +/-- Complete interval computation for depth 11, residue 1196. -/ +theorem bounds_11_1196 : exactInterval 11 1196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1196 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1196) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1196 : oddCount 1196 11 = 5 ∧ acceleratedOrbit 11 1196 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1196 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1196) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1196.1, data_11_1196.2] + +/-- Complete interval computation for depth 11, residue 1197. -/ +theorem bounds_11_1197 : exactInterval 11 1197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1197 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1197) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1197 : oddCount 1197 11 = 5 ∧ acceleratedOrbit 11 1197 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1197 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1197) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1197.1, data_11_1197.2] + +/-- Complete interval computation for depth 11, residue 1198. -/ +theorem bounds_11_1198 : exactInterval 11 1198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1198 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1198) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1198 : oddCount 1198 11 = 5 ∧ acceleratedOrbit 11 1198 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1198 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1198) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1198.1, data_11_1198.2] + +/-- Complete interval computation for depth 11, residue 1199. -/ +theorem bounds_11_1199 : exactInterval 11 1199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1199 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1199) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1199 : oddCount 1199 11 = 7 ∧ acceleratedOrbit 11 1199 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1199 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1199) = 3 ^ 7 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1199.1, data_11_1199.2] + +/-- Complete interval computation for depth 11, residue 1200. -/ +theorem bounds_11_1200 : exactInterval 11 1200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1200 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1200) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1200 : oddCount 1200 11 = 3 ∧ acceleratedOrbit 11 1200 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1200 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1200) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1200.1, data_11_1200.2] + +/-- Complete interval computation for depth 11, residue 1201. -/ +theorem bounds_11_1201 : exactInterval 11 1201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1201 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1201) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1201 : oddCount 1201 11 = 6 ∧ acceleratedOrbit 11 1201 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1201 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1201) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1201.1, data_11_1201.2] + +/-- Complete interval computation for depth 11, residue 1202. -/ +theorem bounds_11_1202 : exactInterval 11 1202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1202 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1202) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1202 : oddCount 1202 11 = 6 ∧ acceleratedOrbit 11 1202 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1202 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1202) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1202.1, data_11_1202.2] + +end Collatz.Research.StoppingAtlas.Batch0145 From 3c2f9d0a78d2ce4c7f087fee0c02e8a046e0f11e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:45 +0530 Subject: [PATCH 0146/1001] proof: certify atlas Batch0146 (11:1203 to 11:1217) --- Collatz/Research/StoppingAtlas/Batch0146.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0146.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0146.lean b/Collatz/Research/StoppingAtlas/Batch0146.lean new file mode 100644 index 00000000..197cc167 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0146.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0146 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1203. -/ +theorem bounds_11_1203 : exactInterval 11 1203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1203 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1203) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1203 : oddCount 1203 11 = 6 ∧ acceleratedOrbit 11 1203 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1203 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1203) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1203.1, data_11_1203.2] + +/-- Complete interval computation for depth 11, residue 1204. -/ +theorem bounds_11_1204 : exactInterval 11 1204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1204 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1204) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1204 : oddCount 1204 11 = 3 ∧ acceleratedOrbit 11 1204 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1204 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1204) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1204.1, data_11_1204.2] + +/-- Complete interval computation for depth 11, residue 1205. -/ +theorem bounds_11_1205 : exactInterval 11 1205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1205 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1205) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1205 : oddCount 1205 11 = 3 ∧ acceleratedOrbit 11 1205 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1205 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1205) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1205.1, data_11_1205.2] + +/-- Complete interval computation for depth 11, residue 1206. -/ +theorem bounds_11_1206 : exactInterval 11 1206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1206 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1206) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1206 : oddCount 1206 11 = 7 ∧ acceleratedOrbit 11 1206 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1206 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1206) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1206.1, data_11_1206.2] + +/-- Complete interval computation for depth 11, residue 1207. -/ +theorem bounds_11_1207 : exactInterval 11 1207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1207 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1207) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1207 : oddCount 1207 11 = 7 ∧ acceleratedOrbit 11 1207 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1207 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1207) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1207.1, data_11_1207.2] + +/-- Complete interval computation for depth 11, residue 1208. -/ +theorem bounds_11_1208 : exactInterval 11 1208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1208 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1208) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1208 : oddCount 1208 11 = 3 ∧ acceleratedOrbit 11 1208 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1208 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1208) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1208.1, data_11_1208.2] + +/-- Complete interval computation for depth 11, residue 1209. -/ +theorem bounds_11_1209 : exactInterval 11 1209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1209 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1209) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1209 : oddCount 1209 11 = 7 ∧ acceleratedOrbit 11 1209 = 1295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1209 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1209) = 3 ^ 7 * m + 1295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1209.1, data_11_1209.2] + +/-- Complete interval computation for depth 11, residue 1210. -/ +theorem bounds_11_1210 : exactInterval 11 1210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1210 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1210) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1210 : oddCount 1210 11 = 3 ∧ acceleratedOrbit 11 1210 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1210 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1210) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1210.1, data_11_1210.2] + +/-- Complete interval computation for depth 11, residue 1211. -/ +theorem bounds_11_1211 : exactInterval 11 1211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1211 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1211) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1211 : oddCount 1211 11 = 8 ∧ acceleratedOrbit 11 1211 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1211 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1211) = 3 ^ 8 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1211.1, data_11_1211.2] + +/-- Complete interval computation for depth 11, residue 1212. -/ +theorem bounds_11_1212 : exactInterval 11 1212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1212 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1212) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1212 : oddCount 1212 11 = 6 ∧ acceleratedOrbit 11 1212 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1212 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1212) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1212.1, data_11_1212.2] + +/-- Complete interval computation for depth 11, residue 1213. -/ +theorem bounds_11_1213 : exactInterval 11 1213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1213 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1213) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1213 : oddCount 1213 11 = 6 ∧ acceleratedOrbit 11 1213 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1213 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1213) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1213.1, data_11_1213.2] + +/-- Complete interval computation for depth 11, residue 1214. -/ +theorem bounds_11_1214 : exactInterval 11 1214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1214 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1214) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1214 : oddCount 1214 11 = 6 ∧ acceleratedOrbit 11 1214 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1214 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1214) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1214.1, data_11_1214.2] + +/-- Complete interval computation for depth 11, residue 1215. -/ +theorem bounds_11_1215 : exactInterval 11 1215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1215 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1215) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1215 : oddCount 1215 11 = 8 ∧ acceleratedOrbit 11 1215 = 3896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1215 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1215) = 3 ^ 8 * m + 3896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1215.1, data_11_1215.2] + +/-- Complete interval computation for depth 11, residue 1216. -/ +theorem bounds_11_1216 : exactInterval 11 1216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1216 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1216) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1216 : oddCount 1216 11 = 3 ∧ acceleratedOrbit 11 1216 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1216 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1216) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1216.1, data_11_1216.2] + +/-- Complete interval computation for depth 11, residue 1217. -/ +theorem bounds_11_1217 : exactInterval 11 1217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1217 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1217) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1217 : oddCount 1217 11 = 5 ∧ acceleratedOrbit 11 1217 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1217 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1217) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1217.1, data_11_1217.2] + +end Collatz.Research.StoppingAtlas.Batch0146 From 1885d5eb1a2201747b9fa06c638c6b714b91319b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:45 +0530 Subject: [PATCH 0147/1001] proof: certify atlas Batch0147 (11:1218 to 11:1232) --- Collatz/Research/StoppingAtlas/Batch0147.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0147.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0147.lean b/Collatz/Research/StoppingAtlas/Batch0147.lean new file mode 100644 index 00000000..ced4aebe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0147.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0147 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1218. -/ +theorem bounds_11_1218 : exactInterval 11 1218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1218 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1218) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1218 : oddCount 1218 11 = 5 ∧ acceleratedOrbit 11 1218 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1218 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1218) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1218.1, data_11_1218.2] + +/-- Complete interval computation for depth 11, residue 1219. -/ +theorem bounds_11_1219 : exactInterval 11 1219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1219 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1219) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1219 : oddCount 1219 11 = 5 ∧ acceleratedOrbit 11 1219 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1219 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1219) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1219.1, data_11_1219.2] + +/-- Complete interval computation for depth 11, residue 1220. -/ +theorem bounds_11_1220 : exactInterval 11 1220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1220 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1220) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1220 : oddCount 1220 11 = 4 ∧ acceleratedOrbit 11 1220 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1220 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1220) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1220.1, data_11_1220.2] + +/-- Complete interval computation for depth 11, residue 1221. -/ +theorem bounds_11_1221 : exactInterval 11 1221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1221 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1221) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1221 : oddCount 1221 11 = 4 ∧ acceleratedOrbit 11 1221 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1221 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1221) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1221.1, data_11_1221.2] + +/-- Complete interval computation for depth 11, residue 1222. -/ +theorem bounds_11_1222 : exactInterval 11 1222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1222 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1222) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1222 : oddCount 1222 11 = 4 ∧ acceleratedOrbit 11 1222 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1222 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1222) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1222.1, data_11_1222.2] + +/-- Complete interval computation for depth 11, residue 1223. -/ +theorem bounds_11_1223 : exactInterval 11 1223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1223 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1223) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1223 : oddCount 1223 11 = 6 ∧ acceleratedOrbit 11 1223 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1223 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1223) = 3 ^ 6 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1223.1, data_11_1223.2] + +/-- Complete interval computation for depth 11, residue 1224. -/ +theorem bounds_11_1224 : exactInterval 11 1224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1224 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1224) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1224 : oddCount 1224 11 = 4 ∧ acceleratedOrbit 11 1224 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1224 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1224) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1224.1, data_11_1224.2] + +/-- Complete interval computation for depth 11, residue 1225. -/ +theorem bounds_11_1225 : exactInterval 11 1225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1225 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1225) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1225 : oddCount 1225 11 = 5 ∧ acceleratedOrbit 11 1225 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1225 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1225) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1225.1, data_11_1225.2] + +/-- Complete interval computation for depth 11, residue 1226. -/ +theorem bounds_11_1226 : exactInterval 11 1226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1226 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1226) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1226 : oddCount 1226 11 = 4 ∧ acceleratedOrbit 11 1226 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1226 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1226) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1226.1, data_11_1226.2] + +/-- Complete interval computation for depth 11, residue 1227. -/ +theorem bounds_11_1227 : exactInterval 11 1227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1227 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1227) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1227 : oddCount 1227 11 = 5 ∧ acceleratedOrbit 11 1227 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1227 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1227) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1227.1, data_11_1227.2] + +/-- Complete interval computation for depth 11, residue 1228. -/ +theorem bounds_11_1228 : exactInterval 11 1228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1228 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1228) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1228 : oddCount 1228 11 = 4 ∧ acceleratedOrbit 11 1228 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1228 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1228) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1228.1, data_11_1228.2] + +/-- Complete interval computation for depth 11, residue 1229. -/ +theorem bounds_11_1229 : exactInterval 11 1229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1229 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1229) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1229 : oddCount 1229 11 = 4 ∧ acceleratedOrbit 11 1229 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1229 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1229) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1229.1, data_11_1229.2] + +/-- Complete interval computation for depth 11, residue 1230. -/ +theorem bounds_11_1230 : exactInterval 11 1230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1230 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1230) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1230 : oddCount 1230 11 = 7 ∧ acceleratedOrbit 11 1230 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1230 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1230) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1230.1, data_11_1230.2] + +/-- Complete interval computation for depth 11, residue 1231. -/ +theorem bounds_11_1231 : exactInterval 11 1231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1231 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1231) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1231 : oddCount 1231 11 = 7 ∧ acceleratedOrbit 11 1231 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1231 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1231) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1231.1, data_11_1231.2] + +/-- Complete interval computation for depth 11, residue 1232. -/ +theorem bounds_11_1232 : exactInterval 11 1232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1232 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1232) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1232 : oddCount 1232 11 = 3 ∧ acceleratedOrbit 11 1232 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1232 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1232) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1232.1, data_11_1232.2] + +end Collatz.Research.StoppingAtlas.Batch0147 From 2e1dfaa6b474a4207458df25a4c5d9aabe9d6c84 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:46 +0530 Subject: [PATCH 0148/1001] proof: certify atlas Batch0148 (11:1233 to 11:1248) --- Collatz/Research/StoppingAtlas/Batch0148.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0148.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0148.lean b/Collatz/Research/StoppingAtlas/Batch0148.lean new file mode 100644 index 00000000..c334450d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0148.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0148 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1233. -/ +theorem bounds_11_1233 : exactInterval 11 1233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1233 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1233) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1233 : oddCount 1233 11 = 7 ∧ acceleratedOrbit 11 1233 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1233 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1233) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1233.1, data_11_1233.2] + +/-- Complete interval computation for depth 11, residue 1234. -/ +theorem bounds_11_1234 : exactInterval 11 1234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1234 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1234) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1234 : oddCount 1234 11 = 7 ∧ acceleratedOrbit 11 1234 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1234 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1234) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1234.1, data_11_1234.2] + +/-- Complete interval computation for depth 11, residue 1235. -/ +theorem bounds_11_1235 : exactInterval 11 1235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1235 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1235) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1235 : oddCount 1235 11 = 7 ∧ acceleratedOrbit 11 1235 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1235 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1235) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1235.1, data_11_1235.2] + +/-- Complete interval computation for depth 11, residue 1236. -/ +theorem bounds_11_1236 : exactInterval 11 1236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1236 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1236) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1236 : oddCount 1236 11 = 3 ∧ acceleratedOrbit 11 1236 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1236 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1236) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1236.1, data_11_1236.2] + +/-- Complete interval computation for depth 11, residue 1237. -/ +theorem bounds_11_1237 : exactInterval 11 1237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1237 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1237) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1237 : oddCount 1237 11 = 3 ∧ acceleratedOrbit 11 1237 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1237 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1237) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1237.1, data_11_1237.2] + +/-- Complete interval computation for depth 11, residue 1238. -/ +theorem bounds_11_1238 : exactInterval 11 1238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1238 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1238) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1238 : oddCount 1238 11 = 6 ∧ acceleratedOrbit 11 1238 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1238 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1238) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1238.1, data_11_1238.2] + +/-- Complete interval computation for depth 11, residue 1239. -/ +theorem bounds_11_1239 : exactInterval 11 1239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1239 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1239) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1239 : oddCount 1239 11 = 6 ∧ acceleratedOrbit 11 1239 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1239 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1239) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1239.1, data_11_1239.2] + +/-- Complete interval computation for depth 11, residue 1240. -/ +theorem bounds_11_1240 : exactInterval 11 1240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1240 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1240) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1240 : oddCount 1240 11 = 6 ∧ acceleratedOrbit 11 1240 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1240 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1240) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1240.1, data_11_1240.2] + +/-- Complete interval computation for depth 11, residue 1241. -/ +theorem bounds_11_1241 : exactInterval 11 1241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1241 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1241) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1241 : oddCount 1241 11 = 5 ∧ acceleratedOrbit 11 1241 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1241 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1241) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1241.1, data_11_1241.2] + +/-- Complete interval computation for depth 11, residue 1242. -/ +theorem bounds_11_1242 : exactInterval 11 1242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1242 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1242) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1242 : oddCount 1242 11 = 6 ∧ acceleratedOrbit 11 1242 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1242 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1242) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1242.1, data_11_1242.2] + +/-- Complete interval computation for depth 11, residue 1243. -/ +theorem bounds_11_1243 : exactInterval 11 1243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1243 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1243) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1243 : oddCount 1243 11 = 6 ∧ acceleratedOrbit 11 1243 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1243 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1243) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1243.1, data_11_1243.2] + +/-- Complete interval computation for depth 11, residue 1244. -/ +theorem bounds_11_1244 : exactInterval 11 1244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1244 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1244) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1244 : oddCount 1244 11 = 6 ∧ acceleratedOrbit 11 1244 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1244 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1244) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1244.1, data_11_1244.2] + +/-- Complete interval computation for depth 11, residue 1245. -/ +theorem bounds_11_1245 : exactInterval 11 1245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1245 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1245) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1245 : oddCount 1245 11 = 6 ∧ acceleratedOrbit 11 1245 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1245 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1245) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1245.1, data_11_1245.2] + +/-- Complete interval computation for depth 11, residue 1246. -/ +theorem bounds_11_1246 : exactInterval 11 1246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1246 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1246) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1246 : oddCount 1246 11 = 7 ∧ acceleratedOrbit 11 1246 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1246 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1246) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1246.1, data_11_1246.2] + +/-- Complete interval computation for depth 11, residue 1247. -/ +theorem bounds_11_1247 : exactInterval 11 1247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1247 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1247) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1247 : oddCount 1247 11 = 7 ∧ acceleratedOrbit 11 1247 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1247 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1247) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1247.1, data_11_1247.2] + +/-- Complete interval computation for depth 11, residue 1248. -/ +theorem bounds_11_1248 : exactInterval 11 1248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1248 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1248) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1248 : oddCount 1248 11 = 5 ∧ acceleratedOrbit 11 1248 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1248 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1248) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1248.1, data_11_1248.2] + +end Collatz.Research.StoppingAtlas.Batch0148 From 955aafb81ea40fa76c5f8e55909d91a5938eaa5e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:46 +0530 Subject: [PATCH 0149/1001] proof: certify atlas Batch0149 (11:1249 to 11:1263) --- Collatz/Research/StoppingAtlas/Batch0149.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0149.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0149.lean b/Collatz/Research/StoppingAtlas/Batch0149.lean new file mode 100644 index 00000000..70996d5e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0149.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0149 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1249. -/ +theorem bounds_11_1249 : exactInterval 11 1249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1249 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1249) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1249 : oddCount 1249 11 = 8 ∧ acceleratedOrbit 11 1249 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1249 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1249) = 3 ^ 8 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1249.1, data_11_1249.2] + +/-- Complete interval computation for depth 11, residue 1250. -/ +theorem bounds_11_1250 : exactInterval 11 1250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1250 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1250) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1250 : oddCount 1250 11 = 3 ∧ acceleratedOrbit 11 1250 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1250 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1250) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1250.1, data_11_1250.2] + +/-- Complete interval computation for depth 11, residue 1251. -/ +theorem bounds_11_1251 : exactInterval 11 1251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1251 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1251) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1251 : oddCount 1251 11 = 3 ∧ acceleratedOrbit 11 1251 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1251 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1251) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1251.1, data_11_1251.2] + +/-- Complete interval computation for depth 11, residue 1252. -/ +theorem bounds_11_1252 : exactInterval 11 1252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1252 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1252) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1252 : oddCount 1252 11 = 6 ∧ acceleratedOrbit 11 1252 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1252 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1252) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1252.1, data_11_1252.2] + +/-- Complete interval computation for depth 11, residue 1253. -/ +theorem bounds_11_1253 : exactInterval 11 1253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1253 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1253) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1253 : oddCount 1253 11 = 6 ∧ acceleratedOrbit 11 1253 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1253 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1253) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1253.1, data_11_1253.2] + +/-- Complete interval computation for depth 11, residue 1254. -/ +theorem bounds_11_1254 : exactInterval 11 1254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1254 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1254) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1254 : oddCount 1254 11 = 6 ∧ acceleratedOrbit 11 1254 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1254 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1254) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1254.1, data_11_1254.2] + +/-- Complete interval computation for depth 11, residue 1255. -/ +theorem bounds_11_1255 : exactInterval 11 1255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1255 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1255) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1255 : oddCount 1255 11 = 8 ∧ acceleratedOrbit 11 1255 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1255 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1255) = 3 ^ 8 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1255.1, data_11_1255.2] + +/-- Complete interval computation for depth 11, residue 1256. -/ +theorem bounds_11_1256 : exactInterval 11 1256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1256 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1256) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1256 : oddCount 1256 11 = 5 ∧ acceleratedOrbit 11 1256 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1256 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1256) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1256.1, data_11_1256.2] + +/-- Complete interval computation for depth 11, residue 1257. -/ +theorem bounds_11_1257 : exactInterval 11 1257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1257 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1257) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1257 : oddCount 1257 11 = 6 ∧ acceleratedOrbit 11 1257 = 448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1257 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1257) = 3 ^ 6 * m + 448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1257.1, data_11_1257.2] + +/-- Complete interval computation for depth 11, residue 1258. -/ +theorem bounds_11_1258 : exactInterval 11 1258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1258 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1258) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1258 : oddCount 1258 11 = 5 ∧ acceleratedOrbit 11 1258 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1258 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1258) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1258.1, data_11_1258.2] + +/-- Complete interval computation for depth 11, residue 1259. -/ +theorem bounds_11_1259 : exactInterval 11 1259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1259 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1259) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1259 : oddCount 1259 11 = 8 ∧ acceleratedOrbit 11 1259 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1259 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1259) = 3 ^ 8 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1259.1, data_11_1259.2] + +/-- Complete interval computation for depth 11, residue 1260. -/ +theorem bounds_11_1260 : exactInterval 11 1260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1260 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1260) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1260 : oddCount 1260 11 = 4 ∧ acceleratedOrbit 11 1260 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1260 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1260) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1260.1, data_11_1260.2] + +/-- Complete interval computation for depth 11, residue 1261. -/ +theorem bounds_11_1261 : exactInterval 11 1261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1261 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1261) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1261 : oddCount 1261 11 = 4 ∧ acceleratedOrbit 11 1261 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1261 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1261) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1261.1, data_11_1261.2] + +/-- Complete interval computation for depth 11, residue 1262. -/ +theorem bounds_11_1262 : exactInterval 11 1262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1262 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1262) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1262 : oddCount 1262 11 = 4 ∧ acceleratedOrbit 11 1262 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1262 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1262) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1262.1, data_11_1262.2] + +/-- Complete interval computation for depth 11, residue 1263. -/ +theorem bounds_11_1263 : exactInterval 11 1263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1263 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1263) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1263 : oddCount 1263 11 = 10 ∧ acceleratedOrbit 11 1263 = 36449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1263 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1263) = 3 ^ 10 * m + 36449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1263.1, data_11_1263.2] + +end Collatz.Research.StoppingAtlas.Batch0149 From f8b4d3e73b16c2379d16b44265ab962189b16fe1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:46 +0530 Subject: [PATCH 0150/1001] proof: certify atlas Batch0150 (11:1264 to 11:1279) --- Collatz/Research/StoppingAtlas/Batch0150.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0150.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0150.lean b/Collatz/Research/StoppingAtlas/Batch0150.lean new file mode 100644 index 00000000..1a46c031 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0150.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0150 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1264. -/ +theorem bounds_11_1264 : exactInterval 11 1264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1264 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1264) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1264 : oddCount 1264 11 = 5 ∧ acceleratedOrbit 11 1264 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1264 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1264) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1264.1, data_11_1264.2] + +/-- Complete interval computation for depth 11, residue 1265. -/ +theorem bounds_11_1265 : exactInterval 11 1265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1265 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1265) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1265 : oddCount 1265 11 = 5 ∧ acceleratedOrbit 11 1265 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1265 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1265) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1265.1, data_11_1265.2] + +/-- Complete interval computation for depth 11, residue 1266. -/ +theorem bounds_11_1266 : exactInterval 11 1266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1266 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1266) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1266 : oddCount 1266 11 = 6 ∧ acceleratedOrbit 11 1266 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1266 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1266) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1266.1, data_11_1266.2] + +/-- Complete interval computation for depth 11, residue 1267. -/ +theorem bounds_11_1267 : exactInterval 11 1267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1267 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1267) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1267 : oddCount 1267 11 = 6 ∧ acceleratedOrbit 11 1267 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1267 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1267) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1267.1, data_11_1267.2] + +/-- Complete interval computation for depth 11, residue 1268. -/ +theorem bounds_11_1268 : exactInterval 11 1268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1268 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1268) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1268 : oddCount 1268 11 = 5 ∧ acceleratedOrbit 11 1268 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1268 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1268) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1268.1, data_11_1268.2] + +/-- Complete interval computation for depth 11, residue 1269. -/ +theorem bounds_11_1269 : exactInterval 11 1269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1269 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1269) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1269 : oddCount 1269 11 = 5 ∧ acceleratedOrbit 11 1269 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1269 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1269) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1269.1, data_11_1269.2] + +/-- Complete interval computation for depth 11, residue 1270. -/ +theorem bounds_11_1270 : exactInterval 11 1270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1270 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1270) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1270 : oddCount 1270 11 = 5 ∧ acceleratedOrbit 11 1270 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1270 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1270) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1270.1, data_11_1270.2] + +/-- Complete interval computation for depth 11, residue 1271. -/ +theorem bounds_11_1271 : exactInterval 11 1271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1271 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1271) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1271 : oddCount 1271 11 = 5 ∧ acceleratedOrbit 11 1271 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1271 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1271) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1271.1, data_11_1271.2] + +/-- Complete interval computation for depth 11, residue 1272. -/ +theorem bounds_11_1272 : exactInterval 11 1272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1272 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1272) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1272 : oddCount 1272 11 = 7 ∧ acceleratedOrbit 11 1272 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1272 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1272) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1272.1, data_11_1272.2] + +/-- Complete interval computation for depth 11, residue 1273. -/ +theorem bounds_11_1273 : exactInterval 11 1273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1273 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1273) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1273 : oddCount 1273 11 = 6 ∧ acceleratedOrbit 11 1273 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1273 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1273) = 3 ^ 6 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1273.1, data_11_1273.2] + +/-- Complete interval computation for depth 11, residue 1274. -/ +theorem bounds_11_1274 : exactInterval 11 1274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1274 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1274) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1274 : oddCount 1274 11 = 7 ∧ acceleratedOrbit 11 1274 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1274 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1274) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1274.1, data_11_1274.2] + +/-- Complete interval computation for depth 11, residue 1275. -/ +theorem bounds_11_1275 : exactInterval 11 1275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1275 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1275) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1275 : oddCount 1275 11 = 8 ∧ acceleratedOrbit 11 1275 = 4090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1275 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1275) = 3 ^ 8 * m + 4090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1275.1, data_11_1275.2] + +/-- Complete interval computation for depth 11, residue 1276. -/ +theorem bounds_11_1276 : exactInterval 11 1276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1276 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1276) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1276 : oddCount 1276 11 = 7 ∧ acceleratedOrbit 11 1276 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1276 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1276) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1276.1, data_11_1276.2] + +/-- Complete interval computation for depth 11, residue 1277. -/ +theorem bounds_11_1277 : exactInterval 11 1277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1277 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1277) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1277 : oddCount 1277 11 = 7 ∧ acceleratedOrbit 11 1277 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1277 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1277) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1277.1, data_11_1277.2] + +/-- Complete interval computation for depth 11, residue 1278. -/ +theorem bounds_11_1278 : exactInterval 11 1278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1278 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1278) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1278 : oddCount 1278 11 = 9 ∧ acceleratedOrbit 11 1278 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1278 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1278) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1278.1, data_11_1278.2] + +/-- Complete interval computation for depth 11, residue 1279. -/ +theorem bounds_11_1279 : exactInterval 11 1279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1279 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1279) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1279 : oddCount 1279 11 = 9 ∧ acceleratedOrbit 11 1279 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1279 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1279) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1279.1, data_11_1279.2] + +end Collatz.Research.StoppingAtlas.Batch0150 From 3fd8710f7e02366781d591e3f92aefe8c0584ed3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:47 +0530 Subject: [PATCH 0151/1001] proof: certify atlas Batch0151 (11:1280 to 11:1294) --- Collatz/Research/StoppingAtlas/Batch0151.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0151.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0151.lean b/Collatz/Research/StoppingAtlas/Batch0151.lean new file mode 100644 index 00000000..9c6e7c8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0151.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0151 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1280. -/ +theorem bounds_11_1280 : exactInterval 11 1280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1280 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1280) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1280 : oddCount 1280 11 = 1 ∧ acceleratedOrbit 11 1280 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1280 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1280) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1280.1, data_11_1280.2] + +/-- Complete interval computation for depth 11, residue 1281. -/ +theorem bounds_11_1281 : exactInterval 11 1281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1281 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1281) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1281 : oddCount 1281 11 = 6 ∧ acceleratedOrbit 11 1281 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1281 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1281) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1281.1, data_11_1281.2] + +/-- Complete interval computation for depth 11, residue 1282. -/ +theorem bounds_11_1282 : exactInterval 11 1282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1282 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1282) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1282 : oddCount 1282 11 = 7 ∧ acceleratedOrbit 11 1282 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1282 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1282) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1282.1, data_11_1282.2] + +/-- Complete interval computation for depth 11, residue 1283. -/ +theorem bounds_11_1283 : exactInterval 11 1283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1283 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1283) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1283 : oddCount 1283 11 = 7 ∧ acceleratedOrbit 11 1283 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1283 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1283) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1283.1, data_11_1283.2] + +/-- Complete interval computation for depth 11, residue 1284. -/ +theorem bounds_11_1284 : exactInterval 11 1284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1284 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1284) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1284 : oddCount 1284 11 = 3 ∧ acceleratedOrbit 11 1284 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1284 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1284) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1284.1, data_11_1284.2] + +/-- Complete interval computation for depth 11, residue 1285. -/ +theorem bounds_11_1285 : exactInterval 11 1285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1285 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1285) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1285 : oddCount 1285 11 = 3 ∧ acceleratedOrbit 11 1285 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1285 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1285) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1285.1, data_11_1285.2] + +/-- Complete interval computation for depth 11, residue 1286. -/ +theorem bounds_11_1286 : exactInterval 11 1286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1286 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1286) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1286 : oddCount 1286 11 = 3 ∧ acceleratedOrbit 11 1286 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1286 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1286) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1286.1, data_11_1286.2] + +/-- Complete interval computation for depth 11, residue 1287. -/ +theorem bounds_11_1287 : exactInterval 11 1287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1287 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1287) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1287 : oddCount 1287 11 = 8 ∧ acceleratedOrbit 11 1287 = 4130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1287 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1287) = 3 ^ 8 * m + 4130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1287.1, data_11_1287.2] + +/-- Complete interval computation for depth 11, residue 1288. -/ +theorem bounds_11_1288 : exactInterval 11 1288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1288 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1288) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1288 : oddCount 1288 11 = 5 ∧ acceleratedOrbit 11 1288 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1288 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1288) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1288.1, data_11_1288.2] + +/-- Complete interval computation for depth 11, residue 1289. -/ +theorem bounds_11_1289 : exactInterval 11 1289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1289 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1289) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1289 : oddCount 1289 11 = 7 ∧ acceleratedOrbit 11 1289 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1289 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1289) = 3 ^ 7 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1289.1, data_11_1289.2] + +/-- Complete interval computation for depth 11, residue 1290. -/ +theorem bounds_11_1290 : exactInterval 11 1290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1290 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1290) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1290 : oddCount 1290 11 = 5 ∧ acceleratedOrbit 11 1290 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1290 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1290) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1290.1, data_11_1290.2] + +/-- Complete interval computation for depth 11, residue 1291. -/ +theorem bounds_11_1291 : exactInterval 11 1291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1291 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1291) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1291 : oddCount 1291 11 = 6 ∧ acceleratedOrbit 11 1291 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1291 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1291) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1291.1, data_11_1291.2] + +/-- Complete interval computation for depth 11, residue 1292. -/ +theorem bounds_11_1292 : exactInterval 11 1292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1292 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1292) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1292 : oddCount 1292 11 = 5 ∧ acceleratedOrbit 11 1292 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1292 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1292) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1292.1, data_11_1292.2] + +/-- Complete interval computation for depth 11, residue 1293. -/ +theorem bounds_11_1293 : exactInterval 11 1293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1293 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1293) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1293 : oddCount 1293 11 = 5 ∧ acceleratedOrbit 11 1293 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1293 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1293) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1293.1, data_11_1293.2] + +/-- Complete interval computation for depth 11, residue 1294. -/ +theorem bounds_11_1294 : exactInterval 11 1294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1294 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1294) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1294 : oddCount 1294 11 = 5 ∧ acceleratedOrbit 11 1294 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1294 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1294) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1294.1, data_11_1294.2] + +end Collatz.Research.StoppingAtlas.Batch0151 From 00812719cdf564e222310d976738a71043ecc01d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:47 +0530 Subject: [PATCH 0152/1001] proof: certify atlas Batch0152 (11:1295 to 11:1309) --- Collatz/Research/StoppingAtlas/Batch0152.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0152.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0152.lean b/Collatz/Research/StoppingAtlas/Batch0152.lean new file mode 100644 index 00000000..a76da1ec --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0152.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0152 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1295. -/ +theorem bounds_11_1295 : exactInterval 11 1295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1295 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1295) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1295 : oddCount 1295 11 = 5 ∧ acceleratedOrbit 11 1295 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1295 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1295) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1295.1, data_11_1295.2] + +/-- Complete interval computation for depth 11, residue 1296. -/ +theorem bounds_11_1296 : exactInterval 11 1296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1296 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1296) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1296 : oddCount 1296 11 = 4 ∧ acceleratedOrbit 11 1296 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1296 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1296) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1296.1, data_11_1296.2] + +/-- Complete interval computation for depth 11, residue 1297. -/ +theorem bounds_11_1297 : exactInterval 11 1297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1297 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1297) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1297 : oddCount 1297 11 = 5 ∧ acceleratedOrbit 11 1297 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1297 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1297) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1297.1, data_11_1297.2] + +/-- Complete interval computation for depth 11, residue 1298. -/ +theorem bounds_11_1298 : exactInterval 11 1298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1298 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1298) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1298 : oddCount 1298 11 = 7 ∧ acceleratedOrbit 11 1298 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1298 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1298) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1298.1, data_11_1298.2] + +/-- Complete interval computation for depth 11, residue 1299. -/ +theorem bounds_11_1299 : exactInterval 11 1299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1299 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1299) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1299 : oddCount 1299 11 = 7 ∧ acceleratedOrbit 11 1299 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1299 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1299) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1299.1, data_11_1299.2] + +/-- Complete interval computation for depth 11, residue 1300. -/ +theorem bounds_11_1300 : exactInterval 11 1300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1300 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1300) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1300 : oddCount 1300 11 = 4 ∧ acceleratedOrbit 11 1300 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1300 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1300) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1300.1, data_11_1300.2] + +/-- Complete interval computation for depth 11, residue 1301. -/ +theorem bounds_11_1301 : exactInterval 11 1301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1301 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1301) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1301 : oddCount 1301 11 = 4 ∧ acceleratedOrbit 11 1301 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1301 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1301) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1301.1, data_11_1301.2] + +/-- Complete interval computation for depth 11, residue 1302. -/ +theorem bounds_11_1302 : exactInterval 11 1302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1302 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1302) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1302 : oddCount 1302 11 = 5 ∧ acceleratedOrbit 11 1302 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1302 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1302) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1302.1, data_11_1302.2] + +/-- Complete interval computation for depth 11, residue 1303. -/ +theorem bounds_11_1303 : exactInterval 11 1303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1303 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1303) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1303 : oddCount 1303 11 = 5 ∧ acceleratedOrbit 11 1303 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1303 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1303) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1303.1, data_11_1303.2] + +/-- Complete interval computation for depth 11, residue 1304. -/ +theorem bounds_11_1304 : exactInterval 11 1304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1304 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1304) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1304 : oddCount 1304 11 = 4 ∧ acceleratedOrbit 11 1304 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1304 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1304) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1304.1, data_11_1304.2] + +/-- Complete interval computation for depth 11, residue 1305. -/ +theorem bounds_11_1305 : exactInterval 11 1305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1305 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1305) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1305 : oddCount 1305 11 = 7 ∧ acceleratedOrbit 11 1305 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1305 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1305) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1305.1, data_11_1305.2] + +/-- Complete interval computation for depth 11, residue 1306. -/ +theorem bounds_11_1306 : exactInterval 11 1306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1306 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1306) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1306 : oddCount 1306 11 = 4 ∧ acceleratedOrbit 11 1306 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1306 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1306) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1306.1, data_11_1306.2] + +/-- Complete interval computation for depth 11, residue 1307. -/ +theorem bounds_11_1307 : exactInterval 11 1307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1307 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1307) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1307 : oddCount 1307 11 = 9 ∧ acceleratedOrbit 11 1307 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1307 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1307) = 3 ^ 9 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1307.1, data_11_1307.2] + +/-- Complete interval computation for depth 11, residue 1308. -/ +theorem bounds_11_1308 : exactInterval 11 1308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1308 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1308) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1308 : oddCount 1308 11 = 7 ∧ acceleratedOrbit 11 1308 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1308 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1308) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1308.1, data_11_1308.2] + +/-- Complete interval computation for depth 11, residue 1309. -/ +theorem bounds_11_1309 : exactInterval 11 1309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1309 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1309) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1309 : oddCount 1309 11 = 7 ∧ acceleratedOrbit 11 1309 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1309 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1309) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1309.1, data_11_1309.2] + +end Collatz.Research.StoppingAtlas.Batch0152 From e50a30ae13484bcdd3e7012b04013057a84ac0f8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:47 +0530 Subject: [PATCH 0153/1001] proof: certify atlas Batch0153 (11:1310 to 11:1325) --- Collatz/Research/StoppingAtlas/Batch0153.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0153.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0153.lean b/Collatz/Research/StoppingAtlas/Batch0153.lean new file mode 100644 index 00000000..e8eacacf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0153.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0153 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1310. -/ +theorem bounds_11_1310 : exactInterval 11 1310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1310 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1310) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1310 : oddCount 1310 11 = 7 ∧ acceleratedOrbit 11 1310 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1310 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1310) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1310.1, data_11_1310.2] + +/-- Complete interval computation for depth 11, residue 1311. -/ +theorem bounds_11_1311 : exactInterval 11 1311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1311 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1311) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1311 : oddCount 1311 11 = 6 ∧ acceleratedOrbit 11 1311 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1311 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1311) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1311.1, data_11_1311.2] + +/-- Complete interval computation for depth 11, residue 1312. -/ +theorem bounds_11_1312 : exactInterval 11 1312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1312 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1312) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1312 : oddCount 1312 11 = 5 ∧ acceleratedOrbit 11 1312 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1312 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1312) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1312.1, data_11_1312.2] + +/-- Complete interval computation for depth 11, residue 1313. -/ +theorem bounds_11_1313 : exactInterval 11 1313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1313 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1313) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1313 : oddCount 1313 11 = 4 ∧ acceleratedOrbit 11 1313 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1313 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1313) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1313.1, data_11_1313.2] + +/-- Complete interval computation for depth 11, residue 1314. -/ +theorem bounds_11_1314 : exactInterval 11 1314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1314 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1314) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1314 : oddCount 1314 11 = 5 ∧ acceleratedOrbit 11 1314 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1314 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1314) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1314.1, data_11_1314.2] + +/-- Complete interval computation for depth 11, residue 1315. -/ +theorem bounds_11_1315 : exactInterval 11 1315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1315 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1315) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1315 : oddCount 1315 11 = 5 ∧ acceleratedOrbit 11 1315 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1315 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1315) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1315.1, data_11_1315.2] + +/-- Complete interval computation for depth 11, residue 1316. -/ +theorem bounds_11_1316 : exactInterval 11 1316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1316 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1316) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1316 : oddCount 1316 11 = 5 ∧ acceleratedOrbit 11 1316 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1316 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1316) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1316.1, data_11_1316.2] + +/-- Complete interval computation for depth 11, residue 1317. -/ +theorem bounds_11_1317 : exactInterval 11 1317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1317 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1317) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1317 : oddCount 1317 11 = 5 ∧ acceleratedOrbit 11 1317 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1317 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1317) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1317.1, data_11_1317.2] + +/-- Complete interval computation for depth 11, residue 1318. -/ +theorem bounds_11_1318 : exactInterval 11 1318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1318 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1318) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1318 : oddCount 1318 11 = 5 ∧ acceleratedOrbit 11 1318 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1318 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1318) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1318.1, data_11_1318.2] + +/-- Complete interval computation for depth 11, residue 1319. -/ +theorem bounds_11_1319 : exactInterval 11 1319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1319 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1319) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1319 : oddCount 1319 11 = 6 ∧ acceleratedOrbit 11 1319 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1319 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1319) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1319.1, data_11_1319.2] + +/-- Complete interval computation for depth 11, residue 1320. -/ +theorem bounds_11_1320 : exactInterval 11 1320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1320 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1320) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1320 : oddCount 1320 11 = 5 ∧ acceleratedOrbit 11 1320 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1320 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1320) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1320.1, data_11_1320.2] + +/-- Complete interval computation for depth 11, residue 1321. -/ +theorem bounds_11_1321 : exactInterval 11 1321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1321 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1321) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1321 : oddCount 1321 11 = 8 ∧ acceleratedOrbit 11 1321 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1321 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1321) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1321.1, data_11_1321.2] + +/-- Complete interval computation for depth 11, residue 1322. -/ +theorem bounds_11_1322 : exactInterval 11 1322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1322 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1322) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1322 : oddCount 1322 11 = 5 ∧ acceleratedOrbit 11 1322 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1322 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1322) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1322.1, data_11_1322.2] + +/-- Complete interval computation for depth 11, residue 1323. -/ +theorem bounds_11_1323 : exactInterval 11 1323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1323 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1323) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1323 : oddCount 1323 11 = 6 ∧ acceleratedOrbit 11 1323 = 472 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1323 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1323) = 3 ^ 6 * m + 472 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1323.1, data_11_1323.2] + +/-- Complete interval computation for depth 11, residue 1324. -/ +theorem bounds_11_1324 : exactInterval 11 1324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1324 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1324) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1324 : oddCount 1324 11 = 4 ∧ acceleratedOrbit 11 1324 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1324 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1324) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1324.1, data_11_1324.2] + +/-- Complete interval computation for depth 11, residue 1325. -/ +theorem bounds_11_1325 : exactInterval 11 1325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1325 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1325) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1325 : oddCount 1325 11 = 4 ∧ acceleratedOrbit 11 1325 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1325 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1325) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1325.1, data_11_1325.2] + +end Collatz.Research.StoppingAtlas.Batch0153 From c5186bbe5478146cb2bd6e4bbd3e53e2946401eb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:48 +0530 Subject: [PATCH 0154/1001] proof: certify atlas Batch0154 (11:1326 to 11:1340) --- Collatz/Research/StoppingAtlas/Batch0154.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0154.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0154.lean b/Collatz/Research/StoppingAtlas/Batch0154.lean new file mode 100644 index 00000000..ed09e542 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0154.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0154 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1326. -/ +theorem bounds_11_1326 : exactInterval 11 1326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1326 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1326) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1326 : oddCount 1326 11 = 4 ∧ acceleratedOrbit 11 1326 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1326 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1326) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1326.1, data_11_1326.2] + +/-- Complete interval computation for depth 11, residue 1327. -/ +theorem bounds_11_1327 : exactInterval 11 1327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1327 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1327) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1327 : oddCount 1327 11 = 8 ∧ acceleratedOrbit 11 1327 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1327 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1327) = 3 ^ 8 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1327.1, data_11_1327.2] + +/-- Complete interval computation for depth 11, residue 1328. -/ +theorem bounds_11_1328 : exactInterval 11 1328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1328 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1328) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1328 : oddCount 1328 11 = 5 ∧ acceleratedOrbit 11 1328 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1328 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1328) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1328.1, data_11_1328.2] + +/-- Complete interval computation for depth 11, residue 1329. -/ +theorem bounds_11_1329 : exactInterval 11 1329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1329 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1329) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1329 : oddCount 1329 11 = 6 ∧ acceleratedOrbit 11 1329 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1329 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1329) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1329.1, data_11_1329.2] + +/-- Complete interval computation for depth 11, residue 1330. -/ +theorem bounds_11_1330 : exactInterval 11 1330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1330 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1330) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1330 : oddCount 1330 11 = 6 ∧ acceleratedOrbit 11 1330 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1330 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1330) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1330.1, data_11_1330.2] + +/-- Complete interval computation for depth 11, residue 1331. -/ +theorem bounds_11_1331 : exactInterval 11 1331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1331 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1331) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1331 : oddCount 1331 11 = 6 ∧ acceleratedOrbit 11 1331 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1331 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1331) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1331.1, data_11_1331.2] + +/-- Complete interval computation for depth 11, residue 1332. -/ +theorem bounds_11_1332 : exactInterval 11 1332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1332 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1332) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1332 : oddCount 1332 11 = 5 ∧ acceleratedOrbit 11 1332 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1332 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1332) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1332.1, data_11_1332.2] + +/-- Complete interval computation for depth 11, residue 1333. -/ +theorem bounds_11_1333 : exactInterval 11 1333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1333 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1333) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1333 : oddCount 1333 11 = 5 ∧ acceleratedOrbit 11 1333 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1333 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1333) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1333.1, data_11_1333.2] + +/-- Complete interval computation for depth 11, residue 1334. -/ +theorem bounds_11_1334 : exactInterval 11 1334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1334 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1334) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1334 : oddCount 1334 11 = 8 ∧ acceleratedOrbit 11 1334 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1334 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1334) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1334.1, data_11_1334.2] + +/-- Complete interval computation for depth 11, residue 1335. -/ +theorem bounds_11_1335 : exactInterval 11 1335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1335 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1335) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1335 : oddCount 1335 11 = 8 ∧ acceleratedOrbit 11 1335 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1335 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1335) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1335.1, data_11_1335.2] + +/-- Complete interval computation for depth 11, residue 1336. -/ +theorem bounds_11_1336 : exactInterval 11 1336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1336 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1336) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1336 : oddCount 1336 11 = 6 ∧ acceleratedOrbit 11 1336 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1336 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1336) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1336.1, data_11_1336.2] + +/-- Complete interval computation for depth 11, residue 1337. -/ +theorem bounds_11_1337 : exactInterval 11 1337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1337 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1337) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1337 : oddCount 1337 11 = 8 ∧ acceleratedOrbit 11 1337 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1337 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1337) = 3 ^ 8 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1337.1, data_11_1337.2] + +/-- Complete interval computation for depth 11, residue 1338. -/ +theorem bounds_11_1338 : exactInterval 11 1338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1338 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1338) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1338 : oddCount 1338 11 = 6 ∧ acceleratedOrbit 11 1338 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1338 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1338) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1338.1, data_11_1338.2] + +/-- Complete interval computation for depth 11, residue 1339. -/ +theorem bounds_11_1339 : exactInterval 11 1339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1339 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1339) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1339 : oddCount 1339 11 = 4 ∧ acceleratedOrbit 11 1339 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1339 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1339) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1339.1, data_11_1339.2] + +/-- Complete interval computation for depth 11, residue 1340. -/ +theorem bounds_11_1340 : exactInterval 11 1340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1340 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1340) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1340 : oddCount 1340 11 = 6 ∧ acceleratedOrbit 11 1340 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1340 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1340) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1340.1, data_11_1340.2] + +end Collatz.Research.StoppingAtlas.Batch0154 From c0ea0cbbf33788ef32d7b6aae63da39b68fe9fc5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:48 +0530 Subject: [PATCH 0155/1001] proof: certify atlas Batch0155 (11:1341 to 11:1355) --- Collatz/Research/StoppingAtlas/Batch0155.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0155.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0155.lean b/Collatz/Research/StoppingAtlas/Batch0155.lean new file mode 100644 index 00000000..9e2902f4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0155.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0155 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1341. -/ +theorem bounds_11_1341 : exactInterval 11 1341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1341 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1341) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1341 : oddCount 1341 11 = 6 ∧ acceleratedOrbit 11 1341 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1341 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1341) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1341.1, data_11_1341.2] + +/-- Complete interval computation for depth 11, residue 1342. -/ +theorem bounds_11_1342 : exactInterval 11 1342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1342 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1342) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1342 : oddCount 1342 11 = 8 ∧ acceleratedOrbit 11 1342 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1342 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1342) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1342.1, data_11_1342.2] + +/-- Complete interval computation for depth 11, residue 1343. -/ +theorem bounds_11_1343 : exactInterval 11 1343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1343 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1343) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1343 : oddCount 1343 11 = 8 ∧ acceleratedOrbit 11 1343 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1343 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1343) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1343.1, data_11_1343.2] + +/-- Complete interval computation for depth 11, residue 1344. -/ +theorem bounds_11_1344 : exactInterval 11 1344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1344 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1344) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1344 : oddCount 1344 11 = 1 ∧ acceleratedOrbit 11 1344 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1344 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1344) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1344.1, data_11_1344.2] + +/-- Complete interval computation for depth 11, residue 1345. -/ +theorem bounds_11_1345 : exactInterval 11 1345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1345 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1345) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1345 : oddCount 1345 11 = 5 ∧ acceleratedOrbit 11 1345 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1345 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1345) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1345.1, data_11_1345.2] + +/-- Complete interval computation for depth 11, residue 1346. -/ +theorem bounds_11_1346 : exactInterval 11 1346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1346 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1346) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1346 : oddCount 1346 11 = 6 ∧ acceleratedOrbit 11 1346 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1346 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1346) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1346.1, data_11_1346.2] + +/-- Complete interval computation for depth 11, residue 1347. -/ +theorem bounds_11_1347 : exactInterval 11 1347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1347 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1347) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1347 : oddCount 1347 11 = 6 ∧ acceleratedOrbit 11 1347 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1347 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1347) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1347.1, data_11_1347.2] + +/-- Complete interval computation for depth 11, residue 1348. -/ +theorem bounds_11_1348 : exactInterval 11 1348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1348 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1348) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1348 : oddCount 1348 11 = 6 ∧ acceleratedOrbit 11 1348 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1348 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1348) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1348.1, data_11_1348.2] + +/-- Complete interval computation for depth 11, residue 1349. -/ +theorem bounds_11_1349 : exactInterval 11 1349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1349 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1349) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1349 : oddCount 1349 11 = 6 ∧ acceleratedOrbit 11 1349 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1349 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1349) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1349.1, data_11_1349.2] + +/-- Complete interval computation for depth 11, residue 1350. -/ +theorem bounds_11_1350 : exactInterval 11 1350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1350 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1350) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1350 : oddCount 1350 11 = 6 ∧ acceleratedOrbit 11 1350 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1350 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1350) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1350.1, data_11_1350.2] + +/-- Complete interval computation for depth 11, residue 1351. -/ +theorem bounds_11_1351 : exactInterval 11 1351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1351 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1351) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1351 : oddCount 1351 11 = 8 ∧ acceleratedOrbit 11 1351 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1351 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1351) = 3 ^ 8 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1351.1, data_11_1351.2] + +/-- Complete interval computation for depth 11, residue 1352. -/ +theorem bounds_11_1352 : exactInterval 11 1352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1352 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1352) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1352 : oddCount 1352 11 = 7 ∧ acceleratedOrbit 11 1352 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1352 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1352) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1352.1, data_11_1352.2] + +/-- Complete interval computation for depth 11, residue 1353. -/ +theorem bounds_11_1353 : exactInterval 11 1353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1353 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1353) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1353 : oddCount 1353 11 = 7 ∧ acceleratedOrbit 11 1353 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1353 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1353) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1353.1, data_11_1353.2] + +/-- Complete interval computation for depth 11, residue 1354. -/ +theorem bounds_11_1354 : exactInterval 11 1354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1354 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1354) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1354 : oddCount 1354 11 = 7 ∧ acceleratedOrbit 11 1354 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1354 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1354) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1354.1, data_11_1354.2] + +/-- Complete interval computation for depth 11, residue 1355. -/ +theorem bounds_11_1355 : exactInterval 11 1355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1355 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1355) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1355 : oddCount 1355 11 = 6 ∧ acceleratedOrbit 11 1355 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1355 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1355) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1355.1, data_11_1355.2] + +end Collatz.Research.StoppingAtlas.Batch0155 From 72406aa7e6706e8c182fe376d63d5ee11387dbda Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:48 +0530 Subject: [PATCH 0156/1001] proof: certify atlas Batch0156 (11:1356 to 11:1371) --- Collatz/Research/StoppingAtlas/Batch0156.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0156.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0156.lean b/Collatz/Research/StoppingAtlas/Batch0156.lean new file mode 100644 index 00000000..a8f51d8d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0156.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0156 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1356. -/ +theorem bounds_11_1356 : exactInterval 11 1356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1356 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1356) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1356 : oddCount 1356 11 = 7 ∧ acceleratedOrbit 11 1356 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1356 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1356) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1356.1, data_11_1356.2] + +/-- Complete interval computation for depth 11, residue 1357. -/ +theorem bounds_11_1357 : exactInterval 11 1357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1357 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1357) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1357 : oddCount 1357 11 = 7 ∧ acceleratedOrbit 11 1357 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1357 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1357) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1357.1, data_11_1357.2] + +/-- Complete interval computation for depth 11, residue 1358. -/ +theorem bounds_11_1358 : exactInterval 11 1358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1358 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1358) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1358 : oddCount 1358 11 = 7 ∧ acceleratedOrbit 11 1358 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1358 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1358) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1358.1, data_11_1358.2] + +/-- Complete interval computation for depth 11, residue 1359. -/ +theorem bounds_11_1359 : exactInterval 11 1359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1359 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1359) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1359 : oddCount 1359 11 = 7 ∧ acceleratedOrbit 11 1359 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1359 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1359) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1359.1, data_11_1359.2] + +/-- Complete interval computation for depth 11, residue 1360. -/ +theorem bounds_11_1360 : exactInterval 11 1360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1360 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1360) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1360 : oddCount 1360 11 = 1 ∧ acceleratedOrbit 11 1360 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1360 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1360) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1360.1, data_11_1360.2] + +/-- Complete interval computation for depth 11, residue 1361. -/ +theorem bounds_11_1361 : exactInterval 11 1361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1361 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1361) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1361 : oddCount 1361 11 = 8 ∧ acceleratedOrbit 11 1361 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1361 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1361) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1361.1, data_11_1361.2] + +/-- Complete interval computation for depth 11, residue 1362. -/ +theorem bounds_11_1362 : exactInterval 11 1362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1362 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1362) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1362 : oddCount 1362 11 = 9 ∧ acceleratedOrbit 11 1362 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1362 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1362) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1362.1, data_11_1362.2] + +/-- Complete interval computation for depth 11, residue 1363. -/ +theorem bounds_11_1363 : exactInterval 11 1363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1363 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1363) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1363 : oddCount 1363 11 = 9 ∧ acceleratedOrbit 11 1363 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1363 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1363) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1363.1, data_11_1363.2] + +/-- Complete interval computation for depth 11, residue 1364. -/ +theorem bounds_11_1364 : exactInterval 11 1364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1364 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1364) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1364 : oddCount 1364 11 = 1 ∧ acceleratedOrbit 11 1364 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1364 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1364) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1364.1, data_11_1364.2] + +/-- Complete interval computation for depth 11, residue 1365. -/ +theorem bounds_11_1365 : exactInterval 11 1365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1365 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1365) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1365 : oddCount 1365 11 = 1 ∧ acceleratedOrbit 11 1365 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1365 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1365) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1365.1, data_11_1365.2] + +/-- Complete interval computation for depth 11, residue 1366. -/ +theorem bounds_11_1366 : exactInterval 11 1366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1366 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1366) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1366 : oddCount 1366 11 = 6 ∧ acceleratedOrbit 11 1366 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1366 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1366) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1366.1, data_11_1366.2] + +/-- Complete interval computation for depth 11, residue 1367. -/ +theorem bounds_11_1367 : exactInterval 11 1367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1367 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1367) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1367 : oddCount 1367 11 = 6 ∧ acceleratedOrbit 11 1367 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1367 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1367) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1367.1, data_11_1367.2] + +/-- Complete interval computation for depth 11, residue 1368. -/ +theorem bounds_11_1368 : exactInterval 11 1368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1368 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1368) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1368 : oddCount 1368 11 = 5 ∧ acceleratedOrbit 11 1368 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1368 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1368) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1368.1, data_11_1368.2] + +/-- Complete interval computation for depth 11, residue 1369. -/ +theorem bounds_11_1369 : exactInterval 11 1369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1369 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1369) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1369 : oddCount 1369 11 = 5 ∧ acceleratedOrbit 11 1369 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1369 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1369) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1369.1, data_11_1369.2] + +/-- Complete interval computation for depth 11, residue 1370. -/ +theorem bounds_11_1370 : exactInterval 11 1370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1370 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1370) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1370 : oddCount 1370 11 = 5 ∧ acceleratedOrbit 11 1370 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1370 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1370) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1370.1, data_11_1370.2] + +/-- Complete interval computation for depth 11, residue 1371. -/ +theorem bounds_11_1371 : exactInterval 11 1371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1371 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1371) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1371 : oddCount 1371 11 = 7 ∧ acceleratedOrbit 11 1371 = 1466 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1371 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1371) = 3 ^ 7 * m + 1466 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1371.1, data_11_1371.2] + +end Collatz.Research.StoppingAtlas.Batch0156 From 92292b2f42859c314ec8179181925c40b004c1f4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:49 +0530 Subject: [PATCH 0157/1001] proof: certify atlas Batch0157 (11:1372 to 11:1386) --- Collatz/Research/StoppingAtlas/Batch0157.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0157.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0157.lean b/Collatz/Research/StoppingAtlas/Batch0157.lean new file mode 100644 index 00000000..fea31b60 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0157.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0157 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1372. -/ +theorem bounds_11_1372 : exactInterval 11 1372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1372 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1372) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1372 : oddCount 1372 11 = 5 ∧ acceleratedOrbit 11 1372 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1372 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1372) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1372.1, data_11_1372.2] + +/-- Complete interval computation for depth 11, residue 1373. -/ +theorem bounds_11_1373 : exactInterval 11 1373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1373 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1373) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1373 : oddCount 1373 11 = 5 ∧ acceleratedOrbit 11 1373 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1373 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1373) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1373.1, data_11_1373.2] + +/-- Complete interval computation for depth 11, residue 1374. -/ +theorem bounds_11_1374 : exactInterval 11 1374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1374 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1374) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1374 : oddCount 1374 11 = 6 ∧ acceleratedOrbit 11 1374 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1374 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1374) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1374.1, data_11_1374.2] + +/-- Complete interval computation for depth 11, residue 1375. -/ +theorem bounds_11_1375 : exactInterval 11 1375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1375 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1375) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1375 : oddCount 1375 11 = 6 ∧ acceleratedOrbit 11 1375 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1375 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1375) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1375.1, data_11_1375.2] + +/-- Complete interval computation for depth 11, residue 1376. -/ +theorem bounds_11_1376 : exactInterval 11 1376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1376 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1376) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1376 : oddCount 1376 11 = 4 ∧ acceleratedOrbit 11 1376 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1376 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1376) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1376.1, data_11_1376.2] + +/-- Complete interval computation for depth 11, residue 1377. -/ +theorem bounds_11_1377 : exactInterval 11 1377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1377 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1377) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1377 : oddCount 1377 11 = 6 ∧ acceleratedOrbit 11 1377 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1377 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1377) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1377.1, data_11_1377.2] + +/-- Complete interval computation for depth 11, residue 1378. -/ +theorem bounds_11_1378 : exactInterval 11 1378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1378 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1378) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1378 : oddCount 1378 11 = 4 ∧ acceleratedOrbit 11 1378 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1378 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1378) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1378.1, data_11_1378.2] + +/-- Complete interval computation for depth 11, residue 1379. -/ +theorem bounds_11_1379 : exactInterval 11 1379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1379 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1379) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1379 : oddCount 1379 11 = 4 ∧ acceleratedOrbit 11 1379 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1379 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1379) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1379.1, data_11_1379.2] + +/-- Complete interval computation for depth 11, residue 1380. -/ +theorem bounds_11_1380 : exactInterval 11 1380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1380 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1380) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1380 : oddCount 1380 11 = 4 ∧ acceleratedOrbit 11 1380 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1380 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1380) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1380.1, data_11_1380.2] + +/-- Complete interval computation for depth 11, residue 1381. -/ +theorem bounds_11_1381 : exactInterval 11 1381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1381 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1381) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1381 : oddCount 1381 11 = 4 ∧ acceleratedOrbit 11 1381 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1381 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1381) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1381.1, data_11_1381.2] + +/-- Complete interval computation for depth 11, residue 1382. -/ +theorem bounds_11_1382 : exactInterval 11 1382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1382 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1382) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1382 : oddCount 1382 11 = 4 ∧ acceleratedOrbit 11 1382 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1382 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1382) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1382.1, data_11_1382.2] + +/-- Complete interval computation for depth 11, residue 1383. -/ +theorem bounds_11_1383 : exactInterval 11 1383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1383 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1383) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1383 : oddCount 1383 11 = 9 ∧ acceleratedOrbit 11 1383 = 13304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1383 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1383) = 3 ^ 9 * m + 13304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1383.1, data_11_1383.2] + +/-- Complete interval computation for depth 11, residue 1384. -/ +theorem bounds_11_1384 : exactInterval 11 1384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1384 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1384) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1384 : oddCount 1384 11 = 4 ∧ acceleratedOrbit 11 1384 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1384 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1384) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1384.1, data_11_1384.2] + +/-- Complete interval computation for depth 11, residue 1385. -/ +theorem bounds_11_1385 : exactInterval 11 1385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1385 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1385) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1385 : oddCount 1385 11 = 6 ∧ acceleratedOrbit 11 1385 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1385 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1385) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1385.1, data_11_1385.2] + +/-- Complete interval computation for depth 11, residue 1386. -/ +theorem bounds_11_1386 : exactInterval 11 1386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1386 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1386) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1386 : oddCount 1386 11 = 4 ∧ acceleratedOrbit 11 1386 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1386 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1386) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1386.1, data_11_1386.2] + +end Collatz.Research.StoppingAtlas.Batch0157 From e64ff1deaf8254fa033b80766e7ab79a1c6a7359 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:49 +0530 Subject: [PATCH 0158/1001] proof: certify atlas Batch0158 (11:1387 to 11:1401) --- Collatz/Research/StoppingAtlas/Batch0158.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0158.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0158.lean b/Collatz/Research/StoppingAtlas/Batch0158.lean new file mode 100644 index 00000000..6391b1b9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0158.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0158 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1387. -/ +theorem bounds_11_1387 : exactInterval 11 1387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1387 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1387) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1387 : oddCount 1387 11 = 7 ∧ acceleratedOrbit 11 1387 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1387 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1387) = 3 ^ 7 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1387.1, data_11_1387.2] + +/-- Complete interval computation for depth 11, residue 1388. -/ +theorem bounds_11_1388 : exactInterval 11 1388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1388 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1388) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1388 : oddCount 1388 11 = 6 ∧ acceleratedOrbit 11 1388 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1388 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1388) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1388.1, data_11_1388.2] + +/-- Complete interval computation for depth 11, residue 1389. -/ +theorem bounds_11_1389 : exactInterval 11 1389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1389 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1389) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1389 : oddCount 1389 11 = 6 ∧ acceleratedOrbit 11 1389 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1389 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1389) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1389.1, data_11_1389.2] + +/-- Complete interval computation for depth 11, residue 1390. -/ +theorem bounds_11_1390 : exactInterval 11 1390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1390 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1390) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1390 : oddCount 1390 11 = 6 ∧ acceleratedOrbit 11 1390 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1390 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1390) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1390.1, data_11_1390.2] + +/-- Complete interval computation for depth 11, residue 1391. -/ +theorem bounds_11_1391 : exactInterval 11 1391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1391 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1391) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1391 : oddCount 1391 11 = 7 ∧ acceleratedOrbit 11 1391 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1391 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1391) = 3 ^ 7 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1391.1, data_11_1391.2] + +/-- Complete interval computation for depth 11, residue 1392. -/ +theorem bounds_11_1392 : exactInterval 11 1392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1392 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1392) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1392 : oddCount 1392 11 = 4 ∧ acceleratedOrbit 11 1392 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1392 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1392) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1392.1, data_11_1392.2] + +/-- Complete interval computation for depth 11, residue 1393. -/ +theorem bounds_11_1393 : exactInterval 11 1393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1393 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1393) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1393 : oddCount 1393 11 = 4 ∧ acceleratedOrbit 11 1393 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1393 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1393) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1393.1, data_11_1393.2] + +/-- Complete interval computation for depth 11, residue 1394. -/ +theorem bounds_11_1394 : exactInterval 11 1394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1394 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1394) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1394 : oddCount 1394 11 = 5 ∧ acceleratedOrbit 11 1394 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1394 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1394) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1394.1, data_11_1394.2] + +/-- Complete interval computation for depth 11, residue 1395. -/ +theorem bounds_11_1395 : exactInterval 11 1395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1395 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1395) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1395 : oddCount 1395 11 = 5 ∧ acceleratedOrbit 11 1395 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1395 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1395) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1395.1, data_11_1395.2] + +/-- Complete interval computation for depth 11, residue 1396. -/ +theorem bounds_11_1396 : exactInterval 11 1396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1396 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1396) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1396 : oddCount 1396 11 = 4 ∧ acceleratedOrbit 11 1396 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1396 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1396) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1396.1, data_11_1396.2] + +/-- Complete interval computation for depth 11, residue 1397. -/ +theorem bounds_11_1397 : exactInterval 11 1397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1397 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1397) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1397 : oddCount 1397 11 = 4 ∧ acceleratedOrbit 11 1397 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1397 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1397) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1397.1, data_11_1397.2] + +/-- Complete interval computation for depth 11, residue 1398. -/ +theorem bounds_11_1398 : exactInterval 11 1398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1398 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1398) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1398 : oddCount 1398 11 = 6 ∧ acceleratedOrbit 11 1398 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1398 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1398) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1398.1, data_11_1398.2] + +/-- Complete interval computation for depth 11, residue 1399. -/ +theorem bounds_11_1399 : exactInterval 11 1399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1399 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1399) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1399 : oddCount 1399 11 = 6 ∧ acceleratedOrbit 11 1399 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1399 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1399) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1399.1, data_11_1399.2] + +/-- Complete interval computation for depth 11, residue 1400. -/ +theorem bounds_11_1400 : exactInterval 11 1400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1400 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1400) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1400 : oddCount 1400 11 = 5 ∧ acceleratedOrbit 11 1400 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1400 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1400) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1400.1, data_11_1400.2] + +/-- Complete interval computation for depth 11, residue 1401. -/ +theorem bounds_11_1401 : exactInterval 11 1401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1401 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1401) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1401 : oddCount 1401 11 = 8 ∧ acceleratedOrbit 11 1401 = 4495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1401 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1401) = 3 ^ 8 * m + 4495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1401.1, data_11_1401.2] + +end Collatz.Research.StoppingAtlas.Batch0158 From f9f3377dca8a4683c30ab21698758da7bd83768a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:49 +0530 Subject: [PATCH 0159/1001] proof: certify atlas Batch0159 (11:1402 to 11:1417) --- Collatz/Research/StoppingAtlas/Batch0159.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0159.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0159.lean b/Collatz/Research/StoppingAtlas/Batch0159.lean new file mode 100644 index 00000000..e4cb3a8b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0159.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0159 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1402. -/ +theorem bounds_11_1402 : exactInterval 11 1402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1402 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1402) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1402 : oddCount 1402 11 = 5 ∧ acceleratedOrbit 11 1402 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1402 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1402) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1402.1, data_11_1402.2] + +/-- Complete interval computation for depth 11, residue 1403. -/ +theorem bounds_11_1403 : exactInterval 11 1403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1403 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1403) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1403 : oddCount 1403 11 = 6 ∧ acceleratedOrbit 11 1403 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1403 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1403) = 3 ^ 6 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1403.1, data_11_1403.2] + +/-- Complete interval computation for depth 11, residue 1404. -/ +theorem bounds_11_1404 : exactInterval 11 1404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1404 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1404) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1404 : oddCount 1404 11 = 5 ∧ acceleratedOrbit 11 1404 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1404 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1404) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1404.1, data_11_1404.2] + +/-- Complete interval computation for depth 11, residue 1405. -/ +theorem bounds_11_1405 : exactInterval 11 1405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1405 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1405) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1405 : oddCount 1405 11 = 5 ∧ acceleratedOrbit 11 1405 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1405 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1405) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1405.1, data_11_1405.2] + +/-- Complete interval computation for depth 11, residue 1406. -/ +theorem bounds_11_1406 : exactInterval 11 1406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1406 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1406) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1406 : oddCount 1406 11 = 8 ∧ acceleratedOrbit 11 1406 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1406 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1406) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1406.1, data_11_1406.2] + +/-- Complete interval computation for depth 11, residue 1407. -/ +theorem bounds_11_1407 : exactInterval 11 1407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1407 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1407) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1407 : oddCount 1407 11 = 8 ∧ acceleratedOrbit 11 1407 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1407 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1407) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1407.1, data_11_1407.2] + +/-- Complete interval computation for depth 11, residue 1408. -/ +theorem bounds_11_1408 : exactInterval 11 1408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1408 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1408) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1408 : oddCount 1408 11 = 3 ∧ acceleratedOrbit 11 1408 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1408 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1408) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1408.1, data_11_1408.2] + +/-- Complete interval computation for depth 11, residue 1409. -/ +theorem bounds_11_1409 : exactInterval 11 1409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1409 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1409) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1409 : oddCount 1409 11 = 6 ∧ acceleratedOrbit 11 1409 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1409 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1409) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1409.1, data_11_1409.2] + +/-- Complete interval computation for depth 11, residue 1410. -/ +theorem bounds_11_1410 : exactInterval 11 1410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1410 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1410) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1410 : oddCount 1410 11 = 4 ∧ acceleratedOrbit 11 1410 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1410 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1410) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1410.1, data_11_1410.2] + +/-- Complete interval computation for depth 11, residue 1411. -/ +theorem bounds_11_1411 : exactInterval 11 1411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1411 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1411) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1411 : oddCount 1411 11 = 4 ∧ acceleratedOrbit 11 1411 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1411 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1411) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1411.1, data_11_1411.2] + +/-- Complete interval computation for depth 11, residue 1412. -/ +theorem bounds_11_1412 : exactInterval 11 1412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1412 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1412) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1412 : oddCount 1412 11 = 6 ∧ acceleratedOrbit 11 1412 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1412 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1412) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1412.1, data_11_1412.2] + +/-- Complete interval computation for depth 11, residue 1413. -/ +theorem bounds_11_1413 : exactInterval 11 1413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1413 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1413) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1413 : oddCount 1413 11 = 6 ∧ acceleratedOrbit 11 1413 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1413 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1413) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1413.1, data_11_1413.2] + +/-- Complete interval computation for depth 11, residue 1414. -/ +theorem bounds_11_1414 : exactInterval 11 1414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1414 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1414) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1414 : oddCount 1414 11 = 6 ∧ acceleratedOrbit 11 1414 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1414 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1414) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1414.1, data_11_1414.2] + +/-- Complete interval computation for depth 11, residue 1415. -/ +theorem bounds_11_1415 : exactInterval 11 1415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1415 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1415) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1415 : oddCount 1415 11 = 4 ∧ acceleratedOrbit 11 1415 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1415 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1415) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1415.1, data_11_1415.2] + +/-- Complete interval computation for depth 11, residue 1416. -/ +theorem bounds_11_1416 : exactInterval 11 1416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1416 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1416) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1416 : oddCount 1416 11 = 3 ∧ acceleratedOrbit 11 1416 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1416 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1416) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1416.1, data_11_1416.2] + +/-- Complete interval computation for depth 11, residue 1417. -/ +theorem bounds_11_1417 : exactInterval 11 1417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1417 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1417) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1417 : oddCount 1417 11 = 6 ∧ acceleratedOrbit 11 1417 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1417 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1417) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1417.1, data_11_1417.2] + +end Collatz.Research.StoppingAtlas.Batch0159 From a5ca2739d7ec4431ea8d01887fc1930b36f432ba Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:49 +0530 Subject: [PATCH 0160/1001] proof: certify atlas Batch0160 (11:1418 to 11:1432) --- Collatz/Research/StoppingAtlas/Batch0160.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0160.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0160.lean b/Collatz/Research/StoppingAtlas/Batch0160.lean new file mode 100644 index 00000000..896f98f9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0160.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0160 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1418. -/ +theorem bounds_11_1418 : exactInterval 11 1418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1418 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1418) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1418 : oddCount 1418 11 = 3 ∧ acceleratedOrbit 11 1418 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1418 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1418) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1418.1, data_11_1418.2] + +/-- Complete interval computation for depth 11, residue 1419. -/ +theorem bounds_11_1419 : exactInterval 11 1419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1419 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1419) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1419 : oddCount 1419 11 = 6 ∧ acceleratedOrbit 11 1419 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1419 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1419) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1419.1, data_11_1419.2] + +/-- Complete interval computation for depth 11, residue 1420. -/ +theorem bounds_11_1420 : exactInterval 11 1420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1420 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1420) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1420 : oddCount 1420 11 = 3 ∧ acceleratedOrbit 11 1420 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1420 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1420) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1420.1, data_11_1420.2] + +/-- Complete interval computation for depth 11, residue 1421. -/ +theorem bounds_11_1421 : exactInterval 11 1421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1421 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1421) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1421 : oddCount 1421 11 = 3 ∧ acceleratedOrbit 11 1421 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1421 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1421) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1421.1, data_11_1421.2] + +/-- Complete interval computation for depth 11, residue 1422. -/ +theorem bounds_11_1422 : exactInterval 11 1422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1422 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1422) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1422 : oddCount 1422 11 = 5 ∧ acceleratedOrbit 11 1422 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1422 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1422) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1422.1, data_11_1422.2] + +/-- Complete interval computation for depth 11, residue 1423. -/ +theorem bounds_11_1423 : exactInterval 11 1423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1423 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1423) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1423 : oddCount 1423 11 = 5 ∧ acceleratedOrbit 11 1423 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1423 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1423) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1423.1, data_11_1423.2] + +/-- Complete interval computation for depth 11, residue 1424. -/ +theorem bounds_11_1424 : exactInterval 11 1424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1424 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1424) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1424 : oddCount 1424 11 = 3 ∧ acceleratedOrbit 11 1424 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1424 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1424) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1424.1, data_11_1424.2] + +/-- Complete interval computation for depth 11, residue 1425. -/ +theorem bounds_11_1425 : exactInterval 11 1425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1425 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1425) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1425 : oddCount 1425 11 = 5 ∧ acceleratedOrbit 11 1425 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1425 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1425) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1425.1, data_11_1425.2] + +/-- Complete interval computation for depth 11, residue 1426. -/ +theorem bounds_11_1426 : exactInterval 11 1426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1426 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1426) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1426 : oddCount 1426 11 = 5 ∧ acceleratedOrbit 11 1426 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1426 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1426) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1426.1, data_11_1426.2] + +/-- Complete interval computation for depth 11, residue 1427. -/ +theorem bounds_11_1427 : exactInterval 11 1427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1427 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1427) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1427 : oddCount 1427 11 = 5 ∧ acceleratedOrbit 11 1427 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1427 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1427) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1427.1, data_11_1427.2] + +/-- Complete interval computation for depth 11, residue 1428. -/ +theorem bounds_11_1428 : exactInterval 11 1428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1428 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1428) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1428 : oddCount 1428 11 = 3 ∧ acceleratedOrbit 11 1428 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1428 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1428) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1428.1, data_11_1428.2] + +/-- Complete interval computation for depth 11, residue 1429. -/ +theorem bounds_11_1429 : exactInterval 11 1429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1429 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1429) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1429 : oddCount 1429 11 = 3 ∧ acceleratedOrbit 11 1429 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1429 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1429) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1429.1, data_11_1429.2] + +/-- Complete interval computation for depth 11, residue 1430. -/ +theorem bounds_11_1430 : exactInterval 11 1430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1430 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1430) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1430 : oddCount 1430 11 = 6 ∧ acceleratedOrbit 11 1430 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1430 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1430) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1430.1, data_11_1430.2] + +/-- Complete interval computation for depth 11, residue 1431. -/ +theorem bounds_11_1431 : exactInterval 11 1431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1431 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1431) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1431 : oddCount 1431 11 = 6 ∧ acceleratedOrbit 11 1431 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1431 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1431) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1431.1, data_11_1431.2] + +/-- Complete interval computation for depth 11, residue 1432. -/ +theorem bounds_11_1432 : exactInterval 11 1432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1432 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1432) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1432 : oddCount 1432 11 = 3 ∧ acceleratedOrbit 11 1432 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1432 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1432) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1432.1, data_11_1432.2] + +end Collatz.Research.StoppingAtlas.Batch0160 From 162598515c5f50e90772b1fed63ab6a1bbfbc539 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:50 +0530 Subject: [PATCH 0161/1001] proof: certify atlas Batch0161 (11:1433 to 11:1447) --- Collatz/Research/StoppingAtlas/Batch0161.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0161.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0161.lean b/Collatz/Research/StoppingAtlas/Batch0161.lean new file mode 100644 index 00000000..46fd60e5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0161.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0161 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1433. -/ +theorem bounds_11_1433 : exactInterval 11 1433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1433 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1433) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1433 : oddCount 1433 11 = 6 ∧ acceleratedOrbit 11 1433 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1433 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1433) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1433.1, data_11_1433.2] + +/-- Complete interval computation for depth 11, residue 1434. -/ +theorem bounds_11_1434 : exactInterval 11 1434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1434 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1434) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1434 : oddCount 1434 11 = 3 ∧ acceleratedOrbit 11 1434 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1434 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1434) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1434.1, data_11_1434.2] + +/-- Complete interval computation for depth 11, residue 1435. -/ +theorem bounds_11_1435 : exactInterval 11 1435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1435 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1435) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1435 : oddCount 1435 11 = 7 ∧ acceleratedOrbit 11 1435 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1435 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1435) = 3 ^ 7 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1435.1, data_11_1435.2] + +/-- Complete interval computation for depth 11, residue 1436. -/ +theorem bounds_11_1436 : exactInterval 11 1436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1436 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1436) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1436 : oddCount 1436 11 = 8 ∧ acceleratedOrbit 11 1436 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1436 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1436) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1436.1, data_11_1436.2] + +/-- Complete interval computation for depth 11, residue 1437. -/ +theorem bounds_11_1437 : exactInterval 11 1437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1437 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1437) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1437 : oddCount 1437 11 = 8 ∧ acceleratedOrbit 11 1437 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1437 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1437) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1437.1, data_11_1437.2] + +/-- Complete interval computation for depth 11, residue 1438. -/ +theorem bounds_11_1438 : exactInterval 11 1438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1438 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1438) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1438 : oddCount 1438 11 = 8 ∧ acceleratedOrbit 11 1438 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1438 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1438) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1438.1, data_11_1438.2] + +/-- Complete interval computation for depth 11, residue 1439. -/ +theorem bounds_11_1439 : exactInterval 11 1439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1439 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1439) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1439 : oddCount 1439 11 = 9 ∧ acceleratedOrbit 11 1439 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1439 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1439) = 3 ^ 9 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1439.1, data_11_1439.2] + +/-- Complete interval computation for depth 11, residue 1440. -/ +theorem bounds_11_1440 : exactInterval 11 1440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1440 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1440) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1440 : oddCount 1440 11 = 3 ∧ acceleratedOrbit 11 1440 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1440 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1440) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1440.1, data_11_1440.2] + +/-- Complete interval computation for depth 11, residue 1441. -/ +theorem bounds_11_1441 : exactInterval 11 1441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1441 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1441) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1441 : oddCount 1441 11 = 6 ∧ acceleratedOrbit 11 1441 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1441 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1441) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1441.1, data_11_1441.2] + +/-- Complete interval computation for depth 11, residue 1442. -/ +theorem bounds_11_1442 : exactInterval 11 1442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1442 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1442) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1442 : oddCount 1442 11 = 5 ∧ acceleratedOrbit 11 1442 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1442 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1442) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1442.1, data_11_1442.2] + +/-- Complete interval computation for depth 11, residue 1443. -/ +theorem bounds_11_1443 : exactInterval 11 1443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1443 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1443) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1443 : oddCount 1443 11 = 5 ∧ acceleratedOrbit 11 1443 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1443 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1443) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1443.1, data_11_1443.2] + +/-- Complete interval computation for depth 11, residue 1444. -/ +theorem bounds_11_1444 : exactInterval 11 1444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1444 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1444) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1444 : oddCount 1444 11 = 5 ∧ acceleratedOrbit 11 1444 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1444 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1444) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1444.1, data_11_1444.2] + +/-- Complete interval computation for depth 11, residue 1445. -/ +theorem bounds_11_1445 : exactInterval 11 1445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1445 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1445) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1445 : oddCount 1445 11 = 5 ∧ acceleratedOrbit 11 1445 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1445 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1445) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1445.1, data_11_1445.2] + +/-- Complete interval computation for depth 11, residue 1446. -/ +theorem bounds_11_1446 : exactInterval 11 1446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1446 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1446) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1446 : oddCount 1446 11 = 5 ∧ acceleratedOrbit 11 1446 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1446 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1446) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1446.1, data_11_1446.2] + +/-- Complete interval computation for depth 11, residue 1447. -/ +theorem bounds_11_1447 : exactInterval 11 1447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1447 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1447) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1447 : oddCount 1447 11 = 7 ∧ acceleratedOrbit 11 1447 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1447 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1447) = 3 ^ 7 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1447.1, data_11_1447.2] + +end Collatz.Research.StoppingAtlas.Batch0161 From 694d3e567bcf25fac3551f392d5d6e50928b02b2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:50 +0530 Subject: [PATCH 0162/1001] proof: certify atlas Batch0162 (11:1448 to 11:1463) --- Collatz/Research/StoppingAtlas/Batch0162.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0162.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0162.lean b/Collatz/Research/StoppingAtlas/Batch0162.lean new file mode 100644 index 00000000..0551f808 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0162.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0162 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1448. -/ +theorem bounds_11_1448 : exactInterval 11 1448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1448 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1448) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1448 : oddCount 1448 11 = 3 ∧ acceleratedOrbit 11 1448 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1448 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1448) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1448.1, data_11_1448.2] + +/-- Complete interval computation for depth 11, residue 1449. -/ +theorem bounds_11_1449 : exactInterval 11 1449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1449 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1449) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1449 : oddCount 1449 11 = 7 ∧ acceleratedOrbit 11 1449 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1449 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1449) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1449.1, data_11_1449.2] + +/-- Complete interval computation for depth 11, residue 1450. -/ +theorem bounds_11_1450 : exactInterval 11 1450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1450 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1450) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1450 : oddCount 1450 11 = 3 ∧ acceleratedOrbit 11 1450 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1450 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1450) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1450.1, data_11_1450.2] + +/-- Complete interval computation for depth 11, residue 1451. -/ +theorem bounds_11_1451 : exactInterval 11 1451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1451 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1451) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1451 : oddCount 1451 11 = 7 ∧ acceleratedOrbit 11 1451 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1451 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1451) = 3 ^ 7 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1451.1, data_11_1451.2] + +/-- Complete interval computation for depth 11, residue 1452. -/ +theorem bounds_11_1452 : exactInterval 11 1452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1452 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1452) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1452 : oddCount 1452 11 = 5 ∧ acceleratedOrbit 11 1452 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1452 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1452) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1452.1, data_11_1452.2] + +/-- Complete interval computation for depth 11, residue 1453. -/ +theorem bounds_11_1453 : exactInterval 11 1453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1453 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1453) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1453 : oddCount 1453 11 = 5 ∧ acceleratedOrbit 11 1453 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1453 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1453) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1453.1, data_11_1453.2] + +/-- Complete interval computation for depth 11, residue 1454. -/ +theorem bounds_11_1454 : exactInterval 11 1454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1454 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1454) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1454 : oddCount 1454 11 = 5 ∧ acceleratedOrbit 11 1454 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1454 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1454) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1454.1, data_11_1454.2] + +/-- Complete interval computation for depth 11, residue 1455. -/ +theorem bounds_11_1455 : exactInterval 11 1455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1455 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1455) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1455 : oddCount 1455 11 = 7 ∧ acceleratedOrbit 11 1455 = 1556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1455 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1455) = 3 ^ 7 * m + 1556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1455.1, data_11_1455.2] + +/-- Complete interval computation for depth 11, residue 1456. -/ +theorem bounds_11_1456 : exactInterval 11 1456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1456 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1456) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1456 : oddCount 1456 11 = 5 ∧ acceleratedOrbit 11 1456 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1456 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1456) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1456.1, data_11_1456.2] + +/-- Complete interval computation for depth 11, residue 1457. -/ +theorem bounds_11_1457 : exactInterval 11 1457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1457 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1457) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1457 : oddCount 1457 11 = 4 ∧ acceleratedOrbit 11 1457 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1457 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1457) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1457.1, data_11_1457.2] + +/-- Complete interval computation for depth 11, residue 1458. -/ +theorem bounds_11_1458 : exactInterval 11 1458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1458 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1458) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1458 : oddCount 1458 11 = 4 ∧ acceleratedOrbit 11 1458 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1458 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1458) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1458.1, data_11_1458.2] + +/-- Complete interval computation for depth 11, residue 1459. -/ +theorem bounds_11_1459 : exactInterval 11 1459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1459 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1459) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1459 : oddCount 1459 11 = 4 ∧ acceleratedOrbit 11 1459 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1459 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1459) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1459.1, data_11_1459.2] + +/-- Complete interval computation for depth 11, residue 1460. -/ +theorem bounds_11_1460 : exactInterval 11 1460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1460 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1460) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1460 : oddCount 1460 11 = 5 ∧ acceleratedOrbit 11 1460 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1460 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1460) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1460.1, data_11_1460.2] + +/-- Complete interval computation for depth 11, residue 1461. -/ +theorem bounds_11_1461 : exactInterval 11 1461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1461 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1461) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1461 : oddCount 1461 11 = 5 ∧ acceleratedOrbit 11 1461 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1461 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1461) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1461.1, data_11_1461.2] + +/-- Complete interval computation for depth 11, residue 1462. -/ +theorem bounds_11_1462 : exactInterval 11 1462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1462 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1462) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1462 : oddCount 1462 11 = 7 ∧ acceleratedOrbit 11 1462 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1462 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1462) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1462.1, data_11_1462.2] + +/-- Complete interval computation for depth 11, residue 1463. -/ +theorem bounds_11_1463 : exactInterval 11 1463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1463 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1463) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1463 : oddCount 1463 11 = 7 ∧ acceleratedOrbit 11 1463 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1463 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1463) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1463.1, data_11_1463.2] + +end Collatz.Research.StoppingAtlas.Batch0162 From cbdb489819235a19f9847cfe5e5313d086cafb57 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:50 +0530 Subject: [PATCH 0163/1001] proof: certify atlas Batch0163 (11:1464 to 11:1478) --- Collatz/Research/StoppingAtlas/Batch0163.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0163.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0163.lean b/Collatz/Research/StoppingAtlas/Batch0163.lean new file mode 100644 index 00000000..a930d59a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0163.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0163 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1464. -/ +theorem bounds_11_1464 : exactInterval 11 1464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1464 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1464) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1464 : oddCount 1464 11 = 5 ∧ acceleratedOrbit 11 1464 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1464 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1464) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1464.1, data_11_1464.2] + +/-- Complete interval computation for depth 11, residue 1465. -/ +theorem bounds_11_1465 : exactInterval 11 1465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1465 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1465) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1465 : oddCount 1465 11 = 4 ∧ acceleratedOrbit 11 1465 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1465 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1465) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1465.1, data_11_1465.2] + +/-- Complete interval computation for depth 11, residue 1466. -/ +theorem bounds_11_1466 : exactInterval 11 1466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1466 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1466) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1466 : oddCount 1466 11 = 5 ∧ acceleratedOrbit 11 1466 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1466 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1466) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1466.1, data_11_1466.2] + +/-- Complete interval computation for depth 11, residue 1467. -/ +theorem bounds_11_1467 : exactInterval 11 1467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1467 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1467) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1467 : oddCount 1467 11 = 6 ∧ acceleratedOrbit 11 1467 = 523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1467 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1467) = 3 ^ 6 * m + 523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1467.1, data_11_1467.2] + +/-- Complete interval computation for depth 11, residue 1468. -/ +theorem bounds_11_1468 : exactInterval 11 1468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1468 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1468) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1468 : oddCount 1468 11 = 6 ∧ acceleratedOrbit 11 1468 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1468 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1468) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1468.1, data_11_1468.2] + +/-- Complete interval computation for depth 11, residue 1469. -/ +theorem bounds_11_1469 : exactInterval 11 1469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1469 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1469) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1469 : oddCount 1469 11 = 6 ∧ acceleratedOrbit 11 1469 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1469 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1469) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1469.1, data_11_1469.2] + +/-- Complete interval computation for depth 11, residue 1470. -/ +theorem bounds_11_1470 : exactInterval 11 1470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1470 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1470) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1470 : oddCount 1470 11 = 6 ∧ acceleratedOrbit 11 1470 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1470 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1470) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1470.1, data_11_1470.2] + +/-- Complete interval computation for depth 11, residue 1471. -/ +theorem bounds_11_1471 : exactInterval 11 1471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1471 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1471) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1471 : oddCount 1471 11 = 10 ∧ acceleratedOrbit 11 1471 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1471 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1471) = 3 ^ 10 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1471.1, data_11_1471.2] + +/-- Complete interval computation for depth 11, residue 1472. -/ +theorem bounds_11_1472 : exactInterval 11 1472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1472 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1472) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1472 : oddCount 1472 11 = 3 ∧ acceleratedOrbit 11 1472 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1472 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1472) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1472.1, data_11_1472.2] + +/-- Complete interval computation for depth 11, residue 1473. -/ +theorem bounds_11_1473 : exactInterval 11 1473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1473 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1473) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1473 : oddCount 1473 11 = 6 ∧ acceleratedOrbit 11 1473 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1473 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1473) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1473.1, data_11_1473.2] + +/-- Complete interval computation for depth 11, residue 1474. -/ +theorem bounds_11_1474 : exactInterval 11 1474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1474 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1474) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1474 : oddCount 1474 11 = 7 ∧ acceleratedOrbit 11 1474 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1474 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1474) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1474.1, data_11_1474.2] + +/-- Complete interval computation for depth 11, residue 1475. -/ +theorem bounds_11_1475 : exactInterval 11 1475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1475 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1475) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1475 : oddCount 1475 11 = 7 ∧ acceleratedOrbit 11 1475 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1475 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1475) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1475.1, data_11_1475.2] + +/-- Complete interval computation for depth 11, residue 1476. -/ +theorem bounds_11_1476 : exactInterval 11 1476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1476 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1476) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1476 : oddCount 1476 11 = 3 ∧ acceleratedOrbit 11 1476 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1476 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1476) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1476.1, data_11_1476.2] + +/-- Complete interval computation for depth 11, residue 1477. -/ +theorem bounds_11_1477 : exactInterval 11 1477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1477 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1477) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1477 : oddCount 1477 11 = 3 ∧ acceleratedOrbit 11 1477 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1477 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1477) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1477.1, data_11_1477.2] + +/-- Complete interval computation for depth 11, residue 1478. -/ +theorem bounds_11_1478 : exactInterval 11 1478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1478 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1478) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1478 : oddCount 1478 11 = 3 ∧ acceleratedOrbit 11 1478 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1478 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1478) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1478.1, data_11_1478.2] + +end Collatz.Research.StoppingAtlas.Batch0163 From b0d981ac8e52489172703da5b4a0e94e31827d76 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:51 +0530 Subject: [PATCH 0164/1001] proof: certify atlas Batch0164 (11:1479 to 11:1494) --- Collatz/Research/StoppingAtlas/Batch0164.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0164.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0164.lean b/Collatz/Research/StoppingAtlas/Batch0164.lean new file mode 100644 index 00000000..6a2469bb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0164.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0164 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1479. -/ +theorem bounds_11_1479 : exactInterval 11 1479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1479 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1479) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1479 : oddCount 1479 11 = 6 ∧ acceleratedOrbit 11 1479 = 527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1479 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1479) = 3 ^ 6 * m + 527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1479.1, data_11_1479.2] + +/-- Complete interval computation for depth 11, residue 1480. -/ +theorem bounds_11_1480 : exactInterval 11 1480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1480 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1480) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1480 : oddCount 1480 11 = 4 ∧ acceleratedOrbit 11 1480 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1480 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1480) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1480.1, data_11_1480.2] + +/-- Complete interval computation for depth 11, residue 1481. -/ +theorem bounds_11_1481 : exactInterval 11 1481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1481 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1481) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1481 : oddCount 1481 11 = 5 ∧ acceleratedOrbit 11 1481 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1481 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1481) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1481.1, data_11_1481.2] + +/-- Complete interval computation for depth 11, residue 1482. -/ +theorem bounds_11_1482 : exactInterval 11 1482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1482 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1482) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1482 : oddCount 1482 11 = 4 ∧ acceleratedOrbit 11 1482 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1482 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1482) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1482.1, data_11_1482.2] + +/-- Complete interval computation for depth 11, residue 1483. -/ +theorem bounds_11_1483 : exactInterval 11 1483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1483 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1483) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1483 : oddCount 1483 11 = 6 ∧ acceleratedOrbit 11 1483 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1483 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1483) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1483.1, data_11_1483.2] + +/-- Complete interval computation for depth 11, residue 1484. -/ +theorem bounds_11_1484 : exactInterval 11 1484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1484 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1484) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1484 : oddCount 1484 11 = 4 ∧ acceleratedOrbit 11 1484 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1484 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1484) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1484.1, data_11_1484.2] + +/-- Complete interval computation for depth 11, residue 1485. -/ +theorem bounds_11_1485 : exactInterval 11 1485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1485 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1485) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1485 : oddCount 1485 11 = 4 ∧ acceleratedOrbit 11 1485 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1485 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1485) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1485.1, data_11_1485.2] + +/-- Complete interval computation for depth 11, residue 1486. -/ +theorem bounds_11_1486 : exactInterval 11 1486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1486 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1486) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1486 : oddCount 1486 11 = 8 ∧ acceleratedOrbit 11 1486 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1486 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1486) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1486.1, data_11_1486.2] + +/-- Complete interval computation for depth 11, residue 1487. -/ +theorem bounds_11_1487 : exactInterval 11 1487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1487 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1487) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1487 : oddCount 1487 11 = 8 ∧ acceleratedOrbit 11 1487 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1487 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1487) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1487.1, data_11_1487.2] + +/-- Complete interval computation for depth 11, residue 1488. -/ +theorem bounds_11_1488 : exactInterval 11 1488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1488 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1488) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1488 : oddCount 1488 11 = 3 ∧ acceleratedOrbit 11 1488 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1488 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1488) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1488.1, data_11_1488.2] + +/-- Complete interval computation for depth 11, residue 1489. -/ +theorem bounds_11_1489 : exactInterval 11 1489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1489 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1489) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1489 : oddCount 1489 11 = 4 ∧ acceleratedOrbit 11 1489 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1489 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1489) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1489.1, data_11_1489.2] + +/-- Complete interval computation for depth 11, residue 1490. -/ +theorem bounds_11_1490 : exactInterval 11 1490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1490 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1490) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1490 : oddCount 1490 11 = 7 ∧ acceleratedOrbit 11 1490 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1490 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1490) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1490.1, data_11_1490.2] + +/-- Complete interval computation for depth 11, residue 1491. -/ +theorem bounds_11_1491 : exactInterval 11 1491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1491 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1491) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1491 : oddCount 1491 11 = 7 ∧ acceleratedOrbit 11 1491 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1491 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1491) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1491.1, data_11_1491.2] + +/-- Complete interval computation for depth 11, residue 1492. -/ +theorem bounds_11_1492 : exactInterval 11 1492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1492 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1492) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1492 : oddCount 1492 11 = 3 ∧ acceleratedOrbit 11 1492 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1492 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1492) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1492.1, data_11_1492.2] + +/-- Complete interval computation for depth 11, residue 1493. -/ +theorem bounds_11_1493 : exactInterval 11 1493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1493 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1493) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1493 : oddCount 1493 11 = 3 ∧ acceleratedOrbit 11 1493 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1493 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1493) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1493.1, data_11_1493.2] + +/-- Complete interval computation for depth 11, residue 1494. -/ +theorem bounds_11_1494 : exactInterval 11 1494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1494 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1494) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1494 : oddCount 1494 11 = 6 ∧ acceleratedOrbit 11 1494 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1494 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1494) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1494.1, data_11_1494.2] + +end Collatz.Research.StoppingAtlas.Batch0164 From 5cb9a0bf1fae92e0fd89495f12d857c2a1957875 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:51 +0530 Subject: [PATCH 0165/1001] proof: certify atlas Batch0165 (11:1495 to 11:1509) --- Collatz/Research/StoppingAtlas/Batch0165.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0165.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0165.lean b/Collatz/Research/StoppingAtlas/Batch0165.lean new file mode 100644 index 00000000..cb57b427 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0165.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0165 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1495. -/ +theorem bounds_11_1495 : exactInterval 11 1495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1495 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1495) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1495 : oddCount 1495 11 = 6 ∧ acceleratedOrbit 11 1495 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1495 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1495) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1495.1, data_11_1495.2] + +/-- Complete interval computation for depth 11, residue 1496. -/ +theorem bounds_11_1496 : exactInterval 11 1496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1496 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1496) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1496 : oddCount 1496 11 = 5 ∧ acceleratedOrbit 11 1496 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1496 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1496) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1496.1, data_11_1496.2] + +/-- Complete interval computation for depth 11, residue 1497. -/ +theorem bounds_11_1497 : exactInterval 11 1497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1497 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1497) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1497 : oddCount 1497 11 = 5 ∧ acceleratedOrbit 11 1497 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1497 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1497) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1497.1, data_11_1497.2] + +/-- Complete interval computation for depth 11, residue 1498. -/ +theorem bounds_11_1498 : exactInterval 11 1498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1498 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1498) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1498 : oddCount 1498 11 = 5 ∧ acceleratedOrbit 11 1498 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1498 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1498) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1498.1, data_11_1498.2] + +/-- Complete interval computation for depth 11, residue 1499. -/ +theorem bounds_11_1499 : exactInterval 11 1499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1499 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1499) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1499 : oddCount 1499 11 = 5 ∧ acceleratedOrbit 11 1499 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1499 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1499) = 3 ^ 5 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1499.1, data_11_1499.2] + +/-- Complete interval computation for depth 11, residue 1500. -/ +theorem bounds_11_1500 : exactInterval 11 1500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1500 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1500) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1500 : oddCount 1500 11 = 5 ∧ acceleratedOrbit 11 1500 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1500 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1500) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1500.1, data_11_1500.2] + +/-- Complete interval computation for depth 11, residue 1501. -/ +theorem bounds_11_1501 : exactInterval 11 1501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1501 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1501) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1501 : oddCount 1501 11 = 5 ∧ acceleratedOrbit 11 1501 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1501 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1501) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1501.1, data_11_1501.2] + +/-- Complete interval computation for depth 11, residue 1502. -/ +theorem bounds_11_1502 : exactInterval 11 1502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1502 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1502) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1502 : oddCount 1502 11 = 8 ∧ acceleratedOrbit 11 1502 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1502 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1502) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1502.1, data_11_1502.2] + +/-- Complete interval computation for depth 11, residue 1503. -/ +theorem bounds_11_1503 : exactInterval 11 1503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1503 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1503) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1503 : oddCount 1503 11 = 8 ∧ acceleratedOrbit 11 1503 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1503 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1503) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1503.1, data_11_1503.2] + +/-- Complete interval computation for depth 11, residue 1504. -/ +theorem bounds_11_1504 : exactInterval 11 1504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1504 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1504) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1504 : oddCount 1504 11 = 5 ∧ acceleratedOrbit 11 1504 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1504 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1504) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1504.1, data_11_1504.2] + +/-- Complete interval computation for depth 11, residue 1505. -/ +theorem bounds_11_1505 : exactInterval 11 1505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1505 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1505) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1505 : oddCount 1505 11 = 7 ∧ acceleratedOrbit 11 1505 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1505 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1505) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1505.1, data_11_1505.2] + +/-- Complete interval computation for depth 11, residue 1506. -/ +theorem bounds_11_1506 : exactInterval 11 1506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1506 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1506) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1506 : oddCount 1506 11 = 3 ∧ acceleratedOrbit 11 1506 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1506 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1506) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1506.1, data_11_1506.2] + +/-- Complete interval computation for depth 11, residue 1507. -/ +theorem bounds_11_1507 : exactInterval 11 1507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1507 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1507) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1507 : oddCount 1507 11 = 3 ∧ acceleratedOrbit 11 1507 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1507 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1507) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1507.1, data_11_1507.2] + +/-- Complete interval computation for depth 11, residue 1508. -/ +theorem bounds_11_1508 : exactInterval 11 1508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1508 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1508) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1508 : oddCount 1508 11 = 7 ∧ acceleratedOrbit 11 1508 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1508 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1508) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1508.1, data_11_1508.2] + +/-- Complete interval computation for depth 11, residue 1509. -/ +theorem bounds_11_1509 : exactInterval 11 1509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1509 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1509) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1509 : oddCount 1509 11 = 7 ∧ acceleratedOrbit 11 1509 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1509 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1509) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1509.1, data_11_1509.2] + +end Collatz.Research.StoppingAtlas.Batch0165 From 27e3a0ea5b9cb558f2760a031935b49bfc01245a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:51 +0530 Subject: [PATCH 0166/1001] proof: certify atlas Batch0166 (11:1510 to 11:1524) --- Collatz/Research/StoppingAtlas/Batch0166.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0166.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0166.lean b/Collatz/Research/StoppingAtlas/Batch0166.lean new file mode 100644 index 00000000..6db2dee4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0166.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0166 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1510. -/ +theorem bounds_11_1510 : exactInterval 11 1510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1510 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1510) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1510 : oddCount 1510 11 = 7 ∧ acceleratedOrbit 11 1510 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1510 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1510) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1510.1, data_11_1510.2] + +/-- Complete interval computation for depth 11, residue 1511. -/ +theorem bounds_11_1511 : exactInterval 11 1511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1511 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1511) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1511 : oddCount 1511 11 = 7 ∧ acceleratedOrbit 11 1511 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1511 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1511) = 3 ^ 7 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1511.1, data_11_1511.2] + +/-- Complete interval computation for depth 11, residue 1512. -/ +theorem bounds_11_1512 : exactInterval 11 1512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1512 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1512) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1512 : oddCount 1512 11 = 5 ∧ acceleratedOrbit 11 1512 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1512 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1512) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1512.1, data_11_1512.2] + +/-- Complete interval computation for depth 11, residue 1513. -/ +theorem bounds_11_1513 : exactInterval 11 1513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1513 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1513) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1513 : oddCount 1513 11 = 8 ∧ acceleratedOrbit 11 1513 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1513 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1513) = 3 ^ 8 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1513.1, data_11_1513.2] + +/-- Complete interval computation for depth 11, residue 1514. -/ +theorem bounds_11_1514 : exactInterval 11 1514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1514 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1514) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1514 : oddCount 1514 11 = 5 ∧ acceleratedOrbit 11 1514 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1514 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1514) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1514.1, data_11_1514.2] + +/-- Complete interval computation for depth 11, residue 1515. -/ +theorem bounds_11_1515 : exactInterval 11 1515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1515 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1515) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1515 : oddCount 1515 11 = 9 ∧ acceleratedOrbit 11 1515 = 14579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1515 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1515) = 3 ^ 9 * m + 14579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1515.1, data_11_1515.2] + +/-- Complete interval computation for depth 11, residue 1516. -/ +theorem bounds_11_1516 : exactInterval 11 1516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1516 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1516) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1516 : oddCount 1516 11 = 6 ∧ acceleratedOrbit 11 1516 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1516 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1516) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1516.1, data_11_1516.2] + +/-- Complete interval computation for depth 11, residue 1517. -/ +theorem bounds_11_1517 : exactInterval 11 1517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1517 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1517) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1517 : oddCount 1517 11 = 6 ∧ acceleratedOrbit 11 1517 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1517 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1517) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1517.1, data_11_1517.2] + +/-- Complete interval computation for depth 11, residue 1518. -/ +theorem bounds_11_1518 : exactInterval 11 1518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1518 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1518) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1518 : oddCount 1518 11 = 6 ∧ acceleratedOrbit 11 1518 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1518 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1518) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1518.1, data_11_1518.2] + +/-- Complete interval computation for depth 11, residue 1519. -/ +theorem bounds_11_1519 : exactInterval 11 1519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1519 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1519) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1519 : oddCount 1519 11 = 8 ∧ acceleratedOrbit 11 1519 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1519 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1519) = 3 ^ 8 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1519.1, data_11_1519.2] + +/-- Complete interval computation for depth 11, residue 1520. -/ +theorem bounds_11_1520 : exactInterval 11 1520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1520 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1520) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1520 : oddCount 1520 11 = 5 ∧ acceleratedOrbit 11 1520 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1520 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1520) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1520.1, data_11_1520.2] + +/-- Complete interval computation for depth 11, residue 1521. -/ +theorem bounds_11_1521 : exactInterval 11 1521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1521 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1521) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1521 : oddCount 1521 11 = 5 ∧ acceleratedOrbit 11 1521 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1521 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1521) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1521.1, data_11_1521.2] + +/-- Complete interval computation for depth 11, residue 1522. -/ +theorem bounds_11_1522 : exactInterval 11 1522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1522 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1522) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1522 : oddCount 1522 11 = 5 ∧ acceleratedOrbit 11 1522 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1522 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1522) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1522.1, data_11_1522.2] + +/-- Complete interval computation for depth 11, residue 1523. -/ +theorem bounds_11_1523 : exactInterval 11 1523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1523 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1523) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1523 : oddCount 1523 11 = 5 ∧ acceleratedOrbit 11 1523 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1523 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1523) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1523.1, data_11_1523.2] + +/-- Complete interval computation for depth 11, residue 1524. -/ +theorem bounds_11_1524 : exactInterval 11 1524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1524 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1524) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1524 : oddCount 1524 11 = 5 ∧ acceleratedOrbit 11 1524 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1524 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1524) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1524.1, data_11_1524.2] + +end Collatz.Research.StoppingAtlas.Batch0166 From 55a4c2b0653904a99cdf656bf4b7012f0a49489e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:52 +0530 Subject: [PATCH 0167/1001] proof: certify atlas Batch0167 (11:1525 to 11:1540) --- Collatz/Research/StoppingAtlas/Batch0167.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0167.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0167.lean b/Collatz/Research/StoppingAtlas/Batch0167.lean new file mode 100644 index 00000000..b4d9693c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0167.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0167 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1525. -/ +theorem bounds_11_1525 : exactInterval 11 1525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1525 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1525) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1525 : oddCount 1525 11 = 5 ∧ acceleratedOrbit 11 1525 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1525 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1525) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1525.1, data_11_1525.2] + +/-- Complete interval computation for depth 11, residue 1526. -/ +theorem bounds_11_1526 : exactInterval 11 1526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1526 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1526) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1526 : oddCount 1526 11 = 7 ∧ acceleratedOrbit 11 1526 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1526 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1526) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1526.1, data_11_1526.2] + +/-- Complete interval computation for depth 11, residue 1527. -/ +theorem bounds_11_1527 : exactInterval 11 1527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1527 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1527) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1527 : oddCount 1527 11 = 7 ∧ acceleratedOrbit 11 1527 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1527 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1527) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1527.1, data_11_1527.2] + +/-- Complete interval computation for depth 11, residue 1528. -/ +theorem bounds_11_1528 : exactInterval 11 1528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1528 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1528) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1528 : oddCount 1528 11 = 7 ∧ acceleratedOrbit 11 1528 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1528 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1528) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1528.1, data_11_1528.2] + +/-- Complete interval computation for depth 11, residue 1529. -/ +theorem bounds_11_1529 : exactInterval 11 1529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1529 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1529) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1529 : oddCount 1529 11 = 6 ∧ acceleratedOrbit 11 1529 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1529 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1529) = 3 ^ 6 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1529.1, data_11_1529.2] + +/-- Complete interval computation for depth 11, residue 1530. -/ +theorem bounds_11_1530 : exactInterval 11 1530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1530 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1530) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1530 : oddCount 1530 11 = 7 ∧ acceleratedOrbit 11 1530 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1530 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1530) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1530.1, data_11_1530.2] + +/-- Complete interval computation for depth 11, residue 1531. -/ +theorem bounds_11_1531 : exactInterval 11 1531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1531 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1531) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1531 : oddCount 1531 11 = 7 ∧ acceleratedOrbit 11 1531 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1531 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1531) = 3 ^ 7 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1531.1, data_11_1531.2] + +/-- Complete interval computation for depth 11, residue 1532. -/ +theorem bounds_11_1532 : exactInterval 11 1532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1532 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1532) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1532 : oddCount 1532 11 = 7 ∧ acceleratedOrbit 11 1532 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1532 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1532) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1532.1, data_11_1532.2] + +/-- Complete interval computation for depth 11, residue 1533. -/ +theorem bounds_11_1533 : exactInterval 11 1533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1533 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1533) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1533 : oddCount 1533 11 = 7 ∧ acceleratedOrbit 11 1533 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1533 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1533) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1533.1, data_11_1533.2] + +/-- Complete interval computation for depth 11, residue 1534. -/ +theorem bounds_11_1534 : exactInterval 11 1534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1534 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1534) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1534 : oddCount 1534 11 = 9 ∧ acceleratedOrbit 11 1534 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1534 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1534) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1534.1, data_11_1534.2] + +/-- Complete interval computation for depth 11, residue 1535. -/ +theorem bounds_11_1535 : exactInterval 11 1535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1535 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1535) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1535 : oddCount 1535 11 = 9 ∧ acceleratedOrbit 11 1535 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1535 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1535) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1535.1, data_11_1535.2] + +/-- Complete interval computation for depth 11, residue 1536. -/ +theorem bounds_11_1536 : exactInterval 11 1536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1536 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1536) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1536 : oddCount 1536 11 = 2 ∧ acceleratedOrbit 11 1536 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1536 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1536) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1536.1, data_11_1536.2] + +/-- Complete interval computation for depth 11, residue 1537. -/ +theorem bounds_11_1537 : exactInterval 11 1537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1537 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1537) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1537 : oddCount 1537 11 = 7 ∧ acceleratedOrbit 11 1537 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1537 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1537) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1537.1, data_11_1537.2] + +/-- Complete interval computation for depth 11, residue 1538. -/ +theorem bounds_11_1538 : exactInterval 11 1538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1538 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1538) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1538 : oddCount 1538 11 = 4 ∧ acceleratedOrbit 11 1538 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1538 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1538) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1538.1, data_11_1538.2] + +/-- Complete interval computation for depth 11, residue 1539. -/ +theorem bounds_11_1539 : exactInterval 11 1539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1539 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1539) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1539 : oddCount 1539 11 = 4 ∧ acceleratedOrbit 11 1539 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1539 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1539) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1539.1, data_11_1539.2] + +/-- Complete interval computation for depth 11, residue 1540. -/ +theorem bounds_11_1540 : exactInterval 11 1540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1540 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1540) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1540 : oddCount 1540 11 = 5 ∧ acceleratedOrbit 11 1540 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1540 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1540) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1540.1, data_11_1540.2] + +end Collatz.Research.StoppingAtlas.Batch0167 From 7ee6f1d3e2f8d637a615d7b6325984a3fe481d9f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:52 +0530 Subject: [PATCH 0168/1001] proof: certify atlas Batch0168 (11:1541 to 11:1555) --- Collatz/Research/StoppingAtlas/Batch0168.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0168.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0168.lean b/Collatz/Research/StoppingAtlas/Batch0168.lean new file mode 100644 index 00000000..4d6b022d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0168.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0168 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1541. -/ +theorem bounds_11_1541 : exactInterval 11 1541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1541 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1541) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1541 : oddCount 1541 11 = 5 ∧ acceleratedOrbit 11 1541 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1541 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1541) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1541.1, data_11_1541.2] + +/-- Complete interval computation for depth 11, residue 1542. -/ +theorem bounds_11_1542 : exactInterval 11 1542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1542 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1542) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1542 : oddCount 1542 11 = 5 ∧ acceleratedOrbit 11 1542 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1542 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1542) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1542.1, data_11_1542.2] + +/-- Complete interval computation for depth 11, residue 1543. -/ +theorem bounds_11_1543 : exactInterval 11 1543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1543 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1543) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1543 : oddCount 1543 11 = 6 ∧ acceleratedOrbit 11 1543 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1543 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1543) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1543.1, data_11_1543.2] + +/-- Complete interval computation for depth 11, residue 1544. -/ +theorem bounds_11_1544 : exactInterval 11 1544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1544 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1544) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1544 : oddCount 1544 11 = 4 ∧ acceleratedOrbit 11 1544 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1544 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1544) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1544.1, data_11_1544.2] + +/-- Complete interval computation for depth 11, residue 1545. -/ +theorem bounds_11_1545 : exactInterval 11 1545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1545 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1545) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1545 : oddCount 1545 11 = 6 ∧ acceleratedOrbit 11 1545 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1545 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1545) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1545.1, data_11_1545.2] + +/-- Complete interval computation for depth 11, residue 1546. -/ +theorem bounds_11_1546 : exactInterval 11 1546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1546 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1546) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1546 : oddCount 1546 11 = 4 ∧ acceleratedOrbit 11 1546 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1546 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1546) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1546.1, data_11_1546.2] + +/-- Complete interval computation for depth 11, residue 1547. -/ +theorem bounds_11_1547 : exactInterval 11 1547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1547 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1547) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1547 : oddCount 1547 11 = 5 ∧ acceleratedOrbit 11 1547 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1547 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1547) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1547.1, data_11_1547.2] + +/-- Complete interval computation for depth 11, residue 1548. -/ +theorem bounds_11_1548 : exactInterval 11 1548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1548 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1548) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1548 : oddCount 1548 11 = 4 ∧ acceleratedOrbit 11 1548 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1548 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1548) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1548.1, data_11_1548.2] + +/-- Complete interval computation for depth 11, residue 1549. -/ +theorem bounds_11_1549 : exactInterval 11 1549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1549 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1549) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1549 : oddCount 1549 11 = 4 ∧ acceleratedOrbit 11 1549 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1549 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1549) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1549.1, data_11_1549.2] + +/-- Complete interval computation for depth 11, residue 1550. -/ +theorem bounds_11_1550 : exactInterval 11 1550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1550 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1550) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1550 : oddCount 1550 11 = 6 ∧ acceleratedOrbit 11 1550 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1550 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1550) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1550.1, data_11_1550.2] + +/-- Complete interval computation for depth 11, residue 1551. -/ +theorem bounds_11_1551 : exactInterval 11 1551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1551 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1551) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1551 : oddCount 1551 11 = 6 ∧ acceleratedOrbit 11 1551 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1551 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1551) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1551.1, data_11_1551.2] + +/-- Complete interval computation for depth 11, residue 1552. -/ +theorem bounds_11_1552 : exactInterval 11 1552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1552 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1552) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1552 : oddCount 1552 11 = 5 ∧ acceleratedOrbit 11 1552 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1552 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1552) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1552.1, data_11_1552.2] + +/-- Complete interval computation for depth 11, residue 1553. -/ +theorem bounds_11_1553 : exactInterval 11 1553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1553 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1553) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1553 : oddCount 1553 11 = 4 ∧ acceleratedOrbit 11 1553 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1553 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1553) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1553.1, data_11_1553.2] + +/-- Complete interval computation for depth 11, residue 1554. -/ +theorem bounds_11_1554 : exactInterval 11 1554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1554 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1554) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1554 : oddCount 1554 11 = 7 ∧ acceleratedOrbit 11 1554 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1554 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1554) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1554.1, data_11_1554.2] + +/-- Complete interval computation for depth 11, residue 1555. -/ +theorem bounds_11_1555 : exactInterval 11 1555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1555 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1555) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1555 : oddCount 1555 11 = 7 ∧ acceleratedOrbit 11 1555 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1555 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1555) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1555.1, data_11_1555.2] + +end Collatz.Research.StoppingAtlas.Batch0168 From 84bee49db88352bb1174c633f9c700887ab1fa06 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:52 +0530 Subject: [PATCH 0169/1001] proof: certify atlas Batch0169 (11:1556 to 11:1570) --- Collatz/Research/StoppingAtlas/Batch0169.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0169.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0169.lean b/Collatz/Research/StoppingAtlas/Batch0169.lean new file mode 100644 index 00000000..13248fc4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0169.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0169 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1556. -/ +theorem bounds_11_1556 : exactInterval 11 1556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1556 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1556) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1556 : oddCount 1556 11 = 5 ∧ acceleratedOrbit 11 1556 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1556 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1556) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1556.1, data_11_1556.2] + +/-- Complete interval computation for depth 11, residue 1557. -/ +theorem bounds_11_1557 : exactInterval 11 1557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1557 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1557) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1557 : oddCount 1557 11 = 5 ∧ acceleratedOrbit 11 1557 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1557 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1557) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1557.1, data_11_1557.2] + +/-- Complete interval computation for depth 11, residue 1558. -/ +theorem bounds_11_1558 : exactInterval 11 1558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1558 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1558) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1558 : oddCount 1558 11 = 6 ∧ acceleratedOrbit 11 1558 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1558 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1558) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1558.1, data_11_1558.2] + +/-- Complete interval computation for depth 11, residue 1559. -/ +theorem bounds_11_1559 : exactInterval 11 1559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1559 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1559) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1559 : oddCount 1559 11 = 6 ∧ acceleratedOrbit 11 1559 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1559 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1559) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1559.1, data_11_1559.2] + +/-- Complete interval computation for depth 11, residue 1560. -/ +theorem bounds_11_1560 : exactInterval 11 1560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1560 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1560) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1560 : oddCount 1560 11 = 5 ∧ acceleratedOrbit 11 1560 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1560 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1560) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1560.1, data_11_1560.2] + +/-- Complete interval computation for depth 11, residue 1561. -/ +theorem bounds_11_1561 : exactInterval 11 1561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1561 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1561) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1561 : oddCount 1561 11 = 6 ∧ acceleratedOrbit 11 1561 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1561 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1561) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1561.1, data_11_1561.2] + +/-- Complete interval computation for depth 11, residue 1562. -/ +theorem bounds_11_1562 : exactInterval 11 1562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1562 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1562) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1562 : oddCount 1562 11 = 5 ∧ acceleratedOrbit 11 1562 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1562 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1562) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1562.1, data_11_1562.2] + +/-- Complete interval computation for depth 11, residue 1563. -/ +theorem bounds_11_1563 : exactInterval 11 1563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1563 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1563) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1563 : oddCount 1563 11 = 8 ∧ acceleratedOrbit 11 1563 = 5012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1563 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1563) = 3 ^ 8 * m + 5012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1563.1, data_11_1563.2] + +/-- Complete interval computation for depth 11, residue 1564. -/ +theorem bounds_11_1564 : exactInterval 11 1564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1564 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1564) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1564 : oddCount 1564 11 = 4 ∧ acceleratedOrbit 11 1564 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1564 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1564) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1564.1, data_11_1564.2] + +/-- Complete interval computation for depth 11, residue 1565. -/ +theorem bounds_11_1565 : exactInterval 11 1565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1565 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1565) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1565 : oddCount 1565 11 = 4 ∧ acceleratedOrbit 11 1565 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1565 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1565) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1565.1, data_11_1565.2] + +/-- Complete interval computation for depth 11, residue 1566. -/ +theorem bounds_11_1566 : exactInterval 11 1566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1566 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1566) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1566 : oddCount 1566 11 = 4 ∧ acceleratedOrbit 11 1566 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1566 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1566) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1566.1, data_11_1566.2] + +/-- Complete interval computation for depth 11, residue 1567. -/ +theorem bounds_11_1567 : exactInterval 11 1567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1567 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1567) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1567 : oddCount 1567 11 = 8 ∧ acceleratedOrbit 11 1567 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1567 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1567) = 3 ^ 8 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1567.1, data_11_1567.2] + +/-- Complete interval computation for depth 11, residue 1568. -/ +theorem bounds_11_1568 : exactInterval 11 1568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1568 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1568) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1568 : oddCount 1568 11 = 2 ∧ acceleratedOrbit 11 1568 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1568 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1568) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1568.1, data_11_1568.2] + +/-- Complete interval computation for depth 11, residue 1569. -/ +theorem bounds_11_1569 : exactInterval 11 1569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1569 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1569) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1569 : oddCount 1569 11 = 6 ∧ acceleratedOrbit 11 1569 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1569 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1569) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1569.1, data_11_1569.2] + +/-- Complete interval computation for depth 11, residue 1570. -/ +theorem bounds_11_1570 : exactInterval 11 1570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1570 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1570) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1570 : oddCount 1570 11 = 5 ∧ acceleratedOrbit 11 1570 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1570 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1570) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1570.1, data_11_1570.2] + +end Collatz.Research.StoppingAtlas.Batch0169 From 2efa713ba89556c80a457d90f7d3bf6016cb2fee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:52 +0530 Subject: [PATCH 0170/1001] proof: certify atlas Batch0170 (11:1571 to 11:1586) --- Collatz/Research/StoppingAtlas/Batch0170.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0170.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0170.lean b/Collatz/Research/StoppingAtlas/Batch0170.lean new file mode 100644 index 00000000..955d6c6b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0170.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0170 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1571. -/ +theorem bounds_11_1571 : exactInterval 11 1571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1571 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1571) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1571 : oddCount 1571 11 = 5 ∧ acceleratedOrbit 11 1571 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1571 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1571) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1571.1, data_11_1571.2] + +/-- Complete interval computation for depth 11, residue 1572. -/ +theorem bounds_11_1572 : exactInterval 11 1572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1572 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1572) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1572 : oddCount 1572 11 = 6 ∧ acceleratedOrbit 11 1572 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1572 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1572) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1572.1, data_11_1572.2] + +/-- Complete interval computation for depth 11, residue 1573. -/ +theorem bounds_11_1573 : exactInterval 11 1573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1573 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1573) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1573 : oddCount 1573 11 = 6 ∧ acceleratedOrbit 11 1573 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1573 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1573) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1573.1, data_11_1573.2] + +/-- Complete interval computation for depth 11, residue 1574. -/ +theorem bounds_11_1574 : exactInterval 11 1574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1574 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1574) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1574 : oddCount 1574 11 = 6 ∧ acceleratedOrbit 11 1574 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1574 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1574) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1574.1, data_11_1574.2] + +/-- Complete interval computation for depth 11, residue 1575. -/ +theorem bounds_11_1575 : exactInterval 11 1575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1575 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1575) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1575 : oddCount 1575 11 = 5 ∧ acceleratedOrbit 11 1575 = 187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1575 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1575) = 3 ^ 5 * m + 187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1575.1, data_11_1575.2] + +/-- Complete interval computation for depth 11, residue 1576. -/ +theorem bounds_11_1576 : exactInterval 11 1576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1576 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1576) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1576 : oddCount 1576 11 = 2 ∧ acceleratedOrbit 11 1576 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1576 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1576) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1576.1, data_11_1576.2] + +/-- Complete interval computation for depth 11, residue 1577. -/ +theorem bounds_11_1577 : exactInterval 11 1577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1577 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1577) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1577 : oddCount 1577 11 = 9 ∧ acceleratedOrbit 11 1577 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1577 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1577) = 3 ^ 9 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1577.1, data_11_1577.2] + +/-- Complete interval computation for depth 11, residue 1578. -/ +theorem bounds_11_1578 : exactInterval 11 1578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1578 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1578) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1578 : oddCount 1578 11 = 2 ∧ acceleratedOrbit 11 1578 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1578 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1578) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1578.1, data_11_1578.2] + +/-- Complete interval computation for depth 11, residue 1579. -/ +theorem bounds_11_1579 : exactInterval 11 1579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1579 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1579) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1579 : oddCount 1579 11 = 5 ∧ acceleratedOrbit 11 1579 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1579 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1579) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1579.1, data_11_1579.2] + +/-- Complete interval computation for depth 11, residue 1580. -/ +theorem bounds_11_1580 : exactInterval 11 1580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1580 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1580) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1580 : oddCount 1580 11 = 6 ∧ acceleratedOrbit 11 1580 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1580 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1580) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1580.1, data_11_1580.2] + +/-- Complete interval computation for depth 11, residue 1581. -/ +theorem bounds_11_1581 : exactInterval 11 1581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1581 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1581) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1581 : oddCount 1581 11 = 6 ∧ acceleratedOrbit 11 1581 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1581 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1581) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1581.1, data_11_1581.2] + +/-- Complete interval computation for depth 11, residue 1582. -/ +theorem bounds_11_1582 : exactInterval 11 1582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1582 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1582) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1582 : oddCount 1582 11 = 6 ∧ acceleratedOrbit 11 1582 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1582 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1582) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1582.1, data_11_1582.2] + +/-- Complete interval computation for depth 11, residue 1583. -/ +theorem bounds_11_1583 : exactInterval 11 1583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1583 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1583) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1583 : oddCount 1583 11 = 9 ∧ acceleratedOrbit 11 1583 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1583 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1583) = 3 ^ 9 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1583.1, data_11_1583.2] + +/-- Complete interval computation for depth 11, residue 1584. -/ +theorem bounds_11_1584 : exactInterval 11 1584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1584 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1584) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1584 : oddCount 1584 11 = 2 ∧ acceleratedOrbit 11 1584 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1584 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1584) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1584.1, data_11_1584.2] + +/-- Complete interval computation for depth 11, residue 1585. -/ +theorem bounds_11_1585 : exactInterval 11 1585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1585 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1585) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1585 : oddCount 1585 11 = 7 ∧ acceleratedOrbit 11 1585 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1585 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1585) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1585.1, data_11_1585.2] + +/-- Complete interval computation for depth 11, residue 1586. -/ +theorem bounds_11_1586 : exactInterval 11 1586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1586 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1586) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1586 : oddCount 1586 11 = 7 ∧ acceleratedOrbit 11 1586 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1586 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1586) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1586.1, data_11_1586.2] + +end Collatz.Research.StoppingAtlas.Batch0170 From 1a79c4a39037ea6d84789d833bc4c2bfffa15442 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:53 +0530 Subject: [PATCH 0171/1001] proof: certify atlas Batch0171 (11:1587 to 11:1601) --- Collatz/Research/StoppingAtlas/Batch0171.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0171.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0171.lean b/Collatz/Research/StoppingAtlas/Batch0171.lean new file mode 100644 index 00000000..86214998 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0171.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0171 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1587. -/ +theorem bounds_11_1587 : exactInterval 11 1587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1587 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1587) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1587 : oddCount 1587 11 = 7 ∧ acceleratedOrbit 11 1587 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1587 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1587) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1587.1, data_11_1587.2] + +/-- Complete interval computation for depth 11, residue 1588. -/ +theorem bounds_11_1588 : exactInterval 11 1588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1588 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1588) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1588 : oddCount 1588 11 = 2 ∧ acceleratedOrbit 11 1588 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1588 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1588) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1588.1, data_11_1588.2] + +/-- Complete interval computation for depth 11, residue 1589. -/ +theorem bounds_11_1589 : exactInterval 11 1589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1589 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1589) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1589 : oddCount 1589 11 = 2 ∧ acceleratedOrbit 11 1589 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1589 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1589) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1589.1, data_11_1589.2] + +/-- Complete interval computation for depth 11, residue 1590. -/ +theorem bounds_11_1590 : exactInterval 11 1590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1590 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1590) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1590 : oddCount 1590 11 = 9 ∧ acceleratedOrbit 11 1590 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1590 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1590) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1590.1, data_11_1590.2] + +/-- Complete interval computation for depth 11, residue 1591. -/ +theorem bounds_11_1591 : exactInterval 11 1591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1591 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1591) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1591 : oddCount 1591 11 = 9 ∧ acceleratedOrbit 11 1591 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1591 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1591) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1591.1, data_11_1591.2] + +/-- Complete interval computation for depth 11, residue 1592. -/ +theorem bounds_11_1592 : exactInterval 11 1592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1592 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1592) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1592 : oddCount 1592 11 = 5 ∧ acceleratedOrbit 11 1592 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1592 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1592) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1592.1, data_11_1592.2] + +/-- Complete interval computation for depth 11, residue 1593. -/ +theorem bounds_11_1593 : exactInterval 11 1593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1593 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1593) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1593 : oddCount 1593 11 = 6 ∧ acceleratedOrbit 11 1593 = 568 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1593 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1593) = 3 ^ 6 * m + 568 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1593.1, data_11_1593.2] + +/-- Complete interval computation for depth 11, residue 1594. -/ +theorem bounds_11_1594 : exactInterval 11 1594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1594 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1594) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1594 : oddCount 1594 11 = 5 ∧ acceleratedOrbit 11 1594 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1594 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1594) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1594.1, data_11_1594.2] + +/-- Complete interval computation for depth 11, residue 1595. -/ +theorem bounds_11_1595 : exactInterval 11 1595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1595 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1595) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1595 : oddCount 1595 11 = 6 ∧ acceleratedOrbit 11 1595 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1595 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1595) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1595.1, data_11_1595.2] + +/-- Complete interval computation for depth 11, residue 1596. -/ +theorem bounds_11_1596 : exactInterval 11 1596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1596 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1596) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1596 : oddCount 1596 11 = 5 ∧ acceleratedOrbit 11 1596 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1596 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1596) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1596.1, data_11_1596.2] + +/-- Complete interval computation for depth 11, residue 1597. -/ +theorem bounds_11_1597 : exactInterval 11 1597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1597 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1597) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1597 : oddCount 1597 11 = 5 ∧ acceleratedOrbit 11 1597 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1597 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1597) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1597.1, data_11_1597.2] + +/-- Complete interval computation for depth 11, residue 1598. -/ +theorem bounds_11_1598 : exactInterval 11 1598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1598 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1598) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1598 : oddCount 1598 11 = 7 ∧ acceleratedOrbit 11 1598 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1598 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1598) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1598.1, data_11_1598.2] + +/-- Complete interval computation for depth 11, residue 1599. -/ +theorem bounds_11_1599 : exactInterval 11 1599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1599 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1599) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1599 : oddCount 1599 11 = 7 ∧ acceleratedOrbit 11 1599 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1599 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1599) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1599.1, data_11_1599.2] + +/-- Complete interval computation for depth 11, residue 1600. -/ +theorem bounds_11_1600 : exactInterval 11 1600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1600 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1600) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1600 : oddCount 1600 11 = 3 ∧ acceleratedOrbit 11 1600 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1600 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1600) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1600.1, data_11_1600.2] + +/-- Complete interval computation for depth 11, residue 1601. -/ +theorem bounds_11_1601 : exactInterval 11 1601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1601 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1601) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1601 : oddCount 1601 11 = 5 ∧ acceleratedOrbit 11 1601 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1601 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1601) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1601.1, data_11_1601.2] + +end Collatz.Research.StoppingAtlas.Batch0171 From 0d4f07459106255bd3c171be72f6dea3bb85e134 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:53 +0530 Subject: [PATCH 0172/1001] proof: certify atlas Batch0172 (11:1602 to 11:1616) --- Collatz/Research/StoppingAtlas/Batch0172.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0172.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0172.lean b/Collatz/Research/StoppingAtlas/Batch0172.lean new file mode 100644 index 00000000..6fb42451 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0172.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0172 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1602. -/ +theorem bounds_11_1602 : exactInterval 11 1602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1602 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1602) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1602 : oddCount 1602 11 = 5 ∧ acceleratedOrbit 11 1602 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1602 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1602) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1602.1, data_11_1602.2] + +/-- Complete interval computation for depth 11, residue 1603. -/ +theorem bounds_11_1603 : exactInterval 11 1603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1603 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1603) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1603 : oddCount 1603 11 = 5 ∧ acceleratedOrbit 11 1603 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1603 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1603) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1603.1, data_11_1603.2] + +/-- Complete interval computation for depth 11, residue 1604. -/ +theorem bounds_11_1604 : exactInterval 11 1604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1604 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1604) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1604 : oddCount 1604 11 = 4 ∧ acceleratedOrbit 11 1604 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1604 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1604) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1604.1, data_11_1604.2] + +/-- Complete interval computation for depth 11, residue 1605. -/ +theorem bounds_11_1605 : exactInterval 11 1605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1605 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1605) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1605 : oddCount 1605 11 = 4 ∧ acceleratedOrbit 11 1605 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1605 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1605) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1605.1, data_11_1605.2] + +/-- Complete interval computation for depth 11, residue 1606. -/ +theorem bounds_11_1606 : exactInterval 11 1606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1606 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1606) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1606 : oddCount 1606 11 = 4 ∧ acceleratedOrbit 11 1606 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1606 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1606) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1606.1, data_11_1606.2] + +/-- Complete interval computation for depth 11, residue 1607. -/ +theorem bounds_11_1607 : exactInterval 11 1607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1607 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1607) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1607 : oddCount 1607 11 = 7 ∧ acceleratedOrbit 11 1607 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1607 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1607) = 3 ^ 7 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1607.1, data_11_1607.2] + +/-- Complete interval computation for depth 11, residue 1608. -/ +theorem bounds_11_1608 : exactInterval 11 1608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1608 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1608) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1608 : oddCount 1608 11 = 4 ∧ acceleratedOrbit 11 1608 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1608 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1608) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1608.1, data_11_1608.2] + +/-- Complete interval computation for depth 11, residue 1609. -/ +theorem bounds_11_1609 : exactInterval 11 1609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1609 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1609) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1609 : oddCount 1609 11 = 7 ∧ acceleratedOrbit 11 1609 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1609 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1609) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1609.1, data_11_1609.2] + +/-- Complete interval computation for depth 11, residue 1610. -/ +theorem bounds_11_1610 : exactInterval 11 1610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1610 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1610) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1610 : oddCount 1610 11 = 4 ∧ acceleratedOrbit 11 1610 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1610 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1610) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1610.1, data_11_1610.2] + +/-- Complete interval computation for depth 11, residue 1611. -/ +theorem bounds_11_1611 : exactInterval 11 1611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1611 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1611) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1611 : oddCount 1611 11 = 4 ∧ acceleratedOrbit 11 1611 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1611 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1611) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1611.1, data_11_1611.2] + +/-- Complete interval computation for depth 11, residue 1612. -/ +theorem bounds_11_1612 : exactInterval 11 1612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1612 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1612) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1612 : oddCount 1612 11 = 4 ∧ acceleratedOrbit 11 1612 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1612 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1612) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1612.1, data_11_1612.2] + +/-- Complete interval computation for depth 11, residue 1613. -/ +theorem bounds_11_1613 : exactInterval 11 1613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1613 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1613) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1613 : oddCount 1613 11 = 4 ∧ acceleratedOrbit 11 1613 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1613 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1613) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1613.1, data_11_1613.2] + +/-- Complete interval computation for depth 11, residue 1614. -/ +theorem bounds_11_1614 : exactInterval 11 1614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1614 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1614) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1614 : oddCount 1614 11 = 7 ∧ acceleratedOrbit 11 1614 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1614 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1614) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1614.1, data_11_1614.2] + +/-- Complete interval computation for depth 11, residue 1615. -/ +theorem bounds_11_1615 : exactInterval 11 1615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1615 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1615) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1615 : oddCount 1615 11 = 7 ∧ acceleratedOrbit 11 1615 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1615 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1615) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1615.1, data_11_1615.2] + +/-- Complete interval computation for depth 11, residue 1616. -/ +theorem bounds_11_1616 : exactInterval 11 1616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1616 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1616) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1616 : oddCount 1616 11 = 3 ∧ acceleratedOrbit 11 1616 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1616 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1616) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1616.1, data_11_1616.2] + +end Collatz.Research.StoppingAtlas.Batch0172 From 0ae9278c9ebc253029bc053e71a13c82bebf13e6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:53 +0530 Subject: [PATCH 0173/1001] proof: certify atlas Batch0173 (11:1617 to 11:1632) --- Collatz/Research/StoppingAtlas/Batch0173.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0173.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0173.lean b/Collatz/Research/StoppingAtlas/Batch0173.lean new file mode 100644 index 00000000..e00c85ec --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0173.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0173 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1617. -/ +theorem bounds_11_1617 : exactInterval 11 1617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1617 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1617) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1617 : oddCount 1617 11 = 6 ∧ acceleratedOrbit 11 1617 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1617 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1617) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1617.1, data_11_1617.2] + +/-- Complete interval computation for depth 11, residue 1618. -/ +theorem bounds_11_1618 : exactInterval 11 1618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1618 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1618) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1618 : oddCount 1618 11 = 6 ∧ acceleratedOrbit 11 1618 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1618 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1618) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1618.1, data_11_1618.2] + +/-- Complete interval computation for depth 11, residue 1619. -/ +theorem bounds_11_1619 : exactInterval 11 1619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1619 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1619) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1619 : oddCount 1619 11 = 6 ∧ acceleratedOrbit 11 1619 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1619 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1619) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1619.1, data_11_1619.2] + +/-- Complete interval computation for depth 11, residue 1620. -/ +theorem bounds_11_1620 : exactInterval 11 1620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1620 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1620) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1620 : oddCount 1620 11 = 3 ∧ acceleratedOrbit 11 1620 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1620 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1620) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1620.1, data_11_1620.2] + +/-- Complete interval computation for depth 11, residue 1621. -/ +theorem bounds_11_1621 : exactInterval 11 1621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1621 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1621) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1621 : oddCount 1621 11 = 3 ∧ acceleratedOrbit 11 1621 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1621 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1621) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1621.1, data_11_1621.2] + +/-- Complete interval computation for depth 11, residue 1622. -/ +theorem bounds_11_1622 : exactInterval 11 1622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1622 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1622) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1622 : oddCount 1622 11 = 5 ∧ acceleratedOrbit 11 1622 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1622 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1622) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1622.1, data_11_1622.2] + +/-- Complete interval computation for depth 11, residue 1623. -/ +theorem bounds_11_1623 : exactInterval 11 1623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1623 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1623) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1623 : oddCount 1623 11 = 5 ∧ acceleratedOrbit 11 1623 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1623 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1623) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1623.1, data_11_1623.2] + +/-- Complete interval computation for depth 11, residue 1624. -/ +theorem bounds_11_1624 : exactInterval 11 1624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1624 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1624) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1624 : oddCount 1624 11 = 4 ∧ acceleratedOrbit 11 1624 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1624 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1624) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1624.1, data_11_1624.2] + +/-- Complete interval computation for depth 11, residue 1625. -/ +theorem bounds_11_1625 : exactInterval 11 1625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1625 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1625) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1625 : oddCount 1625 11 = 6 ∧ acceleratedOrbit 11 1625 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1625 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1625) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1625.1, data_11_1625.2] + +/-- Complete interval computation for depth 11, residue 1626. -/ +theorem bounds_11_1626 : exactInterval 11 1626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1626 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1626) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1626 : oddCount 1626 11 = 4 ∧ acceleratedOrbit 11 1626 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1626 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1626) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1626.1, data_11_1626.2] + +/-- Complete interval computation for depth 11, residue 1627. -/ +theorem bounds_11_1627 : exactInterval 11 1627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1627 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1627) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1627 : oddCount 1627 11 = 7 ∧ acceleratedOrbit 11 1627 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1627 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1627) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1627.1, data_11_1627.2] + +/-- Complete interval computation for depth 11, residue 1628. -/ +theorem bounds_11_1628 : exactInterval 11 1628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1628 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1628) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1628 : oddCount 1628 11 = 4 ∧ acceleratedOrbit 11 1628 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1628 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1628) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1628.1, data_11_1628.2] + +/-- Complete interval computation for depth 11, residue 1629. -/ +theorem bounds_11_1629 : exactInterval 11 1629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1629 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1629) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1629 : oddCount 1629 11 = 4 ∧ acceleratedOrbit 11 1629 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1629 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1629) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1629.1, data_11_1629.2] + +/-- Complete interval computation for depth 11, residue 1630. -/ +theorem bounds_11_1630 : exactInterval 11 1630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1630 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1630) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1630 : oddCount 1630 11 = 6 ∧ acceleratedOrbit 11 1630 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1630 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1630) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1630.1, data_11_1630.2] + +/-- Complete interval computation for depth 11, residue 1631. -/ +theorem bounds_11_1631 : exactInterval 11 1631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1631 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1631) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1631 : oddCount 1631 11 = 6 ∧ acceleratedOrbit 11 1631 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1631 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1631) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1631.1, data_11_1631.2] + +/-- Complete interval computation for depth 11, residue 1632. -/ +theorem bounds_11_1632 : exactInterval 11 1632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1632 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1632) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1632 : oddCount 1632 11 = 3 ∧ acceleratedOrbit 11 1632 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1632 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1632) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1632.1, data_11_1632.2] + +end Collatz.Research.StoppingAtlas.Batch0173 From 31fbd8f04dac9570cf92c274006dc22f134df045 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:54 +0530 Subject: [PATCH 0174/1001] proof: certify atlas Batch0174 (11:1633 to 11:1647) --- Collatz/Research/StoppingAtlas/Batch0174.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0174.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0174.lean b/Collatz/Research/StoppingAtlas/Batch0174.lean new file mode 100644 index 00000000..ec629e79 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0174.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0174 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1633. -/ +theorem bounds_11_1633 : exactInterval 11 1633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1633 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1633) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1633 : oddCount 1633 11 = 5 ∧ acceleratedOrbit 11 1633 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1633 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1633) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1633.1, data_11_1633.2] + +/-- Complete interval computation for depth 11, residue 1634. -/ +theorem bounds_11_1634 : exactInterval 11 1634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1634 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1634) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1634 : oddCount 1634 11 = 4 ∧ acceleratedOrbit 11 1634 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1634 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1634) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1634.1, data_11_1634.2] + +/-- Complete interval computation for depth 11, residue 1635. -/ +theorem bounds_11_1635 : exactInterval 11 1635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1635 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1635) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1635 : oddCount 1635 11 = 4 ∧ acceleratedOrbit 11 1635 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1635 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1635) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1635.1, data_11_1635.2] + +/-- Complete interval computation for depth 11, residue 1636. -/ +theorem bounds_11_1636 : exactInterval 11 1636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1636 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1636) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1636 : oddCount 1636 11 = 4 ∧ acceleratedOrbit 11 1636 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1636 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1636) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1636.1, data_11_1636.2] + +/-- Complete interval computation for depth 11, residue 1637. -/ +theorem bounds_11_1637 : exactInterval 11 1637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1637 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1637) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1637 : oddCount 1637 11 = 4 ∧ acceleratedOrbit 11 1637 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1637 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1637) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1637.1, data_11_1637.2] + +/-- Complete interval computation for depth 11, residue 1638. -/ +theorem bounds_11_1638 : exactInterval 11 1638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1638 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1638) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1638 : oddCount 1638 11 = 4 ∧ acceleratedOrbit 11 1638 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1638 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1638) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1638.1, data_11_1638.2] + +/-- Complete interval computation for depth 11, residue 1639. -/ +theorem bounds_11_1639 : exactInterval 11 1639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1639 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1639) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1639 : oddCount 1639 11 = 8 ∧ acceleratedOrbit 11 1639 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1639 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1639) = 3 ^ 8 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1639.1, data_11_1639.2] + +/-- Complete interval computation for depth 11, residue 1640. -/ +theorem bounds_11_1640 : exactInterval 11 1640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1640 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1640) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1640 : oddCount 1640 11 = 3 ∧ acceleratedOrbit 11 1640 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1640 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1640) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1640.1, data_11_1640.2] + +/-- Complete interval computation for depth 11, residue 1641. -/ +theorem bounds_11_1641 : exactInterval 11 1641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1641 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1641) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1641 : oddCount 1641 11 = 8 ∧ acceleratedOrbit 11 1641 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1641 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1641) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1641.1, data_11_1641.2] + +/-- Complete interval computation for depth 11, residue 1642. -/ +theorem bounds_11_1642 : exactInterval 11 1642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1642 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1642) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1642 : oddCount 1642 11 = 3 ∧ acceleratedOrbit 11 1642 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1642 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1642) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1642.1, data_11_1642.2] + +/-- Complete interval computation for depth 11, residue 1643. -/ +theorem bounds_11_1643 : exactInterval 11 1643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1643 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1643) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1643 : oddCount 1643 11 = 7 ∧ acceleratedOrbit 11 1643 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1643 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1643) = 3 ^ 7 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1643.1, data_11_1643.2] + +/-- Complete interval computation for depth 11, residue 1644. -/ +theorem bounds_11_1644 : exactInterval 11 1644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1644 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1644) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1644 : oddCount 1644 11 = 6 ∧ acceleratedOrbit 11 1644 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1644 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1644) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1644.1, data_11_1644.2] + +/-- Complete interval computation for depth 11, residue 1645. -/ +theorem bounds_11_1645 : exactInterval 11 1645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1645 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1645) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1645 : oddCount 1645 11 = 6 ∧ acceleratedOrbit 11 1645 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1645 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1645) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1645.1, data_11_1645.2] + +/-- Complete interval computation for depth 11, residue 1646. -/ +theorem bounds_11_1646 : exactInterval 11 1646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1646 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1646) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1646 : oddCount 1646 11 = 6 ∧ acceleratedOrbit 11 1646 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1646 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1646) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1646.1, data_11_1646.2] + +/-- Complete interval computation for depth 11, residue 1647. -/ +theorem bounds_11_1647 : exactInterval 11 1647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1647 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1647) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1647 : oddCount 1647 11 = 7 ∧ acceleratedOrbit 11 1647 = 1760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1647 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1647) = 3 ^ 7 * m + 1760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1647.1, data_11_1647.2] + +end Collatz.Research.StoppingAtlas.Batch0174 From 5a067bf890d1a17001d90501a161dc02e4f0db9c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:54 +0530 Subject: [PATCH 0175/1001] proof: certify atlas Batch0175 (11:1648 to 11:1663) --- Collatz/Research/StoppingAtlas/Batch0175.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0175.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0175.lean b/Collatz/Research/StoppingAtlas/Batch0175.lean new file mode 100644 index 00000000..9fb570db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0175.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0175 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1648. -/ +theorem bounds_11_1648 : exactInterval 11 1648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1648 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1648) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1648 : oddCount 1648 11 = 6 ∧ acceleratedOrbit 11 1648 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1648 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1648) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1648.1, data_11_1648.2] + +/-- Complete interval computation for depth 11, residue 1649. -/ +theorem bounds_11_1649 : exactInterval 11 1649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1649 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1649) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1649 : oddCount 1649 11 = 3 ∧ acceleratedOrbit 11 1649 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1649 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1649) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1649.1, data_11_1649.2] + +/-- Complete interval computation for depth 11, residue 1650. -/ +theorem bounds_11_1650 : exactInterval 11 1650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1650 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1650) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1650 : oddCount 1650 11 = 6 ∧ acceleratedOrbit 11 1650 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1650 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1650) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1650.1, data_11_1650.2] + +/-- Complete interval computation for depth 11, residue 1651. -/ +theorem bounds_11_1651 : exactInterval 11 1651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1651 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1651) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1651 : oddCount 1651 11 = 6 ∧ acceleratedOrbit 11 1651 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1651 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1651) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1651.1, data_11_1651.2] + +/-- Complete interval computation for depth 11, residue 1652. -/ +theorem bounds_11_1652 : exactInterval 11 1652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1652 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1652) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1652 : oddCount 1652 11 = 6 ∧ acceleratedOrbit 11 1652 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1652 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1652) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1652.1, data_11_1652.2] + +/-- Complete interval computation for depth 11, residue 1653. -/ +theorem bounds_11_1653 : exactInterval 11 1653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1653 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1653) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1653 : oddCount 1653 11 = 6 ∧ acceleratedOrbit 11 1653 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1653 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1653) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1653.1, data_11_1653.2] + +/-- Complete interval computation for depth 11, residue 1654. -/ +theorem bounds_11_1654 : exactInterval 11 1654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1654 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1654) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1654 : oddCount 1654 11 = 5 ∧ acceleratedOrbit 11 1654 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1654 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1654) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1654.1, data_11_1654.2] + +/-- Complete interval computation for depth 11, residue 1655. -/ +theorem bounds_11_1655 : exactInterval 11 1655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1655 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1655) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1655 : oddCount 1655 11 = 5 ∧ acceleratedOrbit 11 1655 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1655 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1655) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1655.1, data_11_1655.2] + +/-- Complete interval computation for depth 11, residue 1656. -/ +theorem bounds_11_1656 : exactInterval 11 1656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1656 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1656) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1656 : oddCount 1656 11 = 6 ∧ acceleratedOrbit 11 1656 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1656 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1656) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1656.1, data_11_1656.2] + +/-- Complete interval computation for depth 11, residue 1657. -/ +theorem bounds_11_1657 : exactInterval 11 1657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1657 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1657) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1657 : oddCount 1657 11 = 7 ∧ acceleratedOrbit 11 1657 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1657 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1657) = 3 ^ 7 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1657.1, data_11_1657.2] + +/-- Complete interval computation for depth 11, residue 1658. -/ +theorem bounds_11_1658 : exactInterval 11 1658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1658 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1658) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1658 : oddCount 1658 11 = 6 ∧ acceleratedOrbit 11 1658 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1658 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1658) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1658.1, data_11_1658.2] + +/-- Complete interval computation for depth 11, residue 1659. -/ +theorem bounds_11_1659 : exactInterval 11 1659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1659 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1659) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1659 : oddCount 1659 11 = 5 ∧ acceleratedOrbit 11 1659 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1659 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1659) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1659.1, data_11_1659.2] + +/-- Complete interval computation for depth 11, residue 1660. -/ +theorem bounds_11_1660 : exactInterval 11 1660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1660 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1660) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1660 : oddCount 1660 11 = 7 ∧ acceleratedOrbit 11 1660 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1660 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1660) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1660.1, data_11_1660.2] + +/-- Complete interval computation for depth 11, residue 1661. -/ +theorem bounds_11_1661 : exactInterval 11 1661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1661 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1661) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1661 : oddCount 1661 11 = 7 ∧ acceleratedOrbit 11 1661 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1661 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1661) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1661.1, data_11_1661.2] + +/-- Complete interval computation for depth 11, residue 1662. -/ +theorem bounds_11_1662 : exactInterval 11 1662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1662 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1662) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1662 : oddCount 1662 11 = 7 ∧ acceleratedOrbit 11 1662 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1662 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1662) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1662.1, data_11_1662.2] + +/-- Complete interval computation for depth 11, residue 1663. -/ +theorem bounds_11_1663 : exactInterval 11 1663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1663 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1663) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1663 : oddCount 1663 11 = 10 ∧ acceleratedOrbit 11 1663 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1663 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1663) = 3 ^ 10 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1663.1, data_11_1663.2] + +end Collatz.Research.StoppingAtlas.Batch0175 From 5d5be9841c807920da227bd3a3764255c520c76d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:54 +0530 Subject: [PATCH 0176/1001] proof: certify atlas Batch0176 (11:1664 to 11:1678) --- Collatz/Research/StoppingAtlas/Batch0176.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0176.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0176.lean b/Collatz/Research/StoppingAtlas/Batch0176.lean new file mode 100644 index 00000000..05fffb85 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0176.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0176 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1664. -/ +theorem bounds_11_1664 : exactInterval 11 1664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1664 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1664) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1664 : oddCount 1664 11 = 2 ∧ acceleratedOrbit 11 1664 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1664 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1664) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1664.1, data_11_1664.2] + +/-- Complete interval computation for depth 11, residue 1665. -/ +theorem bounds_11_1665 : exactInterval 11 1665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1665 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1665) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1665 : oddCount 1665 11 = 8 ∧ acceleratedOrbit 11 1665 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1665 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1665) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1665.1, data_11_1665.2] + +/-- Complete interval computation for depth 11, residue 1666. -/ +theorem bounds_11_1666 : exactInterval 11 1666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1666 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1666) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1666 : oddCount 1666 11 = 3 ∧ acceleratedOrbit 11 1666 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1666 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1666) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1666.1, data_11_1666.2] + +/-- Complete interval computation for depth 11, residue 1667. -/ +theorem bounds_11_1667 : exactInterval 11 1667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1667 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1667) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1667 : oddCount 1667 11 = 3 ∧ acceleratedOrbit 11 1667 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1667 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1667) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1667.1, data_11_1667.2] + +/-- Complete interval computation for depth 11, residue 1668. -/ +theorem bounds_11_1668 : exactInterval 11 1668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1668 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1668) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1668 : oddCount 1668 11 = 5 ∧ acceleratedOrbit 11 1668 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1668 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1668) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1668.1, data_11_1668.2] + +/-- Complete interval computation for depth 11, residue 1669. -/ +theorem bounds_11_1669 : exactInterval 11 1669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1669 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1669) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1669 : oddCount 1669 11 = 5 ∧ acceleratedOrbit 11 1669 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1669 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1669) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1669.1, data_11_1669.2] + +/-- Complete interval computation for depth 11, residue 1670. -/ +theorem bounds_11_1670 : exactInterval 11 1670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1670 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1670) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1670 : oddCount 1670 11 = 5 ∧ acceleratedOrbit 11 1670 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1670 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1670) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1670.1, data_11_1670.2] + +/-- Complete interval computation for depth 11, residue 1671. -/ +theorem bounds_11_1671 : exactInterval 11 1671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1671 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1671) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1671 : oddCount 1671 11 = 6 ∧ acceleratedOrbit 11 1671 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1671 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1671) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1671.1, data_11_1671.2] + +/-- Complete interval computation for depth 11, residue 1672. -/ +theorem bounds_11_1672 : exactInterval 11 1672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1672 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1672) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1672 : oddCount 1672 11 = 4 ∧ acceleratedOrbit 11 1672 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1672 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1672) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1672.1, data_11_1672.2] + +/-- Complete interval computation for depth 11, residue 1673. -/ +theorem bounds_11_1673 : exactInterval 11 1673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1673 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1673) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1673 : oddCount 1673 11 = 8 ∧ acceleratedOrbit 11 1673 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1673 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1673) = 3 ^ 8 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1673.1, data_11_1673.2] + +/-- Complete interval computation for depth 11, residue 1674. -/ +theorem bounds_11_1674 : exactInterval 11 1674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1674 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1674) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1674 : oddCount 1674 11 = 4 ∧ acceleratedOrbit 11 1674 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1674 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1674) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1674.1, data_11_1674.2] + +/-- Complete interval computation for depth 11, residue 1675. -/ +theorem bounds_11_1675 : exactInterval 11 1675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1675 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1675) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1675 : oddCount 1675 11 = 5 ∧ acceleratedOrbit 11 1675 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1675 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1675) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1675.1, data_11_1675.2] + +/-- Complete interval computation for depth 11, residue 1676. -/ +theorem bounds_11_1676 : exactInterval 11 1676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1676 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1676) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1676 : oddCount 1676 11 = 4 ∧ acceleratedOrbit 11 1676 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1676 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1676) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1676.1, data_11_1676.2] + +/-- Complete interval computation for depth 11, residue 1677. -/ +theorem bounds_11_1677 : exactInterval 11 1677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1677 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1677) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1677 : oddCount 1677 11 = 4 ∧ acceleratedOrbit 11 1677 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1677 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1677) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1677.1, data_11_1677.2] + +/-- Complete interval computation for depth 11, residue 1678. -/ +theorem bounds_11_1678 : exactInterval 11 1678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1678 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1678) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1678 : oddCount 1678 11 = 7 ∧ acceleratedOrbit 11 1678 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1678 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1678) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1678.1, data_11_1678.2] + +end Collatz.Research.StoppingAtlas.Batch0176 From d695f6d94172fda42b70a12ad0334b4f5109466c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:54 +0530 Subject: [PATCH 0177/1001] proof: certify atlas Batch0177 (11:1679 to 11:1693) --- Collatz/Research/StoppingAtlas/Batch0177.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0177.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0177.lean b/Collatz/Research/StoppingAtlas/Batch0177.lean new file mode 100644 index 00000000..6bffe83d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0177.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0177 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1679. -/ +theorem bounds_11_1679 : exactInterval 11 1679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1679 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1679) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1679 : oddCount 1679 11 = 7 ∧ acceleratedOrbit 11 1679 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1679 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1679) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1679.1, data_11_1679.2] + +/-- Complete interval computation for depth 11, residue 1680. -/ +theorem bounds_11_1680 : exactInterval 11 1680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1680 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1680) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1680 : oddCount 1680 11 = 5 ∧ acceleratedOrbit 11 1680 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1680 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1680) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1680.1, data_11_1680.2] + +/-- Complete interval computation for depth 11, residue 1681. -/ +theorem bounds_11_1681 : exactInterval 11 1681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1681 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1681) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1681 : oddCount 1681 11 = 5 ∧ acceleratedOrbit 11 1681 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1681 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1681) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1681.1, data_11_1681.2] + +/-- Complete interval computation for depth 11, residue 1682. -/ +theorem bounds_11_1682 : exactInterval 11 1682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1682 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1682) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1682 : oddCount 1682 11 = 5 ∧ acceleratedOrbit 11 1682 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1682 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1682) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1682.1, data_11_1682.2] + +/-- Complete interval computation for depth 11, residue 1683. -/ +theorem bounds_11_1683 : exactInterval 11 1683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1683 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1683) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1683 : oddCount 1683 11 = 5 ∧ acceleratedOrbit 11 1683 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1683 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1683) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1683.1, data_11_1683.2] + +/-- Complete interval computation for depth 11, residue 1684. -/ +theorem bounds_11_1684 : exactInterval 11 1684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1684 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1684) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1684 : oddCount 1684 11 = 5 ∧ acceleratedOrbit 11 1684 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1684 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1684) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1684.1, data_11_1684.2] + +/-- Complete interval computation for depth 11, residue 1685. -/ +theorem bounds_11_1685 : exactInterval 11 1685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1685 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1685) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1685 : oddCount 1685 11 = 5 ∧ acceleratedOrbit 11 1685 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1685 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1685) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1685.1, data_11_1685.2] + +/-- Complete interval computation for depth 11, residue 1686. -/ +theorem bounds_11_1686 : exactInterval 11 1686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1686 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1686) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1686 : oddCount 1686 11 = 4 ∧ acceleratedOrbit 11 1686 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1686 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1686) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1686.1, data_11_1686.2] + +/-- Complete interval computation for depth 11, residue 1687. -/ +theorem bounds_11_1687 : exactInterval 11 1687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1687 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1687) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1687 : oddCount 1687 11 = 4 ∧ acceleratedOrbit 11 1687 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1687 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1687) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1687.1, data_11_1687.2] + +/-- Complete interval computation for depth 11, residue 1688. -/ +theorem bounds_11_1688 : exactInterval 11 1688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1688 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1688) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1688 : oddCount 1688 11 = 5 ∧ acceleratedOrbit 11 1688 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1688 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1688) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1688.1, data_11_1688.2] + +/-- Complete interval computation for depth 11, residue 1689. -/ +theorem bounds_11_1689 : exactInterval 11 1689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1689 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1689) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1689 : oddCount 1689 11 = 7 ∧ acceleratedOrbit 11 1689 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1689 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1689) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1689.1, data_11_1689.2] + +/-- Complete interval computation for depth 11, residue 1690. -/ +theorem bounds_11_1690 : exactInterval 11 1690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1690 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1690) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1690 : oddCount 1690 11 = 5 ∧ acceleratedOrbit 11 1690 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1690 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1690) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1690.1, data_11_1690.2] + +/-- Complete interval computation for depth 11, residue 1691. -/ +theorem bounds_11_1691 : exactInterval 11 1691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1691 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1691) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1691 : oddCount 1691 11 = 8 ∧ acceleratedOrbit 11 1691 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1691 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1691) = 3 ^ 8 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1691.1, data_11_1691.2] + +/-- Complete interval computation for depth 11, residue 1692. -/ +theorem bounds_11_1692 : exactInterval 11 1692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1692 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1692) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1692 : oddCount 1692 11 = 6 ∧ acceleratedOrbit 11 1692 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1692 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1692) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1692.1, data_11_1692.2] + +/-- Complete interval computation for depth 11, residue 1693. -/ +theorem bounds_11_1693 : exactInterval 11 1693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1693 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1693) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1693 : oddCount 1693 11 = 6 ∧ acceleratedOrbit 11 1693 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1693 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1693) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1693.1, data_11_1693.2] + +end Collatz.Research.StoppingAtlas.Batch0177 From 8c5a23e62e4e2750a831755ab0cd213c019d0c0e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:55 +0530 Subject: [PATCH 0178/1001] proof: certify atlas Batch0178 (11:1694 to 11:1709) --- Collatz/Research/StoppingAtlas/Batch0178.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0178.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0178.lean b/Collatz/Research/StoppingAtlas/Batch0178.lean new file mode 100644 index 00000000..3a3733c0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0178.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0178 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1694. -/ +theorem bounds_11_1694 : exactInterval 11 1694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1694 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1694) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1694 : oddCount 1694 11 = 6 ∧ acceleratedOrbit 11 1694 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1694 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1694) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1694.1, data_11_1694.2] + +/-- Complete interval computation for depth 11, residue 1695. -/ +theorem bounds_11_1695 : exactInterval 11 1695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1695 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1695) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1695 : oddCount 1695 11 = 9 ∧ acceleratedOrbit 11 1695 = 16301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1695 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1695) = 3 ^ 9 * m + 16301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1695.1, data_11_1695.2] + +/-- Complete interval computation for depth 11, residue 1696. -/ +theorem bounds_11_1696 : exactInterval 11 1696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1696 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1696) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1696 : oddCount 1696 11 = 2 ∧ acceleratedOrbit 11 1696 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1696 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1696) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1696.1, data_11_1696.2] + +/-- Complete interval computation for depth 11, residue 1697. -/ +theorem bounds_11_1697 : exactInterval 11 1697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1697 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1697) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1697 : oddCount 1697 11 = 6 ∧ acceleratedOrbit 11 1697 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1697 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1697) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1697.1, data_11_1697.2] + +/-- Complete interval computation for depth 11, residue 1698. -/ +theorem bounds_11_1698 : exactInterval 11 1698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1698 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1698) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1698 : oddCount 1698 11 = 6 ∧ acceleratedOrbit 11 1698 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1698 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1698) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1698.1, data_11_1698.2] + +/-- Complete interval computation for depth 11, residue 1699. -/ +theorem bounds_11_1699 : exactInterval 11 1699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1699 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1699) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1699 : oddCount 1699 11 = 6 ∧ acceleratedOrbit 11 1699 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1699 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1699) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1699.1, data_11_1699.2] + +/-- Complete interval computation for depth 11, residue 1700. -/ +theorem bounds_11_1700 : exactInterval 11 1700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1700 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1700) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1700 : oddCount 1700 11 = 7 ∧ acceleratedOrbit 11 1700 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1700 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1700) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1700.1, data_11_1700.2] + +/-- Complete interval computation for depth 11, residue 1701. -/ +theorem bounds_11_1701 : exactInterval 11 1701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1701 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1701) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1701 : oddCount 1701 11 = 7 ∧ acceleratedOrbit 11 1701 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1701 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1701) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1701.1, data_11_1701.2] + +/-- Complete interval computation for depth 11, residue 1702. -/ +theorem bounds_11_1702 : exactInterval 11 1702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1702 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1702) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1702 : oddCount 1702 11 = 7 ∧ acceleratedOrbit 11 1702 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1702 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1702) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1702.1, data_11_1702.2] + +/-- Complete interval computation for depth 11, residue 1703. -/ +theorem bounds_11_1703 : exactInterval 11 1703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1703 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1703) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1703 : oddCount 1703 11 = 7 ∧ acceleratedOrbit 11 1703 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1703 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1703) = 3 ^ 7 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1703.1, data_11_1703.2] + +/-- Complete interval computation for depth 11, residue 1704. -/ +theorem bounds_11_1704 : exactInterval 11 1704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1704 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1704) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1704 : oddCount 1704 11 = 2 ∧ acceleratedOrbit 11 1704 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1704 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1704) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1704.1, data_11_1704.2] + +/-- Complete interval computation for depth 11, residue 1705. -/ +theorem bounds_11_1705 : exactInterval 11 1705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1705 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1705) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1705 : oddCount 1705 11 = 9 ∧ acceleratedOrbit 11 1705 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1705 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1705) = 3 ^ 9 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1705.1, data_11_1705.2] + +/-- Complete interval computation for depth 11, residue 1706. -/ +theorem bounds_11_1706 : exactInterval 11 1706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1706 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1706) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1706 : oddCount 1706 11 = 2 ∧ acceleratedOrbit 11 1706 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1706 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1706) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1706.1, data_11_1706.2] + +/-- Complete interval computation for depth 11, residue 1707. -/ +theorem bounds_11_1707 : exactInterval 11 1707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1707 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1707) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1707 : oddCount 1707 11 = 7 ∧ acceleratedOrbit 11 1707 = 1826 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1707 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1707) = 3 ^ 7 * m + 1826 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1707.1, data_11_1707.2] + +/-- Complete interval computation for depth 11, residue 1708. -/ +theorem bounds_11_1708 : exactInterval 11 1708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1708 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1708) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1708 : oddCount 1708 11 = 6 ∧ acceleratedOrbit 11 1708 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1708 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1708) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1708.1, data_11_1708.2] + +/-- Complete interval computation for depth 11, residue 1709. -/ +theorem bounds_11_1709 : exactInterval 11 1709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1709 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1709) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1709 : oddCount 1709 11 = 6 ∧ acceleratedOrbit 11 1709 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1709 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1709) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1709.1, data_11_1709.2] + +end Collatz.Research.StoppingAtlas.Batch0178 From 8703b3ce44cbbada4ef9b99ab0129cd85537bb85 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:55 +0530 Subject: [PATCH 0179/1001] proof: certify atlas Batch0179 (11:1710 to 11:1724) --- Collatz/Research/StoppingAtlas/Batch0179.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0179.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0179.lean b/Collatz/Research/StoppingAtlas/Batch0179.lean new file mode 100644 index 00000000..bf9a1968 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0179.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0179 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1710. -/ +theorem bounds_11_1710 : exactInterval 11 1710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1710 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1710) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1710 : oddCount 1710 11 = 6 ∧ acceleratedOrbit 11 1710 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1710 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1710) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1710.1, data_11_1710.2] + +/-- Complete interval computation for depth 11, residue 1711. -/ +theorem bounds_11_1711 : exactInterval 11 1711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1711 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1711) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1711 : oddCount 1711 11 = 7 ∧ acceleratedOrbit 11 1711 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1711 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1711) = 3 ^ 7 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1711.1, data_11_1711.2] + +/-- Complete interval computation for depth 11, residue 1712. -/ +theorem bounds_11_1712 : exactInterval 11 1712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1712 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1712) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1712 : oddCount 1712 11 = 5 ∧ acceleratedOrbit 11 1712 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1712 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1712) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1712.1, data_11_1712.2] + +/-- Complete interval computation for depth 11, residue 1713. -/ +theorem bounds_11_1713 : exactInterval 11 1713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1713 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1713) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1713 : oddCount 1713 11 = 4 ∧ acceleratedOrbit 11 1713 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1713 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1713) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1713.1, data_11_1713.2] + +/-- Complete interval computation for depth 11, residue 1714. -/ +theorem bounds_11_1714 : exactInterval 11 1714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1714 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1714) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1714 : oddCount 1714 11 = 4 ∧ acceleratedOrbit 11 1714 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1714 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1714) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1714.1, data_11_1714.2] + +/-- Complete interval computation for depth 11, residue 1715. -/ +theorem bounds_11_1715 : exactInterval 11 1715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1715 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1715) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1715 : oddCount 1715 11 = 4 ∧ acceleratedOrbit 11 1715 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1715 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1715) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1715.1, data_11_1715.2] + +/-- Complete interval computation for depth 11, residue 1716. -/ +theorem bounds_11_1716 : exactInterval 11 1716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1716 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1716) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1716 : oddCount 1716 11 = 5 ∧ acceleratedOrbit 11 1716 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1716 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1716) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1716.1, data_11_1716.2] + +/-- Complete interval computation for depth 11, residue 1717. -/ +theorem bounds_11_1717 : exactInterval 11 1717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1717 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1717) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1717 : oddCount 1717 11 = 5 ∧ acceleratedOrbit 11 1717 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1717 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1717) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1717.1, data_11_1717.2] + +/-- Complete interval computation for depth 11, residue 1718. -/ +theorem bounds_11_1718 : exactInterval 11 1718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1718 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1718) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1718 : oddCount 1718 11 = 7 ∧ acceleratedOrbit 11 1718 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1718 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1718) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1718.1, data_11_1718.2] + +/-- Complete interval computation for depth 11, residue 1719. -/ +theorem bounds_11_1719 : exactInterval 11 1719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1719 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1719) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1719 : oddCount 1719 11 = 7 ∧ acceleratedOrbit 11 1719 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1719 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1719) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1719.1, data_11_1719.2] + +/-- Complete interval computation for depth 11, residue 1720. -/ +theorem bounds_11_1720 : exactInterval 11 1720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1720 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1720) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1720 : oddCount 1720 11 = 5 ∧ acceleratedOrbit 11 1720 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1720 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1720) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1720.1, data_11_1720.2] + +/-- Complete interval computation for depth 11, residue 1721. -/ +theorem bounds_11_1721 : exactInterval 11 1721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1721 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1721) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1721 : oddCount 1721 11 = 6 ∧ acceleratedOrbit 11 1721 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1721 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1721) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1721.1, data_11_1721.2] + +/-- Complete interval computation for depth 11, residue 1722. -/ +theorem bounds_11_1722 : exactInterval 11 1722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1722 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1722) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1722 : oddCount 1722 11 = 5 ∧ acceleratedOrbit 11 1722 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1722 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1722) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1722.1, data_11_1722.2] + +/-- Complete interval computation for depth 11, residue 1723. -/ +theorem bounds_11_1723 : exactInterval 11 1723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1723 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1723) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1723 : oddCount 1723 11 = 6 ∧ acceleratedOrbit 11 1723 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1723 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1723) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1723.1, data_11_1723.2] + +/-- Complete interval computation for depth 11, residue 1724. -/ +theorem bounds_11_1724 : exactInterval 11 1724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1724 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1724) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1724 : oddCount 1724 11 = 5 ∧ acceleratedOrbit 11 1724 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1724 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1724) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1724.1, data_11_1724.2] + +end Collatz.Research.StoppingAtlas.Batch0179 From 12e575986638792fe2fd0c863971a35f5f47f7c8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:55 +0530 Subject: [PATCH 0180/1001] proof: certify atlas Batch0180 (11:1725 to 11:1739) --- Collatz/Research/StoppingAtlas/Batch0180.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0180.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0180.lean b/Collatz/Research/StoppingAtlas/Batch0180.lean new file mode 100644 index 00000000..37480df5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0180.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0180 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1725. -/ +theorem bounds_11_1725 : exactInterval 11 1725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1725 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1725) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1725 : oddCount 1725 11 = 5 ∧ acceleratedOrbit 11 1725 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1725 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1725) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1725.1, data_11_1725.2] + +/-- Complete interval computation for depth 11, residue 1726. -/ +theorem bounds_11_1726 : exactInterval 11 1726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1726 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1726) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1726 : oddCount 1726 11 = 5 ∧ acceleratedOrbit 11 1726 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1726 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1726) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1726.1, data_11_1726.2] + +/-- Complete interval computation for depth 11, residue 1727. -/ +theorem bounds_11_1727 : exactInterval 11 1727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1727 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1727) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1727 : oddCount 1727 11 = 8 ∧ acceleratedOrbit 11 1727 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1727 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1727) = 3 ^ 8 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1727.1, data_11_1727.2] + +/-- Complete interval computation for depth 11, residue 1728. -/ +theorem bounds_11_1728 : exactInterval 11 1728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1728 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1728) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1728 : oddCount 1728 11 = 4 ∧ acceleratedOrbit 11 1728 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1728 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1728) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1728.1, data_11_1728.2] + +/-- Complete interval computation for depth 11, residue 1729. -/ +theorem bounds_11_1729 : exactInterval 11 1729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1729 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1729) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1729 : oddCount 1729 11 = 5 ∧ acceleratedOrbit 11 1729 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1729 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1729) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1729.1, data_11_1729.2] + +/-- Complete interval computation for depth 11, residue 1730. -/ +theorem bounds_11_1730 : exactInterval 11 1730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1730 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1730) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1730 : oddCount 1730 11 = 7 ∧ acceleratedOrbit 11 1730 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1730 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1730) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1730.1, data_11_1730.2] + +/-- Complete interval computation for depth 11, residue 1731. -/ +theorem bounds_11_1731 : exactInterval 11 1731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1731 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1731) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1731 : oddCount 1731 11 = 7 ∧ acceleratedOrbit 11 1731 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1731 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1731) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1731.1, data_11_1731.2] + +/-- Complete interval computation for depth 11, residue 1732. -/ +theorem bounds_11_1732 : exactInterval 11 1732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1732 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1732) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1732 : oddCount 1732 11 = 3 ∧ acceleratedOrbit 11 1732 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1732 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1732) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1732.1, data_11_1732.2] + +/-- Complete interval computation for depth 11, residue 1733. -/ +theorem bounds_11_1733 : exactInterval 11 1733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1733 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1733) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1733 : oddCount 1733 11 = 3 ∧ acceleratedOrbit 11 1733 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1733 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1733) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1733.1, data_11_1733.2] + +/-- Complete interval computation for depth 11, residue 1734. -/ +theorem bounds_11_1734 : exactInterval 11 1734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1734 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1734) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1734 : oddCount 1734 11 = 3 ∧ acceleratedOrbit 11 1734 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1734 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1734) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1734.1, data_11_1734.2] + +/-- Complete interval computation for depth 11, residue 1735. -/ +theorem bounds_11_1735 : exactInterval 11 1735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1735 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1735) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1735 : oddCount 1735 11 = 5 ∧ acceleratedOrbit 11 1735 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1735 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1735) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1735.1, data_11_1735.2] + +/-- Complete interval computation for depth 11, residue 1736. -/ +theorem bounds_11_1736 : exactInterval 11 1736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1736 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1736) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1736 : oddCount 1736 11 = 3 ∧ acceleratedOrbit 11 1736 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1736 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1736) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1736.1, data_11_1736.2] + +/-- Complete interval computation for depth 11, residue 1737. -/ +theorem bounds_11_1737 : exactInterval 11 1737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1737 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1737) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1737 : oddCount 1737 11 = 6 ∧ acceleratedOrbit 11 1737 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1737 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1737) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1737.1, data_11_1737.2] + +/-- Complete interval computation for depth 11, residue 1738. -/ +theorem bounds_11_1738 : exactInterval 11 1738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1738 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1738) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1738 : oddCount 1738 11 = 3 ∧ acceleratedOrbit 11 1738 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1738 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1738) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1738.1, data_11_1738.2] + +/-- Complete interval computation for depth 11, residue 1739. -/ +theorem bounds_11_1739 : exactInterval 11 1739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1739 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1739) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1739 : oddCount 1739 11 = 7 ∧ acceleratedOrbit 11 1739 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1739 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1739) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1739.1, data_11_1739.2] + +end Collatz.Research.StoppingAtlas.Batch0180 From cf1cdb73bd41a0548f9fa0027aa6a6571aa6daa3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:56 +0530 Subject: [PATCH 0181/1001] proof: certify atlas Batch0181 (11:1740 to 11:1755) --- Collatz/Research/StoppingAtlas/Batch0181.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0181.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0181.lean b/Collatz/Research/StoppingAtlas/Batch0181.lean new file mode 100644 index 00000000..6de9ee86 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0181.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0181 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1740. -/ +theorem bounds_11_1740 : exactInterval 11 1740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1740 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1740) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1740 : oddCount 1740 11 = 3 ∧ acceleratedOrbit 11 1740 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1740 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1740) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1740.1, data_11_1740.2] + +/-- Complete interval computation for depth 11, residue 1741. -/ +theorem bounds_11_1741 : exactInterval 11 1741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1741 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1741) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1741 : oddCount 1741 11 = 3 ∧ acceleratedOrbit 11 1741 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1741 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1741) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1741.1, data_11_1741.2] + +/-- Complete interval computation for depth 11, residue 1742. -/ +theorem bounds_11_1742 : exactInterval 11 1742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1742 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1742) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1742 : oddCount 1742 11 = 9 ∧ acceleratedOrbit 11 1742 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1742 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1742) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1742.1, data_11_1742.2] + +/-- Complete interval computation for depth 11, residue 1743. -/ +theorem bounds_11_1743 : exactInterval 11 1743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1743 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1743) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1743 : oddCount 1743 11 = 9 ∧ acceleratedOrbit 11 1743 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1743 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1743) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1743.1, data_11_1743.2] + +/-- Complete interval computation for depth 11, residue 1744. -/ +theorem bounds_11_1744 : exactInterval 11 1744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1744 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1744) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1744 : oddCount 1744 11 = 4 ∧ acceleratedOrbit 11 1744 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1744 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1744) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1744.1, data_11_1744.2] + +/-- Complete interval computation for depth 11, residue 1745. -/ +theorem bounds_11_1745 : exactInterval 11 1745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1745 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1745) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1745 : oddCount 1745 11 = 6 ∧ acceleratedOrbit 11 1745 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1745 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1745) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1745.1, data_11_1745.2] + +/-- Complete interval computation for depth 11, residue 1746. -/ +theorem bounds_11_1746 : exactInterval 11 1746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1746 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1746) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1746 : oddCount 1746 11 = 6 ∧ acceleratedOrbit 11 1746 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1746 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1746) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1746.1, data_11_1746.2] + +/-- Complete interval computation for depth 11, residue 1747. -/ +theorem bounds_11_1747 : exactInterval 11 1747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1747 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1747) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1747 : oddCount 1747 11 = 6 ∧ acceleratedOrbit 11 1747 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1747 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1747) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1747.1, data_11_1747.2] + +/-- Complete interval computation for depth 11, residue 1748. -/ +theorem bounds_11_1748 : exactInterval 11 1748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1748 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1748) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1748 : oddCount 1748 11 = 4 ∧ acceleratedOrbit 11 1748 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1748 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1748) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1748.1, data_11_1748.2] + +/-- Complete interval computation for depth 11, residue 1749. -/ +theorem bounds_11_1749 : exactInterval 11 1749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1749 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1749) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1749 : oddCount 1749 11 = 4 ∧ acceleratedOrbit 11 1749 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1749 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1749) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1749.1, data_11_1749.2] + +/-- Complete interval computation for depth 11, residue 1750. -/ +theorem bounds_11_1750 : exactInterval 11 1750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1750 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1750) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1750 : oddCount 1750 11 = 5 ∧ acceleratedOrbit 11 1750 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1750 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1750) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1750.1, data_11_1750.2] + +/-- Complete interval computation for depth 11, residue 1751. -/ +theorem bounds_11_1751 : exactInterval 11 1751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1751 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1751) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1751 : oddCount 1751 11 = 5 ∧ acceleratedOrbit 11 1751 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1751 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1751) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1751.1, data_11_1751.2] + +/-- Complete interval computation for depth 11, residue 1752. -/ +theorem bounds_11_1752 : exactInterval 11 1752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1752 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1752) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1752 : oddCount 1752 11 = 5 ∧ acceleratedOrbit 11 1752 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1752 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1752) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1752.1, data_11_1752.2] + +/-- Complete interval computation for depth 11, residue 1753. -/ +theorem bounds_11_1753 : exactInterval 11 1753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1753 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1753) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1753 : oddCount 1753 11 = 5 ∧ acceleratedOrbit 11 1753 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1753 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1753) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1753.1, data_11_1753.2] + +/-- Complete interval computation for depth 11, residue 1754. -/ +theorem bounds_11_1754 : exactInterval 11 1754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1754 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1754) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1754 : oddCount 1754 11 = 5 ∧ acceleratedOrbit 11 1754 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1754 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1754) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1754.1, data_11_1754.2] + +/-- Complete interval computation for depth 11, residue 1755. -/ +theorem bounds_11_1755 : exactInterval 11 1755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1755 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1755) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1755 : oddCount 1755 11 = 7 ∧ acceleratedOrbit 11 1755 = 1876 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1755 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1755) = 3 ^ 7 * m + 1876 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1755.1, data_11_1755.2] + +end Collatz.Research.StoppingAtlas.Batch0181 From 97274827c20b7d85890f10fb418eecb26674e245 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:56 +0530 Subject: [PATCH 0182/1001] proof: certify atlas Batch0182 (11:1756 to 11:1770) --- Collatz/Research/StoppingAtlas/Batch0182.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0182.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0182.lean b/Collatz/Research/StoppingAtlas/Batch0182.lean new file mode 100644 index 00000000..0cd01274 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0182.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0182 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1756. -/ +theorem bounds_11_1756 : exactInterval 11 1756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1756 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1756) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1756 : oddCount 1756 11 = 5 ∧ acceleratedOrbit 11 1756 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1756 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1756) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1756.1, data_11_1756.2] + +/-- Complete interval computation for depth 11, residue 1757. -/ +theorem bounds_11_1757 : exactInterval 11 1757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1757 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1757) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1757 : oddCount 1757 11 = 5 ∧ acceleratedOrbit 11 1757 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1757 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1757) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1757.1, data_11_1757.2] + +/-- Complete interval computation for depth 11, residue 1758. -/ +theorem bounds_11_1758 : exactInterval 11 1758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1758 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1758) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1758 : oddCount 1758 11 = 7 ∧ acceleratedOrbit 11 1758 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1758 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1758) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1758.1, data_11_1758.2] + +/-- Complete interval computation for depth 11, residue 1759. -/ +theorem bounds_11_1759 : exactInterval 11 1759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1759 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1759) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1759 : oddCount 1759 11 = 7 ∧ acceleratedOrbit 11 1759 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1759 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1759) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1759.1, data_11_1759.2] + +/-- Complete interval computation for depth 11, residue 1760. -/ +theorem bounds_11_1760 : exactInterval 11 1760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1760 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1760) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1760 : oddCount 1760 11 = 4 ∧ acceleratedOrbit 11 1760 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1760 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1760) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1760.1, data_11_1760.2] + +/-- Complete interval computation for depth 11, residue 1761. -/ +theorem bounds_11_1761 : exactInterval 11 1761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1761 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1761) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1761 : oddCount 1761 11 = 7 ∧ acceleratedOrbit 11 1761 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1761 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1761) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1761.1, data_11_1761.2] + +/-- Complete interval computation for depth 11, residue 1762. -/ +theorem bounds_11_1762 : exactInterval 11 1762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1762 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1762) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1762 : oddCount 1762 11 = 4 ∧ acceleratedOrbit 11 1762 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1762 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1762) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1762.1, data_11_1762.2] + +/-- Complete interval computation for depth 11, residue 1763. -/ +theorem bounds_11_1763 : exactInterval 11 1763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1763 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1763) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1763 : oddCount 1763 11 = 4 ∧ acceleratedOrbit 11 1763 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1763 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1763) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1763.1, data_11_1763.2] + +/-- Complete interval computation for depth 11, residue 1764. -/ +theorem bounds_11_1764 : exactInterval 11 1764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1764 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1764) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1764 : oddCount 1764 11 = 4 ∧ acceleratedOrbit 11 1764 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1764 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1764) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1764.1, data_11_1764.2] + +/-- Complete interval computation for depth 11, residue 1765. -/ +theorem bounds_11_1765 : exactInterval 11 1765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1765 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1765) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1765 : oddCount 1765 11 = 4 ∧ acceleratedOrbit 11 1765 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1765 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1765) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1765.1, data_11_1765.2] + +/-- Complete interval computation for depth 11, residue 1766. -/ +theorem bounds_11_1766 : exactInterval 11 1766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1766 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1766) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1766 : oddCount 1766 11 = 4 ∧ acceleratedOrbit 11 1766 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1766 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1766) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1766.1, data_11_1766.2] + +/-- Complete interval computation for depth 11, residue 1767. -/ +theorem bounds_11_1767 : exactInterval 11 1767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1767 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1767) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1767 : oddCount 1767 11 = 8 ∧ acceleratedOrbit 11 1767 = 5665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1767 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1767) = 3 ^ 8 * m + 5665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1767.1, data_11_1767.2] + +/-- Complete interval computation for depth 11, residue 1768. -/ +theorem bounds_11_1768 : exactInterval 11 1768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1768 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1768) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1768 : oddCount 1768 11 = 4 ∧ acceleratedOrbit 11 1768 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1768 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1768) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1768.1, data_11_1768.2] + +/-- Complete interval computation for depth 11, residue 1769. -/ +theorem bounds_11_1769 : exactInterval 11 1769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1769 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1769) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1769 : oddCount 1769 11 = 7 ∧ acceleratedOrbit 11 1769 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1769 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1769) = 3 ^ 7 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1769.1, data_11_1769.2] + +/-- Complete interval computation for depth 11, residue 1770. -/ +theorem bounds_11_1770 : exactInterval 11 1770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1770 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1770) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1770 : oddCount 1770 11 = 4 ∧ acceleratedOrbit 11 1770 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1770 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1770) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1770.1, data_11_1770.2] + +end Collatz.Research.StoppingAtlas.Batch0182 From 0f145ddf87e270e455137a26cd56b3a22b676e6b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:56 +0530 Subject: [PATCH 0183/1001] proof: certify atlas Batch0183 (11:1771 to 11:1785) --- Collatz/Research/StoppingAtlas/Batch0183.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0183.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0183.lean b/Collatz/Research/StoppingAtlas/Batch0183.lean new file mode 100644 index 00000000..a8e30ed7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0183.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0183 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1771. -/ +theorem bounds_11_1771 : exactInterval 11 1771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1771 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1771) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1771 : oddCount 1771 11 = 6 ∧ acceleratedOrbit 11 1771 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1771 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1771) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1771.1, data_11_1771.2] + +/-- Complete interval computation for depth 11, residue 1772. -/ +theorem bounds_11_1772 : exactInterval 11 1772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1772 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1772) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1772 : oddCount 1772 11 = 5 ∧ acceleratedOrbit 11 1772 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1772 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1772) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1772.1, data_11_1772.2] + +/-- Complete interval computation for depth 11, residue 1773. -/ +theorem bounds_11_1773 : exactInterval 11 1773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1773 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1773) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1773 : oddCount 1773 11 = 5 ∧ acceleratedOrbit 11 1773 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1773 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1773) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1773.1, data_11_1773.2] + +/-- Complete interval computation for depth 11, residue 1774. -/ +theorem bounds_11_1774 : exactInterval 11 1774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1774 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1774) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1774 : oddCount 1774 11 = 5 ∧ acceleratedOrbit 11 1774 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1774 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1774) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1774.1, data_11_1774.2] + +/-- Complete interval computation for depth 11, residue 1775. -/ +theorem bounds_11_1775 : exactInterval 11 1775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1775 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1775) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1775 : oddCount 1775 11 = 8 ∧ acceleratedOrbit 11 1775 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1775 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1775) = 3 ^ 8 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1775.1, data_11_1775.2] + +/-- Complete interval computation for depth 11, residue 1776. -/ +theorem bounds_11_1776 : exactInterval 11 1776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1776 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1776) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1776 : oddCount 1776 11 = 6 ∧ acceleratedOrbit 11 1776 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1776 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1776) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1776.1, data_11_1776.2] + +/-- Complete interval computation for depth 11, residue 1777. -/ +theorem bounds_11_1777 : exactInterval 11 1777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1777 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1777) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1777 : oddCount 1777 11 = 4 ∧ acceleratedOrbit 11 1777 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1777 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1777) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1777.1, data_11_1777.2] + +/-- Complete interval computation for depth 11, residue 1778. -/ +theorem bounds_11_1778 : exactInterval 11 1778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1778 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1778) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1778 : oddCount 1778 11 = 7 ∧ acceleratedOrbit 11 1778 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1778 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1778) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1778.1, data_11_1778.2] + +/-- Complete interval computation for depth 11, residue 1779. -/ +theorem bounds_11_1779 : exactInterval 11 1779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1779 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1779) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1779 : oddCount 1779 11 = 7 ∧ acceleratedOrbit 11 1779 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1779 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1779) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1779.1, data_11_1779.2] + +/-- Complete interval computation for depth 11, residue 1780. -/ +theorem bounds_11_1780 : exactInterval 11 1780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1780 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1780) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1780 : oddCount 1780 11 = 6 ∧ acceleratedOrbit 11 1780 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1780 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1780) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1780.1, data_11_1780.2] + +/-- Complete interval computation for depth 11, residue 1781. -/ +theorem bounds_11_1781 : exactInterval 11 1781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1781 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1781) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1781 : oddCount 1781 11 = 6 ∧ acceleratedOrbit 11 1781 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1781 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1781) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1781.1, data_11_1781.2] + +/-- Complete interval computation for depth 11, residue 1782. -/ +theorem bounds_11_1782 : exactInterval 11 1782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1782 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1782) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1782 : oddCount 1782 11 = 7 ∧ acceleratedOrbit 11 1782 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1782 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1782) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1782.1, data_11_1782.2] + +/-- Complete interval computation for depth 11, residue 1783. -/ +theorem bounds_11_1783 : exactInterval 11 1783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1783 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1783) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1783 : oddCount 1783 11 = 7 ∧ acceleratedOrbit 11 1783 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1783 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1783) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1783.1, data_11_1783.2] + +/-- Complete interval computation for depth 11, residue 1784. -/ +theorem bounds_11_1784 : exactInterval 11 1784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1784 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1784) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1784 : oddCount 1784 11 = 6 ∧ acceleratedOrbit 11 1784 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1784 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1784) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1784.1, data_11_1784.2] + +/-- Complete interval computation for depth 11, residue 1785. -/ +theorem bounds_11_1785 : exactInterval 11 1785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1785 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1785) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1785 : oddCount 1785 11 = 5 ∧ acceleratedOrbit 11 1785 = 212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1785 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1785) = 3 ^ 5 * m + 212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1785.1, data_11_1785.2] + +end Collatz.Research.StoppingAtlas.Batch0183 From 48145719ac66440aa07fb6174d8c6594016fb54c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:57 +0530 Subject: [PATCH 0184/1001] proof: certify atlas Batch0184 (11:1786 to 11:1801) --- Collatz/Research/StoppingAtlas/Batch0184.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0184.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0184.lean b/Collatz/Research/StoppingAtlas/Batch0184.lean new file mode 100644 index 00000000..ece4a930 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0184.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0184 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1786. -/ +theorem bounds_11_1786 : exactInterval 11 1786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1786 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1786) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1786 : oddCount 1786 11 = 6 ∧ acceleratedOrbit 11 1786 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1786 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1786) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1786.1, data_11_1786.2] + +/-- Complete interval computation for depth 11, residue 1787. -/ +theorem bounds_11_1787 : exactInterval 11 1787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1787 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1787) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1787 : oddCount 1787 11 = 7 ∧ acceleratedOrbit 11 1787 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1787 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1787) = 3 ^ 7 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1787.1, data_11_1787.2] + +/-- Complete interval computation for depth 11, residue 1788. -/ +theorem bounds_11_1788 : exactInterval 11 1788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1788 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1788) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1788 : oddCount 1788 11 = 8 ∧ acceleratedOrbit 11 1788 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1788 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1788) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1788.1, data_11_1788.2] + +/-- Complete interval computation for depth 11, residue 1789. -/ +theorem bounds_11_1789 : exactInterval 11 1789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1789 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1789) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1789 : oddCount 1789 11 = 8 ∧ acceleratedOrbit 11 1789 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1789 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1789) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1789.1, data_11_1789.2] + +/-- Complete interval computation for depth 11, residue 1790. -/ +theorem bounds_11_1790 : exactInterval 11 1790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1790 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1790) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1790 : oddCount 1790 11 = 8 ∧ acceleratedOrbit 11 1790 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1790 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1790) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1790.1, data_11_1790.2] + +/-- Complete interval computation for depth 11, residue 1791. -/ +theorem bounds_11_1791 : exactInterval 11 1791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1791 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1791) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1791 : oddCount 1791 11 = 10 ∧ acceleratedOrbit 11 1791 = 51668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1791 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1791) = 3 ^ 10 * m + 51668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1791.1, data_11_1791.2] + +/-- Complete interval computation for depth 11, residue 1792. -/ +theorem bounds_11_1792 : exactInterval 11 1792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1792 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1792) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1792 : oddCount 1792 11 = 3 ∧ acceleratedOrbit 11 1792 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1792 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1792) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1792.1, data_11_1792.2] + +/-- Complete interval computation for depth 11, residue 1793. -/ +theorem bounds_11_1793 : exactInterval 11 1793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1793 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1793) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1793 : oddCount 1793 11 = 4 ∧ acceleratedOrbit 11 1793 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1793 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1793) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1793.1, data_11_1793.2] + +/-- Complete interval computation for depth 11, residue 1794. -/ +theorem bounds_11_1794 : exactInterval 11 1794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1794 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1794) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1794 : oddCount 1794 11 = 6 ∧ acceleratedOrbit 11 1794 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1794 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1794) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1794.1, data_11_1794.2] + +/-- Complete interval computation for depth 11, residue 1795. -/ +theorem bounds_11_1795 : exactInterval 11 1795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1795 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1795) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1795 : oddCount 1795 11 = 6 ∧ acceleratedOrbit 11 1795 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1795 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1795) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1795.1, data_11_1795.2] + +/-- Complete interval computation for depth 11, residue 1796. -/ +theorem bounds_11_1796 : exactInterval 11 1796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1796 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1796) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1796 : oddCount 1796 11 = 5 ∧ acceleratedOrbit 11 1796 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1796 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1796) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1796.1, data_11_1796.2] + +/-- Complete interval computation for depth 11, residue 1797. -/ +theorem bounds_11_1797 : exactInterval 11 1797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1797 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1797) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1797 : oddCount 1797 11 = 5 ∧ acceleratedOrbit 11 1797 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1797 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1797) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1797.1, data_11_1797.2] + +/-- Complete interval computation for depth 11, residue 1798. -/ +theorem bounds_11_1798 : exactInterval 11 1798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1798 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1798) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1798 : oddCount 1798 11 = 5 ∧ acceleratedOrbit 11 1798 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1798 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1798) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1798.1, data_11_1798.2] + +/-- Complete interval computation for depth 11, residue 1799. -/ +theorem bounds_11_1799 : exactInterval 11 1799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1799 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1799) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1799 : oddCount 1799 11 = 6 ∧ acceleratedOrbit 11 1799 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1799 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1799) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1799.1, data_11_1799.2] + +/-- Complete interval computation for depth 11, residue 1800. -/ +theorem bounds_11_1800 : exactInterval 11 1800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1800 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1800) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1800 : oddCount 1800 11 = 6 ∧ acceleratedOrbit 11 1800 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1800 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1800) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1800.1, data_11_1800.2] + +/-- Complete interval computation for depth 11, residue 1801. -/ +theorem bounds_11_1801 : exactInterval 11 1801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1801 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1801) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1801 : oddCount 1801 11 = 8 ∧ acceleratedOrbit 11 1801 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1801 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1801) = 3 ^ 8 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1801.1, data_11_1801.2] + +end Collatz.Research.StoppingAtlas.Batch0184 From e2dadbe1b31a73448f01357fb29e583f74e4d804 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:57 +0530 Subject: [PATCH 0185/1001] proof: certify atlas Batch0185 (11:1802 to 11:1816) --- Collatz/Research/StoppingAtlas/Batch0185.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0185.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0185.lean b/Collatz/Research/StoppingAtlas/Batch0185.lean new file mode 100644 index 00000000..dc8ea0fe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0185.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0185 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1802. -/ +theorem bounds_11_1802 : exactInterval 11 1802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1802 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1802) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1802 : oddCount 1802 11 = 6 ∧ acceleratedOrbit 11 1802 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1802 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1802) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1802.1, data_11_1802.2] + +/-- Complete interval computation for depth 11, residue 1803. -/ +theorem bounds_11_1803 : exactInterval 11 1803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1803 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1803) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1803 : oddCount 1803 11 = 6 ∧ acceleratedOrbit 11 1803 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1803 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1803) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1803.1, data_11_1803.2] + +/-- Complete interval computation for depth 11, residue 1804. -/ +theorem bounds_11_1804 : exactInterval 11 1804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1804 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1804) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1804 : oddCount 1804 11 = 6 ∧ acceleratedOrbit 11 1804 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1804 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1804) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1804.1, data_11_1804.2] + +/-- Complete interval computation for depth 11, residue 1805. -/ +theorem bounds_11_1805 : exactInterval 11 1805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1805 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1805) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1805 : oddCount 1805 11 = 6 ∧ acceleratedOrbit 11 1805 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1805 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1805) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1805.1, data_11_1805.2] + +/-- Complete interval computation for depth 11, residue 1806. -/ +theorem bounds_11_1806 : exactInterval 11 1806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1806 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1806) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1806 : oddCount 1806 11 = 5 ∧ acceleratedOrbit 11 1806 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1806 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1806) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1806.1, data_11_1806.2] + +/-- Complete interval computation for depth 11, residue 1807. -/ +theorem bounds_11_1807 : exactInterval 11 1807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1807 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1807) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1807 : oddCount 1807 11 = 5 ∧ acceleratedOrbit 11 1807 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1807 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1807) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1807.1, data_11_1807.2] + +/-- Complete interval computation for depth 11, residue 1808. -/ +theorem bounds_11_1808 : exactInterval 11 1808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1808 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1808) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1808 : oddCount 1808 11 = 2 ∧ acceleratedOrbit 11 1808 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1808 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1808) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1808.1, data_11_1808.2] + +/-- Complete interval computation for depth 11, residue 1809. -/ +theorem bounds_11_1809 : exactInterval 11 1809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1809 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1809) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1809 : oddCount 1809 11 = 6 ∧ acceleratedOrbit 11 1809 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1809 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1809) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1809.1, data_11_1809.2] + +/-- Complete interval computation for depth 11, residue 1810. -/ +theorem bounds_11_1810 : exactInterval 11 1810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1810 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1810) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1810 : oddCount 1810 11 = 7 ∧ acceleratedOrbit 11 1810 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1810 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1810) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1810.1, data_11_1810.2] + +/-- Complete interval computation for depth 11, residue 1811. -/ +theorem bounds_11_1811 : exactInterval 11 1811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1811 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1811) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1811 : oddCount 1811 11 = 7 ∧ acceleratedOrbit 11 1811 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1811 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1811) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1811.1, data_11_1811.2] + +/-- Complete interval computation for depth 11, residue 1812. -/ +theorem bounds_11_1812 : exactInterval 11 1812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1812 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1812) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1812 : oddCount 1812 11 = 2 ∧ acceleratedOrbit 11 1812 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1812 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1812) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1812.1, data_11_1812.2] + +/-- Complete interval computation for depth 11, residue 1813. -/ +theorem bounds_11_1813 : exactInterval 11 1813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1813 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1813) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1813 : oddCount 1813 11 = 2 ∧ acceleratedOrbit 11 1813 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1813 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1813) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1813.1, data_11_1813.2] + +/-- Complete interval computation for depth 11, residue 1814. -/ +theorem bounds_11_1814 : exactInterval 11 1814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1814 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1814) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1814 : oddCount 1814 11 = 7 ∧ acceleratedOrbit 11 1814 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1814 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1814) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1814.1, data_11_1814.2] + +/-- Complete interval computation for depth 11, residue 1815. -/ +theorem bounds_11_1815 : exactInterval 11 1815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1815 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1815) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1815 : oddCount 1815 11 = 7 ∧ acceleratedOrbit 11 1815 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1815 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1815) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1815.1, data_11_1815.2] + +/-- Complete interval computation for depth 11, residue 1816. -/ +theorem bounds_11_1816 : exactInterval 11 1816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1816 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1816) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1816 : oddCount 1816 11 = 2 ∧ acceleratedOrbit 11 1816 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1816 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1816) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1816.1, data_11_1816.2] + +end Collatz.Research.StoppingAtlas.Batch0185 From 699677461bfc71facddc43e41e09596a5ac6290c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:57 +0530 Subject: [PATCH 0186/1001] proof: certify atlas Batch0186 (11:1817 to 11:1831) --- Collatz/Research/StoppingAtlas/Batch0186.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0186.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0186.lean b/Collatz/Research/StoppingAtlas/Batch0186.lean new file mode 100644 index 00000000..e81146c0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0186.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0186 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1817. -/ +theorem bounds_11_1817 : exactInterval 11 1817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1817 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1817) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1817 : oddCount 1817 11 = 8 ∧ acceleratedOrbit 11 1817 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1817 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1817) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1817.1, data_11_1817.2] + +/-- Complete interval computation for depth 11, residue 1818. -/ +theorem bounds_11_1818 : exactInterval 11 1818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1818 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1818) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1818 : oddCount 1818 11 = 2 ∧ acceleratedOrbit 11 1818 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1818 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1818) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1818.1, data_11_1818.2] + +/-- Complete interval computation for depth 11, residue 1819. -/ +theorem bounds_11_1819 : exactInterval 11 1819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1819 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1819) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1819 : oddCount 1819 11 = 10 ∧ acceleratedOrbit 11 1819 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1819 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1819) = 3 ^ 10 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1819.1, data_11_1819.2] + +/-- Complete interval computation for depth 11, residue 1820. -/ +theorem bounds_11_1820 : exactInterval 11 1820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1820 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1820) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1820 : oddCount 1820 11 = 6 ∧ acceleratedOrbit 11 1820 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1820 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1820) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1820.1, data_11_1820.2] + +/-- Complete interval computation for depth 11, residue 1821. -/ +theorem bounds_11_1821 : exactInterval 11 1821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1821 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1821) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1821 : oddCount 1821 11 = 6 ∧ acceleratedOrbit 11 1821 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1821 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1821) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1821.1, data_11_1821.2] + +/-- Complete interval computation for depth 11, residue 1822. -/ +theorem bounds_11_1822 : exactInterval 11 1822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1822 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1822) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1822 : oddCount 1822 11 = 6 ∧ acceleratedOrbit 11 1822 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1822 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1822) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1822.1, data_11_1822.2] + +/-- Complete interval computation for depth 11, residue 1823. -/ +theorem bounds_11_1823 : exactInterval 11 1823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1823 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1823) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1823 : oddCount 1823 11 = 7 ∧ acceleratedOrbit 11 1823 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1823 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1823) = 3 ^ 7 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1823.1, data_11_1823.2] + +/-- Complete interval computation for depth 11, residue 1824. -/ +theorem bounds_11_1824 : exactInterval 11 1824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1824 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1824) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1824 : oddCount 1824 11 = 4 ∧ acceleratedOrbit 11 1824 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1824 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1824) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1824.1, data_11_1824.2] + +/-- Complete interval computation for depth 11, residue 1825. -/ +theorem bounds_11_1825 : exactInterval 11 1825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1825 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1825) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1825 : oddCount 1825 11 = 5 ∧ acceleratedOrbit 11 1825 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1825 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1825) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1825.1, data_11_1825.2] + +/-- Complete interval computation for depth 11, residue 1826. -/ +theorem bounds_11_1826 : exactInterval 11 1826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1826 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1826) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1826 : oddCount 1826 11 = 5 ∧ acceleratedOrbit 11 1826 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1826 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1826) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1826.1, data_11_1826.2] + +/-- Complete interval computation for depth 11, residue 1827. -/ +theorem bounds_11_1827 : exactInterval 11 1827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1827 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1827) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1827 : oddCount 1827 11 = 5 ∧ acceleratedOrbit 11 1827 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1827 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1827) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1827.1, data_11_1827.2] + +/-- Complete interval computation for depth 11, residue 1828. -/ +theorem bounds_11_1828 : exactInterval 11 1828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1828 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1828) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1828 : oddCount 1828 11 = 5 ∧ acceleratedOrbit 11 1828 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1828 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1828) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1828.1, data_11_1828.2] + +/-- Complete interval computation for depth 11, residue 1829. -/ +theorem bounds_11_1829 : exactInterval 11 1829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1829 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1829) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1829 : oddCount 1829 11 = 5 ∧ acceleratedOrbit 11 1829 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1829 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1829) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1829.1, data_11_1829.2] + +/-- Complete interval computation for depth 11, residue 1830. -/ +theorem bounds_11_1830 : exactInterval 11 1830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1830 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1830) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1830 : oddCount 1830 11 = 5 ∧ acceleratedOrbit 11 1830 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1830 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1830) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1830.1, data_11_1830.2] + +/-- Complete interval computation for depth 11, residue 1831. -/ +theorem bounds_11_1831 : exactInterval 11 1831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1831 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1831) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1831 : oddCount 1831 11 = 7 ∧ acceleratedOrbit 11 1831 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1831 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1831) = 3 ^ 7 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1831.1, data_11_1831.2] + +end Collatz.Research.StoppingAtlas.Batch0186 From 2cb7b263ef81bff2cdd013fbadcb55f0a38fbbac Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:57 +0530 Subject: [PATCH 0187/1001] proof: certify atlas Batch0187 (11:1832 to 11:1847) --- Collatz/Research/StoppingAtlas/Batch0187.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0187.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0187.lean b/Collatz/Research/StoppingAtlas/Batch0187.lean new file mode 100644 index 00000000..bb2ef336 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0187.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0187 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1832. -/ +theorem bounds_11_1832 : exactInterval 11 1832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1832 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1832) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1832 : oddCount 1832 11 = 4 ∧ acceleratedOrbit 11 1832 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1832 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1832) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1832.1, data_11_1832.2] + +/-- Complete interval computation for depth 11, residue 1833. -/ +theorem bounds_11_1833 : exactInterval 11 1833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1833 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1833) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1833 : oddCount 1833 11 = 6 ∧ acceleratedOrbit 11 1833 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1833 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1833) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1833.1, data_11_1833.2] + +/-- Complete interval computation for depth 11, residue 1834. -/ +theorem bounds_11_1834 : exactInterval 11 1834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1834 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1834) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1834 : oddCount 1834 11 = 4 ∧ acceleratedOrbit 11 1834 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1834 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1834) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1834.1, data_11_1834.2] + +/-- Complete interval computation for depth 11, residue 1835. -/ +theorem bounds_11_1835 : exactInterval 11 1835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1835 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1835) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1835 : oddCount 1835 11 = 5 ∧ acceleratedOrbit 11 1835 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1835 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1835) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1835.1, data_11_1835.2] + +/-- Complete interval computation for depth 11, residue 1836. -/ +theorem bounds_11_1836 : exactInterval 11 1836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1836 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1836) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1836 : oddCount 1836 11 = 4 ∧ acceleratedOrbit 11 1836 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1836 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1836) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1836.1, data_11_1836.2] + +/-- Complete interval computation for depth 11, residue 1837. -/ +theorem bounds_11_1837 : exactInterval 11 1837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1837 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1837) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1837 : oddCount 1837 11 = 4 ∧ acceleratedOrbit 11 1837 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1837 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1837) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1837.1, data_11_1837.2] + +/-- Complete interval computation for depth 11, residue 1838. -/ +theorem bounds_11_1838 : exactInterval 11 1838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1838 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1838) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1838 : oddCount 1838 11 = 4 ∧ acceleratedOrbit 11 1838 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1838 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1838) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1838.1, data_11_1838.2] + +/-- Complete interval computation for depth 11, residue 1839. -/ +theorem bounds_11_1839 : exactInterval 11 1839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1839 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1839) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1839 : oddCount 1839 11 = 6 ∧ acceleratedOrbit 11 1839 = 655 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1839 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1839) = 3 ^ 6 * m + 655 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1839.1, data_11_1839.2] + +/-- Complete interval computation for depth 11, residue 1840. -/ +theorem bounds_11_1840 : exactInterval 11 1840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1840 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1840) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1840 : oddCount 1840 11 = 4 ∧ acceleratedOrbit 11 1840 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1840 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1840) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1840.1, data_11_1840.2] + +/-- Complete interval computation for depth 11, residue 1841. -/ +theorem bounds_11_1841 : exactInterval 11 1841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1841 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1841) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1841 : oddCount 1841 11 = 4 ∧ acceleratedOrbit 11 1841 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1841 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1841) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1841.1, data_11_1841.2] + +/-- Complete interval computation for depth 11, residue 1842. -/ +theorem bounds_11_1842 : exactInterval 11 1842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1842 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1842) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1842 : oddCount 1842 11 = 4 ∧ acceleratedOrbit 11 1842 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1842 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1842) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1842.1, data_11_1842.2] + +/-- Complete interval computation for depth 11, residue 1843. -/ +theorem bounds_11_1843 : exactInterval 11 1843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1843 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1843) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1843 : oddCount 1843 11 = 4 ∧ acceleratedOrbit 11 1843 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1843 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1843) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1843.1, data_11_1843.2] + +/-- Complete interval computation for depth 11, residue 1844. -/ +theorem bounds_11_1844 : exactInterval 11 1844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1844 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1844) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1844 : oddCount 1844 11 = 4 ∧ acceleratedOrbit 11 1844 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1844 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1844) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1844.1, data_11_1844.2] + +/-- Complete interval computation for depth 11, residue 1845. -/ +theorem bounds_11_1845 : exactInterval 11 1845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1845 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1845) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1845 : oddCount 1845 11 = 4 ∧ acceleratedOrbit 11 1845 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1845 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1845) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1845.1, data_11_1845.2] + +/-- Complete interval computation for depth 11, residue 1846. -/ +theorem bounds_11_1846 : exactInterval 11 1846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1846 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1846) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1846 : oddCount 1846 11 = 6 ∧ acceleratedOrbit 11 1846 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1846 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1846) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1846.1, data_11_1846.2] + +/-- Complete interval computation for depth 11, residue 1847. -/ +theorem bounds_11_1847 : exactInterval 11 1847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1847 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1847) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1847 : oddCount 1847 11 = 6 ∧ acceleratedOrbit 11 1847 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1847 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1847) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1847.1, data_11_1847.2] + +end Collatz.Research.StoppingAtlas.Batch0187 From 2566c2c5a46b4182944d2265d456d56a787b10ea Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:58 +0530 Subject: [PATCH 0188/1001] proof: certify atlas Batch0188 (11:1848 to 11:1862) --- Collatz/Research/StoppingAtlas/Batch0188.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0188.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0188.lean b/Collatz/Research/StoppingAtlas/Batch0188.lean new file mode 100644 index 00000000..7ac2a942 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0188.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0188 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1848. -/ +theorem bounds_11_1848 : exactInterval 11 1848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1848 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1848) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1848 : oddCount 1848 11 = 6 ∧ acceleratedOrbit 11 1848 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1848 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1848) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1848.1, data_11_1848.2] + +/-- Complete interval computation for depth 11, residue 1849. -/ +theorem bounds_11_1849 : exactInterval 11 1849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1849 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1849) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1849 : oddCount 1849 11 = 6 ∧ acceleratedOrbit 11 1849 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1849 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1849) = 3 ^ 6 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1849.1, data_11_1849.2] + +/-- Complete interval computation for depth 11, residue 1850. -/ +theorem bounds_11_1850 : exactInterval 11 1850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1850 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1850) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1850 : oddCount 1850 11 = 6 ∧ acceleratedOrbit 11 1850 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1850 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1850) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1850.1, data_11_1850.2] + +/-- Complete interval computation for depth 11, residue 1851. -/ +theorem bounds_11_1851 : exactInterval 11 1851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1851 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1851) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1851 : oddCount 1851 11 = 5 ∧ acceleratedOrbit 11 1851 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1851 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1851) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1851.1, data_11_1851.2] + +/-- Complete interval computation for depth 11, residue 1852. -/ +theorem bounds_11_1852 : exactInterval 11 1852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1852 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1852) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1852 : oddCount 1852 11 = 6 ∧ acceleratedOrbit 11 1852 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1852 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1852) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1852.1, data_11_1852.2] + +/-- Complete interval computation for depth 11, residue 1853. -/ +theorem bounds_11_1853 : exactInterval 11 1853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1853 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1853) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1853 : oddCount 1853 11 = 6 ∧ acceleratedOrbit 11 1853 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1853 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1853) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1853.1, data_11_1853.2] + +/-- Complete interval computation for depth 11, residue 1854. -/ +theorem bounds_11_1854 : exactInterval 11 1854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1854 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1854) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1854 : oddCount 1854 11 = 7 ∧ acceleratedOrbit 11 1854 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1854 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1854) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1854.1, data_11_1854.2] + +/-- Complete interval computation for depth 11, residue 1855. -/ +theorem bounds_11_1855 : exactInterval 11 1855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1855 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1855) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1855 : oddCount 1855 11 = 7 ∧ acceleratedOrbit 11 1855 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1855 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1855) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1855.1, data_11_1855.2] + +/-- Complete interval computation for depth 11, residue 1856. -/ +theorem bounds_11_1856 : exactInterval 11 1856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1856 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1856) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1856 : oddCount 1856 11 = 3 ∧ acceleratedOrbit 11 1856 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1856 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1856) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1856.1, data_11_1856.2] + +/-- Complete interval computation for depth 11, residue 1857. -/ +theorem bounds_11_1857 : exactInterval 11 1857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1857 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1857) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1857 : oddCount 1857 11 = 4 ∧ acceleratedOrbit 11 1857 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1857 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1857) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1857.1, data_11_1857.2] + +/-- Complete interval computation for depth 11, residue 1858. -/ +theorem bounds_11_1858 : exactInterval 11 1858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1858 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1858) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1858 : oddCount 1858 11 = 5 ∧ acceleratedOrbit 11 1858 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1858 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1858) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1858.1, data_11_1858.2] + +/-- Complete interval computation for depth 11, residue 1859. -/ +theorem bounds_11_1859 : exactInterval 11 1859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1859 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1859) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1859 : oddCount 1859 11 = 5 ∧ acceleratedOrbit 11 1859 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1859 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1859) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1859.1, data_11_1859.2] + +/-- Complete interval computation for depth 11, residue 1860. -/ +theorem bounds_11_1860 : exactInterval 11 1860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1860 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1860) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1860 : oddCount 1860 11 = 4 ∧ acceleratedOrbit 11 1860 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1860 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1860) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1860.1, data_11_1860.2] + +/-- Complete interval computation for depth 11, residue 1861. -/ +theorem bounds_11_1861 : exactInterval 11 1861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1861 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1861) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1861 : oddCount 1861 11 = 4 ∧ acceleratedOrbit 11 1861 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1861 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1861) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1861.1, data_11_1861.2] + +/-- Complete interval computation for depth 11, residue 1862. -/ +theorem bounds_11_1862 : exactInterval 11 1862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1862 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1862) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1862 : oddCount 1862 11 = 4 ∧ acceleratedOrbit 11 1862 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1862 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1862) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1862.1, data_11_1862.2] + +end Collatz.Research.StoppingAtlas.Batch0188 From dca0315d36b21f8f88c757b53322267244e3deb9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:58 +0530 Subject: [PATCH 0189/1001] proof: certify atlas Batch0189 (11:1863 to 11:1878) --- Collatz/Research/StoppingAtlas/Batch0189.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0189.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0189.lean b/Collatz/Research/StoppingAtlas/Batch0189.lean new file mode 100644 index 00000000..a47c8a69 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0189.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0189 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1863. -/ +theorem bounds_11_1863 : exactInterval 11 1863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1863 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1863) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1863 : oddCount 1863 11 = 7 ∧ acceleratedOrbit 11 1863 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1863 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1863) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1863.1, data_11_1863.2] + +/-- Complete interval computation for depth 11, residue 1864. -/ +theorem bounds_11_1864 : exactInterval 11 1864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1864 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1864) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1864 : oddCount 1864 11 = 6 ∧ acceleratedOrbit 11 1864 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1864 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1864) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1864.1, data_11_1864.2] + +/-- Complete interval computation for depth 11, residue 1865. -/ +theorem bounds_11_1865 : exactInterval 11 1865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1865 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1865) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1865 : oddCount 1865 11 = 6 ∧ acceleratedOrbit 11 1865 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1865 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1865) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1865.1, data_11_1865.2] + +/-- Complete interval computation for depth 11, residue 1866. -/ +theorem bounds_11_1866 : exactInterval 11 1866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1866 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1866) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1866 : oddCount 1866 11 = 6 ∧ acceleratedOrbit 11 1866 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1866 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1866) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1866.1, data_11_1866.2] + +/-- Complete interval computation for depth 11, residue 1867. -/ +theorem bounds_11_1867 : exactInterval 11 1867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1867 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1867) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1867 : oddCount 1867 11 = 4 ∧ acceleratedOrbit 11 1867 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1867 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1867) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1867.1, data_11_1867.2] + +/-- Complete interval computation for depth 11, residue 1868. -/ +theorem bounds_11_1868 : exactInterval 11 1868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1868 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1868) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1868 : oddCount 1868 11 = 6 ∧ acceleratedOrbit 11 1868 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1868 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1868) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1868.1, data_11_1868.2] + +/-- Complete interval computation for depth 11, residue 1869. -/ +theorem bounds_11_1869 : exactInterval 11 1869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1869 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1869) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1869 : oddCount 1869 11 = 6 ∧ acceleratedOrbit 11 1869 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1869 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1869) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1869.1, data_11_1869.2] + +/-- Complete interval computation for depth 11, residue 1870. -/ +theorem bounds_11_1870 : exactInterval 11 1870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1870 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1870) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1870 : oddCount 1870 11 = 7 ∧ acceleratedOrbit 11 1870 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1870 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1870) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1870.1, data_11_1870.2] + +/-- Complete interval computation for depth 11, residue 1871. -/ +theorem bounds_11_1871 : exactInterval 11 1871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1871 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1871) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1871 : oddCount 1871 11 = 7 ∧ acceleratedOrbit 11 1871 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1871 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1871) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1871.1, data_11_1871.2] + +/-- Complete interval computation for depth 11, residue 1872. -/ +theorem bounds_11_1872 : exactInterval 11 1872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1872 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1872) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1872 : oddCount 1872 11 = 3 ∧ acceleratedOrbit 11 1872 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1872 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1872) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1872.1, data_11_1872.2] + +/-- Complete interval computation for depth 11, residue 1873. -/ +theorem bounds_11_1873 : exactInterval 11 1873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1873 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1873) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1873 : oddCount 1873 11 = 6 ∧ acceleratedOrbit 11 1873 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1873 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1873) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1873.1, data_11_1873.2] + +/-- Complete interval computation for depth 11, residue 1874. -/ +theorem bounds_11_1874 : exactInterval 11 1874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1874 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1874) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1874 : oddCount 1874 11 = 8 ∧ acceleratedOrbit 11 1874 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1874 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1874) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1874.1, data_11_1874.2] + +/-- Complete interval computation for depth 11, residue 1875. -/ +theorem bounds_11_1875 : exactInterval 11 1875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1875 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1875) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1875 : oddCount 1875 11 = 8 ∧ acceleratedOrbit 11 1875 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1875 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1875) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1875.1, data_11_1875.2] + +/-- Complete interval computation for depth 11, residue 1876. -/ +theorem bounds_11_1876 : exactInterval 11 1876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1876 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1876) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1876 : oddCount 1876 11 = 3 ∧ acceleratedOrbit 11 1876 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1876 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1876) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1876.1, data_11_1876.2] + +/-- Complete interval computation for depth 11, residue 1877. -/ +theorem bounds_11_1877 : exactInterval 11 1877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1877 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1877) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1877 : oddCount 1877 11 = 3 ∧ acceleratedOrbit 11 1877 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1877 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1877) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1877.1, data_11_1877.2] + +/-- Complete interval computation for depth 11, residue 1878. -/ +theorem bounds_11_1878 : exactInterval 11 1878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1878 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1878) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1878 : oddCount 1878 11 = 6 ∧ acceleratedOrbit 11 1878 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1878 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1878) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1878.1, data_11_1878.2] + +end Collatz.Research.StoppingAtlas.Batch0189 From 04ca71e08e0c8f80aef16a07221afd24fdcda738 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:58 +0530 Subject: [PATCH 0190/1001] proof: certify atlas Batch0190 (11:1879 to 11:1893) --- Collatz/Research/StoppingAtlas/Batch0190.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0190.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0190.lean b/Collatz/Research/StoppingAtlas/Batch0190.lean new file mode 100644 index 00000000..17db9b28 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0190.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0190 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1879. -/ +theorem bounds_11_1879 : exactInterval 11 1879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1879 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1879) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1879 : oddCount 1879 11 = 6 ∧ acceleratedOrbit 11 1879 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1879 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1879) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1879.1, data_11_1879.2] + +/-- Complete interval computation for depth 11, residue 1880. -/ +theorem bounds_11_1880 : exactInterval 11 1880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1880 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1880) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1880 : oddCount 1880 11 = 6 ∧ acceleratedOrbit 11 1880 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1880 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1880) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1880.1, data_11_1880.2] + +/-- Complete interval computation for depth 11, residue 1881. -/ +theorem bounds_11_1881 : exactInterval 11 1881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1881 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1881) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1881 : oddCount 1881 11 = 5 ∧ acceleratedOrbit 11 1881 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1881 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1881) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1881.1, data_11_1881.2] + +/-- Complete interval computation for depth 11, residue 1882. -/ +theorem bounds_11_1882 : exactInterval 11 1882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1882 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1882) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1882 : oddCount 1882 11 = 6 ∧ acceleratedOrbit 11 1882 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1882 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1882) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1882.1, data_11_1882.2] + +/-- Complete interval computation for depth 11, residue 1883. -/ +theorem bounds_11_1883 : exactInterval 11 1883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1883 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1883) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1883 : oddCount 1883 11 = 8 ∧ acceleratedOrbit 11 1883 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1883 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1883) = 3 ^ 8 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1883.1, data_11_1883.2] + +/-- Complete interval computation for depth 11, residue 1884. -/ +theorem bounds_11_1884 : exactInterval 11 1884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1884 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1884) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1884 : oddCount 1884 11 = 6 ∧ acceleratedOrbit 11 1884 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1884 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1884) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1884.1, data_11_1884.2] + +/-- Complete interval computation for depth 11, residue 1885. -/ +theorem bounds_11_1885 : exactInterval 11 1885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1885 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1885) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1885 : oddCount 1885 11 = 6 ∧ acceleratedOrbit 11 1885 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1885 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1885) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1885.1, data_11_1885.2] + +/-- Complete interval computation for depth 11, residue 1886. -/ +theorem bounds_11_1886 : exactInterval 11 1886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1886 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1886) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1886 : oddCount 1886 11 = 5 ∧ acceleratedOrbit 11 1886 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1886 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1886) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1886.1, data_11_1886.2] + +/-- Complete interval computation for depth 11, residue 1887. -/ +theorem bounds_11_1887 : exactInterval 11 1887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1887 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1887) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1887 : oddCount 1887 11 = 5 ∧ acceleratedOrbit 11 1887 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1887 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1887) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1887.1, data_11_1887.2] + +/-- Complete interval computation for depth 11, residue 1888. -/ +theorem bounds_11_1888 : exactInterval 11 1888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1888 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1888) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1888 : oddCount 1888 11 = 4 ∧ acceleratedOrbit 11 1888 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1888 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1888) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1888.1, data_11_1888.2] + +/-- Complete interval computation for depth 11, residue 1889. -/ +theorem bounds_11_1889 : exactInterval 11 1889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1889 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1889) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1889 : oddCount 1889 11 = 7 ∧ acceleratedOrbit 11 1889 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1889 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1889) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1889.1, data_11_1889.2] + +/-- Complete interval computation for depth 11, residue 1890. -/ +theorem bounds_11_1890 : exactInterval 11 1890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1890 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1890) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1890 : oddCount 1890 11 = 3 ∧ acceleratedOrbit 11 1890 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1890 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1890) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1890.1, data_11_1890.2] + +/-- Complete interval computation for depth 11, residue 1891. -/ +theorem bounds_11_1891 : exactInterval 11 1891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1891 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1891) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1891 : oddCount 1891 11 = 3 ∧ acceleratedOrbit 11 1891 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1891 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1891) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1891.1, data_11_1891.2] + +/-- Complete interval computation for depth 11, residue 1892. -/ +theorem bounds_11_1892 : exactInterval 11 1892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1892 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1892) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1892 : oddCount 1892 11 = 3 ∧ acceleratedOrbit 11 1892 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1892 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1892) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1892.1, data_11_1892.2] + +/-- Complete interval computation for depth 11, residue 1893. -/ +theorem bounds_11_1893 : exactInterval 11 1893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1893 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1893) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1893 : oddCount 1893 11 = 3 ∧ acceleratedOrbit 11 1893 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1893 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1893) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1893.1, data_11_1893.2] + +end Collatz.Research.StoppingAtlas.Batch0190 From 7536b9092f4c21e00d964f38df8f36a4c1f51bf5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:59 +0530 Subject: [PATCH 0191/1001] proof: certify atlas Batch0191 (11:1894 to 11:1908) --- Collatz/Research/StoppingAtlas/Batch0191.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0191.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0191.lean b/Collatz/Research/StoppingAtlas/Batch0191.lean new file mode 100644 index 00000000..0c6a159b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0191.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0191 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1894. -/ +theorem bounds_11_1894 : exactInterval 11 1894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1894 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1894) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1894 : oddCount 1894 11 = 3 ∧ acceleratedOrbit 11 1894 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1894 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1894) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1894.1, data_11_1894.2] + +/-- Complete interval computation for depth 11, residue 1895. -/ +theorem bounds_11_1895 : exactInterval 11 1895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1895 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1895) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1895 : oddCount 1895 11 = 10 ∧ acceleratedOrbit 11 1895 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1895 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1895) = 3 ^ 10 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1895.1, data_11_1895.2] + +/-- Complete interval computation for depth 11, residue 1896. -/ +theorem bounds_11_1896 : exactInterval 11 1896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1896 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1896) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1896 : oddCount 1896 11 = 4 ∧ acceleratedOrbit 11 1896 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1896 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1896) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1896.1, data_11_1896.2] + +/-- Complete interval computation for depth 11, residue 1897. -/ +theorem bounds_11_1897 : exactInterval 11 1897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1897 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1897) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1897 : oddCount 1897 11 = 6 ∧ acceleratedOrbit 11 1897 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1897 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1897) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1897.1, data_11_1897.2] + +/-- Complete interval computation for depth 11, residue 1898. -/ +theorem bounds_11_1898 : exactInterval 11 1898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1898 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1898) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1898 : oddCount 1898 11 = 4 ∧ acceleratedOrbit 11 1898 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1898 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1898) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1898.1, data_11_1898.2] + +/-- Complete interval computation for depth 11, residue 1899. -/ +theorem bounds_11_1899 : exactInterval 11 1899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1899 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1899) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1899 : oddCount 1899 11 = 6 ∧ acceleratedOrbit 11 1899 = 677 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1899 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1899) = 3 ^ 6 * m + 677 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1899.1, data_11_1899.2] + +/-- Complete interval computation for depth 11, residue 1900. -/ +theorem bounds_11_1900 : exactInterval 11 1900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1900 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1900) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1900 : oddCount 1900 11 = 5 ∧ acceleratedOrbit 11 1900 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1900 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1900) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1900.1, data_11_1900.2] + +/-- Complete interval computation for depth 11, residue 1901. -/ +theorem bounds_11_1901 : exactInterval 11 1901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1901 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1901) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1901 : oddCount 1901 11 = 5 ∧ acceleratedOrbit 11 1901 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1901 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1901) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1901.1, data_11_1901.2] + +/-- Complete interval computation for depth 11, residue 1902. -/ +theorem bounds_11_1902 : exactInterval 11 1902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1902 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1902) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1902 : oddCount 1902 11 = 5 ∧ acceleratedOrbit 11 1902 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1902 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1902) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1902.1, data_11_1902.2] + +/-- Complete interval computation for depth 11, residue 1903. -/ +theorem bounds_11_1903 : exactInterval 11 1903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1903 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1903) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1903 : oddCount 1903 11 = 8 ∧ acceleratedOrbit 11 1903 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1903 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1903) = 3 ^ 8 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1903.1, data_11_1903.2] + +/-- Complete interval computation for depth 11, residue 1904. -/ +theorem bounds_11_1904 : exactInterval 11 1904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1904 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1904) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1904 : oddCount 1904 11 = 4 ∧ acceleratedOrbit 11 1904 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1904 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1904) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1904.1, data_11_1904.2] + +/-- Complete interval computation for depth 11, residue 1905. -/ +theorem bounds_11_1905 : exactInterval 11 1905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1905 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1905) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1905 : oddCount 1905 11 = 4 ∧ acceleratedOrbit 11 1905 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1905 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1905) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1905.1, data_11_1905.2] + +/-- Complete interval computation for depth 11, residue 1906. -/ +theorem bounds_11_1906 : exactInterval 11 1906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1906 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1906) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1906 : oddCount 1906 11 = 5 ∧ acceleratedOrbit 11 1906 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1906 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1906) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1906.1, data_11_1906.2] + +/-- Complete interval computation for depth 11, residue 1907. -/ +theorem bounds_11_1907 : exactInterval 11 1907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1907 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1907) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1907 : oddCount 1907 11 = 5 ∧ acceleratedOrbit 11 1907 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1907 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1907) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1907.1, data_11_1907.2] + +/-- Complete interval computation for depth 11, residue 1908. -/ +theorem bounds_11_1908 : exactInterval 11 1908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1908 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1908) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1908 : oddCount 1908 11 = 4 ∧ acceleratedOrbit 11 1908 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1908 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1908) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1908.1, data_11_1908.2] + +end Collatz.Research.StoppingAtlas.Batch0191 From cb045627e6b6c7d5608e7027d3a803faaa64e3c3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:59 +0530 Subject: [PATCH 0192/1001] proof: certify atlas Batch0192 (11:1909 to 11:1924) --- Collatz/Research/StoppingAtlas/Batch0192.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0192.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0192.lean b/Collatz/Research/StoppingAtlas/Batch0192.lean new file mode 100644 index 00000000..2ae80cf2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0192.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0192 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1909. -/ +theorem bounds_11_1909 : exactInterval 11 1909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1909 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1909) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1909 : oddCount 1909 11 = 4 ∧ acceleratedOrbit 11 1909 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1909 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1909) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1909.1, data_11_1909.2] + +/-- Complete interval computation for depth 11, residue 1910. -/ +theorem bounds_11_1910 : exactInterval 11 1910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1910 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1910) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1910 : oddCount 1910 11 = 5 ∧ acceleratedOrbit 11 1910 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1910 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1910) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1910.1, data_11_1910.2] + +/-- Complete interval computation for depth 11, residue 1911. -/ +theorem bounds_11_1911 : exactInterval 11 1911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1911 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1911) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1911 : oddCount 1911 11 = 5 ∧ acceleratedOrbit 11 1911 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1911 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1911) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1911.1, data_11_1911.2] + +/-- Complete interval computation for depth 11, residue 1912. -/ +theorem bounds_11_1912 : exactInterval 11 1912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1912 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1912) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1912 : oddCount 1912 11 = 7 ∧ acceleratedOrbit 11 1912 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1912 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1912) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1912.1, data_11_1912.2] + +/-- Complete interval computation for depth 11, residue 1913. -/ +theorem bounds_11_1913 : exactInterval 11 1913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1913 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1913) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1913 : oddCount 1913 11 = 7 ∧ acceleratedOrbit 11 1913 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1913 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1913) = 3 ^ 7 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1913.1, data_11_1913.2] + +/-- Complete interval computation for depth 11, residue 1914. -/ +theorem bounds_11_1914 : exactInterval 11 1914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1914 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1914) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1914 : oddCount 1914 11 = 7 ∧ acceleratedOrbit 11 1914 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1914 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1914) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1914.1, data_11_1914.2] + +/-- Complete interval computation for depth 11, residue 1915. -/ +theorem bounds_11_1915 : exactInterval 11 1915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1915 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1915) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1915 : oddCount 1915 11 = 7 ∧ acceleratedOrbit 11 1915 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1915 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1915) = 3 ^ 7 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1915.1, data_11_1915.2] + +/-- Complete interval computation for depth 11, residue 1916. -/ +theorem bounds_11_1916 : exactInterval 11 1916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1916 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1916) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1916 : oddCount 1916 11 = 7 ∧ acceleratedOrbit 11 1916 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1916 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1916) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1916.1, data_11_1916.2] + +/-- Complete interval computation for depth 11, residue 1917. -/ +theorem bounds_11_1917 : exactInterval 11 1917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1917 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1917) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1917 : oddCount 1917 11 = 7 ∧ acceleratedOrbit 11 1917 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1917 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1917) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1917.1, data_11_1917.2] + +/-- Complete interval computation for depth 11, residue 1918. -/ +theorem bounds_11_1918 : exactInterval 11 1918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1918 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1918) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1918 : oddCount 1918 11 = 8 ∧ acceleratedOrbit 11 1918 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1918 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1918) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1918.1, data_11_1918.2] + +/-- Complete interval computation for depth 11, residue 1919. -/ +theorem bounds_11_1919 : exactInterval 11 1919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1919 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1919) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1919 : oddCount 1919 11 = 8 ∧ acceleratedOrbit 11 1919 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1919 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1919) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1919.1, data_11_1919.2] + +/-- Complete interval computation for depth 11, residue 1920. -/ +theorem bounds_11_1920 : exactInterval 11 1920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1920 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1920) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1920 : oddCount 1920 11 = 4 ∧ acceleratedOrbit 11 1920 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1920 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1920) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1920.1, data_11_1920.2] + +/-- Complete interval computation for depth 11, residue 1921. -/ +theorem bounds_11_1921 : exactInterval 11 1921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1921 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1921) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1921 : oddCount 1921 11 = 6 ∧ acceleratedOrbit 11 1921 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1921 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1921) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1921.1, data_11_1921.2] + +/-- Complete interval computation for depth 11, residue 1922. -/ +theorem bounds_11_1922 : exactInterval 11 1922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1922 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1922) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1922 : oddCount 1922 11 = 5 ∧ acceleratedOrbit 11 1922 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1922 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1922) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1922.1, data_11_1922.2] + +/-- Complete interval computation for depth 11, residue 1923. -/ +theorem bounds_11_1923 : exactInterval 11 1923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1923 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1923) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1923 : oddCount 1923 11 = 5 ∧ acceleratedOrbit 11 1923 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1923 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1923) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1923.1, data_11_1923.2] + +/-- Complete interval computation for depth 11, residue 1924. -/ +theorem bounds_11_1924 : exactInterval 11 1924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1924 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1924) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1924 : oddCount 1924 11 = 6 ∧ acceleratedOrbit 11 1924 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1924 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1924) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1924.1, data_11_1924.2] + +end Collatz.Research.StoppingAtlas.Batch0192 From dbfb71eb9da143f156f226f4a482f0fe2b968358 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:22:59 +0530 Subject: [PATCH 0193/1001] proof: certify atlas Batch0193 (11:1925 to 11:1939) --- Collatz/Research/StoppingAtlas/Batch0193.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0193.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0193.lean b/Collatz/Research/StoppingAtlas/Batch0193.lean new file mode 100644 index 00000000..75afeb1f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0193.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0193 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1925. -/ +theorem bounds_11_1925 : exactInterval 11 1925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1925 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1925) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1925 : oddCount 1925 11 = 6 ∧ acceleratedOrbit 11 1925 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1925 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1925) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1925.1, data_11_1925.2] + +/-- Complete interval computation for depth 11, residue 1926. -/ +theorem bounds_11_1926 : exactInterval 11 1926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1926 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1926) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1926 : oddCount 1926 11 = 6 ∧ acceleratedOrbit 11 1926 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1926 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1926) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1926.1, data_11_1926.2] + +/-- Complete interval computation for depth 11, residue 1927. -/ +theorem bounds_11_1927 : exactInterval 11 1927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1927 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1927) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1927 : oddCount 1927 11 = 5 ∧ acceleratedOrbit 11 1927 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1927 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1927) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1927.1, data_11_1927.2] + +/-- Complete interval computation for depth 11, residue 1928. -/ +theorem bounds_11_1928 : exactInterval 11 1928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1928 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1928) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1928 : oddCount 1928 11 = 3 ∧ acceleratedOrbit 11 1928 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1928 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1928) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1928.1, data_11_1928.2] + +/-- Complete interval computation for depth 11, residue 1929. -/ +theorem bounds_11_1929 : exactInterval 11 1929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1929 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1929) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1929 : oddCount 1929 11 = 7 ∧ acceleratedOrbit 11 1929 = 2062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1929 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1929) = 3 ^ 7 * m + 2062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1929.1, data_11_1929.2] + +/-- Complete interval computation for depth 11, residue 1930. -/ +theorem bounds_11_1930 : exactInterval 11 1930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1930 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1930) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1930 : oddCount 1930 11 = 3 ∧ acceleratedOrbit 11 1930 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1930 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1930) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1930.1, data_11_1930.2] + +/-- Complete interval computation for depth 11, residue 1931. -/ +theorem bounds_11_1931 : exactInterval 11 1931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1931 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1931) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1931 : oddCount 1931 11 = 7 ∧ acceleratedOrbit 11 1931 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1931 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1931) = 3 ^ 7 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1931.1, data_11_1931.2] + +/-- Complete interval computation for depth 11, residue 1932. -/ +theorem bounds_11_1932 : exactInterval 11 1932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1932 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1932) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1932 : oddCount 1932 11 = 3 ∧ acceleratedOrbit 11 1932 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1932 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1932) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1932.1, data_11_1932.2] + +/-- Complete interval computation for depth 11, residue 1933. -/ +theorem bounds_11_1933 : exactInterval 11 1933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1933 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1933) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1933 : oddCount 1933 11 = 3 ∧ acceleratedOrbit 11 1933 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1933 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1933) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1933.1, data_11_1933.2] + +/-- Complete interval computation for depth 11, residue 1934. -/ +theorem bounds_11_1934 : exactInterval 11 1934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1934 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1934) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1934 : oddCount 1934 11 = 7 ∧ acceleratedOrbit 11 1934 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1934 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1934) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1934.1, data_11_1934.2] + +/-- Complete interval computation for depth 11, residue 1935. -/ +theorem bounds_11_1935 : exactInterval 11 1935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1935 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1935) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1935 : oddCount 1935 11 = 7 ∧ acceleratedOrbit 11 1935 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1935 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1935) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1935.1, data_11_1935.2] + +/-- Complete interval computation for depth 11, residue 1936. -/ +theorem bounds_11_1936 : exactInterval 11 1936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1936 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1936) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1936 : oddCount 1936 11 = 5 ∧ acceleratedOrbit 11 1936 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1936 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1936) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1936.1, data_11_1936.2] + +/-- Complete interval computation for depth 11, residue 1937. -/ +theorem bounds_11_1937 : exactInterval 11 1937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1937 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1937) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1937 : oddCount 1937 11 = 6 ∧ acceleratedOrbit 11 1937 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1937 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1937) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1937.1, data_11_1937.2] + +/-- Complete interval computation for depth 11, residue 1938. -/ +theorem bounds_11_1938 : exactInterval 11 1938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1938 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1938) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1938 : oddCount 1938 11 = 6 ∧ acceleratedOrbit 11 1938 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1938 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1938) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1938.1, data_11_1938.2] + +/-- Complete interval computation for depth 11, residue 1939. -/ +theorem bounds_11_1939 : exactInterval 11 1939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1939 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1939) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1939 : oddCount 1939 11 = 6 ∧ acceleratedOrbit 11 1939 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1939 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1939) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1939.1, data_11_1939.2] + +end Collatz.Research.StoppingAtlas.Batch0193 From fc87bb22bfb40b02f5688c0771f73816554db8e3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:00 +0530 Subject: [PATCH 0194/1001] proof: certify atlas Batch0194 (11:1940 to 11:1954) --- Collatz/Research/StoppingAtlas/Batch0194.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0194.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0194.lean b/Collatz/Research/StoppingAtlas/Batch0194.lean new file mode 100644 index 00000000..36415292 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0194.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0194 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1940. -/ +theorem bounds_11_1940 : exactInterval 11 1940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1940 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1940) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1940 : oddCount 1940 11 = 5 ∧ acceleratedOrbit 11 1940 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1940 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1940) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1940.1, data_11_1940.2] + +/-- Complete interval computation for depth 11, residue 1941. -/ +theorem bounds_11_1941 : exactInterval 11 1941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1941 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1941) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1941 : oddCount 1941 11 = 5 ∧ acceleratedOrbit 11 1941 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1941 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1941) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1941.1, data_11_1941.2] + +/-- Complete interval computation for depth 11, residue 1942. -/ +theorem bounds_11_1942 : exactInterval 11 1942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1942 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1942) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1942 : oddCount 1942 11 = 4 ∧ acceleratedOrbit 11 1942 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1942 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1942) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1942.1, data_11_1942.2] + +/-- Complete interval computation for depth 11, residue 1943. -/ +theorem bounds_11_1943 : exactInterval 11 1943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1943 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1943) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1943 : oddCount 1943 11 = 4 ∧ acceleratedOrbit 11 1943 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1943 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1943) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1943.1, data_11_1943.2] + +/-- Complete interval computation for depth 11, residue 1944. -/ +theorem bounds_11_1944 : exactInterval 11 1944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1944 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1944) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1944 : oddCount 1944 11 = 5 ∧ acceleratedOrbit 11 1944 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1944 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1944) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1944.1, data_11_1944.2] + +/-- Complete interval computation for depth 11, residue 1945. -/ +theorem bounds_11_1945 : exactInterval 11 1945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1945 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1945) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1945 : oddCount 1945 11 = 4 ∧ acceleratedOrbit 11 1945 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1945 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1945) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1945.1, data_11_1945.2] + +/-- Complete interval computation for depth 11, residue 1946. -/ +theorem bounds_11_1946 : exactInterval 11 1946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1946 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1946) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1946 : oddCount 1946 11 = 5 ∧ acceleratedOrbit 11 1946 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1946 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1946) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1946.1, data_11_1946.2] + +/-- Complete interval computation for depth 11, residue 1947. -/ +theorem bounds_11_1947 : exactInterval 11 1947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1947 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1947) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1947 : oddCount 1947 11 = 7 ∧ acceleratedOrbit 11 1947 = 2081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1947 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1947) = 3 ^ 7 * m + 2081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1947.1, data_11_1947.2] + +/-- Complete interval computation for depth 11, residue 1948. -/ +theorem bounds_11_1948 : exactInterval 11 1948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1948 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1948) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1948 : oddCount 1948 11 = 6 ∧ acceleratedOrbit 11 1948 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1948 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1948) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1948.1, data_11_1948.2] + +/-- Complete interval computation for depth 11, residue 1949. -/ +theorem bounds_11_1949 : exactInterval 11 1949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1949 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1949) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1949 : oddCount 1949 11 = 6 ∧ acceleratedOrbit 11 1949 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1949 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1949) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1949.1, data_11_1949.2] + +/-- Complete interval computation for depth 11, residue 1950. -/ +theorem bounds_11_1950 : exactInterval 11 1950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1950 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1950) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1950 : oddCount 1950 11 = 6 ∧ acceleratedOrbit 11 1950 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1950 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1950) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1950.1, data_11_1950.2] + +/-- Complete interval computation for depth 11, residue 1951. -/ +theorem bounds_11_1951 : exactInterval 11 1951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1951 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1951) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1951 : oddCount 1951 11 = 8 ∧ acceleratedOrbit 11 1951 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1951 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1951) = 3 ^ 8 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1951.1, data_11_1951.2] + +/-- Complete interval computation for depth 11, residue 1952. -/ +theorem bounds_11_1952 : exactInterval 11 1952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1952 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1952) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1952 : oddCount 1952 11 = 4 ∧ acceleratedOrbit 11 1952 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1952 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1952) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1952.1, data_11_1952.2] + +/-- Complete interval computation for depth 11, residue 1953. -/ +theorem bounds_11_1953 : exactInterval 11 1953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1953 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1953) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1953 : oddCount 1953 11 = 5 ∧ acceleratedOrbit 11 1953 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1953 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1953) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1953.1, data_11_1953.2] + +/-- Complete interval computation for depth 11, residue 1954. -/ +theorem bounds_11_1954 : exactInterval 11 1954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1954 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1954) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1954 : oddCount 1954 11 = 5 ∧ acceleratedOrbit 11 1954 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1954 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1954) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1954.1, data_11_1954.2] + +end Collatz.Research.StoppingAtlas.Batch0194 From df8d433d8981f51854529db603832b7c42654b1e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:00 +0530 Subject: [PATCH 0195/1001] proof: certify atlas Batch0195 (11:1955 to 11:1970) --- Collatz/Research/StoppingAtlas/Batch0195.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0195.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0195.lean b/Collatz/Research/StoppingAtlas/Batch0195.lean new file mode 100644 index 00000000..c160bfb9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0195.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0195 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1955. -/ +theorem bounds_11_1955 : exactInterval 11 1955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1955 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1955) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1955 : oddCount 1955 11 = 5 ∧ acceleratedOrbit 11 1955 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1955 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1955) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1955.1, data_11_1955.2] + +/-- Complete interval computation for depth 11, residue 1956. -/ +theorem bounds_11_1956 : exactInterval 11 1956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1956 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1956) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1956 : oddCount 1956 11 = 7 ∧ acceleratedOrbit 11 1956 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1956 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1956) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1956.1, data_11_1956.2] + +/-- Complete interval computation for depth 11, residue 1957. -/ +theorem bounds_11_1957 : exactInterval 11 1957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1957 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1957) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1957 : oddCount 1957 11 = 7 ∧ acceleratedOrbit 11 1957 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1957 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1957) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1957.1, data_11_1957.2] + +/-- Complete interval computation for depth 11, residue 1958. -/ +theorem bounds_11_1958 : exactInterval 11 1958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1958 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1958) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1958 : oddCount 1958 11 = 7 ∧ acceleratedOrbit 11 1958 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1958 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1958) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1958.1, data_11_1958.2] + +/-- Complete interval computation for depth 11, residue 1959. -/ +theorem bounds_11_1959 : exactInterval 11 1959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1959 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1959) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1959 : oddCount 1959 11 = 8 ∧ acceleratedOrbit 11 1959 = 6281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1959 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1959) = 3 ^ 8 * m + 6281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1959.1, data_11_1959.2] + +/-- Complete interval computation for depth 11, residue 1960. -/ +theorem bounds_11_1960 : exactInterval 11 1960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1960 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1960) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1960 : oddCount 1960 11 = 4 ∧ acceleratedOrbit 11 1960 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1960 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1960) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1960.1, data_11_1960.2] + +/-- Complete interval computation for depth 11, residue 1961. -/ +theorem bounds_11_1961 : exactInterval 11 1961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1961 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1961) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1961 : oddCount 1961 11 = 9 ∧ acceleratedOrbit 11 1961 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1961 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1961) = 3 ^ 9 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1961.1, data_11_1961.2] + +/-- Complete interval computation for depth 11, residue 1962. -/ +theorem bounds_11_1962 : exactInterval 11 1962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1962 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1962) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1962 : oddCount 1962 11 = 4 ∧ acceleratedOrbit 11 1962 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1962 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1962) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1962.1, data_11_1962.2] + +/-- Complete interval computation for depth 11, residue 1963. -/ +theorem bounds_11_1963 : exactInterval 11 1963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1963 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1963) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1963 : oddCount 1963 11 = 7 ∧ acceleratedOrbit 11 1963 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1963 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1963) = 3 ^ 7 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1963.1, data_11_1963.2] + +/-- Complete interval computation for depth 11, residue 1964. -/ +theorem bounds_11_1964 : exactInterval 11 1964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1964 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1964) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1964 : oddCount 1964 11 = 7 ∧ acceleratedOrbit 11 1964 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1964 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1964) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1964.1, data_11_1964.2] + +/-- Complete interval computation for depth 11, residue 1965. -/ +theorem bounds_11_1965 : exactInterval 11 1965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1965 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1965) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1965 : oddCount 1965 11 = 7 ∧ acceleratedOrbit 11 1965 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1965 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1965) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1965.1, data_11_1965.2] + +/-- Complete interval computation for depth 11, residue 1966. -/ +theorem bounds_11_1966 : exactInterval 11 1966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1966 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1966) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1966 : oddCount 1966 11 = 7 ∧ acceleratedOrbit 11 1966 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1966 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1966) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1966.1, data_11_1966.2] + +/-- Complete interval computation for depth 11, residue 1967. -/ +theorem bounds_11_1967 : exactInterval 11 1967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1967 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1967) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1967 : oddCount 1967 11 = 6 ∧ acceleratedOrbit 11 1967 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1967 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1967) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1967.1, data_11_1967.2] + +/-- Complete interval computation for depth 11, residue 1968. -/ +theorem bounds_11_1968 : exactInterval 11 1968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1968 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1968) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1968 : oddCount 1968 11 = 5 ∧ acceleratedOrbit 11 1968 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1968 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1968) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1968.1, data_11_1968.2] + +/-- Complete interval computation for depth 11, residue 1969. -/ +theorem bounds_11_1969 : exactInterval 11 1969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1969 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1969) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1969 : oddCount 1969 11 = 3 ∧ acceleratedOrbit 11 1969 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1969 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1969) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1969.1, data_11_1969.2] + +/-- Complete interval computation for depth 11, residue 1970. -/ +theorem bounds_11_1970 : exactInterval 11 1970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1970 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1970) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1970 : oddCount 1970 11 = 3 ∧ acceleratedOrbit 11 1970 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1970 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1970) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1970.1, data_11_1970.2] + +end Collatz.Research.StoppingAtlas.Batch0195 From 83da16cffd6fc4cfe44165e72bf87e8cd0801625 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:00 +0530 Subject: [PATCH 0196/1001] proof: certify atlas Batch0196 (11:1971 to 11:1985) --- Collatz/Research/StoppingAtlas/Batch0196.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0196.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0196.lean b/Collatz/Research/StoppingAtlas/Batch0196.lean new file mode 100644 index 00000000..dc591a12 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0196.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0196 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1971. -/ +theorem bounds_11_1971 : exactInterval 11 1971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1971 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1971) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1971 : oddCount 1971 11 = 3 ∧ acceleratedOrbit 11 1971 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1971 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1971) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1971.1, data_11_1971.2] + +/-- Complete interval computation for depth 11, residue 1972. -/ +theorem bounds_11_1972 : exactInterval 11 1972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1972 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1972) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1972 : oddCount 1972 11 = 5 ∧ acceleratedOrbit 11 1972 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1972 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1972) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1972.1, data_11_1972.2] + +/-- Complete interval computation for depth 11, residue 1973. -/ +theorem bounds_11_1973 : exactInterval 11 1973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1973 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1973) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1973 : oddCount 1973 11 = 5 ∧ acceleratedOrbit 11 1973 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1973 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1973) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1973.1, data_11_1973.2] + +/-- Complete interval computation for depth 11, residue 1974. -/ +theorem bounds_11_1974 : exactInterval 11 1974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1974 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1974) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1974 : oddCount 1974 11 = 6 ∧ acceleratedOrbit 11 1974 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1974 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1974) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1974.1, data_11_1974.2] + +/-- Complete interval computation for depth 11, residue 1975. -/ +theorem bounds_11_1975 : exactInterval 11 1975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1975 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1975) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1975 : oddCount 1975 11 = 6 ∧ acceleratedOrbit 11 1975 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1975 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1975) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1975.1, data_11_1975.2] + +/-- Complete interval computation for depth 11, residue 1976. -/ +theorem bounds_11_1976 : exactInterval 11 1976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1976 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1976) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1976 : oddCount 1976 11 = 5 ∧ acceleratedOrbit 11 1976 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1976 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1976) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1976.1, data_11_1976.2] + +/-- Complete interval computation for depth 11, residue 1977. -/ +theorem bounds_11_1977 : exactInterval 11 1977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1977 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1977) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1977 : oddCount 1977 11 = 5 ∧ acceleratedOrbit 11 1977 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1977 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1977) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1977.1, data_11_1977.2] + +/-- Complete interval computation for depth 11, residue 1978. -/ +theorem bounds_11_1978 : exactInterval 11 1978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1978 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1978) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1978 : oddCount 1978 11 = 5 ∧ acceleratedOrbit 11 1978 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1978 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1978) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1978.1, data_11_1978.2] + +/-- Complete interval computation for depth 11, residue 1979. -/ +theorem bounds_11_1979 : exactInterval 11 1979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1979 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1979) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1979 : oddCount 1979 11 = 5 ∧ acceleratedOrbit 11 1979 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1979 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1979) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1979.1, data_11_1979.2] + +/-- Complete interval computation for depth 11, residue 1980. -/ +theorem bounds_11_1980 : exactInterval 11 1980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1980 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1980) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1980 : oddCount 1980 11 = 7 ∧ acceleratedOrbit 11 1980 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1980 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1980) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1980.1, data_11_1980.2] + +/-- Complete interval computation for depth 11, residue 1981. -/ +theorem bounds_11_1981 : exactInterval 11 1981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1981 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1981) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1981 : oddCount 1981 11 = 7 ∧ acceleratedOrbit 11 1981 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1981 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1981) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1981.1, data_11_1981.2] + +/-- Complete interval computation for depth 11, residue 1982. -/ +theorem bounds_11_1982 : exactInterval 11 1982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1982 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1982) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1982 : oddCount 1982 11 = 7 ∧ acceleratedOrbit 11 1982 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1982 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1982) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1982.1, data_11_1982.2] + +/-- Complete interval computation for depth 11, residue 1983. -/ +theorem bounds_11_1983 : exactInterval 11 1983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1983 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1983) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1983 : oddCount 1983 11 = 8 ∧ acceleratedOrbit 11 1983 = 6356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1983 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1983) = 3 ^ 8 * m + 6356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1983.1, data_11_1983.2] + +/-- Complete interval computation for depth 11, residue 1984. -/ +theorem bounds_11_1984 : exactInterval 11 1984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1984 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1984) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1984 : oddCount 1984 11 = 5 ∧ acceleratedOrbit 11 1984 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1984 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1984) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1984.1, data_11_1984.2] + +/-- Complete interval computation for depth 11, residue 1985. -/ +theorem bounds_11_1985 : exactInterval 11 1985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1985 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1985) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1985 : oddCount 1985 11 = 5 ∧ acceleratedOrbit 11 1985 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1985 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1985) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1985.1, data_11_1985.2] + +end Collatz.Research.StoppingAtlas.Batch0196 From 13b7f745493a1a49da3b2ea382b17c31b66f5912 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:01 +0530 Subject: [PATCH 0197/1001] proof: certify atlas Batch0197 (11:1986 to 11:2000) --- Collatz/Research/StoppingAtlas/Batch0197.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0197.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0197.lean b/Collatz/Research/StoppingAtlas/Batch0197.lean new file mode 100644 index 00000000..362b3ca8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0197.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0197 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 1986. -/ +theorem bounds_11_1986 : exactInterval 11 1986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1986 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1986) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1986 : oddCount 1986 11 = 7 ∧ acceleratedOrbit 11 1986 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1986 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1986) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1986.1, data_11_1986.2] + +/-- Complete interval computation for depth 11, residue 1987. -/ +theorem bounds_11_1987 : exactInterval 11 1987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1987 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1987) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1987 : oddCount 1987 11 = 7 ∧ acceleratedOrbit 11 1987 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1987 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1987) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1987.1, data_11_1987.2] + +/-- Complete interval computation for depth 11, residue 1988. -/ +theorem bounds_11_1988 : exactInterval 11 1988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1988 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1988) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1988 : oddCount 1988 11 = 4 ∧ acceleratedOrbit 11 1988 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1988 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1988) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1988.1, data_11_1988.2] + +/-- Complete interval computation for depth 11, residue 1989. -/ +theorem bounds_11_1989 : exactInterval 11 1989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1989 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1989) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1989 : oddCount 1989 11 = 4 ∧ acceleratedOrbit 11 1989 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1989 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1989) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1989.1, data_11_1989.2] + +/-- Complete interval computation for depth 11, residue 1990. -/ +theorem bounds_11_1990 : exactInterval 11 1990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1990 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1990) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1990 : oddCount 1990 11 = 4 ∧ acceleratedOrbit 11 1990 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1990 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1990) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1990.1, data_11_1990.2] + +/-- Complete interval computation for depth 11, residue 1991. -/ +theorem bounds_11_1991 : exactInterval 11 1991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1991 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1991) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1991 : oddCount 1991 11 = 7 ∧ acceleratedOrbit 11 1991 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1991 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1991) = 3 ^ 7 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1991.1, data_11_1991.2] + +/-- Complete interval computation for depth 11, residue 1992. -/ +theorem bounds_11_1992 : exactInterval 11 1992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1992 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1992) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1992 : oddCount 1992 11 = 5 ∧ acceleratedOrbit 11 1992 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1992 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1992) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1992.1, data_11_1992.2] + +/-- Complete interval computation for depth 11, residue 1993. -/ +theorem bounds_11_1993 : exactInterval 11 1993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1993 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1993) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1993 : oddCount 1993 11 = 7 ∧ acceleratedOrbit 11 1993 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1993 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1993) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1993.1, data_11_1993.2] + +/-- Complete interval computation for depth 11, residue 1994. -/ +theorem bounds_11_1994 : exactInterval 11 1994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1994 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1994) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1994 : oddCount 1994 11 = 5 ∧ acceleratedOrbit 11 1994 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1994 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1994) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1994.1, data_11_1994.2] + +/-- Complete interval computation for depth 11, residue 1995. -/ +theorem bounds_11_1995 : exactInterval 11 1995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1995 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1995) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1995 : oddCount 1995 11 = 4 ∧ acceleratedOrbit 11 1995 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1995 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1995) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1995.1, data_11_1995.2] + +/-- Complete interval computation for depth 11, residue 1996. -/ +theorem bounds_11_1996 : exactInterval 11 1996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1996 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1996) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1996 : oddCount 1996 11 = 5 ∧ acceleratedOrbit 11 1996 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1996 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1996) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1996.1, data_11_1996.2] + +/-- Complete interval computation for depth 11, residue 1997. -/ +theorem bounds_11_1997 : exactInterval 11 1997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1997 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1997) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1997 : oddCount 1997 11 = 5 ∧ acceleratedOrbit 11 1997 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1997 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1997) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1997.1, data_11_1997.2] + +/-- Complete interval computation for depth 11, residue 1998. -/ +theorem bounds_11_1998 : exactInterval 11 1998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1998 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1998) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1998 : oddCount 1998 11 = 6 ∧ acceleratedOrbit 11 1998 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1998 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1998) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1998.1, data_11_1998.2] + +/-- Complete interval computation for depth 11, residue 1999. -/ +theorem bounds_11_1999 : exactInterval 11 1999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_1999 (m : Nat) : + stoppingTime (2 ^ 11 * m + 1999) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_1999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_1999 : oddCount 1999 11 = 6 ∧ acceleratedOrbit 11 1999 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_1999 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 1999) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_1999.1, data_11_1999.2] + +/-- Complete interval computation for depth 11, residue 2000. -/ +theorem bounds_11_2000 : exactInterval 11 2000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2000 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2000) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2000 : oddCount 2000 11 = 5 ∧ acceleratedOrbit 11 2000 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2000 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2000) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2000.1, data_11_2000.2] + +end Collatz.Research.StoppingAtlas.Batch0197 From ffb7140a54caf9bbdd910652f4c330e06eae240a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:01 +0530 Subject: [PATCH 0198/1001] proof: certify atlas Batch0198 (11:2001 to 11:2016) --- Collatz/Research/StoppingAtlas/Batch0198.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0198.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0198.lean b/Collatz/Research/StoppingAtlas/Batch0198.lean new file mode 100644 index 00000000..d18dfcda --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0198.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0198 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 2001. -/ +theorem bounds_11_2001 : exactInterval 11 2001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2001 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2001) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2001 : oddCount 2001 11 = 5 ∧ acceleratedOrbit 11 2001 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2001 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2001) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2001.1, data_11_2001.2] + +/-- Complete interval computation for depth 11, residue 2002. -/ +theorem bounds_11_2002 : exactInterval 11 2002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2002 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2002) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2002 : oddCount 2002 11 = 8 ∧ acceleratedOrbit 11 2002 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2002 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2002) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2002.1, data_11_2002.2] + +/-- Complete interval computation for depth 11, residue 2003. -/ +theorem bounds_11_2003 : exactInterval 11 2003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2003 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2003) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2003 : oddCount 2003 11 = 8 ∧ acceleratedOrbit 11 2003 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2003 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2003) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2003.1, data_11_2003.2] + +/-- Complete interval computation for depth 11, residue 2004. -/ +theorem bounds_11_2004 : exactInterval 11 2004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2004 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2004) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2004 : oddCount 2004 11 = 5 ∧ acceleratedOrbit 11 2004 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2004 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2004) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2004.1, data_11_2004.2] + +/-- Complete interval computation for depth 11, residue 2005. -/ +theorem bounds_11_2005 : exactInterval 11 2005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2005 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2005) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2005 : oddCount 2005 11 = 5 ∧ acceleratedOrbit 11 2005 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2005 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2005) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2005.1, data_11_2005.2] + +/-- Complete interval computation for depth 11, residue 2006. -/ +theorem bounds_11_2006 : exactInterval 11 2006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2006 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2006) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2006 : oddCount 2006 11 = 7 ∧ acceleratedOrbit 11 2006 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2006 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2006) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2006.1, data_11_2006.2] + +/-- Complete interval computation for depth 11, residue 2007. -/ +theorem bounds_11_2007 : exactInterval 11 2007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2007 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2007) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2007 : oddCount 2007 11 = 7 ∧ acceleratedOrbit 11 2007 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2007 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2007) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2007.1, data_11_2007.2] + +/-- Complete interval computation for depth 11, residue 2008. -/ +theorem bounds_11_2008 : exactInterval 11 2008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2008 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2008) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2008 : oddCount 2008 11 = 6 ∧ acceleratedOrbit 11 2008 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2008 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2008) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2008.1, data_11_2008.2] + +/-- Complete interval computation for depth 11, residue 2009. -/ +theorem bounds_11_2009 : exactInterval 11 2009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2009 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2009) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2009 : oddCount 2009 11 = 4 ∧ acceleratedOrbit 11 2009 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2009 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2009) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2009.1, data_11_2009.2] + +/-- Complete interval computation for depth 11, residue 2010. -/ +theorem bounds_11_2010 : exactInterval 11 2010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2010 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2010) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2010 : oddCount 2010 11 = 6 ∧ acceleratedOrbit 11 2010 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2010 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2010) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2010.1, data_11_2010.2] + +/-- Complete interval computation for depth 11, residue 2011. -/ +theorem bounds_11_2011 : exactInterval 11 2011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2011 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2011) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2011 : oddCount 2011 11 = 7 ∧ acceleratedOrbit 11 2011 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2011 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2011) = 3 ^ 7 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2011.1, data_11_2011.2] + +/-- Complete interval computation for depth 11, residue 2012. -/ +theorem bounds_11_2012 : exactInterval 11 2012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2012 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2012) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2012 : oddCount 2012 11 = 6 ∧ acceleratedOrbit 11 2012 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2012 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2012) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2012.1, data_11_2012.2] + +/-- Complete interval computation for depth 11, residue 2013. -/ +theorem bounds_11_2013 : exactInterval 11 2013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2013 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2013) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2013 : oddCount 2013 11 = 6 ∧ acceleratedOrbit 11 2013 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2013 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2013) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2013.1, data_11_2013.2] + +/-- Complete interval computation for depth 11, residue 2014. -/ +theorem bounds_11_2014 : exactInterval 11 2014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2014 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2014) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2014 : oddCount 2014 11 = 7 ∧ acceleratedOrbit 11 2014 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2014 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2014) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2014.1, data_11_2014.2] + +/-- Complete interval computation for depth 11, residue 2015. -/ +theorem bounds_11_2015 : exactInterval 11 2015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2015 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2015) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2015 : oddCount 2015 11 = 7 ∧ acceleratedOrbit 11 2015 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2015 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2015) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2015.1, data_11_2015.2] + +/-- Complete interval computation for depth 11, residue 2016. -/ +theorem bounds_11_2016 : exactInterval 11 2016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2016 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2016) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2016 : oddCount 2016 11 = 6 ∧ acceleratedOrbit 11 2016 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2016 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2016) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2016.1, data_11_2016.2] + +end Collatz.Research.StoppingAtlas.Batch0198 From 14827f970e57fa8570caa9fffbf52254b9bee5f4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:01 +0530 Subject: [PATCH 0199/1001] proof: certify atlas Batch0199 (11:2017 to 11:2031) --- Collatz/Research/StoppingAtlas/Batch0199.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0199.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0199.lean b/Collatz/Research/StoppingAtlas/Batch0199.lean new file mode 100644 index 00000000..39caca8c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0199.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0199 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 2017. -/ +theorem bounds_11_2017 : exactInterval 11 2017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2017 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2017) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2017 : oddCount 2017 11 = 8 ∧ acceleratedOrbit 11 2017 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2017 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2017) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2017.1, data_11_2017.2] + +/-- Complete interval computation for depth 11, residue 2018. -/ +theorem bounds_11_2018 : exactInterval 11 2018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2018 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2018) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2018 : oddCount 2018 11 = 5 ∧ acceleratedOrbit 11 2018 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2018 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2018) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2018.1, data_11_2018.2] + +/-- Complete interval computation for depth 11, residue 2019. -/ +theorem bounds_11_2019 : exactInterval 11 2019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2019 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2019) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2019 : oddCount 2019 11 = 5 ∧ acceleratedOrbit 11 2019 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2019 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2019) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2019.1, data_11_2019.2] + +/-- Complete interval computation for depth 11, residue 2020. -/ +theorem bounds_11_2020 : exactInterval 11 2020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2020 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2020) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2020 : oddCount 2020 11 = 6 ∧ acceleratedOrbit 11 2020 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2020 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2020) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2020.1, data_11_2020.2] + +/-- Complete interval computation for depth 11, residue 2021. -/ +theorem bounds_11_2021 : exactInterval 11 2021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2021 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2021) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2021 : oddCount 2021 11 = 6 ∧ acceleratedOrbit 11 2021 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2021 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2021) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2021.1, data_11_2021.2] + +/-- Complete interval computation for depth 11, residue 2022. -/ +theorem bounds_11_2022 : exactInterval 11 2022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2022 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2022) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2022 : oddCount 2022 11 = 6 ∧ acceleratedOrbit 11 2022 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2022 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2022) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2022.1, data_11_2022.2] + +/-- Complete interval computation for depth 11, residue 2023. -/ +theorem bounds_11_2023 : exactInterval 11 2023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2023 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2023) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2023 : oddCount 2023 11 = 7 ∧ acceleratedOrbit 11 2023 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2023 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2023) = 3 ^ 7 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2023.1, data_11_2023.2] + +/-- Complete interval computation for depth 11, residue 2024. -/ +theorem bounds_11_2024 : exactInterval 11 2024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2024 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2024) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2024 : oddCount 2024 11 = 6 ∧ acceleratedOrbit 11 2024 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2024 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2024) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2024.1, data_11_2024.2] + +/-- Complete interval computation for depth 11, residue 2025. -/ +theorem bounds_11_2025 : exactInterval 11 2025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2025 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2025) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2025 : oddCount 2025 11 = 8 ∧ acceleratedOrbit 11 2025 = 6493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2025 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2025) = 3 ^ 8 * m + 6493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2025.1, data_11_2025.2] + +/-- Complete interval computation for depth 11, residue 2026. -/ +theorem bounds_11_2026 : exactInterval 11 2026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2026 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2026) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2026 : oddCount 2026 11 = 6 ∧ acceleratedOrbit 11 2026 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2026 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2026) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2026.1, data_11_2026.2] + +/-- Complete interval computation for depth 11, residue 2027. -/ +theorem bounds_11_2027 : exactInterval 11 2027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2027 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2027) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2027 : oddCount 2027 11 = 8 ∧ acceleratedOrbit 11 2027 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2027 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2027) = 3 ^ 8 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2027.1, data_11_2027.2] + +/-- Complete interval computation for depth 11, residue 2028. -/ +theorem bounds_11_2028 : exactInterval 11 2028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2028 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2028) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2028 : oddCount 2028 11 = 6 ∧ acceleratedOrbit 11 2028 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2028 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2028) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2028.1, data_11_2028.2] + +/-- Complete interval computation for depth 11, residue 2029. -/ +theorem bounds_11_2029 : exactInterval 11 2029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2029 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2029) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2029 : oddCount 2029 11 = 6 ∧ acceleratedOrbit 11 2029 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2029 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2029) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2029.1, data_11_2029.2] + +/-- Complete interval computation for depth 11, residue 2030. -/ +theorem bounds_11_2030 : exactInterval 11 2030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2030 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2030) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2030 : oddCount 2030 11 = 6 ∧ acceleratedOrbit 11 2030 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2030 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2030) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2030.1, data_11_2030.2] + +/-- Complete interval computation for depth 11, residue 2031. -/ +theorem bounds_11_2031 : exactInterval 11 2031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2031 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2031) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2031 : oddCount 2031 11 = 7 ∧ acceleratedOrbit 11 2031 = 2170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2031 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2031) = 3 ^ 7 * m + 2170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2031.1, data_11_2031.2] + +end Collatz.Research.StoppingAtlas.Batch0199 From 68724bd7b05e1711a3c52f23a9c91f609691ae53 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:02 +0530 Subject: [PATCH 0200/1001] proof: certify atlas Batch0200 (11:2032 to 11:2047) --- Collatz/Research/StoppingAtlas/Batch0200.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0200.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0200.lean b/Collatz/Research/StoppingAtlas/Batch0200.lean new file mode 100644 index 00000000..fabaeb93 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0200.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0200 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 11, residue 2032. -/ +theorem bounds_11_2032 : exactInterval 11 2032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2032 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2032) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2032 : oddCount 2032 11 = 7 ∧ acceleratedOrbit 11 2032 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2032 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2032) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2032.1, data_11_2032.2] + +/-- Complete interval computation for depth 11, residue 2033. -/ +theorem bounds_11_2033 : exactInterval 11 2033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2033 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2033) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2033 : oddCount 2033 11 = 6 ∧ acceleratedOrbit 11 2033 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2033 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2033) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2033.1, data_11_2033.2] + +/-- Complete interval computation for depth 11, residue 2034. -/ +theorem bounds_11_2034 : exactInterval 11 2034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2034 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2034) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2034 : oddCount 2034 11 = 7 ∧ acceleratedOrbit 11 2034 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2034 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2034) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2034.1, data_11_2034.2] + +/-- Complete interval computation for depth 11, residue 2035. -/ +theorem bounds_11_2035 : exactInterval 11 2035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2035 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2035) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2035 : oddCount 2035 11 = 7 ∧ acceleratedOrbit 11 2035 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2035 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2035) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2035.1, data_11_2035.2] + +/-- Complete interval computation for depth 11, residue 2036. -/ +theorem bounds_11_2036 : exactInterval 11 2036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2036 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2036) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2036 : oddCount 2036 11 = 7 ∧ acceleratedOrbit 11 2036 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2036 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2036) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2036.1, data_11_2036.2] + +/-- Complete interval computation for depth 11, residue 2037. -/ +theorem bounds_11_2037 : exactInterval 11 2037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2037 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2037) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2037 : oddCount 2037 11 = 7 ∧ acceleratedOrbit 11 2037 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2037 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2037) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2037.1, data_11_2037.2] + +/-- Complete interval computation for depth 11, residue 2038. -/ +theorem bounds_11_2038 : exactInterval 11 2038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2038 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2038) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2038 : oddCount 2038 11 = 7 ∧ acceleratedOrbit 11 2038 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2038 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2038) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2038.1, data_11_2038.2] + +/-- Complete interval computation for depth 11, residue 2039. -/ +theorem bounds_11_2039 : exactInterval 11 2039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2039 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2039) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2039 : oddCount 2039 11 = 7 ∧ acceleratedOrbit 11 2039 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2039 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2039) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2039.1, data_11_2039.2] + +/-- Complete interval computation for depth 11, residue 2040. -/ +theorem bounds_11_2040 : exactInterval 11 2040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2040 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2040) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2040 : oddCount 2040 11 = 8 ∧ acceleratedOrbit 11 2040 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2040 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2040) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2040.1, data_11_2040.2] + +/-- Complete interval computation for depth 11, residue 2041. -/ +theorem bounds_11_2041 : exactInterval 11 2041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2041 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2041) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2041 : oddCount 2041 11 = 7 ∧ acceleratedOrbit 11 2041 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2041 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2041) = 3 ^ 7 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2041.1, data_11_2041.2] + +/-- Complete interval computation for depth 11, residue 2042. -/ +theorem bounds_11_2042 : exactInterval 11 2042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2042 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2042) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2042 : oddCount 2042 11 = 8 ∧ acceleratedOrbit 11 2042 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2042 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2042) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2042.1, data_11_2042.2] + +/-- Complete interval computation for depth 11, residue 2043. -/ +theorem bounds_11_2043 : exactInterval 11 2043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2043 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2043) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2043 : oddCount 2043 11 = 8 ∧ acceleratedOrbit 11 2043 = 6551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2043 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2043) = 3 ^ 8 * m + 6551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2043.1, data_11_2043.2] + +/-- Complete interval computation for depth 11, residue 2044. -/ +theorem bounds_11_2044 : exactInterval 11 2044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2044 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2044) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2044 : oddCount 2044 11 = 9 ∧ acceleratedOrbit 11 2044 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2044 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2044) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2044.1, data_11_2044.2] + +/-- Complete interval computation for depth 11, residue 2045. -/ +theorem bounds_11_2045 : exactInterval 11 2045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2045 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2045) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2045 : oddCount 2045 11 = 9 ∧ acceleratedOrbit 11 2045 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2045 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2045) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2045.1, data_11_2045.2] + +/-- Complete interval computation for depth 11, residue 2046. -/ +theorem bounds_11_2046 : exactInterval 11 2046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2046 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2046) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2046 : oddCount 2046 11 = 10 ∧ acceleratedOrbit 11 2046 = 59048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2046 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2046) = 3 ^ 10 * m + 59048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2046.1, data_11_2046.2] + +/-- Complete interval computation for depth 11, residue 2047. -/ +theorem bounds_11_2047 : exactInterval 11 2047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_11_2047 (m : Nat) : + stoppingTime (2 ^ 11 * m + 2047) 11 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_11_2047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_11_2047 : oddCount 2047 11 = 11 ∧ acceleratedOrbit 11 2047 = 177146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_11_2047 (m : Nat) : + acceleratedOrbit 11 (2 ^ 11 * m + 2047) = 3 ^ 11 * m + 177146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_11_2047.1, data_11_2047.2] + +end Collatz.Research.StoppingAtlas.Batch0200 From 1f83002858fe134e0614eacc3c0a217881906159 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:02 +0530 Subject: [PATCH 0201/1001] proof: certify atlas Batch0201 (12:0 to 12:14) --- Collatz/Research/StoppingAtlas/Batch0201.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0201.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0201.lean b/Collatz/Research/StoppingAtlas/Batch0201.lean new file mode 100644 index 00000000..ef1d7c49 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0201.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0201 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 0. -/ +theorem bounds_12_0 : exactInterval 12 0 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_0 (m : Nat) : + stoppingTime (2 ^ 12 * m + 0) 12 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_0 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_0 : oddCount 0 12 = 0 ∧ acceleratedOrbit 12 0 = 0 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_0 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 0) = 3 ^ 0 * m + 0 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_0.1, data_12_0.2] + +/-- Complete interval computation for depth 12, residue 1. -/ +theorem bounds_12_1 : exactInterval 12 1 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1) 12 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1 : oddCount 1 12 = 6 ∧ acceleratedOrbit 12 1 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1) = 3 ^ 6 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1.1, data_12_1.2] + +/-- Complete interval computation for depth 12, residue 2. -/ +theorem bounds_12_2 : exactInterval 12 2 = ⟨1, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2) 12 ↔ 1 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2 : oddCount 2 12 = 6 ∧ acceleratedOrbit 12 2 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2.1, data_12_2.2] + +/-- Complete interval computation for depth 12, residue 3. -/ +theorem bounds_12_3 : exactInterval 12 3 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3 : oddCount 3 12 = 6 ∧ acceleratedOrbit 12 3 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3.1, data_12_3.2] + +/-- Complete interval computation for depth 12, residue 4. -/ +theorem bounds_12_4 : exactInterval 12 4 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4 : oddCount 4 12 = 5 ∧ acceleratedOrbit 12 4 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4.1, data_12_4.2] + +/-- Complete interval computation for depth 12, residue 5. -/ +theorem bounds_12_5 : exactInterval 12 5 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_5 (m : Nat) : + stoppingTime (2 ^ 12 * m + 5) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_5 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_5 : oddCount 5 12 = 5 ∧ acceleratedOrbit 12 5 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_5 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 5) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_5.1, data_12_5.2] + +/-- Complete interval computation for depth 12, residue 6. -/ +theorem bounds_12_6 : exactInterval 12 6 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_6 (m : Nat) : + stoppingTime (2 ^ 12 * m + 6) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_6 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_6 : oddCount 6 12 = 5 ∧ acceleratedOrbit 12 6 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_6 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 6) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_6.1, data_12_6.2] + +/-- Complete interval computation for depth 12, residue 7. -/ +theorem bounds_12_7 : exactInterval 12 7 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_7 (m : Nat) : + stoppingTime (2 ^ 12 * m + 7) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_7 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_7 : oddCount 7 12 = 6 ∧ acceleratedOrbit 12 7 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_7 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 7) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_7.1, data_12_7.2] + +/-- Complete interval computation for depth 12, residue 8. -/ +theorem bounds_12_8 : exactInterval 12 8 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_8 (m : Nat) : + stoppingTime (2 ^ 12 * m + 8) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_8 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_8 : oddCount 8 12 = 5 ∧ acceleratedOrbit 12 8 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_8 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 8) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_8.1, data_12_8.2] + +/-- Complete interval computation for depth 12, residue 9. -/ +theorem bounds_12_9 : exactInterval 12 9 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_9 (m : Nat) : + stoppingTime (2 ^ 12 * m + 9) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_9 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_9 : oddCount 9 12 = 6 ∧ acceleratedOrbit 12 9 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_9 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 9) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_9.1, data_12_9.2] + +/-- Complete interval computation for depth 12, residue 10. -/ +theorem bounds_12_10 : exactInterval 12 10 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_10 (m : Nat) : + stoppingTime (2 ^ 12 * m + 10) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_10 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_10 : oddCount 10 12 = 5 ∧ acceleratedOrbit 12 10 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_10 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 10) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_10.1, data_12_10.2] + +/-- Complete interval computation for depth 12, residue 11. -/ +theorem bounds_12_11 : exactInterval 12 11 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_11 (m : Nat) : + stoppingTime (2 ^ 12 * m + 11) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_11 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_11 : oddCount 11 12 = 5 ∧ acceleratedOrbit 12 11 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_11 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 11) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_11.1, data_12_11.2] + +/-- Complete interval computation for depth 12, residue 12. -/ +theorem bounds_12_12 : exactInterval 12 12 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_12 (m : Nat) : + stoppingTime (2 ^ 12 * m + 12) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_12 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_12 : oddCount 12 12 = 5 ∧ acceleratedOrbit 12 12 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_12 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 12) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_12.1, data_12_12.2] + +/-- Complete interval computation for depth 12, residue 13. -/ +theorem bounds_12_13 : exactInterval 12 13 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_13 (m : Nat) : + stoppingTime (2 ^ 12 * m + 13) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_13 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_13 : oddCount 13 12 = 5 ∧ acceleratedOrbit 12 13 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_13 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 13) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_13.1, data_12_13.2] + +/-- Complete interval computation for depth 12, residue 14. -/ +theorem bounds_12_14 : exactInterval 12 14 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_14 (m : Nat) : + stoppingTime (2 ^ 12 * m + 14) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_14 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_14 : oddCount 14 12 = 5 ∧ acceleratedOrbit 12 14 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_14 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 14) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_14.1, data_12_14.2] + +end Collatz.Research.StoppingAtlas.Batch0201 From 209b28a9453bf7a5a9bc6938f6c49c09f5fce048 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:02 +0530 Subject: [PATCH 0202/1001] proof: certify atlas Batch0202 (12:15 to 12:29) --- Collatz/Research/StoppingAtlas/Batch0202.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0202.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0202.lean b/Collatz/Research/StoppingAtlas/Batch0202.lean new file mode 100644 index 00000000..b65a5f38 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0202.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0202 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 15. -/ +theorem bounds_12_15 : exactInterval 12 15 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_15 (m : Nat) : + stoppingTime (2 ^ 12 * m + 15) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_15 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_15 : oddCount 15 12 = 5 ∧ acceleratedOrbit 12 15 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_15 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 15) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_15.1, data_12_15.2] + +/-- Complete interval computation for depth 12, residue 16. -/ +theorem bounds_12_16 : exactInterval 12 16 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_16 (m : Nat) : + stoppingTime (2 ^ 12 * m + 16) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_16 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_16 : oddCount 16 12 = 4 ∧ acceleratedOrbit 12 16 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_16 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 16) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_16.1, data_12_16.2] + +/-- Complete interval computation for depth 12, residue 17. -/ +theorem bounds_12_17 : exactInterval 12 17 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_17 (m : Nat) : + stoppingTime (2 ^ 12 * m + 17) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_17 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_17 : oddCount 17 12 = 5 ∧ acceleratedOrbit 12 17 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_17 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 17) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_17.1, data_12_17.2] + +/-- Complete interval computation for depth 12, residue 18. -/ +theorem bounds_12_18 : exactInterval 12 18 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_18 (m : Nat) : + stoppingTime (2 ^ 12 * m + 18) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_18 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_18 : oddCount 18 12 = 6 ∧ acceleratedOrbit 12 18 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_18 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 18) = 3 ^ 6 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_18.1, data_12_18.2] + +/-- Complete interval computation for depth 12, residue 19. -/ +theorem bounds_12_19 : exactInterval 12 19 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_19 (m : Nat) : + stoppingTime (2 ^ 12 * m + 19) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_19 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_19 : oddCount 19 12 = 6 ∧ acceleratedOrbit 12 19 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_19 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 19) = 3 ^ 6 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_19.1, data_12_19.2] + +/-- Complete interval computation for depth 12, residue 20. -/ +theorem bounds_12_20 : exactInterval 12 20 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_20 (m : Nat) : + stoppingTime (2 ^ 12 * m + 20) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_20 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_20 : oddCount 20 12 = 4 ∧ acceleratedOrbit 12 20 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_20 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 20) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_20.1, data_12_20.2] + +/-- Complete interval computation for depth 12, residue 21. -/ +theorem bounds_12_21 : exactInterval 12 21 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_21 (m : Nat) : + stoppingTime (2 ^ 12 * m + 21) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_21 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_21 : oddCount 21 12 = 4 ∧ acceleratedOrbit 12 21 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_21 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 21) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_21.1, data_12_21.2] + +/-- Complete interval computation for depth 12, residue 22. -/ +theorem bounds_12_22 : exactInterval 12 22 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_22 (m : Nat) : + stoppingTime (2 ^ 12 * m + 22) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_22 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_22 : oddCount 22 12 = 5 ∧ acceleratedOrbit 12 22 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_22 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 22) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_22.1, data_12_22.2] + +/-- Complete interval computation for depth 12, residue 23. -/ +theorem bounds_12_23 : exactInterval 12 23 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_23 (m : Nat) : + stoppingTime (2 ^ 12 * m + 23) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_23 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_23 : oddCount 23 12 = 5 ∧ acceleratedOrbit 12 23 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_23 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 23) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_23.1, data_12_23.2] + +/-- Complete interval computation for depth 12, residue 24. -/ +theorem bounds_12_24 : exactInterval 12 24 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_24 (m : Nat) : + stoppingTime (2 ^ 12 * m + 24) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_24 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_24 : oddCount 24 12 = 4 ∧ acceleratedOrbit 12 24 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_24 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 24) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_24.1, data_12_24.2] + +/-- Complete interval computation for depth 12, residue 25. -/ +theorem bounds_12_25 : exactInterval 12 25 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_25 (m : Nat) : + stoppingTime (2 ^ 12 * m + 25) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_25 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_25 : oddCount 25 12 = 6 ∧ acceleratedOrbit 12 25 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_25 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 25) = 3 ^ 6 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_25.1, data_12_25.2] + +/-- Complete interval computation for depth 12, residue 26. -/ +theorem bounds_12_26 : exactInterval 12 26 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_26 (m : Nat) : + stoppingTime (2 ^ 12 * m + 26) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_26 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_26 : oddCount 26 12 = 4 ∧ acceleratedOrbit 12 26 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_26 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 26) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_26.1, data_12_26.2] + +/-- Complete interval computation for depth 12, residue 27. -/ +theorem bounds_12_27 : exactInterval 12 27 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_27 (m : Nat) : + stoppingTime (2 ^ 12 * m + 27) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_27 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_27 : oddCount 27 12 = 9 ∧ acceleratedOrbit 12 27 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_27 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 27) = 3 ^ 9 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_27.1, data_12_27.2] + +/-- Complete interval computation for depth 12, residue 28. -/ +theorem bounds_12_28 : exactInterval 12 28 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_28 (m : Nat) : + stoppingTime (2 ^ 12 * m + 28) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_28 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_28 : oddCount 28 12 = 5 ∧ acceleratedOrbit 12 28 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_28 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 28) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_28.1, data_12_28.2] + +/-- Complete interval computation for depth 12, residue 29. -/ +theorem bounds_12_29 : exactInterval 12 29 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_29 (m : Nat) : + stoppingTime (2 ^ 12 * m + 29) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_29 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_29 : oddCount 29 12 = 5 ∧ acceleratedOrbit 12 29 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_29 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 29) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_29.1, data_12_29.2] + +end Collatz.Research.StoppingAtlas.Batch0202 From 89904b5de029d8b546af2a8ca425716d3a5401e6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:03 +0530 Subject: [PATCH 0203/1001] proof: certify atlas Batch0203 (12:30 to 12:45) --- Collatz/Research/StoppingAtlas/Batch0203.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0203.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0203.lean b/Collatz/Research/StoppingAtlas/Batch0203.lean new file mode 100644 index 00000000..3b5a225e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0203.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0203 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 30. -/ +theorem bounds_12_30 : exactInterval 12 30 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_30 (m : Nat) : + stoppingTime (2 ^ 12 * m + 30) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_30 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_30 : oddCount 30 12 = 5 ∧ acceleratedOrbit 12 30 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_30 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 30) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_30.1, data_12_30.2] + +/-- Complete interval computation for depth 12, residue 31. -/ +theorem bounds_12_31 : exactInterval 12 31 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_31 (m : Nat) : + stoppingTime (2 ^ 12 * m + 31) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_31 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_31 : oddCount 31 12 = 9 ∧ acceleratedOrbit 12 31 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_31 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 31) = 3 ^ 9 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_31.1, data_12_31.2] + +/-- Complete interval computation for depth 12, residue 32. -/ +theorem bounds_12_32 : exactInterval 12 32 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_32 (m : Nat) : + stoppingTime (2 ^ 12 * m + 32) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_32 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_32 : oddCount 32 12 = 4 ∧ acceleratedOrbit 12 32 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_32 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 32) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_32.1, data_12_32.2] + +/-- Complete interval computation for depth 12, residue 33. -/ +theorem bounds_12_33 : exactInterval 12 33 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_33 (m : Nat) : + stoppingTime (2 ^ 12 * m + 33) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_33 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_33 : oddCount 33 12 = 7 ∧ acceleratedOrbit 12 33 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_33 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 33) = 3 ^ 7 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_33.1, data_12_33.2] + +/-- Complete interval computation for depth 12, residue 34. -/ +theorem bounds_12_34 : exactInterval 12 34 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_34 (m : Nat) : + stoppingTime (2 ^ 12 * m + 34) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_34 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_34 : oddCount 34 12 = 4 ∧ acceleratedOrbit 12 34 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_34 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 34) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_34.1, data_12_34.2] + +/-- Complete interval computation for depth 12, residue 35. -/ +theorem bounds_12_35 : exactInterval 12 35 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_35 (m : Nat) : + stoppingTime (2 ^ 12 * m + 35) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_35 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_35 : oddCount 35 12 = 4 ∧ acceleratedOrbit 12 35 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_35 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 35) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_35.1, data_12_35.2] + +/-- Complete interval computation for depth 12, residue 36. -/ +theorem bounds_12_36 : exactInterval 12 36 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_36 (m : Nat) : + stoppingTime (2 ^ 12 * m + 36) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_36 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_36 : oddCount 36 12 = 6 ∧ acceleratedOrbit 12 36 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_36 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 36) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_36.1, data_12_36.2] + +/-- Complete interval computation for depth 12, residue 37. -/ +theorem bounds_12_37 : exactInterval 12 37 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_37 (m : Nat) : + stoppingTime (2 ^ 12 * m + 37) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_37 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_37 : oddCount 37 12 = 6 ∧ acceleratedOrbit 12 37 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_37 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 37) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_37.1, data_12_37.2] + +/-- Complete interval computation for depth 12, residue 38. -/ +theorem bounds_12_38 : exactInterval 12 38 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_38 (m : Nat) : + stoppingTime (2 ^ 12 * m + 38) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_38 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_38 : oddCount 38 12 = 6 ∧ acceleratedOrbit 12 38 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_38 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 38) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_38.1, data_12_38.2] + +/-- Complete interval computation for depth 12, residue 39. -/ +theorem bounds_12_39 : exactInterval 12 39 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_39 (m : Nat) : + stoppingTime (2 ^ 12 * m + 39) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_39 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_39 : oddCount 39 12 = 7 ∧ acceleratedOrbit 12 39 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_39 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 39) = 3 ^ 7 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_39.1, data_12_39.2] + +/-- Complete interval computation for depth 12, residue 40. -/ +theorem bounds_12_40 : exactInterval 12 40 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_40 (m : Nat) : + stoppingTime (2 ^ 12 * m + 40) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_40 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_40 : oddCount 40 12 = 4 ∧ acceleratedOrbit 12 40 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_40 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 40) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_40.1, data_12_40.2] + +/-- Complete interval computation for depth 12, residue 41. -/ +theorem bounds_12_41 : exactInterval 12 41 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_41 (m : Nat) : + stoppingTime (2 ^ 12 * m + 41) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_41 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_41 : oddCount 41 12 = 9 ∧ acceleratedOrbit 12 41 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_41 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 41) = 3 ^ 9 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_41.1, data_12_41.2] + +/-- Complete interval computation for depth 12, residue 42. -/ +theorem bounds_12_42 : exactInterval 12 42 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_42 (m : Nat) : + stoppingTime (2 ^ 12 * m + 42) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_42 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_42 : oddCount 42 12 = 4 ∧ acceleratedOrbit 12 42 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_42 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 42) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_42.1, data_12_42.2] + +/-- Complete interval computation for depth 12, residue 43. -/ +theorem bounds_12_43 : exactInterval 12 43 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_43 (m : Nat) : + stoppingTime (2 ^ 12 * m + 43) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_43 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_43 : oddCount 43 12 = 7 ∧ acceleratedOrbit 12 43 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_43 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 43) = 3 ^ 7 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_43.1, data_12_43.2] + +/-- Complete interval computation for depth 12, residue 44. -/ +theorem bounds_12_44 : exactInterval 12 44 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_44 (m : Nat) : + stoppingTime (2 ^ 12 * m + 44) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_44 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_44 : oddCount 44 12 = 4 ∧ acceleratedOrbit 12 44 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_44 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 44) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_44.1, data_12_44.2] + +/-- Complete interval computation for depth 12, residue 45. -/ +theorem bounds_12_45 : exactInterval 12 45 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_45 (m : Nat) : + stoppingTime (2 ^ 12 * m + 45) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_45 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_45 : oddCount 45 12 = 4 ∧ acceleratedOrbit 12 45 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_45 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 45) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_45.1, data_12_45.2] + +end Collatz.Research.StoppingAtlas.Batch0203 From c6d1854b3bd365cf25a2642ccf96060026f501b1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:03 +0530 Subject: [PATCH 0204/1001] proof: certify atlas Batch0204 (12:46 to 12:60) --- Collatz/Research/StoppingAtlas/Batch0204.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0204.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0204.lean b/Collatz/Research/StoppingAtlas/Batch0204.lean new file mode 100644 index 00000000..aabb38fa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0204.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0204 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 46. -/ +theorem bounds_12_46 : exactInterval 12 46 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_46 (m : Nat) : + stoppingTime (2 ^ 12 * m + 46) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_46 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_46 : oddCount 46 12 = 4 ∧ acceleratedOrbit 12 46 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_46 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 46) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_46.1, data_12_46.2] + +/-- Complete interval computation for depth 12, residue 47. -/ +theorem bounds_12_47 : exactInterval 12 47 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_47 (m : Nat) : + stoppingTime (2 ^ 12 * m + 47) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_47 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_47 : oddCount 47 12 = 9 ∧ acceleratedOrbit 12 47 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_47 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 47) = 3 ^ 9 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_47.1, data_12_47.2] + +/-- Complete interval computation for depth 12, residue 48. -/ +theorem bounds_12_48 : exactInterval 12 48 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_48 (m : Nat) : + stoppingTime (2 ^ 12 * m + 48) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_48 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_48 : oddCount 48 12 = 4 ∧ acceleratedOrbit 12 48 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_48 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 48) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_48.1, data_12_48.2] + +/-- Complete interval computation for depth 12, residue 49. -/ +theorem bounds_12_49 : exactInterval 12 49 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_49 (m : Nat) : + stoppingTime (2 ^ 12 * m + 49) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_49 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_49 : oddCount 49 12 = 6 ∧ acceleratedOrbit 12 49 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_49 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 49) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_49.1, data_12_49.2] + +/-- Complete interval computation for depth 12, residue 50. -/ +theorem bounds_12_50 : exactInterval 12 50 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_50 (m : Nat) : + stoppingTime (2 ^ 12 * m + 50) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_50 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_50 : oddCount 50 12 = 6 ∧ acceleratedOrbit 12 50 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_50 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 50) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_50.1, data_12_50.2] + +/-- Complete interval computation for depth 12, residue 51. -/ +theorem bounds_12_51 : exactInterval 12 51 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_51 (m : Nat) : + stoppingTime (2 ^ 12 * m + 51) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_51 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_51 : oddCount 51 12 = 6 ∧ acceleratedOrbit 12 51 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_51 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 51) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_51.1, data_12_51.2] + +/-- Complete interval computation for depth 12, residue 52. -/ +theorem bounds_12_52 : exactInterval 12 52 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_52 (m : Nat) : + stoppingTime (2 ^ 12 * m + 52) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_52 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_52 : oddCount 52 12 = 4 ∧ acceleratedOrbit 12 52 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_52 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 52) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_52.1, data_12_52.2] + +/-- Complete interval computation for depth 12, residue 53. -/ +theorem bounds_12_53 : exactInterval 12 53 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_53 (m : Nat) : + stoppingTime (2 ^ 12 * m + 53) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_53 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_53 : oddCount 53 12 = 4 ∧ acceleratedOrbit 12 53 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_53 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 53) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_53.1, data_12_53.2] + +/-- Complete interval computation for depth 12, residue 54. -/ +theorem bounds_12_54 : exactInterval 12 54 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_54 (m : Nat) : + stoppingTime (2 ^ 12 * m + 54) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_54 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_54 : oddCount 54 12 = 8 ∧ acceleratedOrbit 12 54 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_54 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 54) = 3 ^ 8 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_54.1, data_12_54.2] + +/-- Complete interval computation for depth 12, residue 55. -/ +theorem bounds_12_55 : exactInterval 12 55 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_55 (m : Nat) : + stoppingTime (2 ^ 12 * m + 55) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_55 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_55 : oddCount 55 12 = 8 ∧ acceleratedOrbit 12 55 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_55 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 55) = 3 ^ 8 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_55.1, data_12_55.2] + +/-- Complete interval computation for depth 12, residue 56. -/ +theorem bounds_12_56 : exactInterval 12 56 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_56 (m : Nat) : + stoppingTime (2 ^ 12 * m + 56) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_56 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_56 : oddCount 56 12 = 5 ∧ acceleratedOrbit 12 56 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_56 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 56) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_56.1, data_12_56.2] + +/-- Complete interval computation for depth 12, residue 57. -/ +theorem bounds_12_57 : exactInterval 12 57 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_57 (m : Nat) : + stoppingTime (2 ^ 12 * m + 57) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_57 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_57 : oddCount 57 12 = 6 ∧ acceleratedOrbit 12 57 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_57 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 57) = 3 ^ 6 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_57.1, data_12_57.2] + +/-- Complete interval computation for depth 12, residue 58. -/ +theorem bounds_12_58 : exactInterval 12 58 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_58 (m : Nat) : + stoppingTime (2 ^ 12 * m + 58) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_58 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_58 : oddCount 58 12 = 5 ∧ acceleratedOrbit 12 58 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_58 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 58) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_58.1, data_12_58.2] + +/-- Complete interval computation for depth 12, residue 59. -/ +theorem bounds_12_59 : exactInterval 12 59 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_59 (m : Nat) : + stoppingTime (2 ^ 12 * m + 59) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_59 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_59 : oddCount 59 12 = 6 ∧ acceleratedOrbit 12 59 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_59 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 59) = 3 ^ 6 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_59.1, data_12_59.2] + +/-- Complete interval computation for depth 12, residue 60. -/ +theorem bounds_12_60 : exactInterval 12 60 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_60 (m : Nat) : + stoppingTime (2 ^ 12 * m + 60) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_60 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_60 : oddCount 60 12 = 5 ∧ acceleratedOrbit 12 60 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_60 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 60) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_60.1, data_12_60.2] + +end Collatz.Research.StoppingAtlas.Batch0204 From e27ccfd27465a201c5f272d58982c951d3281fed Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:03 +0530 Subject: [PATCH 0205/1001] proof: certify atlas Batch0205 (12:61 to 12:75) --- Collatz/Research/StoppingAtlas/Batch0205.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0205.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0205.lean b/Collatz/Research/StoppingAtlas/Batch0205.lean new file mode 100644 index 00000000..739ce310 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0205.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0205 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 61. -/ +theorem bounds_12_61 : exactInterval 12 61 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_61 (m : Nat) : + stoppingTime (2 ^ 12 * m + 61) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_61 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_61 : oddCount 61 12 = 5 ∧ acceleratedOrbit 12 61 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_61 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 61) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_61.1, data_12_61.2] + +/-- Complete interval computation for depth 12, residue 62. -/ +theorem bounds_12_62 : exactInterval 12 62 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_62 (m : Nat) : + stoppingTime (2 ^ 12 * m + 62) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_62 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_62 : oddCount 62 12 = 8 ∧ acceleratedOrbit 12 62 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_62 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 62) = 3 ^ 8 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_62.1, data_12_62.2] + +/-- Complete interval computation for depth 12, residue 63. -/ +theorem bounds_12_63 : exactInterval 12 63 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_63 (m : Nat) : + stoppingTime (2 ^ 12 * m + 63) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_63 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_63 : oddCount 63 12 = 8 ∧ acceleratedOrbit 12 63 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_63 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 63) = 3 ^ 8 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_63.1, data_12_63.2] + +/-- Complete interval computation for depth 12, residue 64. -/ +theorem bounds_12_64 : exactInterval 12 64 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_64 (m : Nat) : + stoppingTime (2 ^ 12 * m + 64) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_64 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_64 : oddCount 64 12 = 3 ∧ acceleratedOrbit 12 64 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_64 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 64) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_64.1, data_12_64.2] + +/-- Complete interval computation for depth 12, residue 65. -/ +theorem bounds_12_65 : exactInterval 12 65 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_65 (m : Nat) : + stoppingTime (2 ^ 12 * m + 65) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_65 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_65 : oddCount 65 12 = 6 ∧ acceleratedOrbit 12 65 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_65 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 65) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_65.1, data_12_65.2] + +/-- Complete interval computation for depth 12, residue 66. -/ +theorem bounds_12_66 : exactInterval 12 66 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_66 (m : Nat) : + stoppingTime (2 ^ 12 * m + 66) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_66 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_66 : oddCount 66 12 = 6 ∧ acceleratedOrbit 12 66 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_66 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 66) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_66.1, data_12_66.2] + +/-- Complete interval computation for depth 12, residue 67. -/ +theorem bounds_12_67 : exactInterval 12 67 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_67 (m : Nat) : + stoppingTime (2 ^ 12 * m + 67) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_67 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_67 : oddCount 67 12 = 6 ∧ acceleratedOrbit 12 67 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_67 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 67) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_67.1, data_12_67.2] + +/-- Complete interval computation for depth 12, residue 68. -/ +theorem bounds_12_68 : exactInterval 12 68 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_68 (m : Nat) : + stoppingTime (2 ^ 12 * m + 68) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_68 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_68 : oddCount 68 12 = 4 ∧ acceleratedOrbit 12 68 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_68 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 68) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_68.1, data_12_68.2] + +/-- Complete interval computation for depth 12, residue 69. -/ +theorem bounds_12_69 : exactInterval 12 69 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_69 (m : Nat) : + stoppingTime (2 ^ 12 * m + 69) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_69 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_69 : oddCount 69 12 = 4 ∧ acceleratedOrbit 12 69 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_69 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 69) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_69.1, data_12_69.2] + +/-- Complete interval computation for depth 12, residue 70. -/ +theorem bounds_12_70 : exactInterval 12 70 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_70 (m : Nat) : + stoppingTime (2 ^ 12 * m + 70) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_70 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_70 : oddCount 70 12 = 4 ∧ acceleratedOrbit 12 70 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_70 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 70) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_70.1, data_12_70.2] + +/-- Complete interval computation for depth 12, residue 71. -/ +theorem bounds_12_71 : exactInterval 12 71 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_71 (m : Nat) : + stoppingTime (2 ^ 12 * m + 71) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_71 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_71 : oddCount 71 12 = 9 ∧ acceleratedOrbit 12 71 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_71 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 71) = 3 ^ 9 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_71.1, data_12_71.2] + +/-- Complete interval computation for depth 12, residue 72. -/ +theorem bounds_12_72 : exactInterval 12 72 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_72 (m : Nat) : + stoppingTime (2 ^ 12 * m + 72) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_72 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_72 : oddCount 72 12 = 5 ∧ acceleratedOrbit 12 72 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_72 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 72) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_72.1, data_12_72.2] + +/-- Complete interval computation for depth 12, residue 73. -/ +theorem bounds_12_73 : exactInterval 12 73 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_73 (m : Nat) : + stoppingTime (2 ^ 12 * m + 73) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_73 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_73 : oddCount 73 12 = 8 ∧ acceleratedOrbit 12 73 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_73 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 73) = 3 ^ 8 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_73.1, data_12_73.2] + +/-- Complete interval computation for depth 12, residue 74. -/ +theorem bounds_12_74 : exactInterval 12 74 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_74 (m : Nat) : + stoppingTime (2 ^ 12 * m + 74) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_74 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_74 : oddCount 74 12 = 5 ∧ acceleratedOrbit 12 74 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_74 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 74) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_74.1, data_12_74.2] + +/-- Complete interval computation for depth 12, residue 75. -/ +theorem bounds_12_75 : exactInterval 12 75 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_75 (m : Nat) : + stoppingTime (2 ^ 12 * m + 75) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_75 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_75 : oddCount 75 12 = 4 ∧ acceleratedOrbit 12 75 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_75 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 75) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_75.1, data_12_75.2] + +end Collatz.Research.StoppingAtlas.Batch0205 From fb1db104b9569f7bbdbf5f8022c7404946ed4480 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:04 +0530 Subject: [PATCH 0206/1001] proof: certify atlas Batch0206 (12:76 to 12:91) --- Collatz/Research/StoppingAtlas/Batch0206.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0206.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0206.lean b/Collatz/Research/StoppingAtlas/Batch0206.lean new file mode 100644 index 00000000..c564f5dd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0206.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0206 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 76. -/ +theorem bounds_12_76 : exactInterval 12 76 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_76 (m : Nat) : + stoppingTime (2 ^ 12 * m + 76) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_76 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_76 : oddCount 76 12 = 5 ∧ acceleratedOrbit 12 76 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_76 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 76) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_76.1, data_12_76.2] + +/-- Complete interval computation for depth 12, residue 77. -/ +theorem bounds_12_77 : exactInterval 12 77 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_77 (m : Nat) : + stoppingTime (2 ^ 12 * m + 77) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_77 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_77 : oddCount 77 12 = 5 ∧ acceleratedOrbit 12 77 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_77 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 77) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_77.1, data_12_77.2] + +/-- Complete interval computation for depth 12, residue 78. -/ +theorem bounds_12_78 : exactInterval 12 78 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_78 (m : Nat) : + stoppingTime (2 ^ 12 * m + 78) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_78 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_78 : oddCount 78 12 = 7 ∧ acceleratedOrbit 12 78 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_78 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 78) = 3 ^ 7 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_78.1, data_12_78.2] + +/-- Complete interval computation for depth 12, residue 79. -/ +theorem bounds_12_79 : exactInterval 12 79 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_79 (m : Nat) : + stoppingTime (2 ^ 12 * m + 79) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_79 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_79 : oddCount 79 12 = 7 ∧ acceleratedOrbit 12 79 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_79 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 79) = 3 ^ 7 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_79.1, data_12_79.2] + +/-- Complete interval computation for depth 12, residue 80. -/ +theorem bounds_12_80 : exactInterval 12 80 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_80 (m : Nat) : + stoppingTime (2 ^ 12 * m + 80) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_80 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_80 : oddCount 80 12 = 3 ∧ acceleratedOrbit 12 80 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_80 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 80) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_80.1, data_12_80.2] + +/-- Complete interval computation for depth 12, residue 81. -/ +theorem bounds_12_81 : exactInterval 12 81 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_81 (m : Nat) : + stoppingTime (2 ^ 12 * m + 81) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_81 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_81 : oddCount 81 12 = 5 ∧ acceleratedOrbit 12 81 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_81 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 81) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_81.1, data_12_81.2] + +/-- Complete interval computation for depth 12, residue 82. -/ +theorem bounds_12_82 : exactInterval 12 82 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_82 (m : Nat) : + stoppingTime (2 ^ 12 * m + 82) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_82 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_82 : oddCount 82 12 = 8 ∧ acceleratedOrbit 12 82 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_82 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 82) = 3 ^ 8 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_82.1, data_12_82.2] + +/-- Complete interval computation for depth 12, residue 83. -/ +theorem bounds_12_83 : exactInterval 12 83 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_83 (m : Nat) : + stoppingTime (2 ^ 12 * m + 83) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_83 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_83 : oddCount 83 12 = 8 ∧ acceleratedOrbit 12 83 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_83 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 83) = 3 ^ 8 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_83.1, data_12_83.2] + +/-- Complete interval computation for depth 12, residue 84. -/ +theorem bounds_12_84 : exactInterval 12 84 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_84 (m : Nat) : + stoppingTime (2 ^ 12 * m + 84) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_84 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_84 : oddCount 84 12 = 3 ∧ acceleratedOrbit 12 84 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_84 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 84) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_84.1, data_12_84.2] + +/-- Complete interval computation for depth 12, residue 85. -/ +theorem bounds_12_85 : exactInterval 12 85 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_85 (m : Nat) : + stoppingTime (2 ^ 12 * m + 85) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_85 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_85 : oddCount 85 12 = 3 ∧ acceleratedOrbit 12 85 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_85 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 85) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_85.1, data_12_85.2] + +/-- Complete interval computation for depth 12, residue 86. -/ +theorem bounds_12_86 : exactInterval 12 86 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_86 (m : Nat) : + stoppingTime (2 ^ 12 * m + 86) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_86 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_86 : oddCount 86 12 = 6 ∧ acceleratedOrbit 12 86 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_86 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 86) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_86.1, data_12_86.2] + +/-- Complete interval computation for depth 12, residue 87. -/ +theorem bounds_12_87 : exactInterval 12 87 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_87 (m : Nat) : + stoppingTime (2 ^ 12 * m + 87) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_87 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_87 : oddCount 87 12 = 6 ∧ acceleratedOrbit 12 87 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_87 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 87) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_87.1, data_12_87.2] + +/-- Complete interval computation for depth 12, residue 88. -/ +theorem bounds_12_88 : exactInterval 12 88 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_88 (m : Nat) : + stoppingTime (2 ^ 12 * m + 88) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_88 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_88 : oddCount 88 12 = 4 ∧ acceleratedOrbit 12 88 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_88 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 88) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_88.1, data_12_88.2] + +/-- Complete interval computation for depth 12, residue 89. -/ +theorem bounds_12_89 : exactInterval 12 89 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_89 (m : Nat) : + stoppingTime (2 ^ 12 * m + 89) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_89 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_89 : oddCount 89 12 = 6 ∧ acceleratedOrbit 12 89 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_89 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 89) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_89.1, data_12_89.2] + +/-- Complete interval computation for depth 12, residue 90. -/ +theorem bounds_12_90 : exactInterval 12 90 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_90 (m : Nat) : + stoppingTime (2 ^ 12 * m + 90) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_90 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_90 : oddCount 90 12 = 4 ∧ acceleratedOrbit 12 90 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_90 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 90) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_90.1, data_12_90.2] + +/-- Complete interval computation for depth 12, residue 91. -/ +theorem bounds_12_91 : exactInterval 12 91 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_91 (m : Nat) : + stoppingTime (2 ^ 12 * m + 91) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_91 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_91 : oddCount 91 12 = 9 ∧ acceleratedOrbit 12 91 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_91 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 91) = 3 ^ 9 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_91.1, data_12_91.2] + +end Collatz.Research.StoppingAtlas.Batch0206 From 3d47447f59d5dbc707df2cd3e394e0b92571cca3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:04 +0530 Subject: [PATCH 0207/1001] proof: certify atlas Batch0207 (12:92 to 12:106) --- Collatz/Research/StoppingAtlas/Batch0207.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0207.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0207.lean b/Collatz/Research/StoppingAtlas/Batch0207.lean new file mode 100644 index 00000000..2f2db7fd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0207.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0207 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 92. -/ +theorem bounds_12_92 : exactInterval 12 92 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_92 (m : Nat) : + stoppingTime (2 ^ 12 * m + 92) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_92 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_92 : oddCount 92 12 = 4 ∧ acceleratedOrbit 12 92 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_92 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 92) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_92.1, data_12_92.2] + +/-- Complete interval computation for depth 12, residue 93. -/ +theorem bounds_12_93 : exactInterval 12 93 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_93 (m : Nat) : + stoppingTime (2 ^ 12 * m + 93) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_93 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_93 : oddCount 93 12 = 4 ∧ acceleratedOrbit 12 93 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_93 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 93) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_93.1, data_12_93.2] + +/-- Complete interval computation for depth 12, residue 94. -/ +theorem bounds_12_94 : exactInterval 12 94 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_94 (m : Nat) : + stoppingTime (2 ^ 12 * m + 94) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_94 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_94 : oddCount 94 12 = 8 ∧ acceleratedOrbit 12 94 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_94 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 94) = 3 ^ 8 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_94.1, data_12_94.2] + +/-- Complete interval computation for depth 12, residue 95. -/ +theorem bounds_12_95 : exactInterval 12 95 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_95 (m : Nat) : + stoppingTime (2 ^ 12 * m + 95) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_95 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_95 : oddCount 95 12 = 8 ∧ acceleratedOrbit 12 95 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_95 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 95) = 3 ^ 8 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_95.1, data_12_95.2] + +/-- Complete interval computation for depth 12, residue 96. -/ +theorem bounds_12_96 : exactInterval 12 96 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_96 (m : Nat) : + stoppingTime (2 ^ 12 * m + 96) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_96 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_96 : oddCount 96 12 = 3 ∧ acceleratedOrbit 12 96 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_96 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 96) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_96.1, data_12_96.2] + +/-- Complete interval computation for depth 12, residue 97. -/ +theorem bounds_12_97 : exactInterval 12 97 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_97 (m : Nat) : + stoppingTime (2 ^ 12 * m + 97) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_97 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_97 : oddCount 97 12 = 8 ∧ acceleratedOrbit 12 97 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_97 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 97) = 3 ^ 8 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_97.1, data_12_97.2] + +/-- Complete interval computation for depth 12, residue 98. -/ +theorem bounds_12_98 : exactInterval 12 98 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_98 (m : Nat) : + stoppingTime (2 ^ 12 * m + 98) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_98 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_98 : oddCount 98 12 = 6 ∧ acceleratedOrbit 12 98 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_98 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 98) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_98.1, data_12_98.2] + +/-- Complete interval computation for depth 12, residue 99. -/ +theorem bounds_12_99 : exactInterval 12 99 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_99 (m : Nat) : + stoppingTime (2 ^ 12 * m + 99) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_99 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_99 : oddCount 99 12 = 6 ∧ acceleratedOrbit 12 99 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_99 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 99) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_99.1, data_12_99.2] + +/-- Complete interval computation for depth 12, residue 100. -/ +theorem bounds_12_100 : exactInterval 12 100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_100 (m : Nat) : + stoppingTime (2 ^ 12 * m + 100) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_100 : oddCount 100 12 = 6 ∧ acceleratedOrbit 12 100 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_100 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 100) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_100.1, data_12_100.2] + +/-- Complete interval computation for depth 12, residue 101. -/ +theorem bounds_12_101 : exactInterval 12 101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_101 (m : Nat) : + stoppingTime (2 ^ 12 * m + 101) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_101 : oddCount 101 12 = 6 ∧ acceleratedOrbit 12 101 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_101 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 101) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_101.1, data_12_101.2] + +/-- Complete interval computation for depth 12, residue 102. -/ +theorem bounds_12_102 : exactInterval 12 102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_102 (m : Nat) : + stoppingTime (2 ^ 12 * m + 102) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_102 : oddCount 102 12 = 6 ∧ acceleratedOrbit 12 102 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_102 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 102) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_102.1, data_12_102.2] + +/-- Complete interval computation for depth 12, residue 103. -/ +theorem bounds_12_103 : exactInterval 12 103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_103 (m : Nat) : + stoppingTime (2 ^ 12 * m + 103) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_103 : oddCount 103 12 = 8 ∧ acceleratedOrbit 12 103 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_103 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 103) = 3 ^ 8 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_103.1, data_12_103.2] + +/-- Complete interval computation for depth 12, residue 104. -/ +theorem bounds_12_104 : exactInterval 12 104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_104 (m : Nat) : + stoppingTime (2 ^ 12 * m + 104) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_104 : oddCount 104 12 = 3 ∧ acceleratedOrbit 12 104 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_104 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 104) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_104.1, data_12_104.2] + +/-- Complete interval computation for depth 12, residue 105. -/ +theorem bounds_12_105 : exactInterval 12 105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_105 (m : Nat) : + stoppingTime (2 ^ 12 * m + 105) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_105 : oddCount 105 12 = 6 ∧ acceleratedOrbit 12 105 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_105 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 105) = 3 ^ 6 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_105.1, data_12_105.2] + +/-- Complete interval computation for depth 12, residue 106. -/ +theorem bounds_12_106 : exactInterval 12 106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_106 (m : Nat) : + stoppingTime (2 ^ 12 * m + 106) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_106 : oddCount 106 12 = 3 ∧ acceleratedOrbit 12 106 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_106 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 106) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_106.1, data_12_106.2] + +end Collatz.Research.StoppingAtlas.Batch0207 From 057b98990f122c540a7a5ab1a8dd048ee1d28195 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:04 +0530 Subject: [PATCH 0208/1001] proof: certify atlas Batch0208 (12:107 to 12:121) --- Collatz/Research/StoppingAtlas/Batch0208.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0208.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0208.lean b/Collatz/Research/StoppingAtlas/Batch0208.lean new file mode 100644 index 00000000..d0a69833 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0208.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0208 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 107. -/ +theorem bounds_12_107 : exactInterval 12 107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_107 (m : Nat) : + stoppingTime (2 ^ 12 * m + 107) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_107 : oddCount 107 12 = 8 ∧ acceleratedOrbit 12 107 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_107 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 107) = 3 ^ 8 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_107.1, data_12_107.2] + +/-- Complete interval computation for depth 12, residue 108. -/ +theorem bounds_12_108 : exactInterval 12 108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_108 (m : Nat) : + stoppingTime (2 ^ 12 * m + 108) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_108 : oddCount 108 12 = 8 ∧ acceleratedOrbit 12 108 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_108 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 108) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_108.1, data_12_108.2] + +/-- Complete interval computation for depth 12, residue 109. -/ +theorem bounds_12_109 : exactInterval 12 109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_109 (m : Nat) : + stoppingTime (2 ^ 12 * m + 109) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_109 : oddCount 109 12 = 8 ∧ acceleratedOrbit 12 109 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_109 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 109) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_109.1, data_12_109.2] + +/-- Complete interval computation for depth 12, residue 110. -/ +theorem bounds_12_110 : exactInterval 12 110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_110 (m : Nat) : + stoppingTime (2 ^ 12 * m + 110) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_110 : oddCount 110 12 = 8 ∧ acceleratedOrbit 12 110 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_110 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 110) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_110.1, data_12_110.2] + +/-- Complete interval computation for depth 12, residue 111. -/ +theorem bounds_12_111 : exactInterval 12 111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_111 (m : Nat) : + stoppingTime (2 ^ 12 * m + 111) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_111 : oddCount 111 12 = 10 ∧ acceleratedOrbit 12 111 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_111 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 111) = 3 ^ 10 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_111.1, data_12_111.2] + +/-- Complete interval computation for depth 12, residue 112. -/ +theorem bounds_12_112 : exactInterval 12 112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_112 (m : Nat) : + stoppingTime (2 ^ 12 * m + 112) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_112 : oddCount 112 12 = 5 ∧ acceleratedOrbit 12 112 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_112 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 112) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_112.1, data_12_112.2] + +/-- Complete interval computation for depth 12, residue 113. -/ +theorem bounds_12_113 : exactInterval 12 113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_113 (m : Nat) : + stoppingTime (2 ^ 12 * m + 113) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_113 : oddCount 113 12 = 3 ∧ acceleratedOrbit 12 113 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_113 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 113) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_113.1, data_12_113.2] + +/-- Complete interval computation for depth 12, residue 114. -/ +theorem bounds_12_114 : exactInterval 12 114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_114 (m : Nat) : + stoppingTime (2 ^ 12 * m + 114) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_114 : oddCount 114 12 = 5 ∧ acceleratedOrbit 12 114 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_114 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 114) = 3 ^ 5 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_114.1, data_12_114.2] + +/-- Complete interval computation for depth 12, residue 115. -/ +theorem bounds_12_115 : exactInterval 12 115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_115 (m : Nat) : + stoppingTime (2 ^ 12 * m + 115) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_115 : oddCount 115 12 = 5 ∧ acceleratedOrbit 12 115 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_115 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 115) = 3 ^ 5 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_115.1, data_12_115.2] + +/-- Complete interval computation for depth 12, residue 116. -/ +theorem bounds_12_116 : exactInterval 12 116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_116 (m : Nat) : + stoppingTime (2 ^ 12 * m + 116) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_116 : oddCount 116 12 = 5 ∧ acceleratedOrbit 12 116 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_116 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 116) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_116.1, data_12_116.2] + +/-- Complete interval computation for depth 12, residue 117. -/ +theorem bounds_12_117 : exactInterval 12 117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_117 (m : Nat) : + stoppingTime (2 ^ 12 * m + 117) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_117 : oddCount 117 12 = 5 ∧ acceleratedOrbit 12 117 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_117 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 117) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_117.1, data_12_117.2] + +/-- Complete interval computation for depth 12, residue 118. -/ +theorem bounds_12_118 : exactInterval 12 118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_118 (m : Nat) : + stoppingTime (2 ^ 12 * m + 118) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_118 : oddCount 118 12 = 6 ∧ acceleratedOrbit 12 118 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_118 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 118) = 3 ^ 6 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_118.1, data_12_118.2] + +/-- Complete interval computation for depth 12, residue 119. -/ +theorem bounds_12_119 : exactInterval 12 119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_119 (m : Nat) : + stoppingTime (2 ^ 12 * m + 119) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_119 : oddCount 119 12 = 6 ∧ acceleratedOrbit 12 119 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_119 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 119) = 3 ^ 6 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_119.1, data_12_119.2] + +/-- Complete interval computation for depth 12, residue 120. -/ +theorem bounds_12_120 : exactInterval 12 120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_120 (m : Nat) : + stoppingTime (2 ^ 12 * m + 120) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_120 : oddCount 120 12 = 5 ∧ acceleratedOrbit 12 120 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_120 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 120) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_120.1, data_12_120.2] + +/-- Complete interval computation for depth 12, residue 121. -/ +theorem bounds_12_121 : exactInterval 12 121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_121 (m : Nat) : + stoppingTime (2 ^ 12 * m + 121) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_121 : oddCount 121 12 = 9 ∧ acceleratedOrbit 12 121 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_121 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 121) = 3 ^ 9 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_121.1, data_12_121.2] + +end Collatz.Research.StoppingAtlas.Batch0208 From 97275490dfb36a9a48f557eef1224790603e7d2a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:05 +0530 Subject: [PATCH 0209/1001] proof: certify atlas Batch0209 (12:122 to 12:137) --- Collatz/Research/StoppingAtlas/Batch0209.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0209.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0209.lean b/Collatz/Research/StoppingAtlas/Batch0209.lean new file mode 100644 index 00000000..e70c6e5b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0209.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0209 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 122. -/ +theorem bounds_12_122 : exactInterval 12 122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_122 (m : Nat) : + stoppingTime (2 ^ 12 * m + 122) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_122 : oddCount 122 12 = 5 ∧ acceleratedOrbit 12 122 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_122 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 122) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_122.1, data_12_122.2] + +/-- Complete interval computation for depth 12, residue 123. -/ +theorem bounds_12_123 : exactInterval 12 123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_123 (m : Nat) : + stoppingTime (2 ^ 12 * m + 123) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_123 : oddCount 123 12 = 7 ∧ acceleratedOrbit 12 123 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_123 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 123) = 3 ^ 7 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_123.1, data_12_123.2] + +/-- Complete interval computation for depth 12, residue 124. -/ +theorem bounds_12_124 : exactInterval 12 124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_124 (m : Nat) : + stoppingTime (2 ^ 12 * m + 124) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_124 : oddCount 124 12 = 8 ∧ acceleratedOrbit 12 124 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_124 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 124) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_124.1, data_12_124.2] + +/-- Complete interval computation for depth 12, residue 125. -/ +theorem bounds_12_125 : exactInterval 12 125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_125 (m : Nat) : + stoppingTime (2 ^ 12 * m + 125) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_125 : oddCount 125 12 = 8 ∧ acceleratedOrbit 12 125 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_125 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 125) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_125.1, data_12_125.2] + +/-- Complete interval computation for depth 12, residue 126. -/ +theorem bounds_12_126 : exactInterval 12 126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_126 (m : Nat) : + stoppingTime (2 ^ 12 * m + 126) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_126 : oddCount 126 12 = 8 ∧ acceleratedOrbit 12 126 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_126 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 126) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_126.1, data_12_126.2] + +/-- Complete interval computation for depth 12, residue 127. -/ +theorem bounds_12_127 : exactInterval 12 127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_127 (m : Nat) : + stoppingTime (2 ^ 12 * m + 127) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_127 : oddCount 127 12 = 8 ∧ acceleratedOrbit 12 127 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_127 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 127) = 3 ^ 8 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_127.1, data_12_127.2] + +/-- Complete interval computation for depth 12, residue 128. -/ +theorem bounds_12_128 : exactInterval 12 128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_128 (m : Nat) : + stoppingTime (2 ^ 12 * m + 128) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_128 : oddCount 128 12 = 3 ∧ acceleratedOrbit 12 128 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_128 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 128) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_128.1, data_12_128.2] + +/-- Complete interval computation for depth 12, residue 129. -/ +theorem bounds_12_129 : exactInterval 12 129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_129 (m : Nat) : + stoppingTime (2 ^ 12 * m + 129) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_129 : oddCount 129 12 = 7 ∧ acceleratedOrbit 12 129 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_129 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 129) = 3 ^ 7 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_129.1, data_12_129.2] + +/-- Complete interval computation for depth 12, residue 130. -/ +theorem bounds_12_130 : exactInterval 12 130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_130 (m : Nat) : + stoppingTime (2 ^ 12 * m + 130) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_130 : oddCount 130 12 = 6 ∧ acceleratedOrbit 12 130 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_130 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 130) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_130.1, data_12_130.2] + +/-- Complete interval computation for depth 12, residue 131. -/ +theorem bounds_12_131 : exactInterval 12 131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_131 (m : Nat) : + stoppingTime (2 ^ 12 * m + 131) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_131 : oddCount 131 12 = 6 ∧ acceleratedOrbit 12 131 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_131 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 131) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_131.1, data_12_131.2] + +/-- Complete interval computation for depth 12, residue 132. -/ +theorem bounds_12_132 : exactInterval 12 132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_132 (m : Nat) : + stoppingTime (2 ^ 12 * m + 132) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_132 : oddCount 132 12 = 6 ∧ acceleratedOrbit 12 132 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_132 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 132) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_132.1, data_12_132.2] + +/-- Complete interval computation for depth 12, residue 133. -/ +theorem bounds_12_133 : exactInterval 12 133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_133 (m : Nat) : + stoppingTime (2 ^ 12 * m + 133) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_133 : oddCount 133 12 = 6 ∧ acceleratedOrbit 12 133 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_133 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 133) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_133.1, data_12_133.2] + +/-- Complete interval computation for depth 12, residue 134. -/ +theorem bounds_12_134 : exactInterval 12 134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_134 (m : Nat) : + stoppingTime (2 ^ 12 * m + 134) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_134 : oddCount 134 12 = 6 ∧ acceleratedOrbit 12 134 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_134 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 134) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_134.1, data_12_134.2] + +/-- Complete interval computation for depth 12, residue 135. -/ +theorem bounds_12_135 : exactInterval 12 135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_135 (m : Nat) : + stoppingTime (2 ^ 12 * m + 135) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_135 : oddCount 135 12 = 7 ∧ acceleratedOrbit 12 135 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_135 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 135) = 3 ^ 7 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_135.1, data_12_135.2] + +/-- Complete interval computation for depth 12, residue 136. -/ +theorem bounds_12_136 : exactInterval 12 136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_136 (m : Nat) : + stoppingTime (2 ^ 12 * m + 136) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_136 : oddCount 136 12 = 3 ∧ acceleratedOrbit 12 136 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_136 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 136) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_136.1, data_12_136.2] + +/-- Complete interval computation for depth 12, residue 137. -/ +theorem bounds_12_137 : exactInterval 12 137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_137 (m : Nat) : + stoppingTime (2 ^ 12 * m + 137) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_137 : oddCount 137 12 = 9 ∧ acceleratedOrbit 12 137 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_137 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 137) = 3 ^ 9 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_137.1, data_12_137.2] + +end Collatz.Research.StoppingAtlas.Batch0209 From cd06c80b7eb8af0050fdc7e2334fb69a6c2e5e55 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:05 +0530 Subject: [PATCH 0210/1001] proof: certify atlas Batch0210 (12:138 to 12:152) --- Collatz/Research/StoppingAtlas/Batch0210.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0210.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0210.lean b/Collatz/Research/StoppingAtlas/Batch0210.lean new file mode 100644 index 00000000..a91115d6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0210.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0210 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 138. -/ +theorem bounds_12_138 : exactInterval 12 138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_138 (m : Nat) : + stoppingTime (2 ^ 12 * m + 138) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_138 : oddCount 138 12 = 3 ∧ acceleratedOrbit 12 138 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_138 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 138) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_138.1, data_12_138.2] + +/-- Complete interval computation for depth 12, residue 139. -/ +theorem bounds_12_139 : exactInterval 12 139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_139 (m : Nat) : + stoppingTime (2 ^ 12 * m + 139) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_139 : oddCount 139 12 = 7 ∧ acceleratedOrbit 12 139 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_139 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 139) = 3 ^ 7 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_139.1, data_12_139.2] + +/-- Complete interval computation for depth 12, residue 140. -/ +theorem bounds_12_140 : exactInterval 12 140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_140 (m : Nat) : + stoppingTime (2 ^ 12 * m + 140) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_140 : oddCount 140 12 = 3 ∧ acceleratedOrbit 12 140 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_140 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 140) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_140.1, data_12_140.2] + +/-- Complete interval computation for depth 12, residue 141. -/ +theorem bounds_12_141 : exactInterval 12 141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_141 (m : Nat) : + stoppingTime (2 ^ 12 * m + 141) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_141 : oddCount 141 12 = 3 ∧ acceleratedOrbit 12 141 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_141 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 141) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_141.1, data_12_141.2] + +/-- Complete interval computation for depth 12, residue 142. -/ +theorem bounds_12_142 : exactInterval 12 142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_142 (m : Nat) : + stoppingTime (2 ^ 12 * m + 142) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_142 : oddCount 142 12 = 8 ∧ acceleratedOrbit 12 142 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_142 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 142) = 3 ^ 8 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_142.1, data_12_142.2] + +/-- Complete interval computation for depth 12, residue 143. -/ +theorem bounds_12_143 : exactInterval 12 143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_143 (m : Nat) : + stoppingTime (2 ^ 12 * m + 143) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_143 : oddCount 143 12 = 8 ∧ acceleratedOrbit 12 143 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_143 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 143) = 3 ^ 8 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_143.1, data_12_143.2] + +/-- Complete interval computation for depth 12, residue 144. -/ +theorem bounds_12_144 : exactInterval 12 144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_144 (m : Nat) : + stoppingTime (2 ^ 12 * m + 144) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_144 : oddCount 144 12 = 5 ∧ acceleratedOrbit 12 144 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_144 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 144) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_144.1, data_12_144.2] + +/-- Complete interval computation for depth 12, residue 145. -/ +theorem bounds_12_145 : exactInterval 12 145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_145 (m : Nat) : + stoppingTime (2 ^ 12 * m + 145) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_145 : oddCount 145 12 = 8 ∧ acceleratedOrbit 12 145 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_145 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 145) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_145.1, data_12_145.2] + +/-- Complete interval computation for depth 12, residue 146. -/ +theorem bounds_12_146 : exactInterval 12 146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_146 (m : Nat) : + stoppingTime (2 ^ 12 * m + 146) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_146 : oddCount 146 12 = 8 ∧ acceleratedOrbit 12 146 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_146 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 146) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_146.1, data_12_146.2] + +/-- Complete interval computation for depth 12, residue 147. -/ +theorem bounds_12_147 : exactInterval 12 147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_147 (m : Nat) : + stoppingTime (2 ^ 12 * m + 147) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_147 : oddCount 147 12 = 8 ∧ acceleratedOrbit 12 147 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_147 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 147) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_147.1, data_12_147.2] + +/-- Complete interval computation for depth 12, residue 148. -/ +theorem bounds_12_148 : exactInterval 12 148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_148 (m : Nat) : + stoppingTime (2 ^ 12 * m + 148) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_148 : oddCount 148 12 = 5 ∧ acceleratedOrbit 12 148 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_148 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 148) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_148.1, data_12_148.2] + +/-- Complete interval computation for depth 12, residue 149. -/ +theorem bounds_12_149 : exactInterval 12 149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_149 (m : Nat) : + stoppingTime (2 ^ 12 * m + 149) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_149 : oddCount 149 12 = 5 ∧ acceleratedOrbit 12 149 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_149 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 149) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_149.1, data_12_149.2] + +/-- Complete interval computation for depth 12, residue 150. -/ +theorem bounds_12_150 : exactInterval 12 150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_150 (m : Nat) : + stoppingTime (2 ^ 12 * m + 150) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_150 : oddCount 150 12 = 3 ∧ acceleratedOrbit 12 150 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_150 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 150) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_150.1, data_12_150.2] + +/-- Complete interval computation for depth 12, residue 151. -/ +theorem bounds_12_151 : exactInterval 12 151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_151 (m : Nat) : + stoppingTime (2 ^ 12 * m + 151) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_151 : oddCount 151 12 = 3 ∧ acceleratedOrbit 12 151 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_151 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 151) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_151.1, data_12_151.2] + +/-- Complete interval computation for depth 12, residue 152. -/ +theorem bounds_12_152 : exactInterval 12 152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_152 (m : Nat) : + stoppingTime (2 ^ 12 * m + 152) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_152 : oddCount 152 12 = 5 ∧ acceleratedOrbit 12 152 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_152 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 152) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_152.1, data_12_152.2] + +end Collatz.Research.StoppingAtlas.Batch0210 From c257b71f16dfb3008284a8d4ed927238357e35f0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:05 +0530 Subject: [PATCH 0211/1001] proof: certify atlas Batch0211 (12:153 to 12:167) --- Collatz/Research/StoppingAtlas/Batch0211.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0211.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0211.lean b/Collatz/Research/StoppingAtlas/Batch0211.lean new file mode 100644 index 00000000..14b544b4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0211.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0211 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 153. -/ +theorem bounds_12_153 : exactInterval 12 153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_153 (m : Nat) : + stoppingTime (2 ^ 12 * m + 153) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_153 : oddCount 153 12 = 6 ∧ acceleratedOrbit 12 153 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_153 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 153) = 3 ^ 6 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_153.1, data_12_153.2] + +/-- Complete interval computation for depth 12, residue 154. -/ +theorem bounds_12_154 : exactInterval 12 154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_154 (m : Nat) : + stoppingTime (2 ^ 12 * m + 154) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_154 : oddCount 154 12 = 5 ∧ acceleratedOrbit 12 154 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_154 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 154) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_154.1, data_12_154.2] + +/-- Complete interval computation for depth 12, residue 155. -/ +theorem bounds_12_155 : exactInterval 12 155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_155 (m : Nat) : + stoppingTime (2 ^ 12 * m + 155) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_155 : oddCount 155 12 = 8 ∧ acceleratedOrbit 12 155 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_155 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 155) = 3 ^ 8 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_155.1, data_12_155.2] + +/-- Complete interval computation for depth 12, residue 156. -/ +theorem bounds_12_156 : exactInterval 12 156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_156 (m : Nat) : + stoppingTime (2 ^ 12 * m + 156) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_156 : oddCount 156 12 = 6 ∧ acceleratedOrbit 12 156 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_156 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 156) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_156.1, data_12_156.2] + +/-- Complete interval computation for depth 12, residue 157. -/ +theorem bounds_12_157 : exactInterval 12 157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_157 (m : Nat) : + stoppingTime (2 ^ 12 * m + 157) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_157 : oddCount 157 12 = 6 ∧ acceleratedOrbit 12 157 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_157 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 157) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_157.1, data_12_157.2] + +/-- Complete interval computation for depth 12, residue 158. -/ +theorem bounds_12_158 : exactInterval 12 158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_158 (m : Nat) : + stoppingTime (2 ^ 12 * m + 158) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_158 : oddCount 158 12 = 6 ∧ acceleratedOrbit 12 158 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_158 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 158) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_158.1, data_12_158.2] + +/-- Complete interval computation for depth 12, residue 159. -/ +theorem bounds_12_159 : exactInterval 12 159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_159 (m : Nat) : + stoppingTime (2 ^ 12 * m + 159) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_159 : oddCount 159 12 = 10 ∧ acceleratedOrbit 12 159 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_159 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 159) = 3 ^ 10 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_159.1, data_12_159.2] + +/-- Complete interval computation for depth 12, residue 160. -/ +theorem bounds_12_160 : exactInterval 12 160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_160 (m : Nat) : + stoppingTime (2 ^ 12 * m + 160) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_160 : oddCount 160 12 = 3 ∧ acceleratedOrbit 12 160 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_160 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 160) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_160.1, data_12_160.2] + +/-- Complete interval computation for depth 12, residue 161. -/ +theorem bounds_12_161 : exactInterval 12 161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_161 (m : Nat) : + stoppingTime (2 ^ 12 * m + 161) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_161 : oddCount 161 12 = 8 ∧ acceleratedOrbit 12 161 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_161 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 161) = 3 ^ 8 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_161.1, data_12_161.2] + +/-- Complete interval computation for depth 12, residue 162. -/ +theorem bounds_12_162 : exactInterval 12 162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_162 (m : Nat) : + stoppingTime (2 ^ 12 * m + 162) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_162 : oddCount 162 12 = 5 ∧ acceleratedOrbit 12 162 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_162 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 162) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_162.1, data_12_162.2] + +/-- Complete interval computation for depth 12, residue 163. -/ +theorem bounds_12_163 : exactInterval 12 163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_163 (m : Nat) : + stoppingTime (2 ^ 12 * m + 163) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_163 : oddCount 163 12 = 5 ∧ acceleratedOrbit 12 163 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_163 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 163) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_163.1, data_12_163.2] + +/-- Complete interval computation for depth 12, residue 164. -/ +theorem bounds_12_164 : exactInterval 12 164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_164 (m : Nat) : + stoppingTime (2 ^ 12 * m + 164) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_164 : oddCount 164 12 = 7 ∧ acceleratedOrbit 12 164 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_164 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 164) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_164.1, data_12_164.2] + +/-- Complete interval computation for depth 12, residue 165. -/ +theorem bounds_12_165 : exactInterval 12 165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_165 (m : Nat) : + stoppingTime (2 ^ 12 * m + 165) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_165 : oddCount 165 12 = 7 ∧ acceleratedOrbit 12 165 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_165 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 165) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_165.1, data_12_165.2] + +/-- Complete interval computation for depth 12, residue 166. -/ +theorem bounds_12_166 : exactInterval 12 166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_166 (m : Nat) : + stoppingTime (2 ^ 12 * m + 166) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_166 : oddCount 166 12 = 7 ∧ acceleratedOrbit 12 166 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_166 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 166) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_166.1, data_12_166.2] + +/-- Complete interval computation for depth 12, residue 167. -/ +theorem bounds_12_167 : exactInterval 12 167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_167 (m : Nat) : + stoppingTime (2 ^ 12 * m + 167) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_167 : oddCount 167 12 = 10 ∧ acceleratedOrbit 12 167 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_167 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 167) = 3 ^ 10 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_167.1, data_12_167.2] + +end Collatz.Research.StoppingAtlas.Batch0211 From 71dac8d557c92e52176f7e4a6a227d7478b74a85 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:06 +0530 Subject: [PATCH 0212/1001] proof: certify atlas Batch0212 (12:168 to 12:183) --- Collatz/Research/StoppingAtlas/Batch0212.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0212.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0212.lean b/Collatz/Research/StoppingAtlas/Batch0212.lean new file mode 100644 index 00000000..a6c3d22b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0212.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0212 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 168. -/ +theorem bounds_12_168 : exactInterval 12 168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_168 (m : Nat) : + stoppingTime (2 ^ 12 * m + 168) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_168 : oddCount 168 12 = 3 ∧ acceleratedOrbit 12 168 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_168 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 168) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_168.1, data_12_168.2] + +/-- Complete interval computation for depth 12, residue 169. -/ +theorem bounds_12_169 : exactInterval 12 169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_169 (m : Nat) : + stoppingTime (2 ^ 12 * m + 169) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_169 : oddCount 169 12 = 9 ∧ acceleratedOrbit 12 169 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_169 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 169) = 3 ^ 9 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_169.1, data_12_169.2] + +/-- Complete interval computation for depth 12, residue 170. -/ +theorem bounds_12_170 : exactInterval 12 170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_170 (m : Nat) : + stoppingTime (2 ^ 12 * m + 170) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_170 : oddCount 170 12 = 3 ∧ acceleratedOrbit 12 170 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_170 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 170) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_170.1, data_12_170.2] + +/-- Complete interval computation for depth 12, residue 171. -/ +theorem bounds_12_171 : exactInterval 12 171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_171 (m : Nat) : + stoppingTime (2 ^ 12 * m + 171) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_171 : oddCount 171 12 = 6 ∧ acceleratedOrbit 12 171 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_171 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 171) = 3 ^ 6 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_171.1, data_12_171.2] + +/-- Complete interval computation for depth 12, residue 172. -/ +theorem bounds_12_172 : exactInterval 12 172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_172 (m : Nat) : + stoppingTime (2 ^ 12 * m + 172) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_172 : oddCount 172 12 = 5 ∧ acceleratedOrbit 12 172 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_172 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 172) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_172.1, data_12_172.2] + +/-- Complete interval computation for depth 12, residue 173. -/ +theorem bounds_12_173 : exactInterval 12 173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_173 (m : Nat) : + stoppingTime (2 ^ 12 * m + 173) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_173 : oddCount 173 12 = 5 ∧ acceleratedOrbit 12 173 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_173 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 173) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_173.1, data_12_173.2] + +/-- Complete interval computation for depth 12, residue 174. -/ +theorem bounds_12_174 : exactInterval 12 174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_174 (m : Nat) : + stoppingTime (2 ^ 12 * m + 174) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_174 : oddCount 174 12 = 5 ∧ acceleratedOrbit 12 174 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_174 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 174) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_174.1, data_12_174.2] + +/-- Complete interval computation for depth 12, residue 175. -/ +theorem bounds_12_175 : exactInterval 12 175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_175 (m : Nat) : + stoppingTime (2 ^ 12 * m + 175) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_175 : oddCount 175 12 = 8 ∧ acceleratedOrbit 12 175 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_175 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 175) = 3 ^ 8 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_175.1, data_12_175.2] + +/-- Complete interval computation for depth 12, residue 176. -/ +theorem bounds_12_176 : exactInterval 12 176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_176 (m : Nat) : + stoppingTime (2 ^ 12 * m + 176) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_176 : oddCount 176 12 = 4 ∧ acceleratedOrbit 12 176 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_176 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 176) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_176.1, data_12_176.2] + +/-- Complete interval computation for depth 12, residue 177. -/ +theorem bounds_12_177 : exactInterval 12 177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_177 (m : Nat) : + stoppingTime (2 ^ 12 * m + 177) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_177 : oddCount 177 12 = 5 ∧ acceleratedOrbit 12 177 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_177 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 177) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_177.1, data_12_177.2] + +/-- Complete interval computation for depth 12, residue 178. -/ +theorem bounds_12_178 : exactInterval 12 178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_178 (m : Nat) : + stoppingTime (2 ^ 12 * m + 178) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_178 : oddCount 178 12 = 5 ∧ acceleratedOrbit 12 178 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_178 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 178) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_178.1, data_12_178.2] + +/-- Complete interval computation for depth 12, residue 179. -/ +theorem bounds_12_179 : exactInterval 12 179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_179 (m : Nat) : + stoppingTime (2 ^ 12 * m + 179) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_179 : oddCount 179 12 = 5 ∧ acceleratedOrbit 12 179 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_179 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 179) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_179.1, data_12_179.2] + +/-- Complete interval computation for depth 12, residue 180. -/ +theorem bounds_12_180 : exactInterval 12 180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_180 (m : Nat) : + stoppingTime (2 ^ 12 * m + 180) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_180 : oddCount 180 12 = 4 ∧ acceleratedOrbit 12 180 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_180 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 180) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_180.1, data_12_180.2] + +/-- Complete interval computation for depth 12, residue 181. -/ +theorem bounds_12_181 : exactInterval 12 181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_181 (m : Nat) : + stoppingTime (2 ^ 12 * m + 181) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_181 : oddCount 181 12 = 4 ∧ acceleratedOrbit 12 181 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_181 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 181) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_181.1, data_12_181.2] + +/-- Complete interval computation for depth 12, residue 182. -/ +theorem bounds_12_182 : exactInterval 12 182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_182 (m : Nat) : + stoppingTime (2 ^ 12 * m + 182) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_182 : oddCount 182 12 = 9 ∧ acceleratedOrbit 12 182 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_182 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 182) = 3 ^ 9 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_182.1, data_12_182.2] + +/-- Complete interval computation for depth 12, residue 183. -/ +theorem bounds_12_183 : exactInterval 12 183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_183 (m : Nat) : + stoppingTime (2 ^ 12 * m + 183) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_183 : oddCount 183 12 = 9 ∧ acceleratedOrbit 12 183 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_183 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 183) = 3 ^ 9 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_183.1, data_12_183.2] + +end Collatz.Research.StoppingAtlas.Batch0212 From 67161b6992328e5226bbb08d689cd132ac6d9b4a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:06 +0530 Subject: [PATCH 0213/1001] proof: certify atlas Batch0213 (12:184 to 12:198) --- Collatz/Research/StoppingAtlas/Batch0213.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0213.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0213.lean b/Collatz/Research/StoppingAtlas/Batch0213.lean new file mode 100644 index 00000000..675209aa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0213.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0213 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 184. -/ +theorem bounds_12_184 : exactInterval 12 184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_184 (m : Nat) : + stoppingTime (2 ^ 12 * m + 184) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_184 : oddCount 184 12 = 4 ∧ acceleratedOrbit 12 184 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_184 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 184) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_184.1, data_12_184.2] + +/-- Complete interval computation for depth 12, residue 185. -/ +theorem bounds_12_185 : exactInterval 12 185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_185 (m : Nat) : + stoppingTime (2 ^ 12 * m + 185) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_185 : oddCount 185 12 = 7 ∧ acceleratedOrbit 12 185 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_185 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 185) = 3 ^ 7 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_185.1, data_12_185.2] + +/-- Complete interval computation for depth 12, residue 186. -/ +theorem bounds_12_186 : exactInterval 12 186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_186 (m : Nat) : + stoppingTime (2 ^ 12 * m + 186) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_186 : oddCount 186 12 = 4 ∧ acceleratedOrbit 12 186 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_186 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 186) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_186.1, data_12_186.2] + +/-- Complete interval computation for depth 12, residue 187. -/ +theorem bounds_12_187 : exactInterval 12 187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_187 (m : Nat) : + stoppingTime (2 ^ 12 * m + 187) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_187 : oddCount 187 12 = 7 ∧ acceleratedOrbit 12 187 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_187 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 187) = 3 ^ 7 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_187.1, data_12_187.2] + +/-- Complete interval computation for depth 12, residue 188. -/ +theorem bounds_12_188 : exactInterval 12 188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_188 (m : Nat) : + stoppingTime (2 ^ 12 * m + 188) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_188 : oddCount 188 12 = 7 ∧ acceleratedOrbit 12 188 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_188 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 188) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_188.1, data_12_188.2] + +/-- Complete interval computation for depth 12, residue 189. -/ +theorem bounds_12_189 : exactInterval 12 189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_189 (m : Nat) : + stoppingTime (2 ^ 12 * m + 189) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_189 : oddCount 189 12 = 7 ∧ acceleratedOrbit 12 189 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_189 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 189) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_189.1, data_12_189.2] + +/-- Complete interval computation for depth 12, residue 190. -/ +theorem bounds_12_190 : exactInterval 12 190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_190 (m : Nat) : + stoppingTime (2 ^ 12 * m + 190) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_190 : oddCount 190 12 = 7 ∧ acceleratedOrbit 12 190 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_190 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 190) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_190.1, data_12_190.2] + +/-- Complete interval computation for depth 12, residue 191. -/ +theorem bounds_12_191 : exactInterval 12 191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_191 (m : Nat) : + stoppingTime (2 ^ 12 * m + 191) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_191 : oddCount 191 12 = 8 ∧ acceleratedOrbit 12 191 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_191 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 191) = 3 ^ 8 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_191.1, data_12_191.2] + +/-- Complete interval computation for depth 12, residue 192. -/ +theorem bounds_12_192 : exactInterval 12 192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_192 (m : Nat) : + stoppingTime (2 ^ 12 * m + 192) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_192 : oddCount 192 12 = 3 ∧ acceleratedOrbit 12 192 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_192 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 192) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_192.1, data_12_192.2] + +/-- Complete interval computation for depth 12, residue 193. -/ +theorem bounds_12_193 : exactInterval 12 193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_193 (m : Nat) : + stoppingTime (2 ^ 12 * m + 193) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_193 : oddCount 193 12 = 7 ∧ acceleratedOrbit 12 193 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_193 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 193) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_193.1, data_12_193.2] + +/-- Complete interval computation for depth 12, residue 194. -/ +theorem bounds_12_194 : exactInterval 12 194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_194 (m : Nat) : + stoppingTime (2 ^ 12 * m + 194) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_194 : oddCount 194 12 = 7 ∧ acceleratedOrbit 12 194 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_194 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 194) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_194.1, data_12_194.2] + +/-- Complete interval computation for depth 12, residue 195. -/ +theorem bounds_12_195 : exactInterval 12 195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_195 (m : Nat) : + stoppingTime (2 ^ 12 * m + 195) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_195 : oddCount 195 12 = 7 ∧ acceleratedOrbit 12 195 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_195 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 195) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_195.1, data_12_195.2] + +/-- Complete interval computation for depth 12, residue 196. -/ +theorem bounds_12_196 : exactInterval 12 196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_196 (m : Nat) : + stoppingTime (2 ^ 12 * m + 196) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_196 : oddCount 196 12 = 5 ∧ acceleratedOrbit 12 196 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_196 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 196) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_196.1, data_12_196.2] + +/-- Complete interval computation for depth 12, residue 197. -/ +theorem bounds_12_197 : exactInterval 12 197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_197 (m : Nat) : + stoppingTime (2 ^ 12 * m + 197) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_197 : oddCount 197 12 = 5 ∧ acceleratedOrbit 12 197 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_197 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 197) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_197.1, data_12_197.2] + +/-- Complete interval computation for depth 12, residue 198. -/ +theorem bounds_12_198 : exactInterval 12 198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_198 (m : Nat) : + stoppingTime (2 ^ 12 * m + 198) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_198 : oddCount 198 12 = 5 ∧ acceleratedOrbit 12 198 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_198 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 198) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_198.1, data_12_198.2] + +end Collatz.Research.StoppingAtlas.Batch0213 From 34549a814dced163c1f9cc340b7cf30d8c868aad Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:06 +0530 Subject: [PATCH 0214/1001] proof: certify atlas Batch0214 (12:199 to 12:214) --- Collatz/Research/StoppingAtlas/Batch0214.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0214.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0214.lean b/Collatz/Research/StoppingAtlas/Batch0214.lean new file mode 100644 index 00000000..ba533bee --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0214.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0214 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 199. -/ +theorem bounds_12_199 : exactInterval 12 199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_199 (m : Nat) : + stoppingTime (2 ^ 12 * m + 199) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_199 : oddCount 199 12 = 8 ∧ acceleratedOrbit 12 199 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_199 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 199) = 3 ^ 8 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_199.1, data_12_199.2] + +/-- Complete interval computation for depth 12, residue 200. -/ +theorem bounds_12_200 : exactInterval 12 200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_200 (m : Nat) : + stoppingTime (2 ^ 12 * m + 200) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_200 : oddCount 200 12 = 5 ∧ acceleratedOrbit 12 200 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_200 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 200) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_200.1, data_12_200.2] + +/-- Complete interval computation for depth 12, residue 201. -/ +theorem bounds_12_201 : exactInterval 12 201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_201 (m : Nat) : + stoppingTime (2 ^ 12 * m + 201) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_201 : oddCount 201 12 = 4 ∧ acceleratedOrbit 12 201 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_201 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 201) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_201.1, data_12_201.2] + +/-- Complete interval computation for depth 12, residue 202. -/ +theorem bounds_12_202 : exactInterval 12 202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_202 (m : Nat) : + stoppingTime (2 ^ 12 * m + 202) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_202 : oddCount 202 12 = 5 ∧ acceleratedOrbit 12 202 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_202 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 202) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_202.1, data_12_202.2] + +/-- Complete interval computation for depth 12, residue 203. -/ +theorem bounds_12_203 : exactInterval 12 203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_203 (m : Nat) : + stoppingTime (2 ^ 12 * m + 203) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_203 : oddCount 203 12 = 6 ∧ acceleratedOrbit 12 203 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_203 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 203) = 3 ^ 6 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_203.1, data_12_203.2] + +/-- Complete interval computation for depth 12, residue 204. -/ +theorem bounds_12_204 : exactInterval 12 204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_204 (m : Nat) : + stoppingTime (2 ^ 12 * m + 204) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_204 : oddCount 204 12 = 5 ∧ acceleratedOrbit 12 204 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_204 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 204) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_204.1, data_12_204.2] + +/-- Complete interval computation for depth 12, residue 205. -/ +theorem bounds_12_205 : exactInterval 12 205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_205 (m : Nat) : + stoppingTime (2 ^ 12 * m + 205) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_205 : oddCount 205 12 = 5 ∧ acceleratedOrbit 12 205 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_205 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 205) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_205.1, data_12_205.2] + +/-- Complete interval computation for depth 12, residue 206. -/ +theorem bounds_12_206 : exactInterval 12 206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_206 (m : Nat) : + stoppingTime (2 ^ 12 * m + 206) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_206 : oddCount 206 12 = 8 ∧ acceleratedOrbit 12 206 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_206 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 206) = 3 ^ 8 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_206.1, data_12_206.2] + +/-- Complete interval computation for depth 12, residue 207. -/ +theorem bounds_12_207 : exactInterval 12 207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_207 (m : Nat) : + stoppingTime (2 ^ 12 * m + 207) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_207 : oddCount 207 12 = 8 ∧ acceleratedOrbit 12 207 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_207 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 207) = 3 ^ 8 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_207.1, data_12_207.2] + +/-- Complete interval computation for depth 12, residue 208. -/ +theorem bounds_12_208 : exactInterval 12 208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_208 (m : Nat) : + stoppingTime (2 ^ 12 * m + 208) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_208 : oddCount 208 12 = 3 ∧ acceleratedOrbit 12 208 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_208 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 208) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_208.1, data_12_208.2] + +/-- Complete interval computation for depth 12, residue 209. -/ +theorem bounds_12_209 : exactInterval 12 209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_209 (m : Nat) : + stoppingTime (2 ^ 12 * m + 209) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_209 : oddCount 209 12 = 6 ∧ acceleratedOrbit 12 209 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_209 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 209) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_209.1, data_12_209.2] + +/-- Complete interval computation for depth 12, residue 210. -/ +theorem bounds_12_210 : exactInterval 12 210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_210 (m : Nat) : + stoppingTime (2 ^ 12 * m + 210) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_210 : oddCount 210 12 = 6 ∧ acceleratedOrbit 12 210 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_210 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 210) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_210.1, data_12_210.2] + +/-- Complete interval computation for depth 12, residue 211. -/ +theorem bounds_12_211 : exactInterval 12 211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_211 (m : Nat) : + stoppingTime (2 ^ 12 * m + 211) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_211 : oddCount 211 12 = 6 ∧ acceleratedOrbit 12 211 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_211 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 211) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_211.1, data_12_211.2] + +/-- Complete interval computation for depth 12, residue 212. -/ +theorem bounds_12_212 : exactInterval 12 212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_212 (m : Nat) : + stoppingTime (2 ^ 12 * m + 212) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_212 : oddCount 212 12 = 3 ∧ acceleratedOrbit 12 212 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_212 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 212) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_212.1, data_12_212.2] + +/-- Complete interval computation for depth 12, residue 213. -/ +theorem bounds_12_213 : exactInterval 12 213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_213 (m : Nat) : + stoppingTime (2 ^ 12 * m + 213) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_213 : oddCount 213 12 = 3 ∧ acceleratedOrbit 12 213 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_213 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 213) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_213.1, data_12_213.2] + +/-- Complete interval computation for depth 12, residue 214. -/ +theorem bounds_12_214 : exactInterval 12 214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_214 (m : Nat) : + stoppingTime (2 ^ 12 * m + 214) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_214 : oddCount 214 12 = 8 ∧ acceleratedOrbit 12 214 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_214 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 214) = 3 ^ 8 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_214.1, data_12_214.2] + +end Collatz.Research.StoppingAtlas.Batch0214 From a86bb464819a63fb91b4acd266902192b6a1f4cf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:06 +0530 Subject: [PATCH 0215/1001] proof: certify atlas Batch0215 (12:215 to 12:229) --- Collatz/Research/StoppingAtlas/Batch0215.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0215.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0215.lean b/Collatz/Research/StoppingAtlas/Batch0215.lean new file mode 100644 index 00000000..fd661b30 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0215.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0215 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 215. -/ +theorem bounds_12_215 : exactInterval 12 215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_215 (m : Nat) : + stoppingTime (2 ^ 12 * m + 215) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_215 : oddCount 215 12 = 8 ∧ acceleratedOrbit 12 215 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_215 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 215) = 3 ^ 8 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_215.1, data_12_215.2] + +/-- Complete interval computation for depth 12, residue 216. -/ +theorem bounds_12_216 : exactInterval 12 216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_216 (m : Nat) : + stoppingTime (2 ^ 12 * m + 216) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_216 : oddCount 216 12 = 7 ∧ acceleratedOrbit 12 216 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_216 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 216) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_216.1, data_12_216.2] + +/-- Complete interval computation for depth 12, residue 217. -/ +theorem bounds_12_217 : exactInterval 12 217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_217 (m : Nat) : + stoppingTime (2 ^ 12 * m + 217) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_217 : oddCount 217 12 = 6 ∧ acceleratedOrbit 12 217 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_217 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 217) = 3 ^ 6 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_217.1, data_12_217.2] + +/-- Complete interval computation for depth 12, residue 218. -/ +theorem bounds_12_218 : exactInterval 12 218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_218 (m : Nat) : + stoppingTime (2 ^ 12 * m + 218) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_218 : oddCount 218 12 = 7 ∧ acceleratedOrbit 12 218 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_218 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 218) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_218.1, data_12_218.2] + +/-- Complete interval computation for depth 12, residue 219. -/ +theorem bounds_12_219 : exactInterval 12 219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_219 (m : Nat) : + stoppingTime (2 ^ 12 * m + 219) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_219 : oddCount 219 12 = 7 ∧ acceleratedOrbit 12 219 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_219 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 219) = 3 ^ 7 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_219.1, data_12_219.2] + +/-- Complete interval computation for depth 12, residue 220. -/ +theorem bounds_12_220 : exactInterval 12 220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_220 (m : Nat) : + stoppingTime (2 ^ 12 * m + 220) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_220 : oddCount 220 12 = 7 ∧ acceleratedOrbit 12 220 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_220 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 220) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_220.1, data_12_220.2] + +/-- Complete interval computation for depth 12, residue 221. -/ +theorem bounds_12_221 : exactInterval 12 221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_221 (m : Nat) : + stoppingTime (2 ^ 12 * m + 221) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_221 : oddCount 221 12 = 7 ∧ acceleratedOrbit 12 221 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_221 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 221) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_221.1, data_12_221.2] + +/-- Complete interval computation for depth 12, residue 222. -/ +theorem bounds_12_222 : exactInterval 12 222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_222 (m : Nat) : + stoppingTime (2 ^ 12 * m + 222) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_222 : oddCount 222 12 = 9 ∧ acceleratedOrbit 12 222 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_222 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 222) = 3 ^ 9 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_222.1, data_12_222.2] + +/-- Complete interval computation for depth 12, residue 223. -/ +theorem bounds_12_223 : exactInterval 12 223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_223 (m : Nat) : + stoppingTime (2 ^ 12 * m + 223) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_223 : oddCount 223 12 = 9 ∧ acceleratedOrbit 12 223 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_223 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 223) = 3 ^ 9 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_223.1, data_12_223.2] + +/-- Complete interval computation for depth 12, residue 224. -/ +theorem bounds_12_224 : exactInterval 12 224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_224 (m : Nat) : + stoppingTime (2 ^ 12 * m + 224) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_224 : oddCount 224 12 = 4 ∧ acceleratedOrbit 12 224 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_224 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 224) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_224.1, data_12_224.2] + +/-- Complete interval computation for depth 12, residue 225. -/ +theorem bounds_12_225 : exactInterval 12 225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_225 (m : Nat) : + stoppingTime (2 ^ 12 * m + 225) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_225 : oddCount 225 12 = 9 ∧ acceleratedOrbit 12 225 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_225 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 225) = 3 ^ 9 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_225.1, data_12_225.2] + +/-- Complete interval computation for depth 12, residue 226. -/ +theorem bounds_12_226 : exactInterval 12 226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_226 (m : Nat) : + stoppingTime (2 ^ 12 * m + 226) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_226 : oddCount 226 12 = 3 ∧ acceleratedOrbit 12 226 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_226 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 226) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_226.1, data_12_226.2] + +/-- Complete interval computation for depth 12, residue 227. -/ +theorem bounds_12_227 : exactInterval 12 227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_227 (m : Nat) : + stoppingTime (2 ^ 12 * m + 227) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_227 : oddCount 227 12 = 3 ∧ acceleratedOrbit 12 227 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_227 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 227) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_227.1, data_12_227.2] + +/-- Complete interval computation for depth 12, residue 228. -/ +theorem bounds_12_228 : exactInterval 12 228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_228 (m : Nat) : + stoppingTime (2 ^ 12 * m + 228) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_228 : oddCount 228 12 = 5 ∧ acceleratedOrbit 12 228 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_228 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 228) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_228.1, data_12_228.2] + +/-- Complete interval computation for depth 12, residue 229. -/ +theorem bounds_12_229 : exactInterval 12 229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_229 (m : Nat) : + stoppingTime (2 ^ 12 * m + 229) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_229 : oddCount 229 12 = 5 ∧ acceleratedOrbit 12 229 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_229 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 229) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_229.1, data_12_229.2] + +end Collatz.Research.StoppingAtlas.Batch0215 From b85ae5c9cc6d7073489514381f2b1b2304cbf564 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:07 +0530 Subject: [PATCH 0216/1001] proof: certify atlas Batch0216 (12:230 to 12:244) --- Collatz/Research/StoppingAtlas/Batch0216.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0216.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0216.lean b/Collatz/Research/StoppingAtlas/Batch0216.lean new file mode 100644 index 00000000..95bc1cea --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0216.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0216 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 230. -/ +theorem bounds_12_230 : exactInterval 12 230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_230 (m : Nat) : + stoppingTime (2 ^ 12 * m + 230) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_230 : oddCount 230 12 = 5 ∧ acceleratedOrbit 12 230 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_230 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 230) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_230.1, data_12_230.2] + +/-- Complete interval computation for depth 12, residue 231. -/ +theorem bounds_12_231 : exactInterval 12 231 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_231 (m : Nat) : + stoppingTime (2 ^ 12 * m + 231) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_231 : oddCount 231 12 = 7 ∧ acceleratedOrbit 12 231 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_231 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 231) = 3 ^ 7 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_231.1, data_12_231.2] + +/-- Complete interval computation for depth 12, residue 232. -/ +theorem bounds_12_232 : exactInterval 12 232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_232 (m : Nat) : + stoppingTime (2 ^ 12 * m + 232) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_232 : oddCount 232 12 = 4 ∧ acceleratedOrbit 12 232 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_232 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 232) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_232.1, data_12_232.2] + +/-- Complete interval computation for depth 12, residue 233. -/ +theorem bounds_12_233 : exactInterval 12 233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_233 (m : Nat) : + stoppingTime (2 ^ 12 * m + 233) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_233 : oddCount 233 12 = 8 ∧ acceleratedOrbit 12 233 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_233 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 233) = 3 ^ 8 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_233.1, data_12_233.2] + +/-- Complete interval computation for depth 12, residue 234. -/ +theorem bounds_12_234 : exactInterval 12 234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_234 (m : Nat) : + stoppingTime (2 ^ 12 * m + 234) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_234 : oddCount 234 12 = 4 ∧ acceleratedOrbit 12 234 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_234 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 234) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_234.1, data_12_234.2] + +/-- Complete interval computation for depth 12, residue 235. -/ +theorem bounds_12_235 : exactInterval 12 235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_235 (m : Nat) : + stoppingTime (2 ^ 12 * m + 235) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_235 : oddCount 235 12 = 8 ∧ acceleratedOrbit 12 235 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_235 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 235) = 3 ^ 8 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_235.1, data_12_235.2] + +/-- Complete interval computation for depth 12, residue 236. -/ +theorem bounds_12_236 : exactInterval 12 236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_236 (m : Nat) : + stoppingTime (2 ^ 12 * m + 236) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_236 : oddCount 236 12 = 6 ∧ acceleratedOrbit 12 236 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_236 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 236) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_236.1, data_12_236.2] + +/-- Complete interval computation for depth 12, residue 237. -/ +theorem bounds_12_237 : exactInterval 12 237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_237 (m : Nat) : + stoppingTime (2 ^ 12 * m + 237) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_237 : oddCount 237 12 = 6 ∧ acceleratedOrbit 12 237 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_237 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 237) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_237.1, data_12_237.2] + +/-- Complete interval computation for depth 12, residue 238. -/ +theorem bounds_12_238 : exactInterval 12 238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_238 (m : Nat) : + stoppingTime (2 ^ 12 * m + 238) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_238 : oddCount 238 12 = 6 ∧ acceleratedOrbit 12 238 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_238 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 238) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_238.1, data_12_238.2] + +/-- Complete interval computation for depth 12, residue 239. -/ +theorem bounds_12_239 : exactInterval 12 239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_239 (m : Nat) : + stoppingTime (2 ^ 12 * m + 239) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_239 : oddCount 239 12 = 9 ∧ acceleratedOrbit 12 239 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_239 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 239) = 3 ^ 9 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_239.1, data_12_239.2] + +/-- Complete interval computation for depth 12, residue 240. -/ +theorem bounds_12_240 : exactInterval 12 240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_240 (m : Nat) : + stoppingTime (2 ^ 12 * m + 240) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_240 : oddCount 240 12 = 4 ∧ acceleratedOrbit 12 240 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_240 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 240) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_240.1, data_12_240.2] + +/-- Complete interval computation for depth 12, residue 241. -/ +theorem bounds_12_241 : exactInterval 12 241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_241 (m : Nat) : + stoppingTime (2 ^ 12 * m + 241) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_241 : oddCount 241 12 = 4 ∧ acceleratedOrbit 12 241 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_241 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 241) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_241.1, data_12_241.2] + +/-- Complete interval computation for depth 12, residue 242. -/ +theorem bounds_12_242 : exactInterval 12 242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_242 (m : Nat) : + stoppingTime (2 ^ 12 * m + 242) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_242 : oddCount 242 12 = 8 ∧ acceleratedOrbit 12 242 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_242 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 242) = 3 ^ 8 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_242.1, data_12_242.2] + +/-- Complete interval computation for depth 12, residue 243. -/ +theorem bounds_12_243 : exactInterval 12 243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_243 (m : Nat) : + stoppingTime (2 ^ 12 * m + 243) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_243 : oddCount 243 12 = 8 ∧ acceleratedOrbit 12 243 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_243 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 243) = 3 ^ 8 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_243.1, data_12_243.2] + +/-- Complete interval computation for depth 12, residue 244. -/ +theorem bounds_12_244 : exactInterval 12 244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_244 (m : Nat) : + stoppingTime (2 ^ 12 * m + 244) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_244 : oddCount 244 12 = 4 ∧ acceleratedOrbit 12 244 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_244 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 244) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_244.1, data_12_244.2] + +end Collatz.Research.StoppingAtlas.Batch0216 From b3265951c853ab9d4ebe8029d8a2b4966981ab15 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:07 +0530 Subject: [PATCH 0217/1001] proof: certify atlas Batch0217 (12:245 to 12:260) --- Collatz/Research/StoppingAtlas/Batch0217.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0217.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0217.lean b/Collatz/Research/StoppingAtlas/Batch0217.lean new file mode 100644 index 00000000..74e3846e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0217.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0217 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 245. -/ +theorem bounds_12_245 : exactInterval 12 245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_245 (m : Nat) : + stoppingTime (2 ^ 12 * m + 245) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_245 : oddCount 245 12 = 4 ∧ acceleratedOrbit 12 245 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_245 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 245) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_245.1, data_12_245.2] + +/-- Complete interval computation for depth 12, residue 246. -/ +theorem bounds_12_246 : exactInterval 12 246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_246 (m : Nat) : + stoppingTime (2 ^ 12 * m + 246) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_246 : oddCount 246 12 = 7 ∧ acceleratedOrbit 12 246 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_246 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 246) = 3 ^ 7 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_246.1, data_12_246.2] + +/-- Complete interval computation for depth 12, residue 247. -/ +theorem bounds_12_247 : exactInterval 12 247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_247 (m : Nat) : + stoppingTime (2 ^ 12 * m + 247) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_247 : oddCount 247 12 = 7 ∧ acceleratedOrbit 12 247 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_247 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 247) = 3 ^ 7 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_247.1, data_12_247.2] + +/-- Complete interval computation for depth 12, residue 248. -/ +theorem bounds_12_248 : exactInterval 12 248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_248 (m : Nat) : + stoppingTime (2 ^ 12 * m + 248) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_248 : oddCount 248 12 = 7 ∧ acceleratedOrbit 12 248 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_248 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 248) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_248.1, data_12_248.2] + +/-- Complete interval computation for depth 12, residue 249. -/ +theorem bounds_12_249 : exactInterval 12 249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_249 (m : Nat) : + stoppingTime (2 ^ 12 * m + 249) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_249 : oddCount 249 12 = 8 ∧ acceleratedOrbit 12 249 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_249 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 249) = 3 ^ 8 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_249.1, data_12_249.2] + +/-- Complete interval computation for depth 12, residue 250. -/ +theorem bounds_12_250 : exactInterval 12 250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_250 (m : Nat) : + stoppingTime (2 ^ 12 * m + 250) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_250 : oddCount 250 12 = 7 ∧ acceleratedOrbit 12 250 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_250 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 250) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_250.1, data_12_250.2] + +/-- Complete interval computation for depth 12, residue 251. -/ +theorem bounds_12_251 : exactInterval 12 251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_251 (m : Nat) : + stoppingTime (2 ^ 12 * m + 251) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_251 : oddCount 251 12 = 10 ∧ acceleratedOrbit 12 251 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_251 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 251) = 3 ^ 10 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_251.1, data_12_251.2] + +/-- Complete interval computation for depth 12, residue 252. -/ +theorem bounds_12_252 : exactInterval 12 252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_252 (m : Nat) : + stoppingTime (2 ^ 12 * m + 252) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_252 : oddCount 252 12 = 7 ∧ acceleratedOrbit 12 252 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_252 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 252) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_252.1, data_12_252.2] + +/-- Complete interval computation for depth 12, residue 253. -/ +theorem bounds_12_253 : exactInterval 12 253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_253 (m : Nat) : + stoppingTime (2 ^ 12 * m + 253) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_253 : oddCount 253 12 = 7 ∧ acceleratedOrbit 12 253 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_253 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 253) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_253.1, data_12_253.2] + +/-- Complete interval computation for depth 12, residue 254. -/ +theorem bounds_12_254 : exactInterval 12 254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_254 (m : Nat) : + stoppingTime (2 ^ 12 * m + 254) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_254 : oddCount 254 12 = 8 ∧ acceleratedOrbit 12 254 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_254 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 254) = 3 ^ 8 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_254.1, data_12_254.2] + +/-- Complete interval computation for depth 12, residue 255. -/ +theorem bounds_12_255 : exactInterval 12 255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_255 (m : Nat) : + stoppingTime (2 ^ 12 * m + 255) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_255 : oddCount 255 12 = 8 ∧ acceleratedOrbit 12 255 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_255 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 255) = 3 ^ 8 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_255.1, data_12_255.2] + +/-- Complete interval computation for depth 12, residue 256. -/ +theorem bounds_12_256 : exactInterval 12 256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_256 (m : Nat) : + stoppingTime (2 ^ 12 * m + 256) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_256 : oddCount 256 12 = 2 ∧ acceleratedOrbit 12 256 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_256 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 256) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_256.1, data_12_256.2] + +/-- Complete interval computation for depth 12, residue 257. -/ +theorem bounds_12_257 : exactInterval 12 257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_257 (m : Nat) : + stoppingTime (2 ^ 12 * m + 257) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_257 : oddCount 257 12 = 6 ∧ acceleratedOrbit 12 257 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_257 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 257) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_257.1, data_12_257.2] + +/-- Complete interval computation for depth 12, residue 258. -/ +theorem bounds_12_258 : exactInterval 12 258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_258 (m : Nat) : + stoppingTime (2 ^ 12 * m + 258) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_258 : oddCount 258 12 = 6 ∧ acceleratedOrbit 12 258 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_258 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 258) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_258.1, data_12_258.2] + +/-- Complete interval computation for depth 12, residue 259. -/ +theorem bounds_12_259 : exactInterval 12 259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_259 (m : Nat) : + stoppingTime (2 ^ 12 * m + 259) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_259 : oddCount 259 12 = 6 ∧ acceleratedOrbit 12 259 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_259 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 259) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_259.1, data_12_259.2] + +/-- Complete interval computation for depth 12, residue 260. -/ +theorem bounds_12_260 : exactInterval 12 260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_260 (m : Nat) : + stoppingTime (2 ^ 12 * m + 260) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_260 : oddCount 260 12 = 5 ∧ acceleratedOrbit 12 260 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_260 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 260) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_260.1, data_12_260.2] + +end Collatz.Research.StoppingAtlas.Batch0217 From 53b957877aa47d601566fb245ab12ab3fc5b0f33 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:08 +0530 Subject: [PATCH 0218/1001] proof: certify atlas Batch0218 (12:261 to 12:275) --- Collatz/Research/StoppingAtlas/Batch0218.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0218.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0218.lean b/Collatz/Research/StoppingAtlas/Batch0218.lean new file mode 100644 index 00000000..c52c5806 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0218.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0218 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 261. -/ +theorem bounds_12_261 : exactInterval 12 261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_261 (m : Nat) : + stoppingTime (2 ^ 12 * m + 261) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_261 : oddCount 261 12 = 5 ∧ acceleratedOrbit 12 261 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_261 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 261) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_261.1, data_12_261.2] + +/-- Complete interval computation for depth 12, residue 262. -/ +theorem bounds_12_262 : exactInterval 12 262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_262 (m : Nat) : + stoppingTime (2 ^ 12 * m + 262) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_262 : oddCount 262 12 = 5 ∧ acceleratedOrbit 12 262 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_262 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 262) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_262.1, data_12_262.2] + +/-- Complete interval computation for depth 12, residue 263. -/ +theorem bounds_12_263 : exactInterval 12 263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_263 (m : Nat) : + stoppingTime (2 ^ 12 * m + 263) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_263 : oddCount 263 12 = 8 ∧ acceleratedOrbit 12 263 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_263 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 263) = 3 ^ 8 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_263.1, data_12_263.2] + +/-- Complete interval computation for depth 12, residue 264. -/ +theorem bounds_12_264 : exactInterval 12 264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_264 (m : Nat) : + stoppingTime (2 ^ 12 * m + 264) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_264 : oddCount 264 12 = 5 ∧ acceleratedOrbit 12 264 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_264 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 264) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_264.1, data_12_264.2] + +/-- Complete interval computation for depth 12, residue 265. -/ +theorem bounds_12_265 : exactInterval 12 265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_265 (m : Nat) : + stoppingTime (2 ^ 12 * m + 265) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_265 : oddCount 265 12 = 7 ∧ acceleratedOrbit 12 265 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_265 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 265) = 3 ^ 7 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_265.1, data_12_265.2] + +/-- Complete interval computation for depth 12, residue 266. -/ +theorem bounds_12_266 : exactInterval 12 266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_266 (m : Nat) : + stoppingTime (2 ^ 12 * m + 266) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_266 : oddCount 266 12 = 5 ∧ acceleratedOrbit 12 266 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_266 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 266) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_266.1, data_12_266.2] + +/-- Complete interval computation for depth 12, residue 267. -/ +theorem bounds_12_267 : exactInterval 12 267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_267 (m : Nat) : + stoppingTime (2 ^ 12 * m + 267) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_267 : oddCount 267 12 = 5 ∧ acceleratedOrbit 12 267 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_267 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 267) = 3 ^ 5 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_267.1, data_12_267.2] + +/-- Complete interval computation for depth 12, residue 268. -/ +theorem bounds_12_268 : exactInterval 12 268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_268 (m : Nat) : + stoppingTime (2 ^ 12 * m + 268) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_268 : oddCount 268 12 = 5 ∧ acceleratedOrbit 12 268 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_268 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 268) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_268.1, data_12_268.2] + +/-- Complete interval computation for depth 12, residue 269. -/ +theorem bounds_12_269 : exactInterval 12 269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_269 (m : Nat) : + stoppingTime (2 ^ 12 * m + 269) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_269 : oddCount 269 12 = 5 ∧ acceleratedOrbit 12 269 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_269 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 269) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_269.1, data_12_269.2] + +/-- Complete interval computation for depth 12, residue 270. -/ +theorem bounds_12_270 : exactInterval 12 270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_270 (m : Nat) : + stoppingTime (2 ^ 12 * m + 270) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_270 : oddCount 270 12 = 6 ∧ acceleratedOrbit 12 270 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_270 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 270) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_270.1, data_12_270.2] + +/-- Complete interval computation for depth 12, residue 271. -/ +theorem bounds_12_271 : exactInterval 12 271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_271 (m : Nat) : + stoppingTime (2 ^ 12 * m + 271) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_271 : oddCount 271 12 = 6 ∧ acceleratedOrbit 12 271 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_271 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 271) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_271.1, data_12_271.2] + +/-- Complete interval computation for depth 12, residue 272. -/ +theorem bounds_12_272 : exactInterval 12 272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_272 (m : Nat) : + stoppingTime (2 ^ 12 * m + 272) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_272 : oddCount 272 12 = 3 ∧ acceleratedOrbit 12 272 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_272 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 272) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_272.1, data_12_272.2] + +/-- Complete interval computation for depth 12, residue 273. -/ +theorem bounds_12_273 : exactInterval 12 273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_273 (m : Nat) : + stoppingTime (2 ^ 12 * m + 273) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_273 : oddCount 273 12 = 5 ∧ acceleratedOrbit 12 273 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_273 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 273) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_273.1, data_12_273.2] + +/-- Complete interval computation for depth 12, residue 274. -/ +theorem bounds_12_274 : exactInterval 12 274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_274 (m : Nat) : + stoppingTime (2 ^ 12 * m + 274) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_274 : oddCount 274 12 = 8 ∧ acceleratedOrbit 12 274 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_274 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 274) = 3 ^ 8 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_274.1, data_12_274.2] + +/-- Complete interval computation for depth 12, residue 275. -/ +theorem bounds_12_275 : exactInterval 12 275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_275 (m : Nat) : + stoppingTime (2 ^ 12 * m + 275) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_275 : oddCount 275 12 = 8 ∧ acceleratedOrbit 12 275 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_275 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 275) = 3 ^ 8 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_275.1, data_12_275.2] + +end Collatz.Research.StoppingAtlas.Batch0218 From e143d3146ca99f38030e5cca9034770e27c212aa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:08 +0530 Subject: [PATCH 0219/1001] proof: certify atlas Batch0219 (12:276 to 12:290) --- Collatz/Research/StoppingAtlas/Batch0219.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0219.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0219.lean b/Collatz/Research/StoppingAtlas/Batch0219.lean new file mode 100644 index 00000000..1c492c41 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0219.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0219 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 276. -/ +theorem bounds_12_276 : exactInterval 12 276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_276 (m : Nat) : + stoppingTime (2 ^ 12 * m + 276) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_276 : oddCount 276 12 = 3 ∧ acceleratedOrbit 12 276 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_276 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 276) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_276.1, data_12_276.2] + +/-- Complete interval computation for depth 12, residue 277. -/ +theorem bounds_12_277 : exactInterval 12 277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_277 (m : Nat) : + stoppingTime (2 ^ 12 * m + 277) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_277 : oddCount 277 12 = 3 ∧ acceleratedOrbit 12 277 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_277 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 277) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_277.1, data_12_277.2] + +/-- Complete interval computation for depth 12, residue 278. -/ +theorem bounds_12_278 : exactInterval 12 278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_278 (m : Nat) : + stoppingTime (2 ^ 12 * m + 278) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_278 : oddCount 278 12 = 7 ∧ acceleratedOrbit 12 278 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_278 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 278) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_278.1, data_12_278.2] + +/-- Complete interval computation for depth 12, residue 279. -/ +theorem bounds_12_279 : exactInterval 12 279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_279 (m : Nat) : + stoppingTime (2 ^ 12 * m + 279) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_279 : oddCount 279 12 = 7 ∧ acceleratedOrbit 12 279 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_279 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 279) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_279.1, data_12_279.2] + +/-- Complete interval computation for depth 12, residue 280. -/ +theorem bounds_12_280 : exactInterval 12 280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_280 (m : Nat) : + stoppingTime (2 ^ 12 * m + 280) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_280 : oddCount 280 12 = 3 ∧ acceleratedOrbit 12 280 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_280 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 280) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_280.1, data_12_280.2] + +/-- Complete interval computation for depth 12, residue 281. -/ +theorem bounds_12_281 : exactInterval 12 281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_281 (m : Nat) : + stoppingTime (2 ^ 12 * m + 281) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_281 : oddCount 281 12 = 7 ∧ acceleratedOrbit 12 281 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_281 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 281) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_281.1, data_12_281.2] + +/-- Complete interval computation for depth 12, residue 282. -/ +theorem bounds_12_282 : exactInterval 12 282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_282 (m : Nat) : + stoppingTime (2 ^ 12 * m + 282) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_282 : oddCount 282 12 = 3 ∧ acceleratedOrbit 12 282 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_282 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 282) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_282.1, data_12_282.2] + +/-- Complete interval computation for depth 12, residue 283. -/ +theorem bounds_12_283 : exactInterval 12 283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_283 (m : Nat) : + stoppingTime (2 ^ 12 * m + 283) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_283 : oddCount 283 12 = 9 ∧ acceleratedOrbit 12 283 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_283 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 283) = 3 ^ 9 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_283.1, data_12_283.2] + +/-- Complete interval computation for depth 12, residue 284. -/ +theorem bounds_12_284 : exactInterval 12 284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_284 (m : Nat) : + stoppingTime (2 ^ 12 * m + 284) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_284 : oddCount 284 12 = 7 ∧ acceleratedOrbit 12 284 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_284 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 284) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_284.1, data_12_284.2] + +/-- Complete interval computation for depth 12, residue 285. -/ +theorem bounds_12_285 : exactInterval 12 285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_285 (m : Nat) : + stoppingTime (2 ^ 12 * m + 285) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_285 : oddCount 285 12 = 7 ∧ acceleratedOrbit 12 285 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_285 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 285) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_285.1, data_12_285.2] + +/-- Complete interval computation for depth 12, residue 286. -/ +theorem bounds_12_286 : exactInterval 12 286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_286 (m : Nat) : + stoppingTime (2 ^ 12 * m + 286) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_286 : oddCount 286 12 = 7 ∧ acceleratedOrbit 12 286 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_286 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 286) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_286.1, data_12_286.2] + +/-- Complete interval computation for depth 12, residue 287. -/ +theorem bounds_12_287 : exactInterval 12 287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_287 (m : Nat) : + stoppingTime (2 ^ 12 * m + 287) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_287 : oddCount 287 12 = 7 ∧ acceleratedOrbit 12 287 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_287 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 287) = 3 ^ 7 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_287.1, data_12_287.2] + +/-- Complete interval computation for depth 12, residue 288. -/ +theorem bounds_12_288 : exactInterval 12 288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_288 (m : Nat) : + stoppingTime (2 ^ 12 * m + 288) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_288 : oddCount 288 12 = 5 ∧ acceleratedOrbit 12 288 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_288 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 288) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_288.1, data_12_288.2] + +/-- Complete interval computation for depth 12, residue 289. -/ +theorem bounds_12_289 : exactInterval 12 289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_289 (m : Nat) : + stoppingTime (2 ^ 12 * m + 289) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_289 : oddCount 289 12 = 6 ∧ acceleratedOrbit 12 289 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_289 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 289) = 3 ^ 6 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_289.1, data_12_289.2] + +/-- Complete interval computation for depth 12, residue 290. -/ +theorem bounds_12_290 : exactInterval 12 290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_290 (m : Nat) : + stoppingTime (2 ^ 12 * m + 290) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_290 : oddCount 290 12 = 7 ∧ acceleratedOrbit 12 290 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_290 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 290) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_290.1, data_12_290.2] + +end Collatz.Research.StoppingAtlas.Batch0219 From 713b079ebb5fc9ab49821baaeca17e73e9904c16 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:08 +0530 Subject: [PATCH 0220/1001] proof: certify atlas Batch0220 (12:291 to 12:306) --- Collatz/Research/StoppingAtlas/Batch0220.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0220.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0220.lean b/Collatz/Research/StoppingAtlas/Batch0220.lean new file mode 100644 index 00000000..ba5672cf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0220.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0220 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 291. -/ +theorem bounds_12_291 : exactInterval 12 291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_291 (m : Nat) : + stoppingTime (2 ^ 12 * m + 291) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_291 : oddCount 291 12 = 7 ∧ acceleratedOrbit 12 291 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_291 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 291) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_291.1, data_12_291.2] + +/-- Complete interval computation for depth 12, residue 292. -/ +theorem bounds_12_292 : exactInterval 12 292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_292 (m : Nat) : + stoppingTime (2 ^ 12 * m + 292) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_292 : oddCount 292 12 = 7 ∧ acceleratedOrbit 12 292 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_292 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 292) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_292.1, data_12_292.2] + +/-- Complete interval computation for depth 12, residue 293. -/ +theorem bounds_12_293 : exactInterval 12 293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_293 (m : Nat) : + stoppingTime (2 ^ 12 * m + 293) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_293 : oddCount 293 12 = 7 ∧ acceleratedOrbit 12 293 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_293 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 293) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_293.1, data_12_293.2] + +/-- Complete interval computation for depth 12, residue 294. -/ +theorem bounds_12_294 : exactInterval 12 294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_294 (m : Nat) : + stoppingTime (2 ^ 12 * m + 294) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_294 : oddCount 294 12 = 7 ∧ acceleratedOrbit 12 294 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_294 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 294) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_294.1, data_12_294.2] + +/-- Complete interval computation for depth 12, residue 295. -/ +theorem bounds_12_295 : exactInterval 12 295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_295 (m : Nat) : + stoppingTime (2 ^ 12 * m + 295) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_295 : oddCount 295 12 = 8 ∧ acceleratedOrbit 12 295 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_295 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 295) = 3 ^ 8 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_295.1, data_12_295.2] + +/-- Complete interval computation for depth 12, residue 296. -/ +theorem bounds_12_296 : exactInterval 12 296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_296 (m : Nat) : + stoppingTime (2 ^ 12 * m + 296) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_296 : oddCount 296 12 = 5 ∧ acceleratedOrbit 12 296 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_296 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 296) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_296.1, data_12_296.2] + +/-- Complete interval computation for depth 12, residue 297. -/ +theorem bounds_12_297 : exactInterval 12 297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_297 (m : Nat) : + stoppingTime (2 ^ 12 * m + 297) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_297 : oddCount 297 12 = 8 ∧ acceleratedOrbit 12 297 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_297 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 297) = 3 ^ 8 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_297.1, data_12_297.2] + +/-- Complete interval computation for depth 12, residue 298. -/ +theorem bounds_12_298 : exactInterval 12 298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_298 (m : Nat) : + stoppingTime (2 ^ 12 * m + 298) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_298 : oddCount 298 12 = 5 ∧ acceleratedOrbit 12 298 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_298 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 298) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_298.1, data_12_298.2] + +/-- Complete interval computation for depth 12, residue 299. -/ +theorem bounds_12_299 : exactInterval 12 299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_299 (m : Nat) : + stoppingTime (2 ^ 12 * m + 299) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_299 : oddCount 299 12 = 8 ∧ acceleratedOrbit 12 299 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_299 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 299) = 3 ^ 8 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_299.1, data_12_299.2] + +/-- Complete interval computation for depth 12, residue 300. -/ +theorem bounds_12_300 : exactInterval 12 300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_300 (m : Nat) : + stoppingTime (2 ^ 12 * m + 300) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_300 : oddCount 300 12 = 3 ∧ acceleratedOrbit 12 300 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_300 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 300) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_300.1, data_12_300.2] + +/-- Complete interval computation for depth 12, residue 301. -/ +theorem bounds_12_301 : exactInterval 12 301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_301 (m : Nat) : + stoppingTime (2 ^ 12 * m + 301) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_301 : oddCount 301 12 = 3 ∧ acceleratedOrbit 12 301 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_301 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 301) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_301.1, data_12_301.2] + +/-- Complete interval computation for depth 12, residue 302. -/ +theorem bounds_12_302 : exactInterval 12 302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_302 (m : Nat) : + stoppingTime (2 ^ 12 * m + 302) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_302 : oddCount 302 12 = 3 ∧ acceleratedOrbit 12 302 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_302 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 302) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_302.1, data_12_302.2] + +/-- Complete interval computation for depth 12, residue 303. -/ +theorem bounds_12_303 : exactInterval 12 303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_303 (m : Nat) : + stoppingTime (2 ^ 12 * m + 303) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_303 : oddCount 303 12 = 8 ∧ acceleratedOrbit 12 303 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_303 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 303) = 3 ^ 8 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_303.1, data_12_303.2] + +/-- Complete interval computation for depth 12, residue 304. -/ +theorem bounds_12_304 : exactInterval 12 304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_304 (m : Nat) : + stoppingTime (2 ^ 12 * m + 304) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_304 : oddCount 304 12 = 5 ∧ acceleratedOrbit 12 304 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_304 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 304) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_304.1, data_12_304.2] + +/-- Complete interval computation for depth 12, residue 305. -/ +theorem bounds_12_305 : exactInterval 12 305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_305 (m : Nat) : + stoppingTime (2 ^ 12 * m + 305) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_305 : oddCount 305 12 = 6 ∧ acceleratedOrbit 12 305 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_305 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 305) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_305.1, data_12_305.2] + +/-- Complete interval computation for depth 12, residue 306. -/ +theorem bounds_12_306 : exactInterval 12 306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_306 (m : Nat) : + stoppingTime (2 ^ 12 * m + 306) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_306 : oddCount 306 12 = 6 ∧ acceleratedOrbit 12 306 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_306 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 306) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_306.1, data_12_306.2] + +end Collatz.Research.StoppingAtlas.Batch0220 From 453634b6488df2f67c3a718860a02e0c3407052e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:08 +0530 Subject: [PATCH 0221/1001] proof: certify atlas Batch0221 (12:307 to 12:321) --- Collatz/Research/StoppingAtlas/Batch0221.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0221.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0221.lean b/Collatz/Research/StoppingAtlas/Batch0221.lean new file mode 100644 index 00000000..aab1767f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0221.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0221 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 307. -/ +theorem bounds_12_307 : exactInterval 12 307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_307 (m : Nat) : + stoppingTime (2 ^ 12 * m + 307) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_307 : oddCount 307 12 = 6 ∧ acceleratedOrbit 12 307 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_307 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 307) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_307.1, data_12_307.2] + +/-- Complete interval computation for depth 12, residue 308. -/ +theorem bounds_12_308 : exactInterval 12 308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_308 (m : Nat) : + stoppingTime (2 ^ 12 * m + 308) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_308 : oddCount 308 12 = 5 ∧ acceleratedOrbit 12 308 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_308 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 308) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_308.1, data_12_308.2] + +/-- Complete interval computation for depth 12, residue 309. -/ +theorem bounds_12_309 : exactInterval 12 309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_309 (m : Nat) : + stoppingTime (2 ^ 12 * m + 309) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_309 : oddCount 309 12 = 5 ∧ acceleratedOrbit 12 309 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_309 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 309) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_309.1, data_12_309.2] + +/-- Complete interval computation for depth 12, residue 310. -/ +theorem bounds_12_310 : exactInterval 12 310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_310 (m : Nat) : + stoppingTime (2 ^ 12 * m + 310) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_310 : oddCount 310 12 = 7 ∧ acceleratedOrbit 12 310 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_310 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 310) = 3 ^ 7 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_310.1, data_12_310.2] + +/-- Complete interval computation for depth 12, residue 311. -/ +theorem bounds_12_311 : exactInterval 12 311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_311 (m : Nat) : + stoppingTime (2 ^ 12 * m + 311) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_311 : oddCount 311 12 = 7 ∧ acceleratedOrbit 12 311 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_311 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 311) = 3 ^ 7 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_311.1, data_12_311.2] + +/-- Complete interval computation for depth 12, residue 312. -/ +theorem bounds_12_312 : exactInterval 12 312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_312 (m : Nat) : + stoppingTime (2 ^ 12 * m + 312) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_312 : oddCount 312 12 = 5 ∧ acceleratedOrbit 12 312 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_312 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 312) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_312.1, data_12_312.2] + +/-- Complete interval computation for depth 12, residue 313. -/ +theorem bounds_12_313 : exactInterval 12 313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_313 (m : Nat) : + stoppingTime (2 ^ 12 * m + 313) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_313 : oddCount 313 12 = 8 ∧ acceleratedOrbit 12 313 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_313 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 313) = 3 ^ 8 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_313.1, data_12_313.2] + +/-- Complete interval computation for depth 12, residue 314. -/ +theorem bounds_12_314 : exactInterval 12 314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_314 (m : Nat) : + stoppingTime (2 ^ 12 * m + 314) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_314 : oddCount 314 12 = 5 ∧ acceleratedOrbit 12 314 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_314 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 314) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_314.1, data_12_314.2] + +/-- Complete interval computation for depth 12, residue 315. -/ +theorem bounds_12_315 : exactInterval 12 315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_315 (m : Nat) : + stoppingTime (2 ^ 12 * m + 315) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_315 : oddCount 315 12 = 5 ∧ acceleratedOrbit 12 315 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_315 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 315) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_315.1, data_12_315.2] + +/-- Complete interval computation for depth 12, residue 316. -/ +theorem bounds_12_316 : exactInterval 12 316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_316 (m : Nat) : + stoppingTime (2 ^ 12 * m + 316) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_316 : oddCount 316 12 = 5 ∧ acceleratedOrbit 12 316 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_316 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 316) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_316.1, data_12_316.2] + +/-- Complete interval computation for depth 12, residue 317. -/ +theorem bounds_12_317 : exactInterval 12 317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_317 (m : Nat) : + stoppingTime (2 ^ 12 * m + 317) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_317 : oddCount 317 12 = 5 ∧ acceleratedOrbit 12 317 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_317 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 317) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_317.1, data_12_317.2] + +/-- Complete interval computation for depth 12, residue 318. -/ +theorem bounds_12_318 : exactInterval 12 318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_318 (m : Nat) : + stoppingTime (2 ^ 12 * m + 318) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_318 : oddCount 318 12 = 10 ∧ acceleratedOrbit 12 318 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_318 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 318) = 3 ^ 10 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_318.1, data_12_318.2] + +/-- Complete interval computation for depth 12, residue 319. -/ +theorem bounds_12_319 : exactInterval 12 319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_319 (m : Nat) : + stoppingTime (2 ^ 12 * m + 319) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_319 : oddCount 319 12 = 10 ∧ acceleratedOrbit 12 319 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_319 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 319) = 3 ^ 10 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_319.1, data_12_319.2] + +/-- Complete interval computation for depth 12, residue 320. -/ +theorem bounds_12_320 : exactInterval 12 320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_320 (m : Nat) : + stoppingTime (2 ^ 12 * m + 320) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_320 : oddCount 320 12 = 2 ∧ acceleratedOrbit 12 320 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_320 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 320) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_320.1, data_12_320.2] + +/-- Complete interval computation for depth 12, residue 321. -/ +theorem bounds_12_321 : exactInterval 12 321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_321 (m : Nat) : + stoppingTime (2 ^ 12 * m + 321) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_321 : oddCount 321 12 = 5 ∧ acceleratedOrbit 12 321 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_321 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 321) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_321.1, data_12_321.2] + +end Collatz.Research.StoppingAtlas.Batch0221 From 832ecac311d89c83dd1c37b0c470c0ad2bf6f555 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:09 +0530 Subject: [PATCH 0222/1001] proof: certify atlas Batch0222 (12:322 to 12:336) --- Collatz/Research/StoppingAtlas/Batch0222.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0222.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0222.lean b/Collatz/Research/StoppingAtlas/Batch0222.lean new file mode 100644 index 00000000..b222cf50 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0222.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0222 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 322. -/ +theorem bounds_12_322 : exactInterval 12 322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_322 (m : Nat) : + stoppingTime (2 ^ 12 * m + 322) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_322 : oddCount 322 12 = 7 ∧ acceleratedOrbit 12 322 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_322 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 322) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_322.1, data_12_322.2] + +/-- Complete interval computation for depth 12, residue 323. -/ +theorem bounds_12_323 : exactInterval 12 323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_323 (m : Nat) : + stoppingTime (2 ^ 12 * m + 323) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_323 : oddCount 323 12 = 7 ∧ acceleratedOrbit 12 323 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_323 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 323) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_323.1, data_12_323.2] + +/-- Complete interval computation for depth 12, residue 324. -/ +theorem bounds_12_324 : exactInterval 12 324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_324 (m : Nat) : + stoppingTime (2 ^ 12 * m + 324) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_324 : oddCount 324 12 = 5 ∧ acceleratedOrbit 12 324 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_324 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 324) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_324.1, data_12_324.2] + +/-- Complete interval computation for depth 12, residue 325. -/ +theorem bounds_12_325 : exactInterval 12 325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_325 (m : Nat) : + stoppingTime (2 ^ 12 * m + 325) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_325 : oddCount 325 12 = 5 ∧ acceleratedOrbit 12 325 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_325 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 325) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_325.1, data_12_325.2] + +/-- Complete interval computation for depth 12, residue 326. -/ +theorem bounds_12_326 : exactInterval 12 326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_326 (m : Nat) : + stoppingTime (2 ^ 12 * m + 326) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_326 : oddCount 326 12 = 5 ∧ acceleratedOrbit 12 326 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_326 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 326) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_326.1, data_12_326.2] + +/-- Complete interval computation for depth 12, residue 327. -/ +theorem bounds_12_327 : exactInterval 12 327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_327 (m : Nat) : + stoppingTime (2 ^ 12 * m + 327) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_327 : oddCount 327 12 = 9 ∧ acceleratedOrbit 12 327 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_327 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 327) = 3 ^ 9 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_327.1, data_12_327.2] + +/-- Complete interval computation for depth 12, residue 328. -/ +theorem bounds_12_328 : exactInterval 12 328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_328 (m : Nat) : + stoppingTime (2 ^ 12 * m + 328) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_328 : oddCount 328 12 = 7 ∧ acceleratedOrbit 12 328 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_328 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 328) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_328.1, data_12_328.2] + +/-- Complete interval computation for depth 12, residue 329. -/ +theorem bounds_12_329 : exactInterval 12 329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_329 (m : Nat) : + stoppingTime (2 ^ 12 * m + 329) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_329 : oddCount 329 12 = 6 ∧ acceleratedOrbit 12 329 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_329 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 329) = 3 ^ 6 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_329.1, data_12_329.2] + +/-- Complete interval computation for depth 12, residue 330. -/ +theorem bounds_12_330 : exactInterval 12 330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_330 (m : Nat) : + stoppingTime (2 ^ 12 * m + 330) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_330 : oddCount 330 12 = 7 ∧ acceleratedOrbit 12 330 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_330 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 330) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_330.1, data_12_330.2] + +/-- Complete interval computation for depth 12, residue 331. -/ +theorem bounds_12_331 : exactInterval 12 331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_331 (m : Nat) : + stoppingTime (2 ^ 12 * m + 331) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_331 : oddCount 331 12 = 5 ∧ acceleratedOrbit 12 331 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_331 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 331) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_331.1, data_12_331.2] + +/-- Complete interval computation for depth 12, residue 332. -/ +theorem bounds_12_332 : exactInterval 12 332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_332 (m : Nat) : + stoppingTime (2 ^ 12 * m + 332) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_332 : oddCount 332 12 = 7 ∧ acceleratedOrbit 12 332 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_332 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 332) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_332.1, data_12_332.2] + +/-- Complete interval computation for depth 12, residue 333. -/ +theorem bounds_12_333 : exactInterval 12 333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_333 (m : Nat) : + stoppingTime (2 ^ 12 * m + 333) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_333 : oddCount 333 12 = 7 ∧ acceleratedOrbit 12 333 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_333 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 333) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_333.1, data_12_333.2] + +/-- Complete interval computation for depth 12, residue 334. -/ +theorem bounds_12_334 : exactInterval 12 334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_334 (m : Nat) : + stoppingTime (2 ^ 12 * m + 334) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_334 : oddCount 334 12 = 9 ∧ acceleratedOrbit 12 334 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_334 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 334) = 3 ^ 9 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_334.1, data_12_334.2] + +/-- Complete interval computation for depth 12, residue 335. -/ +theorem bounds_12_335 : exactInterval 12 335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_335 (m : Nat) : + stoppingTime (2 ^ 12 * m + 335) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_335 : oddCount 335 12 = 9 ∧ acceleratedOrbit 12 335 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_335 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 335) = 3 ^ 9 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_335.1, data_12_335.2] + +/-- Complete interval computation for depth 12, residue 336. -/ +theorem bounds_12_336 : exactInterval 12 336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_336 (m : Nat) : + stoppingTime (2 ^ 12 * m + 336) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_336 : oddCount 336 12 = 2 ∧ acceleratedOrbit 12 336 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_336 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 336) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_336.1, data_12_336.2] + +end Collatz.Research.StoppingAtlas.Batch0222 From 749e8d62ee5ea5e2929eb98f66f8f2854b51eb01 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:09 +0530 Subject: [PATCH 0223/1001] proof: certify atlas Batch0223 (12:337 to 12:352) --- Collatz/Research/StoppingAtlas/Batch0223.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0223.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0223.lean b/Collatz/Research/StoppingAtlas/Batch0223.lean new file mode 100644 index 00000000..0dce9fd2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0223.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0223 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 337. -/ +theorem bounds_12_337 : exactInterval 12 337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_337 (m : Nat) : + stoppingTime (2 ^ 12 * m + 337) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_337 : oddCount 337 12 = 7 ∧ acceleratedOrbit 12 337 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_337 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 337) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_337.1, data_12_337.2] + +/-- Complete interval computation for depth 12, residue 338. -/ +theorem bounds_12_338 : exactInterval 12 338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_338 (m : Nat) : + stoppingTime (2 ^ 12 * m + 338) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_338 : oddCount 338 12 = 9 ∧ acceleratedOrbit 12 338 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_338 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 338) = 3 ^ 9 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_338.1, data_12_338.2] + +/-- Complete interval computation for depth 12, residue 339. -/ +theorem bounds_12_339 : exactInterval 12 339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_339 (m : Nat) : + stoppingTime (2 ^ 12 * m + 339) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_339 : oddCount 339 12 = 9 ∧ acceleratedOrbit 12 339 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_339 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 339) = 3 ^ 9 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_339.1, data_12_339.2] + +/-- Complete interval computation for depth 12, residue 340. -/ +theorem bounds_12_340 : exactInterval 12 340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_340 (m : Nat) : + stoppingTime (2 ^ 12 * m + 340) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_340 : oddCount 340 12 = 2 ∧ acceleratedOrbit 12 340 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_340 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 340) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_340.1, data_12_340.2] + +/-- Complete interval computation for depth 12, residue 341. -/ +theorem bounds_12_341 : exactInterval 12 341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_341 (m : Nat) : + stoppingTime (2 ^ 12 * m + 341) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_341 : oddCount 341 12 = 2 ∧ acceleratedOrbit 12 341 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_341 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 341) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_341.1, data_12_341.2] + +/-- Complete interval computation for depth 12, residue 342. -/ +theorem bounds_12_342 : exactInterval 12 342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_342 (m : Nat) : + stoppingTime (2 ^ 12 * m + 342) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_342 : oddCount 342 12 = 6 ∧ acceleratedOrbit 12 342 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_342 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 342) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_342.1, data_12_342.2] + +/-- Complete interval computation for depth 12, residue 343. -/ +theorem bounds_12_343 : exactInterval 12 343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_343 (m : Nat) : + stoppingTime (2 ^ 12 * m + 343) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_343 : oddCount 343 12 = 6 ∧ acceleratedOrbit 12 343 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_343 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 343) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_343.1, data_12_343.2] + +/-- Complete interval computation for depth 12, residue 344. -/ +theorem bounds_12_344 : exactInterval 12 344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_344 (m : Nat) : + stoppingTime (2 ^ 12 * m + 344) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_344 : oddCount 344 12 = 4 ∧ acceleratedOrbit 12 344 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_344 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 344) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_344.1, data_12_344.2] + +/-- Complete interval computation for depth 12, residue 345. -/ +theorem bounds_12_345 : exactInterval 12 345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_345 (m : Nat) : + stoppingTime (2 ^ 12 * m + 345) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_345 : oddCount 345 12 = 7 ∧ acceleratedOrbit 12 345 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_345 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 345) = 3 ^ 7 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_345.1, data_12_345.2] + +/-- Complete interval computation for depth 12, residue 346. -/ +theorem bounds_12_346 : exactInterval 12 346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_346 (m : Nat) : + stoppingTime (2 ^ 12 * m + 346) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_346 : oddCount 346 12 = 4 ∧ acceleratedOrbit 12 346 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_346 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 346) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_346.1, data_12_346.2] + +/-- Complete interval computation for depth 12, residue 347. -/ +theorem bounds_12_347 : exactInterval 12 347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_347 (m : Nat) : + stoppingTime (2 ^ 12 * m + 347) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_347 : oddCount 347 12 = 6 ∧ acceleratedOrbit 12 347 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_347 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 347) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_347.1, data_12_347.2] + +/-- Complete interval computation for depth 12, residue 348. -/ +theorem bounds_12_348 : exactInterval 12 348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_348 (m : Nat) : + stoppingTime (2 ^ 12 * m + 348) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_348 : oddCount 348 12 = 4 ∧ acceleratedOrbit 12 348 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_348 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 348) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_348.1, data_12_348.2] + +/-- Complete interval computation for depth 12, residue 349. -/ +theorem bounds_12_349 : exactInterval 12 349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_349 (m : Nat) : + stoppingTime (2 ^ 12 * m + 349) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_349 : oddCount 349 12 = 4 ∧ acceleratedOrbit 12 349 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_349 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 349) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_349.1, data_12_349.2] + +/-- Complete interval computation for depth 12, residue 350. -/ +theorem bounds_12_350 : exactInterval 12 350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_350 (m : Nat) : + stoppingTime (2 ^ 12 * m + 350) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_350 : oddCount 350 12 = 8 ∧ acceleratedOrbit 12 350 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_350 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 350) = 3 ^ 8 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_350.1, data_12_350.2] + +/-- Complete interval computation for depth 12, residue 351. -/ +theorem bounds_12_351 : exactInterval 12 351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_351 (m : Nat) : + stoppingTime (2 ^ 12 * m + 351) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_351 : oddCount 351 12 = 8 ∧ acceleratedOrbit 12 351 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_351 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 351) = 3 ^ 8 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_351.1, data_12_351.2] + +/-- Complete interval computation for depth 12, residue 352. -/ +theorem bounds_12_352 : exactInterval 12 352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_352 (m : Nat) : + stoppingTime (2 ^ 12 * m + 352) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_352 : oddCount 352 12 = 4 ∧ acceleratedOrbit 12 352 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_352 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 352) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_352.1, data_12_352.2] + +end Collatz.Research.StoppingAtlas.Batch0223 From caab12eb164c4ca82e85bf060def53957c00a701 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:09 +0530 Subject: [PATCH 0224/1001] proof: certify atlas Batch0224 (12:353 to 12:367) --- Collatz/Research/StoppingAtlas/Batch0224.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0224.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0224.lean b/Collatz/Research/StoppingAtlas/Batch0224.lean new file mode 100644 index 00000000..db0ea791 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0224.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0224 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 353. -/ +theorem bounds_12_353 : exactInterval 12 353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_353 (m : Nat) : + stoppingTime (2 ^ 12 * m + 353) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_353 : oddCount 353 12 = 7 ∧ acceleratedOrbit 12 353 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_353 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 353) = 3 ^ 7 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_353.1, data_12_353.2] + +/-- Complete interval computation for depth 12, residue 354. -/ +theorem bounds_12_354 : exactInterval 12 354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_354 (m : Nat) : + stoppingTime (2 ^ 12 * m + 354) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_354 : oddCount 354 12 = 5 ∧ acceleratedOrbit 12 354 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_354 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 354) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_354.1, data_12_354.2] + +/-- Complete interval computation for depth 12, residue 355. -/ +theorem bounds_12_355 : exactInterval 12 355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_355 (m : Nat) : + stoppingTime (2 ^ 12 * m + 355) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_355 : oddCount 355 12 = 5 ∧ acceleratedOrbit 12 355 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_355 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 355) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_355.1, data_12_355.2] + +/-- Complete interval computation for depth 12, residue 356. -/ +theorem bounds_12_356 : exactInterval 12 356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_356 (m : Nat) : + stoppingTime (2 ^ 12 * m + 356) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_356 : oddCount 356 12 = 5 ∧ acceleratedOrbit 12 356 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_356 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 356) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_356.1, data_12_356.2] + +/-- Complete interval computation for depth 12, residue 357. -/ +theorem bounds_12_357 : exactInterval 12 357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_357 (m : Nat) : + stoppingTime (2 ^ 12 * m + 357) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_357 : oddCount 357 12 = 5 ∧ acceleratedOrbit 12 357 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_357 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 357) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_357.1, data_12_357.2] + +/-- Complete interval computation for depth 12, residue 358. -/ +theorem bounds_12_358 : exactInterval 12 358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_358 (m : Nat) : + stoppingTime (2 ^ 12 * m + 358) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_358 : oddCount 358 12 = 5 ∧ acceleratedOrbit 12 358 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_358 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 358) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_358.1, data_12_358.2] + +/-- Complete interval computation for depth 12, residue 359. -/ +theorem bounds_12_359 : exactInterval 12 359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_359 (m : Nat) : + stoppingTime (2 ^ 12 * m + 359) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_359 : oddCount 359 12 = 8 ∧ acceleratedOrbit 12 359 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_359 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 359) = 3 ^ 8 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_359.1, data_12_359.2] + +/-- Complete interval computation for depth 12, residue 360. -/ +theorem bounds_12_360 : exactInterval 12 360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_360 (m : Nat) : + stoppingTime (2 ^ 12 * m + 360) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_360 : oddCount 360 12 = 4 ∧ acceleratedOrbit 12 360 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_360 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 360) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_360.1, data_12_360.2] + +/-- Complete interval computation for depth 12, residue 361. -/ +theorem bounds_12_361 : exactInterval 12 361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_361 (m : Nat) : + stoppingTime (2 ^ 12 * m + 361) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_361 : oddCount 361 12 = 6 ∧ acceleratedOrbit 12 361 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_361 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 361) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_361.1, data_12_361.2] + +/-- Complete interval computation for depth 12, residue 362. -/ +theorem bounds_12_362 : exactInterval 12 362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_362 (m : Nat) : + stoppingTime (2 ^ 12 * m + 362) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_362 : oddCount 362 12 = 4 ∧ acceleratedOrbit 12 362 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_362 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 362) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_362.1, data_12_362.2] + +/-- Complete interval computation for depth 12, residue 363. -/ +theorem bounds_12_363 : exactInterval 12 363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_363 (m : Nat) : + stoppingTime (2 ^ 12 * m + 363) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_363 : oddCount 363 12 = 6 ∧ acceleratedOrbit 12 363 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_363 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 363) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_363.1, data_12_363.2] + +/-- Complete interval computation for depth 12, residue 364. -/ +theorem bounds_12_364 : exactInterval 12 364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_364 (m : Nat) : + stoppingTime (2 ^ 12 * m + 364) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_364 : oddCount 364 12 = 8 ∧ acceleratedOrbit 12 364 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_364 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 364) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_364.1, data_12_364.2] + +/-- Complete interval computation for depth 12, residue 365. -/ +theorem bounds_12_365 : exactInterval 12 365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_365 (m : Nat) : + stoppingTime (2 ^ 12 * m + 365) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_365 : oddCount 365 12 = 8 ∧ acceleratedOrbit 12 365 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_365 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 365) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_365.1, data_12_365.2] + +/-- Complete interval computation for depth 12, residue 366. -/ +theorem bounds_12_366 : exactInterval 12 366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_366 (m : Nat) : + stoppingTime (2 ^ 12 * m + 366) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_366 : oddCount 366 12 = 8 ∧ acceleratedOrbit 12 366 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_366 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 366) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_366.1, data_12_366.2] + +/-- Complete interval computation for depth 12, residue 367. -/ +theorem bounds_12_367 : exactInterval 12 367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_367 (m : Nat) : + stoppingTime (2 ^ 12 * m + 367) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_367 : oddCount 367 12 = 7 ∧ acceleratedOrbit 12 367 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_367 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 367) = 3 ^ 7 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_367.1, data_12_367.2] + +end Collatz.Research.StoppingAtlas.Batch0224 From 98ccd3a986ef96f9a0e53a2e2530de62944b237c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:10 +0530 Subject: [PATCH 0225/1001] proof: certify atlas Batch0225 (12:368 to 12:383) --- Collatz/Research/StoppingAtlas/Batch0225.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0225.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0225.lean b/Collatz/Research/StoppingAtlas/Batch0225.lean new file mode 100644 index 00000000..6a75aab9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0225.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0225 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 368. -/ +theorem bounds_12_368 : exactInterval 12 368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_368 (m : Nat) : + stoppingTime (2 ^ 12 * m + 368) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_368 : oddCount 368 12 = 4 ∧ acceleratedOrbit 12 368 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_368 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 368) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_368.1, data_12_368.2] + +/-- Complete interval computation for depth 12, residue 369. -/ +theorem bounds_12_369 : exactInterval 12 369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_369 (m : Nat) : + stoppingTime (2 ^ 12 * m + 369) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_369 : oddCount 369 12 = 4 ∧ acceleratedOrbit 12 369 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_369 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 369) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_369.1, data_12_369.2] + +/-- Complete interval computation for depth 12, residue 370. -/ +theorem bounds_12_370 : exactInterval 12 370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_370 (m : Nat) : + stoppingTime (2 ^ 12 * m + 370) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_370 : oddCount 370 12 = 6 ∧ acceleratedOrbit 12 370 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_370 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 370) = 3 ^ 6 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_370.1, data_12_370.2] + +/-- Complete interval computation for depth 12, residue 371. -/ +theorem bounds_12_371 : exactInterval 12 371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_371 (m : Nat) : + stoppingTime (2 ^ 12 * m + 371) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_371 : oddCount 371 12 = 6 ∧ acceleratedOrbit 12 371 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_371 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 371) = 3 ^ 6 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_371.1, data_12_371.2] + +/-- Complete interval computation for depth 12, residue 372. -/ +theorem bounds_12_372 : exactInterval 12 372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_372 (m : Nat) : + stoppingTime (2 ^ 12 * m + 372) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_372 : oddCount 372 12 = 4 ∧ acceleratedOrbit 12 372 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_372 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 372) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_372.1, data_12_372.2] + +/-- Complete interval computation for depth 12, residue 373. -/ +theorem bounds_12_373 : exactInterval 12 373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_373 (m : Nat) : + stoppingTime (2 ^ 12 * m + 373) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_373 : oddCount 373 12 = 4 ∧ acceleratedOrbit 12 373 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_373 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 373) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_373.1, data_12_373.2] + +/-- Complete interval computation for depth 12, residue 374. -/ +theorem bounds_12_374 : exactInterval 12 374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_374 (m : Nat) : + stoppingTime (2 ^ 12 * m + 374) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_374 : oddCount 374 12 = 7 ∧ acceleratedOrbit 12 374 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_374 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 374) = 3 ^ 7 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_374.1, data_12_374.2] + +/-- Complete interval computation for depth 12, residue 375. -/ +theorem bounds_12_375 : exactInterval 12 375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_375 (m : Nat) : + stoppingTime (2 ^ 12 * m + 375) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_375 : oddCount 375 12 = 7 ∧ acceleratedOrbit 12 375 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_375 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 375) = 3 ^ 7 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_375.1, data_12_375.2] + +/-- Complete interval computation for depth 12, residue 376. -/ +theorem bounds_12_376 : exactInterval 12 376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_376 (m : Nat) : + stoppingTime (2 ^ 12 * m + 376) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_376 : oddCount 376 12 = 7 ∧ acceleratedOrbit 12 376 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_376 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 376) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_376.1, data_12_376.2] + +/-- Complete interval computation for depth 12, residue 377. -/ +theorem bounds_12_377 : exactInterval 12 377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_377 (m : Nat) : + stoppingTime (2 ^ 12 * m + 377) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_377 : oddCount 377 12 = 9 ∧ acceleratedOrbit 12 377 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_377 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 377) = 3 ^ 9 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_377.1, data_12_377.2] + +/-- Complete interval computation for depth 12, residue 378. -/ +theorem bounds_12_378 : exactInterval 12 378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_378 (m : Nat) : + stoppingTime (2 ^ 12 * m + 378) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_378 : oddCount 378 12 = 7 ∧ acceleratedOrbit 12 378 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_378 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 378) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_378.1, data_12_378.2] + +/-- Complete interval computation for depth 12, residue 379. -/ +theorem bounds_12_379 : exactInterval 12 379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_379 (m : Nat) : + stoppingTime (2 ^ 12 * m + 379) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_379 : oddCount 379 12 = 8 ∧ acceleratedOrbit 12 379 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_379 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 379) = 3 ^ 8 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_379.1, data_12_379.2] + +/-- Complete interval computation for depth 12, residue 380. -/ +theorem bounds_12_380 : exactInterval 12 380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_380 (m : Nat) : + stoppingTime (2 ^ 12 * m + 380) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_380 : oddCount 380 12 = 7 ∧ acceleratedOrbit 12 380 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_380 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 380) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_380.1, data_12_380.2] + +/-- Complete interval computation for depth 12, residue 381. -/ +theorem bounds_12_381 : exactInterval 12 381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_381 (m : Nat) : + stoppingTime (2 ^ 12 * m + 381) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_381 : oddCount 381 12 = 7 ∧ acceleratedOrbit 12 381 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_381 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 381) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_381.1, data_12_381.2] + +/-- Complete interval computation for depth 12, residue 382. -/ +theorem bounds_12_382 : exactInterval 12 382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_382 (m : Nat) : + stoppingTime (2 ^ 12 * m + 382) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_382 : oddCount 382 12 = 7 ∧ acceleratedOrbit 12 382 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_382 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 382) = 3 ^ 7 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_382.1, data_12_382.2] + +/-- Complete interval computation for depth 12, residue 383. -/ +theorem bounds_12_383 : exactInterval 12 383 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_383 (m : Nat) : + stoppingTime (2 ^ 12 * m + 383) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_383 : oddCount 383 12 = 7 ∧ acceleratedOrbit 12 383 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_383 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 383) = 3 ^ 7 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_383.1, data_12_383.2] + +end Collatz.Research.StoppingAtlas.Batch0225 From 672cd046a06783a5c32b544ee89ed45841684e8f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:10 +0530 Subject: [PATCH 0226/1001] proof: certify atlas Batch0226 (12:384 to 12:398) --- Collatz/Research/StoppingAtlas/Batch0226.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0226.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0226.lean b/Collatz/Research/StoppingAtlas/Batch0226.lean new file mode 100644 index 00000000..e95427b8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0226.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0226 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 384. -/ +theorem bounds_12_384 : exactInterval 12 384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_384 (m : Nat) : + stoppingTime (2 ^ 12 * m + 384) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_384 : oddCount 384 12 = 2 ∧ acceleratedOrbit 12 384 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_384 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 384) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_384.1, data_12_384.2] + +/-- Complete interval computation for depth 12, residue 385. -/ +theorem bounds_12_385 : exactInterval 12 385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_385 (m : Nat) : + stoppingTime (2 ^ 12 * m + 385) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_385 : oddCount 385 12 = 5 ∧ acceleratedOrbit 12 385 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_385 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 385) = 3 ^ 5 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_385.1, data_12_385.2] + +/-- Complete interval computation for depth 12, residue 386. -/ +theorem bounds_12_386 : exactInterval 12 386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_386 (m : Nat) : + stoppingTime (2 ^ 12 * m + 386) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_386 : oddCount 386 12 = 6 ∧ acceleratedOrbit 12 386 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_386 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 386) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_386.1, data_12_386.2] + +/-- Complete interval computation for depth 12, residue 387. -/ +theorem bounds_12_387 : exactInterval 12 387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_387 (m : Nat) : + stoppingTime (2 ^ 12 * m + 387) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_387 : oddCount 387 12 = 6 ∧ acceleratedOrbit 12 387 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_387 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 387) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_387.1, data_12_387.2] + +/-- Complete interval computation for depth 12, residue 388. -/ +theorem bounds_12_388 : exactInterval 12 388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_388 (m : Nat) : + stoppingTime (2 ^ 12 * m + 388) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_388 : oddCount 388 12 = 6 ∧ acceleratedOrbit 12 388 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_388 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 388) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_388.1, data_12_388.2] + +/-- Complete interval computation for depth 12, residue 389. -/ +theorem bounds_12_389 : exactInterval 12 389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_389 (m : Nat) : + stoppingTime (2 ^ 12 * m + 389) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_389 : oddCount 389 12 = 6 ∧ acceleratedOrbit 12 389 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_389 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 389) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_389.1, data_12_389.2] + +/-- Complete interval computation for depth 12, residue 390. -/ +theorem bounds_12_390 : exactInterval 12 390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_390 (m : Nat) : + stoppingTime (2 ^ 12 * m + 390) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_390 : oddCount 390 12 = 6 ∧ acceleratedOrbit 12 390 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_390 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 390) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_390.1, data_12_390.2] + +/-- Complete interval computation for depth 12, residue 391. -/ +theorem bounds_12_391 : exactInterval 12 391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_391 (m : Nat) : + stoppingTime (2 ^ 12 * m + 391) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_391 : oddCount 391 12 = 6 ∧ acceleratedOrbit 12 391 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_391 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 391) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_391.1, data_12_391.2] + +/-- Complete interval computation for depth 12, residue 392. -/ +theorem bounds_12_392 : exactInterval 12 392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_392 (m : Nat) : + stoppingTime (2 ^ 12 * m + 392) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_392 : oddCount 392 12 = 5 ∧ acceleratedOrbit 12 392 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_392 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 392) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_392.1, data_12_392.2] + +/-- Complete interval computation for depth 12, residue 393. -/ +theorem bounds_12_393 : exactInterval 12 393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_393 (m : Nat) : + stoppingTime (2 ^ 12 * m + 393) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_393 : oddCount 393 12 = 7 ∧ acceleratedOrbit 12 393 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_393 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 393) = 3 ^ 7 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_393.1, data_12_393.2] + +/-- Complete interval computation for depth 12, residue 394. -/ +theorem bounds_12_394 : exactInterval 12 394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_394 (m : Nat) : + stoppingTime (2 ^ 12 * m + 394) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_394 : oddCount 394 12 = 5 ∧ acceleratedOrbit 12 394 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_394 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 394) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_394.1, data_12_394.2] + +/-- Complete interval computation for depth 12, residue 395. -/ +theorem bounds_12_395 : exactInterval 12 395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_395 (m : Nat) : + stoppingTime (2 ^ 12 * m + 395) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_395 : oddCount 395 12 = 8 ∧ acceleratedOrbit 12 395 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_395 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 395) = 3 ^ 8 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_395.1, data_12_395.2] + +/-- Complete interval computation for depth 12, residue 396. -/ +theorem bounds_12_396 : exactInterval 12 396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_396 (m : Nat) : + stoppingTime (2 ^ 12 * m + 396) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_396 : oddCount 396 12 = 5 ∧ acceleratedOrbit 12 396 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_396 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 396) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_396.1, data_12_396.2] + +/-- Complete interval computation for depth 12, residue 397. -/ +theorem bounds_12_397 : exactInterval 12 397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_397 (m : Nat) : + stoppingTime (2 ^ 12 * m + 397) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_397 : oddCount 397 12 = 5 ∧ acceleratedOrbit 12 397 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_397 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 397) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_397.1, data_12_397.2] + +/-- Complete interval computation for depth 12, residue 398. -/ +theorem bounds_12_398 : exactInterval 12 398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_398 (m : Nat) : + stoppingTime (2 ^ 12 * m + 398) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_398 : oddCount 398 12 = 7 ∧ acceleratedOrbit 12 398 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_398 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 398) = 3 ^ 7 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_398.1, data_12_398.2] + +end Collatz.Research.StoppingAtlas.Batch0226 From 2c83a19fde4ce3de060aed29acbe8073b44029d3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:10 +0530 Subject: [PATCH 0227/1001] proof: certify atlas Batch0227 (12:399 to 12:413) --- Collatz/Research/StoppingAtlas/Batch0227.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0227.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0227.lean b/Collatz/Research/StoppingAtlas/Batch0227.lean new file mode 100644 index 00000000..11721fbf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0227.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0227 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 399. -/ +theorem bounds_12_399 : exactInterval 12 399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_399 (m : Nat) : + stoppingTime (2 ^ 12 * m + 399) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_399 : oddCount 399 12 = 7 ∧ acceleratedOrbit 12 399 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_399 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 399) = 3 ^ 7 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_399.1, data_12_399.2] + +/-- Complete interval computation for depth 12, residue 400. -/ +theorem bounds_12_400 : exactInterval 12 400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_400 (m : Nat) : + stoppingTime (2 ^ 12 * m + 400) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_400 : oddCount 400 12 = 5 ∧ acceleratedOrbit 12 400 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_400 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 400) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_400.1, data_12_400.2] + +/-- Complete interval computation for depth 12, residue 401. -/ +theorem bounds_12_401 : exactInterval 12 401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_401 (m : Nat) : + stoppingTime (2 ^ 12 * m + 401) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_401 : oddCount 401 12 = 4 ∧ acceleratedOrbit 12 401 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_401 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 401) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_401.1, data_12_401.2] + +/-- Complete interval computation for depth 12, residue 402. -/ +theorem bounds_12_402 : exactInterval 12 402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_402 (m : Nat) : + stoppingTime (2 ^ 12 * m + 402) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_402 : oddCount 402 12 = 4 ∧ acceleratedOrbit 12 402 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_402 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 402) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_402.1, data_12_402.2] + +/-- Complete interval computation for depth 12, residue 403. -/ +theorem bounds_12_403 : exactInterval 12 403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_403 (m : Nat) : + stoppingTime (2 ^ 12 * m + 403) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_403 : oddCount 403 12 = 4 ∧ acceleratedOrbit 12 403 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_403 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 403) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_403.1, data_12_403.2] + +/-- Complete interval computation for depth 12, residue 404. -/ +theorem bounds_12_404 : exactInterval 12 404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_404 (m : Nat) : + stoppingTime (2 ^ 12 * m + 404) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_404 : oddCount 404 12 = 5 ∧ acceleratedOrbit 12 404 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_404 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 404) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_404.1, data_12_404.2] + +/-- Complete interval computation for depth 12, residue 405. -/ +theorem bounds_12_405 : exactInterval 12 405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_405 (m : Nat) : + stoppingTime (2 ^ 12 * m + 405) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_405 : oddCount 405 12 = 5 ∧ acceleratedOrbit 12 405 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_405 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 405) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_405.1, data_12_405.2] + +/-- Complete interval computation for depth 12, residue 406. -/ +theorem bounds_12_406 : exactInterval 12 406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_406 (m : Nat) : + stoppingTime (2 ^ 12 * m + 406) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_406 : oddCount 406 12 = 6 ∧ acceleratedOrbit 12 406 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_406 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 406) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_406.1, data_12_406.2] + +/-- Complete interval computation for depth 12, residue 407. -/ +theorem bounds_12_407 : exactInterval 12 407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_407 (m : Nat) : + stoppingTime (2 ^ 12 * m + 407) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_407 : oddCount 407 12 = 6 ∧ acceleratedOrbit 12 407 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_407 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 407) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_407.1, data_12_407.2] + +/-- Complete interval computation for depth 12, residue 408. -/ +theorem bounds_12_408 : exactInterval 12 408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_408 (m : Nat) : + stoppingTime (2 ^ 12 * m + 408) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_408 : oddCount 408 12 = 5 ∧ acceleratedOrbit 12 408 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_408 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 408) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_408.1, data_12_408.2] + +/-- Complete interval computation for depth 12, residue 409. -/ +theorem bounds_12_409 : exactInterval 12 409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_409 (m : Nat) : + stoppingTime (2 ^ 12 * m + 409) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_409 : oddCount 409 12 = 6 ∧ acceleratedOrbit 12 409 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_409 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 409) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_409.1, data_12_409.2] + +/-- Complete interval computation for depth 12, residue 410. -/ +theorem bounds_12_410 : exactInterval 12 410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_410 (m : Nat) : + stoppingTime (2 ^ 12 * m + 410) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_410 : oddCount 410 12 = 5 ∧ acceleratedOrbit 12 410 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_410 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 410) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_410.1, data_12_410.2] + +/-- Complete interval computation for depth 12, residue 411. -/ +theorem bounds_12_411 : exactInterval 12 411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_411 (m : Nat) : + stoppingTime (2 ^ 12 * m + 411) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_411 : oddCount 411 12 = 8 ∧ acceleratedOrbit 12 411 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_411 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 411) = 3 ^ 8 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_411.1, data_12_411.2] + +/-- Complete interval computation for depth 12, residue 412. -/ +theorem bounds_12_412 : exactInterval 12 412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_412 (m : Nat) : + stoppingTime (2 ^ 12 * m + 412) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_412 : oddCount 412 12 = 8 ∧ acceleratedOrbit 12 412 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_412 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 412) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_412.1, data_12_412.2] + +/-- Complete interval computation for depth 12, residue 413. -/ +theorem bounds_12_413 : exactInterval 12 413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_413 (m : Nat) : + stoppingTime (2 ^ 12 * m + 413) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_413 : oddCount 413 12 = 8 ∧ acceleratedOrbit 12 413 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_413 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 413) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_413.1, data_12_413.2] + +end Collatz.Research.StoppingAtlas.Batch0227 From aac5729e5662f90837277c7c9bc7ef6cae8ae95f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:11 +0530 Subject: [PATCH 0228/1001] proof: certify atlas Batch0228 (12:414 to 12:429) --- Collatz/Research/StoppingAtlas/Batch0228.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0228.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0228.lean b/Collatz/Research/StoppingAtlas/Batch0228.lean new file mode 100644 index 00000000..95ebeba1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0228.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0228 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 414. -/ +theorem bounds_12_414 : exactInterval 12 414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_414 (m : Nat) : + stoppingTime (2 ^ 12 * m + 414) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_414 : oddCount 414 12 = 8 ∧ acceleratedOrbit 12 414 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_414 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 414) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_414.1, data_12_414.2] + +/-- Complete interval computation for depth 12, residue 415. -/ +theorem bounds_12_415 : exactInterval 12 415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_415 (m : Nat) : + stoppingTime (2 ^ 12 * m + 415) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_415 : oddCount 415 12 = 9 ∧ acceleratedOrbit 12 415 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_415 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 415) = 3 ^ 9 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_415.1, data_12_415.2] + +/-- Complete interval computation for depth 12, residue 416. -/ +theorem bounds_12_416 : exactInterval 12 416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_416 (m : Nat) : + stoppingTime (2 ^ 12 * m + 416) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_416 : oddCount 416 12 = 2 ∧ acceleratedOrbit 12 416 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_416 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 416) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_416.1, data_12_416.2] + +/-- Complete interval computation for depth 12, residue 417. -/ +theorem bounds_12_417 : exactInterval 12 417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_417 (m : Nat) : + stoppingTime (2 ^ 12 * m + 417) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_417 : oddCount 417 12 = 8 ∧ acceleratedOrbit 12 417 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_417 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 417) = 3 ^ 8 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_417.1, data_12_417.2] + +/-- Complete interval computation for depth 12, residue 418. -/ +theorem bounds_12_418 : exactInterval 12 418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_418 (m : Nat) : + stoppingTime (2 ^ 12 * m + 418) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_418 : oddCount 418 12 = 6 ∧ acceleratedOrbit 12 418 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_418 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 418) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_418.1, data_12_418.2] + +/-- Complete interval computation for depth 12, residue 419. -/ +theorem bounds_12_419 : exactInterval 12 419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_419 (m : Nat) : + stoppingTime (2 ^ 12 * m + 419) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_419 : oddCount 419 12 = 6 ∧ acceleratedOrbit 12 419 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_419 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 419) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_419.1, data_12_419.2] + +/-- Complete interval computation for depth 12, residue 420. -/ +theorem bounds_12_420 : exactInterval 12 420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_420 (m : Nat) : + stoppingTime (2 ^ 12 * m + 420) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_420 : oddCount 420 12 = 6 ∧ acceleratedOrbit 12 420 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_420 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 420) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_420.1, data_12_420.2] + +/-- Complete interval computation for depth 12, residue 421. -/ +theorem bounds_12_421 : exactInterval 12 421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_421 (m : Nat) : + stoppingTime (2 ^ 12 * m + 421) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_421 : oddCount 421 12 = 6 ∧ acceleratedOrbit 12 421 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_421 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 421) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_421.1, data_12_421.2] + +/-- Complete interval computation for depth 12, residue 422. -/ +theorem bounds_12_422 : exactInterval 12 422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_422 (m : Nat) : + stoppingTime (2 ^ 12 * m + 422) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_422 : oddCount 422 12 = 6 ∧ acceleratedOrbit 12 422 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_422 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 422) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_422.1, data_12_422.2] + +/-- Complete interval computation for depth 12, residue 423. -/ +theorem bounds_12_423 : exactInterval 12 423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_423 (m : Nat) : + stoppingTime (2 ^ 12 * m + 423) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_423 : oddCount 423 12 = 7 ∧ acceleratedOrbit 12 423 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_423 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 423) = 3 ^ 7 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_423.1, data_12_423.2] + +/-- Complete interval computation for depth 12, residue 424. -/ +theorem bounds_12_424 : exactInterval 12 424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_424 (m : Nat) : + stoppingTime (2 ^ 12 * m + 424) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_424 : oddCount 424 12 = 2 ∧ acceleratedOrbit 12 424 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_424 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 424) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_424.1, data_12_424.2] + +/-- Complete interval computation for depth 12, residue 425. -/ +theorem bounds_12_425 : exactInterval 12 425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_425 (m : Nat) : + stoppingTime (2 ^ 12 * m + 425) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_425 : oddCount 425 12 = 9 ∧ acceleratedOrbit 12 425 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_425 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 425) = 3 ^ 9 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_425.1, data_12_425.2] + +/-- Complete interval computation for depth 12, residue 426. -/ +theorem bounds_12_426 : exactInterval 12 426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_426 (m : Nat) : + stoppingTime (2 ^ 12 * m + 426) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_426 : oddCount 426 12 = 2 ∧ acceleratedOrbit 12 426 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_426 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 426) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_426.1, data_12_426.2] + +/-- Complete interval computation for depth 12, residue 427. -/ +theorem bounds_12_427 : exactInterval 12 427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_427 (m : Nat) : + stoppingTime (2 ^ 12 * m + 427) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_427 : oddCount 427 12 = 8 ∧ acceleratedOrbit 12 427 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_427 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 427) = 3 ^ 8 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_427.1, data_12_427.2] + +/-- Complete interval computation for depth 12, residue 428. -/ +theorem bounds_12_428 : exactInterval 12 428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_428 (m : Nat) : + stoppingTime (2 ^ 12 * m + 428) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_428 : oddCount 428 12 = 7 ∧ acceleratedOrbit 12 428 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_428 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 428) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_428.1, data_12_428.2] + +/-- Complete interval computation for depth 12, residue 429. -/ +theorem bounds_12_429 : exactInterval 12 429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_429 (m : Nat) : + stoppingTime (2 ^ 12 * m + 429) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_429 : oddCount 429 12 = 7 ∧ acceleratedOrbit 12 429 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_429 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 429) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_429.1, data_12_429.2] + +end Collatz.Research.StoppingAtlas.Batch0228 From f7e1182ef3d4f05528a8021be2209d8931db07bf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:11 +0530 Subject: [PATCH 0229/1001] proof: certify atlas Batch0229 (12:430 to 12:444) --- Collatz/Research/StoppingAtlas/Batch0229.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0229.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0229.lean b/Collatz/Research/StoppingAtlas/Batch0229.lean new file mode 100644 index 00000000..11fca565 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0229.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0229 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 430. -/ +theorem bounds_12_430 : exactInterval 12 430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_430 (m : Nat) : + stoppingTime (2 ^ 12 * m + 430) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_430 : oddCount 430 12 = 7 ∧ acceleratedOrbit 12 430 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_430 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 430) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_430.1, data_12_430.2] + +/-- Complete interval computation for depth 12, residue 431. -/ +theorem bounds_12_431 : exactInterval 12 431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_431 (m : Nat) : + stoppingTime (2 ^ 12 * m + 431) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_431 : oddCount 431 12 = 6 ∧ acceleratedOrbit 12 431 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_431 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 431) = 3 ^ 6 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_431.1, data_12_431.2] + +/-- Complete interval computation for depth 12, residue 432. -/ +theorem bounds_12_432 : exactInterval 12 432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_432 (m : Nat) : + stoppingTime (2 ^ 12 * m + 432) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_432 : oddCount 432 12 = 7 ∧ acceleratedOrbit 12 432 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_432 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 432) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_432.1, data_12_432.2] + +/-- Complete interval computation for depth 12, residue 433. -/ +theorem bounds_12_433 : exactInterval 12 433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_433 (m : Nat) : + stoppingTime (2 ^ 12 * m + 433) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_433 : oddCount 433 12 = 6 ∧ acceleratedOrbit 12 433 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_433 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 433) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_433.1, data_12_433.2] + +/-- Complete interval computation for depth 12, residue 434. -/ +theorem bounds_12_434 : exactInterval 12 434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_434 (m : Nat) : + stoppingTime (2 ^ 12 * m + 434) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_434 : oddCount 434 12 = 6 ∧ acceleratedOrbit 12 434 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_434 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 434) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_434.1, data_12_434.2] + +/-- Complete interval computation for depth 12, residue 435. -/ +theorem bounds_12_435 : exactInterval 12 435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_435 (m : Nat) : + stoppingTime (2 ^ 12 * m + 435) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_435 : oddCount 435 12 = 6 ∧ acceleratedOrbit 12 435 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_435 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 435) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_435.1, data_12_435.2] + +/-- Complete interval computation for depth 12, residue 436. -/ +theorem bounds_12_436 : exactInterval 12 436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_436 (m : Nat) : + stoppingTime (2 ^ 12 * m + 436) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_436 : oddCount 436 12 = 7 ∧ acceleratedOrbit 12 436 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_436 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 436) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_436.1, data_12_436.2] + +/-- Complete interval computation for depth 12, residue 437. -/ +theorem bounds_12_437 : exactInterval 12 437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_437 (m : Nat) : + stoppingTime (2 ^ 12 * m + 437) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_437 : oddCount 437 12 = 7 ∧ acceleratedOrbit 12 437 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_437 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 437) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_437.1, data_12_437.2] + +/-- Complete interval computation for depth 12, residue 438. -/ +theorem bounds_12_438 : exactInterval 12 438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_438 (m : Nat) : + stoppingTime (2 ^ 12 * m + 438) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_438 : oddCount 438 12 = 7 ∧ acceleratedOrbit 12 438 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_438 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 438) = 3 ^ 7 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_438.1, data_12_438.2] + +/-- Complete interval computation for depth 12, residue 439. -/ +theorem bounds_12_439 : exactInterval 12 439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_439 (m : Nat) : + stoppingTime (2 ^ 12 * m + 439) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_439 : oddCount 439 12 = 7 ∧ acceleratedOrbit 12 439 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_439 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 439) = 3 ^ 7 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_439.1, data_12_439.2] + +/-- Complete interval computation for depth 12, residue 440. -/ +theorem bounds_12_440 : exactInterval 12 440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_440 (m : Nat) : + stoppingTime (2 ^ 12 * m + 440) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_440 : oddCount 440 12 = 7 ∧ acceleratedOrbit 12 440 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_440 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 440) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_440.1, data_12_440.2] + +/-- Complete interval computation for depth 12, residue 441. -/ +theorem bounds_12_441 : exactInterval 12 441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_441 (m : Nat) : + stoppingTime (2 ^ 12 * m + 441) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_441 : oddCount 441 12 = 6 ∧ acceleratedOrbit 12 441 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_441 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 441) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_441.1, data_12_441.2] + +/-- Complete interval computation for depth 12, residue 442. -/ +theorem bounds_12_442 : exactInterval 12 442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_442 (m : Nat) : + stoppingTime (2 ^ 12 * m + 442) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_442 : oddCount 442 12 = 7 ∧ acceleratedOrbit 12 442 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_442 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 442) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_442.1, data_12_442.2] + +/-- Complete interval computation for depth 12, residue 443. -/ +theorem bounds_12_443 : exactInterval 12 443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_443 (m : Nat) : + stoppingTime (2 ^ 12 * m + 443) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_443 : oddCount 443 12 = 7 ∧ acceleratedOrbit 12 443 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_443 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 443) = 3 ^ 7 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_443.1, data_12_443.2] + +/-- Complete interval computation for depth 12, residue 444. -/ +theorem bounds_12_444 : exactInterval 12 444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_444 (m : Nat) : + stoppingTime (2 ^ 12 * m + 444) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_444 : oddCount 444 12 = 8 ∧ acceleratedOrbit 12 444 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_444 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 444) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_444.1, data_12_444.2] + +end Collatz.Research.StoppingAtlas.Batch0229 From a36b630502eeb92235aaaf62bad1b96c652ab731 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:12 +0530 Subject: [PATCH 0230/1001] proof: certify atlas Batch0230 (12:445 to 12:459) --- Collatz/Research/StoppingAtlas/Batch0230.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0230.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0230.lean b/Collatz/Research/StoppingAtlas/Batch0230.lean new file mode 100644 index 00000000..8c63fc81 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0230.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0230 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 445. -/ +theorem bounds_12_445 : exactInterval 12 445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_445 (m : Nat) : + stoppingTime (2 ^ 12 * m + 445) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_445 : oddCount 445 12 = 8 ∧ acceleratedOrbit 12 445 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_445 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 445) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_445.1, data_12_445.2] + +/-- Complete interval computation for depth 12, residue 446. -/ +theorem bounds_12_446 : exactInterval 12 446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_446 (m : Nat) : + stoppingTime (2 ^ 12 * m + 446) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_446 : oddCount 446 12 = 8 ∧ acceleratedOrbit 12 446 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_446 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 446) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_446.1, data_12_446.2] + +/-- Complete interval computation for depth 12, residue 447. -/ +theorem bounds_12_447 : exactInterval 12 447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_447 (m : Nat) : + stoppingTime (2 ^ 12 * m + 447) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_447 : oddCount 447 12 = 9 ∧ acceleratedOrbit 12 447 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_447 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 447) = 3 ^ 9 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_447.1, data_12_447.2] + +/-- Complete interval computation for depth 12, residue 448. -/ +theorem bounds_12_448 : exactInterval 12 448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_448 (m : Nat) : + stoppingTime (2 ^ 12 * m + 448) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_448 : oddCount 448 12 = 4 ∧ acceleratedOrbit 12 448 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_448 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 448) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_448.1, data_12_448.2] + +/-- Complete interval computation for depth 12, residue 449. -/ +theorem bounds_12_449 : exactInterval 12 449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_449 (m : Nat) : + stoppingTime (2 ^ 12 * m + 449) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_449 : oddCount 449 12 = 8 ∧ acceleratedOrbit 12 449 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_449 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 449) = 3 ^ 8 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_449.1, data_12_449.2] + +/-- Complete interval computation for depth 12, residue 450. -/ +theorem bounds_12_450 : exactInterval 12 450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_450 (m : Nat) : + stoppingTime (2 ^ 12 * m + 450) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_450 : oddCount 450 12 = 9 ∧ acceleratedOrbit 12 450 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_450 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 450) = 3 ^ 9 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_450.1, data_12_450.2] + +/-- Complete interval computation for depth 12, residue 451. -/ +theorem bounds_12_451 : exactInterval 12 451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_451 (m : Nat) : + stoppingTime (2 ^ 12 * m + 451) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_451 : oddCount 451 12 = 9 ∧ acceleratedOrbit 12 451 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_451 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 451) = 3 ^ 9 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_451.1, data_12_451.2] + +/-- Complete interval computation for depth 12, residue 452. -/ +theorem bounds_12_452 : exactInterval 12 452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_452 (m : Nat) : + stoppingTime (2 ^ 12 * m + 452) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_452 : oddCount 452 12 = 2 ∧ acceleratedOrbit 12 452 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_452 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 452) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_452.1, data_12_452.2] + +/-- Complete interval computation for depth 12, residue 453. -/ +theorem bounds_12_453 : exactInterval 12 453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_453 (m : Nat) : + stoppingTime (2 ^ 12 * m + 453) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_453 : oddCount 453 12 = 2 ∧ acceleratedOrbit 12 453 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_453 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 453) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_453.1, data_12_453.2] + +/-- Complete interval computation for depth 12, residue 454. -/ +theorem bounds_12_454 : exactInterval 12 454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_454 (m : Nat) : + stoppingTime (2 ^ 12 * m + 454) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_454 : oddCount 454 12 = 2 ∧ acceleratedOrbit 12 454 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_454 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 454) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_454.1, data_12_454.2] + +/-- Complete interval computation for depth 12, residue 455. -/ +theorem bounds_12_455 : exactInterval 12 455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_455 (m : Nat) : + stoppingTime (2 ^ 12 * m + 455) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_455 : oddCount 455 12 = 7 ∧ acceleratedOrbit 12 455 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_455 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 455) = 3 ^ 7 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_455.1, data_12_455.2] + +/-- Complete interval computation for depth 12, residue 456. -/ +theorem bounds_12_456 : exactInterval 12 456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_456 (m : Nat) : + stoppingTime (2 ^ 12 * m + 456) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_456 : oddCount 456 12 = 5 ∧ acceleratedOrbit 12 456 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_456 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 456) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_456.1, data_12_456.2] + +/-- Complete interval computation for depth 12, residue 457. -/ +theorem bounds_12_457 : exactInterval 12 457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_457 (m : Nat) : + stoppingTime (2 ^ 12 * m + 457) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_457 : oddCount 457 12 = 6 ∧ acceleratedOrbit 12 457 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_457 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 457) = 3 ^ 6 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_457.1, data_12_457.2] + +/-- Complete interval computation for depth 12, residue 458. -/ +theorem bounds_12_458 : exactInterval 12 458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_458 (m : Nat) : + stoppingTime (2 ^ 12 * m + 458) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_458 : oddCount 458 12 = 5 ∧ acceleratedOrbit 12 458 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_458 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 458) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_458.1, data_12_458.2] + +/-- Complete interval computation for depth 12, residue 459. -/ +theorem bounds_12_459 : exactInterval 12 459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_459 (m : Nat) : + stoppingTime (2 ^ 12 * m + 459) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_459 : oddCount 459 12 = 6 ∧ acceleratedOrbit 12 459 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_459 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 459) = 3 ^ 6 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_459.1, data_12_459.2] + +end Collatz.Research.StoppingAtlas.Batch0230 From 930c4ef8e4413eee7a95e6afe2de81040841b8a2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:12 +0530 Subject: [PATCH 0231/1001] proof: certify atlas Batch0231 (12:460 to 12:475) --- Collatz/Research/StoppingAtlas/Batch0231.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0231.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0231.lean b/Collatz/Research/StoppingAtlas/Batch0231.lean new file mode 100644 index 00000000..f8c49ef3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0231.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0231 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 460. -/ +theorem bounds_12_460 : exactInterval 12 460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_460 (m : Nat) : + stoppingTime (2 ^ 12 * m + 460) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_460 : oddCount 460 12 = 5 ∧ acceleratedOrbit 12 460 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_460 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 460) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_460.1, data_12_460.2] + +/-- Complete interval computation for depth 12, residue 461. -/ +theorem bounds_12_461 : exactInterval 12 461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_461 (m : Nat) : + stoppingTime (2 ^ 12 * m + 461) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_461 : oddCount 461 12 = 5 ∧ acceleratedOrbit 12 461 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_461 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 461) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_461.1, data_12_461.2] + +/-- Complete interval computation for depth 12, residue 462. -/ +theorem bounds_12_462 : exactInterval 12 462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_462 (m : Nat) : + stoppingTime (2 ^ 12 * m + 462) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_462 : oddCount 462 12 = 7 ∧ acceleratedOrbit 12 462 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_462 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 462) = 3 ^ 7 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_462.1, data_12_462.2] + +/-- Complete interval computation for depth 12, residue 463. -/ +theorem bounds_12_463 : exactInterval 12 463 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_463 (m : Nat) : + stoppingTime (2 ^ 12 * m + 463) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_463 : oddCount 463 12 = 7 ∧ acceleratedOrbit 12 463 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_463 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 463) = 3 ^ 7 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_463.1, data_12_463.2] + +/-- Complete interval computation for depth 12, residue 464. -/ +theorem bounds_12_464 : exactInterval 12 464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_464 (m : Nat) : + stoppingTime (2 ^ 12 * m + 464) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_464 : oddCount 464 12 = 4 ∧ acceleratedOrbit 12 464 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_464 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 464) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_464.1, data_12_464.2] + +/-- Complete interval computation for depth 12, residue 465. -/ +theorem bounds_12_465 : exactInterval 12 465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_465 (m : Nat) : + stoppingTime (2 ^ 12 * m + 465) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_465 : oddCount 465 12 = 5 ∧ acceleratedOrbit 12 465 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_465 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 465) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_465.1, data_12_465.2] + +/-- Complete interval computation for depth 12, residue 466. -/ +theorem bounds_12_466 : exactInterval 12 466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_466 (m : Nat) : + stoppingTime (2 ^ 12 * m + 466) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_466 : oddCount 466 12 = 7 ∧ acceleratedOrbit 12 466 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_466 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 466) = 3 ^ 7 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_466.1, data_12_466.2] + +/-- Complete interval computation for depth 12, residue 467. -/ +theorem bounds_12_467 : exactInterval 12 467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_467 (m : Nat) : + stoppingTime (2 ^ 12 * m + 467) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_467 : oddCount 467 12 = 7 ∧ acceleratedOrbit 12 467 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_467 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 467) = 3 ^ 7 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_467.1, data_12_467.2] + +/-- Complete interval computation for depth 12, residue 468. -/ +theorem bounds_12_468 : exactInterval 12 468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_468 (m : Nat) : + stoppingTime (2 ^ 12 * m + 468) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_468 : oddCount 468 12 = 4 ∧ acceleratedOrbit 12 468 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_468 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 468) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_468.1, data_12_468.2] + +/-- Complete interval computation for depth 12, residue 469. -/ +theorem bounds_12_469 : exactInterval 12 469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_469 (m : Nat) : + stoppingTime (2 ^ 12 * m + 469) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_469 : oddCount 469 12 = 4 ∧ acceleratedOrbit 12 469 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_469 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 469) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_469.1, data_12_469.2] + +/-- Complete interval computation for depth 12, residue 470. -/ +theorem bounds_12_470 : exactInterval 12 470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_470 (m : Nat) : + stoppingTime (2 ^ 12 * m + 470) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_470 : oddCount 470 12 = 7 ∧ acceleratedOrbit 12 470 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_470 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 470) = 3 ^ 7 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_470.1, data_12_470.2] + +/-- Complete interval computation for depth 12, residue 471. -/ +theorem bounds_12_471 : exactInterval 12 471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_471 (m : Nat) : + stoppingTime (2 ^ 12 * m + 471) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_471 : oddCount 471 12 = 7 ∧ acceleratedOrbit 12 471 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_471 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 471) = 3 ^ 7 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_471.1, data_12_471.2] + +/-- Complete interval computation for depth 12, residue 472. -/ +theorem bounds_12_472 : exactInterval 12 472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_472 (m : Nat) : + stoppingTime (2 ^ 12 * m + 472) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_472 : oddCount 472 12 = 5 ∧ acceleratedOrbit 12 472 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_472 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 472) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_472.1, data_12_472.2] + +/-- Complete interval computation for depth 12, residue 473. -/ +theorem bounds_12_473 : exactInterval 12 473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_473 (m : Nat) : + stoppingTime (2 ^ 12 * m + 473) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_473 : oddCount 473 12 = 5 ∧ acceleratedOrbit 12 473 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_473 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 473) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_473.1, data_12_473.2] + +/-- Complete interval computation for depth 12, residue 474. -/ +theorem bounds_12_474 : exactInterval 12 474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_474 (m : Nat) : + stoppingTime (2 ^ 12 * m + 474) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_474 : oddCount 474 12 = 5 ∧ acceleratedOrbit 12 474 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_474 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 474) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_474.1, data_12_474.2] + +/-- Complete interval computation for depth 12, residue 475. -/ +theorem bounds_12_475 : exactInterval 12 475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_475 (m : Nat) : + stoppingTime (2 ^ 12 * m + 475) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_475 : oddCount 475 12 = 6 ∧ acceleratedOrbit 12 475 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_475 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 475) = 3 ^ 6 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_475.1, data_12_475.2] + +end Collatz.Research.StoppingAtlas.Batch0231 From 27c0a556b971de87bd9e9c311627e52ceba3fe9f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:12 +0530 Subject: [PATCH 0232/1001] proof: certify atlas Batch0232 (12:476 to 12:490) --- Collatz/Research/StoppingAtlas/Batch0232.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0232.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0232.lean b/Collatz/Research/StoppingAtlas/Batch0232.lean new file mode 100644 index 00000000..3960171d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0232.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0232 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 476. -/ +theorem bounds_12_476 : exactInterval 12 476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_476 (m : Nat) : + stoppingTime (2 ^ 12 * m + 476) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_476 : oddCount 476 12 = 5 ∧ acceleratedOrbit 12 476 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_476 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 476) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_476.1, data_12_476.2] + +/-- Complete interval computation for depth 12, residue 477. -/ +theorem bounds_12_477 : exactInterval 12 477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_477 (m : Nat) : + stoppingTime (2 ^ 12 * m + 477) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_477 : oddCount 477 12 = 5 ∧ acceleratedOrbit 12 477 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_477 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 477) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_477.1, data_12_477.2] + +/-- Complete interval computation for depth 12, residue 478. -/ +theorem bounds_12_478 : exactInterval 12 478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_478 (m : Nat) : + stoppingTime (2 ^ 12 * m + 478) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_478 : oddCount 478 12 = 9 ∧ acceleratedOrbit 12 478 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_478 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 478) = 3 ^ 9 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_478.1, data_12_478.2] + +/-- Complete interval computation for depth 12, residue 479. -/ +theorem bounds_12_479 : exactInterval 12 479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_479 (m : Nat) : + stoppingTime (2 ^ 12 * m + 479) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_479 : oddCount 479 12 = 9 ∧ acceleratedOrbit 12 479 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_479 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 479) = 3 ^ 9 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_479.1, data_12_479.2] + +/-- Complete interval computation for depth 12, residue 480. -/ +theorem bounds_12_480 : exactInterval 12 480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_480 (m : Nat) : + stoppingTime (2 ^ 12 * m + 480) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_480 : oddCount 480 12 = 4 ∧ acceleratedOrbit 12 480 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_480 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 480) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_480.1, data_12_480.2] + +/-- Complete interval computation for depth 12, residue 481. -/ +theorem bounds_12_481 : exactInterval 12 481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_481 (m : Nat) : + stoppingTime (2 ^ 12 * m + 481) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_481 : oddCount 481 12 = 6 ∧ acceleratedOrbit 12 481 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_481 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 481) = 3 ^ 6 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_481.1, data_12_481.2] + +/-- Complete interval computation for depth 12, residue 482. -/ +theorem bounds_12_482 : exactInterval 12 482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_482 (m : Nat) : + stoppingTime (2 ^ 12 * m + 482) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_482 : oddCount 482 12 = 4 ∧ acceleratedOrbit 12 482 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_482 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 482) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_482.1, data_12_482.2] + +/-- Complete interval computation for depth 12, residue 483. -/ +theorem bounds_12_483 : exactInterval 12 483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_483 (m : Nat) : + stoppingTime (2 ^ 12 * m + 483) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_483 : oddCount 483 12 = 4 ∧ acceleratedOrbit 12 483 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_483 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 483) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_483.1, data_12_483.2] + +/-- Complete interval computation for depth 12, residue 484. -/ +theorem bounds_12_484 : exactInterval 12 484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_484 (m : Nat) : + stoppingTime (2 ^ 12 * m + 484) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_484 : oddCount 484 12 = 7 ∧ acceleratedOrbit 12 484 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_484 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 484) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_484.1, data_12_484.2] + +/-- Complete interval computation for depth 12, residue 485. -/ +theorem bounds_12_485 : exactInterval 12 485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_485 (m : Nat) : + stoppingTime (2 ^ 12 * m + 485) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_485 : oddCount 485 12 = 7 ∧ acceleratedOrbit 12 485 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_485 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 485) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_485.1, data_12_485.2] + +/-- Complete interval computation for depth 12, residue 486. -/ +theorem bounds_12_486 : exactInterval 12 486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_486 (m : Nat) : + stoppingTime (2 ^ 12 * m + 486) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_486 : oddCount 486 12 = 7 ∧ acceleratedOrbit 12 486 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_486 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 486) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_486.1, data_12_486.2] + +/-- Complete interval computation for depth 12, residue 487. -/ +theorem bounds_12_487 : exactInterval 12 487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_487 (m : Nat) : + stoppingTime (2 ^ 12 * m + 487) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_487 : oddCount 487 12 = 9 ∧ acceleratedOrbit 12 487 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_487 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 487) = 3 ^ 9 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_487.1, data_12_487.2] + +/-- Complete interval computation for depth 12, residue 488. -/ +theorem bounds_12_488 : exactInterval 12 488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_488 (m : Nat) : + stoppingTime (2 ^ 12 * m + 488) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_488 : oddCount 488 12 = 4 ∧ acceleratedOrbit 12 488 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_488 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 488) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_488.1, data_12_488.2] + +/-- Complete interval computation for depth 12, residue 489. -/ +theorem bounds_12_489 : exactInterval 12 489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_489 (m : Nat) : + stoppingTime (2 ^ 12 * m + 489) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_489 : oddCount 489 12 = 7 ∧ acceleratedOrbit 12 489 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_489 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 489) = 3 ^ 7 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_489.1, data_12_489.2] + +/-- Complete interval computation for depth 12, residue 490. -/ +theorem bounds_12_490 : exactInterval 12 490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_490 (m : Nat) : + stoppingTime (2 ^ 12 * m + 490) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_490 : oddCount 490 12 = 4 ∧ acceleratedOrbit 12 490 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_490 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 490) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_490.1, data_12_490.2] + +end Collatz.Research.StoppingAtlas.Batch0232 From ada0ace52a66c67a415586bef9e23352d528665c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:12 +0530 Subject: [PATCH 0233/1001] proof: certify atlas Batch0233 (12:491 to 12:505) --- Collatz/Research/StoppingAtlas/Batch0233.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0233.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0233.lean b/Collatz/Research/StoppingAtlas/Batch0233.lean new file mode 100644 index 00000000..e48026e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0233.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0233 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 491. -/ +theorem bounds_12_491 : exactInterval 12 491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_491 (m : Nat) : + stoppingTime (2 ^ 12 * m + 491) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_491 : oddCount 491 12 = 9 ∧ acceleratedOrbit 12 491 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_491 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 491) = 3 ^ 9 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_491.1, data_12_491.2] + +/-- Complete interval computation for depth 12, residue 492. -/ +theorem bounds_12_492 : exactInterval 12 492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_492 (m : Nat) : + stoppingTime (2 ^ 12 * m + 492) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_492 : oddCount 492 12 = 6 ∧ acceleratedOrbit 12 492 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_492 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 492) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_492.1, data_12_492.2] + +/-- Complete interval computation for depth 12, residue 493. -/ +theorem bounds_12_493 : exactInterval 12 493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_493 (m : Nat) : + stoppingTime (2 ^ 12 * m + 493) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_493 : oddCount 493 12 = 6 ∧ acceleratedOrbit 12 493 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_493 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 493) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_493.1, data_12_493.2] + +/-- Complete interval computation for depth 12, residue 494. -/ +theorem bounds_12_494 : exactInterval 12 494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_494 (m : Nat) : + stoppingTime (2 ^ 12 * m + 494) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_494 : oddCount 494 12 = 6 ∧ acceleratedOrbit 12 494 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_494 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 494) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_494.1, data_12_494.2] + +/-- Complete interval computation for depth 12, residue 495. -/ +theorem bounds_12_495 : exactInterval 12 495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_495 (m : Nat) : + stoppingTime (2 ^ 12 * m + 495) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_495 : oddCount 495 12 = 10 ∧ acceleratedOrbit 12 495 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_495 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 495) = 3 ^ 10 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_495.1, data_12_495.2] + +/-- Complete interval computation for depth 12, residue 496. -/ +theorem bounds_12_496 : exactInterval 12 496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_496 (m : Nat) : + stoppingTime (2 ^ 12 * m + 496) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_496 : oddCount 496 12 = 6 ∧ acceleratedOrbit 12 496 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_496 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 496) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_496.1, data_12_496.2] + +/-- Complete interval computation for depth 12, residue 497. -/ +theorem bounds_12_497 : exactInterval 12 497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_497 (m : Nat) : + stoppingTime (2 ^ 12 * m + 497) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_497 : oddCount 497 12 = 4 ∧ acceleratedOrbit 12 497 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_497 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 497) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_497.1, data_12_497.2] + +/-- Complete interval computation for depth 12, residue 498. -/ +theorem bounds_12_498 : exactInterval 12 498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_498 (m : Nat) : + stoppingTime (2 ^ 12 * m + 498) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_498 : oddCount 498 12 = 7 ∧ acceleratedOrbit 12 498 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_498 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 498) = 3 ^ 7 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_498.1, data_12_498.2] + +/-- Complete interval computation for depth 12, residue 499. -/ +theorem bounds_12_499 : exactInterval 12 499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_499 (m : Nat) : + stoppingTime (2 ^ 12 * m + 499) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_499 : oddCount 499 12 = 7 ∧ acceleratedOrbit 12 499 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_499 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 499) = 3 ^ 7 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_499.1, data_12_499.2] + +/-- Complete interval computation for depth 12, residue 500. -/ +theorem bounds_12_500 : exactInterval 12 500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_500 (m : Nat) : + stoppingTime (2 ^ 12 * m + 500) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_500 : oddCount 500 12 = 6 ∧ acceleratedOrbit 12 500 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_500 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 500) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_500.1, data_12_500.2] + +/-- Complete interval computation for depth 12, residue 501. -/ +theorem bounds_12_501 : exactInterval 12 501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_501 (m : Nat) : + stoppingTime (2 ^ 12 * m + 501) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_501 : oddCount 501 12 = 6 ∧ acceleratedOrbit 12 501 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_501 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 501) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_501.1, data_12_501.2] + +/-- Complete interval computation for depth 12, residue 502. -/ +theorem bounds_12_502 : exactInterval 12 502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_502 (m : Nat) : + stoppingTime (2 ^ 12 * m + 502) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_502 : oddCount 502 12 = 9 ∧ acceleratedOrbit 12 502 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_502 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 502) = 3 ^ 9 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_502.1, data_12_502.2] + +/-- Complete interval computation for depth 12, residue 503. -/ +theorem bounds_12_503 : exactInterval 12 503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_503 (m : Nat) : + stoppingTime (2 ^ 12 * m + 503) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_503 : oddCount 503 12 = 9 ∧ acceleratedOrbit 12 503 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_503 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 503) = 3 ^ 9 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_503.1, data_12_503.2] + +/-- Complete interval computation for depth 12, residue 504. -/ +theorem bounds_12_504 : exactInterval 12 504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_504 (m : Nat) : + stoppingTime (2 ^ 12 * m + 504) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_504 : oddCount 504 12 = 6 ∧ acceleratedOrbit 12 504 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_504 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 504) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_504.1, data_12_504.2] + +/-- Complete interval computation for depth 12, residue 505. -/ +theorem bounds_12_505 : exactInterval 12 505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_505 (m : Nat) : + stoppingTime (2 ^ 12 * m + 505) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_505 : oddCount 505 12 = 7 ∧ acceleratedOrbit 12 505 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_505 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 505) = 3 ^ 7 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_505.1, data_12_505.2] + +end Collatz.Research.StoppingAtlas.Batch0233 From 2bdca0bc4809c168cfc3c5c0636513a175aa1c3d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:13 +0530 Subject: [PATCH 0234/1001] proof: certify atlas Batch0234 (12:506 to 12:521) --- Collatz/Research/StoppingAtlas/Batch0234.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0234.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0234.lean b/Collatz/Research/StoppingAtlas/Batch0234.lean new file mode 100644 index 00000000..b66067b7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0234.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0234 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 506. -/ +theorem bounds_12_506 : exactInterval 12 506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_506 (m : Nat) : + stoppingTime (2 ^ 12 * m + 506) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_506 : oddCount 506 12 = 6 ∧ acceleratedOrbit 12 506 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_506 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 506) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_506.1, data_12_506.2] + +/-- Complete interval computation for depth 12, residue 507. -/ +theorem bounds_12_507 : exactInterval 12 507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_507 (m : Nat) : + stoppingTime (2 ^ 12 * m + 507) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_507 : oddCount 507 12 = 7 ∧ acceleratedOrbit 12 507 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_507 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 507) = 3 ^ 7 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_507.1, data_12_507.2] + +/-- Complete interval computation for depth 12, residue 508. -/ +theorem bounds_12_508 : exactInterval 12 508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_508 (m : Nat) : + stoppingTime (2 ^ 12 * m + 508) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_508 : oddCount 508 12 = 8 ∧ acceleratedOrbit 12 508 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_508 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 508) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_508.1, data_12_508.2] + +/-- Complete interval computation for depth 12, residue 509. -/ +theorem bounds_12_509 : exactInterval 12 509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_509 (m : Nat) : + stoppingTime (2 ^ 12 * m + 509) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_509 : oddCount 509 12 = 8 ∧ acceleratedOrbit 12 509 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_509 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 509) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_509.1, data_12_509.2] + +/-- Complete interval computation for depth 12, residue 510. -/ +theorem bounds_12_510 : exactInterval 12 510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_510 (m : Nat) : + stoppingTime (2 ^ 12 * m + 510) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_510 : oddCount 510 12 = 8 ∧ acceleratedOrbit 12 510 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_510 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 510) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_510.1, data_12_510.2] + +/-- Complete interval computation for depth 12, residue 511. -/ +theorem bounds_12_511 : exactInterval 12 511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_511 (m : Nat) : + stoppingTime (2 ^ 12 * m + 511) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_511 : oddCount 511 12 = 10 ∧ acceleratedOrbit 12 511 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_511 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 511) = 3 ^ 10 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_511.1, data_12_511.2] + +/-- Complete interval computation for depth 12, residue 512. -/ +theorem bounds_12_512 : exactInterval 12 512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_512 (m : Nat) : + stoppingTime (2 ^ 12 * m + 512) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_512 : oddCount 512 12 = 2 ∧ acceleratedOrbit 12 512 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_512 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 512) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_512.1, data_12_512.2] + +/-- Complete interval computation for depth 12, residue 513. -/ +theorem bounds_12_513 : exactInterval 12 513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_513 (m : Nat) : + stoppingTime (2 ^ 12 * m + 513) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_513 : oddCount 513 12 = 6 ∧ acceleratedOrbit 12 513 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_513 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 513) = 3 ^ 6 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_513.1, data_12_513.2] + +/-- Complete interval computation for depth 12, residue 514. -/ +theorem bounds_12_514 : exactInterval 12 514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_514 (m : Nat) : + stoppingTime (2 ^ 12 * m + 514) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_514 : oddCount 514 12 = 5 ∧ acceleratedOrbit 12 514 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_514 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 514) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_514.1, data_12_514.2] + +/-- Complete interval computation for depth 12, residue 515. -/ +theorem bounds_12_515 : exactInterval 12 515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_515 (m : Nat) : + stoppingTime (2 ^ 12 * m + 515) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_515 : oddCount 515 12 = 5 ∧ acceleratedOrbit 12 515 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_515 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 515) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_515.1, data_12_515.2] + +/-- Complete interval computation for depth 12, residue 516. -/ +theorem bounds_12_516 : exactInterval 12 516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_516 (m : Nat) : + stoppingTime (2 ^ 12 * m + 516) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_516 : oddCount 516 12 = 6 ∧ acceleratedOrbit 12 516 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_516 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 516) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_516.1, data_12_516.2] + +/-- Complete interval computation for depth 12, residue 517. -/ +theorem bounds_12_517 : exactInterval 12 517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_517 (m : Nat) : + stoppingTime (2 ^ 12 * m + 517) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_517 : oddCount 517 12 = 6 ∧ acceleratedOrbit 12 517 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_517 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 517) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_517.1, data_12_517.2] + +/-- Complete interval computation for depth 12, residue 518. -/ +theorem bounds_12_518 : exactInterval 12 518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_518 (m : Nat) : + stoppingTime (2 ^ 12 * m + 518) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_518 : oddCount 518 12 = 6 ∧ acceleratedOrbit 12 518 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_518 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 518) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_518.1, data_12_518.2] + +/-- Complete interval computation for depth 12, residue 519. -/ +theorem bounds_12_519 : exactInterval 12 519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_519 (m : Nat) : + stoppingTime (2 ^ 12 * m + 519) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_519 : oddCount 519 12 = 8 ∧ acceleratedOrbit 12 519 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_519 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 519) = 3 ^ 8 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_519.1, data_12_519.2] + +/-- Complete interval computation for depth 12, residue 520. -/ +theorem bounds_12_520 : exactInterval 12 520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_520 (m : Nat) : + stoppingTime (2 ^ 12 * m + 520) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_520 : oddCount 520 12 = 4 ∧ acceleratedOrbit 12 520 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_520 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 520) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_520.1, data_12_520.2] + +/-- Complete interval computation for depth 12, residue 521. -/ +theorem bounds_12_521 : exactInterval 12 521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_521 (m : Nat) : + stoppingTime (2 ^ 12 * m + 521) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_521 : oddCount 521 12 = 5 ∧ acceleratedOrbit 12 521 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_521 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 521) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_521.1, data_12_521.2] + +end Collatz.Research.StoppingAtlas.Batch0234 From 8a53170cd9bd46cd4e41e4f171f0f85811106451 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:13 +0530 Subject: [PATCH 0235/1001] proof: certify atlas Batch0235 (12:522 to 12:536) --- Collatz/Research/StoppingAtlas/Batch0235.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0235.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0235.lean b/Collatz/Research/StoppingAtlas/Batch0235.lean new file mode 100644 index 00000000..6db5c52e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0235.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0235 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 522. -/ +theorem bounds_12_522 : exactInterval 12 522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_522 (m : Nat) : + stoppingTime (2 ^ 12 * m + 522) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_522 : oddCount 522 12 = 4 ∧ acceleratedOrbit 12 522 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_522 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 522) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_522.1, data_12_522.2] + +/-- Complete interval computation for depth 12, residue 523. -/ +theorem bounds_12_523 : exactInterval 12 523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_523 (m : Nat) : + stoppingTime (2 ^ 12 * m + 523) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_523 : oddCount 523 12 = 6 ∧ acceleratedOrbit 12 523 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_523 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 523) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_523.1, data_12_523.2] + +/-- Complete interval computation for depth 12, residue 524. -/ +theorem bounds_12_524 : exactInterval 12 524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_524 (m : Nat) : + stoppingTime (2 ^ 12 * m + 524) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_524 : oddCount 524 12 = 4 ∧ acceleratedOrbit 12 524 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_524 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 524) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_524.1, data_12_524.2] + +/-- Complete interval computation for depth 12, residue 525. -/ +theorem bounds_12_525 : exactInterval 12 525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_525 (m : Nat) : + stoppingTime (2 ^ 12 * m + 525) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_525 : oddCount 525 12 = 4 ∧ acceleratedOrbit 12 525 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_525 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 525) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_525.1, data_12_525.2] + +/-- Complete interval computation for depth 12, residue 526. -/ +theorem bounds_12_526 : exactInterval 12 526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_526 (m : Nat) : + stoppingTime (2 ^ 12 * m + 526) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_526 : oddCount 526 12 = 7 ∧ acceleratedOrbit 12 526 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_526 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 526) = 3 ^ 7 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_526.1, data_12_526.2] + +/-- Complete interval computation for depth 12, residue 527. -/ +theorem bounds_12_527 : exactInterval 12 527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_527 (m : Nat) : + stoppingTime (2 ^ 12 * m + 527) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_527 : oddCount 527 12 = 7 ∧ acceleratedOrbit 12 527 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_527 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 527) = 3 ^ 7 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_527.1, data_12_527.2] + +/-- Complete interval computation for depth 12, residue 528. -/ +theorem bounds_12_528 : exactInterval 12 528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_528 (m : Nat) : + stoppingTime (2 ^ 12 * m + 528) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_528 : oddCount 528 12 = 4 ∧ acceleratedOrbit 12 528 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_528 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 528) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_528.1, data_12_528.2] + +/-- Complete interval computation for depth 12, residue 529. -/ +theorem bounds_12_529 : exactInterval 12 529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_529 (m : Nat) : + stoppingTime (2 ^ 12 * m + 529) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_529 : oddCount 529 12 = 4 ∧ acceleratedOrbit 12 529 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_529 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 529) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_529.1, data_12_529.2] + +/-- Complete interval computation for depth 12, residue 530. -/ +theorem bounds_12_530 : exactInterval 12 530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_530 (m : Nat) : + stoppingTime (2 ^ 12 * m + 530) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_530 : oddCount 530 12 = 6 ∧ acceleratedOrbit 12 530 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_530 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 530) = 3 ^ 6 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_530.1, data_12_530.2] + +/-- Complete interval computation for depth 12, residue 531. -/ +theorem bounds_12_531 : exactInterval 12 531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_531 (m : Nat) : + stoppingTime (2 ^ 12 * m + 531) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_531 : oddCount 531 12 = 6 ∧ acceleratedOrbit 12 531 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_531 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 531) = 3 ^ 6 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_531.1, data_12_531.2] + +/-- Complete interval computation for depth 12, residue 532. -/ +theorem bounds_12_532 : exactInterval 12 532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_532 (m : Nat) : + stoppingTime (2 ^ 12 * m + 532) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_532 : oddCount 532 12 = 4 ∧ acceleratedOrbit 12 532 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_532 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 532) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_532.1, data_12_532.2] + +/-- Complete interval computation for depth 12, residue 533. -/ +theorem bounds_12_533 : exactInterval 12 533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_533 (m : Nat) : + stoppingTime (2 ^ 12 * m + 533) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_533 : oddCount 533 12 = 4 ∧ acceleratedOrbit 12 533 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_533 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 533) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_533.1, data_12_533.2] + +/-- Complete interval computation for depth 12, residue 534. -/ +theorem bounds_12_534 : exactInterval 12 534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_534 (m : Nat) : + stoppingTime (2 ^ 12 * m + 534) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_534 : oddCount 534 12 = 5 ∧ acceleratedOrbit 12 534 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_534 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 534) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_534.1, data_12_534.2] + +/-- Complete interval computation for depth 12, residue 535. -/ +theorem bounds_12_535 : exactInterval 12 535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_535 (m : Nat) : + stoppingTime (2 ^ 12 * m + 535) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_535 : oddCount 535 12 = 5 ∧ acceleratedOrbit 12 535 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_535 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 535) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_535.1, data_12_535.2] + +/-- Complete interval computation for depth 12, residue 536. -/ +theorem bounds_12_536 : exactInterval 12 536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_536 (m : Nat) : + stoppingTime (2 ^ 12 * m + 536) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_536 : oddCount 536 12 = 4 ∧ acceleratedOrbit 12 536 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_536 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 536) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_536.1, data_12_536.2] + +end Collatz.Research.StoppingAtlas.Batch0235 From c4d5a389ee3cc09d5bd9d7153d02704134e2a81a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:14 +0530 Subject: [PATCH 0236/1001] proof: certify atlas Batch0236 (12:537 to 12:551) --- Collatz/Research/StoppingAtlas/Batch0236.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0236.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0236.lean b/Collatz/Research/StoppingAtlas/Batch0236.lean new file mode 100644 index 00000000..5246d60a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0236.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0236 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 537. -/ +theorem bounds_12_537 : exactInterval 12 537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_537 (m : Nat) : + stoppingTime (2 ^ 12 * m + 537) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_537 : oddCount 537 12 = 5 ∧ acceleratedOrbit 12 537 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_537 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 537) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_537.1, data_12_537.2] + +/-- Complete interval computation for depth 12, residue 538. -/ +theorem bounds_12_538 : exactInterval 12 538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_538 (m : Nat) : + stoppingTime (2 ^ 12 * m + 538) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_538 : oddCount 538 12 = 4 ∧ acceleratedOrbit 12 538 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_538 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 538) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_538.1, data_12_538.2] + +/-- Complete interval computation for depth 12, residue 539. -/ +theorem bounds_12_539 : exactInterval 12 539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_539 (m : Nat) : + stoppingTime (2 ^ 12 * m + 539) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_539 : oddCount 539 12 = 8 ∧ acceleratedOrbit 12 539 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_539 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 539) = 3 ^ 8 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_539.1, data_12_539.2] + +/-- Complete interval computation for depth 12, residue 540. -/ +theorem bounds_12_540 : exactInterval 12 540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_540 (m : Nat) : + stoppingTime (2 ^ 12 * m + 540) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_540 : oddCount 540 12 = 6 ∧ acceleratedOrbit 12 540 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_540 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 540) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_540.1, data_12_540.2] + +/-- Complete interval computation for depth 12, residue 541. -/ +theorem bounds_12_541 : exactInterval 12 541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_541 (m : Nat) : + stoppingTime (2 ^ 12 * m + 541) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_541 : oddCount 541 12 = 6 ∧ acceleratedOrbit 12 541 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_541 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 541) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_541.1, data_12_541.2] + +/-- Complete interval computation for depth 12, residue 542. -/ +theorem bounds_12_542 : exactInterval 12 542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_542 (m : Nat) : + stoppingTime (2 ^ 12 * m + 542) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_542 : oddCount 542 12 = 6 ∧ acceleratedOrbit 12 542 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_542 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 542) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_542.1, data_12_542.2] + +/-- Complete interval computation for depth 12, residue 543. -/ +theorem bounds_12_543 : exactInterval 12 543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_543 (m : Nat) : + stoppingTime (2 ^ 12 * m + 543) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_543 : oddCount 543 12 = 8 ∧ acceleratedOrbit 12 543 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_543 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 543) = 3 ^ 8 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_543.1, data_12_543.2] + +/-- Complete interval computation for depth 12, residue 544. -/ +theorem bounds_12_544 : exactInterval 12 544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_544 (m : Nat) : + stoppingTime (2 ^ 12 * m + 544) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_544 : oddCount 544 12 = 3 ∧ acceleratedOrbit 12 544 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_544 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 544) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_544.1, data_12_544.2] + +/-- Complete interval computation for depth 12, residue 545. -/ +theorem bounds_12_545 : exactInterval 12 545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_545 (m : Nat) : + stoppingTime (2 ^ 12 * m + 545) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_545 : oddCount 545 12 = 6 ∧ acceleratedOrbit 12 545 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_545 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 545) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_545.1, data_12_545.2] + +/-- Complete interval computation for depth 12, residue 546. -/ +theorem bounds_12_546 : exactInterval 12 546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_546 (m : Nat) : + stoppingTime (2 ^ 12 * m + 546) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_546 : oddCount 546 12 = 4 ∧ acceleratedOrbit 12 546 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_546 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 546) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_546.1, data_12_546.2] + +/-- Complete interval computation for depth 12, residue 547. -/ +theorem bounds_12_547 : exactInterval 12 547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_547 (m : Nat) : + stoppingTime (2 ^ 12 * m + 547) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_547 : oddCount 547 12 = 4 ∧ acceleratedOrbit 12 547 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_547 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 547) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_547.1, data_12_547.2] + +/-- Complete interval computation for depth 12, residue 548. -/ +theorem bounds_12_548 : exactInterval 12 548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_548 (m : Nat) : + stoppingTime (2 ^ 12 * m + 548) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_548 : oddCount 548 12 = 8 ∧ acceleratedOrbit 12 548 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_548 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 548) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_548.1, data_12_548.2] + +/-- Complete interval computation for depth 12, residue 549. -/ +theorem bounds_12_549 : exactInterval 12 549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_549 (m : Nat) : + stoppingTime (2 ^ 12 * m + 549) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_549 : oddCount 549 12 = 8 ∧ acceleratedOrbit 12 549 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_549 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 549) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_549.1, data_12_549.2] + +/-- Complete interval computation for depth 12, residue 550. -/ +theorem bounds_12_550 : exactInterval 12 550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_550 (m : Nat) : + stoppingTime (2 ^ 12 * m + 550) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_550 : oddCount 550 12 = 8 ∧ acceleratedOrbit 12 550 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_550 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 550) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_550.1, data_12_550.2] + +/-- Complete interval computation for depth 12, residue 551. -/ +theorem bounds_12_551 : exactInterval 12 551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_551 (m : Nat) : + stoppingTime (2 ^ 12 * m + 551) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_551 : oddCount 551 12 = 7 ∧ acceleratedOrbit 12 551 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_551 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 551) = 3 ^ 7 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_551.1, data_12_551.2] + +end Collatz.Research.StoppingAtlas.Batch0236 From 873f91f97cebb542452e7a46c366c5afc325ec4e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:14 +0530 Subject: [PATCH 0237/1001] proof: certify atlas Batch0237 (12:552 to 12:567) --- Collatz/Research/StoppingAtlas/Batch0237.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0237.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0237.lean b/Collatz/Research/StoppingAtlas/Batch0237.lean new file mode 100644 index 00000000..3eeeab4a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0237.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0237 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 552. -/ +theorem bounds_12_552 : exactInterval 12 552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_552 (m : Nat) : + stoppingTime (2 ^ 12 * m + 552) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_552 : oddCount 552 12 = 3 ∧ acceleratedOrbit 12 552 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_552 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 552) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_552.1, data_12_552.2] + +/-- Complete interval computation for depth 12, residue 553. -/ +theorem bounds_12_553 : exactInterval 12 553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_553 (m : Nat) : + stoppingTime (2 ^ 12 * m + 553) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_553 : oddCount 553 12 = 9 ∧ acceleratedOrbit 12 553 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_553 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 553) = 3 ^ 9 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_553.1, data_12_553.2] + +/-- Complete interval computation for depth 12, residue 554. -/ +theorem bounds_12_554 : exactInterval 12 554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_554 (m : Nat) : + stoppingTime (2 ^ 12 * m + 554) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_554 : oddCount 554 12 = 3 ∧ acceleratedOrbit 12 554 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_554 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 554) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_554.1, data_12_554.2] + +/-- Complete interval computation for depth 12, residue 555. -/ +theorem bounds_12_555 : exactInterval 12 555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_555 (m : Nat) : + stoppingTime (2 ^ 12 * m + 555) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_555 : oddCount 555 12 = 4 ∧ acceleratedOrbit 12 555 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_555 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 555) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_555.1, data_12_555.2] + +/-- Complete interval computation for depth 12, residue 556. -/ +theorem bounds_12_556 : exactInterval 12 556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_556 (m : Nat) : + stoppingTime (2 ^ 12 * m + 556) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_556 : oddCount 556 12 = 6 ∧ acceleratedOrbit 12 556 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_556 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 556) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_556.1, data_12_556.2] + +/-- Complete interval computation for depth 12, residue 557. -/ +theorem bounds_12_557 : exactInterval 12 557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_557 (m : Nat) : + stoppingTime (2 ^ 12 * m + 557) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_557 : oddCount 557 12 = 6 ∧ acceleratedOrbit 12 557 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_557 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 557) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_557.1, data_12_557.2] + +/-- Complete interval computation for depth 12, residue 558. -/ +theorem bounds_12_558 : exactInterval 12 558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_558 (m : Nat) : + stoppingTime (2 ^ 12 * m + 558) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_558 : oddCount 558 12 = 6 ∧ acceleratedOrbit 12 558 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_558 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 558) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_558.1, data_12_558.2] + +/-- Complete interval computation for depth 12, residue 559. -/ +theorem bounds_12_559 : exactInterval 12 559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_559 (m : Nat) : + stoppingTime (2 ^ 12 * m + 559) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_559 : oddCount 559 12 = 9 ∧ acceleratedOrbit 12 559 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_559 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 559) = 3 ^ 9 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_559.1, data_12_559.2] + +/-- Complete interval computation for depth 12, residue 560. -/ +theorem bounds_12_560 : exactInterval 12 560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_560 (m : Nat) : + stoppingTime (2 ^ 12 * m + 560) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_560 : oddCount 560 12 = 3 ∧ acceleratedOrbit 12 560 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_560 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 560) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_560.1, data_12_560.2] + +/-- Complete interval computation for depth 12, residue 561. -/ +theorem bounds_12_561 : exactInterval 12 561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_561 (m : Nat) : + stoppingTime (2 ^ 12 * m + 561) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_561 : oddCount 561 12 = 6 ∧ acceleratedOrbit 12 561 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_561 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 561) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_561.1, data_12_561.2] + +/-- Complete interval computation for depth 12, residue 562. -/ +theorem bounds_12_562 : exactInterval 12 562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_562 (m : Nat) : + stoppingTime (2 ^ 12 * m + 562) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_562 : oddCount 562 12 = 6 ∧ acceleratedOrbit 12 562 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_562 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 562) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_562.1, data_12_562.2] + +/-- Complete interval computation for depth 12, residue 563. -/ +theorem bounds_12_563 : exactInterval 12 563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_563 (m : Nat) : + stoppingTime (2 ^ 12 * m + 563) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_563 : oddCount 563 12 = 6 ∧ acceleratedOrbit 12 563 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_563 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 563) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_563.1, data_12_563.2] + +/-- Complete interval computation for depth 12, residue 564. -/ +theorem bounds_12_564 : exactInterval 12 564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_564 (m : Nat) : + stoppingTime (2 ^ 12 * m + 564) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_564 : oddCount 564 12 = 3 ∧ acceleratedOrbit 12 564 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_564 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 564) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_564.1, data_12_564.2] + +/-- Complete interval computation for depth 12, residue 565. -/ +theorem bounds_12_565 : exactInterval 12 565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_565 (m : Nat) : + stoppingTime (2 ^ 12 * m + 565) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_565 : oddCount 565 12 = 3 ∧ acceleratedOrbit 12 565 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_565 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 565) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_565.1, data_12_565.2] + +/-- Complete interval computation for depth 12, residue 566. -/ +theorem bounds_12_566 : exactInterval 12 566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_566 (m : Nat) : + stoppingTime (2 ^ 12 * m + 566) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_566 : oddCount 566 12 = 8 ∧ acceleratedOrbit 12 566 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_566 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 566) = 3 ^ 8 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_566.1, data_12_566.2] + +/-- Complete interval computation for depth 12, residue 567. -/ +theorem bounds_12_567 : exactInterval 12 567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_567 (m : Nat) : + stoppingTime (2 ^ 12 * m + 567) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_567 : oddCount 567 12 = 8 ∧ acceleratedOrbit 12 567 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_567 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 567) = 3 ^ 8 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_567.1, data_12_567.2] + +end Collatz.Research.StoppingAtlas.Batch0237 From e5e1213aa5bdb5a1d49d65122677a8424d92e58e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:14 +0530 Subject: [PATCH 0238/1001] proof: certify atlas Batch0238 (12:568 to 12:582) --- Collatz/Research/StoppingAtlas/Batch0238.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0238.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0238.lean b/Collatz/Research/StoppingAtlas/Batch0238.lean new file mode 100644 index 00000000..d4e977a9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0238.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0238 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 568. -/ +theorem bounds_12_568 : exactInterval 12 568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_568 (m : Nat) : + stoppingTime (2 ^ 12 * m + 568) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_568 : oddCount 568 12 = 6 ∧ acceleratedOrbit 12 568 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_568 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 568) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_568.1, data_12_568.2] + +/-- Complete interval computation for depth 12, residue 569. -/ +theorem bounds_12_569 : exactInterval 12 569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_569 (m : Nat) : + stoppingTime (2 ^ 12 * m + 569) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_569 : oddCount 569 12 = 8 ∧ acceleratedOrbit 12 569 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_569 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 569) = 3 ^ 8 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_569.1, data_12_569.2] + +/-- Complete interval computation for depth 12, residue 570. -/ +theorem bounds_12_570 : exactInterval 12 570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_570 (m : Nat) : + stoppingTime (2 ^ 12 * m + 570) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_570 : oddCount 570 12 = 6 ∧ acceleratedOrbit 12 570 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_570 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 570) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_570.1, data_12_570.2] + +/-- Complete interval computation for depth 12, residue 571. -/ +theorem bounds_12_571 : exactInterval 12 571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_571 (m : Nat) : + stoppingTime (2 ^ 12 * m + 571) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_571 : oddCount 571 12 = 5 ∧ acceleratedOrbit 12 571 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_571 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 571) = 3 ^ 5 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_571.1, data_12_571.2] + +/-- Complete interval computation for depth 12, residue 572. -/ +theorem bounds_12_572 : exactInterval 12 572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_572 (m : Nat) : + stoppingTime (2 ^ 12 * m + 572) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_572 : oddCount 572 12 = 6 ∧ acceleratedOrbit 12 572 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_572 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 572) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_572.1, data_12_572.2] + +/-- Complete interval computation for depth 12, residue 573. -/ +theorem bounds_12_573 : exactInterval 12 573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_573 (m : Nat) : + stoppingTime (2 ^ 12 * m + 573) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_573 : oddCount 573 12 = 6 ∧ acceleratedOrbit 12 573 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_573 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 573) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_573.1, data_12_573.2] + +/-- Complete interval computation for depth 12, residue 574. -/ +theorem bounds_12_574 : exactInterval 12 574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_574 (m : Nat) : + stoppingTime (2 ^ 12 * m + 574) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_574 : oddCount 574 12 = 7 ∧ acceleratedOrbit 12 574 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_574 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 574) = 3 ^ 7 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_574.1, data_12_574.2] + +/-- Complete interval computation for depth 12, residue 575. -/ +theorem bounds_12_575 : exactInterval 12 575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_575 (m : Nat) : + stoppingTime (2 ^ 12 * m + 575) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_575 : oddCount 575 12 = 7 ∧ acceleratedOrbit 12 575 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_575 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 575) = 3 ^ 7 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_575.1, data_12_575.2] + +/-- Complete interval computation for depth 12, residue 576. -/ +theorem bounds_12_576 : exactInterval 12 576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_576 (m : Nat) : + stoppingTime (2 ^ 12 * m + 576) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_576 : oddCount 576 12 = 4 ∧ acceleratedOrbit 12 576 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_576 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 576) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_576.1, data_12_576.2] + +/-- Complete interval computation for depth 12, residue 577. -/ +theorem bounds_12_577 : exactInterval 12 577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_577 (m : Nat) : + stoppingTime (2 ^ 12 * m + 577) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_577 : oddCount 577 12 = 5 ∧ acceleratedOrbit 12 577 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_577 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 577) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_577.1, data_12_577.2] + +/-- Complete interval computation for depth 12, residue 578. -/ +theorem bounds_12_578 : exactInterval 12 578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_578 (m : Nat) : + stoppingTime (2 ^ 12 * m + 578) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_578 : oddCount 578 12 = 5 ∧ acceleratedOrbit 12 578 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_578 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 578) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_578.1, data_12_578.2] + +/-- Complete interval computation for depth 12, residue 579. -/ +theorem bounds_12_579 : exactInterval 12 579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_579 (m : Nat) : + stoppingTime (2 ^ 12 * m + 579) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_579 : oddCount 579 12 = 5 ∧ acceleratedOrbit 12 579 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_579 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 579) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_579.1, data_12_579.2] + +/-- Complete interval computation for depth 12, residue 580. -/ +theorem bounds_12_580 : exactInterval 12 580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_580 (m : Nat) : + stoppingTime (2 ^ 12 * m + 580) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_580 : oddCount 580 12 = 6 ∧ acceleratedOrbit 12 580 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_580 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 580) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_580.1, data_12_580.2] + +/-- Complete interval computation for depth 12, residue 581. -/ +theorem bounds_12_581 : exactInterval 12 581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_581 (m : Nat) : + stoppingTime (2 ^ 12 * m + 581) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_581 : oddCount 581 12 = 6 ∧ acceleratedOrbit 12 581 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_581 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 581) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_581.1, data_12_581.2] + +/-- Complete interval computation for depth 12, residue 582. -/ +theorem bounds_12_582 : exactInterval 12 582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_582 (m : Nat) : + stoppingTime (2 ^ 12 * m + 582) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_582 : oddCount 582 12 = 6 ∧ acceleratedOrbit 12 582 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_582 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 582) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_582.1, data_12_582.2] + +end Collatz.Research.StoppingAtlas.Batch0238 From b914f3f0cb21b08e04ed33e4d017cc4c3a5b734c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:15 +0530 Subject: [PATCH 0239/1001] proof: certify atlas Batch0239 (12:583 to 12:598) --- Collatz/Research/StoppingAtlas/Batch0239.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0239.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0239.lean b/Collatz/Research/StoppingAtlas/Batch0239.lean new file mode 100644 index 00000000..70f5bc9b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0239.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0239 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 583. -/ +theorem bounds_12_583 : exactInterval 12 583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_583 (m : Nat) : + stoppingTime (2 ^ 12 * m + 583) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_583 : oddCount 583 12 = 6 ∧ acceleratedOrbit 12 583 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_583 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 583) = 3 ^ 6 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_583.1, data_12_583.2] + +/-- Complete interval computation for depth 12, residue 584. -/ +theorem bounds_12_584 : exactInterval 12 584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_584 (m : Nat) : + stoppingTime (2 ^ 12 * m + 584) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_584 : oddCount 584 12 = 6 ∧ acceleratedOrbit 12 584 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_584 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 584) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_584.1, data_12_584.2] + +/-- Complete interval computation for depth 12, residue 585. -/ +theorem bounds_12_585 : exactInterval 12 585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_585 (m : Nat) : + stoppingTime (2 ^ 12 * m + 585) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_585 : oddCount 585 12 = 7 ∧ acceleratedOrbit 12 585 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_585 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 585) = 3 ^ 7 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_585.1, data_12_585.2] + +/-- Complete interval computation for depth 12, residue 586. -/ +theorem bounds_12_586 : exactInterval 12 586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_586 (m : Nat) : + stoppingTime (2 ^ 12 * m + 586) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_586 : oddCount 586 12 = 6 ∧ acceleratedOrbit 12 586 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_586 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 586) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_586.1, data_12_586.2] + +/-- Complete interval computation for depth 12, residue 587. -/ +theorem bounds_12_587 : exactInterval 12 587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_587 (m : Nat) : + stoppingTime (2 ^ 12 * m + 587) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_587 : oddCount 587 12 = 6 ∧ acceleratedOrbit 12 587 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_587 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 587) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_587.1, data_12_587.2] + +/-- Complete interval computation for depth 12, residue 588. -/ +theorem bounds_12_588 : exactInterval 12 588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_588 (m : Nat) : + stoppingTime (2 ^ 12 * m + 588) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_588 : oddCount 588 12 = 6 ∧ acceleratedOrbit 12 588 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_588 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 588) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_588.1, data_12_588.2] + +/-- Complete interval computation for depth 12, residue 589. -/ +theorem bounds_12_589 : exactInterval 12 589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_589 (m : Nat) : + stoppingTime (2 ^ 12 * m + 589) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_589 : oddCount 589 12 = 6 ∧ acceleratedOrbit 12 589 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_589 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 589) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_589.1, data_12_589.2] + +/-- Complete interval computation for depth 12, residue 590. -/ +theorem bounds_12_590 : exactInterval 12 590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_590 (m : Nat) : + stoppingTime (2 ^ 12 * m + 590) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_590 : oddCount 590 12 = 7 ∧ acceleratedOrbit 12 590 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_590 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 590) = 3 ^ 7 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_590.1, data_12_590.2] + +/-- Complete interval computation for depth 12, residue 591. -/ +theorem bounds_12_591 : exactInterval 12 591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_591 (m : Nat) : + stoppingTime (2 ^ 12 * m + 591) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_591 : oddCount 591 12 = 7 ∧ acceleratedOrbit 12 591 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_591 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 591) = 3 ^ 7 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_591.1, data_12_591.2] + +/-- Complete interval computation for depth 12, residue 592. -/ +theorem bounds_12_592 : exactInterval 12 592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_592 (m : Nat) : + stoppingTime (2 ^ 12 * m + 592) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_592 : oddCount 592 12 = 4 ∧ acceleratedOrbit 12 592 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_592 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 592) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_592.1, data_12_592.2] + +/-- Complete interval computation for depth 12, residue 593. -/ +theorem bounds_12_593 : exactInterval 12 593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_593 (m : Nat) : + stoppingTime (2 ^ 12 * m + 593) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_593 : oddCount 593 12 = 7 ∧ acceleratedOrbit 12 593 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_593 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 593) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_593.1, data_12_593.2] + +/-- Complete interval computation for depth 12, residue 594. -/ +theorem bounds_12_594 : exactInterval 12 594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_594 (m : Nat) : + stoppingTime (2 ^ 12 * m + 594) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_594 : oddCount 594 12 = 7 ∧ acceleratedOrbit 12 594 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_594 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 594) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_594.1, data_12_594.2] + +/-- Complete interval computation for depth 12, residue 595. -/ +theorem bounds_12_595 : exactInterval 12 595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_595 (m : Nat) : + stoppingTime (2 ^ 12 * m + 595) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_595 : oddCount 595 12 = 7 ∧ acceleratedOrbit 12 595 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_595 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 595) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_595.1, data_12_595.2] + +/-- Complete interval computation for depth 12, residue 596. -/ +theorem bounds_12_596 : exactInterval 12 596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_596 (m : Nat) : + stoppingTime (2 ^ 12 * m + 596) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_596 : oddCount 596 12 = 4 ∧ acceleratedOrbit 12 596 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_596 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 596) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_596.1, data_12_596.2] + +/-- Complete interval computation for depth 12, residue 597. -/ +theorem bounds_12_597 : exactInterval 12 597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_597 (m : Nat) : + stoppingTime (2 ^ 12 * m + 597) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_597 : oddCount 597 12 = 4 ∧ acceleratedOrbit 12 597 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_597 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 597) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_597.1, data_12_597.2] + +/-- Complete interval computation for depth 12, residue 598. -/ +theorem bounds_12_598 : exactInterval 12 598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_598 (m : Nat) : + stoppingTime (2 ^ 12 * m + 598) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_598 : oddCount 598 12 = 7 ∧ acceleratedOrbit 12 598 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_598 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 598) = 3 ^ 7 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_598.1, data_12_598.2] + +end Collatz.Research.StoppingAtlas.Batch0239 From 46973f4f400e1b2bbd1634e5bf56309564b4d000 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:15 +0530 Subject: [PATCH 0240/1001] proof: certify atlas Batch0240 (12:599 to 12:613) --- Collatz/Research/StoppingAtlas/Batch0240.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0240.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0240.lean b/Collatz/Research/StoppingAtlas/Batch0240.lean new file mode 100644 index 00000000..6a92cb95 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0240.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0240 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 599. -/ +theorem bounds_12_599 : exactInterval 12 599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_599 (m : Nat) : + stoppingTime (2 ^ 12 * m + 599) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_599 : oddCount 599 12 = 7 ∧ acceleratedOrbit 12 599 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_599 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 599) = 3 ^ 7 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_599.1, data_12_599.2] + +/-- Complete interval computation for depth 12, residue 600. -/ +theorem bounds_12_600 : exactInterval 12 600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_600 (m : Nat) : + stoppingTime (2 ^ 12 * m + 600) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_600 : oddCount 600 12 = 3 ∧ acceleratedOrbit 12 600 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_600 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 600) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_600.1, data_12_600.2] + +/-- Complete interval computation for depth 12, residue 601. -/ +theorem bounds_12_601 : exactInterval 12 601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_601 (m : Nat) : + stoppingTime (2 ^ 12 * m + 601) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_601 : oddCount 601 12 = 8 ∧ acceleratedOrbit 12 601 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_601 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 601) = 3 ^ 8 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_601.1, data_12_601.2] + +/-- Complete interval computation for depth 12, residue 602. -/ +theorem bounds_12_602 : exactInterval 12 602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_602 (m : Nat) : + stoppingTime (2 ^ 12 * m + 602) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_602 : oddCount 602 12 = 3 ∧ acceleratedOrbit 12 602 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_602 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 602) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_602.1, data_12_602.2] + +/-- Complete interval computation for depth 12, residue 603. -/ +theorem bounds_12_603 : exactInterval 12 603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_603 (m : Nat) : + stoppingTime (2 ^ 12 * m + 603) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_603 : oddCount 603 12 = 9 ∧ acceleratedOrbit 12 603 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_603 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 603) = 3 ^ 9 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_603.1, data_12_603.2] + +/-- Complete interval computation for depth 12, residue 604. -/ +theorem bounds_12_604 : exactInterval 12 604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_604 (m : Nat) : + stoppingTime (2 ^ 12 * m + 604) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_604 : oddCount 604 12 = 3 ∧ acceleratedOrbit 12 604 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_604 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 604) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_604.1, data_12_604.2] + +/-- Complete interval computation for depth 12, residue 605. -/ +theorem bounds_12_605 : exactInterval 12 605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_605 (m : Nat) : + stoppingTime (2 ^ 12 * m + 605) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_605 : oddCount 605 12 = 3 ∧ acceleratedOrbit 12 605 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_605 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 605) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_605.1, data_12_605.2] + +/-- Complete interval computation for depth 12, residue 606. -/ +theorem bounds_12_606 : exactInterval 12 606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_606 (m : Nat) : + stoppingTime (2 ^ 12 * m + 606) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_606 : oddCount 606 12 = 7 ∧ acceleratedOrbit 12 606 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_606 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 606) = 3 ^ 7 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_606.1, data_12_606.2] + +/-- Complete interval computation for depth 12, residue 607. -/ +theorem bounds_12_607 : exactInterval 12 607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_607 (m : Nat) : + stoppingTime (2 ^ 12 * m + 607) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_607 : oddCount 607 12 = 7 ∧ acceleratedOrbit 12 607 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_607 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 607) = 3 ^ 7 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_607.1, data_12_607.2] + +/-- Complete interval computation for depth 12, residue 608. -/ +theorem bounds_12_608 : exactInterval 12 608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_608 (m : Nat) : + stoppingTime (2 ^ 12 * m + 608) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_608 : oddCount 608 12 = 4 ∧ acceleratedOrbit 12 608 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_608 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 608) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_608.1, data_12_608.2] + +/-- Complete interval computation for depth 12, residue 609. -/ +theorem bounds_12_609 : exactInterval 12 609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_609 (m : Nat) : + stoppingTime (2 ^ 12 * m + 609) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_609 : oddCount 609 12 = 6 ∧ acceleratedOrbit 12 609 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_609 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 609) = 3 ^ 6 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_609.1, data_12_609.2] + +/-- Complete interval computation for depth 12, residue 610. -/ +theorem bounds_12_610 : exactInterval 12 610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_610 (m : Nat) : + stoppingTime (2 ^ 12 * m + 610) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_610 : oddCount 610 12 = 5 ∧ acceleratedOrbit 12 610 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_610 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 610) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_610.1, data_12_610.2] + +/-- Complete interval computation for depth 12, residue 611. -/ +theorem bounds_12_611 : exactInterval 12 611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_611 (m : Nat) : + stoppingTime (2 ^ 12 * m + 611) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_611 : oddCount 611 12 = 5 ∧ acceleratedOrbit 12 611 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_611 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 611) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_611.1, data_12_611.2] + +/-- Complete interval computation for depth 12, residue 612. -/ +theorem bounds_12_612 : exactInterval 12 612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_612 (m : Nat) : + stoppingTime (2 ^ 12 * m + 612) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_612 : oddCount 612 12 = 5 ∧ acceleratedOrbit 12 612 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_612 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 612) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_612.1, data_12_612.2] + +/-- Complete interval computation for depth 12, residue 613. -/ +theorem bounds_12_613 : exactInterval 12 613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_613 (m : Nat) : + stoppingTime (2 ^ 12 * m + 613) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_613 : oddCount 613 12 = 5 ∧ acceleratedOrbit 12 613 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_613 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 613) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_613.1, data_12_613.2] + +end Collatz.Research.StoppingAtlas.Batch0240 From 71c934d94f8c4e51f92305dc10eee3f9c732f863 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:15 +0530 Subject: [PATCH 0241/1001] proof: certify atlas Batch0241 (12:614 to 12:628) --- Collatz/Research/StoppingAtlas/Batch0241.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0241.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0241.lean b/Collatz/Research/StoppingAtlas/Batch0241.lean new file mode 100644 index 00000000..304248bb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0241.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0241 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 614. -/ +theorem bounds_12_614 : exactInterval 12 614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_614 (m : Nat) : + stoppingTime (2 ^ 12 * m + 614) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_614 : oddCount 614 12 = 5 ∧ acceleratedOrbit 12 614 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_614 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 614) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_614.1, data_12_614.2] + +/-- Complete interval computation for depth 12, residue 615. -/ +theorem bounds_12_615 : exactInterval 12 615 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_615 (m : Nat) : + stoppingTime (2 ^ 12 * m + 615) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_615 : oddCount 615 12 = 7 ∧ acceleratedOrbit 12 615 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_615 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 615) = 3 ^ 7 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_615.1, data_12_615.2] + +/-- Complete interval computation for depth 12, residue 616. -/ +theorem bounds_12_616 : exactInterval 12 616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_616 (m : Nat) : + stoppingTime (2 ^ 12 * m + 616) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_616 : oddCount 616 12 = 4 ∧ acceleratedOrbit 12 616 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_616 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 616) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_616.1, data_12_616.2] + +/-- Complete interval computation for depth 12, residue 617. -/ +theorem bounds_12_617 : exactInterval 12 617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_617 (m : Nat) : + stoppingTime (2 ^ 12 * m + 617) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_617 : oddCount 617 12 = 8 ∧ acceleratedOrbit 12 617 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_617 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 617) = 3 ^ 8 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_617.1, data_12_617.2] + +/-- Complete interval computation for depth 12, residue 618. -/ +theorem bounds_12_618 : exactInterval 12 618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_618 (m : Nat) : + stoppingTime (2 ^ 12 * m + 618) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_618 : oddCount 618 12 = 4 ∧ acceleratedOrbit 12 618 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_618 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 618) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_618.1, data_12_618.2] + +/-- Complete interval computation for depth 12, residue 619. -/ +theorem bounds_12_619 : exactInterval 12 619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_619 (m : Nat) : + stoppingTime (2 ^ 12 * m + 619) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_619 : oddCount 619 12 = 7 ∧ acceleratedOrbit 12 619 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_619 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 619) = 3 ^ 7 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_619.1, data_12_619.2] + +/-- Complete interval computation for depth 12, residue 620. -/ +theorem bounds_12_620 : exactInterval 12 620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_620 (m : Nat) : + stoppingTime (2 ^ 12 * m + 620) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_620 : oddCount 620 12 = 7 ∧ acceleratedOrbit 12 620 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_620 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 620) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_620.1, data_12_620.2] + +/-- Complete interval computation for depth 12, residue 621. -/ +theorem bounds_12_621 : exactInterval 12 621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_621 (m : Nat) : + stoppingTime (2 ^ 12 * m + 621) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_621 : oddCount 621 12 = 7 ∧ acceleratedOrbit 12 621 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_621 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 621) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_621.1, data_12_621.2] + +/-- Complete interval computation for depth 12, residue 622. -/ +theorem bounds_12_622 : exactInterval 12 622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_622 (m : Nat) : + stoppingTime (2 ^ 12 * m + 622) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_622 : oddCount 622 12 = 7 ∧ acceleratedOrbit 12 622 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_622 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 622) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_622.1, data_12_622.2] + +/-- Complete interval computation for depth 12, residue 623. -/ +theorem bounds_12_623 : exactInterval 12 623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_623 (m : Nat) : + stoppingTime (2 ^ 12 * m + 623) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_623 : oddCount 623 12 = 8 ∧ acceleratedOrbit 12 623 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_623 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 623) = 3 ^ 8 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_623.1, data_12_623.2] + +/-- Complete interval computation for depth 12, residue 624. -/ +theorem bounds_12_624 : exactInterval 12 624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_624 (m : Nat) : + stoppingTime (2 ^ 12 * m + 624) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_624 : oddCount 624 12 = 5 ∧ acceleratedOrbit 12 624 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_624 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 624) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_624.1, data_12_624.2] + +/-- Complete interval computation for depth 12, residue 625. -/ +theorem bounds_12_625 : exactInterval 12 625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_625 (m : Nat) : + stoppingTime (2 ^ 12 * m + 625) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_625 : oddCount 625 12 = 4 ∧ acceleratedOrbit 12 625 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_625 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 625) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_625.1, data_12_625.2] + +/-- Complete interval computation for depth 12, residue 626. -/ +theorem bounds_12_626 : exactInterval 12 626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_626 (m : Nat) : + stoppingTime (2 ^ 12 * m + 626) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_626 : oddCount 626 12 = 7 ∧ acceleratedOrbit 12 626 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_626 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 626) = 3 ^ 7 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_626.1, data_12_626.2] + +/-- Complete interval computation for depth 12, residue 627. -/ +theorem bounds_12_627 : exactInterval 12 627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_627 (m : Nat) : + stoppingTime (2 ^ 12 * m + 627) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_627 : oddCount 627 12 = 7 ∧ acceleratedOrbit 12 627 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_627 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 627) = 3 ^ 7 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_627.1, data_12_627.2] + +/-- Complete interval computation for depth 12, residue 628. -/ +theorem bounds_12_628 : exactInterval 12 628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_628 (m : Nat) : + stoppingTime (2 ^ 12 * m + 628) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_628 : oddCount 628 12 = 5 ∧ acceleratedOrbit 12 628 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_628 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 628) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_628.1, data_12_628.2] + +end Collatz.Research.StoppingAtlas.Batch0241 From 7e61a35f2433d1a49e620895aaec200190a7e8db Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:16 +0530 Subject: [PATCH 0242/1001] proof: certify atlas Batch0242 (12:629 to 12:644) --- Collatz/Research/StoppingAtlas/Batch0242.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0242.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0242.lean b/Collatz/Research/StoppingAtlas/Batch0242.lean new file mode 100644 index 00000000..1ff6b48c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0242.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0242 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 629. -/ +theorem bounds_12_629 : exactInterval 12 629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_629 (m : Nat) : + stoppingTime (2 ^ 12 * m + 629) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_629 : oddCount 629 12 = 5 ∧ acceleratedOrbit 12 629 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_629 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 629) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_629.1, data_12_629.2] + +/-- Complete interval computation for depth 12, residue 630. -/ +theorem bounds_12_630 : exactInterval 12 630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_630 (m : Nat) : + stoppingTime (2 ^ 12 * m + 630) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_630 : oddCount 630 12 = 5 ∧ acceleratedOrbit 12 630 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_630 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 630) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_630.1, data_12_630.2] + +/-- Complete interval computation for depth 12, residue 631. -/ +theorem bounds_12_631 : exactInterval 12 631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_631 (m : Nat) : + stoppingTime (2 ^ 12 * m + 631) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_631 : oddCount 631 12 = 5 ∧ acceleratedOrbit 12 631 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_631 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 631) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_631.1, data_12_631.2] + +/-- Complete interval computation for depth 12, residue 632. -/ +theorem bounds_12_632 : exactInterval 12 632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_632 (m : Nat) : + stoppingTime (2 ^ 12 * m + 632) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_632 : oddCount 632 12 = 5 ∧ acceleratedOrbit 12 632 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_632 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 632) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_632.1, data_12_632.2] + +/-- Complete interval computation for depth 12, residue 633. -/ +theorem bounds_12_633 : exactInterval 12 633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_633 (m : Nat) : + stoppingTime (2 ^ 12 * m + 633) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_633 : oddCount 633 12 = 6 ∧ acceleratedOrbit 12 633 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_633 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 633) = 3 ^ 6 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_633.1, data_12_633.2] + +/-- Complete interval computation for depth 12, residue 634. -/ +theorem bounds_12_634 : exactInterval 12 634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_634 (m : Nat) : + stoppingTime (2 ^ 12 * m + 634) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_634 : oddCount 634 12 = 5 ∧ acceleratedOrbit 12 634 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_634 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 634) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_634.1, data_12_634.2] + +/-- Complete interval computation for depth 12, residue 635. -/ +theorem bounds_12_635 : exactInterval 12 635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_635 (m : Nat) : + stoppingTime (2 ^ 12 * m + 635) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_635 : oddCount 635 12 = 7 ∧ acceleratedOrbit 12 635 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_635 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 635) = 3 ^ 7 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_635.1, data_12_635.2] + +/-- Complete interval computation for depth 12, residue 636. -/ +theorem bounds_12_636 : exactInterval 12 636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_636 (m : Nat) : + stoppingTime (2 ^ 12 * m + 636) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_636 : oddCount 636 12 = 9 ∧ acceleratedOrbit 12 636 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_636 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 636) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_636.1, data_12_636.2] + +/-- Complete interval computation for depth 12, residue 637. -/ +theorem bounds_12_637 : exactInterval 12 637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_637 (m : Nat) : + stoppingTime (2 ^ 12 * m + 637) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_637 : oddCount 637 12 = 9 ∧ acceleratedOrbit 12 637 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_637 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 637) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_637.1, data_12_637.2] + +/-- Complete interval computation for depth 12, residue 638. -/ +theorem bounds_12_638 : exactInterval 12 638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_638 (m : Nat) : + stoppingTime (2 ^ 12 * m + 638) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_638 : oddCount 638 12 = 9 ∧ acceleratedOrbit 12 638 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_638 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 638) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_638.1, data_12_638.2] + +/-- Complete interval computation for depth 12, residue 639. -/ +theorem bounds_12_639 : exactInterval 12 639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_639 (m : Nat) : + stoppingTime (2 ^ 12 * m + 639) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_639 : oddCount 639 12 = 10 ∧ acceleratedOrbit 12 639 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_639 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 639) = 3 ^ 10 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_639.1, data_12_639.2] + +/-- Complete interval computation for depth 12, residue 640. -/ +theorem bounds_12_640 : exactInterval 12 640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_640 (m : Nat) : + stoppingTime (2 ^ 12 * m + 640) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_640 : oddCount 640 12 = 2 ∧ acceleratedOrbit 12 640 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_640 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 640) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_640.1, data_12_640.2] + +/-- Complete interval computation for depth 12, residue 641. -/ +theorem bounds_12_641 : exactInterval 12 641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_641 (m : Nat) : + stoppingTime (2 ^ 12 * m + 641) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_641 : oddCount 641 12 = 7 ∧ acceleratedOrbit 12 641 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_641 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 641) = 3 ^ 7 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_641.1, data_12_641.2] + +/-- Complete interval computation for depth 12, residue 642. -/ +theorem bounds_12_642 : exactInterval 12 642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_642 (m : Nat) : + stoppingTime (2 ^ 12 * m + 642) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_642 : oddCount 642 12 = 4 ∧ acceleratedOrbit 12 642 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_642 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 642) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_642.1, data_12_642.2] + +/-- Complete interval computation for depth 12, residue 643. -/ +theorem bounds_12_643 : exactInterval 12 643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_643 (m : Nat) : + stoppingTime (2 ^ 12 * m + 643) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_643 : oddCount 643 12 = 4 ∧ acceleratedOrbit 12 643 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_643 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 643) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_643.1, data_12_643.2] + +/-- Complete interval computation for depth 12, residue 644. -/ +theorem bounds_12_644 : exactInterval 12 644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_644 (m : Nat) : + stoppingTime (2 ^ 12 * m + 644) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_644 : oddCount 644 12 = 7 ∧ acceleratedOrbit 12 644 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_644 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 644) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_644.1, data_12_644.2] + +end Collatz.Research.StoppingAtlas.Batch0242 From e6693e2c3a5e37743837b6854f4a48317086d524 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:16 +0530 Subject: [PATCH 0243/1001] proof: certify atlas Batch0243 (12:645 to 12:659) --- Collatz/Research/StoppingAtlas/Batch0243.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0243.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0243.lean b/Collatz/Research/StoppingAtlas/Batch0243.lean new file mode 100644 index 00000000..e7ff6a5a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0243.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0243 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 645. -/ +theorem bounds_12_645 : exactInterval 12 645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_645 (m : Nat) : + stoppingTime (2 ^ 12 * m + 645) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_645 : oddCount 645 12 = 7 ∧ acceleratedOrbit 12 645 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_645 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 645) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_645.1, data_12_645.2] + +/-- Complete interval computation for depth 12, residue 646. -/ +theorem bounds_12_646 : exactInterval 12 646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_646 (m : Nat) : + stoppingTime (2 ^ 12 * m + 646) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_646 : oddCount 646 12 = 7 ∧ acceleratedOrbit 12 646 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_646 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 646) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_646.1, data_12_646.2] + +/-- Complete interval computation for depth 12, residue 647. -/ +theorem bounds_12_647 : exactInterval 12 647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_647 (m : Nat) : + stoppingTime (2 ^ 12 * m + 647) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_647 : oddCount 647 12 = 6 ∧ acceleratedOrbit 12 647 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_647 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 647) = 3 ^ 6 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_647.1, data_12_647.2] + +/-- Complete interval computation for depth 12, residue 648. -/ +theorem bounds_12_648 : exactInterval 12 648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_648 (m : Nat) : + stoppingTime (2 ^ 12 * m + 648) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_648 : oddCount 648 12 = 5 ∧ acceleratedOrbit 12 648 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_648 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 648) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_648.1, data_12_648.2] + +/-- Complete interval computation for depth 12, residue 649. -/ +theorem bounds_12_649 : exactInterval 12 649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_649 (m : Nat) : + stoppingTime (2 ^ 12 * m + 649) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_649 : oddCount 649 12 = 8 ∧ acceleratedOrbit 12 649 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_649 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 649) = 3 ^ 8 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_649.1, data_12_649.2] + +/-- Complete interval computation for depth 12, residue 650. -/ +theorem bounds_12_650 : exactInterval 12 650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_650 (m : Nat) : + stoppingTime (2 ^ 12 * m + 650) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_650 : oddCount 650 12 = 5 ∧ acceleratedOrbit 12 650 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_650 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 650) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_650.1, data_12_650.2] + +/-- Complete interval computation for depth 12, residue 651. -/ +theorem bounds_12_651 : exactInterval 12 651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_651 (m : Nat) : + stoppingTime (2 ^ 12 * m + 651) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_651 : oddCount 651 12 = 7 ∧ acceleratedOrbit 12 651 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_651 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 651) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_651.1, data_12_651.2] + +/-- Complete interval computation for depth 12, residue 652. -/ +theorem bounds_12_652 : exactInterval 12 652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_652 (m : Nat) : + stoppingTime (2 ^ 12 * m + 652) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_652 : oddCount 652 12 = 5 ∧ acceleratedOrbit 12 652 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_652 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 652) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_652.1, data_12_652.2] + +/-- Complete interval computation for depth 12, residue 653. -/ +theorem bounds_12_653 : exactInterval 12 653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_653 (m : Nat) : + stoppingTime (2 ^ 12 * m + 653) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_653 : oddCount 653 12 = 5 ∧ acceleratedOrbit 12 653 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_653 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 653) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_653.1, data_12_653.2] + +/-- Complete interval computation for depth 12, residue 654. -/ +theorem bounds_12_654 : exactInterval 12 654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_654 (m : Nat) : + stoppingTime (2 ^ 12 * m + 654) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_654 : oddCount 654 12 = 9 ∧ acceleratedOrbit 12 654 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_654 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 654) = 3 ^ 9 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_654.1, data_12_654.2] + +/-- Complete interval computation for depth 12, residue 655. -/ +theorem bounds_12_655 : exactInterval 12 655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_655 (m : Nat) : + stoppingTime (2 ^ 12 * m + 655) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_655 : oddCount 655 12 = 9 ∧ acceleratedOrbit 12 655 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_655 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 655) = 3 ^ 9 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_655.1, data_12_655.2] + +/-- Complete interval computation for depth 12, residue 656. -/ +theorem bounds_12_656 : exactInterval 12 656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_656 (m : Nat) : + stoppingTime (2 ^ 12 * m + 656) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_656 : oddCount 656 12 = 6 ∧ acceleratedOrbit 12 656 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_656 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 656) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_656.1, data_12_656.2] + +/-- Complete interval computation for depth 12, residue 657. -/ +theorem bounds_12_657 : exactInterval 12 657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_657 (m : Nat) : + stoppingTime (2 ^ 12 * m + 657) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_657 : oddCount 657 12 = 6 ∧ acceleratedOrbit 12 657 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_657 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 657) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_657.1, data_12_657.2] + +/-- Complete interval computation for depth 12, residue 658. -/ +theorem bounds_12_658 : exactInterval 12 658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_658 (m : Nat) : + stoppingTime (2 ^ 12 * m + 658) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_658 : oddCount 658 12 = 6 ∧ acceleratedOrbit 12 658 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_658 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 658) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_658.1, data_12_658.2] + +/-- Complete interval computation for depth 12, residue 659. -/ +theorem bounds_12_659 : exactInterval 12 659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_659 (m : Nat) : + stoppingTime (2 ^ 12 * m + 659) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_659 : oddCount 659 12 = 6 ∧ acceleratedOrbit 12 659 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_659 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 659) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_659.1, data_12_659.2] + +end Collatz.Research.StoppingAtlas.Batch0243 From 41519b8920dc9ffaf290d858af9087de503fbc79 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:16 +0530 Subject: [PATCH 0244/1001] proof: certify atlas Batch0244 (12:660 to 12:674) --- Collatz/Research/StoppingAtlas/Batch0244.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0244.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0244.lean b/Collatz/Research/StoppingAtlas/Batch0244.lean new file mode 100644 index 00000000..1d34d2fe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0244.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0244 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 660. -/ +theorem bounds_12_660 : exactInterval 12 660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_660 (m : Nat) : + stoppingTime (2 ^ 12 * m + 660) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_660 : oddCount 660 12 = 6 ∧ acceleratedOrbit 12 660 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_660 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 660) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_660.1, data_12_660.2] + +/-- Complete interval computation for depth 12, residue 661. -/ +theorem bounds_12_661 : exactInterval 12 661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_661 (m : Nat) : + stoppingTime (2 ^ 12 * m + 661) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_661 : oddCount 661 12 = 6 ∧ acceleratedOrbit 12 661 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_661 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 661) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_661.1, data_12_661.2] + +/-- Complete interval computation for depth 12, residue 662. -/ +theorem bounds_12_662 : exactInterval 12 662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_662 (m : Nat) : + stoppingTime (2 ^ 12 * m + 662) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_662 : oddCount 662 12 = 5 ∧ acceleratedOrbit 12 662 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_662 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 662) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_662.1, data_12_662.2] + +/-- Complete interval computation for depth 12, residue 663. -/ +theorem bounds_12_663 : exactInterval 12 663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_663 (m : Nat) : + stoppingTime (2 ^ 12 * m + 663) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_663 : oddCount 663 12 = 5 ∧ acceleratedOrbit 12 663 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_663 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 663) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_663.1, data_12_663.2] + +/-- Complete interval computation for depth 12, residue 664. -/ +theorem bounds_12_664 : exactInterval 12 664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_664 (m : Nat) : + stoppingTime (2 ^ 12 * m + 664) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_664 : oddCount 664 12 = 6 ∧ acceleratedOrbit 12 664 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_664 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 664) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_664.1, data_12_664.2] + +/-- Complete interval computation for depth 12, residue 665. -/ +theorem bounds_12_665 : exactInterval 12 665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_665 (m : Nat) : + stoppingTime (2 ^ 12 * m + 665) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_665 : oddCount 665 12 = 6 ∧ acceleratedOrbit 12 665 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_665 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 665) = 3 ^ 6 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_665.1, data_12_665.2] + +/-- Complete interval computation for depth 12, residue 666. -/ +theorem bounds_12_666 : exactInterval 12 666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_666 (m : Nat) : + stoppingTime (2 ^ 12 * m + 666) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_666 : oddCount 666 12 = 6 ∧ acceleratedOrbit 12 666 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_666 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 666) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_666.1, data_12_666.2] + +/-- Complete interval computation for depth 12, residue 667. -/ +theorem bounds_12_667 : exactInterval 12 667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_667 (m : Nat) : + stoppingTime (2 ^ 12 * m + 667) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_667 : oddCount 667 12 = 10 ∧ acceleratedOrbit 12 667 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_667 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 667) = 3 ^ 10 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_667.1, data_12_667.2] + +/-- Complete interval computation for depth 12, residue 668. -/ +theorem bounds_12_668 : exactInterval 12 668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_668 (m : Nat) : + stoppingTime (2 ^ 12 * m + 668) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_668 : oddCount 668 12 = 8 ∧ acceleratedOrbit 12 668 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_668 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 668) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_668.1, data_12_668.2] + +/-- Complete interval computation for depth 12, residue 669. -/ +theorem bounds_12_669 : exactInterval 12 669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_669 (m : Nat) : + stoppingTime (2 ^ 12 * m + 669) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_669 : oddCount 669 12 = 8 ∧ acceleratedOrbit 12 669 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_669 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 669) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_669.1, data_12_669.2] + +/-- Complete interval computation for depth 12, residue 670. -/ +theorem bounds_12_670 : exactInterval 12 670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_670 (m : Nat) : + stoppingTime (2 ^ 12 * m + 670) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_670 : oddCount 670 12 = 8 ∧ acceleratedOrbit 12 670 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_670 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 670) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_670.1, data_12_670.2] + +/-- Complete interval computation for depth 12, residue 671. -/ +theorem bounds_12_671 : exactInterval 12 671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_671 (m : Nat) : + stoppingTime (2 ^ 12 * m + 671) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_671 : oddCount 671 12 = 9 ∧ acceleratedOrbit 12 671 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_671 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 671) = 3 ^ 9 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_671.1, data_12_671.2] + +/-- Complete interval computation for depth 12, residue 672. -/ +theorem bounds_12_672 : exactInterval 12 672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_672 (m : Nat) : + stoppingTime (2 ^ 12 * m + 672) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_672 : oddCount 672 12 = 2 ∧ acceleratedOrbit 12 672 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_672 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 672) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_672.1, data_12_672.2] + +/-- Complete interval computation for depth 12, residue 673. -/ +theorem bounds_12_673 : exactInterval 12 673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_673 (m : Nat) : + stoppingTime (2 ^ 12 * m + 673) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_673 : oddCount 673 12 = 7 ∧ acceleratedOrbit 12 673 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_673 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 673) = 3 ^ 7 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_673.1, data_12_673.2] + +/-- Complete interval computation for depth 12, residue 674. -/ +theorem bounds_12_674 : exactInterval 12 674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_674 (m : Nat) : + stoppingTime (2 ^ 12 * m + 674) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_674 : oddCount 674 12 = 7 ∧ acceleratedOrbit 12 674 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_674 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 674) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_674.1, data_12_674.2] + +end Collatz.Research.StoppingAtlas.Batch0244 From 7bf6d5a5bc2044be8e7f0351b1332f1add69398d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:16 +0530 Subject: [PATCH 0245/1001] proof: certify atlas Batch0245 (12:675 to 12:690) --- Collatz/Research/StoppingAtlas/Batch0245.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0245.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0245.lean b/Collatz/Research/StoppingAtlas/Batch0245.lean new file mode 100644 index 00000000..a4eb89db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0245.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0245 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 675. -/ +theorem bounds_12_675 : exactInterval 12 675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_675 (m : Nat) : + stoppingTime (2 ^ 12 * m + 675) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_675 : oddCount 675 12 = 7 ∧ acceleratedOrbit 12 675 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_675 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 675) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_675.1, data_12_675.2] + +/-- Complete interval computation for depth 12, residue 676. -/ +theorem bounds_12_676 : exactInterval 12 676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_676 (m : Nat) : + stoppingTime (2 ^ 12 * m + 676) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_676 : oddCount 676 12 = 8 ∧ acceleratedOrbit 12 676 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_676 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 676) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_676.1, data_12_676.2] + +/-- Complete interval computation for depth 12, residue 677. -/ +theorem bounds_12_677 : exactInterval 12 677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_677 (m : Nat) : + stoppingTime (2 ^ 12 * m + 677) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_677 : oddCount 677 12 = 8 ∧ acceleratedOrbit 12 677 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_677 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 677) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_677.1, data_12_677.2] + +/-- Complete interval computation for depth 12, residue 678. -/ +theorem bounds_12_678 : exactInterval 12 678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_678 (m : Nat) : + stoppingTime (2 ^ 12 * m + 678) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_678 : oddCount 678 12 = 8 ∧ acceleratedOrbit 12 678 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_678 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 678) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_678.1, data_12_678.2] + +/-- Complete interval computation for depth 12, residue 679. -/ +theorem bounds_12_679 : exactInterval 12 679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_679 (m : Nat) : + stoppingTime (2 ^ 12 * m + 679) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_679 : oddCount 679 12 = 8 ∧ acceleratedOrbit 12 679 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_679 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 679) = 3 ^ 8 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_679.1, data_12_679.2] + +/-- Complete interval computation for depth 12, residue 680. -/ +theorem bounds_12_680 : exactInterval 12 680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_680 (m : Nat) : + stoppingTime (2 ^ 12 * m + 680) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_680 : oddCount 680 12 = 2 ∧ acceleratedOrbit 12 680 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_680 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 680) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_680.1, data_12_680.2] + +/-- Complete interval computation for depth 12, residue 681. -/ +theorem bounds_12_681 : exactInterval 12 681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_681 (m : Nat) : + stoppingTime (2 ^ 12 * m + 681) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_681 : oddCount 681 12 = 10 ∧ acceleratedOrbit 12 681 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_681 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 681) = 3 ^ 10 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_681.1, data_12_681.2] + +/-- Complete interval computation for depth 12, residue 682. -/ +theorem bounds_12_682 : exactInterval 12 682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_682 (m : Nat) : + stoppingTime (2 ^ 12 * m + 682) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_682 : oddCount 682 12 = 2 ∧ acceleratedOrbit 12 682 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_682 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 682) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_682.1, data_12_682.2] + +/-- Complete interval computation for depth 12, residue 683. -/ +theorem bounds_12_683 : exactInterval 12 683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_683 (m : Nat) : + stoppingTime (2 ^ 12 * m + 683) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_683 : oddCount 683 12 = 6 ∧ acceleratedOrbit 12 683 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_683 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 683) = 3 ^ 6 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_683.1, data_12_683.2] + +/-- Complete interval computation for depth 12, residue 684. -/ +theorem bounds_12_684 : exactInterval 12 684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_684 (m : Nat) : + stoppingTime (2 ^ 12 * m + 684) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_684 : oddCount 684 12 = 5 ∧ acceleratedOrbit 12 684 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_684 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 684) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_684.1, data_12_684.2] + +/-- Complete interval computation for depth 12, residue 685. -/ +theorem bounds_12_685 : exactInterval 12 685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_685 (m : Nat) : + stoppingTime (2 ^ 12 * m + 685) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_685 : oddCount 685 12 = 5 ∧ acceleratedOrbit 12 685 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_685 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 685) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_685.1, data_12_685.2] + +/-- Complete interval computation for depth 12, residue 686. -/ +theorem bounds_12_686 : exactInterval 12 686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_686 (m : Nat) : + stoppingTime (2 ^ 12 * m + 686) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_686 : oddCount 686 12 = 5 ∧ acceleratedOrbit 12 686 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_686 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 686) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_686.1, data_12_686.2] + +/-- Complete interval computation for depth 12, residue 687. -/ +theorem bounds_12_687 : exactInterval 12 687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_687 (m : Nat) : + stoppingTime (2 ^ 12 * m + 687) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_687 : oddCount 687 12 = 7 ∧ acceleratedOrbit 12 687 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_687 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 687) = 3 ^ 7 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_687.1, data_12_687.2] + +/-- Complete interval computation for depth 12, residue 688. -/ +theorem bounds_12_688 : exactInterval 12 688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_688 (m : Nat) : + stoppingTime (2 ^ 12 * m + 688) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_688 : oddCount 688 12 = 4 ∧ acceleratedOrbit 12 688 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_688 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 688) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_688.1, data_12_688.2] + +/-- Complete interval computation for depth 12, residue 689. -/ +theorem bounds_12_689 : exactInterval 12 689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_689 (m : Nat) : + stoppingTime (2 ^ 12 * m + 689) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_689 : oddCount 689 12 = 6 ∧ acceleratedOrbit 12 689 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_689 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 689) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_689.1, data_12_689.2] + +/-- Complete interval computation for depth 12, residue 690. -/ +theorem bounds_12_690 : exactInterval 12 690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_690 (m : Nat) : + stoppingTime (2 ^ 12 * m + 690) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_690 : oddCount 690 12 = 6 ∧ acceleratedOrbit 12 690 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_690 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 690) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_690.1, data_12_690.2] + +end Collatz.Research.StoppingAtlas.Batch0245 From d16ddec0bb36a44d63feae989b89439f0b91d41f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:17 +0530 Subject: [PATCH 0246/1001] proof: certify atlas Batch0246 (12:691 to 12:705) --- Collatz/Research/StoppingAtlas/Batch0246.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0246.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0246.lean b/Collatz/Research/StoppingAtlas/Batch0246.lean new file mode 100644 index 00000000..4139d232 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0246.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0246 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 691. -/ +theorem bounds_12_691 : exactInterval 12 691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_691 (m : Nat) : + stoppingTime (2 ^ 12 * m + 691) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_691 : oddCount 691 12 = 6 ∧ acceleratedOrbit 12 691 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_691 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 691) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_691.1, data_12_691.2] + +/-- Complete interval computation for depth 12, residue 692. -/ +theorem bounds_12_692 : exactInterval 12 692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_692 (m : Nat) : + stoppingTime (2 ^ 12 * m + 692) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_692 : oddCount 692 12 = 4 ∧ acceleratedOrbit 12 692 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_692 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 692) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_692.1, data_12_692.2] + +/-- Complete interval computation for depth 12, residue 693. -/ +theorem bounds_12_693 : exactInterval 12 693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_693 (m : Nat) : + stoppingTime (2 ^ 12 * m + 693) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_693 : oddCount 693 12 = 4 ∧ acceleratedOrbit 12 693 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_693 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 693) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_693.1, data_12_693.2] + +/-- Complete interval computation for depth 12, residue 694. -/ +theorem bounds_12_694 : exactInterval 12 694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_694 (m : Nat) : + stoppingTime (2 ^ 12 * m + 694) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_694 : oddCount 694 12 = 6 ∧ acceleratedOrbit 12 694 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_694 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 694) = 3 ^ 6 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_694.1, data_12_694.2] + +/-- Complete interval computation for depth 12, residue 695. -/ +theorem bounds_12_695 : exactInterval 12 695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_695 (m : Nat) : + stoppingTime (2 ^ 12 * m + 695) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_695 : oddCount 695 12 = 6 ∧ acceleratedOrbit 12 695 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_695 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 695) = 3 ^ 6 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_695.1, data_12_695.2] + +/-- Complete interval computation for depth 12, residue 696. -/ +theorem bounds_12_696 : exactInterval 12 696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_696 (m : Nat) : + stoppingTime (2 ^ 12 * m + 696) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_696 : oddCount 696 12 = 4 ∧ acceleratedOrbit 12 696 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_696 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 696) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_696.1, data_12_696.2] + +/-- Complete interval computation for depth 12, residue 697. -/ +theorem bounds_12_697 : exactInterval 12 697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_697 (m : Nat) : + stoppingTime (2 ^ 12 * m + 697) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_697 : oddCount 697 12 = 6 ∧ acceleratedOrbit 12 697 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_697 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 697) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_697.1, data_12_697.2] + +/-- Complete interval computation for depth 12, residue 698. -/ +theorem bounds_12_698 : exactInterval 12 698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_698 (m : Nat) : + stoppingTime (2 ^ 12 * m + 698) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_698 : oddCount 698 12 = 4 ∧ acceleratedOrbit 12 698 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_698 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 698) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_698.1, data_12_698.2] + +/-- Complete interval computation for depth 12, residue 699. -/ +theorem bounds_12_699 : exactInterval 12 699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_699 (m : Nat) : + stoppingTime (2 ^ 12 * m + 699) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_699 : oddCount 699 12 = 8 ∧ acceleratedOrbit 12 699 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_699 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 699) = 3 ^ 8 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_699.1, data_12_699.2] + +/-- Complete interval computation for depth 12, residue 700. -/ +theorem bounds_12_700 : exactInterval 12 700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_700 (m : Nat) : + stoppingTime (2 ^ 12 * m + 700) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_700 : oddCount 700 12 = 7 ∧ acceleratedOrbit 12 700 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_700 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 700) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_700.1, data_12_700.2] + +/-- Complete interval computation for depth 12, residue 701. -/ +theorem bounds_12_701 : exactInterval 12 701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_701 (m : Nat) : + stoppingTime (2 ^ 12 * m + 701) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_701 : oddCount 701 12 = 7 ∧ acceleratedOrbit 12 701 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_701 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 701) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_701.1, data_12_701.2] + +/-- Complete interval computation for depth 12, residue 702. -/ +theorem bounds_12_702 : exactInterval 12 702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_702 (m : Nat) : + stoppingTime (2 ^ 12 * m + 702) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_702 : oddCount 702 12 = 7 ∧ acceleratedOrbit 12 702 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_702 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 702) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_702.1, data_12_702.2] + +/-- Complete interval computation for depth 12, residue 703. -/ +theorem bounds_12_703 : exactInterval 12 703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_703 (m : Nat) : + stoppingTime (2 ^ 12 * m + 703) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_703 : oddCount 703 12 = 10 ∧ acceleratedOrbit 12 703 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_703 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 703) = 3 ^ 10 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_703.1, data_12_703.2] + +/-- Complete interval computation for depth 12, residue 704. -/ +theorem bounds_12_704 : exactInterval 12 704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_704 (m : Nat) : + stoppingTime (2 ^ 12 * m + 704) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_704 : oddCount 704 12 = 3 ∧ acceleratedOrbit 12 704 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_704 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 704) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_704.1, data_12_704.2] + +/-- Complete interval computation for depth 12, residue 705. -/ +theorem bounds_12_705 : exactInterval 12 705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_705 (m : Nat) : + stoppingTime (2 ^ 12 * m + 705) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_705 : oddCount 705 12 = 4 ∧ acceleratedOrbit 12 705 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_705 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 705) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_705.1, data_12_705.2] + +end Collatz.Research.StoppingAtlas.Batch0246 From 549df35003c2adb79600f418dac34d5e02cd1dfa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:17 +0530 Subject: [PATCH 0247/1001] proof: certify atlas Batch0247 (12:706 to 12:720) --- Collatz/Research/StoppingAtlas/Batch0247.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0247.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0247.lean b/Collatz/Research/StoppingAtlas/Batch0247.lean new file mode 100644 index 00000000..b1de0fe4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0247.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0247 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 706. -/ +theorem bounds_12_706 : exactInterval 12 706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_706 (m : Nat) : + stoppingTime (2 ^ 12 * m + 706) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_706 : oddCount 706 12 = 7 ∧ acceleratedOrbit 12 706 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_706 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 706) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_706.1, data_12_706.2] + +/-- Complete interval computation for depth 12, residue 707. -/ +theorem bounds_12_707 : exactInterval 12 707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_707 (m : Nat) : + stoppingTime (2 ^ 12 * m + 707) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_707 : oddCount 707 12 = 7 ∧ acceleratedOrbit 12 707 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_707 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 707) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_707.1, data_12_707.2] + +/-- Complete interval computation for depth 12, residue 708. -/ +theorem bounds_12_708 : exactInterval 12 708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_708 (m : Nat) : + stoppingTime (2 ^ 12 * m + 708) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_708 : oddCount 708 12 = 5 ∧ acceleratedOrbit 12 708 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_708 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 708) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_708.1, data_12_708.2] + +/-- Complete interval computation for depth 12, residue 709. -/ +theorem bounds_12_709 : exactInterval 12 709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_709 (m : Nat) : + stoppingTime (2 ^ 12 * m + 709) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_709 : oddCount 709 12 = 5 ∧ acceleratedOrbit 12 709 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_709 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 709) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_709.1, data_12_709.2] + +/-- Complete interval computation for depth 12, residue 710. -/ +theorem bounds_12_710 : exactInterval 12 710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_710 (m : Nat) : + stoppingTime (2 ^ 12 * m + 710) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_710 : oddCount 710 12 = 5 ∧ acceleratedOrbit 12 710 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_710 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 710) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_710.1, data_12_710.2] + +/-- Complete interval computation for depth 12, residue 711. -/ +theorem bounds_12_711 : exactInterval 12 711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_711 (m : Nat) : + stoppingTime (2 ^ 12 * m + 711) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_711 : oddCount 711 12 = 6 ∧ acceleratedOrbit 12 711 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_711 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 711) = 3 ^ 6 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_711.1, data_12_711.2] + +/-- Complete interval computation for depth 12, residue 712. -/ +theorem bounds_12_712 : exactInterval 12 712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_712 (m : Nat) : + stoppingTime (2 ^ 12 * m + 712) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_712 : oddCount 712 12 = 5 ∧ acceleratedOrbit 12 712 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_712 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 712) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_712.1, data_12_712.2] + +/-- Complete interval computation for depth 12, residue 713. -/ +theorem bounds_12_713 : exactInterval 12 713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_713 (m : Nat) : + stoppingTime (2 ^ 12 * m + 713) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_713 : oddCount 713 12 = 6 ∧ acceleratedOrbit 12 713 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_713 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 713) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_713.1, data_12_713.2] + +/-- Complete interval computation for depth 12, residue 714. -/ +theorem bounds_12_714 : exactInterval 12 714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_714 (m : Nat) : + stoppingTime (2 ^ 12 * m + 714) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_714 : oddCount 714 12 = 5 ∧ acceleratedOrbit 12 714 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_714 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 714) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_714.1, data_12_714.2] + +/-- Complete interval computation for depth 12, residue 715. -/ +theorem bounds_12_715 : exactInterval 12 715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_715 (m : Nat) : + stoppingTime (2 ^ 12 * m + 715) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_715 : oddCount 715 12 = 6 ∧ acceleratedOrbit 12 715 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_715 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 715) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_715.1, data_12_715.2] + +/-- Complete interval computation for depth 12, residue 716. -/ +theorem bounds_12_716 : exactInterval 12 716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_716 (m : Nat) : + stoppingTime (2 ^ 12 * m + 716) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_716 : oddCount 716 12 = 5 ∧ acceleratedOrbit 12 716 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_716 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 716) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_716.1, data_12_716.2] + +/-- Complete interval computation for depth 12, residue 717. -/ +theorem bounds_12_717 : exactInterval 12 717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_717 (m : Nat) : + stoppingTime (2 ^ 12 * m + 717) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_717 : oddCount 717 12 = 5 ∧ acceleratedOrbit 12 717 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_717 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 717) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_717.1, data_12_717.2] + +/-- Complete interval computation for depth 12, residue 718. -/ +theorem bounds_12_718 : exactInterval 12 718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_718 (m : Nat) : + stoppingTime (2 ^ 12 * m + 718) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_718 : oddCount 718 12 = 8 ∧ acceleratedOrbit 12 718 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_718 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 718) = 3 ^ 8 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_718.1, data_12_718.2] + +/-- Complete interval computation for depth 12, residue 719. -/ +theorem bounds_12_719 : exactInterval 12 719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_719 (m : Nat) : + stoppingTime (2 ^ 12 * m + 719) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_719 : oddCount 719 12 = 8 ∧ acceleratedOrbit 12 719 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_719 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 719) = 3 ^ 8 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_719.1, data_12_719.2] + +/-- Complete interval computation for depth 12, residue 720. -/ +theorem bounds_12_720 : exactInterval 12 720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_720 (m : Nat) : + stoppingTime (2 ^ 12 * m + 720) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_720 : oddCount 720 12 = 3 ∧ acceleratedOrbit 12 720 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_720 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 720) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_720.1, data_12_720.2] + +end Collatz.Research.StoppingAtlas.Batch0247 From 1ef030063c48c9508c22fb0557563437e2f94491 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:18 +0530 Subject: [PATCH 0248/1001] proof: certify atlas Batch0248 (12:721 to 12:736) --- Collatz/Research/StoppingAtlas/Batch0248.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0248.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0248.lean b/Collatz/Research/StoppingAtlas/Batch0248.lean new file mode 100644 index 00000000..c055d60d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0248.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0248 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 721. -/ +theorem bounds_12_721 : exactInterval 12 721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_721 (m : Nat) : + stoppingTime (2 ^ 12 * m + 721) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_721 : oddCount 721 12 = 5 ∧ acceleratedOrbit 12 721 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_721 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 721) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_721.1, data_12_721.2] + +/-- Complete interval computation for depth 12, residue 722. -/ +theorem bounds_12_722 : exactInterval 12 722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_722 (m : Nat) : + stoppingTime (2 ^ 12 * m + 722) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_722 : oddCount 722 12 = 5 ∧ acceleratedOrbit 12 722 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_722 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 722) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_722.1, data_12_722.2] + +/-- Complete interval computation for depth 12, residue 723. -/ +theorem bounds_12_723 : exactInterval 12 723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_723 (m : Nat) : + stoppingTime (2 ^ 12 * m + 723) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_723 : oddCount 723 12 = 5 ∧ acceleratedOrbit 12 723 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_723 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 723) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_723.1, data_12_723.2] + +/-- Complete interval computation for depth 12, residue 724. -/ +theorem bounds_12_724 : exactInterval 12 724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_724 (m : Nat) : + stoppingTime (2 ^ 12 * m + 724) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_724 : oddCount 724 12 = 3 ∧ acceleratedOrbit 12 724 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_724 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 724) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_724.1, data_12_724.2] + +/-- Complete interval computation for depth 12, residue 725. -/ +theorem bounds_12_725 : exactInterval 12 725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_725 (m : Nat) : + stoppingTime (2 ^ 12 * m + 725) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_725 : oddCount 725 12 = 3 ∧ acceleratedOrbit 12 725 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_725 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 725) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_725.1, data_12_725.2] + +/-- Complete interval computation for depth 12, residue 726. -/ +theorem bounds_12_726 : exactInterval 12 726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_726 (m : Nat) : + stoppingTime (2 ^ 12 * m + 726) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_726 : oddCount 726 12 = 6 ∧ acceleratedOrbit 12 726 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_726 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 726) = 3 ^ 6 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_726.1, data_12_726.2] + +/-- Complete interval computation for depth 12, residue 727. -/ +theorem bounds_12_727 : exactInterval 12 727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_727 (m : Nat) : + stoppingTime (2 ^ 12 * m + 727) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_727 : oddCount 727 12 = 6 ∧ acceleratedOrbit 12 727 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_727 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 727) = 3 ^ 6 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_727.1, data_12_727.2] + +/-- Complete interval computation for depth 12, residue 728. -/ +theorem bounds_12_728 : exactInterval 12 728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_728 (m : Nat) : + stoppingTime (2 ^ 12 * m + 728) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_728 : oddCount 728 12 = 7 ∧ acceleratedOrbit 12 728 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_728 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 728) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_728.1, data_12_728.2] + +/-- Complete interval computation for depth 12, residue 729. -/ +theorem bounds_12_729 : exactInterval 12 729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_729 (m : Nat) : + stoppingTime (2 ^ 12 * m + 729) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_729 : oddCount 729 12 = 5 ∧ acceleratedOrbit 12 729 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_729 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 729) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_729.1, data_12_729.2] + +/-- Complete interval computation for depth 12, residue 730. -/ +theorem bounds_12_730 : exactInterval 12 730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_730 (m : Nat) : + stoppingTime (2 ^ 12 * m + 730) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_730 : oddCount 730 12 = 7 ∧ acceleratedOrbit 12 730 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_730 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 730) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_730.1, data_12_730.2] + +/-- Complete interval computation for depth 12, residue 731. -/ +theorem bounds_12_731 : exactInterval 12 731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_731 (m : Nat) : + stoppingTime (2 ^ 12 * m + 731) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_731 : oddCount 731 12 = 8 ∧ acceleratedOrbit 12 731 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_731 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 731) = 3 ^ 8 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_731.1, data_12_731.2] + +/-- Complete interval computation for depth 12, residue 732. -/ +theorem bounds_12_732 : exactInterval 12 732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_732 (m : Nat) : + stoppingTime (2 ^ 12 * m + 732) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_732 : oddCount 732 12 = 7 ∧ acceleratedOrbit 12 732 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_732 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 732) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_732.1, data_12_732.2] + +/-- Complete interval computation for depth 12, residue 733. -/ +theorem bounds_12_733 : exactInterval 12 733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_733 (m : Nat) : + stoppingTime (2 ^ 12 * m + 733) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_733 : oddCount 733 12 = 7 ∧ acceleratedOrbit 12 733 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_733 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 733) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_733.1, data_12_733.2] + +/-- Complete interval computation for depth 12, residue 734. -/ +theorem bounds_12_734 : exactInterval 12 734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_734 (m : Nat) : + stoppingTime (2 ^ 12 * m + 734) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_734 : oddCount 734 12 = 6 ∧ acceleratedOrbit 12 734 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_734 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 734) = 3 ^ 6 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_734.1, data_12_734.2] + +/-- Complete interval computation for depth 12, residue 735. -/ +theorem bounds_12_735 : exactInterval 12 735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_735 (m : Nat) : + stoppingTime (2 ^ 12 * m + 735) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_735 : oddCount 735 12 = 6 ∧ acceleratedOrbit 12 735 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_735 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 735) = 3 ^ 6 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_735.1, data_12_735.2] + +/-- Complete interval computation for depth 12, residue 736. -/ +theorem bounds_12_736 : exactInterval 12 736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_736 (m : Nat) : + stoppingTime (2 ^ 12 * m + 736) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_736 : oddCount 736 12 = 3 ∧ acceleratedOrbit 12 736 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_736 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 736) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_736.1, data_12_736.2] + +end Collatz.Research.StoppingAtlas.Batch0248 From 9a90177dd9980f44023af0f996eaf6e475e392b2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:18 +0530 Subject: [PATCH 0249/1001] proof: certify atlas Batch0249 (12:737 to 12:751) --- Collatz/Research/StoppingAtlas/Batch0249.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0249.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0249.lean b/Collatz/Research/StoppingAtlas/Batch0249.lean new file mode 100644 index 00000000..ebbc85db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0249.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0249 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 737. -/ +theorem bounds_12_737 : exactInterval 12 737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_737 (m : Nat) : + stoppingTime (2 ^ 12 * m + 737) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_737 : oddCount 737 12 = 9 ∧ acceleratedOrbit 12 737 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_737 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 737) = 3 ^ 9 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_737.1, data_12_737.2] + +/-- Complete interval computation for depth 12, residue 738. -/ +theorem bounds_12_738 : exactInterval 12 738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_738 (m : Nat) : + stoppingTime (2 ^ 12 * m + 738) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_738 : oddCount 738 12 = 3 ∧ acceleratedOrbit 12 738 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_738 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 738) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_738.1, data_12_738.2] + +/-- Complete interval computation for depth 12, residue 739. -/ +theorem bounds_12_739 : exactInterval 12 739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_739 (m : Nat) : + stoppingTime (2 ^ 12 * m + 739) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_739 : oddCount 739 12 = 3 ∧ acceleratedOrbit 12 739 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_739 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 739) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_739.1, data_12_739.2] + +/-- Complete interval computation for depth 12, residue 740. -/ +theorem bounds_12_740 : exactInterval 12 740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_740 (m : Nat) : + stoppingTime (2 ^ 12 * m + 740) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_740 : oddCount 740 12 = 6 ∧ acceleratedOrbit 12 740 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_740 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 740) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_740.1, data_12_740.2] + +/-- Complete interval computation for depth 12, residue 741. -/ +theorem bounds_12_741 : exactInterval 12 741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_741 (m : Nat) : + stoppingTime (2 ^ 12 * m + 741) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_741 : oddCount 741 12 = 6 ∧ acceleratedOrbit 12 741 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_741 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 741) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_741.1, data_12_741.2] + +/-- Complete interval computation for depth 12, residue 742. -/ +theorem bounds_12_742 : exactInterval 12 742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_742 (m : Nat) : + stoppingTime (2 ^ 12 * m + 742) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_742 : oddCount 742 12 = 6 ∧ acceleratedOrbit 12 742 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_742 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 742) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_742.1, data_12_742.2] + +/-- Complete interval computation for depth 12, residue 743. -/ +theorem bounds_12_743 : exactInterval 12 743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_743 (m : Nat) : + stoppingTime (2 ^ 12 * m + 743) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_743 : oddCount 743 12 = 9 ∧ acceleratedOrbit 12 743 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_743 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 743) = 3 ^ 9 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_743.1, data_12_743.2] + +/-- Complete interval computation for depth 12, residue 744. -/ +theorem bounds_12_744 : exactInterval 12 744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_744 (m : Nat) : + stoppingTime (2 ^ 12 * m + 744) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_744 : oddCount 744 12 = 3 ∧ acceleratedOrbit 12 744 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_744 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 744) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_744.1, data_12_744.2] + +/-- Complete interval computation for depth 12, residue 745. -/ +theorem bounds_12_745 : exactInterval 12 745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_745 (m : Nat) : + stoppingTime (2 ^ 12 * m + 745) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_745 : oddCount 745 12 = 9 ∧ acceleratedOrbit 12 745 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_745 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 745) = 3 ^ 9 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_745.1, data_12_745.2] + +/-- Complete interval computation for depth 12, residue 746. -/ +theorem bounds_12_746 : exactInterval 12 746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_746 (m : Nat) : + stoppingTime (2 ^ 12 * m + 746) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_746 : oddCount 746 12 = 3 ∧ acceleratedOrbit 12 746 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_746 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 746) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_746.1, data_12_746.2] + +/-- Complete interval computation for depth 12, residue 747. -/ +theorem bounds_12_747 : exactInterval 12 747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_747 (m : Nat) : + stoppingTime (2 ^ 12 * m + 747) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_747 : oddCount 747 12 = 7 ∧ acceleratedOrbit 12 747 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_747 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 747) = 3 ^ 7 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_747.1, data_12_747.2] + +/-- Complete interval computation for depth 12, residue 748. -/ +theorem bounds_12_748 : exactInterval 12 748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_748 (m : Nat) : + stoppingTime (2 ^ 12 * m + 748) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_748 : oddCount 748 12 = 7 ∧ acceleratedOrbit 12 748 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_748 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 748) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_748.1, data_12_748.2] + +/-- Complete interval computation for depth 12, residue 749. -/ +theorem bounds_12_749 : exactInterval 12 749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_749 (m : Nat) : + stoppingTime (2 ^ 12 * m + 749) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_749 : oddCount 749 12 = 7 ∧ acceleratedOrbit 12 749 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_749 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 749) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_749.1, data_12_749.2] + +/-- Complete interval computation for depth 12, residue 750. -/ +theorem bounds_12_750 : exactInterval 12 750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_750 (m : Nat) : + stoppingTime (2 ^ 12 * m + 750) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_750 : oddCount 750 12 = 7 ∧ acceleratedOrbit 12 750 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_750 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 750) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_750.1, data_12_750.2] + +/-- Complete interval computation for depth 12, residue 751. -/ +theorem bounds_12_751 : exactInterval 12 751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_751 (m : Nat) : + stoppingTime (2 ^ 12 * m + 751) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_751 : oddCount 751 12 = 10 ∧ acceleratedOrbit 12 751 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_751 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 751) = 3 ^ 10 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_751.1, data_12_751.2] + +end Collatz.Research.StoppingAtlas.Batch0249 From 7fca5f389dffd539f71196e3033b8cd114a1630f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:18 +0530 Subject: [PATCH 0250/1001] proof: certify atlas Batch0250 (12:752 to 12:767) --- Collatz/Research/StoppingAtlas/Batch0250.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0250.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0250.lean b/Collatz/Research/StoppingAtlas/Batch0250.lean new file mode 100644 index 00000000..ef2f8eda --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0250.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0250 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 752. -/ +theorem bounds_12_752 : exactInterval 12 752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_752 (m : Nat) : + stoppingTime (2 ^ 12 * m + 752) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_752 : oddCount 752 12 = 6 ∧ acceleratedOrbit 12 752 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_752 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 752) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_752.1, data_12_752.2] + +/-- Complete interval computation for depth 12, residue 753. -/ +theorem bounds_12_753 : exactInterval 12 753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_753 (m : Nat) : + stoppingTime (2 ^ 12 * m + 753) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_753 : oddCount 753 12 = 3 ∧ acceleratedOrbit 12 753 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_753 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 753) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_753.1, data_12_753.2] + +/-- Complete interval computation for depth 12, residue 754. -/ +theorem bounds_12_754 : exactInterval 12 754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_754 (m : Nat) : + stoppingTime (2 ^ 12 * m + 754) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_754 : oddCount 754 12 = 9 ∧ acceleratedOrbit 12 754 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_754 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 754) = 3 ^ 9 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_754.1, data_12_754.2] + +/-- Complete interval computation for depth 12, residue 755. -/ +theorem bounds_12_755 : exactInterval 12 755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_755 (m : Nat) : + stoppingTime (2 ^ 12 * m + 755) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_755 : oddCount 755 12 = 9 ∧ acceleratedOrbit 12 755 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_755 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 755) = 3 ^ 9 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_755.1, data_12_755.2] + +/-- Complete interval computation for depth 12, residue 756. -/ +theorem bounds_12_756 : exactInterval 12 756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_756 (m : Nat) : + stoppingTime (2 ^ 12 * m + 756) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_756 : oddCount 756 12 = 6 ∧ acceleratedOrbit 12 756 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_756 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 756) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_756.1, data_12_756.2] + +/-- Complete interval computation for depth 12, residue 757. -/ +theorem bounds_12_757 : exactInterval 12 757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_757 (m : Nat) : + stoppingTime (2 ^ 12 * m + 757) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_757 : oddCount 757 12 = 6 ∧ acceleratedOrbit 12 757 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_757 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 757) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_757.1, data_12_757.2] + +/-- Complete interval computation for depth 12, residue 758. -/ +theorem bounds_12_758 : exactInterval 12 758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_758 (m : Nat) : + stoppingTime (2 ^ 12 * m + 758) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_758 : oddCount 758 12 = 7 ∧ acceleratedOrbit 12 758 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_758 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 758) = 3 ^ 7 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_758.1, data_12_758.2] + +/-- Complete interval computation for depth 12, residue 759. -/ +theorem bounds_12_759 : exactInterval 12 759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_759 (m : Nat) : + stoppingTime (2 ^ 12 * m + 759) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_759 : oddCount 759 12 = 7 ∧ acceleratedOrbit 12 759 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_759 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 759) = 3 ^ 7 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_759.1, data_12_759.2] + +/-- Complete interval computation for depth 12, residue 760. -/ +theorem bounds_12_760 : exactInterval 12 760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_760 (m : Nat) : + stoppingTime (2 ^ 12 * m + 760) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_760 : oddCount 760 12 = 6 ∧ acceleratedOrbit 12 760 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_760 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 760) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_760.1, data_12_760.2] + +/-- Complete interval computation for depth 12, residue 761. -/ +theorem bounds_12_761 : exactInterval 12 761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_761 (m : Nat) : + stoppingTime (2 ^ 12 * m + 761) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_761 : oddCount 761 12 = 6 ∧ acceleratedOrbit 12 761 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_761 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 761) = 3 ^ 6 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_761.1, data_12_761.2] + +/-- Complete interval computation for depth 12, residue 762. -/ +theorem bounds_12_762 : exactInterval 12 762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_762 (m : Nat) : + stoppingTime (2 ^ 12 * m + 762) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_762 : oddCount 762 12 = 6 ∧ acceleratedOrbit 12 762 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_762 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 762) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_762.1, data_12_762.2] + +/-- Complete interval computation for depth 12, residue 763. -/ +theorem bounds_12_763 : exactInterval 12 763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_763 (m : Nat) : + stoppingTime (2 ^ 12 * m + 763) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_763 : oddCount 763 12 = 8 ∧ acceleratedOrbit 12 763 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_763 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 763) = 3 ^ 8 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_763.1, data_12_763.2] + +/-- Complete interval computation for depth 12, residue 764. -/ +theorem bounds_12_764 : exactInterval 12 764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_764 (m : Nat) : + stoppingTime (2 ^ 12 * m + 764) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_764 : oddCount 764 12 = 7 ∧ acceleratedOrbit 12 764 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_764 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 764) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_764.1, data_12_764.2] + +/-- Complete interval computation for depth 12, residue 765. -/ +theorem bounds_12_765 : exactInterval 12 765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_765 (m : Nat) : + stoppingTime (2 ^ 12 * m + 765) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_765 : oddCount 765 12 = 7 ∧ acceleratedOrbit 12 765 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_765 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 765) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_765.1, data_12_765.2] + +/-- Complete interval computation for depth 12, residue 766. -/ +theorem bounds_12_766 : exactInterval 12 766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_766 (m : Nat) : + stoppingTime (2 ^ 12 * m + 766) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_766 : oddCount 766 12 = 7 ∧ acceleratedOrbit 12 766 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_766 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 766) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_766.1, data_12_766.2] + +/-- Complete interval computation for depth 12, residue 767. -/ +theorem bounds_12_767 : exactInterval 12 767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_767 (m : Nat) : + stoppingTime (2 ^ 12 * m + 767) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_767 : oddCount 767 12 = 10 ∧ acceleratedOrbit 12 767 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_767 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 767) = 3 ^ 10 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_767.1, data_12_767.2] + +end Collatz.Research.StoppingAtlas.Batch0250 From 17af2cfac20cc4eed8414a476cd37c9f08a4beee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:19 +0530 Subject: [PATCH 0251/1001] proof: certify atlas Batch0251 (12:768 to 12:782) --- Collatz/Research/StoppingAtlas/Batch0251.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0251.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0251.lean b/Collatz/Research/StoppingAtlas/Batch0251.lean new file mode 100644 index 00000000..4c774234 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0251.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0251 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 768. -/ +theorem bounds_12_768 : exactInterval 12 768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_768 (m : Nat) : + stoppingTime (2 ^ 12 * m + 768) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_768 : oddCount 768 12 = 2 ∧ acceleratedOrbit 12 768 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_768 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 768) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_768.1, data_12_768.2] + +/-- Complete interval computation for depth 12, residue 769. -/ +theorem bounds_12_769 : exactInterval 12 769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_769 (m : Nat) : + stoppingTime (2 ^ 12 * m + 769) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_769 : oddCount 769 12 = 5 ∧ acceleratedOrbit 12 769 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_769 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 769) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_769.1, data_12_769.2] + +/-- Complete interval computation for depth 12, residue 770. -/ +theorem bounds_12_770 : exactInterval 12 770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_770 (m : Nat) : + stoppingTime (2 ^ 12 * m + 770) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_770 : oddCount 770 12 = 5 ∧ acceleratedOrbit 12 770 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_770 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 770) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_770.1, data_12_770.2] + +/-- Complete interval computation for depth 12, residue 771. -/ +theorem bounds_12_771 : exactInterval 12 771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_771 (m : Nat) : + stoppingTime (2 ^ 12 * m + 771) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_771 : oddCount 771 12 = 5 ∧ acceleratedOrbit 12 771 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_771 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 771) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_771.1, data_12_771.2] + +/-- Complete interval computation for depth 12, residue 772. -/ +theorem bounds_12_772 : exactInterval 12 772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_772 (m : Nat) : + stoppingTime (2 ^ 12 * m + 772) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_772 : oddCount 772 12 = 5 ∧ acceleratedOrbit 12 772 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_772 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 772) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_772.1, data_12_772.2] + +/-- Complete interval computation for depth 12, residue 773. -/ +theorem bounds_12_773 : exactInterval 12 773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_773 (m : Nat) : + stoppingTime (2 ^ 12 * m + 773) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_773 : oddCount 773 12 = 5 ∧ acceleratedOrbit 12 773 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_773 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 773) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_773.1, data_12_773.2] + +/-- Complete interval computation for depth 12, residue 774. -/ +theorem bounds_12_774 : exactInterval 12 774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_774 (m : Nat) : + stoppingTime (2 ^ 12 * m + 774) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_774 : oddCount 774 12 = 5 ∧ acceleratedOrbit 12 774 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_774 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 774) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_774.1, data_12_774.2] + +/-- Complete interval computation for depth 12, residue 775. -/ +theorem bounds_12_775 : exactInterval 12 775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_775 (m : Nat) : + stoppingTime (2 ^ 12 * m + 775) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_775 : oddCount 775 12 = 7 ∧ acceleratedOrbit 12 775 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_775 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 775) = 3 ^ 7 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_775.1, data_12_775.2] + +/-- Complete interval computation for depth 12, residue 776. -/ +theorem bounds_12_776 : exactInterval 12 776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_776 (m : Nat) : + stoppingTime (2 ^ 12 * m + 776) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_776 : oddCount 776 12 = 5 ∧ acceleratedOrbit 12 776 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_776 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 776) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_776.1, data_12_776.2] + +/-- Complete interval computation for depth 12, residue 777. -/ +theorem bounds_12_777 : exactInterval 12 777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_777 (m : Nat) : + stoppingTime (2 ^ 12 * m + 777) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_777 : oddCount 777 12 = 7 ∧ acceleratedOrbit 12 777 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_777 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 777) = 3 ^ 7 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_777.1, data_12_777.2] + +/-- Complete interval computation for depth 12, residue 778. -/ +theorem bounds_12_778 : exactInterval 12 778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_778 (m : Nat) : + stoppingTime (2 ^ 12 * m + 778) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_778 : oddCount 778 12 = 5 ∧ acceleratedOrbit 12 778 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_778 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 778) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_778.1, data_12_778.2] + +/-- Complete interval computation for depth 12, residue 779. -/ +theorem bounds_12_779 : exactInterval 12 779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_779 (m : Nat) : + stoppingTime (2 ^ 12 * m + 779) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_779 : oddCount 779 12 = 7 ∧ acceleratedOrbit 12 779 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_779 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 779) = 3 ^ 7 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_779.1, data_12_779.2] + +/-- Complete interval computation for depth 12, residue 780. -/ +theorem bounds_12_780 : exactInterval 12 780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_780 (m : Nat) : + stoppingTime (2 ^ 12 * m + 780) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_780 : oddCount 780 12 = 5 ∧ acceleratedOrbit 12 780 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_780 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 780) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_780.1, data_12_780.2] + +/-- Complete interval computation for depth 12, residue 781. -/ +theorem bounds_12_781 : exactInterval 12 781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_781 (m : Nat) : + stoppingTime (2 ^ 12 * m + 781) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_781 : oddCount 781 12 = 5 ∧ acceleratedOrbit 12 781 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_781 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 781) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_781.1, data_12_781.2] + +/-- Complete interval computation for depth 12, residue 782. -/ +theorem bounds_12_782 : exactInterval 12 782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_782 (m : Nat) : + stoppingTime (2 ^ 12 * m + 782) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_782 : oddCount 782 12 = 5 ∧ acceleratedOrbit 12 782 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_782 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 782) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_782.1, data_12_782.2] + +end Collatz.Research.StoppingAtlas.Batch0251 From 794e6b2cc2d2d1fdfd376e78c3804d1c5f117ac3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:19 +0530 Subject: [PATCH 0252/1001] proof: certify atlas Batch0252 (12:783 to 12:797) --- Collatz/Research/StoppingAtlas/Batch0252.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0252.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0252.lean b/Collatz/Research/StoppingAtlas/Batch0252.lean new file mode 100644 index 00000000..f9b81309 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0252.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0252 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 783. -/ +theorem bounds_12_783 : exactInterval 12 783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_783 (m : Nat) : + stoppingTime (2 ^ 12 * m + 783) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_783 : oddCount 783 12 = 5 ∧ acceleratedOrbit 12 783 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_783 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 783) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_783.1, data_12_783.2] + +/-- Complete interval computation for depth 12, residue 784. -/ +theorem bounds_12_784 : exactInterval 12 784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_784 (m : Nat) : + stoppingTime (2 ^ 12 * m + 784) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_784 : oddCount 784 12 = 4 ∧ acceleratedOrbit 12 784 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_784 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 784) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_784.1, data_12_784.2] + +/-- Complete interval computation for depth 12, residue 785. -/ +theorem bounds_12_785 : exactInterval 12 785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_785 (m : Nat) : + stoppingTime (2 ^ 12 * m + 785) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_785 : oddCount 785 12 = 5 ∧ acceleratedOrbit 12 785 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_785 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 785) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_785.1, data_12_785.2] + +/-- Complete interval computation for depth 12, residue 786. -/ +theorem bounds_12_786 : exactInterval 12 786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_786 (m : Nat) : + stoppingTime (2 ^ 12 * m + 786) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_786 : oddCount 786 12 = 7 ∧ acceleratedOrbit 12 786 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_786 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 786) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_786.1, data_12_786.2] + +/-- Complete interval computation for depth 12, residue 787. -/ +theorem bounds_12_787 : exactInterval 12 787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_787 (m : Nat) : + stoppingTime (2 ^ 12 * m + 787) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_787 : oddCount 787 12 = 7 ∧ acceleratedOrbit 12 787 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_787 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 787) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_787.1, data_12_787.2] + +/-- Complete interval computation for depth 12, residue 788. -/ +theorem bounds_12_788 : exactInterval 12 788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_788 (m : Nat) : + stoppingTime (2 ^ 12 * m + 788) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_788 : oddCount 788 12 = 4 ∧ acceleratedOrbit 12 788 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_788 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 788) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_788.1, data_12_788.2] + +/-- Complete interval computation for depth 12, residue 789. -/ +theorem bounds_12_789 : exactInterval 12 789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_789 (m : Nat) : + stoppingTime (2 ^ 12 * m + 789) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_789 : oddCount 789 12 = 4 ∧ acceleratedOrbit 12 789 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_789 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 789) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_789.1, data_12_789.2] + +/-- Complete interval computation for depth 12, residue 790. -/ +theorem bounds_12_790 : exactInterval 12 790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_790 (m : Nat) : + stoppingTime (2 ^ 12 * m + 790) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_790 : oddCount 790 12 = 7 ∧ acceleratedOrbit 12 790 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_790 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 790) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_790.1, data_12_790.2] + +/-- Complete interval computation for depth 12, residue 791. -/ +theorem bounds_12_791 : exactInterval 12 791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_791 (m : Nat) : + stoppingTime (2 ^ 12 * m + 791) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_791 : oddCount 791 12 = 7 ∧ acceleratedOrbit 12 791 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_791 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 791) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_791.1, data_12_791.2] + +/-- Complete interval computation for depth 12, residue 792. -/ +theorem bounds_12_792 : exactInterval 12 792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_792 (m : Nat) : + stoppingTime (2 ^ 12 * m + 792) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_792 : oddCount 792 12 = 4 ∧ acceleratedOrbit 12 792 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_792 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 792) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_792.1, data_12_792.2] + +/-- Complete interval computation for depth 12, residue 793. -/ +theorem bounds_12_793 : exactInterval 12 793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_793 (m : Nat) : + stoppingTime (2 ^ 12 * m + 793) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_793 : oddCount 793 12 = 7 ∧ acceleratedOrbit 12 793 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_793 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 793) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_793.1, data_12_793.2] + +/-- Complete interval computation for depth 12, residue 794. -/ +theorem bounds_12_794 : exactInterval 12 794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_794 (m : Nat) : + stoppingTime (2 ^ 12 * m + 794) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_794 : oddCount 794 12 = 4 ∧ acceleratedOrbit 12 794 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_794 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 794) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_794.1, data_12_794.2] + +/-- Complete interval computation for depth 12, residue 795. -/ +theorem bounds_12_795 : exactInterval 12 795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_795 (m : Nat) : + stoppingTime (2 ^ 12 * m + 795) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_795 : oddCount 795 12 = 9 ∧ acceleratedOrbit 12 795 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_795 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 795) = 3 ^ 9 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_795.1, data_12_795.2] + +/-- Complete interval computation for depth 12, residue 796. -/ +theorem bounds_12_796 : exactInterval 12 796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_796 (m : Nat) : + stoppingTime (2 ^ 12 * m + 796) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_796 : oddCount 796 12 = 6 ∧ acceleratedOrbit 12 796 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_796 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 796) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_796.1, data_12_796.2] + +/-- Complete interval computation for depth 12, residue 797. -/ +theorem bounds_12_797 : exactInterval 12 797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_797 (m : Nat) : + stoppingTime (2 ^ 12 * m + 797) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_797 : oddCount 797 12 = 6 ∧ acceleratedOrbit 12 797 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_797 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 797) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_797.1, data_12_797.2] + +end Collatz.Research.StoppingAtlas.Batch0252 From 37041a58b612648ec63ec8b0f65ed957230eb3bb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:19 +0530 Subject: [PATCH 0253/1001] proof: certify atlas Batch0253 (12:798 to 12:813) --- Collatz/Research/StoppingAtlas/Batch0253.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0253.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0253.lean b/Collatz/Research/StoppingAtlas/Batch0253.lean new file mode 100644 index 00000000..51075118 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0253.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0253 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 798. -/ +theorem bounds_12_798 : exactInterval 12 798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_798 (m : Nat) : + stoppingTime (2 ^ 12 * m + 798) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_798 : oddCount 798 12 = 6 ∧ acceleratedOrbit 12 798 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_798 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 798) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_798.1, data_12_798.2] + +/-- Complete interval computation for depth 12, residue 799. -/ +theorem bounds_12_799 : exactInterval 12 799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_799 (m : Nat) : + stoppingTime (2 ^ 12 * m + 799) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_799 : oddCount 799 12 = 8 ∧ acceleratedOrbit 12 799 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_799 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 799) = 3 ^ 8 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_799.1, data_12_799.2] + +/-- Complete interval computation for depth 12, residue 800. -/ +theorem bounds_12_800 : exactInterval 12 800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_800 (m : Nat) : + stoppingTime (2 ^ 12 * m + 800) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_800 : oddCount 800 12 = 4 ∧ acceleratedOrbit 12 800 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_800 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 800) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_800.1, data_12_800.2] + +/-- Complete interval computation for depth 12, residue 801. -/ +theorem bounds_12_801 : exactInterval 12 801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_801 (m : Nat) : + stoppingTime (2 ^ 12 * m + 801) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_801 : oddCount 801 12 = 7 ∧ acceleratedOrbit 12 801 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_801 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 801) = 3 ^ 7 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_801.1, data_12_801.2] + +/-- Complete interval computation for depth 12, residue 802. -/ +theorem bounds_12_802 : exactInterval 12 802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_802 (m : Nat) : + stoppingTime (2 ^ 12 * m + 802) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_802 : oddCount 802 12 = 4 ∧ acceleratedOrbit 12 802 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_802 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 802) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_802.1, data_12_802.2] + +/-- Complete interval computation for depth 12, residue 803. -/ +theorem bounds_12_803 : exactInterval 12 803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_803 (m : Nat) : + stoppingTime (2 ^ 12 * m + 803) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_803 : oddCount 803 12 = 4 ∧ acceleratedOrbit 12 803 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_803 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 803) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_803.1, data_12_803.2] + +/-- Complete interval computation for depth 12, residue 804. -/ +theorem bounds_12_804 : exactInterval 12 804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_804 (m : Nat) : + stoppingTime (2 ^ 12 * m + 804) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_804 : oddCount 804 12 = 4 ∧ acceleratedOrbit 12 804 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_804 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 804) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_804.1, data_12_804.2] + +/-- Complete interval computation for depth 12, residue 805. -/ +theorem bounds_12_805 : exactInterval 12 805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_805 (m : Nat) : + stoppingTime (2 ^ 12 * m + 805) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_805 : oddCount 805 12 = 4 ∧ acceleratedOrbit 12 805 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_805 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 805) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_805.1, data_12_805.2] + +/-- Complete interval computation for depth 12, residue 806. -/ +theorem bounds_12_806 : exactInterval 12 806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_806 (m : Nat) : + stoppingTime (2 ^ 12 * m + 806) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_806 : oddCount 806 12 = 4 ∧ acceleratedOrbit 12 806 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_806 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 806) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_806.1, data_12_806.2] + +/-- Complete interval computation for depth 12, residue 807. -/ +theorem bounds_12_807 : exactInterval 12 807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_807 (m : Nat) : + stoppingTime (2 ^ 12 * m + 807) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_807 : oddCount 807 12 = 9 ∧ acceleratedOrbit 12 807 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_807 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 807) = 3 ^ 9 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_807.1, data_12_807.2] + +/-- Complete interval computation for depth 12, residue 808. -/ +theorem bounds_12_808 : exactInterval 12 808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_808 (m : Nat) : + stoppingTime (2 ^ 12 * m + 808) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_808 : oddCount 808 12 = 4 ∧ acceleratedOrbit 12 808 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_808 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 808) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_808.1, data_12_808.2] + +/-- Complete interval computation for depth 12, residue 809. -/ +theorem bounds_12_809 : exactInterval 12 809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_809 (m : Nat) : + stoppingTime (2 ^ 12 * m + 809) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_809 : oddCount 809 12 = 7 ∧ acceleratedOrbit 12 809 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_809 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 809) = 3 ^ 7 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_809.1, data_12_809.2] + +/-- Complete interval computation for depth 12, residue 810. -/ +theorem bounds_12_810 : exactInterval 12 810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_810 (m : Nat) : + stoppingTime (2 ^ 12 * m + 810) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_810 : oddCount 810 12 = 4 ∧ acceleratedOrbit 12 810 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_810 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 810) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_810.1, data_12_810.2] + +/-- Complete interval computation for depth 12, residue 811. -/ +theorem bounds_12_811 : exactInterval 12 811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_811 (m : Nat) : + stoppingTime (2 ^ 12 * m + 811) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_811 : oddCount 811 12 = 6 ∧ acceleratedOrbit 12 811 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_811 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 811) = 3 ^ 6 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_811.1, data_12_811.2] + +/-- Complete interval computation for depth 12, residue 812. -/ +theorem bounds_12_812 : exactInterval 12 812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_812 (m : Nat) : + stoppingTime (2 ^ 12 * m + 812) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_812 : oddCount 812 12 = 5 ∧ acceleratedOrbit 12 812 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_812 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 812) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_812.1, data_12_812.2] + +/-- Complete interval computation for depth 12, residue 813. -/ +theorem bounds_12_813 : exactInterval 12 813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_813 (m : Nat) : + stoppingTime (2 ^ 12 * m + 813) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_813 : oddCount 813 12 = 5 ∧ acceleratedOrbit 12 813 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_813 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 813) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_813.1, data_12_813.2] + +end Collatz.Research.StoppingAtlas.Batch0253 From 526cdfdc4198c6b21dd661e668e31093eabd5a4e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:20 +0530 Subject: [PATCH 0254/1001] proof: certify atlas Batch0254 (12:814 to 12:828) --- Collatz/Research/StoppingAtlas/Batch0254.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0254.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0254.lean b/Collatz/Research/StoppingAtlas/Batch0254.lean new file mode 100644 index 00000000..a211208b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0254.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0254 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 814. -/ +theorem bounds_12_814 : exactInterval 12 814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_814 (m : Nat) : + stoppingTime (2 ^ 12 * m + 814) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_814 : oddCount 814 12 = 5 ∧ acceleratedOrbit 12 814 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_814 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 814) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_814.1, data_12_814.2] + +/-- Complete interval computation for depth 12, residue 815. -/ +theorem bounds_12_815 : exactInterval 12 815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_815 (m : Nat) : + stoppingTime (2 ^ 12 * m + 815) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_815 : oddCount 815 12 = 7 ∧ acceleratedOrbit 12 815 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_815 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 815) = 3 ^ 7 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_815.1, data_12_815.2] + +/-- Complete interval computation for depth 12, residue 816. -/ +theorem bounds_12_816 : exactInterval 12 816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_816 (m : Nat) : + stoppingTime (2 ^ 12 * m + 816) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_816 : oddCount 816 12 = 4 ∧ acceleratedOrbit 12 816 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_816 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 816) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_816.1, data_12_816.2] + +/-- Complete interval computation for depth 12, residue 817. -/ +theorem bounds_12_817 : exactInterval 12 817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_817 (m : Nat) : + stoppingTime (2 ^ 12 * m + 817) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_817 : oddCount 817 12 = 5 ∧ acceleratedOrbit 12 817 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_817 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 817) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_817.1, data_12_817.2] + +/-- Complete interval computation for depth 12, residue 818. -/ +theorem bounds_12_818 : exactInterval 12 818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_818 (m : Nat) : + stoppingTime (2 ^ 12 * m + 818) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_818 : oddCount 818 12 = 5 ∧ acceleratedOrbit 12 818 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_818 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 818) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_818.1, data_12_818.2] + +/-- Complete interval computation for depth 12, residue 819. -/ +theorem bounds_12_819 : exactInterval 12 819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_819 (m : Nat) : + stoppingTime (2 ^ 12 * m + 819) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_819 : oddCount 819 12 = 5 ∧ acceleratedOrbit 12 819 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_819 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 819) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_819.1, data_12_819.2] + +/-- Complete interval computation for depth 12, residue 820. -/ +theorem bounds_12_820 : exactInterval 12 820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_820 (m : Nat) : + stoppingTime (2 ^ 12 * m + 820) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_820 : oddCount 820 12 = 4 ∧ acceleratedOrbit 12 820 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_820 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 820) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_820.1, data_12_820.2] + +/-- Complete interval computation for depth 12, residue 821. -/ +theorem bounds_12_821 : exactInterval 12 821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_821 (m : Nat) : + stoppingTime (2 ^ 12 * m + 821) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_821 : oddCount 821 12 = 4 ∧ acceleratedOrbit 12 821 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_821 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 821) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_821.1, data_12_821.2] + +/-- Complete interval computation for depth 12, residue 822. -/ +theorem bounds_12_822 : exactInterval 12 822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_822 (m : Nat) : + stoppingTime (2 ^ 12 * m + 822) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_822 : oddCount 822 12 = 8 ∧ acceleratedOrbit 12 822 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_822 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 822) = 3 ^ 8 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_822.1, data_12_822.2] + +/-- Complete interval computation for depth 12, residue 823. -/ +theorem bounds_12_823 : exactInterval 12 823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_823 (m : Nat) : + stoppingTime (2 ^ 12 * m + 823) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_823 : oddCount 823 12 = 8 ∧ acceleratedOrbit 12 823 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_823 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 823) = 3 ^ 8 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_823.1, data_12_823.2] + +/-- Complete interval computation for depth 12, residue 824. -/ +theorem bounds_12_824 : exactInterval 12 824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_824 (m : Nat) : + stoppingTime (2 ^ 12 * m + 824) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_824 : oddCount 824 12 = 7 ∧ acceleratedOrbit 12 824 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_824 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 824) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_824.1, data_12_824.2] + +/-- Complete interval computation for depth 12, residue 825. -/ +theorem bounds_12_825 : exactInterval 12 825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_825 (m : Nat) : + stoppingTime (2 ^ 12 * m + 825) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_825 : oddCount 825 12 = 7 ∧ acceleratedOrbit 12 825 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_825 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 825) = 3 ^ 7 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_825.1, data_12_825.2] + +/-- Complete interval computation for depth 12, residue 826. -/ +theorem bounds_12_826 : exactInterval 12 826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_826 (m : Nat) : + stoppingTime (2 ^ 12 * m + 826) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_826 : oddCount 826 12 = 7 ∧ acceleratedOrbit 12 826 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_826 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 826) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_826.1, data_12_826.2] + +/-- Complete interval computation for depth 12, residue 827. -/ +theorem bounds_12_827 : exactInterval 12 827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_827 (m : Nat) : + stoppingTime (2 ^ 12 * m + 827) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_827 : oddCount 827 12 = 6 ∧ acceleratedOrbit 12 827 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_827 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 827) = 3 ^ 6 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_827.1, data_12_827.2] + +/-- Complete interval computation for depth 12, residue 828. -/ +theorem bounds_12_828 : exactInterval 12 828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_828 (m : Nat) : + stoppingTime (2 ^ 12 * m + 828) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_828 : oddCount 828 12 = 7 ∧ acceleratedOrbit 12 828 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_828 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 828) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_828.1, data_12_828.2] + +end Collatz.Research.StoppingAtlas.Batch0254 From bad0f544de1f96746a2d975454a0209b06f80b90 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:20 +0530 Subject: [PATCH 0255/1001] proof: certify atlas Batch0255 (12:829 to 12:843) --- Collatz/Research/StoppingAtlas/Batch0255.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0255.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0255.lean b/Collatz/Research/StoppingAtlas/Batch0255.lean new file mode 100644 index 00000000..552fe5f3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0255.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0255 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 829. -/ +theorem bounds_12_829 : exactInterval 12 829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_829 (m : Nat) : + stoppingTime (2 ^ 12 * m + 829) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_829 : oddCount 829 12 = 7 ∧ acceleratedOrbit 12 829 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_829 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 829) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_829.1, data_12_829.2] + +/-- Complete interval computation for depth 12, residue 830. -/ +theorem bounds_12_830 : exactInterval 12 830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_830 (m : Nat) : + stoppingTime (2 ^ 12 * m + 830) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_830 : oddCount 830 12 = 8 ∧ acceleratedOrbit 12 830 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_830 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 830) = 3 ^ 8 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_830.1, data_12_830.2] + +/-- Complete interval computation for depth 12, residue 831. -/ +theorem bounds_12_831 : exactInterval 12 831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_831 (m : Nat) : + stoppingTime (2 ^ 12 * m + 831) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_831 : oddCount 831 12 = 8 ∧ acceleratedOrbit 12 831 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_831 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 831) = 3 ^ 8 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_831.1, data_12_831.2] + +/-- Complete interval computation for depth 12, residue 832. -/ +theorem bounds_12_832 : exactInterval 12 832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_832 (m : Nat) : + stoppingTime (2 ^ 12 * m + 832) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_832 : oddCount 832 12 = 2 ∧ acceleratedOrbit 12 832 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_832 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 832) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_832.1, data_12_832.2] + +/-- Complete interval computation for depth 12, residue 833. -/ +theorem bounds_12_833 : exactInterval 12 833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_833 (m : Nat) : + stoppingTime (2 ^ 12 * m + 833) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_833 : oddCount 833 12 = 4 ∧ acceleratedOrbit 12 833 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_833 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 833) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_833.1, data_12_833.2] + +/-- Complete interval computation for depth 12, residue 834. -/ +theorem bounds_12_834 : exactInterval 12 834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_834 (m : Nat) : + stoppingTime (2 ^ 12 * m + 834) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_834 : oddCount 834 12 = 7 ∧ acceleratedOrbit 12 834 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_834 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 834) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_834.1, data_12_834.2] + +/-- Complete interval computation for depth 12, residue 835. -/ +theorem bounds_12_835 : exactInterval 12 835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_835 (m : Nat) : + stoppingTime (2 ^ 12 * m + 835) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_835 : oddCount 835 12 = 7 ∧ acceleratedOrbit 12 835 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_835 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 835) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_835.1, data_12_835.2] + +/-- Complete interval computation for depth 12, residue 836. -/ +theorem bounds_12_836 : exactInterval 12 836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_836 (m : Nat) : + stoppingTime (2 ^ 12 * m + 836) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_836 : oddCount 836 12 = 6 ∧ acceleratedOrbit 12 836 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_836 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 836) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_836.1, data_12_836.2] + +/-- Complete interval computation for depth 12, residue 837. -/ +theorem bounds_12_837 : exactInterval 12 837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_837 (m : Nat) : + stoppingTime (2 ^ 12 * m + 837) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_837 : oddCount 837 12 = 6 ∧ acceleratedOrbit 12 837 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_837 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 837) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_837.1, data_12_837.2] + +/-- Complete interval computation for depth 12, residue 838. -/ +theorem bounds_12_838 : exactInterval 12 838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_838 (m : Nat) : + stoppingTime (2 ^ 12 * m + 838) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_838 : oddCount 838 12 = 6 ∧ acceleratedOrbit 12 838 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_838 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 838) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_838.1, data_12_838.2] + +/-- Complete interval computation for depth 12, residue 839. -/ +theorem bounds_12_839 : exactInterval 12 839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_839 (m : Nat) : + stoppingTime (2 ^ 12 * m + 839) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_839 : oddCount 839 12 = 9 ∧ acceleratedOrbit 12 839 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_839 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 839) = 3 ^ 9 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_839.1, data_12_839.2] + +/-- Complete interval computation for depth 12, residue 840. -/ +theorem bounds_12_840 : exactInterval 12 840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_840 (m : Nat) : + stoppingTime (2 ^ 12 * m + 840) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_840 : oddCount 840 12 = 6 ∧ acceleratedOrbit 12 840 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_840 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 840) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_840.1, data_12_840.2] + +/-- Complete interval computation for depth 12, residue 841. -/ +theorem bounds_12_841 : exactInterval 12 841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_841 (m : Nat) : + stoppingTime (2 ^ 12 * m + 841) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_841 : oddCount 841 12 = 5 ∧ acceleratedOrbit 12 841 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_841 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 841) = 3 ^ 5 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_841.1, data_12_841.2] + +/-- Complete interval computation for depth 12, residue 842. -/ +theorem bounds_12_842 : exactInterval 12 842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_842 (m : Nat) : + stoppingTime (2 ^ 12 * m + 842) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_842 : oddCount 842 12 = 6 ∧ acceleratedOrbit 12 842 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_842 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 842) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_842.1, data_12_842.2] + +/-- Complete interval computation for depth 12, residue 843. -/ +theorem bounds_12_843 : exactInterval 12 843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_843 (m : Nat) : + stoppingTime (2 ^ 12 * m + 843) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_843 : oddCount 843 12 = 6 ∧ acceleratedOrbit 12 843 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_843 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 843) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_843.1, data_12_843.2] + +end Collatz.Research.StoppingAtlas.Batch0255 From 574661e5e9f7af4f4b852596a26789a4ec73da5d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:20 +0530 Subject: [PATCH 0256/1001] proof: certify atlas Batch0256 (12:844 to 12:859) --- Collatz/Research/StoppingAtlas/Batch0256.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0256.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0256.lean b/Collatz/Research/StoppingAtlas/Batch0256.lean new file mode 100644 index 00000000..9bd90a79 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0256.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0256 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 844. -/ +theorem bounds_12_844 : exactInterval 12 844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_844 (m : Nat) : + stoppingTime (2 ^ 12 * m + 844) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_844 : oddCount 844 12 = 6 ∧ acceleratedOrbit 12 844 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_844 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 844) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_844.1, data_12_844.2] + +/-- Complete interval computation for depth 12, residue 845. -/ +theorem bounds_12_845 : exactInterval 12 845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_845 (m : Nat) : + stoppingTime (2 ^ 12 * m + 845) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_845 : oddCount 845 12 = 6 ∧ acceleratedOrbit 12 845 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_845 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 845) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_845.1, data_12_845.2] + +/-- Complete interval computation for depth 12, residue 846. -/ +theorem bounds_12_846 : exactInterval 12 846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_846 (m : Nat) : + stoppingTime (2 ^ 12 * m + 846) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_846 : oddCount 846 12 = 6 ∧ acceleratedOrbit 12 846 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_846 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 846) = 3 ^ 6 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_846.1, data_12_846.2] + +/-- Complete interval computation for depth 12, residue 847. -/ +theorem bounds_12_847 : exactInterval 12 847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_847 (m : Nat) : + stoppingTime (2 ^ 12 * m + 847) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_847 : oddCount 847 12 = 6 ∧ acceleratedOrbit 12 847 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_847 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 847) = 3 ^ 6 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_847.1, data_12_847.2] + +/-- Complete interval computation for depth 12, residue 848. -/ +theorem bounds_12_848 : exactInterval 12 848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_848 (m : Nat) : + stoppingTime (2 ^ 12 * m + 848) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_848 : oddCount 848 12 = 2 ∧ acceleratedOrbit 12 848 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_848 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 848) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_848.1, data_12_848.2] + +/-- Complete interval computation for depth 12, residue 849. -/ +theorem bounds_12_849 : exactInterval 12 849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_849 (m : Nat) : + stoppingTime (2 ^ 12 * m + 849) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_849 : oddCount 849 12 = 8 ∧ acceleratedOrbit 12 849 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_849 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 849) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_849.1, data_12_849.2] + +/-- Complete interval computation for depth 12, residue 850. -/ +theorem bounds_12_850 : exactInterval 12 850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_850 (m : Nat) : + stoppingTime (2 ^ 12 * m + 850) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_850 : oddCount 850 12 = 8 ∧ acceleratedOrbit 12 850 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_850 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 850) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_850.1, data_12_850.2] + +/-- Complete interval computation for depth 12, residue 851. -/ +theorem bounds_12_851 : exactInterval 12 851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_851 (m : Nat) : + stoppingTime (2 ^ 12 * m + 851) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_851 : oddCount 851 12 = 8 ∧ acceleratedOrbit 12 851 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_851 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 851) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_851.1, data_12_851.2] + +/-- Complete interval computation for depth 12, residue 852. -/ +theorem bounds_12_852 : exactInterval 12 852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_852 (m : Nat) : + stoppingTime (2 ^ 12 * m + 852) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_852 : oddCount 852 12 = 2 ∧ acceleratedOrbit 12 852 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_852 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 852) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_852.1, data_12_852.2] + +/-- Complete interval computation for depth 12, residue 853. -/ +theorem bounds_12_853 : exactInterval 12 853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_853 (m : Nat) : + stoppingTime (2 ^ 12 * m + 853) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_853 : oddCount 853 12 = 2 ∧ acceleratedOrbit 12 853 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_853 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 853) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_853.1, data_12_853.2] + +/-- Complete interval computation for depth 12, residue 854. -/ +theorem bounds_12_854 : exactInterval 12 854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_854 (m : Nat) : + stoppingTime (2 ^ 12 * m + 854) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_854 : oddCount 854 12 = 8 ∧ acceleratedOrbit 12 854 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_854 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 854) = 3 ^ 8 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_854.1, data_12_854.2] + +/-- Complete interval computation for depth 12, residue 855. -/ +theorem bounds_12_855 : exactInterval 12 855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_855 (m : Nat) : + stoppingTime (2 ^ 12 * m + 855) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_855 : oddCount 855 12 = 8 ∧ acceleratedOrbit 12 855 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_855 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 855) = 3 ^ 8 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_855.1, data_12_855.2] + +/-- Complete interval computation for depth 12, residue 856. -/ +theorem bounds_12_856 : exactInterval 12 856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_856 (m : Nat) : + stoppingTime (2 ^ 12 * m + 856) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_856 : oddCount 856 12 = 6 ∧ acceleratedOrbit 12 856 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_856 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 856) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_856.1, data_12_856.2] + +/-- Complete interval computation for depth 12, residue 857. -/ +theorem bounds_12_857 : exactInterval 12 857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_857 (m : Nat) : + stoppingTime (2 ^ 12 * m + 857) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_857 : oddCount 857 12 = 4 ∧ acceleratedOrbit 12 857 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_857 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 857) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_857.1, data_12_857.2] + +/-- Complete interval computation for depth 12, residue 858. -/ +theorem bounds_12_858 : exactInterval 12 858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_858 (m : Nat) : + stoppingTime (2 ^ 12 * m + 858) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_858 : oddCount 858 12 = 6 ∧ acceleratedOrbit 12 858 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_858 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 858) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_858.1, data_12_858.2] + +/-- Complete interval computation for depth 12, residue 859. -/ +theorem bounds_12_859 : exactInterval 12 859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_859 (m : Nat) : + stoppingTime (2 ^ 12 * m + 859) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_859 : oddCount 859 12 = 8 ∧ acceleratedOrbit 12 859 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_859 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 859) = 3 ^ 8 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_859.1, data_12_859.2] + +end Collatz.Research.StoppingAtlas.Batch0256 From 4a3a267426447eca45cc114c37baa084f0987bc3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:20 +0530 Subject: [PATCH 0257/1001] proof: certify atlas Batch0257 (12:860 to 12:874) --- Collatz/Research/StoppingAtlas/Batch0257.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0257.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0257.lean b/Collatz/Research/StoppingAtlas/Batch0257.lean new file mode 100644 index 00000000..e5469ded --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0257.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0257 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 860. -/ +theorem bounds_12_860 : exactInterval 12 860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_860 (m : Nat) : + stoppingTime (2 ^ 12 * m + 860) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_860 : oddCount 860 12 = 6 ∧ acceleratedOrbit 12 860 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_860 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 860) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_860.1, data_12_860.2] + +/-- Complete interval computation for depth 12, residue 861. -/ +theorem bounds_12_861 : exactInterval 12 861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_861 (m : Nat) : + stoppingTime (2 ^ 12 * m + 861) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_861 : oddCount 861 12 = 6 ∧ acceleratedOrbit 12 861 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_861 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 861) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_861.1, data_12_861.2] + +/-- Complete interval computation for depth 12, residue 862. -/ +theorem bounds_12_862 : exactInterval 12 862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_862 (m : Nat) : + stoppingTime (2 ^ 12 * m + 862) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_862 : oddCount 862 12 = 6 ∧ acceleratedOrbit 12 862 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_862 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 862) = 3 ^ 6 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_862.1, data_12_862.2] + +/-- Complete interval computation for depth 12, residue 863. -/ +theorem bounds_12_863 : exactInterval 12 863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_863 (m : Nat) : + stoppingTime (2 ^ 12 * m + 863) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_863 : oddCount 863 12 = 6 ∧ acceleratedOrbit 12 863 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_863 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 863) = 3 ^ 6 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_863.1, data_12_863.2] + +/-- Complete interval computation for depth 12, residue 864. -/ +theorem bounds_12_864 : exactInterval 12 864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_864 (m : Nat) : + stoppingTime (2 ^ 12 * m + 864) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_864 : oddCount 864 12 = 6 ∧ acceleratedOrbit 12 864 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_864 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 864) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_864.1, data_12_864.2] + +/-- Complete interval computation for depth 12, residue 865. -/ +theorem bounds_12_865 : exactInterval 12 865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_865 (m : Nat) : + stoppingTime (2 ^ 12 * m + 865) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_865 : oddCount 865 12 = 8 ∧ acceleratedOrbit 12 865 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_865 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 865) = 3 ^ 8 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_865.1, data_12_865.2] + +/-- Complete interval computation for depth 12, residue 866. -/ +theorem bounds_12_866 : exactInterval 12 866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_866 (m : Nat) : + stoppingTime (2 ^ 12 * m + 866) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_866 : oddCount 866 12 = 5 ∧ acceleratedOrbit 12 866 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_866 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 866) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_866.1, data_12_866.2] + +/-- Complete interval computation for depth 12, residue 867. -/ +theorem bounds_12_867 : exactInterval 12 867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_867 (m : Nat) : + stoppingTime (2 ^ 12 * m + 867) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_867 : oddCount 867 12 = 5 ∧ acceleratedOrbit 12 867 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_867 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 867) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_867.1, data_12_867.2] + +/-- Complete interval computation for depth 12, residue 868. -/ +theorem bounds_12_868 : exactInterval 12 868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_868 (m : Nat) : + stoppingTime (2 ^ 12 * m + 868) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_868 : oddCount 868 12 = 5 ∧ acceleratedOrbit 12 868 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_868 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 868) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_868.1, data_12_868.2] + +/-- Complete interval computation for depth 12, residue 869. -/ +theorem bounds_12_869 : exactInterval 12 869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_869 (m : Nat) : + stoppingTime (2 ^ 12 * m + 869) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_869 : oddCount 869 12 = 5 ∧ acceleratedOrbit 12 869 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_869 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 869) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_869.1, data_12_869.2] + +/-- Complete interval computation for depth 12, residue 870. -/ +theorem bounds_12_870 : exactInterval 12 870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_870 (m : Nat) : + stoppingTime (2 ^ 12 * m + 870) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_870 : oddCount 870 12 = 5 ∧ acceleratedOrbit 12 870 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_870 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 870) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_870.1, data_12_870.2] + +/-- Complete interval computation for depth 12, residue 871. -/ +theorem bounds_12_871 : exactInterval 12 871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_871 (m : Nat) : + stoppingTime (2 ^ 12 * m + 871) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_871 : oddCount 871 12 = 10 ∧ acceleratedOrbit 12 871 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_871 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 871) = 3 ^ 10 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_871.1, data_12_871.2] + +/-- Complete interval computation for depth 12, residue 872. -/ +theorem bounds_12_872 : exactInterval 12 872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_872 (m : Nat) : + stoppingTime (2 ^ 12 * m + 872) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_872 : oddCount 872 12 = 6 ∧ acceleratedOrbit 12 872 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_872 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 872) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_872.1, data_12_872.2] + +/-- Complete interval computation for depth 12, residue 873. -/ +theorem bounds_12_873 : exactInterval 12 873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_873 (m : Nat) : + stoppingTime (2 ^ 12 * m + 873) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_873 : oddCount 873 12 = 8 ∧ acceleratedOrbit 12 873 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_873 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 873) = 3 ^ 8 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_873.1, data_12_873.2] + +/-- Complete interval computation for depth 12, residue 874. -/ +theorem bounds_12_874 : exactInterval 12 874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_874 (m : Nat) : + stoppingTime (2 ^ 12 * m + 874) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_874 : oddCount 874 12 = 6 ∧ acceleratedOrbit 12 874 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_874 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 874) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_874.1, data_12_874.2] + +end Collatz.Research.StoppingAtlas.Batch0257 From fc9d9805ec55fcdbc0b2a7cc7ce7be52532b29d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:21 +0530 Subject: [PATCH 0258/1001] proof: certify atlas Batch0258 (12:875 to 12:889) --- Collatz/Research/StoppingAtlas/Batch0258.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0258.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0258.lean b/Collatz/Research/StoppingAtlas/Batch0258.lean new file mode 100644 index 00000000..47b4bd18 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0258.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0258 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 875. -/ +theorem bounds_12_875 : exactInterval 12 875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_875 (m : Nat) : + stoppingTime (2 ^ 12 * m + 875) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_875 : oddCount 875 12 = 5 ∧ acceleratedOrbit 12 875 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_875 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 875) = 3 ^ 5 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_875.1, data_12_875.2] + +/-- Complete interval computation for depth 12, residue 876. -/ +theorem bounds_12_876 : exactInterval 12 876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_876 (m : Nat) : + stoppingTime (2 ^ 12 * m + 876) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_876 : oddCount 876 12 = 6 ∧ acceleratedOrbit 12 876 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_876 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 876) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_876.1, data_12_876.2] + +/-- Complete interval computation for depth 12, residue 877. -/ +theorem bounds_12_877 : exactInterval 12 877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_877 (m : Nat) : + stoppingTime (2 ^ 12 * m + 877) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_877 : oddCount 877 12 = 6 ∧ acceleratedOrbit 12 877 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_877 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 877) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_877.1, data_12_877.2] + +/-- Complete interval computation for depth 12, residue 878. -/ +theorem bounds_12_878 : exactInterval 12 878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_878 (m : Nat) : + stoppingTime (2 ^ 12 * m + 878) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_878 : oddCount 878 12 = 6 ∧ acceleratedOrbit 12 878 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_878 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 878) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_878.1, data_12_878.2] + +/-- Complete interval computation for depth 12, residue 879. -/ +theorem bounds_12_879 : exactInterval 12 879 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_879 (m : Nat) : + stoppingTime (2 ^ 12 * m + 879) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_879 : oddCount 879 12 = 7 ∧ acceleratedOrbit 12 879 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_879 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 879) = 3 ^ 7 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_879.1, data_12_879.2] + +/-- Complete interval computation for depth 12, residue 880. -/ +theorem bounds_12_880 : exactInterval 12 880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_880 (m : Nat) : + stoppingTime (2 ^ 12 * m + 880) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_880 : oddCount 880 12 = 6 ∧ acceleratedOrbit 12 880 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_880 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 880) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_880.1, data_12_880.2] + +/-- Complete interval computation for depth 12, residue 881. -/ +theorem bounds_12_881 : exactInterval 12 881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_881 (m : Nat) : + stoppingTime (2 ^ 12 * m + 881) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_881 : oddCount 881 12 = 6 ∧ acceleratedOrbit 12 881 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_881 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 881) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_881.1, data_12_881.2] + +/-- Complete interval computation for depth 12, residue 882. -/ +theorem bounds_12_882 : exactInterval 12 882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_882 (m : Nat) : + stoppingTime (2 ^ 12 * m + 882) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_882 : oddCount 882 12 = 5 ∧ acceleratedOrbit 12 882 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_882 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 882) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_882.1, data_12_882.2] + +/-- Complete interval computation for depth 12, residue 883. -/ +theorem bounds_12_883 : exactInterval 12 883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_883 (m : Nat) : + stoppingTime (2 ^ 12 * m + 883) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_883 : oddCount 883 12 = 5 ∧ acceleratedOrbit 12 883 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_883 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 883) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_883.1, data_12_883.2] + +/-- Complete interval computation for depth 12, residue 884. -/ +theorem bounds_12_884 : exactInterval 12 884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_884 (m : Nat) : + stoppingTime (2 ^ 12 * m + 884) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_884 : oddCount 884 12 = 6 ∧ acceleratedOrbit 12 884 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_884 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 884) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_884.1, data_12_884.2] + +/-- Complete interval computation for depth 12, residue 885. -/ +theorem bounds_12_885 : exactInterval 12 885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_885 (m : Nat) : + stoppingTime (2 ^ 12 * m + 885) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_885 : oddCount 885 12 = 6 ∧ acceleratedOrbit 12 885 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_885 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 885) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_885.1, data_12_885.2] + +/-- Complete interval computation for depth 12, residue 886. -/ +theorem bounds_12_886 : exactInterval 12 886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_886 (m : Nat) : + stoppingTime (2 ^ 12 * m + 886) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_886 : oddCount 886 12 = 7 ∧ acceleratedOrbit 12 886 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_886 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 886) = 3 ^ 7 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_886.1, data_12_886.2] + +/-- Complete interval computation for depth 12, residue 887. -/ +theorem bounds_12_887 : exactInterval 12 887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_887 (m : Nat) : + stoppingTime (2 ^ 12 * m + 887) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_887 : oddCount 887 12 = 7 ∧ acceleratedOrbit 12 887 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_887 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 887) = 3 ^ 7 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_887.1, data_12_887.2] + +/-- Complete interval computation for depth 12, residue 888. -/ +theorem bounds_12_888 : exactInterval 12 888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_888 (m : Nat) : + stoppingTime (2 ^ 12 * m + 888) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_888 : oddCount 888 12 = 7 ∧ acceleratedOrbit 12 888 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_888 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 888) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_888.1, data_12_888.2] + +/-- Complete interval computation for depth 12, residue 889. -/ +theorem bounds_12_889 : exactInterval 12 889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_889 (m : Nat) : + stoppingTime (2 ^ 12 * m + 889) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_889 : oddCount 889 12 = 9 ∧ acceleratedOrbit 12 889 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_889 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 889) = 3 ^ 9 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_889.1, data_12_889.2] + +end Collatz.Research.StoppingAtlas.Batch0258 From 38c4d3677f127efa13151868a2c83eb52453cffc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:21 +0530 Subject: [PATCH 0259/1001] proof: certify atlas Batch0259 (12:890 to 12:905) --- Collatz/Research/StoppingAtlas/Batch0259.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0259.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0259.lean b/Collatz/Research/StoppingAtlas/Batch0259.lean new file mode 100644 index 00000000..f33dcc53 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0259.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0259 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 890. -/ +theorem bounds_12_890 : exactInterval 12 890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_890 (m : Nat) : + stoppingTime (2 ^ 12 * m + 890) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_890 : oddCount 890 12 = 7 ∧ acceleratedOrbit 12 890 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_890 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 890) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_890.1, data_12_890.2] + +/-- Complete interval computation for depth 12, residue 891. -/ +theorem bounds_12_891 : exactInterval 12 891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_891 (m : Nat) : + stoppingTime (2 ^ 12 * m + 891) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_891 : oddCount 891 12 = 9 ∧ acceleratedOrbit 12 891 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_891 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 891) = 3 ^ 9 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_891.1, data_12_891.2] + +/-- Complete interval computation for depth 12, residue 892. -/ +theorem bounds_12_892 : exactInterval 12 892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_892 (m : Nat) : + stoppingTime (2 ^ 12 * m + 892) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_892 : oddCount 892 12 = 7 ∧ acceleratedOrbit 12 892 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_892 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 892) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_892.1, data_12_892.2] + +/-- Complete interval computation for depth 12, residue 893. -/ +theorem bounds_12_893 : exactInterval 12 893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_893 (m : Nat) : + stoppingTime (2 ^ 12 * m + 893) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_893 : oddCount 893 12 = 7 ∧ acceleratedOrbit 12 893 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_893 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 893) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_893.1, data_12_893.2] + +/-- Complete interval computation for depth 12, residue 894. -/ +theorem bounds_12_894 : exactInterval 12 894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_894 (m : Nat) : + stoppingTime (2 ^ 12 * m + 894) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_894 : oddCount 894 12 = 9 ∧ acceleratedOrbit 12 894 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_894 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 894) = 3 ^ 9 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_894.1, data_12_894.2] + +/-- Complete interval computation for depth 12, residue 895. -/ +theorem bounds_12_895 : exactInterval 12 895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_895 (m : Nat) : + stoppingTime (2 ^ 12 * m + 895) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_895 : oddCount 895 12 = 9 ∧ acceleratedOrbit 12 895 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_895 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 895) = 3 ^ 9 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_895.1, data_12_895.2] + +/-- Complete interval computation for depth 12, residue 896. -/ +theorem bounds_12_896 : exactInterval 12 896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_896 (m : Nat) : + stoppingTime (2 ^ 12 * m + 896) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_896 : oddCount 896 12 = 4 ∧ acceleratedOrbit 12 896 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_896 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 896) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_896.1, data_12_896.2] + +/-- Complete interval computation for depth 12, residue 897. -/ +theorem bounds_12_897 : exactInterval 12 897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_897 (m : Nat) : + stoppingTime (2 ^ 12 * m + 897) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_897 : oddCount 897 12 = 7 ∧ acceleratedOrbit 12 897 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_897 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 897) = 3 ^ 7 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_897.1, data_12_897.2] + +/-- Complete interval computation for depth 12, residue 898. -/ +theorem bounds_12_898 : exactInterval 12 898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_898 (m : Nat) : + stoppingTime (2 ^ 12 * m + 898) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_898 : oddCount 898 12 = 7 ∧ acceleratedOrbit 12 898 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_898 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 898) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_898.1, data_12_898.2] + +/-- Complete interval computation for depth 12, residue 899. -/ +theorem bounds_12_899 : exactInterval 12 899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_899 (m : Nat) : + stoppingTime (2 ^ 12 * m + 899) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_899 : oddCount 899 12 = 7 ∧ acceleratedOrbit 12 899 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_899 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 899) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_899.1, data_12_899.2] + +/-- Complete interval computation for depth 12, residue 900. -/ +theorem bounds_12_900 : exactInterval 12 900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_900 (m : Nat) : + stoppingTime (2 ^ 12 * m + 900) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_900 : oddCount 900 12 = 8 ∧ acceleratedOrbit 12 900 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_900 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 900) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_900.1, data_12_900.2] + +/-- Complete interval computation for depth 12, residue 901. -/ +theorem bounds_12_901 : exactInterval 12 901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_901 (m : Nat) : + stoppingTime (2 ^ 12 * m + 901) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_901 : oddCount 901 12 = 8 ∧ acceleratedOrbit 12 901 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_901 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 901) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_901.1, data_12_901.2] + +/-- Complete interval computation for depth 12, residue 902. -/ +theorem bounds_12_902 : exactInterval 12 902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_902 (m : Nat) : + stoppingTime (2 ^ 12 * m + 902) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_902 : oddCount 902 12 = 8 ∧ acceleratedOrbit 12 902 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_902 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 902) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_902.1, data_12_902.2] + +/-- Complete interval computation for depth 12, residue 903. -/ +theorem bounds_12_903 : exactInterval 12 903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_903 (m : Nat) : + stoppingTime (2 ^ 12 * m + 903) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_903 : oddCount 903 12 = 7 ∧ acceleratedOrbit 12 903 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_903 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 903) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_903.1, data_12_903.2] + +/-- Complete interval computation for depth 12, residue 904. -/ +theorem bounds_12_904 : exactInterval 12 904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_904 (m : Nat) : + stoppingTime (2 ^ 12 * m + 904) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_904 : oddCount 904 12 = 2 ∧ acceleratedOrbit 12 904 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_904 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 904) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_904.1, data_12_904.2] + +/-- Complete interval computation for depth 12, residue 905. -/ +theorem bounds_12_905 : exactInterval 12 905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_905 (m : Nat) : + stoppingTime (2 ^ 12 * m + 905) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_905 : oddCount 905 12 = 8 ∧ acceleratedOrbit 12 905 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_905 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 905) = 3 ^ 8 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_905.1, data_12_905.2] + +end Collatz.Research.StoppingAtlas.Batch0259 From 2a370f8bb70aed295da856befc47ef0801f4c0d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:22 +0530 Subject: [PATCH 0260/1001] proof: certify atlas Batch0260 (12:906 to 12:920) --- Collatz/Research/StoppingAtlas/Batch0260.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0260.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0260.lean b/Collatz/Research/StoppingAtlas/Batch0260.lean new file mode 100644 index 00000000..b11556a8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0260.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0260 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 906. -/ +theorem bounds_12_906 : exactInterval 12 906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_906 (m : Nat) : + stoppingTime (2 ^ 12 * m + 906) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_906 : oddCount 906 12 = 2 ∧ acceleratedOrbit 12 906 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_906 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 906) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_906.1, data_12_906.2] + +/-- Complete interval computation for depth 12, residue 907. -/ +theorem bounds_12_907 : exactInterval 12 907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_907 (m : Nat) : + stoppingTime (2 ^ 12 * m + 907) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_907 : oddCount 907 12 = 9 ∧ acceleratedOrbit 12 907 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_907 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 907) = 3 ^ 9 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_907.1, data_12_907.2] + +/-- Complete interval computation for depth 12, residue 908. -/ +theorem bounds_12_908 : exactInterval 12 908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_908 (m : Nat) : + stoppingTime (2 ^ 12 * m + 908) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_908 : oddCount 908 12 = 2 ∧ acceleratedOrbit 12 908 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_908 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 908) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_908.1, data_12_908.2] + +/-- Complete interval computation for depth 12, residue 909. -/ +theorem bounds_12_909 : exactInterval 12 909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_909 (m : Nat) : + stoppingTime (2 ^ 12 * m + 909) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_909 : oddCount 909 12 = 2 ∧ acceleratedOrbit 12 909 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_909 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 909) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_909.1, data_12_909.2] + +/-- Complete interval computation for depth 12, residue 910. -/ +theorem bounds_12_910 : exactInterval 12 910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_910 (m : Nat) : + stoppingTime (2 ^ 12 * m + 910) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_910 : oddCount 910 12 = 7 ∧ acceleratedOrbit 12 910 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_910 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 910) = 3 ^ 7 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_910.1, data_12_910.2] + +/-- Complete interval computation for depth 12, residue 911. -/ +theorem bounds_12_911 : exactInterval 12 911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_911 (m : Nat) : + stoppingTime (2 ^ 12 * m + 911) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_911 : oddCount 911 12 = 7 ∧ acceleratedOrbit 12 911 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_911 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 911) = 3 ^ 7 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_911.1, data_12_911.2] + +/-- Complete interval computation for depth 12, residue 912. -/ +theorem bounds_12_912 : exactInterval 12 912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_912 (m : Nat) : + stoppingTime (2 ^ 12 * m + 912) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_912 : oddCount 912 12 = 5 ∧ acceleratedOrbit 12 912 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_912 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 912) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_912.1, data_12_912.2] + +/-- Complete interval computation for depth 12, residue 913. -/ +theorem bounds_12_913 : exactInterval 12 913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_913 (m : Nat) : + stoppingTime (2 ^ 12 * m + 913) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_913 : oddCount 913 12 = 6 ∧ acceleratedOrbit 12 913 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_913 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 913) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_913.1, data_12_913.2] + +/-- Complete interval computation for depth 12, residue 914. -/ +theorem bounds_12_914 : exactInterval 12 914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_914 (m : Nat) : + stoppingTime (2 ^ 12 * m + 914) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_914 : oddCount 914 12 = 6 ∧ acceleratedOrbit 12 914 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_914 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 914) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_914.1, data_12_914.2] + +/-- Complete interval computation for depth 12, residue 915. -/ +theorem bounds_12_915 : exactInterval 12 915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_915 (m : Nat) : + stoppingTime (2 ^ 12 * m + 915) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_915 : oddCount 915 12 = 6 ∧ acceleratedOrbit 12 915 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_915 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 915) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_915.1, data_12_915.2] + +/-- Complete interval computation for depth 12, residue 916. -/ +theorem bounds_12_916 : exactInterval 12 916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_916 (m : Nat) : + stoppingTime (2 ^ 12 * m + 916) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_916 : oddCount 916 12 = 5 ∧ acceleratedOrbit 12 916 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_916 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 916) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_916.1, data_12_916.2] + +/-- Complete interval computation for depth 12, residue 917. -/ +theorem bounds_12_917 : exactInterval 12 917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_917 (m : Nat) : + stoppingTime (2 ^ 12 * m + 917) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_917 : oddCount 917 12 = 5 ∧ acceleratedOrbit 12 917 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_917 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 917) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_917.1, data_12_917.2] + +/-- Complete interval computation for depth 12, residue 918. -/ +theorem bounds_12_918 : exactInterval 12 918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_918 (m : Nat) : + stoppingTime (2 ^ 12 * m + 918) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_918 : oddCount 918 12 = 5 ∧ acceleratedOrbit 12 918 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_918 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 918) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_918.1, data_12_918.2] + +/-- Complete interval computation for depth 12, residue 919. -/ +theorem bounds_12_919 : exactInterval 12 919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_919 (m : Nat) : + stoppingTime (2 ^ 12 * m + 919) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_919 : oddCount 919 12 = 5 ∧ acceleratedOrbit 12 919 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_919 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 919) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_919.1, data_12_919.2] + +/-- Complete interval computation for depth 12, residue 920. -/ +theorem bounds_12_920 : exactInterval 12 920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_920 (m : Nat) : + stoppingTime (2 ^ 12 * m + 920) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_920 : oddCount 920 12 = 5 ∧ acceleratedOrbit 12 920 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_920 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 920) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_920.1, data_12_920.2] + +end Collatz.Research.StoppingAtlas.Batch0260 From 0b70292a2150657b6b1772b836d5f8f42c05e700 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:22 +0530 Subject: [PATCH 0261/1001] proof: certify atlas Batch0261 (12:921 to 12:935) --- Collatz/Research/StoppingAtlas/Batch0261.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0261.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0261.lean b/Collatz/Research/StoppingAtlas/Batch0261.lean new file mode 100644 index 00000000..bd522dc5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0261.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0261 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 921. -/ +theorem bounds_12_921 : exactInterval 12 921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_921 (m : Nat) : + stoppingTime (2 ^ 12 * m + 921) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_921 : oddCount 921 12 = 5 ∧ acceleratedOrbit 12 921 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_921 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 921) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_921.1, data_12_921.2] + +/-- Complete interval computation for depth 12, residue 922. -/ +theorem bounds_12_922 : exactInterval 12 922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_922 (m : Nat) : + stoppingTime (2 ^ 12 * m + 922) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_922 : oddCount 922 12 = 5 ∧ acceleratedOrbit 12 922 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_922 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 922) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_922.1, data_12_922.2] + +/-- Complete interval computation for depth 12, residue 923. -/ +theorem bounds_12_923 : exactInterval 12 923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_923 (m : Nat) : + stoppingTime (2 ^ 12 * m + 923) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_923 : oddCount 923 12 = 7 ∧ acceleratedOrbit 12 923 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_923 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 923) = 3 ^ 7 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_923.1, data_12_923.2] + +/-- Complete interval computation for depth 12, residue 924. -/ +theorem bounds_12_924 : exactInterval 12 924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_924 (m : Nat) : + stoppingTime (2 ^ 12 * m + 924) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_924 : oddCount 924 12 = 7 ∧ acceleratedOrbit 12 924 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_924 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 924) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_924.1, data_12_924.2] + +/-- Complete interval computation for depth 12, residue 925. -/ +theorem bounds_12_925 : exactInterval 12 925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_925 (m : Nat) : + stoppingTime (2 ^ 12 * m + 925) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_925 : oddCount 925 12 = 7 ∧ acceleratedOrbit 12 925 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_925 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 925) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_925.1, data_12_925.2] + +/-- Complete interval computation for depth 12, residue 926. -/ +theorem bounds_12_926 : exactInterval 12 926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_926 (m : Nat) : + stoppingTime (2 ^ 12 * m + 926) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_926 : oddCount 926 12 = 7 ∧ acceleratedOrbit 12 926 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_926 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 926) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_926.1, data_12_926.2] + +/-- Complete interval computation for depth 12, residue 927. -/ +theorem bounds_12_927 : exactInterval 12 927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_927 (m : Nat) : + stoppingTime (2 ^ 12 * m + 927) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_927 : oddCount 927 12 = 8 ∧ acceleratedOrbit 12 927 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_927 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 927) = 3 ^ 8 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_927.1, data_12_927.2] + +/-- Complete interval computation for depth 12, residue 928. -/ +theorem bounds_12_928 : exactInterval 12 928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_928 (m : Nat) : + stoppingTime (2 ^ 12 * m + 928) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_928 : oddCount 928 12 = 4 ∧ acceleratedOrbit 12 928 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_928 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 928) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_928.1, data_12_928.2] + +/-- Complete interval computation for depth 12, residue 929. -/ +theorem bounds_12_929 : exactInterval 12 929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_929 (m : Nat) : + stoppingTime (2 ^ 12 * m + 929) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_929 : oddCount 929 12 = 6 ∧ acceleratedOrbit 12 929 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_929 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 929) = 3 ^ 6 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_929.1, data_12_929.2] + +/-- Complete interval computation for depth 12, residue 930. -/ +theorem bounds_12_930 : exactInterval 12 930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_930 (m : Nat) : + stoppingTime (2 ^ 12 * m + 930) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_930 : oddCount 930 12 = 5 ∧ acceleratedOrbit 12 930 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_930 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 930) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_930.1, data_12_930.2] + +/-- Complete interval computation for depth 12, residue 931. -/ +theorem bounds_12_931 : exactInterval 12 931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_931 (m : Nat) : + stoppingTime (2 ^ 12 * m + 931) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_931 : oddCount 931 12 = 5 ∧ acceleratedOrbit 12 931 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_931 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 931) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_931.1, data_12_931.2] + +/-- Complete interval computation for depth 12, residue 932. -/ +theorem bounds_12_932 : exactInterval 12 932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_932 (m : Nat) : + stoppingTime (2 ^ 12 * m + 932) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_932 : oddCount 932 12 = 6 ∧ acceleratedOrbit 12 932 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_932 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 932) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_932.1, data_12_932.2] + +/-- Complete interval computation for depth 12, residue 933. -/ +theorem bounds_12_933 : exactInterval 12 933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_933 (m : Nat) : + stoppingTime (2 ^ 12 * m + 933) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_933 : oddCount 933 12 = 6 ∧ acceleratedOrbit 12 933 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_933 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 933) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_933.1, data_12_933.2] + +/-- Complete interval computation for depth 12, residue 934. -/ +theorem bounds_12_934 : exactInterval 12 934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_934 (m : Nat) : + stoppingTime (2 ^ 12 * m + 934) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_934 : oddCount 934 12 = 6 ∧ acceleratedOrbit 12 934 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_934 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 934) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_934.1, data_12_934.2] + +/-- Complete interval computation for depth 12, residue 935. -/ +theorem bounds_12_935 : exactInterval 12 935 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_935 (m : Nat) : + stoppingTime (2 ^ 12 * m + 935) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_935 : oddCount 935 12 = 7 ∧ acceleratedOrbit 12 935 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_935 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 935) = 3 ^ 7 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_935.1, data_12_935.2] + +end Collatz.Research.StoppingAtlas.Batch0261 From c80404ffc575f89f0dfdc321bdaad44262b3f135 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:22 +0530 Subject: [PATCH 0262/1001] proof: certify atlas Batch0262 (12:936 to 12:951) --- Collatz/Research/StoppingAtlas/Batch0262.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0262.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0262.lean b/Collatz/Research/StoppingAtlas/Batch0262.lean new file mode 100644 index 00000000..5731a7b3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0262.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0262 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 936. -/ +theorem bounds_12_936 : exactInterval 12 936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_936 (m : Nat) : + stoppingTime (2 ^ 12 * m + 936) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_936 : oddCount 936 12 = 4 ∧ acceleratedOrbit 12 936 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_936 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 936) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_936.1, data_12_936.2] + +/-- Complete interval computation for depth 12, residue 937. -/ +theorem bounds_12_937 : exactInterval 12 937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_937 (m : Nat) : + stoppingTime (2 ^ 12 * m + 937) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_937 : oddCount 937 12 = 9 ∧ acceleratedOrbit 12 937 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_937 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 937) = 3 ^ 9 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_937.1, data_12_937.2] + +/-- Complete interval computation for depth 12, residue 938. -/ +theorem bounds_12_938 : exactInterval 12 938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_938 (m : Nat) : + stoppingTime (2 ^ 12 * m + 938) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_938 : oddCount 938 12 = 4 ∧ acceleratedOrbit 12 938 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_938 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 938) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_938.1, data_12_938.2] + +/-- Complete interval computation for depth 12, residue 939. -/ +theorem bounds_12_939 : exactInterval 12 939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_939 (m : Nat) : + stoppingTime (2 ^ 12 * m + 939) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_939 : oddCount 939 12 = 7 ∧ acceleratedOrbit 12 939 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_939 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 939) = 3 ^ 7 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_939.1, data_12_939.2] + +/-- Complete interval computation for depth 12, residue 940. -/ +theorem bounds_12_940 : exactInterval 12 940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_940 (m : Nat) : + stoppingTime (2 ^ 12 * m + 940) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_940 : oddCount 940 12 = 7 ∧ acceleratedOrbit 12 940 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_940 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 940) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_940.1, data_12_940.2] + +/-- Complete interval computation for depth 12, residue 941. -/ +theorem bounds_12_941 : exactInterval 12 941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_941 (m : Nat) : + stoppingTime (2 ^ 12 * m + 941) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_941 : oddCount 941 12 = 7 ∧ acceleratedOrbit 12 941 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_941 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 941) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_941.1, data_12_941.2] + +/-- Complete interval computation for depth 12, residue 942. -/ +theorem bounds_12_942 : exactInterval 12 942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_942 (m : Nat) : + stoppingTime (2 ^ 12 * m + 942) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_942 : oddCount 942 12 = 7 ∧ acceleratedOrbit 12 942 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_942 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 942) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_942.1, data_12_942.2] + +/-- Complete interval computation for depth 12, residue 943. -/ +theorem bounds_12_943 : exactInterval 12 943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_943 (m : Nat) : + stoppingTime (2 ^ 12 * m + 943) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_943 : oddCount 943 12 = 5 ∧ acceleratedOrbit 12 943 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_943 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 943) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_943.1, data_12_943.2] + +/-- Complete interval computation for depth 12, residue 944. -/ +theorem bounds_12_944 : exactInterval 12 944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_944 (m : Nat) : + stoppingTime (2 ^ 12 * m + 944) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_944 : oddCount 944 12 = 4 ∧ acceleratedOrbit 12 944 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_944 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 944) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_944.1, data_12_944.2] + +/-- Complete interval computation for depth 12, residue 945. -/ +theorem bounds_12_945 : exactInterval 12 945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_945 (m : Nat) : + stoppingTime (2 ^ 12 * m + 945) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_945 : oddCount 945 12 = 4 ∧ acceleratedOrbit 12 945 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_945 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 945) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_945.1, data_12_945.2] + +/-- Complete interval computation for depth 12, residue 946. -/ +theorem bounds_12_946 : exactInterval 12 946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_946 (m : Nat) : + stoppingTime (2 ^ 12 * m + 946) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_946 : oddCount 946 12 = 4 ∧ acceleratedOrbit 12 946 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_946 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 946) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_946.1, data_12_946.2] + +/-- Complete interval computation for depth 12, residue 947. -/ +theorem bounds_12_947 : exactInterval 12 947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_947 (m : Nat) : + stoppingTime (2 ^ 12 * m + 947) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_947 : oddCount 947 12 = 4 ∧ acceleratedOrbit 12 947 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_947 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 947) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_947.1, data_12_947.2] + +/-- Complete interval computation for depth 12, residue 948. -/ +theorem bounds_12_948 : exactInterval 12 948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_948 (m : Nat) : + stoppingTime (2 ^ 12 * m + 948) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_948 : oddCount 948 12 = 4 ∧ acceleratedOrbit 12 948 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_948 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 948) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_948.1, data_12_948.2] + +/-- Complete interval computation for depth 12, residue 949. -/ +theorem bounds_12_949 : exactInterval 12 949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_949 (m : Nat) : + stoppingTime (2 ^ 12 * m + 949) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_949 : oddCount 949 12 = 4 ∧ acceleratedOrbit 12 949 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_949 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 949) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_949.1, data_12_949.2] + +/-- Complete interval computation for depth 12, residue 950. -/ +theorem bounds_12_950 : exactInterval 12 950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_950 (m : Nat) : + stoppingTime (2 ^ 12 * m + 950) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_950 : oddCount 950 12 = 6 ∧ acceleratedOrbit 12 950 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_950 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 950) = 3 ^ 6 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_950.1, data_12_950.2] + +/-- Complete interval computation for depth 12, residue 951. -/ +theorem bounds_12_951 : exactInterval 12 951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_951 (m : Nat) : + stoppingTime (2 ^ 12 * m + 951) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_951 : oddCount 951 12 = 6 ∧ acceleratedOrbit 12 951 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_951 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 951) = 3 ^ 6 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_951.1, data_12_951.2] + +end Collatz.Research.StoppingAtlas.Batch0262 From b12ae85a3a3b3ec42d90c676a0d02955fc32b716 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:22 +0530 Subject: [PATCH 0263/1001] proof: certify atlas Batch0263 (12:952 to 12:966) --- Collatz/Research/StoppingAtlas/Batch0263.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0263.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0263.lean b/Collatz/Research/StoppingAtlas/Batch0263.lean new file mode 100644 index 00000000..f8a4da85 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0263.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0263 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 952. -/ +theorem bounds_12_952 : exactInterval 12 952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_952 (m : Nat) : + stoppingTime (2 ^ 12 * m + 952) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_952 : oddCount 952 12 = 4 ∧ acceleratedOrbit 12 952 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_952 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 952) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_952.1, data_12_952.2] + +/-- Complete interval computation for depth 12, residue 953. -/ +theorem bounds_12_953 : exactInterval 12 953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_953 (m : Nat) : + stoppingTime (2 ^ 12 * m + 953) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_953 : oddCount 953 12 = 7 ∧ acceleratedOrbit 12 953 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_953 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 953) = 3 ^ 7 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_953.1, data_12_953.2] + +/-- Complete interval computation for depth 12, residue 954. -/ +theorem bounds_12_954 : exactInterval 12 954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_954 (m : Nat) : + stoppingTime (2 ^ 12 * m + 954) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_954 : oddCount 954 12 = 4 ∧ acceleratedOrbit 12 954 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_954 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 954) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_954.1, data_12_954.2] + +/-- Complete interval computation for depth 12, residue 955. -/ +theorem bounds_12_955 : exactInterval 12 955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_955 (m : Nat) : + stoppingTime (2 ^ 12 * m + 955) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_955 : oddCount 955 12 = 7 ∧ acceleratedOrbit 12 955 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_955 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 955) = 3 ^ 7 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_955.1, data_12_955.2] + +/-- Complete interval computation for depth 12, residue 956. -/ +theorem bounds_12_956 : exactInterval 12 956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_956 (m : Nat) : + stoppingTime (2 ^ 12 * m + 956) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_956 : oddCount 956 12 = 9 ∧ acceleratedOrbit 12 956 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_956 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 956) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_956.1, data_12_956.2] + +/-- Complete interval computation for depth 12, residue 957. -/ +theorem bounds_12_957 : exactInterval 12 957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_957 (m : Nat) : + stoppingTime (2 ^ 12 * m + 957) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_957 : oddCount 957 12 = 9 ∧ acceleratedOrbit 12 957 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_957 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 957) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_957.1, data_12_957.2] + +/-- Complete interval computation for depth 12, residue 958. -/ +theorem bounds_12_958 : exactInterval 12 958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_958 (m : Nat) : + stoppingTime (2 ^ 12 * m + 958) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_958 : oddCount 958 12 = 9 ∧ acceleratedOrbit 12 958 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_958 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 958) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_958.1, data_12_958.2] + +/-- Complete interval computation for depth 12, residue 959. -/ +theorem bounds_12_959 : exactInterval 12 959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_959 (m : Nat) : + stoppingTime (2 ^ 12 * m + 959) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_959 : oddCount 959 12 = 10 ∧ acceleratedOrbit 12 959 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_959 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 959) = 3 ^ 10 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_959.1, data_12_959.2] + +/-- Complete interval computation for depth 12, residue 960. -/ +theorem bounds_12_960 : exactInterval 12 960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_960 (m : Nat) : + stoppingTime (2 ^ 12 * m + 960) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_960 : oddCount 960 12 = 4 ∧ acceleratedOrbit 12 960 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_960 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 960) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_960.1, data_12_960.2] + +/-- Complete interval computation for depth 12, residue 961. -/ +theorem bounds_12_961 : exactInterval 12 961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_961 (m : Nat) : + stoppingTime (2 ^ 12 * m + 961) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_961 : oddCount 961 12 = 6 ∧ acceleratedOrbit 12 961 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_961 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 961) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_961.1, data_12_961.2] + +/-- Complete interval computation for depth 12, residue 962. -/ +theorem bounds_12_962 : exactInterval 12 962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_962 (m : Nat) : + stoppingTime (2 ^ 12 * m + 962) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_962 : oddCount 962 12 = 6 ∧ acceleratedOrbit 12 962 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_962 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 962) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_962.1, data_12_962.2] + +/-- Complete interval computation for depth 12, residue 963. -/ +theorem bounds_12_963 : exactInterval 12 963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_963 (m : Nat) : + stoppingTime (2 ^ 12 * m + 963) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_963 : oddCount 963 12 = 6 ∧ acceleratedOrbit 12 963 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_963 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 963) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_963.1, data_12_963.2] + +/-- Complete interval computation for depth 12, residue 964. -/ +theorem bounds_12_964 : exactInterval 12 964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_964 (m : Nat) : + stoppingTime (2 ^ 12 * m + 964) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_964 : oddCount 964 12 = 4 ∧ acceleratedOrbit 12 964 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_964 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 964) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_964.1, data_12_964.2] + +/-- Complete interval computation for depth 12, residue 965. -/ +theorem bounds_12_965 : exactInterval 12 965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_965 (m : Nat) : + stoppingTime (2 ^ 12 * m + 965) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_965 : oddCount 965 12 = 4 ∧ acceleratedOrbit 12 965 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_965 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 965) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_965.1, data_12_965.2] + +/-- Complete interval computation for depth 12, residue 966. -/ +theorem bounds_12_966 : exactInterval 12 966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_966 (m : Nat) : + stoppingTime (2 ^ 12 * m + 966) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_966 : oddCount 966 12 = 4 ∧ acceleratedOrbit 12 966 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_966 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 966) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_966.1, data_12_966.2] + +end Collatz.Research.StoppingAtlas.Batch0263 From 4763d5d393eee091b7b0decd8a8b9269b59d12bd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:23 +0530 Subject: [PATCH 0264/1001] proof: certify atlas Batch0264 (12:967 to 12:982) --- Collatz/Research/StoppingAtlas/Batch0264.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0264.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0264.lean b/Collatz/Research/StoppingAtlas/Batch0264.lean new file mode 100644 index 00000000..26fd4087 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0264.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0264 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 967. -/ +theorem bounds_12_967 : exactInterval 12 967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_967 (m : Nat) : + stoppingTime (2 ^ 12 * m + 967) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_967 : oddCount 967 12 = 8 ∧ acceleratedOrbit 12 967 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_967 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 967) = 3 ^ 8 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_967.1, data_12_967.2] + +/-- Complete interval computation for depth 12, residue 968. -/ +theorem bounds_12_968 : exactInterval 12 968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_968 (m : Nat) : + stoppingTime (2 ^ 12 * m + 968) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_968 : oddCount 968 12 = 6 ∧ acceleratedOrbit 12 968 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_968 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 968) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_968.1, data_12_968.2] + +/-- Complete interval computation for depth 12, residue 969. -/ +theorem bounds_12_969 : exactInterval 12 969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_969 (m : Nat) : + stoppingTime (2 ^ 12 * m + 969) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_969 : oddCount 969 12 = 6 ∧ acceleratedOrbit 12 969 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_969 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 969) = 3 ^ 6 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_969.1, data_12_969.2] + +/-- Complete interval computation for depth 12, residue 970. -/ +theorem bounds_12_970 : exactInterval 12 970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_970 (m : Nat) : + stoppingTime (2 ^ 12 * m + 970) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_970 : oddCount 970 12 = 6 ∧ acceleratedOrbit 12 970 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_970 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 970) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_970.1, data_12_970.2] + +/-- Complete interval computation for depth 12, residue 971. -/ +theorem bounds_12_971 : exactInterval 12 971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_971 (m : Nat) : + stoppingTime (2 ^ 12 * m + 971) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_971 : oddCount 971 12 = 5 ∧ acceleratedOrbit 12 971 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_971 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 971) = 3 ^ 5 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_971.1, data_12_971.2] + +/-- Complete interval computation for depth 12, residue 972. -/ +theorem bounds_12_972 : exactInterval 12 972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_972 (m : Nat) : + stoppingTime (2 ^ 12 * m + 972) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_972 : oddCount 972 12 = 6 ∧ acceleratedOrbit 12 972 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_972 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 972) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_972.1, data_12_972.2] + +/-- Complete interval computation for depth 12, residue 973. -/ +theorem bounds_12_973 : exactInterval 12 973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_973 (m : Nat) : + stoppingTime (2 ^ 12 * m + 973) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_973 : oddCount 973 12 = 6 ∧ acceleratedOrbit 12 973 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_973 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 973) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_973.1, data_12_973.2] + +/-- Complete interval computation for depth 12, residue 974. -/ +theorem bounds_12_974 : exactInterval 12 974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_974 (m : Nat) : + stoppingTime (2 ^ 12 * m + 974) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_974 : oddCount 974 12 = 8 ∧ acceleratedOrbit 12 974 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_974 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 974) = 3 ^ 8 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_974.1, data_12_974.2] + +/-- Complete interval computation for depth 12, residue 975. -/ +theorem bounds_12_975 : exactInterval 12 975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_975 (m : Nat) : + stoppingTime (2 ^ 12 * m + 975) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_975 : oddCount 975 12 = 8 ∧ acceleratedOrbit 12 975 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_975 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 975) = 3 ^ 8 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_975.1, data_12_975.2] + +/-- Complete interval computation for depth 12, residue 976. -/ +theorem bounds_12_976 : exactInterval 12 976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_976 (m : Nat) : + stoppingTime (2 ^ 12 * m + 976) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_976 : oddCount 976 12 = 4 ∧ acceleratedOrbit 12 976 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_976 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 976) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_976.1, data_12_976.2] + +/-- Complete interval computation for depth 12, residue 977. -/ +theorem bounds_12_977 : exactInterval 12 977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_977 (m : Nat) : + stoppingTime (2 ^ 12 * m + 977) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_977 : oddCount 977 12 = 6 ∧ acceleratedOrbit 12 977 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_977 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 977) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_977.1, data_12_977.2] + +/-- Complete interval computation for depth 12, residue 978. -/ +theorem bounds_12_978 : exactInterval 12 978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_978 (m : Nat) : + stoppingTime (2 ^ 12 * m + 978) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_978 : oddCount 978 12 = 7 ∧ acceleratedOrbit 12 978 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_978 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 978) = 3 ^ 7 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_978.1, data_12_978.2] + +/-- Complete interval computation for depth 12, residue 979. -/ +theorem bounds_12_979 : exactInterval 12 979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_979 (m : Nat) : + stoppingTime (2 ^ 12 * m + 979) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_979 : oddCount 979 12 = 7 ∧ acceleratedOrbit 12 979 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_979 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 979) = 3 ^ 7 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_979.1, data_12_979.2] + +/-- Complete interval computation for depth 12, residue 980. -/ +theorem bounds_12_980 : exactInterval 12 980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_980 (m : Nat) : + stoppingTime (2 ^ 12 * m + 980) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_980 : oddCount 980 12 = 4 ∧ acceleratedOrbit 12 980 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_980 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 980) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_980.1, data_12_980.2] + +/-- Complete interval computation for depth 12, residue 981. -/ +theorem bounds_12_981 : exactInterval 12 981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_981 (m : Nat) : + stoppingTime (2 ^ 12 * m + 981) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_981 : oddCount 981 12 = 4 ∧ acceleratedOrbit 12 981 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_981 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 981) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_981.1, data_12_981.2] + +/-- Complete interval computation for depth 12, residue 982. -/ +theorem bounds_12_982 : exactInterval 12 982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_982 (m : Nat) : + stoppingTime (2 ^ 12 * m + 982) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_982 : oddCount 982 12 = 8 ∧ acceleratedOrbit 12 982 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_982 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 982) = 3 ^ 8 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_982.1, data_12_982.2] + +end Collatz.Research.StoppingAtlas.Batch0264 From 94e05c6392fce8ce1beb247ed69469163166dc15 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:23 +0530 Subject: [PATCH 0265/1001] proof: certify atlas Batch0265 (12:983 to 12:997) --- Collatz/Research/StoppingAtlas/Batch0265.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0265.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0265.lean b/Collatz/Research/StoppingAtlas/Batch0265.lean new file mode 100644 index 00000000..9362332a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0265.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0265 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 983. -/ +theorem bounds_12_983 : exactInterval 12 983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_983 (m : Nat) : + stoppingTime (2 ^ 12 * m + 983) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_983 : oddCount 983 12 = 8 ∧ acceleratedOrbit 12 983 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_983 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 983) = 3 ^ 8 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_983.1, data_12_983.2] + +/-- Complete interval computation for depth 12, residue 984. -/ +theorem bounds_12_984 : exactInterval 12 984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_984 (m : Nat) : + stoppingTime (2 ^ 12 * m + 984) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_984 : oddCount 984 12 = 5 ∧ acceleratedOrbit 12 984 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_984 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 984) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_984.1, data_12_984.2] + +/-- Complete interval computation for depth 12, residue 985. -/ +theorem bounds_12_985 : exactInterval 12 985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_985 (m : Nat) : + stoppingTime (2 ^ 12 * m + 985) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_985 : oddCount 985 12 = 4 ∧ acceleratedOrbit 12 985 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_985 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 985) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_985.1, data_12_985.2] + +/-- Complete interval computation for depth 12, residue 986. -/ +theorem bounds_12_986 : exactInterval 12 986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_986 (m : Nat) : + stoppingTime (2 ^ 12 * m + 986) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_986 : oddCount 986 12 = 5 ∧ acceleratedOrbit 12 986 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_986 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 986) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_986.1, data_12_986.2] + +/-- Complete interval computation for depth 12, residue 987. -/ +theorem bounds_12_987 : exactInterval 12 987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_987 (m : Nat) : + stoppingTime (2 ^ 12 * m + 987) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_987 : oddCount 987 12 = 6 ∧ acceleratedOrbit 12 987 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_987 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 987) = 3 ^ 6 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_987.1, data_12_987.2] + +/-- Complete interval computation for depth 12, residue 988. -/ +theorem bounds_12_988 : exactInterval 12 988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_988 (m : Nat) : + stoppingTime (2 ^ 12 * m + 988) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_988 : oddCount 988 12 = 5 ∧ acceleratedOrbit 12 988 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_988 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 988) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_988.1, data_12_988.2] + +/-- Complete interval computation for depth 12, residue 989. -/ +theorem bounds_12_989 : exactInterval 12 989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_989 (m : Nat) : + stoppingTime (2 ^ 12 * m + 989) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_989 : oddCount 989 12 = 5 ∧ acceleratedOrbit 12 989 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_989 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 989) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_989.1, data_12_989.2] + +/-- Complete interval computation for depth 12, residue 990. -/ +theorem bounds_12_990 : exactInterval 12 990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_990 (m : Nat) : + stoppingTime (2 ^ 12 * m + 990) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_990 : oddCount 990 12 = 9 ∧ acceleratedOrbit 12 990 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_990 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 990) = 3 ^ 9 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_990.1, data_12_990.2] + +/-- Complete interval computation for depth 12, residue 991. -/ +theorem bounds_12_991 : exactInterval 12 991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_991 (m : Nat) : + stoppingTime (2 ^ 12 * m + 991) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_991 : oddCount 991 12 = 9 ∧ acceleratedOrbit 12 991 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_991 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 991) = 3 ^ 9 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_991.1, data_12_991.2] + +/-- Complete interval computation for depth 12, residue 992. -/ +theorem bounds_12_992 : exactInterval 12 992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_992 (m : Nat) : + stoppingTime (2 ^ 12 * m + 992) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_992 : oddCount 992 12 = 6 ∧ acceleratedOrbit 12 992 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_992 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 992) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_992.1, data_12_992.2] + +/-- Complete interval computation for depth 12, residue 993. -/ +theorem bounds_12_993 : exactInterval 12 993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_993 (m : Nat) : + stoppingTime (2 ^ 12 * m + 993) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_993 : oddCount 993 12 = 8 ∧ acceleratedOrbit 12 993 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_993 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 993) = 3 ^ 8 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_993.1, data_12_993.2] + +/-- Complete interval computation for depth 12, residue 994. -/ +theorem bounds_12_994 : exactInterval 12 994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_994 (m : Nat) : + stoppingTime (2 ^ 12 * m + 994) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_994 : oddCount 994 12 = 4 ∧ acceleratedOrbit 12 994 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_994 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 994) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_994.1, data_12_994.2] + +/-- Complete interval computation for depth 12, residue 995. -/ +theorem bounds_12_995 : exactInterval 12 995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_995 (m : Nat) : + stoppingTime (2 ^ 12 * m + 995) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_995 : oddCount 995 12 = 4 ∧ acceleratedOrbit 12 995 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_995 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 995) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_995.1, data_12_995.2] + +/-- Complete interval computation for depth 12, residue 996. -/ +theorem bounds_12_996 : exactInterval 12 996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_996 (m : Nat) : + stoppingTime (2 ^ 12 * m + 996) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_996 : oddCount 996 12 = 6 ∧ acceleratedOrbit 12 996 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_996 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 996) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_996.1, data_12_996.2] + +/-- Complete interval computation for depth 12, residue 997. -/ +theorem bounds_12_997 : exactInterval 12 997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_997 (m : Nat) : + stoppingTime (2 ^ 12 * m + 997) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_997 : oddCount 997 12 = 6 ∧ acceleratedOrbit 12 997 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_997 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 997) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_997.1, data_12_997.2] + +end Collatz.Research.StoppingAtlas.Batch0265 From a655baff8c4507f789db7840eb5782fbc3a8bd8a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:24 +0530 Subject: [PATCH 0266/1001] proof: certify atlas Batch0266 (12:998 to 12:1012) --- Collatz/Research/StoppingAtlas/Batch0266.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0266.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0266.lean b/Collatz/Research/StoppingAtlas/Batch0266.lean new file mode 100644 index 00000000..387216ea --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0266.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0266 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 998. -/ +theorem bounds_12_998 : exactInterval 12 998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_998 (m : Nat) : + stoppingTime (2 ^ 12 * m + 998) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_998 : oddCount 998 12 = 6 ∧ acceleratedOrbit 12 998 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_998 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 998) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_998.1, data_12_998.2] + +/-- Complete interval computation for depth 12, residue 999. -/ +theorem bounds_12_999 : exactInterval 12 999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_999 (m : Nat) : + stoppingTime (2 ^ 12 * m + 999) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_999 : oddCount 999 12 = 6 ∧ acceleratedOrbit 12 999 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_999 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 999) = 3 ^ 6 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_999.1, data_12_999.2] + +/-- Complete interval computation for depth 12, residue 1000. -/ +theorem bounds_12_1000 : exactInterval 12 1000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1000 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1000) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1000 : oddCount 1000 12 = 6 ∧ acceleratedOrbit 12 1000 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1000 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1000) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1000.1, data_12_1000.2] + +/-- Complete interval computation for depth 12, residue 1001. -/ +theorem bounds_12_1001 : exactInterval 12 1001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1001 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1001) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1001 : oddCount 1001 12 = 9 ∧ acceleratedOrbit 12 1001 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1001 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1001) = 3 ^ 9 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1001.1, data_12_1001.2] + +/-- Complete interval computation for depth 12, residue 1002. -/ +theorem bounds_12_1002 : exactInterval 12 1002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1002 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1002) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1002 : oddCount 1002 12 = 6 ∧ acceleratedOrbit 12 1002 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1002 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1002) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1002.1, data_12_1002.2] + +/-- Complete interval computation for depth 12, residue 1003. -/ +theorem bounds_12_1003 : exactInterval 12 1003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1003 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1003) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1003 : oddCount 1003 12 = 8 ∧ acceleratedOrbit 12 1003 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1003 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1003) = 3 ^ 8 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1003.1, data_12_1003.2] + +/-- Complete interval computation for depth 12, residue 1004. -/ +theorem bounds_12_1004 : exactInterval 12 1004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1004 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1004) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1004 : oddCount 1004 12 = 8 ∧ acceleratedOrbit 12 1004 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1004 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1004) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1004.1, data_12_1004.2] + +/-- Complete interval computation for depth 12, residue 1005. -/ +theorem bounds_12_1005 : exactInterval 12 1005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1005 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1005) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1005 : oddCount 1005 12 = 8 ∧ acceleratedOrbit 12 1005 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1005 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1005) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1005.1, data_12_1005.2] + +/-- Complete interval computation for depth 12, residue 1006. -/ +theorem bounds_12_1006 : exactInterval 12 1006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1006 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1006) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1006 : oddCount 1006 12 = 8 ∧ acceleratedOrbit 12 1006 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1006 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1006) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1006.1, data_12_1006.2] + +/-- Complete interval computation for depth 12, residue 1007. -/ +theorem bounds_12_1007 : exactInterval 12 1007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1007 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1007) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1007 : oddCount 1007 12 = 8 ∧ acceleratedOrbit 12 1007 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1007 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1007) = 3 ^ 8 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1007.1, data_12_1007.2] + +/-- Complete interval computation for depth 12, residue 1008. -/ +theorem bounds_12_1008 : exactInterval 12 1008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1008 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1008) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1008 : oddCount 1008 12 = 6 ∧ acceleratedOrbit 12 1008 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1008 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1008) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1008.1, data_12_1008.2] + +/-- Complete interval computation for depth 12, residue 1009. -/ +theorem bounds_12_1009 : exactInterval 12 1009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1009 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1009) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1009 : oddCount 1009 12 = 6 ∧ acceleratedOrbit 12 1009 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1009 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1009) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1009.1, data_12_1009.2] + +/-- Complete interval computation for depth 12, residue 1010. -/ +theorem bounds_12_1010 : exactInterval 12 1010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1010 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1010) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1010 : oddCount 1010 12 = 7 ∧ acceleratedOrbit 12 1010 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1010 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1010) = 3 ^ 7 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1010.1, data_12_1010.2] + +/-- Complete interval computation for depth 12, residue 1011. -/ +theorem bounds_12_1011 : exactInterval 12 1011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1011 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1011) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1011 : oddCount 1011 12 = 7 ∧ acceleratedOrbit 12 1011 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1011 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1011) = 3 ^ 7 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1011.1, data_12_1011.2] + +/-- Complete interval computation for depth 12, residue 1012. -/ +theorem bounds_12_1012 : exactInterval 12 1012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1012 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1012) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1012 : oddCount 1012 12 = 6 ∧ acceleratedOrbit 12 1012 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1012 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1012) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1012.1, data_12_1012.2] + +end Collatz.Research.StoppingAtlas.Batch0266 From 6f4250b9a3618af10f32167a10417748ee080b21 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:24 +0530 Subject: [PATCH 0267/1001] proof: certify atlas Batch0267 (12:1013 to 12:1028) --- Collatz/Research/StoppingAtlas/Batch0267.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0267.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0267.lean b/Collatz/Research/StoppingAtlas/Batch0267.lean new file mode 100644 index 00000000..7c097c43 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0267.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0267 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1013. -/ +theorem bounds_12_1013 : exactInterval 12 1013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1013 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1013) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1013 : oddCount 1013 12 = 6 ∧ acceleratedOrbit 12 1013 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1013 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1013) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1013.1, data_12_1013.2] + +/-- Complete interval computation for depth 12, residue 1014. -/ +theorem bounds_12_1014 : exactInterval 12 1014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1014 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1014) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1014 : oddCount 1014 12 = 6 ∧ acceleratedOrbit 12 1014 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1014 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1014) = 3 ^ 6 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1014.1, data_12_1014.2] + +/-- Complete interval computation for depth 12, residue 1015. -/ +theorem bounds_12_1015 : exactInterval 12 1015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1015 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1015) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1015 : oddCount 1015 12 = 6 ∧ acceleratedOrbit 12 1015 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1015 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1015) = 3 ^ 6 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1015.1, data_12_1015.2] + +/-- Complete interval computation for depth 12, residue 1016. -/ +theorem bounds_12_1016 : exactInterval 12 1016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1016 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1016) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1016 : oddCount 1016 12 = 8 ∧ acceleratedOrbit 12 1016 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1016 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1016) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1016.1, data_12_1016.2] + +/-- Complete interval computation for depth 12, residue 1017. -/ +theorem bounds_12_1017 : exactInterval 12 1017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1017 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1017) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1017 : oddCount 1017 12 = 8 ∧ acceleratedOrbit 12 1017 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1017 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1017) = 3 ^ 8 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1017.1, data_12_1017.2] + +/-- Complete interval computation for depth 12, residue 1018. -/ +theorem bounds_12_1018 : exactInterval 12 1018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1018 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1018) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1018 : oddCount 1018 12 = 8 ∧ acceleratedOrbit 12 1018 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1018 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1018) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1018.1, data_12_1018.2] + +/-- Complete interval computation for depth 12, residue 1019. -/ +theorem bounds_12_1019 : exactInterval 12 1019 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1019 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1019) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1019 : oddCount 1019 12 = 7 ∧ acceleratedOrbit 12 1019 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1019 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1019) = 3 ^ 7 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1019.1, data_12_1019.2] + +/-- Complete interval computation for depth 12, residue 1020. -/ +theorem bounds_12_1020 : exactInterval 12 1020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1020 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1020) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1020 : oddCount 1020 12 = 8 ∧ acceleratedOrbit 12 1020 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1020 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1020) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1020.1, data_12_1020.2] + +/-- Complete interval computation for depth 12, residue 1021. -/ +theorem bounds_12_1021 : exactInterval 12 1021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1021 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1021) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1021 : oddCount 1021 12 = 8 ∧ acceleratedOrbit 12 1021 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1021 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1021) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1021.1, data_12_1021.2] + +/-- Complete interval computation for depth 12, residue 1022. -/ +theorem bounds_12_1022 : exactInterval 12 1022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1022 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1022) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1022 : oddCount 1022 12 = 10 ∧ acceleratedOrbit 12 1022 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1022 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1022) = 3 ^ 10 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1022.1, data_12_1022.2] + +/-- Complete interval computation for depth 12, residue 1023. -/ +theorem bounds_12_1023 : exactInterval 12 1023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1023 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1023) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1023 : oddCount 1023 12 = 10 ∧ acceleratedOrbit 12 1023 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1023 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1023) = 3 ^ 10 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1023.1, data_12_1023.2] + +/-- Complete interval computation for depth 12, residue 1024. -/ +theorem bounds_12_1024 : exactInterval 12 1024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1024 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1024) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1024 : oddCount 1024 12 = 1 ∧ acceleratedOrbit 12 1024 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1024 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1024) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1024.1, data_12_1024.2] + +/-- Complete interval computation for depth 12, residue 1025. -/ +theorem bounds_12_1025 : exactInterval 12 1025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1025 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1025) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1025 : oddCount 1025 12 = 5 ∧ acceleratedOrbit 12 1025 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1025 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1025) = 3 ^ 5 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1025.1, data_12_1025.2] + +/-- Complete interval computation for depth 12, residue 1026. -/ +theorem bounds_12_1026 : exactInterval 12 1026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1026 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1026) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1026 : oddCount 1026 12 = 6 ∧ acceleratedOrbit 12 1026 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1026 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1026) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1026.1, data_12_1026.2] + +/-- Complete interval computation for depth 12, residue 1027. -/ +theorem bounds_12_1027 : exactInterval 12 1027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1027 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1027) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1027 : oddCount 1027 12 = 6 ∧ acceleratedOrbit 12 1027 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1027 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1027) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1027.1, data_12_1027.2] + +/-- Complete interval computation for depth 12, residue 1028. -/ +theorem bounds_12_1028 : exactInterval 12 1028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1028 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1028) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1028 : oddCount 1028 12 = 5 ∧ acceleratedOrbit 12 1028 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1028 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1028) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1028.1, data_12_1028.2] + +end Collatz.Research.StoppingAtlas.Batch0267 From 1658b54c157499f2c543bd8da491be176f8c2e79 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:24 +0530 Subject: [PATCH 0268/1001] proof: certify atlas Batch0268 (12:1029 to 12:1043) --- Collatz/Research/StoppingAtlas/Batch0268.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0268.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0268.lean b/Collatz/Research/StoppingAtlas/Batch0268.lean new file mode 100644 index 00000000..bd25ec72 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0268.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0268 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1029. -/ +theorem bounds_12_1029 : exactInterval 12 1029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1029 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1029) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1029 : oddCount 1029 12 = 5 ∧ acceleratedOrbit 12 1029 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1029 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1029) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1029.1, data_12_1029.2] + +/-- Complete interval computation for depth 12, residue 1030. -/ +theorem bounds_12_1030 : exactInterval 12 1030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1030 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1030) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1030 : oddCount 1030 12 = 5 ∧ acceleratedOrbit 12 1030 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1030 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1030) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1030.1, data_12_1030.2] + +/-- Complete interval computation for depth 12, residue 1031. -/ +theorem bounds_12_1031 : exactInterval 12 1031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1031 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1031) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1031 : oddCount 1031 12 = 6 ∧ acceleratedOrbit 12 1031 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1031 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1031) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1031.1, data_12_1031.2] + +/-- Complete interval computation for depth 12, residue 1032. -/ +theorem bounds_12_1032 : exactInterval 12 1032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1032 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1032) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1032 : oddCount 1032 12 = 6 ∧ acceleratedOrbit 12 1032 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1032 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1032) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1032.1, data_12_1032.2] + +/-- Complete interval computation for depth 12, residue 1033. -/ +theorem bounds_12_1033 : exactInterval 12 1033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1033 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1033) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1033 : oddCount 1033 12 = 7 ∧ acceleratedOrbit 12 1033 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1033 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1033) = 3 ^ 7 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1033.1, data_12_1033.2] + +/-- Complete interval computation for depth 12, residue 1034. -/ +theorem bounds_12_1034 : exactInterval 12 1034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1034 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1034) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1034 : oddCount 1034 12 = 6 ∧ acceleratedOrbit 12 1034 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1034 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1034) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1034.1, data_12_1034.2] + +/-- Complete interval computation for depth 12, residue 1035. -/ +theorem bounds_12_1035 : exactInterval 12 1035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1035 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1035) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1035 : oddCount 1035 12 = 5 ∧ acceleratedOrbit 12 1035 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1035 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1035) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1035.1, data_12_1035.2] + +/-- Complete interval computation for depth 12, residue 1036. -/ +theorem bounds_12_1036 : exactInterval 12 1036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1036 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1036) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1036 : oddCount 1036 12 = 6 ∧ acceleratedOrbit 12 1036 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1036 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1036) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1036.1, data_12_1036.2] + +/-- Complete interval computation for depth 12, residue 1037. -/ +theorem bounds_12_1037 : exactInterval 12 1037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1037 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1037) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1037 : oddCount 1037 12 = 6 ∧ acceleratedOrbit 12 1037 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1037 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1037) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1037.1, data_12_1037.2] + +/-- Complete interval computation for depth 12, residue 1038. -/ +theorem bounds_12_1038 : exactInterval 12 1038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1038 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1038) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1038 : oddCount 1038 12 = 7 ∧ acceleratedOrbit 12 1038 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1038 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1038) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1038.1, data_12_1038.2] + +/-- Complete interval computation for depth 12, residue 1039. -/ +theorem bounds_12_1039 : exactInterval 12 1039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1039 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1039) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1039 : oddCount 1039 12 = 7 ∧ acceleratedOrbit 12 1039 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1039 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1039) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1039.1, data_12_1039.2] + +/-- Complete interval computation for depth 12, residue 1040. -/ +theorem bounds_12_1040 : exactInterval 12 1040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1040 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1040) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1040 : oddCount 1040 12 = 3 ∧ acceleratedOrbit 12 1040 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1040 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1040) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1040.1, data_12_1040.2] + +/-- Complete interval computation for depth 12, residue 1041. -/ +theorem bounds_12_1041 : exactInterval 12 1041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1041 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1041) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1041 : oddCount 1041 12 = 6 ∧ acceleratedOrbit 12 1041 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1041 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1041) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1041.1, data_12_1041.2] + +/-- Complete interval computation for depth 12, residue 1042. -/ +theorem bounds_12_1042 : exactInterval 12 1042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1042 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1042) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1042 : oddCount 1042 12 = 5 ∧ acceleratedOrbit 12 1042 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1042 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1042) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1042.1, data_12_1042.2] + +/-- Complete interval computation for depth 12, residue 1043. -/ +theorem bounds_12_1043 : exactInterval 12 1043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1043 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1043) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1043 : oddCount 1043 12 = 5 ∧ acceleratedOrbit 12 1043 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1043 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1043) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1043.1, data_12_1043.2] + +end Collatz.Research.StoppingAtlas.Batch0268 From 0ecd232078c404436ccbc666d2a64c10344a167a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:24 +0530 Subject: [PATCH 0269/1001] proof: certify atlas Batch0269 (12:1044 to 12:1058) --- Collatz/Research/StoppingAtlas/Batch0269.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0269.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0269.lean b/Collatz/Research/StoppingAtlas/Batch0269.lean new file mode 100644 index 00000000..5dd1359b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0269.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0269 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1044. -/ +theorem bounds_12_1044 : exactInterval 12 1044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1044 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1044) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1044 : oddCount 1044 12 = 3 ∧ acceleratedOrbit 12 1044 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1044 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1044) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1044.1, data_12_1044.2] + +/-- Complete interval computation for depth 12, residue 1045. -/ +theorem bounds_12_1045 : exactInterval 12 1045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1045 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1045) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1045 : oddCount 1045 12 = 3 ∧ acceleratedOrbit 12 1045 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1045 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1045) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1045.1, data_12_1045.2] + +/-- Complete interval computation for depth 12, residue 1046. -/ +theorem bounds_12_1046 : exactInterval 12 1046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1046 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1046) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1046 : oddCount 1046 12 = 6 ∧ acceleratedOrbit 12 1046 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1046 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1046) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1046.1, data_12_1046.2] + +/-- Complete interval computation for depth 12, residue 1047. -/ +theorem bounds_12_1047 : exactInterval 12 1047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1047 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1047) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1047 : oddCount 1047 12 = 6 ∧ acceleratedOrbit 12 1047 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1047 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1047) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1047.1, data_12_1047.2] + +/-- Complete interval computation for depth 12, residue 1048. -/ +theorem bounds_12_1048 : exactInterval 12 1048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1048 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1048) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1048 : oddCount 1048 12 = 3 ∧ acceleratedOrbit 12 1048 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1048 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1048) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1048.1, data_12_1048.2] + +/-- Complete interval computation for depth 12, residue 1049. -/ +theorem bounds_12_1049 : exactInterval 12 1049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1049 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1049) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1049 : oddCount 1049 12 = 7 ∧ acceleratedOrbit 12 1049 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1049 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1049) = 3 ^ 7 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1049.1, data_12_1049.2] + +/-- Complete interval computation for depth 12, residue 1050. -/ +theorem bounds_12_1050 : exactInterval 12 1050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1050 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1050) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1050 : oddCount 1050 12 = 3 ∧ acceleratedOrbit 12 1050 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1050 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1050) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1050.1, data_12_1050.2] + +/-- Complete interval computation for depth 12, residue 1051. -/ +theorem bounds_12_1051 : exactInterval 12 1051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1051 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1051) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1051 : oddCount 1051 12 = 10 ∧ acceleratedOrbit 12 1051 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1051 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1051) = 3 ^ 10 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1051.1, data_12_1051.2] + +/-- Complete interval computation for depth 12, residue 1052. -/ +theorem bounds_12_1052 : exactInterval 12 1052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1052 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1052) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1052 : oddCount 1052 12 = 7 ∧ acceleratedOrbit 12 1052 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1052 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1052) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1052.1, data_12_1052.2] + +/-- Complete interval computation for depth 12, residue 1053. -/ +theorem bounds_12_1053 : exactInterval 12 1053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1053 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1053) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1053 : oddCount 1053 12 = 7 ∧ acceleratedOrbit 12 1053 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1053 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1053) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1053.1, data_12_1053.2] + +/-- Complete interval computation for depth 12, residue 1054. -/ +theorem bounds_12_1054 : exactInterval 12 1054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1054 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1054) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1054 : oddCount 1054 12 = 7 ∧ acceleratedOrbit 12 1054 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1054 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1054) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1054.1, data_12_1054.2] + +/-- Complete interval computation for depth 12, residue 1055. -/ +theorem bounds_12_1055 : exactInterval 12 1055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1055 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1055) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1055 : oddCount 1055 12 = 10 ∧ acceleratedOrbit 12 1055 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1055 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1055) = 3 ^ 10 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1055.1, data_12_1055.2] + +/-- Complete interval computation for depth 12, residue 1056. -/ +theorem bounds_12_1056 : exactInterval 12 1056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1056 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1056) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1056 : oddCount 1056 12 = 4 ∧ acceleratedOrbit 12 1056 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1056 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1056) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1056.1, data_12_1056.2] + +/-- Complete interval computation for depth 12, residue 1057. -/ +theorem bounds_12_1057 : exactInterval 12 1057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1057 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1057) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1057 : oddCount 1057 12 = 8 ∧ acceleratedOrbit 12 1057 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1057 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1057) = 3 ^ 8 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1057.1, data_12_1057.2] + +/-- Complete interval computation for depth 12, residue 1058. -/ +theorem bounds_12_1058 : exactInterval 12 1058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1058 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1058) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1058 : oddCount 1058 12 = 3 ∧ acceleratedOrbit 12 1058 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1058 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1058) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1058.1, data_12_1058.2] + +end Collatz.Research.StoppingAtlas.Batch0269 From 3646c6eeaaeaa6122ac4496a1e3d3b0dc565af31 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:25 +0530 Subject: [PATCH 0270/1001] proof: certify atlas Batch0270 (12:1059 to 12:1074) --- Collatz/Research/StoppingAtlas/Batch0270.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0270.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0270.lean b/Collatz/Research/StoppingAtlas/Batch0270.lean new file mode 100644 index 00000000..6da2c78e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0270.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0270 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1059. -/ +theorem bounds_12_1059 : exactInterval 12 1059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1059 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1059) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1059 : oddCount 1059 12 = 3 ∧ acceleratedOrbit 12 1059 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1059 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1059) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1059.1, data_12_1059.2] + +/-- Complete interval computation for depth 12, residue 1060. -/ +theorem bounds_12_1060 : exactInterval 12 1060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1060 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1060) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1060 : oddCount 1060 12 = 6 ∧ acceleratedOrbit 12 1060 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1060 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1060) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1060.1, data_12_1060.2] + +/-- Complete interval computation for depth 12, residue 1061. -/ +theorem bounds_12_1061 : exactInterval 12 1061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1061 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1061) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1061 : oddCount 1061 12 = 6 ∧ acceleratedOrbit 12 1061 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1061 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1061) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1061.1, data_12_1061.2] + +/-- Complete interval computation for depth 12, residue 1062. -/ +theorem bounds_12_1062 : exactInterval 12 1062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1062 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1062) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1062 : oddCount 1062 12 = 6 ∧ acceleratedOrbit 12 1062 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1062 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1062) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1062.1, data_12_1062.2] + +/-- Complete interval computation for depth 12, residue 1063. -/ +theorem bounds_12_1063 : exactInterval 12 1063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1063 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1063) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1063 : oddCount 1063 12 = 7 ∧ acceleratedOrbit 12 1063 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1063 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1063) = 3 ^ 7 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1063.1, data_12_1063.2] + +/-- Complete interval computation for depth 12, residue 1064. -/ +theorem bounds_12_1064 : exactInterval 12 1064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1064 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1064) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1064 : oddCount 1064 12 = 4 ∧ acceleratedOrbit 12 1064 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1064 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1064) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1064.1, data_12_1064.2] + +/-- Complete interval computation for depth 12, residue 1065. -/ +theorem bounds_12_1065 : exactInterval 12 1065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1065 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1065) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1065 : oddCount 1065 12 = 8 ∧ acceleratedOrbit 12 1065 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1065 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1065) = 3 ^ 8 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1065.1, data_12_1065.2] + +/-- Complete interval computation for depth 12, residue 1066. -/ +theorem bounds_12_1066 : exactInterval 12 1066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1066 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1066) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1066 : oddCount 1066 12 = 4 ∧ acceleratedOrbit 12 1066 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1066 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1066) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1066.1, data_12_1066.2] + +/-- Complete interval computation for depth 12, residue 1067. -/ +theorem bounds_12_1067 : exactInterval 12 1067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1067 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1067) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1067 : oddCount 1067 12 = 6 ∧ acceleratedOrbit 12 1067 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1067 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1067) = 3 ^ 6 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1067.1, data_12_1067.2] + +/-- Complete interval computation for depth 12, residue 1068. -/ +theorem bounds_12_1068 : exactInterval 12 1068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1068 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1068) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1068 : oddCount 1068 12 = 5 ∧ acceleratedOrbit 12 1068 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1068 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1068) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1068.1, data_12_1068.2] + +/-- Complete interval computation for depth 12, residue 1069. -/ +theorem bounds_12_1069 : exactInterval 12 1069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1069 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1069) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1069 : oddCount 1069 12 = 5 ∧ acceleratedOrbit 12 1069 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1069 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1069) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1069.1, data_12_1069.2] + +/-- Complete interval computation for depth 12, residue 1070. -/ +theorem bounds_12_1070 : exactInterval 12 1070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1070 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1070) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1070 : oddCount 1070 12 = 5 ∧ acceleratedOrbit 12 1070 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1070 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1070) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1070.1, data_12_1070.2] + +/-- Complete interval computation for depth 12, residue 1071. -/ +theorem bounds_12_1071 : exactInterval 12 1071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1071 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1071) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1071 : oddCount 1071 12 = 8 ∧ acceleratedOrbit 12 1071 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1071 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1071) = 3 ^ 8 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1071.1, data_12_1071.2] + +/-- Complete interval computation for depth 12, residue 1072. -/ +theorem bounds_12_1072 : exactInterval 12 1072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1072 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1072) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1072 : oddCount 1072 12 = 4 ∧ acceleratedOrbit 12 1072 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1072 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1072) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1072.1, data_12_1072.2] + +/-- Complete interval computation for depth 12, residue 1073. -/ +theorem bounds_12_1073 : exactInterval 12 1073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1073 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1073) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1073 : oddCount 1073 12 = 5 ∧ acceleratedOrbit 12 1073 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1073 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1073) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1073.1, data_12_1073.2] + +/-- Complete interval computation for depth 12, residue 1074. -/ +theorem bounds_12_1074 : exactInterval 12 1074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1074 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1074) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1074 : oddCount 1074 12 = 5 ∧ acceleratedOrbit 12 1074 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1074 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1074) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1074.1, data_12_1074.2] + +end Collatz.Research.StoppingAtlas.Batch0270 From 0bb17e9f8cf5e224e391763fcbda486c3c6cb62d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:25 +0530 Subject: [PATCH 0271/1001] proof: certify atlas Batch0271 (12:1075 to 12:1089) --- Collatz/Research/StoppingAtlas/Batch0271.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0271.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0271.lean b/Collatz/Research/StoppingAtlas/Batch0271.lean new file mode 100644 index 00000000..a29c21ac --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0271.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0271 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1075. -/ +theorem bounds_12_1075 : exactInterval 12 1075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1075 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1075) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1075 : oddCount 1075 12 = 5 ∧ acceleratedOrbit 12 1075 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1075 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1075) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1075.1, data_12_1075.2] + +/-- Complete interval computation for depth 12, residue 1076. -/ +theorem bounds_12_1076 : exactInterval 12 1076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1076 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1076) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1076 : oddCount 1076 12 = 4 ∧ acceleratedOrbit 12 1076 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1076 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1076) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1076.1, data_12_1076.2] + +/-- Complete interval computation for depth 12, residue 1077. -/ +theorem bounds_12_1077 : exactInterval 12 1077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1077 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1077) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1077 : oddCount 1077 12 = 4 ∧ acceleratedOrbit 12 1077 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1077 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1077) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1077.1, data_12_1077.2] + +/-- Complete interval computation for depth 12, residue 1078. -/ +theorem bounds_12_1078 : exactInterval 12 1078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1078 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1078) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1078 : oddCount 1078 12 = 7 ∧ acceleratedOrbit 12 1078 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1078 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1078) = 3 ^ 7 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1078.1, data_12_1078.2] + +/-- Complete interval computation for depth 12, residue 1079. -/ +theorem bounds_12_1079 : exactInterval 12 1079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1079 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1079) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1079 : oddCount 1079 12 = 7 ∧ acceleratedOrbit 12 1079 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1079 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1079) = 3 ^ 7 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1079.1, data_12_1079.2] + +/-- Complete interval computation for depth 12, residue 1080. -/ +theorem bounds_12_1080 : exactInterval 12 1080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1080 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1080) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1080 : oddCount 1080 12 = 5 ∧ acceleratedOrbit 12 1080 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1080 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1080) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1080.1, data_12_1080.2] + +/-- Complete interval computation for depth 12, residue 1081. -/ +theorem bounds_12_1081 : exactInterval 12 1081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1081 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1081) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1081 : oddCount 1081 12 = 6 ∧ acceleratedOrbit 12 1081 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1081 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1081) = 3 ^ 6 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1081.1, data_12_1081.2] + +/-- Complete interval computation for depth 12, residue 1082. -/ +theorem bounds_12_1082 : exactInterval 12 1082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1082 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1082) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1082 : oddCount 1082 12 = 5 ∧ acceleratedOrbit 12 1082 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1082 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1082) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1082.1, data_12_1082.2] + +/-- Complete interval computation for depth 12, residue 1083. -/ +theorem bounds_12_1083 : exactInterval 12 1083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1083 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1083) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1083 : oddCount 1083 12 = 7 ∧ acceleratedOrbit 12 1083 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1083 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1083) = 3 ^ 7 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1083.1, data_12_1083.2] + +/-- Complete interval computation for depth 12, residue 1084. -/ +theorem bounds_12_1084 : exactInterval 12 1084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1084 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1084) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1084 : oddCount 1084 12 = 5 ∧ acceleratedOrbit 12 1084 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1084 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1084) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1084.1, data_12_1084.2] + +/-- Complete interval computation for depth 12, residue 1085. -/ +theorem bounds_12_1085 : exactInterval 12 1085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1085 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1085) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1085 : oddCount 1085 12 = 5 ∧ acceleratedOrbit 12 1085 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1085 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1085) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1085.1, data_12_1085.2] + +/-- Complete interval computation for depth 12, residue 1086. -/ +theorem bounds_12_1086 : exactInterval 12 1086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1086 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1086) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1086 : oddCount 1086 12 = 7 ∧ acceleratedOrbit 12 1086 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1086 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1086) = 3 ^ 7 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1086.1, data_12_1086.2] + +/-- Complete interval computation for depth 12, residue 1087. -/ +theorem bounds_12_1087 : exactInterval 12 1087 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1087 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1087) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1087 : oddCount 1087 12 = 7 ∧ acceleratedOrbit 12 1087 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1087 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1087) = 3 ^ 7 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1087.1, data_12_1087.2] + +/-- Complete interval computation for depth 12, residue 1088. -/ +theorem bounds_12_1088 : exactInterval 12 1088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1088 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1088) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1088 : oddCount 1088 12 = 3 ∧ acceleratedOrbit 12 1088 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1088 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1088) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1088.1, data_12_1088.2] + +/-- Complete interval computation for depth 12, residue 1089. -/ +theorem bounds_12_1089 : exactInterval 12 1089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1089 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1089) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1089 : oddCount 1089 12 = 5 ∧ acceleratedOrbit 12 1089 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1089 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1089) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1089.1, data_12_1089.2] + +end Collatz.Research.StoppingAtlas.Batch0271 From 712b3cf0ac6800950e525983d3a4973ee29b93d8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:25 +0530 Subject: [PATCH 0272/1001] proof: certify atlas Batch0272 (12:1090 to 12:1104) --- Collatz/Research/StoppingAtlas/Batch0272.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0272.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0272.lean b/Collatz/Research/StoppingAtlas/Batch0272.lean new file mode 100644 index 00000000..58aae175 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0272.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0272 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1090. -/ +theorem bounds_12_1090 : exactInterval 12 1090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1090 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1090) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1090 : oddCount 1090 12 = 5 ∧ acceleratedOrbit 12 1090 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1090 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1090) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1090.1, data_12_1090.2] + +/-- Complete interval computation for depth 12, residue 1091. -/ +theorem bounds_12_1091 : exactInterval 12 1091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1091 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1091) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1091 : oddCount 1091 12 = 5 ∧ acceleratedOrbit 12 1091 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1091 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1091) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1091.1, data_12_1091.2] + +/-- Complete interval computation for depth 12, residue 1092. -/ +theorem bounds_12_1092 : exactInterval 12 1092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1092 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1092) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1092 : oddCount 1092 12 = 4 ∧ acceleratedOrbit 12 1092 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1092 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1092) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1092.1, data_12_1092.2] + +/-- Complete interval computation for depth 12, residue 1093. -/ +theorem bounds_12_1093 : exactInterval 12 1093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1093 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1093) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1093 : oddCount 1093 12 = 4 ∧ acceleratedOrbit 12 1093 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1093 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1093) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1093.1, data_12_1093.2] + +/-- Complete interval computation for depth 12, residue 1094. -/ +theorem bounds_12_1094 : exactInterval 12 1094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1094 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1094) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1094 : oddCount 1094 12 = 4 ∧ acceleratedOrbit 12 1094 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1094 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1094) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1094.1, data_12_1094.2] + +/-- Complete interval computation for depth 12, residue 1095. -/ +theorem bounds_12_1095 : exactInterval 12 1095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1095 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1095) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1095 : oddCount 1095 12 = 8 ∧ acceleratedOrbit 12 1095 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1095 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1095) = 3 ^ 8 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1095.1, data_12_1095.2] + +/-- Complete interval computation for depth 12, residue 1096. -/ +theorem bounds_12_1096 : exactInterval 12 1096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1096 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1096) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1096 : oddCount 1096 12 = 7 ∧ acceleratedOrbit 12 1096 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1096 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1096) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1096.1, data_12_1096.2] + +/-- Complete interval computation for depth 12, residue 1097. -/ +theorem bounds_12_1097 : exactInterval 12 1097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1097 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1097) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1097 : oddCount 1097 12 = 7 ∧ acceleratedOrbit 12 1097 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1097 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1097) = 3 ^ 7 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1097.1, data_12_1097.2] + +/-- Complete interval computation for depth 12, residue 1098. -/ +theorem bounds_12_1098 : exactInterval 12 1098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1098 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1098) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1098 : oddCount 1098 12 = 7 ∧ acceleratedOrbit 12 1098 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1098 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1098) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1098.1, data_12_1098.2] + +/-- Complete interval computation for depth 12, residue 1099. -/ +theorem bounds_12_1099 : exactInterval 12 1099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1099 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1099) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1099 : oddCount 1099 12 = 4 ∧ acceleratedOrbit 12 1099 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1099 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1099) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1099.1, data_12_1099.2] + +/-- Complete interval computation for depth 12, residue 1100. -/ +theorem bounds_12_1100 : exactInterval 12 1100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1100 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1100) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1100 : oddCount 1100 12 = 7 ∧ acceleratedOrbit 12 1100 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1100 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1100) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1100.1, data_12_1100.2] + +/-- Complete interval computation for depth 12, residue 1101. -/ +theorem bounds_12_1101 : exactInterval 12 1101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1101 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1101) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1101 : oddCount 1101 12 = 7 ∧ acceleratedOrbit 12 1101 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1101 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1101) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1101.1, data_12_1101.2] + +/-- Complete interval computation for depth 12, residue 1102. -/ +theorem bounds_12_1102 : exactInterval 12 1102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1102 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1102) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1102 : oddCount 1102 12 = 6 ∧ acceleratedOrbit 12 1102 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1102 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1102) = 3 ^ 6 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1102.1, data_12_1102.2] + +/-- Complete interval computation for depth 12, residue 1103. -/ +theorem bounds_12_1103 : exactInterval 12 1103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1103 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1103) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1103 : oddCount 1103 12 = 6 ∧ acceleratedOrbit 12 1103 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1103 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1103) = 3 ^ 6 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1103.1, data_12_1103.2] + +/-- Complete interval computation for depth 12, residue 1104. -/ +theorem bounds_12_1104 : exactInterval 12 1104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1104 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1104) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1104 : oddCount 1104 12 = 3 ∧ acceleratedOrbit 12 1104 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1104 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1104) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1104.1, data_12_1104.2] + +end Collatz.Research.StoppingAtlas.Batch0272 From 44a1218407fc5c5c43911ff25681595d45cc9cc3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:26 +0530 Subject: [PATCH 0273/1001] proof: certify atlas Batch0273 (12:1105 to 12:1120) --- Collatz/Research/StoppingAtlas/Batch0273.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0273.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0273.lean b/Collatz/Research/StoppingAtlas/Batch0273.lean new file mode 100644 index 00000000..c8604ed9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0273.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0273 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1105. -/ +theorem bounds_12_1105 : exactInterval 12 1105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1105 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1105) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1105 : oddCount 1105 12 = 7 ∧ acceleratedOrbit 12 1105 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1105 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1105) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1105.1, data_12_1105.2] + +/-- Complete interval computation for depth 12, residue 1106. -/ +theorem bounds_12_1106 : exactInterval 12 1106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1106 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1106) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1106 : oddCount 1106 12 = 8 ∧ acceleratedOrbit 12 1106 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1106 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1106) = 3 ^ 8 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1106.1, data_12_1106.2] + +/-- Complete interval computation for depth 12, residue 1107. -/ +theorem bounds_12_1107 : exactInterval 12 1107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1107 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1107) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1107 : oddCount 1107 12 = 8 ∧ acceleratedOrbit 12 1107 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1107 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1107) = 3 ^ 8 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1107.1, data_12_1107.2] + +/-- Complete interval computation for depth 12, residue 1108. -/ +theorem bounds_12_1108 : exactInterval 12 1108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1108 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1108) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1108 : oddCount 1108 12 = 3 ∧ acceleratedOrbit 12 1108 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1108 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1108) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1108.1, data_12_1108.2] + +/-- Complete interval computation for depth 12, residue 1109. -/ +theorem bounds_12_1109 : exactInterval 12 1109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1109 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1109) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1109 : oddCount 1109 12 = 3 ∧ acceleratedOrbit 12 1109 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1109 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1109) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1109.1, data_12_1109.2] + +/-- Complete interval computation for depth 12, residue 1110. -/ +theorem bounds_12_1110 : exactInterval 12 1110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1110 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1110) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1110 : oddCount 1110 12 = 4 ∧ acceleratedOrbit 12 1110 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1110 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1110) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1110.1, data_12_1110.2] + +/-- Complete interval computation for depth 12, residue 1111. -/ +theorem bounds_12_1111 : exactInterval 12 1111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1111 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1111) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1111 : oddCount 1111 12 = 4 ∧ acceleratedOrbit 12 1111 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1111 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1111) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1111.1, data_12_1111.2] + +/-- Complete interval computation for depth 12, residue 1112. -/ +theorem bounds_12_1112 : exactInterval 12 1112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1112 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1112) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1112 : oddCount 1112 12 = 5 ∧ acceleratedOrbit 12 1112 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1112 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1112) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1112.1, data_12_1112.2] + +/-- Complete interval computation for depth 12, residue 1113. -/ +theorem bounds_12_1113 : exactInterval 12 1113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1113 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1113) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1113 : oddCount 1113 12 = 6 ∧ acceleratedOrbit 12 1113 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1113 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1113) = 3 ^ 6 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1113.1, data_12_1113.2] + +/-- Complete interval computation for depth 12, residue 1114. -/ +theorem bounds_12_1114 : exactInterval 12 1114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1114 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1114) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1114 : oddCount 1114 12 = 5 ∧ acceleratedOrbit 12 1114 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1114 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1114) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1114.1, data_12_1114.2] + +/-- Complete interval computation for depth 12, residue 1115. -/ +theorem bounds_12_1115 : exactInterval 12 1115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1115 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1115) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1115 : oddCount 1115 12 = 9 ∧ acceleratedOrbit 12 1115 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1115 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1115) = 3 ^ 9 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1115.1, data_12_1115.2] + +/-- Complete interval computation for depth 12, residue 1116. -/ +theorem bounds_12_1116 : exactInterval 12 1116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1116 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1116) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1116 : oddCount 1116 12 = 5 ∧ acceleratedOrbit 12 1116 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1116 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1116) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1116.1, data_12_1116.2] + +/-- Complete interval computation for depth 12, residue 1117. -/ +theorem bounds_12_1117 : exactInterval 12 1117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1117 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1117) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1117 : oddCount 1117 12 = 5 ∧ acceleratedOrbit 12 1117 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1117 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1117) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1117.1, data_12_1117.2] + +/-- Complete interval computation for depth 12, residue 1118. -/ +theorem bounds_12_1118 : exactInterval 12 1118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1118 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1118) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1118 : oddCount 1118 12 = 8 ∧ acceleratedOrbit 12 1118 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1118 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1118) = 3 ^ 8 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1118.1, data_12_1118.2] + +/-- Complete interval computation for depth 12, residue 1119. -/ +theorem bounds_12_1119 : exactInterval 12 1119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1119 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1119) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1119 : oddCount 1119 12 = 8 ∧ acceleratedOrbit 12 1119 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1119 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1119) = 3 ^ 8 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1119.1, data_12_1119.2] + +/-- Complete interval computation for depth 12, residue 1120. -/ +theorem bounds_12_1120 : exactInterval 12 1120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1120 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1120) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1120 : oddCount 1120 12 = 3 ∧ acceleratedOrbit 12 1120 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1120 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1120) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1120.1, data_12_1120.2] + +end Collatz.Research.StoppingAtlas.Batch0273 From 4f1ff9bc7a4d67748e193605559ba5832775b563 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:26 +0530 Subject: [PATCH 0274/1001] proof: certify atlas Batch0274 (12:1121 to 12:1135) --- Collatz/Research/StoppingAtlas/Batch0274.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0274.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0274.lean b/Collatz/Research/StoppingAtlas/Batch0274.lean new file mode 100644 index 00000000..d516313d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0274.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0274 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1121. -/ +theorem bounds_12_1121 : exactInterval 12 1121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1121 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1121) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1121 : oddCount 1121 12 = 6 ∧ acceleratedOrbit 12 1121 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1121 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1121) = 3 ^ 6 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1121.1, data_12_1121.2] + +/-- Complete interval computation for depth 12, residue 1122. -/ +theorem bounds_12_1122 : exactInterval 12 1122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1122 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1122) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1122 : oddCount 1122 12 = 6 ∧ acceleratedOrbit 12 1122 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1122 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1122) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1122.1, data_12_1122.2] + +/-- Complete interval computation for depth 12, residue 1123. -/ +theorem bounds_12_1123 : exactInterval 12 1123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1123 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1123) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1123 : oddCount 1123 12 = 6 ∧ acceleratedOrbit 12 1123 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1123 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1123) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1123.1, data_12_1123.2] + +/-- Complete interval computation for depth 12, residue 1124. -/ +theorem bounds_12_1124 : exactInterval 12 1124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1124 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1124) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1124 : oddCount 1124 12 = 6 ∧ acceleratedOrbit 12 1124 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1124 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1124) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1124.1, data_12_1124.2] + +/-- Complete interval computation for depth 12, residue 1125. -/ +theorem bounds_12_1125 : exactInterval 12 1125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1125 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1125) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1125 : oddCount 1125 12 = 6 ∧ acceleratedOrbit 12 1125 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1125 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1125) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1125.1, data_12_1125.2] + +/-- Complete interval computation for depth 12, residue 1126. -/ +theorem bounds_12_1126 : exactInterval 12 1126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1126 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1126) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1126 : oddCount 1126 12 = 6 ∧ acceleratedOrbit 12 1126 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1126 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1126) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1126.1, data_12_1126.2] + +/-- Complete interval computation for depth 12, residue 1127. -/ +theorem bounds_12_1127 : exactInterval 12 1127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1127 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1127) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1127 : oddCount 1127 12 = 9 ∧ acceleratedOrbit 12 1127 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1127 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1127) = 3 ^ 9 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1127.1, data_12_1127.2] + +/-- Complete interval computation for depth 12, residue 1128. -/ +theorem bounds_12_1128 : exactInterval 12 1128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1128 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1128) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1128 : oddCount 1128 12 = 3 ∧ acceleratedOrbit 12 1128 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1128 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1128) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1128.1, data_12_1128.2] + +/-- Complete interval computation for depth 12, residue 1129. -/ +theorem bounds_12_1129 : exactInterval 12 1129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1129 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1129) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1129 : oddCount 1129 12 = 7 ∧ acceleratedOrbit 12 1129 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1129 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1129) = 3 ^ 7 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1129.1, data_12_1129.2] + +/-- Complete interval computation for depth 12, residue 1130. -/ +theorem bounds_12_1130 : exactInterval 12 1130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1130 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1130) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1130 : oddCount 1130 12 = 3 ∧ acceleratedOrbit 12 1130 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1130 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1130) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1130.1, data_12_1130.2] + +/-- Complete interval computation for depth 12, residue 1131. -/ +theorem bounds_12_1131 : exactInterval 12 1131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1131 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1131) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1131 : oddCount 1131 12 = 7 ∧ acceleratedOrbit 12 1131 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1131 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1131) = 3 ^ 7 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1131.1, data_12_1131.2] + +/-- Complete interval computation for depth 12, residue 1132. -/ +theorem bounds_12_1132 : exactInterval 12 1132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1132 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1132) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1132 : oddCount 1132 12 = 8 ∧ acceleratedOrbit 12 1132 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1132 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1132) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1132.1, data_12_1132.2] + +/-- Complete interval computation for depth 12, residue 1133. -/ +theorem bounds_12_1133 : exactInterval 12 1133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1133 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1133) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1133 : oddCount 1133 12 = 8 ∧ acceleratedOrbit 12 1133 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1133 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1133) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1133.1, data_12_1133.2] + +/-- Complete interval computation for depth 12, residue 1134. -/ +theorem bounds_12_1134 : exactInterval 12 1134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1134 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1134) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1134 : oddCount 1134 12 = 8 ∧ acceleratedOrbit 12 1134 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1134 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1134) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1134.1, data_12_1134.2] + +/-- Complete interval computation for depth 12, residue 1135. -/ +theorem bounds_12_1135 : exactInterval 12 1135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1135 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1135) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1135 : oddCount 1135 12 = 8 ∧ acceleratedOrbit 12 1135 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1135 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1135) = 3 ^ 8 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1135.1, data_12_1135.2] + +end Collatz.Research.StoppingAtlas.Batch0274 From 1e0fad49ab2e709b69714664bcb890c985411486 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:26 +0530 Subject: [PATCH 0275/1001] proof: certify atlas Batch0275 (12:1136 to 12:1151) --- Collatz/Research/StoppingAtlas/Batch0275.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0275.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0275.lean b/Collatz/Research/StoppingAtlas/Batch0275.lean new file mode 100644 index 00000000..0aebb7e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0275.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0275 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1136. -/ +theorem bounds_12_1136 : exactInterval 12 1136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1136 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1136) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1136 : oddCount 1136 12 = 6 ∧ acceleratedOrbit 12 1136 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1136 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1136) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1136.1, data_12_1136.2] + +/-- Complete interval computation for depth 12, residue 1137. -/ +theorem bounds_12_1137 : exactInterval 12 1137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1137 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1137) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1137 : oddCount 1137 12 = 3 ∧ acceleratedOrbit 12 1137 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1137 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1137) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1137.1, data_12_1137.2] + +/-- Complete interval computation for depth 12, residue 1138. -/ +theorem bounds_12_1138 : exactInterval 12 1138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1138 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1138) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1138 : oddCount 1138 12 = 7 ∧ acceleratedOrbit 12 1138 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1138 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1138) = 3 ^ 7 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1138.1, data_12_1138.2] + +/-- Complete interval computation for depth 12, residue 1139. -/ +theorem bounds_12_1139 : exactInterval 12 1139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1139 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1139) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1139 : oddCount 1139 12 = 7 ∧ acceleratedOrbit 12 1139 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1139 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1139) = 3 ^ 7 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1139.1, data_12_1139.2] + +/-- Complete interval computation for depth 12, residue 1140. -/ +theorem bounds_12_1140 : exactInterval 12 1140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1140 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1140) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1140 : oddCount 1140 12 = 6 ∧ acceleratedOrbit 12 1140 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1140 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1140) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1140.1, data_12_1140.2] + +/-- Complete interval computation for depth 12, residue 1141. -/ +theorem bounds_12_1141 : exactInterval 12 1141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1141 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1141) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1141 : oddCount 1141 12 = 6 ∧ acceleratedOrbit 12 1141 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1141 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1141) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1141.1, data_12_1141.2] + +/-- Complete interval computation for depth 12, residue 1142. -/ +theorem bounds_12_1142 : exactInterval 12 1142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1142 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1142) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1142 : oddCount 1142 12 = 5 ∧ acceleratedOrbit 12 1142 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1142 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1142) = 3 ^ 5 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1142.1, data_12_1142.2] + +/-- Complete interval computation for depth 12, residue 1143. -/ +theorem bounds_12_1143 : exactInterval 12 1143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1143 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1143) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1143 : oddCount 1143 12 = 5 ∧ acceleratedOrbit 12 1143 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1143 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1143) = 3 ^ 5 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1143.1, data_12_1143.2] + +/-- Complete interval computation for depth 12, residue 1144. -/ +theorem bounds_12_1144 : exactInterval 12 1144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1144 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1144) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1144 : oddCount 1144 12 = 6 ∧ acceleratedOrbit 12 1144 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1144 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1144) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1144.1, data_12_1144.2] + +/-- Complete interval computation for depth 12, residue 1145. -/ +theorem bounds_12_1145 : exactInterval 12 1145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1145 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1145) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1145 : oddCount 1145 12 = 8 ∧ acceleratedOrbit 12 1145 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1145 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1145) = 3 ^ 8 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1145.1, data_12_1145.2] + +/-- Complete interval computation for depth 12, residue 1146. -/ +theorem bounds_12_1146 : exactInterval 12 1146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1146 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1146) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1146 : oddCount 1146 12 = 6 ∧ acceleratedOrbit 12 1146 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1146 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1146) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1146.1, data_12_1146.2] + +/-- Complete interval computation for depth 12, residue 1147. -/ +theorem bounds_12_1147 : exactInterval 12 1147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1147 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1147) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1147 : oddCount 1147 12 = 7 ∧ acceleratedOrbit 12 1147 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1147 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1147) = 3 ^ 7 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1147.1, data_12_1147.2] + +/-- Complete interval computation for depth 12, residue 1148. -/ +theorem bounds_12_1148 : exactInterval 12 1148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1148 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1148) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1148 : oddCount 1148 12 = 6 ∧ acceleratedOrbit 12 1148 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1148 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1148) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1148.1, data_12_1148.2] + +/-- Complete interval computation for depth 12, residue 1149. -/ +theorem bounds_12_1149 : exactInterval 12 1149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1149 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1149) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1149 : oddCount 1149 12 = 6 ∧ acceleratedOrbit 12 1149 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1149 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1149) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1149.1, data_12_1149.2] + +/-- Complete interval computation for depth 12, residue 1150. -/ +theorem bounds_12_1150 : exactInterval 12 1150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1150 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1150) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1150 : oddCount 1150 12 = 6 ∧ acceleratedOrbit 12 1150 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1150 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1150) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1150.1, data_12_1150.2] + +/-- Complete interval computation for depth 12, residue 1151. -/ +theorem bounds_12_1151 : exactInterval 12 1151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1151 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1151) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1151 : oddCount 1151 12 = 9 ∧ acceleratedOrbit 12 1151 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1151 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1151) = 3 ^ 9 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1151.1, data_12_1151.2] + +end Collatz.Research.StoppingAtlas.Batch0275 From 4f393a0b3e11288d40aeac7acb1179359f788f9b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:27 +0530 Subject: [PATCH 0276/1001] proof: certify atlas Batch0276 (12:1152 to 12:1166) --- Collatz/Research/StoppingAtlas/Batch0276.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0276.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0276.lean b/Collatz/Research/StoppingAtlas/Batch0276.lean new file mode 100644 index 00000000..da2d025f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0276.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0276 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1152. -/ +theorem bounds_12_1152 : exactInterval 12 1152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1152 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1152) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1152 : oddCount 1152 12 = 4 ∧ acceleratedOrbit 12 1152 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1152 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1152) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1152.1, data_12_1152.2] + +/-- Complete interval computation for depth 12, residue 1153. -/ +theorem bounds_12_1153 : exactInterval 12 1153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1153 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1153) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1153 : oddCount 1153 12 = 8 ∧ acceleratedOrbit 12 1153 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1153 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1153) = 3 ^ 8 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1153.1, data_12_1153.2] + +/-- Complete interval computation for depth 12, residue 1154. -/ +theorem bounds_12_1154 : exactInterval 12 1154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1154 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1154) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1154 : oddCount 1154 12 = 4 ∧ acceleratedOrbit 12 1154 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1154 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1154) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1154.1, data_12_1154.2] + +/-- Complete interval computation for depth 12, residue 1155. -/ +theorem bounds_12_1155 : exactInterval 12 1155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1155 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1155) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1155 : oddCount 1155 12 = 4 ∧ acceleratedOrbit 12 1155 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1155 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1155) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1155.1, data_12_1155.2] + +/-- Complete interval computation for depth 12, residue 1156. -/ +theorem bounds_12_1156 : exactInterval 12 1156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1156 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1156) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1156 : oddCount 1156 12 = 4 ∧ acceleratedOrbit 12 1156 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1156 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1156) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1156.1, data_12_1156.2] + +/-- Complete interval computation for depth 12, residue 1157. -/ +theorem bounds_12_1157 : exactInterval 12 1157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1157 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1157) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1157 : oddCount 1157 12 = 4 ∧ acceleratedOrbit 12 1157 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1157 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1157) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1157.1, data_12_1157.2] + +/-- Complete interval computation for depth 12, residue 1158. -/ +theorem bounds_12_1158 : exactInterval 12 1158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1158 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1158) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1158 : oddCount 1158 12 = 4 ∧ acceleratedOrbit 12 1158 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1158 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1158) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1158.1, data_12_1158.2] + +/-- Complete interval computation for depth 12, residue 1159. -/ +theorem bounds_12_1159 : exactInterval 12 1159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1159 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1159) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1159 : oddCount 1159 12 = 8 ∧ acceleratedOrbit 12 1159 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1159 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1159) = 3 ^ 8 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1159.1, data_12_1159.2] + +/-- Complete interval computation for depth 12, residue 1160. -/ +theorem bounds_12_1160 : exactInterval 12 1160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1160 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1160) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1160 : oddCount 1160 12 = 5 ∧ acceleratedOrbit 12 1160 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1160 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1160) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1160.1, data_12_1160.2] + +/-- Complete interval computation for depth 12, residue 1161. -/ +theorem bounds_12_1161 : exactInterval 12 1161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1161 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1161) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1161 : oddCount 1161 12 = 10 ∧ acceleratedOrbit 12 1161 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1161 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1161) = 3 ^ 10 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1161.1, data_12_1161.2] + +/-- Complete interval computation for depth 12, residue 1162. -/ +theorem bounds_12_1162 : exactInterval 12 1162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1162 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1162) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1162 : oddCount 1162 12 = 5 ∧ acceleratedOrbit 12 1162 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1162 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1162) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1162.1, data_12_1162.2] + +/-- Complete interval computation for depth 12, residue 1163. -/ +theorem bounds_12_1163 : exactInterval 12 1163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1163 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1163) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1163 : oddCount 1163 12 = 7 ∧ acceleratedOrbit 12 1163 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1163 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1163) = 3 ^ 7 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1163.1, data_12_1163.2] + +/-- Complete interval computation for depth 12, residue 1164. -/ +theorem bounds_12_1164 : exactInterval 12 1164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1164 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1164) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1164 : oddCount 1164 12 = 5 ∧ acceleratedOrbit 12 1164 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1164 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1164) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1164.1, data_12_1164.2] + +/-- Complete interval computation for depth 12, residue 1165. -/ +theorem bounds_12_1165 : exactInterval 12 1165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1165 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1165) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1165 : oddCount 1165 12 = 5 ∧ acceleratedOrbit 12 1165 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1165 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1165) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1165.1, data_12_1165.2] + +/-- Complete interval computation for depth 12, residue 1166. -/ +theorem bounds_12_1166 : exactInterval 12 1166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1166 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1166) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1166 : oddCount 1166 12 = 6 ∧ acceleratedOrbit 12 1166 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1166 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1166) = 3 ^ 6 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1166.1, data_12_1166.2] + +end Collatz.Research.StoppingAtlas.Batch0276 From 85028813a4cc4402e8faf773b52af40fb196fe2e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:27 +0530 Subject: [PATCH 0277/1001] proof: certify atlas Batch0277 (12:1167 to 12:1181) --- Collatz/Research/StoppingAtlas/Batch0277.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0277.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0277.lean b/Collatz/Research/StoppingAtlas/Batch0277.lean new file mode 100644 index 00000000..4e15d3f6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0277.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0277 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1167. -/ +theorem bounds_12_1167 : exactInterval 12 1167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1167 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1167) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1167 : oddCount 1167 12 = 6 ∧ acceleratedOrbit 12 1167 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1167 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1167) = 3 ^ 6 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1167.1, data_12_1167.2] + +/-- Complete interval computation for depth 12, residue 1168. -/ +theorem bounds_12_1168 : exactInterval 12 1168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1168 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1168) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1168 : oddCount 1168 12 = 5 ∧ acceleratedOrbit 12 1168 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1168 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1168) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1168.1, data_12_1168.2] + +/-- Complete interval computation for depth 12, residue 1169. -/ +theorem bounds_12_1169 : exactInterval 12 1169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1169 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1169) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1169 : oddCount 1169 12 = 6 ∧ acceleratedOrbit 12 1169 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1169 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1169) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1169.1, data_12_1169.2] + +/-- Complete interval computation for depth 12, residue 1170. -/ +theorem bounds_12_1170 : exactInterval 12 1170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1170 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1170) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1170 : oddCount 1170 12 = 6 ∧ acceleratedOrbit 12 1170 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1170 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1170) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1170.1, data_12_1170.2] + +/-- Complete interval computation for depth 12, residue 1171. -/ +theorem bounds_12_1171 : exactInterval 12 1171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1171 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1171) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1171 : oddCount 1171 12 = 6 ∧ acceleratedOrbit 12 1171 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1171 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1171) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1171.1, data_12_1171.2] + +/-- Complete interval computation for depth 12, residue 1172. -/ +theorem bounds_12_1172 : exactInterval 12 1172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1172 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1172) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1172 : oddCount 1172 12 = 5 ∧ acceleratedOrbit 12 1172 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1172 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1172) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1172.1, data_12_1172.2] + +/-- Complete interval computation for depth 12, residue 1173. -/ +theorem bounds_12_1173 : exactInterval 12 1173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1173 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1173) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1173 : oddCount 1173 12 = 5 ∧ acceleratedOrbit 12 1173 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1173 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1173) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1173.1, data_12_1173.2] + +/-- Complete interval computation for depth 12, residue 1174. -/ +theorem bounds_12_1174 : exactInterval 12 1174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1174 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1174) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1174 : oddCount 1174 12 = 5 ∧ acceleratedOrbit 12 1174 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1174 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1174) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1174.1, data_12_1174.2] + +/-- Complete interval computation for depth 12, residue 1175. -/ +theorem bounds_12_1175 : exactInterval 12 1175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1175 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1175) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1175 : oddCount 1175 12 = 5 ∧ acceleratedOrbit 12 1175 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1175 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1175) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1175.1, data_12_1175.2] + +/-- Complete interval computation for depth 12, residue 1176. -/ +theorem bounds_12_1176 : exactInterval 12 1176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1176 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1176) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1176 : oddCount 1176 12 = 5 ∧ acceleratedOrbit 12 1176 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1176 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1176) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1176.1, data_12_1176.2] + +/-- Complete interval computation for depth 12, residue 1177. -/ +theorem bounds_12_1177 : exactInterval 12 1177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1177 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1177) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1177 : oddCount 1177 12 = 5 ∧ acceleratedOrbit 12 1177 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1177 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1177) = 3 ^ 5 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1177.1, data_12_1177.2] + +/-- Complete interval computation for depth 12, residue 1178. -/ +theorem bounds_12_1178 : exactInterval 12 1178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1178 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1178) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1178 : oddCount 1178 12 = 5 ∧ acceleratedOrbit 12 1178 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1178 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1178) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1178.1, data_12_1178.2] + +/-- Complete interval computation for depth 12, residue 1179. -/ +theorem bounds_12_1179 : exactInterval 12 1179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1179 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1179) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1179 : oddCount 1179 12 = 8 ∧ acceleratedOrbit 12 1179 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1179 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1179) = 3 ^ 8 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1179.1, data_12_1179.2] + +/-- Complete interval computation for depth 12, residue 1180. -/ +theorem bounds_12_1180 : exactInterval 12 1180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1180 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1180) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1180 : oddCount 1180 12 = 6 ∧ acceleratedOrbit 12 1180 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1180 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1180) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1180.1, data_12_1180.2] + +/-- Complete interval computation for depth 12, residue 1181. -/ +theorem bounds_12_1181 : exactInterval 12 1181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1181 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1181) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1181 : oddCount 1181 12 = 6 ∧ acceleratedOrbit 12 1181 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1181 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1181) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1181.1, data_12_1181.2] + +end Collatz.Research.StoppingAtlas.Batch0277 From 2c451f7be23a6f260b50e91ce30e0015cea03f8e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:28 +0530 Subject: [PATCH 0278/1001] proof: certify atlas Batch0278 (12:1182 to 12:1197) --- Collatz/Research/StoppingAtlas/Batch0278.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0278.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0278.lean b/Collatz/Research/StoppingAtlas/Batch0278.lean new file mode 100644 index 00000000..11227caf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0278.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0278 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1182. -/ +theorem bounds_12_1182 : exactInterval 12 1182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1182 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1182) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1182 : oddCount 1182 12 = 6 ∧ acceleratedOrbit 12 1182 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1182 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1182) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1182.1, data_12_1182.2] + +/-- Complete interval computation for depth 12, residue 1183. -/ +theorem bounds_12_1183 : exactInterval 12 1183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1183 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1183) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1183 : oddCount 1183 12 = 9 ∧ acceleratedOrbit 12 1183 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1183 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1183) = 3 ^ 9 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1183.1, data_12_1183.2] + +/-- Complete interval computation for depth 12, residue 1184. -/ +theorem bounds_12_1184 : exactInterval 12 1184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1184 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1184) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1184 : oddCount 1184 12 = 4 ∧ acceleratedOrbit 12 1184 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1184 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1184) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1184.1, data_12_1184.2] + +/-- Complete interval computation for depth 12, residue 1185. -/ +theorem bounds_12_1185 : exactInterval 12 1185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1185 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1185) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1185 : oddCount 1185 12 = 8 ∧ acceleratedOrbit 12 1185 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1185 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1185) = 3 ^ 8 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1185.1, data_12_1185.2] + +/-- Complete interval computation for depth 12, residue 1186. -/ +theorem bounds_12_1186 : exactInterval 12 1186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1186 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1186) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1186 : oddCount 1186 12 = 7 ∧ acceleratedOrbit 12 1186 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1186 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1186) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1186.1, data_12_1186.2] + +/-- Complete interval computation for depth 12, residue 1187. -/ +theorem bounds_12_1187 : exactInterval 12 1187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1187 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1187) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1187 : oddCount 1187 12 = 7 ∧ acceleratedOrbit 12 1187 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1187 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1187) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1187.1, data_12_1187.2] + +/-- Complete interval computation for depth 12, residue 1188. -/ +theorem bounds_12_1188 : exactInterval 12 1188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1188 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1188) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1188 : oddCount 1188 12 = 7 ∧ acceleratedOrbit 12 1188 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1188 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1188) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1188.1, data_12_1188.2] + +/-- Complete interval computation for depth 12, residue 1189. -/ +theorem bounds_12_1189 : exactInterval 12 1189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1189 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1189) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1189 : oddCount 1189 12 = 7 ∧ acceleratedOrbit 12 1189 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1189 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1189) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1189.1, data_12_1189.2] + +/-- Complete interval computation for depth 12, residue 1190. -/ +theorem bounds_12_1190 : exactInterval 12 1190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1190 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1190) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1190 : oddCount 1190 12 = 7 ∧ acceleratedOrbit 12 1190 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1190 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1190) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1190.1, data_12_1190.2] + +/-- Complete interval computation for depth 12, residue 1191. -/ +theorem bounds_12_1191 : exactInterval 12 1191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1191 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1191) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1191 : oddCount 1191 12 = 8 ∧ acceleratedOrbit 12 1191 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1191 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1191) = 3 ^ 8 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1191.1, data_12_1191.2] + +/-- Complete interval computation for depth 12, residue 1192. -/ +theorem bounds_12_1192 : exactInterval 12 1192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1192 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1192) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1192 : oddCount 1192 12 = 4 ∧ acceleratedOrbit 12 1192 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1192 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1192) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1192.1, data_12_1192.2] + +/-- Complete interval computation for depth 12, residue 1193. -/ +theorem bounds_12_1193 : exactInterval 12 1193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1193 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1193) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1193 : oddCount 1193 12 = 9 ∧ acceleratedOrbit 12 1193 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1193 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1193) = 3 ^ 9 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1193.1, data_12_1193.2] + +/-- Complete interval computation for depth 12, residue 1194. -/ +theorem bounds_12_1194 : exactInterval 12 1194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1194 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1194) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1194 : oddCount 1194 12 = 4 ∧ acceleratedOrbit 12 1194 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1194 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1194) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1194.1, data_12_1194.2] + +/-- Complete interval computation for depth 12, residue 1195. -/ +theorem bounds_12_1195 : exactInterval 12 1195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1195 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1195) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1195 : oddCount 1195 12 = 5 ∧ acceleratedOrbit 12 1195 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1195 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1195) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1195.1, data_12_1195.2] + +/-- Complete interval computation for depth 12, residue 1196. -/ +theorem bounds_12_1196 : exactInterval 12 1196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1196 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1196) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1196 : oddCount 1196 12 = 6 ∧ acceleratedOrbit 12 1196 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1196 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1196) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1196.1, data_12_1196.2] + +/-- Complete interval computation for depth 12, residue 1197. -/ +theorem bounds_12_1197 : exactInterval 12 1197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1197 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1197) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1197 : oddCount 1197 12 = 6 ∧ acceleratedOrbit 12 1197 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1197 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1197) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1197.1, data_12_1197.2] + +end Collatz.Research.StoppingAtlas.Batch0278 From 180739119c82a22e60a506d1ccbcfbce9b372fbc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:28 +0530 Subject: [PATCH 0279/1001] proof: certify atlas Batch0279 (12:1198 to 12:1212) --- Collatz/Research/StoppingAtlas/Batch0279.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0279.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0279.lean b/Collatz/Research/StoppingAtlas/Batch0279.lean new file mode 100644 index 00000000..8545f8d9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0279.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0279 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1198. -/ +theorem bounds_12_1198 : exactInterval 12 1198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1198 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1198) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1198 : oddCount 1198 12 = 6 ∧ acceleratedOrbit 12 1198 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1198 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1198) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1198.1, data_12_1198.2] + +/-- Complete interval computation for depth 12, residue 1199. -/ +theorem bounds_12_1199 : exactInterval 12 1199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1199 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1199) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1199 : oddCount 1199 12 = 7 ∧ acceleratedOrbit 12 1199 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1199 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1199) = 3 ^ 7 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1199.1, data_12_1199.2] + +/-- Complete interval computation for depth 12, residue 1200. -/ +theorem bounds_12_1200 : exactInterval 12 1200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1200 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1200) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1200 : oddCount 1200 12 = 3 ∧ acceleratedOrbit 12 1200 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1200 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1200) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1200.1, data_12_1200.2] + +/-- Complete interval computation for depth 12, residue 1201. -/ +theorem bounds_12_1201 : exactInterval 12 1201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1201 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1201) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1201 : oddCount 1201 12 = 7 ∧ acceleratedOrbit 12 1201 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1201 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1201) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1201.1, data_12_1201.2] + +/-- Complete interval computation for depth 12, residue 1202. -/ +theorem bounds_12_1202 : exactInterval 12 1202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1202 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1202) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1202 : oddCount 1202 12 = 7 ∧ acceleratedOrbit 12 1202 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1202 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1202) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1202.1, data_12_1202.2] + +/-- Complete interval computation for depth 12, residue 1203. -/ +theorem bounds_12_1203 : exactInterval 12 1203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1203 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1203) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1203 : oddCount 1203 12 = 7 ∧ acceleratedOrbit 12 1203 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1203 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1203) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1203.1, data_12_1203.2] + +/-- Complete interval computation for depth 12, residue 1204. -/ +theorem bounds_12_1204 : exactInterval 12 1204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1204 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1204) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1204 : oddCount 1204 12 = 3 ∧ acceleratedOrbit 12 1204 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1204 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1204) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1204.1, data_12_1204.2] + +/-- Complete interval computation for depth 12, residue 1205. -/ +theorem bounds_12_1205 : exactInterval 12 1205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1205 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1205) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1205 : oddCount 1205 12 = 3 ∧ acceleratedOrbit 12 1205 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1205 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1205) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1205.1, data_12_1205.2] + +/-- Complete interval computation for depth 12, residue 1206. -/ +theorem bounds_12_1206 : exactInterval 12 1206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1206 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1206) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1206 : oddCount 1206 12 = 8 ∧ acceleratedOrbit 12 1206 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1206 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1206) = 3 ^ 8 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1206.1, data_12_1206.2] + +/-- Complete interval computation for depth 12, residue 1207. -/ +theorem bounds_12_1207 : exactInterval 12 1207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1207 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1207) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1207 : oddCount 1207 12 = 8 ∧ acceleratedOrbit 12 1207 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1207 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1207) = 3 ^ 8 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1207.1, data_12_1207.2] + +/-- Complete interval computation for depth 12, residue 1208. -/ +theorem bounds_12_1208 : exactInterval 12 1208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1208 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1208) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1208 : oddCount 1208 12 = 3 ∧ acceleratedOrbit 12 1208 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1208 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1208) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1208.1, data_12_1208.2] + +/-- Complete interval computation for depth 12, residue 1209. -/ +theorem bounds_12_1209 : exactInterval 12 1209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1209 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1209) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1209 : oddCount 1209 12 = 8 ∧ acceleratedOrbit 12 1209 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1209 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1209) = 3 ^ 8 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1209.1, data_12_1209.2] + +/-- Complete interval computation for depth 12, residue 1210. -/ +theorem bounds_12_1210 : exactInterval 12 1210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1210 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1210) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1210 : oddCount 1210 12 = 3 ∧ acceleratedOrbit 12 1210 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1210 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1210) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1210.1, data_12_1210.2] + +/-- Complete interval computation for depth 12, residue 1211. -/ +theorem bounds_12_1211 : exactInterval 12 1211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1211 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1211) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1211 : oddCount 1211 12 = 9 ∧ acceleratedOrbit 12 1211 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1211 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1211) = 3 ^ 9 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1211.1, data_12_1211.2] + +/-- Complete interval computation for depth 12, residue 1212. -/ +theorem bounds_12_1212 : exactInterval 12 1212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1212 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1212) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1212 : oddCount 1212 12 = 7 ∧ acceleratedOrbit 12 1212 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1212 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1212) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1212.1, data_12_1212.2] + +end Collatz.Research.StoppingAtlas.Batch0279 From 0a384d5ccf8f6d1fb725fbcda33d4d51ed397834 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:28 +0530 Subject: [PATCH 0280/1001] proof: certify atlas Batch0280 (12:1213 to 12:1227) --- Collatz/Research/StoppingAtlas/Batch0280.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0280.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0280.lean b/Collatz/Research/StoppingAtlas/Batch0280.lean new file mode 100644 index 00000000..b2c51eb2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0280.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0280 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1213. -/ +theorem bounds_12_1213 : exactInterval 12 1213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1213 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1213) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1213 : oddCount 1213 12 = 7 ∧ acceleratedOrbit 12 1213 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1213 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1213) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1213.1, data_12_1213.2] + +/-- Complete interval computation for depth 12, residue 1214. -/ +theorem bounds_12_1214 : exactInterval 12 1214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1214 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1214) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1214 : oddCount 1214 12 = 7 ∧ acceleratedOrbit 12 1214 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1214 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1214) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1214.1, data_12_1214.2] + +/-- Complete interval computation for depth 12, residue 1215. -/ +theorem bounds_12_1215 : exactInterval 12 1215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1215 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1215) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1215 : oddCount 1215 12 = 8 ∧ acceleratedOrbit 12 1215 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1215 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1215) = 3 ^ 8 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1215.1, data_12_1215.2] + +/-- Complete interval computation for depth 12, residue 1216. -/ +theorem bounds_12_1216 : exactInterval 12 1216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1216 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1216) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1216 : oddCount 1216 12 = 4 ∧ acceleratedOrbit 12 1216 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1216 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1216) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1216.1, data_12_1216.2] + +/-- Complete interval computation for depth 12, residue 1217. -/ +theorem bounds_12_1217 : exactInterval 12 1217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1217 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1217) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1217 : oddCount 1217 12 = 6 ∧ acceleratedOrbit 12 1217 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1217 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1217) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1217.1, data_12_1217.2] + +/-- Complete interval computation for depth 12, residue 1218. -/ +theorem bounds_12_1218 : exactInterval 12 1218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1218 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1218) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1218 : oddCount 1218 12 = 6 ∧ acceleratedOrbit 12 1218 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1218 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1218) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1218.1, data_12_1218.2] + +/-- Complete interval computation for depth 12, residue 1219. -/ +theorem bounds_12_1219 : exactInterval 12 1219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1219 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1219) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1219 : oddCount 1219 12 = 6 ∧ acceleratedOrbit 12 1219 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1219 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1219) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1219.1, data_12_1219.2] + +/-- Complete interval computation for depth 12, residue 1220. -/ +theorem bounds_12_1220 : exactInterval 12 1220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1220 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1220) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1220 : oddCount 1220 12 = 5 ∧ acceleratedOrbit 12 1220 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1220 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1220) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1220.1, data_12_1220.2] + +/-- Complete interval computation for depth 12, residue 1221. -/ +theorem bounds_12_1221 : exactInterval 12 1221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1221 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1221) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1221 : oddCount 1221 12 = 5 ∧ acceleratedOrbit 12 1221 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1221 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1221) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1221.1, data_12_1221.2] + +/-- Complete interval computation for depth 12, residue 1222. -/ +theorem bounds_12_1222 : exactInterval 12 1222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1222 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1222) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1222 : oddCount 1222 12 = 5 ∧ acceleratedOrbit 12 1222 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1222 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1222) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1222.1, data_12_1222.2] + +/-- Complete interval computation for depth 12, residue 1223. -/ +theorem bounds_12_1223 : exactInterval 12 1223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1223 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1223) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1223 : oddCount 1223 12 = 6 ∧ acceleratedOrbit 12 1223 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1223 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1223) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1223.1, data_12_1223.2] + +/-- Complete interval computation for depth 12, residue 1224. -/ +theorem bounds_12_1224 : exactInterval 12 1224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1224 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1224) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1224 : oddCount 1224 12 = 5 ∧ acceleratedOrbit 12 1224 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1224 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1224) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1224.1, data_12_1224.2] + +/-- Complete interval computation for depth 12, residue 1225. -/ +theorem bounds_12_1225 : exactInterval 12 1225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1225 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1225) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1225 : oddCount 1225 12 = 5 ∧ acceleratedOrbit 12 1225 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1225 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1225) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1225.1, data_12_1225.2] + +/-- Complete interval computation for depth 12, residue 1226. -/ +theorem bounds_12_1226 : exactInterval 12 1226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1226 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1226) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1226 : oddCount 1226 12 = 5 ∧ acceleratedOrbit 12 1226 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1226 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1226) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1226.1, data_12_1226.2] + +/-- Complete interval computation for depth 12, residue 1227. -/ +theorem bounds_12_1227 : exactInterval 12 1227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1227 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1227) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1227 : oddCount 1227 12 = 5 ∧ acceleratedOrbit 12 1227 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1227 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1227) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1227.1, data_12_1227.2] + +end Collatz.Research.StoppingAtlas.Batch0280 From f6b00ba57dccc747bb44d4d0c3058592d3fe2e4b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:28 +0530 Subject: [PATCH 0281/1001] proof: certify atlas Batch0281 (12:1228 to 12:1243) --- Collatz/Research/StoppingAtlas/Batch0281.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0281.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0281.lean b/Collatz/Research/StoppingAtlas/Batch0281.lean new file mode 100644 index 00000000..6395811c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0281.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0281 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1228. -/ +theorem bounds_12_1228 : exactInterval 12 1228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1228 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1228) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1228 : oddCount 1228 12 = 5 ∧ acceleratedOrbit 12 1228 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1228 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1228) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1228.1, data_12_1228.2] + +/-- Complete interval computation for depth 12, residue 1229. -/ +theorem bounds_12_1229 : exactInterval 12 1229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1229 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1229) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1229 : oddCount 1229 12 = 5 ∧ acceleratedOrbit 12 1229 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1229 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1229) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1229.1, data_12_1229.2] + +/-- Complete interval computation for depth 12, residue 1230. -/ +theorem bounds_12_1230 : exactInterval 12 1230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1230 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1230) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1230 : oddCount 1230 12 = 7 ∧ acceleratedOrbit 12 1230 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1230 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1230) = 3 ^ 7 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1230.1, data_12_1230.2] + +/-- Complete interval computation for depth 12, residue 1231. -/ +theorem bounds_12_1231 : exactInterval 12 1231 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1231 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1231) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1231 : oddCount 1231 12 = 7 ∧ acceleratedOrbit 12 1231 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1231 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1231) = 3 ^ 7 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1231.1, data_12_1231.2] + +/-- Complete interval computation for depth 12, residue 1232. -/ +theorem bounds_12_1232 : exactInterval 12 1232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1232 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1232) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1232 : oddCount 1232 12 = 4 ∧ acceleratedOrbit 12 1232 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1232 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1232) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1232.1, data_12_1232.2] + +/-- Complete interval computation for depth 12, residue 1233. -/ +theorem bounds_12_1233 : exactInterval 12 1233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1233 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1233) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1233 : oddCount 1233 12 = 7 ∧ acceleratedOrbit 12 1233 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1233 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1233) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1233.1, data_12_1233.2] + +/-- Complete interval computation for depth 12, residue 1234. -/ +theorem bounds_12_1234 : exactInterval 12 1234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1234 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1234) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1234 : oddCount 1234 12 = 7 ∧ acceleratedOrbit 12 1234 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1234 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1234) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1234.1, data_12_1234.2] + +/-- Complete interval computation for depth 12, residue 1235. -/ +theorem bounds_12_1235 : exactInterval 12 1235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1235 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1235) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1235 : oddCount 1235 12 = 7 ∧ acceleratedOrbit 12 1235 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1235 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1235) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1235.1, data_12_1235.2] + +/-- Complete interval computation for depth 12, residue 1236. -/ +theorem bounds_12_1236 : exactInterval 12 1236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1236 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1236) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1236 : oddCount 1236 12 = 4 ∧ acceleratedOrbit 12 1236 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1236 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1236) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1236.1, data_12_1236.2] + +/-- Complete interval computation for depth 12, residue 1237. -/ +theorem bounds_12_1237 : exactInterval 12 1237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1237 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1237) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1237 : oddCount 1237 12 = 4 ∧ acceleratedOrbit 12 1237 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1237 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1237) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1237.1, data_12_1237.2] + +/-- Complete interval computation for depth 12, residue 1238. -/ +theorem bounds_12_1238 : exactInterval 12 1238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1238 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1238) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1238 : oddCount 1238 12 = 6 ∧ acceleratedOrbit 12 1238 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1238 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1238) = 3 ^ 6 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1238.1, data_12_1238.2] + +/-- Complete interval computation for depth 12, residue 1239. -/ +theorem bounds_12_1239 : exactInterval 12 1239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1239 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1239) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1239 : oddCount 1239 12 = 6 ∧ acceleratedOrbit 12 1239 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1239 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1239) = 3 ^ 6 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1239.1, data_12_1239.2] + +/-- Complete interval computation for depth 12, residue 1240. -/ +theorem bounds_12_1240 : exactInterval 12 1240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1240 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1240) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1240 : oddCount 1240 12 = 7 ∧ acceleratedOrbit 12 1240 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1240 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1240) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1240.1, data_12_1240.2] + +/-- Complete interval computation for depth 12, residue 1241. -/ +theorem bounds_12_1241 : exactInterval 12 1241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1241 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1241) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1241 : oddCount 1241 12 = 5 ∧ acceleratedOrbit 12 1241 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1241 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1241) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1241.1, data_12_1241.2] + +/-- Complete interval computation for depth 12, residue 1242. -/ +theorem bounds_12_1242 : exactInterval 12 1242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1242 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1242) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1242 : oddCount 1242 12 = 7 ∧ acceleratedOrbit 12 1242 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1242 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1242) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1242.1, data_12_1242.2] + +/-- Complete interval computation for depth 12, residue 1243. -/ +theorem bounds_12_1243 : exactInterval 12 1243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1243 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1243) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1243 : oddCount 1243 12 = 7 ∧ acceleratedOrbit 12 1243 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1243 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1243) = 3 ^ 7 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1243.1, data_12_1243.2] + +end Collatz.Research.StoppingAtlas.Batch0281 From cc322bcd74daa22a1f8cc5075299ea70fb3f96ac Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:29 +0530 Subject: [PATCH 0282/1001] proof: certify atlas Batch0282 (12:1244 to 12:1258) --- Collatz/Research/StoppingAtlas/Batch0282.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0282.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0282.lean b/Collatz/Research/StoppingAtlas/Batch0282.lean new file mode 100644 index 00000000..89cf7c40 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0282.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0282 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1244. -/ +theorem bounds_12_1244 : exactInterval 12 1244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1244 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1244) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1244 : oddCount 1244 12 = 7 ∧ acceleratedOrbit 12 1244 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1244 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1244) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1244.1, data_12_1244.2] + +/-- Complete interval computation for depth 12, residue 1245. -/ +theorem bounds_12_1245 : exactInterval 12 1245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1245 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1245) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1245 : oddCount 1245 12 = 7 ∧ acceleratedOrbit 12 1245 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1245 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1245) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1245.1, data_12_1245.2] + +/-- Complete interval computation for depth 12, residue 1246. -/ +theorem bounds_12_1246 : exactInterval 12 1246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1246 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1246) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1246 : oddCount 1246 12 = 8 ∧ acceleratedOrbit 12 1246 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1246 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1246) = 3 ^ 8 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1246.1, data_12_1246.2] + +/-- Complete interval computation for depth 12, residue 1247. -/ +theorem bounds_12_1247 : exactInterval 12 1247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1247 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1247) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1247 : oddCount 1247 12 = 8 ∧ acceleratedOrbit 12 1247 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1247 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1247) = 3 ^ 8 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1247.1, data_12_1247.2] + +/-- Complete interval computation for depth 12, residue 1248. -/ +theorem bounds_12_1248 : exactInterval 12 1248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1248 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1248) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1248 : oddCount 1248 12 = 5 ∧ acceleratedOrbit 12 1248 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1248 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1248) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1248.1, data_12_1248.2] + +/-- Complete interval computation for depth 12, residue 1249. -/ +theorem bounds_12_1249 : exactInterval 12 1249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1249 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1249) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1249 : oddCount 1249 12 = 9 ∧ acceleratedOrbit 12 1249 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1249 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1249) = 3 ^ 9 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1249.1, data_12_1249.2] + +/-- Complete interval computation for depth 12, residue 1250. -/ +theorem bounds_12_1250 : exactInterval 12 1250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1250 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1250) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1250 : oddCount 1250 12 = 4 ∧ acceleratedOrbit 12 1250 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1250 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1250) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1250.1, data_12_1250.2] + +/-- Complete interval computation for depth 12, residue 1251. -/ +theorem bounds_12_1251 : exactInterval 12 1251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1251 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1251) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1251 : oddCount 1251 12 = 4 ∧ acceleratedOrbit 12 1251 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1251 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1251) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1251.1, data_12_1251.2] + +/-- Complete interval computation for depth 12, residue 1252. -/ +theorem bounds_12_1252 : exactInterval 12 1252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1252 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1252) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1252 : oddCount 1252 12 = 7 ∧ acceleratedOrbit 12 1252 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1252 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1252) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1252.1, data_12_1252.2] + +/-- Complete interval computation for depth 12, residue 1253. -/ +theorem bounds_12_1253 : exactInterval 12 1253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1253 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1253) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1253 : oddCount 1253 12 = 7 ∧ acceleratedOrbit 12 1253 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1253 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1253) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1253.1, data_12_1253.2] + +/-- Complete interval computation for depth 12, residue 1254. -/ +theorem bounds_12_1254 : exactInterval 12 1254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1254 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1254) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1254 : oddCount 1254 12 = 7 ∧ acceleratedOrbit 12 1254 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1254 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1254) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1254.1, data_12_1254.2] + +/-- Complete interval computation for depth 12, residue 1255. -/ +theorem bounds_12_1255 : exactInterval 12 1255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1255 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1255) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1255 : oddCount 1255 12 = 9 ∧ acceleratedOrbit 12 1255 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1255 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1255) = 3 ^ 9 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1255.1, data_12_1255.2] + +/-- Complete interval computation for depth 12, residue 1256. -/ +theorem bounds_12_1256 : exactInterval 12 1256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1256 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1256) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1256 : oddCount 1256 12 = 5 ∧ acceleratedOrbit 12 1256 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1256 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1256) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1256.1, data_12_1256.2] + +/-- Complete interval computation for depth 12, residue 1257. -/ +theorem bounds_12_1257 : exactInterval 12 1257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1257 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1257) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1257 : oddCount 1257 12 = 6 ∧ acceleratedOrbit 12 1257 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1257 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1257) = 3 ^ 6 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1257.1, data_12_1257.2] + +/-- Complete interval computation for depth 12, residue 1258. -/ +theorem bounds_12_1258 : exactInterval 12 1258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1258 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1258) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1258 : oddCount 1258 12 = 5 ∧ acceleratedOrbit 12 1258 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1258 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1258) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1258.1, data_12_1258.2] + +end Collatz.Research.StoppingAtlas.Batch0282 From 8115540db196723545533bb9490825404df250e2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:29 +0530 Subject: [PATCH 0283/1001] proof: certify atlas Batch0283 (12:1259 to 12:1273) --- Collatz/Research/StoppingAtlas/Batch0283.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0283.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0283.lean b/Collatz/Research/StoppingAtlas/Batch0283.lean new file mode 100644 index 00000000..26fbe3cd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0283.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0283 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1259. -/ +theorem bounds_12_1259 : exactInterval 12 1259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1259 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1259) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1259 : oddCount 1259 12 = 8 ∧ acceleratedOrbit 12 1259 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1259 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1259) = 3 ^ 8 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1259.1, data_12_1259.2] + +/-- Complete interval computation for depth 12, residue 1260. -/ +theorem bounds_12_1260 : exactInterval 12 1260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1260 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1260) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1260 : oddCount 1260 12 = 4 ∧ acceleratedOrbit 12 1260 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1260 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1260) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1260.1, data_12_1260.2] + +/-- Complete interval computation for depth 12, residue 1261. -/ +theorem bounds_12_1261 : exactInterval 12 1261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1261 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1261) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1261 : oddCount 1261 12 = 4 ∧ acceleratedOrbit 12 1261 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1261 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1261) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1261.1, data_12_1261.2] + +/-- Complete interval computation for depth 12, residue 1262. -/ +theorem bounds_12_1262 : exactInterval 12 1262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1262 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1262) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1262 : oddCount 1262 12 = 4 ∧ acceleratedOrbit 12 1262 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1262 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1262) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1262.1, data_12_1262.2] + +/-- Complete interval computation for depth 12, residue 1263. -/ +theorem bounds_12_1263 : exactInterval 12 1263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1263 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1263) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1263 : oddCount 1263 12 = 11 ∧ acceleratedOrbit 12 1263 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1263 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1263) = 3 ^ 11 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1263.1, data_12_1263.2] + +/-- Complete interval computation for depth 12, residue 1264. -/ +theorem bounds_12_1264 : exactInterval 12 1264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1264 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1264) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1264 : oddCount 1264 12 = 5 ∧ acceleratedOrbit 12 1264 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1264 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1264) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1264.1, data_12_1264.2] + +/-- Complete interval computation for depth 12, residue 1265. -/ +theorem bounds_12_1265 : exactInterval 12 1265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1265 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1265) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1265 : oddCount 1265 12 = 5 ∧ acceleratedOrbit 12 1265 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1265 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1265) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1265.1, data_12_1265.2] + +/-- Complete interval computation for depth 12, residue 1266. -/ +theorem bounds_12_1266 : exactInterval 12 1266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1266 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1266) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1266 : oddCount 1266 12 = 6 ∧ acceleratedOrbit 12 1266 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1266 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1266) = 3 ^ 6 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1266.1, data_12_1266.2] + +/-- Complete interval computation for depth 12, residue 1267. -/ +theorem bounds_12_1267 : exactInterval 12 1267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1267 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1267) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1267 : oddCount 1267 12 = 6 ∧ acceleratedOrbit 12 1267 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1267 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1267) = 3 ^ 6 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1267.1, data_12_1267.2] + +/-- Complete interval computation for depth 12, residue 1268. -/ +theorem bounds_12_1268 : exactInterval 12 1268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1268 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1268) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1268 : oddCount 1268 12 = 5 ∧ acceleratedOrbit 12 1268 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1268 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1268) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1268.1, data_12_1268.2] + +/-- Complete interval computation for depth 12, residue 1269. -/ +theorem bounds_12_1269 : exactInterval 12 1269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1269 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1269) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1269 : oddCount 1269 12 = 5 ∧ acceleratedOrbit 12 1269 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1269 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1269) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1269.1, data_12_1269.2] + +/-- Complete interval computation for depth 12, residue 1270. -/ +theorem bounds_12_1270 : exactInterval 12 1270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1270 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1270) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1270 : oddCount 1270 12 = 6 ∧ acceleratedOrbit 12 1270 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1270 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1270) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1270.1, data_12_1270.2] + +/-- Complete interval computation for depth 12, residue 1271. -/ +theorem bounds_12_1271 : exactInterval 12 1271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1271 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1271) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1271 : oddCount 1271 12 = 6 ∧ acceleratedOrbit 12 1271 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1271 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1271) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1271.1, data_12_1271.2] + +/-- Complete interval computation for depth 12, residue 1272. -/ +theorem bounds_12_1272 : exactInterval 12 1272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1272 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1272) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1272 : oddCount 1272 12 = 8 ∧ acceleratedOrbit 12 1272 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1272 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1272) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1272.1, data_12_1272.2] + +/-- Complete interval computation for depth 12, residue 1273. -/ +theorem bounds_12_1273 : exactInterval 12 1273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1273 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1273) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1273 : oddCount 1273 12 = 6 ∧ acceleratedOrbit 12 1273 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1273 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1273) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1273.1, data_12_1273.2] + +end Collatz.Research.StoppingAtlas.Batch0283 From dab99b338dcf17d6617e7948158de77de9ce9427 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:29 +0530 Subject: [PATCH 0284/1001] proof: certify atlas Batch0284 (12:1274 to 12:1289) --- Collatz/Research/StoppingAtlas/Batch0284.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0284.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0284.lean b/Collatz/Research/StoppingAtlas/Batch0284.lean new file mode 100644 index 00000000..dd7f731b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0284.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0284 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1274. -/ +theorem bounds_12_1274 : exactInterval 12 1274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1274 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1274) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1274 : oddCount 1274 12 = 8 ∧ acceleratedOrbit 12 1274 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1274 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1274) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1274.1, data_12_1274.2] + +/-- Complete interval computation for depth 12, residue 1275. -/ +theorem bounds_12_1275 : exactInterval 12 1275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1275 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1275) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1275 : oddCount 1275 12 = 8 ∧ acceleratedOrbit 12 1275 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1275 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1275) = 3 ^ 8 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1275.1, data_12_1275.2] + +/-- Complete interval computation for depth 12, residue 1276. -/ +theorem bounds_12_1276 : exactInterval 12 1276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1276 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1276) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1276 : oddCount 1276 12 = 8 ∧ acceleratedOrbit 12 1276 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1276 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1276) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1276.1, data_12_1276.2] + +/-- Complete interval computation for depth 12, residue 1277. -/ +theorem bounds_12_1277 : exactInterval 12 1277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1277 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1277) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1277 : oddCount 1277 12 = 8 ∧ acceleratedOrbit 12 1277 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1277 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1277) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1277.1, data_12_1277.2] + +/-- Complete interval computation for depth 12, residue 1278. -/ +theorem bounds_12_1278 : exactInterval 12 1278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1278 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1278) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1278 : oddCount 1278 12 = 9 ∧ acceleratedOrbit 12 1278 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1278 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1278) = 3 ^ 9 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1278.1, data_12_1278.2] + +/-- Complete interval computation for depth 12, residue 1279. -/ +theorem bounds_12_1279 : exactInterval 12 1279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1279 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1279) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1279 : oddCount 1279 12 = 9 ∧ acceleratedOrbit 12 1279 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1279 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1279) = 3 ^ 9 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1279.1, data_12_1279.2] + +/-- Complete interval computation for depth 12, residue 1280. -/ +theorem bounds_12_1280 : exactInterval 12 1280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1280 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1280) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1280 : oddCount 1280 12 = 1 ∧ acceleratedOrbit 12 1280 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1280 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1280) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1280.1, data_12_1280.2] + +/-- Complete interval computation for depth 12, residue 1281. -/ +theorem bounds_12_1281 : exactInterval 12 1281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1281 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1281) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1281 : oddCount 1281 12 = 6 ∧ acceleratedOrbit 12 1281 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1281 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1281) = 3 ^ 6 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1281.1, data_12_1281.2] + +/-- Complete interval computation for depth 12, residue 1282. -/ +theorem bounds_12_1282 : exactInterval 12 1282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1282 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1282) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1282 : oddCount 1282 12 = 7 ∧ acceleratedOrbit 12 1282 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1282 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1282) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1282.1, data_12_1282.2] + +/-- Complete interval computation for depth 12, residue 1283. -/ +theorem bounds_12_1283 : exactInterval 12 1283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1283 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1283) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1283 : oddCount 1283 12 = 7 ∧ acceleratedOrbit 12 1283 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1283 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1283) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1283.1, data_12_1283.2] + +/-- Complete interval computation for depth 12, residue 1284. -/ +theorem bounds_12_1284 : exactInterval 12 1284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1284 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1284) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1284 : oddCount 1284 12 = 4 ∧ acceleratedOrbit 12 1284 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1284 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1284) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1284.1, data_12_1284.2] + +/-- Complete interval computation for depth 12, residue 1285. -/ +theorem bounds_12_1285 : exactInterval 12 1285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1285 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1285) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1285 : oddCount 1285 12 = 4 ∧ acceleratedOrbit 12 1285 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1285 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1285) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1285.1, data_12_1285.2] + +/-- Complete interval computation for depth 12, residue 1286. -/ +theorem bounds_12_1286 : exactInterval 12 1286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1286 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1286) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1286 : oddCount 1286 12 = 4 ∧ acceleratedOrbit 12 1286 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1286 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1286) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1286.1, data_12_1286.2] + +/-- Complete interval computation for depth 12, residue 1287. -/ +theorem bounds_12_1287 : exactInterval 12 1287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1287 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1287) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1287 : oddCount 1287 12 = 8 ∧ acceleratedOrbit 12 1287 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1287 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1287) = 3 ^ 8 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1287.1, data_12_1287.2] + +/-- Complete interval computation for depth 12, residue 1288. -/ +theorem bounds_12_1288 : exactInterval 12 1288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1288 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1288) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1288 : oddCount 1288 12 = 6 ∧ acceleratedOrbit 12 1288 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1288 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1288) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1288.1, data_12_1288.2] + +/-- Complete interval computation for depth 12, residue 1289. -/ +theorem bounds_12_1289 : exactInterval 12 1289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1289 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1289) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1289 : oddCount 1289 12 = 8 ∧ acceleratedOrbit 12 1289 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1289 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1289) = 3 ^ 8 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1289.1, data_12_1289.2] + +end Collatz.Research.StoppingAtlas.Batch0284 From a0d5a603449ae2933506431dc94d05a55d4f0533 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:29 +0530 Subject: [PATCH 0285/1001] proof: certify atlas Batch0285 (12:1290 to 12:1304) --- Collatz/Research/StoppingAtlas/Batch0285.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0285.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0285.lean b/Collatz/Research/StoppingAtlas/Batch0285.lean new file mode 100644 index 00000000..b1e7d652 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0285.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0285 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1290. -/ +theorem bounds_12_1290 : exactInterval 12 1290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1290 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1290) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1290 : oddCount 1290 12 = 6 ∧ acceleratedOrbit 12 1290 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1290 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1290) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1290.1, data_12_1290.2] + +/-- Complete interval computation for depth 12, residue 1291. -/ +theorem bounds_12_1291 : exactInterval 12 1291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1291 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1291) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1291 : oddCount 1291 12 = 7 ∧ acceleratedOrbit 12 1291 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1291 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1291) = 3 ^ 7 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1291.1, data_12_1291.2] + +/-- Complete interval computation for depth 12, residue 1292. -/ +theorem bounds_12_1292 : exactInterval 12 1292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1292 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1292) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1292 : oddCount 1292 12 = 6 ∧ acceleratedOrbit 12 1292 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1292 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1292) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1292.1, data_12_1292.2] + +/-- Complete interval computation for depth 12, residue 1293. -/ +theorem bounds_12_1293 : exactInterval 12 1293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1293 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1293) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1293 : oddCount 1293 12 = 6 ∧ acceleratedOrbit 12 1293 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1293 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1293) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1293.1, data_12_1293.2] + +/-- Complete interval computation for depth 12, residue 1294. -/ +theorem bounds_12_1294 : exactInterval 12 1294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1294 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1294) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1294 : oddCount 1294 12 = 5 ∧ acceleratedOrbit 12 1294 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1294 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1294) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1294.1, data_12_1294.2] + +/-- Complete interval computation for depth 12, residue 1295. -/ +theorem bounds_12_1295 : exactInterval 12 1295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1295 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1295) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1295 : oddCount 1295 12 = 5 ∧ acceleratedOrbit 12 1295 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1295 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1295) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1295.1, data_12_1295.2] + +/-- Complete interval computation for depth 12, residue 1296. -/ +theorem bounds_12_1296 : exactInterval 12 1296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1296 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1296) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1296 : oddCount 1296 12 = 5 ∧ acceleratedOrbit 12 1296 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1296 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1296) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1296.1, data_12_1296.2] + +/-- Complete interval computation for depth 12, residue 1297. -/ +theorem bounds_12_1297 : exactInterval 12 1297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1297 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1297) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1297 : oddCount 1297 12 = 6 ∧ acceleratedOrbit 12 1297 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1297 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1297) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1297.1, data_12_1297.2] + +/-- Complete interval computation for depth 12, residue 1298. -/ +theorem bounds_12_1298 : exactInterval 12 1298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1298 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1298) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1298 : oddCount 1298 12 = 7 ∧ acceleratedOrbit 12 1298 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1298 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1298) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1298.1, data_12_1298.2] + +/-- Complete interval computation for depth 12, residue 1299. -/ +theorem bounds_12_1299 : exactInterval 12 1299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1299 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1299) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1299 : oddCount 1299 12 = 7 ∧ acceleratedOrbit 12 1299 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1299 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1299) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1299.1, data_12_1299.2] + +/-- Complete interval computation for depth 12, residue 1300. -/ +theorem bounds_12_1300 : exactInterval 12 1300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1300 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1300) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1300 : oddCount 1300 12 = 5 ∧ acceleratedOrbit 12 1300 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1300 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1300) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1300.1, data_12_1300.2] + +/-- Complete interval computation for depth 12, residue 1301. -/ +theorem bounds_12_1301 : exactInterval 12 1301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1301 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1301) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1301 : oddCount 1301 12 = 5 ∧ acceleratedOrbit 12 1301 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1301 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1301) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1301.1, data_12_1301.2] + +/-- Complete interval computation for depth 12, residue 1302. -/ +theorem bounds_12_1302 : exactInterval 12 1302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1302 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1302) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1302 : oddCount 1302 12 = 6 ∧ acceleratedOrbit 12 1302 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1302 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1302) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1302.1, data_12_1302.2] + +/-- Complete interval computation for depth 12, residue 1303. -/ +theorem bounds_12_1303 : exactInterval 12 1303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1303 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1303) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1303 : oddCount 1303 12 = 6 ∧ acceleratedOrbit 12 1303 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1303 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1303) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1303.1, data_12_1303.2] + +/-- Complete interval computation for depth 12, residue 1304. -/ +theorem bounds_12_1304 : exactInterval 12 1304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1304 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1304) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1304 : oddCount 1304 12 = 5 ∧ acceleratedOrbit 12 1304 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1304 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1304) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1304.1, data_12_1304.2] + +end Collatz.Research.StoppingAtlas.Batch0285 From 294531cf3f94458e9ed770ebd51b32d484783da7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:30 +0530 Subject: [PATCH 0286/1001] proof: certify atlas Batch0286 (12:1305 to 12:1319) --- Collatz/Research/StoppingAtlas/Batch0286.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0286.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0286.lean b/Collatz/Research/StoppingAtlas/Batch0286.lean new file mode 100644 index 00000000..1513dd63 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0286.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0286 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1305. -/ +theorem bounds_12_1305 : exactInterval 12 1305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1305 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1305) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1305 : oddCount 1305 12 = 8 ∧ acceleratedOrbit 12 1305 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1305 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1305) = 3 ^ 8 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1305.1, data_12_1305.2] + +/-- Complete interval computation for depth 12, residue 1306. -/ +theorem bounds_12_1306 : exactInterval 12 1306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1306 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1306) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1306 : oddCount 1306 12 = 5 ∧ acceleratedOrbit 12 1306 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1306 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1306) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1306.1, data_12_1306.2] + +/-- Complete interval computation for depth 12, residue 1307. -/ +theorem bounds_12_1307 : exactInterval 12 1307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1307 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1307) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1307 : oddCount 1307 12 = 10 ∧ acceleratedOrbit 12 1307 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1307 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1307) = 3 ^ 10 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1307.1, data_12_1307.2] + +/-- Complete interval computation for depth 12, residue 1308. -/ +theorem bounds_12_1308 : exactInterval 12 1308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1308 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1308) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1308 : oddCount 1308 12 = 8 ∧ acceleratedOrbit 12 1308 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1308 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1308) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1308.1, data_12_1308.2] + +/-- Complete interval computation for depth 12, residue 1309. -/ +theorem bounds_12_1309 : exactInterval 12 1309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1309 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1309) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1309 : oddCount 1309 12 = 8 ∧ acceleratedOrbit 12 1309 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1309 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1309) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1309.1, data_12_1309.2] + +/-- Complete interval computation for depth 12, residue 1310. -/ +theorem bounds_12_1310 : exactInterval 12 1310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1310 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1310) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1310 : oddCount 1310 12 = 8 ∧ acceleratedOrbit 12 1310 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1310 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1310) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1310.1, data_12_1310.2] + +/-- Complete interval computation for depth 12, residue 1311. -/ +theorem bounds_12_1311 : exactInterval 12 1311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1311 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1311) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1311 : oddCount 1311 12 = 7 ∧ acceleratedOrbit 12 1311 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1311 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1311) = 3 ^ 7 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1311.1, data_12_1311.2] + +/-- Complete interval computation for depth 12, residue 1312. -/ +theorem bounds_12_1312 : exactInterval 12 1312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1312 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1312) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1312 : oddCount 1312 12 = 6 ∧ acceleratedOrbit 12 1312 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1312 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1312) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1312.1, data_12_1312.2] + +/-- Complete interval computation for depth 12, residue 1313. -/ +theorem bounds_12_1313 : exactInterval 12 1313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1313 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1313) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1313 : oddCount 1313 12 = 4 ∧ acceleratedOrbit 12 1313 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1313 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1313) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1313.1, data_12_1313.2] + +/-- Complete interval computation for depth 12, residue 1314. -/ +theorem bounds_12_1314 : exactInterval 12 1314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1314 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1314) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1314 : oddCount 1314 12 = 6 ∧ acceleratedOrbit 12 1314 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1314 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1314) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1314.1, data_12_1314.2] + +/-- Complete interval computation for depth 12, residue 1315. -/ +theorem bounds_12_1315 : exactInterval 12 1315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1315 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1315) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1315 : oddCount 1315 12 = 6 ∧ acceleratedOrbit 12 1315 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1315 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1315) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1315.1, data_12_1315.2] + +/-- Complete interval computation for depth 12, residue 1316. -/ +theorem bounds_12_1316 : exactInterval 12 1316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1316 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1316) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1316 : oddCount 1316 12 = 6 ∧ acceleratedOrbit 12 1316 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1316 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1316) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1316.1, data_12_1316.2] + +/-- Complete interval computation for depth 12, residue 1317. -/ +theorem bounds_12_1317 : exactInterval 12 1317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1317 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1317) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1317 : oddCount 1317 12 = 6 ∧ acceleratedOrbit 12 1317 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1317 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1317) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1317.1, data_12_1317.2] + +/-- Complete interval computation for depth 12, residue 1318. -/ +theorem bounds_12_1318 : exactInterval 12 1318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1318 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1318) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1318 : oddCount 1318 12 = 6 ∧ acceleratedOrbit 12 1318 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1318 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1318) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1318.1, data_12_1318.2] + +/-- Complete interval computation for depth 12, residue 1319. -/ +theorem bounds_12_1319 : exactInterval 12 1319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1319 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1319) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1319 : oddCount 1319 12 = 6 ∧ acceleratedOrbit 12 1319 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1319 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1319) = 3 ^ 6 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1319.1, data_12_1319.2] + +end Collatz.Research.StoppingAtlas.Batch0286 From de15a66b3aefcaad812a0e5a59bb2bf617172f25 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:30 +0530 Subject: [PATCH 0287/1001] proof: certify atlas Batch0287 (12:1320 to 12:1335) --- Collatz/Research/StoppingAtlas/Batch0287.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0287.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0287.lean b/Collatz/Research/StoppingAtlas/Batch0287.lean new file mode 100644 index 00000000..2a9345f7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0287.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0287 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1320. -/ +theorem bounds_12_1320 : exactInterval 12 1320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1320 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1320) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1320 : oddCount 1320 12 = 6 ∧ acceleratedOrbit 12 1320 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1320 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1320) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1320.1, data_12_1320.2] + +/-- Complete interval computation for depth 12, residue 1321. -/ +theorem bounds_12_1321 : exactInterval 12 1321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1321 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1321) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1321 : oddCount 1321 12 = 8 ∧ acceleratedOrbit 12 1321 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1321 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1321) = 3 ^ 8 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1321.1, data_12_1321.2] + +/-- Complete interval computation for depth 12, residue 1322. -/ +theorem bounds_12_1322 : exactInterval 12 1322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1322 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1322) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1322 : oddCount 1322 12 = 6 ∧ acceleratedOrbit 12 1322 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1322 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1322) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1322.1, data_12_1322.2] + +/-- Complete interval computation for depth 12, residue 1323. -/ +theorem bounds_12_1323 : exactInterval 12 1323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1323 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1323) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1323 : oddCount 1323 12 = 6 ∧ acceleratedOrbit 12 1323 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1323 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1323) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1323.1, data_12_1323.2] + +/-- Complete interval computation for depth 12, residue 1324. -/ +theorem bounds_12_1324 : exactInterval 12 1324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1324 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1324) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1324 : oddCount 1324 12 = 5 ∧ acceleratedOrbit 12 1324 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1324 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1324) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1324.1, data_12_1324.2] + +/-- Complete interval computation for depth 12, residue 1325. -/ +theorem bounds_12_1325 : exactInterval 12 1325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1325 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1325) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1325 : oddCount 1325 12 = 5 ∧ acceleratedOrbit 12 1325 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1325 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1325) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1325.1, data_12_1325.2] + +/-- Complete interval computation for depth 12, residue 1326. -/ +theorem bounds_12_1326 : exactInterval 12 1326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1326 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1326) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1326 : oddCount 1326 12 = 5 ∧ acceleratedOrbit 12 1326 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1326 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1326) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1326.1, data_12_1326.2] + +/-- Complete interval computation for depth 12, residue 1327. -/ +theorem bounds_12_1327 : exactInterval 12 1327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1327 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1327) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1327 : oddCount 1327 12 = 8 ∧ acceleratedOrbit 12 1327 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1327 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1327) = 3 ^ 8 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1327.1, data_12_1327.2] + +/-- Complete interval computation for depth 12, residue 1328. -/ +theorem bounds_12_1328 : exactInterval 12 1328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1328 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1328) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1328 : oddCount 1328 12 = 6 ∧ acceleratedOrbit 12 1328 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1328 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1328) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1328.1, data_12_1328.2] + +/-- Complete interval computation for depth 12, residue 1329. -/ +theorem bounds_12_1329 : exactInterval 12 1329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1329 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1329) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1329 : oddCount 1329 12 = 6 ∧ acceleratedOrbit 12 1329 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1329 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1329) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1329.1, data_12_1329.2] + +/-- Complete interval computation for depth 12, residue 1330. -/ +theorem bounds_12_1330 : exactInterval 12 1330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1330 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1330) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1330 : oddCount 1330 12 = 6 ∧ acceleratedOrbit 12 1330 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1330 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1330) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1330.1, data_12_1330.2] + +/-- Complete interval computation for depth 12, residue 1331. -/ +theorem bounds_12_1331 : exactInterval 12 1331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1331 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1331) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1331 : oddCount 1331 12 = 6 ∧ acceleratedOrbit 12 1331 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1331 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1331) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1331.1, data_12_1331.2] + +/-- Complete interval computation for depth 12, residue 1332. -/ +theorem bounds_12_1332 : exactInterval 12 1332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1332 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1332) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1332 : oddCount 1332 12 = 6 ∧ acceleratedOrbit 12 1332 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1332 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1332) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1332.1, data_12_1332.2] + +/-- Complete interval computation for depth 12, residue 1333. -/ +theorem bounds_12_1333 : exactInterval 12 1333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1333 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1333) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1333 : oddCount 1333 12 = 6 ∧ acceleratedOrbit 12 1333 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1333 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1333) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1333.1, data_12_1333.2] + +/-- Complete interval computation for depth 12, residue 1334. -/ +theorem bounds_12_1334 : exactInterval 12 1334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1334 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1334) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1334 : oddCount 1334 12 = 9 ∧ acceleratedOrbit 12 1334 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1334 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1334) = 3 ^ 9 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1334.1, data_12_1334.2] + +/-- Complete interval computation for depth 12, residue 1335. -/ +theorem bounds_12_1335 : exactInterval 12 1335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1335 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1335) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1335 : oddCount 1335 12 = 9 ∧ acceleratedOrbit 12 1335 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1335 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1335) = 3 ^ 9 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1335.1, data_12_1335.2] + +end Collatz.Research.StoppingAtlas.Batch0287 From 33a87d8c9d55e0dca678f299634ea8942c3f6f71 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:31 +0530 Subject: [PATCH 0288/1001] proof: certify atlas Batch0288 (12:1336 to 12:1350) --- Collatz/Research/StoppingAtlas/Batch0288.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0288.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0288.lean b/Collatz/Research/StoppingAtlas/Batch0288.lean new file mode 100644 index 00000000..ea99faeb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0288.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0288 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1336. -/ +theorem bounds_12_1336 : exactInterval 12 1336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1336 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1336) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1336 : oddCount 1336 12 = 7 ∧ acceleratedOrbit 12 1336 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1336 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1336) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1336.1, data_12_1336.2] + +/-- Complete interval computation for depth 12, residue 1337. -/ +theorem bounds_12_1337 : exactInterval 12 1337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1337 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1337) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1337 : oddCount 1337 12 = 8 ∧ acceleratedOrbit 12 1337 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1337 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1337) = 3 ^ 8 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1337.1, data_12_1337.2] + +/-- Complete interval computation for depth 12, residue 1338. -/ +theorem bounds_12_1338 : exactInterval 12 1338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1338 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1338) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1338 : oddCount 1338 12 = 7 ∧ acceleratedOrbit 12 1338 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1338 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1338) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1338.1, data_12_1338.2] + +/-- Complete interval computation for depth 12, residue 1339. -/ +theorem bounds_12_1339 : exactInterval 12 1339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1339 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1339) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1339 : oddCount 1339 12 = 5 ∧ acceleratedOrbit 12 1339 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1339 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1339) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1339.1, data_12_1339.2] + +/-- Complete interval computation for depth 12, residue 1340. -/ +theorem bounds_12_1340 : exactInterval 12 1340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1340 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1340) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1340 : oddCount 1340 12 = 7 ∧ acceleratedOrbit 12 1340 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1340 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1340) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1340.1, data_12_1340.2] + +/-- Complete interval computation for depth 12, residue 1341. -/ +theorem bounds_12_1341 : exactInterval 12 1341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1341 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1341) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1341 : oddCount 1341 12 = 7 ∧ acceleratedOrbit 12 1341 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1341 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1341) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1341.1, data_12_1341.2] + +/-- Complete interval computation for depth 12, residue 1342. -/ +theorem bounds_12_1342 : exactInterval 12 1342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1342 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1342) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1342 : oddCount 1342 12 = 8 ∧ acceleratedOrbit 12 1342 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1342 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1342) = 3 ^ 8 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1342.1, data_12_1342.2] + +/-- Complete interval computation for depth 12, residue 1343. -/ +theorem bounds_12_1343 : exactInterval 12 1343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1343 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1343) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1343 : oddCount 1343 12 = 8 ∧ acceleratedOrbit 12 1343 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1343 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1343) = 3 ^ 8 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1343.1, data_12_1343.2] + +/-- Complete interval computation for depth 12, residue 1344. -/ +theorem bounds_12_1344 : exactInterval 12 1344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1344 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1344) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1344 : oddCount 1344 12 = 1 ∧ acceleratedOrbit 12 1344 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1344 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1344) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1344.1, data_12_1344.2] + +/-- Complete interval computation for depth 12, residue 1345. -/ +theorem bounds_12_1345 : exactInterval 12 1345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1345 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1345) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1345 : oddCount 1345 12 = 6 ∧ acceleratedOrbit 12 1345 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1345 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1345) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1345.1, data_12_1345.2] + +/-- Complete interval computation for depth 12, residue 1346. -/ +theorem bounds_12_1346 : exactInterval 12 1346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1346 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1346) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1346 : oddCount 1346 12 = 7 ∧ acceleratedOrbit 12 1346 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1346 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1346) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1346.1, data_12_1346.2] + +/-- Complete interval computation for depth 12, residue 1347. -/ +theorem bounds_12_1347 : exactInterval 12 1347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1347 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1347) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1347 : oddCount 1347 12 = 7 ∧ acceleratedOrbit 12 1347 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1347 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1347) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1347.1, data_12_1347.2] + +/-- Complete interval computation for depth 12, residue 1348. -/ +theorem bounds_12_1348 : exactInterval 12 1348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1348 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1348) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1348 : oddCount 1348 12 = 7 ∧ acceleratedOrbit 12 1348 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1348 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1348) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1348.1, data_12_1348.2] + +/-- Complete interval computation for depth 12, residue 1349. -/ +theorem bounds_12_1349 : exactInterval 12 1349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1349 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1349) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1349 : oddCount 1349 12 = 7 ∧ acceleratedOrbit 12 1349 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1349 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1349) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1349.1, data_12_1349.2] + +/-- Complete interval computation for depth 12, residue 1350. -/ +theorem bounds_12_1350 : exactInterval 12 1350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1350 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1350) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1350 : oddCount 1350 12 = 7 ∧ acceleratedOrbit 12 1350 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1350 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1350) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1350.1, data_12_1350.2] + +end Collatz.Research.StoppingAtlas.Batch0288 From 44caf6324bff7149c143819f8bd0705c3bac4d38 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:31 +0530 Subject: [PATCH 0289/1001] proof: certify atlas Batch0289 (12:1351 to 12:1366) --- Collatz/Research/StoppingAtlas/Batch0289.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0289.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0289.lean b/Collatz/Research/StoppingAtlas/Batch0289.lean new file mode 100644 index 00000000..f9c7131b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0289.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0289 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1351. -/ +theorem bounds_12_1351 : exactInterval 12 1351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1351 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1351) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1351 : oddCount 1351 12 = 9 ∧ acceleratedOrbit 12 1351 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1351 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1351) = 3 ^ 9 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1351.1, data_12_1351.2] + +/-- Complete interval computation for depth 12, residue 1352. -/ +theorem bounds_12_1352 : exactInterval 12 1352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1352 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1352) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1352 : oddCount 1352 12 = 8 ∧ acceleratedOrbit 12 1352 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1352 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1352) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1352.1, data_12_1352.2] + +/-- Complete interval computation for depth 12, residue 1353. -/ +theorem bounds_12_1353 : exactInterval 12 1353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1353 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1353) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1353 : oddCount 1353 12 = 7 ∧ acceleratedOrbit 12 1353 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1353 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1353) = 3 ^ 7 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1353.1, data_12_1353.2] + +/-- Complete interval computation for depth 12, residue 1354. -/ +theorem bounds_12_1354 : exactInterval 12 1354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1354 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1354) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1354 : oddCount 1354 12 = 8 ∧ acceleratedOrbit 12 1354 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1354 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1354) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1354.1, data_12_1354.2] + +/-- Complete interval computation for depth 12, residue 1355. -/ +theorem bounds_12_1355 : exactInterval 12 1355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1355 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1355) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1355 : oddCount 1355 12 = 7 ∧ acceleratedOrbit 12 1355 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1355 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1355) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1355.1, data_12_1355.2] + +/-- Complete interval computation for depth 12, residue 1356. -/ +theorem bounds_12_1356 : exactInterval 12 1356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1356 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1356) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1356 : oddCount 1356 12 = 8 ∧ acceleratedOrbit 12 1356 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1356 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1356) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1356.1, data_12_1356.2] + +/-- Complete interval computation for depth 12, residue 1357. -/ +theorem bounds_12_1357 : exactInterval 12 1357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1357 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1357) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1357 : oddCount 1357 12 = 8 ∧ acceleratedOrbit 12 1357 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1357 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1357) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1357.1, data_12_1357.2] + +/-- Complete interval computation for depth 12, residue 1358. -/ +theorem bounds_12_1358 : exactInterval 12 1358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1358 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1358) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1358 : oddCount 1358 12 = 8 ∧ acceleratedOrbit 12 1358 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1358 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1358) = 3 ^ 8 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1358.1, data_12_1358.2] + +/-- Complete interval computation for depth 12, residue 1359. -/ +theorem bounds_12_1359 : exactInterval 12 1359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1359 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1359) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1359 : oddCount 1359 12 = 8 ∧ acceleratedOrbit 12 1359 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1359 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1359) = 3 ^ 8 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1359.1, data_12_1359.2] + +/-- Complete interval computation for depth 12, residue 1360. -/ +theorem bounds_12_1360 : exactInterval 12 1360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1360 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1360) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1360 : oddCount 1360 12 = 1 ∧ acceleratedOrbit 12 1360 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1360 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1360) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1360.1, data_12_1360.2] + +/-- Complete interval computation for depth 12, residue 1361. -/ +theorem bounds_12_1361 : exactInterval 12 1361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1361 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1361) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1361 : oddCount 1361 12 = 9 ∧ acceleratedOrbit 12 1361 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1361 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1361) = 3 ^ 9 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1361.1, data_12_1361.2] + +/-- Complete interval computation for depth 12, residue 1362. -/ +theorem bounds_12_1362 : exactInterval 12 1362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1362 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1362) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1362 : oddCount 1362 12 = 10 ∧ acceleratedOrbit 12 1362 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1362 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1362) = 3 ^ 10 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1362.1, data_12_1362.2] + +/-- Complete interval computation for depth 12, residue 1363. -/ +theorem bounds_12_1363 : exactInterval 12 1363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1363 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1363) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1363 : oddCount 1363 12 = 10 ∧ acceleratedOrbit 12 1363 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1363 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1363) = 3 ^ 10 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1363.1, data_12_1363.2] + +/-- Complete interval computation for depth 12, residue 1364. -/ +theorem bounds_12_1364 : exactInterval 12 1364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1364 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1364) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1364 : oddCount 1364 12 = 1 ∧ acceleratedOrbit 12 1364 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1364 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1364) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1364.1, data_12_1364.2] + +/-- Complete interval computation for depth 12, residue 1365. -/ +theorem bounds_12_1365 : exactInterval 12 1365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1365 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1365) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1365 : oddCount 1365 12 = 1 ∧ acceleratedOrbit 12 1365 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1365 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1365) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1365.1, data_12_1365.2] + +/-- Complete interval computation for depth 12, residue 1366. -/ +theorem bounds_12_1366 : exactInterval 12 1366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1366 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1366) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1366 : oddCount 1366 12 = 6 ∧ acceleratedOrbit 12 1366 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1366 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1366) = 3 ^ 6 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1366.1, data_12_1366.2] + +end Collatz.Research.StoppingAtlas.Batch0289 From 028091140690b4b3ded75fbdc53a46992df4e390 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:31 +0530 Subject: [PATCH 0290/1001] proof: certify atlas Batch0290 (12:1367 to 12:1381) --- Collatz/Research/StoppingAtlas/Batch0290.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0290.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0290.lean b/Collatz/Research/StoppingAtlas/Batch0290.lean new file mode 100644 index 00000000..781978ed --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0290.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0290 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1367. -/ +theorem bounds_12_1367 : exactInterval 12 1367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1367 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1367) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1367 : oddCount 1367 12 = 6 ∧ acceleratedOrbit 12 1367 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1367 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1367) = 3 ^ 6 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1367.1, data_12_1367.2] + +/-- Complete interval computation for depth 12, residue 1368. -/ +theorem bounds_12_1368 : exactInterval 12 1368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1368 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1368) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1368 : oddCount 1368 12 = 5 ∧ acceleratedOrbit 12 1368 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1368 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1368) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1368.1, data_12_1368.2] + +/-- Complete interval computation for depth 12, residue 1369. -/ +theorem bounds_12_1369 : exactInterval 12 1369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1369 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1369) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1369 : oddCount 1369 12 = 6 ∧ acceleratedOrbit 12 1369 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1369 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1369) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1369.1, data_12_1369.2] + +/-- Complete interval computation for depth 12, residue 1370. -/ +theorem bounds_12_1370 : exactInterval 12 1370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1370 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1370) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1370 : oddCount 1370 12 = 5 ∧ acceleratedOrbit 12 1370 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1370 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1370) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1370.1, data_12_1370.2] + +/-- Complete interval computation for depth 12, residue 1371. -/ +theorem bounds_12_1371 : exactInterval 12 1371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1371 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1371) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1371 : oddCount 1371 12 = 7 ∧ acceleratedOrbit 12 1371 = 733 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1371 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1371) = 3 ^ 7 * m + 733 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1371.1, data_12_1371.2] + +/-- Complete interval computation for depth 12, residue 1372. -/ +theorem bounds_12_1372 : exactInterval 12 1372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1372 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1372) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1372 : oddCount 1372 12 = 5 ∧ acceleratedOrbit 12 1372 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1372 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1372) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1372.1, data_12_1372.2] + +/-- Complete interval computation for depth 12, residue 1373. -/ +theorem bounds_12_1373 : exactInterval 12 1373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1373 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1373) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1373 : oddCount 1373 12 = 5 ∧ acceleratedOrbit 12 1373 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1373 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1373) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1373.1, data_12_1373.2] + +/-- Complete interval computation for depth 12, residue 1374. -/ +theorem bounds_12_1374 : exactInterval 12 1374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1374 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1374) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1374 : oddCount 1374 12 = 6 ∧ acceleratedOrbit 12 1374 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1374 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1374) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1374.1, data_12_1374.2] + +/-- Complete interval computation for depth 12, residue 1375. -/ +theorem bounds_12_1375 : exactInterval 12 1375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1375 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1375) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1375 : oddCount 1375 12 = 6 ∧ acceleratedOrbit 12 1375 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1375 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1375) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1375.1, data_12_1375.2] + +/-- Complete interval computation for depth 12, residue 1376. -/ +theorem bounds_12_1376 : exactInterval 12 1376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1376 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1376) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1376 : oddCount 1376 12 = 4 ∧ acceleratedOrbit 12 1376 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1376 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1376) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1376.1, data_12_1376.2] + +/-- Complete interval computation for depth 12, residue 1377. -/ +theorem bounds_12_1377 : exactInterval 12 1377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1377 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1377) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1377 : oddCount 1377 12 = 7 ∧ acceleratedOrbit 12 1377 = 737 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1377 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1377) = 3 ^ 7 * m + 737 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1377.1, data_12_1377.2] + +/-- Complete interval computation for depth 12, residue 1378. -/ +theorem bounds_12_1378 : exactInterval 12 1378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1378 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1378) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1378 : oddCount 1378 12 = 5 ∧ acceleratedOrbit 12 1378 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1378 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1378) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1378.1, data_12_1378.2] + +/-- Complete interval computation for depth 12, residue 1379. -/ +theorem bounds_12_1379 : exactInterval 12 1379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1379 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1379) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1379 : oddCount 1379 12 = 5 ∧ acceleratedOrbit 12 1379 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1379 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1379) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1379.1, data_12_1379.2] + +/-- Complete interval computation for depth 12, residue 1380. -/ +theorem bounds_12_1380 : exactInterval 12 1380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1380 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1380) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1380 : oddCount 1380 12 = 5 ∧ acceleratedOrbit 12 1380 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1380 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1380) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1380.1, data_12_1380.2] + +/-- Complete interval computation for depth 12, residue 1381. -/ +theorem bounds_12_1381 : exactInterval 12 1381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1381 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1381) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1381 : oddCount 1381 12 = 5 ∧ acceleratedOrbit 12 1381 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1381 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1381) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1381.1, data_12_1381.2] + +end Collatz.Research.StoppingAtlas.Batch0290 From 269e6b2bd8fc2d417b6129c34f14e319f2d9a52e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:32 +0530 Subject: [PATCH 0291/1001] proof: certify atlas Batch0291 (12:1382 to 12:1396) --- Collatz/Research/StoppingAtlas/Batch0291.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0291.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0291.lean b/Collatz/Research/StoppingAtlas/Batch0291.lean new file mode 100644 index 00000000..5732db24 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0291.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0291 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1382. -/ +theorem bounds_12_1382 : exactInterval 12 1382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1382 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1382) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1382 : oddCount 1382 12 = 5 ∧ acceleratedOrbit 12 1382 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1382 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1382) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1382.1, data_12_1382.2] + +/-- Complete interval computation for depth 12, residue 1383. -/ +theorem bounds_12_1383 : exactInterval 12 1383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1383 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1383) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1383 : oddCount 1383 12 = 9 ∧ acceleratedOrbit 12 1383 = 6652 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1383 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1383) = 3 ^ 9 * m + 6652 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1383.1, data_12_1383.2] + +/-- Complete interval computation for depth 12, residue 1384. -/ +theorem bounds_12_1384 : exactInterval 12 1384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1384 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1384) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1384 : oddCount 1384 12 = 4 ∧ acceleratedOrbit 12 1384 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1384 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1384) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1384.1, data_12_1384.2] + +/-- Complete interval computation for depth 12, residue 1385. -/ +theorem bounds_12_1385 : exactInterval 12 1385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1385 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1385) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1385 : oddCount 1385 12 = 6 ∧ acceleratedOrbit 12 1385 = 247 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1385 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1385) = 3 ^ 6 * m + 247 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1385.1, data_12_1385.2] + +/-- Complete interval computation for depth 12, residue 1386. -/ +theorem bounds_12_1386 : exactInterval 12 1386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1386 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1386) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1386 : oddCount 1386 12 = 4 ∧ acceleratedOrbit 12 1386 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1386 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1386) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1386.1, data_12_1386.2] + +/-- Complete interval computation for depth 12, residue 1387. -/ +theorem bounds_12_1387 : exactInterval 12 1387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1387 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1387) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1387 : oddCount 1387 12 = 7 ∧ acceleratedOrbit 12 1387 = 742 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1387 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1387) = 3 ^ 7 * m + 742 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1387.1, data_12_1387.2] + +/-- Complete interval computation for depth 12, residue 1388. -/ +theorem bounds_12_1388 : exactInterval 12 1388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1388 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1388) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1388 : oddCount 1388 12 = 6 ∧ acceleratedOrbit 12 1388 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1388 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1388) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1388.1, data_12_1388.2] + +/-- Complete interval computation for depth 12, residue 1389. -/ +theorem bounds_12_1389 : exactInterval 12 1389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1389 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1389) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1389 : oddCount 1389 12 = 6 ∧ acceleratedOrbit 12 1389 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1389 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1389) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1389.1, data_12_1389.2] + +/-- Complete interval computation for depth 12, residue 1390. -/ +theorem bounds_12_1390 : exactInterval 12 1390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1390 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1390) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1390 : oddCount 1390 12 = 6 ∧ acceleratedOrbit 12 1390 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1390 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1390) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1390.1, data_12_1390.2] + +/-- Complete interval computation for depth 12, residue 1391. -/ +theorem bounds_12_1391 : exactInterval 12 1391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1391 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1391) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1391 : oddCount 1391 12 = 8 ∧ acceleratedOrbit 12 1391 = 2231 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1391 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1391) = 3 ^ 8 * m + 2231 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1391.1, data_12_1391.2] + +/-- Complete interval computation for depth 12, residue 1392. -/ +theorem bounds_12_1392 : exactInterval 12 1392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1392 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1392) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1392 : oddCount 1392 12 = 4 ∧ acceleratedOrbit 12 1392 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1392 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1392) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1392.1, data_12_1392.2] + +/-- Complete interval computation for depth 12, residue 1393. -/ +theorem bounds_12_1393 : exactInterval 12 1393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1393 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1393) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1393 : oddCount 1393 12 = 4 ∧ acceleratedOrbit 12 1393 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1393 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1393) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1393.1, data_12_1393.2] + +/-- Complete interval computation for depth 12, residue 1394. -/ +theorem bounds_12_1394 : exactInterval 12 1394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1394 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1394) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1394 : oddCount 1394 12 = 5 ∧ acceleratedOrbit 12 1394 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1394 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1394) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1394.1, data_12_1394.2] + +/-- Complete interval computation for depth 12, residue 1395. -/ +theorem bounds_12_1395 : exactInterval 12 1395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1395 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1395) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1395 : oddCount 1395 12 = 5 ∧ acceleratedOrbit 12 1395 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1395 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1395) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1395.1, data_12_1395.2] + +/-- Complete interval computation for depth 12, residue 1396. -/ +theorem bounds_12_1396 : exactInterval 12 1396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1396 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1396) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1396 : oddCount 1396 12 = 4 ∧ acceleratedOrbit 12 1396 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1396 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1396) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1396.1, data_12_1396.2] + +end Collatz.Research.StoppingAtlas.Batch0291 From db59d34e4d27c30f95faa83956d6499be3e18110 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:32 +0530 Subject: [PATCH 0292/1001] proof: certify atlas Batch0292 (12:1397 to 12:1412) --- Collatz/Research/StoppingAtlas/Batch0292.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0292.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0292.lean b/Collatz/Research/StoppingAtlas/Batch0292.lean new file mode 100644 index 00000000..80c65a8c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0292.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0292 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1397. -/ +theorem bounds_12_1397 : exactInterval 12 1397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1397 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1397) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1397 : oddCount 1397 12 = 4 ∧ acceleratedOrbit 12 1397 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1397 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1397) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1397.1, data_12_1397.2] + +/-- Complete interval computation for depth 12, residue 1398. -/ +theorem bounds_12_1398 : exactInterval 12 1398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1398 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1398) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1398 : oddCount 1398 12 = 7 ∧ acceleratedOrbit 12 1398 = 749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1398 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1398) = 3 ^ 7 * m + 749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1398.1, data_12_1398.2] + +/-- Complete interval computation for depth 12, residue 1399. -/ +theorem bounds_12_1399 : exactInterval 12 1399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1399 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1399) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1399 : oddCount 1399 12 = 7 ∧ acceleratedOrbit 12 1399 = 749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1399 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1399) = 3 ^ 7 * m + 749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1399.1, data_12_1399.2] + +/-- Complete interval computation for depth 12, residue 1400. -/ +theorem bounds_12_1400 : exactInterval 12 1400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1400 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1400) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1400 : oddCount 1400 12 = 6 ∧ acceleratedOrbit 12 1400 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1400 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1400) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1400.1, data_12_1400.2] + +/-- Complete interval computation for depth 12, residue 1401. -/ +theorem bounds_12_1401 : exactInterval 12 1401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1401 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1401) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1401 : oddCount 1401 12 = 9 ∧ acceleratedOrbit 12 1401 = 6743 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1401 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1401) = 3 ^ 9 * m + 6743 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1401.1, data_12_1401.2] + +/-- Complete interval computation for depth 12, residue 1402. -/ +theorem bounds_12_1402 : exactInterval 12 1402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1402 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1402) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1402 : oddCount 1402 12 = 6 ∧ acceleratedOrbit 12 1402 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1402 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1402) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1402.1, data_12_1402.2] + +/-- Complete interval computation for depth 12, residue 1403. -/ +theorem bounds_12_1403 : exactInterval 12 1403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1403 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1403) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1403 : oddCount 1403 12 = 6 ∧ acceleratedOrbit 12 1403 = 250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1403 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1403) = 3 ^ 6 * m + 250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1403.1, data_12_1403.2] + +/-- Complete interval computation for depth 12, residue 1404. -/ +theorem bounds_12_1404 : exactInterval 12 1404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1404 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1404) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1404 : oddCount 1404 12 = 6 ∧ acceleratedOrbit 12 1404 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1404 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1404) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1404.1, data_12_1404.2] + +/-- Complete interval computation for depth 12, residue 1405. -/ +theorem bounds_12_1405 : exactInterval 12 1405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1405 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1405) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1405 : oddCount 1405 12 = 6 ∧ acceleratedOrbit 12 1405 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1405 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1405) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1405.1, data_12_1405.2] + +/-- Complete interval computation for depth 12, residue 1406. -/ +theorem bounds_12_1406 : exactInterval 12 1406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1406 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1406) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1406 : oddCount 1406 12 = 9 ∧ acceleratedOrbit 12 1406 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1406 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1406) = 3 ^ 9 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1406.1, data_12_1406.2] + +/-- Complete interval computation for depth 12, residue 1407. -/ +theorem bounds_12_1407 : exactInterval 12 1407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1407 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1407) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1407 : oddCount 1407 12 = 9 ∧ acceleratedOrbit 12 1407 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1407 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1407) = 3 ^ 9 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1407.1, data_12_1407.2] + +/-- Complete interval computation for depth 12, residue 1408. -/ +theorem bounds_12_1408 : exactInterval 12 1408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1408 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1408) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1408 : oddCount 1408 12 = 3 ∧ acceleratedOrbit 12 1408 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1408 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1408) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1408.1, data_12_1408.2] + +/-- Complete interval computation for depth 12, residue 1409. -/ +theorem bounds_12_1409 : exactInterval 12 1409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1409 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1409) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1409 : oddCount 1409 12 = 7 ∧ acceleratedOrbit 12 1409 = 755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1409 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1409) = 3 ^ 7 * m + 755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1409.1, data_12_1409.2] + +/-- Complete interval computation for depth 12, residue 1410. -/ +theorem bounds_12_1410 : exactInterval 12 1410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1410 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1410) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1410 : oddCount 1410 12 = 4 ∧ acceleratedOrbit 12 1410 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1410 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1410) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1410.1, data_12_1410.2] + +/-- Complete interval computation for depth 12, residue 1411. -/ +theorem bounds_12_1411 : exactInterval 12 1411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1411 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1411) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1411 : oddCount 1411 12 = 4 ∧ acceleratedOrbit 12 1411 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1411 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1411) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1411.1, data_12_1411.2] + +/-- Complete interval computation for depth 12, residue 1412. -/ +theorem bounds_12_1412 : exactInterval 12 1412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1412 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1412) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1412 : oddCount 1412 12 = 6 ∧ acceleratedOrbit 12 1412 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1412 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1412) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1412.1, data_12_1412.2] + +end Collatz.Research.StoppingAtlas.Batch0292 From 48d878319dcc74150179bee81621c7c620edfd4f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:32 +0530 Subject: [PATCH 0293/1001] proof: certify atlas Batch0293 (12:1413 to 12:1427) --- Collatz/Research/StoppingAtlas/Batch0293.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0293.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0293.lean b/Collatz/Research/StoppingAtlas/Batch0293.lean new file mode 100644 index 00000000..4b1705a6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0293.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0293 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1413. -/ +theorem bounds_12_1413 : exactInterval 12 1413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1413 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1413) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1413 : oddCount 1413 12 = 6 ∧ acceleratedOrbit 12 1413 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1413 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1413) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1413.1, data_12_1413.2] + +/-- Complete interval computation for depth 12, residue 1414. -/ +theorem bounds_12_1414 : exactInterval 12 1414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1414 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1414) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1414 : oddCount 1414 12 = 6 ∧ acceleratedOrbit 12 1414 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1414 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1414) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1414.1, data_12_1414.2] + +/-- Complete interval computation for depth 12, residue 1415. -/ +theorem bounds_12_1415 : exactInterval 12 1415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1415 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1415) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1415 : oddCount 1415 12 = 4 ∧ acceleratedOrbit 12 1415 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1415 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1415) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1415.1, data_12_1415.2] + +/-- Complete interval computation for depth 12, residue 1416. -/ +theorem bounds_12_1416 : exactInterval 12 1416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1416 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1416) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1416 : oddCount 1416 12 = 4 ∧ acceleratedOrbit 12 1416 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1416 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1416) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1416.1, data_12_1416.2] + +/-- Complete interval computation for depth 12, residue 1417. -/ +theorem bounds_12_1417 : exactInterval 12 1417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1417 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1417) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1417 : oddCount 1417 12 = 7 ∧ acceleratedOrbit 12 1417 = 758 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1417 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1417) = 3 ^ 7 * m + 758 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1417.1, data_12_1417.2] + +/-- Complete interval computation for depth 12, residue 1418. -/ +theorem bounds_12_1418 : exactInterval 12 1418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1418 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1418) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1418 : oddCount 1418 12 = 4 ∧ acceleratedOrbit 12 1418 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1418 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1418) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1418.1, data_12_1418.2] + +/-- Complete interval computation for depth 12, residue 1419. -/ +theorem bounds_12_1419 : exactInterval 12 1419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1419 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1419) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1419 : oddCount 1419 12 = 6 ∧ acceleratedOrbit 12 1419 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1419 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1419) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1419.1, data_12_1419.2] + +/-- Complete interval computation for depth 12, residue 1420. -/ +theorem bounds_12_1420 : exactInterval 12 1420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1420 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1420) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1420 : oddCount 1420 12 = 4 ∧ acceleratedOrbit 12 1420 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1420 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1420) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1420.1, data_12_1420.2] + +/-- Complete interval computation for depth 12, residue 1421. -/ +theorem bounds_12_1421 : exactInterval 12 1421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1421 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1421) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1421 : oddCount 1421 12 = 4 ∧ acceleratedOrbit 12 1421 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1421 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1421) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1421.1, data_12_1421.2] + +/-- Complete interval computation for depth 12, residue 1422. -/ +theorem bounds_12_1422 : exactInterval 12 1422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1422 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1422) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1422 : oddCount 1422 12 = 6 ∧ acceleratedOrbit 12 1422 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1422 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1422) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1422.1, data_12_1422.2] + +/-- Complete interval computation for depth 12, residue 1423. -/ +theorem bounds_12_1423 : exactInterval 12 1423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1423 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1423) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1423 : oddCount 1423 12 = 6 ∧ acceleratedOrbit 12 1423 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1423 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1423) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1423.1, data_12_1423.2] + +/-- Complete interval computation for depth 12, residue 1424. -/ +theorem bounds_12_1424 : exactInterval 12 1424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1424 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1424) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1424 : oddCount 1424 12 = 4 ∧ acceleratedOrbit 12 1424 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1424 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1424) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1424.1, data_12_1424.2] + +/-- Complete interval computation for depth 12, residue 1425. -/ +theorem bounds_12_1425 : exactInterval 12 1425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1425 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1425) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1425 : oddCount 1425 12 = 5 ∧ acceleratedOrbit 12 1425 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1425 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1425) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1425.1, data_12_1425.2] + +/-- Complete interval computation for depth 12, residue 1426. -/ +theorem bounds_12_1426 : exactInterval 12 1426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1426 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1426) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1426 : oddCount 1426 12 = 5 ∧ acceleratedOrbit 12 1426 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1426 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1426) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1426.1, data_12_1426.2] + +/-- Complete interval computation for depth 12, residue 1427. -/ +theorem bounds_12_1427 : exactInterval 12 1427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1427 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1427) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1427 : oddCount 1427 12 = 5 ∧ acceleratedOrbit 12 1427 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1427 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1427) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1427.1, data_12_1427.2] + +end Collatz.Research.StoppingAtlas.Batch0293 From 93f627c875c4843668b93a20e684641ca416ec7c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:33 +0530 Subject: [PATCH 0294/1001] proof: certify atlas Batch0294 (12:1428 to 12:1442) --- Collatz/Research/StoppingAtlas/Batch0294.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0294.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0294.lean b/Collatz/Research/StoppingAtlas/Batch0294.lean new file mode 100644 index 00000000..bde64471 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0294.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0294 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1428. -/ +theorem bounds_12_1428 : exactInterval 12 1428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1428 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1428) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1428 : oddCount 1428 12 = 4 ∧ acceleratedOrbit 12 1428 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1428 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1428) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1428.1, data_12_1428.2] + +/-- Complete interval computation for depth 12, residue 1429. -/ +theorem bounds_12_1429 : exactInterval 12 1429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1429 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1429) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1429 : oddCount 1429 12 = 4 ∧ acceleratedOrbit 12 1429 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1429 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1429) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1429.1, data_12_1429.2] + +/-- Complete interval computation for depth 12, residue 1430. -/ +theorem bounds_12_1430 : exactInterval 12 1430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1430 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1430) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1430 : oddCount 1430 12 = 6 ∧ acceleratedOrbit 12 1430 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1430 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1430) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1430.1, data_12_1430.2] + +/-- Complete interval computation for depth 12, residue 1431. -/ +theorem bounds_12_1431 : exactInterval 12 1431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1431 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1431) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1431 : oddCount 1431 12 = 6 ∧ acceleratedOrbit 12 1431 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1431 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1431) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1431.1, data_12_1431.2] + +/-- Complete interval computation for depth 12, residue 1432. -/ +theorem bounds_12_1432 : exactInterval 12 1432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1432 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1432) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1432 : oddCount 1432 12 = 4 ∧ acceleratedOrbit 12 1432 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1432 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1432) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1432.1, data_12_1432.2] + +/-- Complete interval computation for depth 12, residue 1433. -/ +theorem bounds_12_1433 : exactInterval 12 1433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1433 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1433) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1433 : oddCount 1433 12 = 6 ∧ acceleratedOrbit 12 1433 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1433 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1433) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1433.1, data_12_1433.2] + +/-- Complete interval computation for depth 12, residue 1434. -/ +theorem bounds_12_1434 : exactInterval 12 1434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1434 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1434) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1434 : oddCount 1434 12 = 4 ∧ acceleratedOrbit 12 1434 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1434 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1434) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1434.1, data_12_1434.2] + +/-- Complete interval computation for depth 12, residue 1435. -/ +theorem bounds_12_1435 : exactInterval 12 1435 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1435 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1435) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1435 : oddCount 1435 12 = 7 ∧ acceleratedOrbit 12 1435 = 767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1435 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1435) = 3 ^ 7 * m + 767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1435.1, data_12_1435.2] + +/-- Complete interval computation for depth 12, residue 1436. -/ +theorem bounds_12_1436 : exactInterval 12 1436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1436 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1436) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1436 : oddCount 1436 12 = 8 ∧ acceleratedOrbit 12 1436 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1436 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1436) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1436.1, data_12_1436.2] + +/-- Complete interval computation for depth 12, residue 1437. -/ +theorem bounds_12_1437 : exactInterval 12 1437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1437 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1437) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1437 : oddCount 1437 12 = 8 ∧ acceleratedOrbit 12 1437 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1437 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1437) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1437.1, data_12_1437.2] + +/-- Complete interval computation for depth 12, residue 1438. -/ +theorem bounds_12_1438 : exactInterval 12 1438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1438 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1438) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1438 : oddCount 1438 12 = 8 ∧ acceleratedOrbit 12 1438 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1438 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1438) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1438.1, data_12_1438.2] + +/-- Complete interval computation for depth 12, residue 1439. -/ +theorem bounds_12_1439 : exactInterval 12 1439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1439 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1439) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1439 : oddCount 1439 12 = 10 ∧ acceleratedOrbit 12 1439 = 20762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1439 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1439) = 3 ^ 10 * m + 20762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1439.1, data_12_1439.2] + +/-- Complete interval computation for depth 12, residue 1440. -/ +theorem bounds_12_1440 : exactInterval 12 1440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1440 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1440) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1440 : oddCount 1440 12 = 3 ∧ acceleratedOrbit 12 1440 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1440 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1440) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1440.1, data_12_1440.2] + +/-- Complete interval computation for depth 12, residue 1441. -/ +theorem bounds_12_1441 : exactInterval 12 1441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1441 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1441) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1441 : oddCount 1441 12 = 6 ∧ acceleratedOrbit 12 1441 = 257 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1441 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1441) = 3 ^ 6 * m + 257 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1441.1, data_12_1441.2] + +/-- Complete interval computation for depth 12, residue 1442. -/ +theorem bounds_12_1442 : exactInterval 12 1442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1442 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1442) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1442 : oddCount 1442 12 = 5 ∧ acceleratedOrbit 12 1442 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1442 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1442) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1442.1, data_12_1442.2] + +end Collatz.Research.StoppingAtlas.Batch0294 From cd8fd4f2410e3bc5a3df46926d66f6d5d9d75905 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:33 +0530 Subject: [PATCH 0295/1001] proof: certify atlas Batch0295 (12:1443 to 12:1458) --- Collatz/Research/StoppingAtlas/Batch0295.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0295.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0295.lean b/Collatz/Research/StoppingAtlas/Batch0295.lean new file mode 100644 index 00000000..141dd4bd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0295.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0295 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1443. -/ +theorem bounds_12_1443 : exactInterval 12 1443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1443 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1443) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1443 : oddCount 1443 12 = 5 ∧ acceleratedOrbit 12 1443 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1443 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1443) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1443.1, data_12_1443.2] + +/-- Complete interval computation for depth 12, residue 1444. -/ +theorem bounds_12_1444 : exactInterval 12 1444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1444 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1444) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1444 : oddCount 1444 12 = 5 ∧ acceleratedOrbit 12 1444 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1444 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1444) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1444.1, data_12_1444.2] + +/-- Complete interval computation for depth 12, residue 1445. -/ +theorem bounds_12_1445 : exactInterval 12 1445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1445 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1445) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1445 : oddCount 1445 12 = 5 ∧ acceleratedOrbit 12 1445 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1445 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1445) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1445.1, data_12_1445.2] + +/-- Complete interval computation for depth 12, residue 1446. -/ +theorem bounds_12_1446 : exactInterval 12 1446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1446 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1446) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1446 : oddCount 1446 12 = 5 ∧ acceleratedOrbit 12 1446 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1446 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1446) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1446.1, data_12_1446.2] + +/-- Complete interval computation for depth 12, residue 1447. -/ +theorem bounds_12_1447 : exactInterval 12 1447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1447 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1447) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1447 : oddCount 1447 12 = 8 ∧ acceleratedOrbit 12 1447 = 2321 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1447 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1447) = 3 ^ 8 * m + 2321 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1447.1, data_12_1447.2] + +/-- Complete interval computation for depth 12, residue 1448. -/ +theorem bounds_12_1448 : exactInterval 12 1448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1448 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1448) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1448 : oddCount 1448 12 = 3 ∧ acceleratedOrbit 12 1448 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1448 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1448) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1448.1, data_12_1448.2] + +/-- Complete interval computation for depth 12, residue 1449. -/ +theorem bounds_12_1449 : exactInterval 12 1449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1449 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1449) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1449 : oddCount 1449 12 = 8 ∧ acceleratedOrbit 12 1449 = 2324 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1449 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1449) = 3 ^ 8 * m + 2324 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1449.1, data_12_1449.2] + +/-- Complete interval computation for depth 12, residue 1450. -/ +theorem bounds_12_1450 : exactInterval 12 1450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1450 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1450) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1450 : oddCount 1450 12 = 3 ∧ acceleratedOrbit 12 1450 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1450 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1450) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1450.1, data_12_1450.2] + +/-- Complete interval computation for depth 12, residue 1451. -/ +theorem bounds_12_1451 : exactInterval 12 1451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1451 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1451) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1451 : oddCount 1451 12 = 7 ∧ acceleratedOrbit 12 1451 = 776 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1451 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1451) = 3 ^ 7 * m + 776 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1451.1, data_12_1451.2] + +/-- Complete interval computation for depth 12, residue 1452. -/ +theorem bounds_12_1452 : exactInterval 12 1452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1452 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1452) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1452 : oddCount 1452 12 = 6 ∧ acceleratedOrbit 12 1452 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1452 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1452) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1452.1, data_12_1452.2] + +/-- Complete interval computation for depth 12, residue 1453. -/ +theorem bounds_12_1453 : exactInterval 12 1453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1453 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1453) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1453 : oddCount 1453 12 = 6 ∧ acceleratedOrbit 12 1453 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1453 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1453) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1453.1, data_12_1453.2] + +/-- Complete interval computation for depth 12, residue 1454. -/ +theorem bounds_12_1454 : exactInterval 12 1454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1454 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1454) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1454 : oddCount 1454 12 = 6 ∧ acceleratedOrbit 12 1454 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1454 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1454) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1454.1, data_12_1454.2] + +/-- Complete interval computation for depth 12, residue 1455. -/ +theorem bounds_12_1455 : exactInterval 12 1455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1455 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1455) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1455 : oddCount 1455 12 = 7 ∧ acceleratedOrbit 12 1455 = 778 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1455 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1455) = 3 ^ 7 * m + 778 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1455.1, data_12_1455.2] + +/-- Complete interval computation for depth 12, residue 1456. -/ +theorem bounds_12_1456 : exactInterval 12 1456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1456 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1456) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1456 : oddCount 1456 12 = 6 ∧ acceleratedOrbit 12 1456 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1456 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1456) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1456.1, data_12_1456.2] + +/-- Complete interval computation for depth 12, residue 1457. -/ +theorem bounds_12_1457 : exactInterval 12 1457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1457 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1457) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1457 : oddCount 1457 12 = 4 ∧ acceleratedOrbit 12 1457 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1457 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1457) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1457.1, data_12_1457.2] + +/-- Complete interval computation for depth 12, residue 1458. -/ +theorem bounds_12_1458 : exactInterval 12 1458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1458 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1458) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1458 : oddCount 1458 12 = 4 ∧ acceleratedOrbit 12 1458 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1458 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1458) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1458.1, data_12_1458.2] + +end Collatz.Research.StoppingAtlas.Batch0295 From c062a5a8e47d51bf7556537947d0274ea6d62975 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:33 +0530 Subject: [PATCH 0296/1001] proof: certify atlas Batch0296 (12:1459 to 12:1473) --- Collatz/Research/StoppingAtlas/Batch0296.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0296.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0296.lean b/Collatz/Research/StoppingAtlas/Batch0296.lean new file mode 100644 index 00000000..423e1972 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0296.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0296 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1459. -/ +theorem bounds_12_1459 : exactInterval 12 1459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1459 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1459) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1459 : oddCount 1459 12 = 4 ∧ acceleratedOrbit 12 1459 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1459 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1459) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1459.1, data_12_1459.2] + +/-- Complete interval computation for depth 12, residue 1460. -/ +theorem bounds_12_1460 : exactInterval 12 1460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1460 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1460) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1460 : oddCount 1460 12 = 6 ∧ acceleratedOrbit 12 1460 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1460 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1460) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1460.1, data_12_1460.2] + +/-- Complete interval computation for depth 12, residue 1461. -/ +theorem bounds_12_1461 : exactInterval 12 1461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1461 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1461) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1461 : oddCount 1461 12 = 6 ∧ acceleratedOrbit 12 1461 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1461 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1461) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1461.1, data_12_1461.2] + +/-- Complete interval computation for depth 12, residue 1462. -/ +theorem bounds_12_1462 : exactInterval 12 1462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1462 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1462) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1462 : oddCount 1462 12 = 8 ∧ acceleratedOrbit 12 1462 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1462 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1462) = 3 ^ 8 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1462.1, data_12_1462.2] + +/-- Complete interval computation for depth 12, residue 1463. -/ +theorem bounds_12_1463 : exactInterval 12 1463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1463 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1463) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1463 : oddCount 1463 12 = 8 ∧ acceleratedOrbit 12 1463 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1463 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1463) = 3 ^ 8 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1463.1, data_12_1463.2] + +/-- Complete interval computation for depth 12, residue 1464. -/ +theorem bounds_12_1464 : exactInterval 12 1464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1464 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1464) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1464 : oddCount 1464 12 = 6 ∧ acceleratedOrbit 12 1464 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1464 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1464) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1464.1, data_12_1464.2] + +/-- Complete interval computation for depth 12, residue 1465. -/ +theorem bounds_12_1465 : exactInterval 12 1465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1465 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1465) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1465 : oddCount 1465 12 = 4 ∧ acceleratedOrbit 12 1465 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1465 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1465) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1465.1, data_12_1465.2] + +/-- Complete interval computation for depth 12, residue 1466. -/ +theorem bounds_12_1466 : exactInterval 12 1466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1466 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1466) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1466 : oddCount 1466 12 = 6 ∧ acceleratedOrbit 12 1466 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1466 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1466) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1466.1, data_12_1466.2] + +/-- Complete interval computation for depth 12, residue 1467. -/ +theorem bounds_12_1467 : exactInterval 12 1467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1467 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1467) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1467 : oddCount 1467 12 = 7 ∧ acceleratedOrbit 12 1467 = 785 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1467 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1467) = 3 ^ 7 * m + 785 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1467.1, data_12_1467.2] + +/-- Complete interval computation for depth 12, residue 1468. -/ +theorem bounds_12_1468 : exactInterval 12 1468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1468 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1468) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1468 : oddCount 1468 12 = 6 ∧ acceleratedOrbit 12 1468 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1468 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1468) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1468.1, data_12_1468.2] + +/-- Complete interval computation for depth 12, residue 1469. -/ +theorem bounds_12_1469 : exactInterval 12 1469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1469 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1469) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1469 : oddCount 1469 12 = 6 ∧ acceleratedOrbit 12 1469 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1469 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1469) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1469.1, data_12_1469.2] + +/-- Complete interval computation for depth 12, residue 1470. -/ +theorem bounds_12_1470 : exactInterval 12 1470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1470 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1470) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1470 : oddCount 1470 12 = 6 ∧ acceleratedOrbit 12 1470 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1470 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1470) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1470.1, data_12_1470.2] + +/-- Complete interval computation for depth 12, residue 1471. -/ +theorem bounds_12_1471 : exactInterval 12 1471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1471 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1471) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1471 : oddCount 1471 12 = 11 ∧ acceleratedOrbit 12 1471 = 63665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1471 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1471) = 3 ^ 11 * m + 63665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1471.1, data_12_1471.2] + +/-- Complete interval computation for depth 12, residue 1472. -/ +theorem bounds_12_1472 : exactInterval 12 1472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1472 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1472) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1472 : oddCount 1472 12 = 3 ∧ acceleratedOrbit 12 1472 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1472 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1472) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1472.1, data_12_1472.2] + +/-- Complete interval computation for depth 12, residue 1473. -/ +theorem bounds_12_1473 : exactInterval 12 1473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1473 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1473) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1473 : oddCount 1473 12 = 6 ∧ acceleratedOrbit 12 1473 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1473 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1473) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1473.1, data_12_1473.2] + +end Collatz.Research.StoppingAtlas.Batch0296 From 6d0ae11500a2ffa8c74311ecaf7cec9085466bf0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:33 +0530 Subject: [PATCH 0297/1001] proof: certify atlas Batch0297 (12:1474 to 12:1488) --- Collatz/Research/StoppingAtlas/Batch0297.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0297.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0297.lean b/Collatz/Research/StoppingAtlas/Batch0297.lean new file mode 100644 index 00000000..284ba8e4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0297.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0297 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1474. -/ +theorem bounds_12_1474 : exactInterval 12 1474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1474 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1474) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1474 : oddCount 1474 12 = 8 ∧ acceleratedOrbit 12 1474 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1474 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1474) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1474.1, data_12_1474.2] + +/-- Complete interval computation for depth 12, residue 1475. -/ +theorem bounds_12_1475 : exactInterval 12 1475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1475 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1475) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1475 : oddCount 1475 12 = 8 ∧ acceleratedOrbit 12 1475 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1475 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1475) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1475.1, data_12_1475.2] + +/-- Complete interval computation for depth 12, residue 1476. -/ +theorem bounds_12_1476 : exactInterval 12 1476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1476 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1476) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1476 : oddCount 1476 12 = 3 ∧ acceleratedOrbit 12 1476 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1476 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1476) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1476.1, data_12_1476.2] + +/-- Complete interval computation for depth 12, residue 1477. -/ +theorem bounds_12_1477 : exactInterval 12 1477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1477 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1477) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1477 : oddCount 1477 12 = 3 ∧ acceleratedOrbit 12 1477 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1477 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1477) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1477.1, data_12_1477.2] + +/-- Complete interval computation for depth 12, residue 1478. -/ +theorem bounds_12_1478 : exactInterval 12 1478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1478 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1478) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1478 : oddCount 1478 12 = 3 ∧ acceleratedOrbit 12 1478 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1478 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1478) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1478.1, data_12_1478.2] + +/-- Complete interval computation for depth 12, residue 1479. -/ +theorem bounds_12_1479 : exactInterval 12 1479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1479 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1479) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1479 : oddCount 1479 12 = 7 ∧ acceleratedOrbit 12 1479 = 791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1479 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1479) = 3 ^ 7 * m + 791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1479.1, data_12_1479.2] + +/-- Complete interval computation for depth 12, residue 1480. -/ +theorem bounds_12_1480 : exactInterval 12 1480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1480 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1480) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1480 : oddCount 1480 12 = 5 ∧ acceleratedOrbit 12 1480 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1480 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1480) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1480.1, data_12_1480.2] + +/-- Complete interval computation for depth 12, residue 1481. -/ +theorem bounds_12_1481 : exactInterval 12 1481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1481 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1481) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1481 : oddCount 1481 12 = 5 ∧ acceleratedOrbit 12 1481 = 88 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1481 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1481) = 3 ^ 5 * m + 88 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1481.1, data_12_1481.2] + +/-- Complete interval computation for depth 12, residue 1482. -/ +theorem bounds_12_1482 : exactInterval 12 1482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1482 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1482) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1482 : oddCount 1482 12 = 5 ∧ acceleratedOrbit 12 1482 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1482 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1482) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1482.1, data_12_1482.2] + +/-- Complete interval computation for depth 12, residue 1483. -/ +theorem bounds_12_1483 : exactInterval 12 1483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1483 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1483) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1483 : oddCount 1483 12 = 6 ∧ acceleratedOrbit 12 1483 = 265 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1483 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1483) = 3 ^ 6 * m + 265 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1483.1, data_12_1483.2] + +/-- Complete interval computation for depth 12, residue 1484. -/ +theorem bounds_12_1484 : exactInterval 12 1484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1484 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1484) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1484 : oddCount 1484 12 = 5 ∧ acceleratedOrbit 12 1484 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1484 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1484) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1484.1, data_12_1484.2] + +/-- Complete interval computation for depth 12, residue 1485. -/ +theorem bounds_12_1485 : exactInterval 12 1485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1485 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1485) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1485 : oddCount 1485 12 = 5 ∧ acceleratedOrbit 12 1485 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1485 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1485) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1485.1, data_12_1485.2] + +/-- Complete interval computation for depth 12, residue 1486. -/ +theorem bounds_12_1486 : exactInterval 12 1486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1486 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1486) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1486 : oddCount 1486 12 = 9 ∧ acceleratedOrbit 12 1486 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1486 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1486) = 3 ^ 9 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1486.1, data_12_1486.2] + +/-- Complete interval computation for depth 12, residue 1487. -/ +theorem bounds_12_1487 : exactInterval 12 1487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1487 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1487) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1487 : oddCount 1487 12 = 9 ∧ acceleratedOrbit 12 1487 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1487 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1487) = 3 ^ 9 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1487.1, data_12_1487.2] + +/-- Complete interval computation for depth 12, residue 1488. -/ +theorem bounds_12_1488 : exactInterval 12 1488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1488 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1488) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1488 : oddCount 1488 12 = 3 ∧ acceleratedOrbit 12 1488 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1488 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1488) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1488.1, data_12_1488.2] + +end Collatz.Research.StoppingAtlas.Batch0297 From 163f9a5d248a8890b6c69c18f76ef206fbb32686 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:34 +0530 Subject: [PATCH 0298/1001] proof: certify atlas Batch0298 (12:1489 to 12:1504) --- Collatz/Research/StoppingAtlas/Batch0298.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0298.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0298.lean b/Collatz/Research/StoppingAtlas/Batch0298.lean new file mode 100644 index 00000000..f832bb98 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0298.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0298 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1489. -/ +theorem bounds_12_1489 : exactInterval 12 1489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1489 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1489) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1489 : oddCount 1489 12 = 5 ∧ acceleratedOrbit 12 1489 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1489 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1489) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1489.1, data_12_1489.2] + +/-- Complete interval computation for depth 12, residue 1490. -/ +theorem bounds_12_1490 : exactInterval 12 1490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1490 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1490) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1490 : oddCount 1490 12 = 8 ∧ acceleratedOrbit 12 1490 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1490 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1490) = 3 ^ 8 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1490.1, data_12_1490.2] + +/-- Complete interval computation for depth 12, residue 1491. -/ +theorem bounds_12_1491 : exactInterval 12 1491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1491 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1491) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1491 : oddCount 1491 12 = 8 ∧ acceleratedOrbit 12 1491 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1491 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1491) = 3 ^ 8 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1491.1, data_12_1491.2] + +/-- Complete interval computation for depth 12, residue 1492. -/ +theorem bounds_12_1492 : exactInterval 12 1492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1492 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1492) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1492 : oddCount 1492 12 = 3 ∧ acceleratedOrbit 12 1492 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1492 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1492) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1492.1, data_12_1492.2] + +/-- Complete interval computation for depth 12, residue 1493. -/ +theorem bounds_12_1493 : exactInterval 12 1493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1493 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1493) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1493 : oddCount 1493 12 = 3 ∧ acceleratedOrbit 12 1493 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1493 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1493) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1493.1, data_12_1493.2] + +/-- Complete interval computation for depth 12, residue 1494. -/ +theorem bounds_12_1494 : exactInterval 12 1494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1494 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1494) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1494 : oddCount 1494 12 = 7 ∧ acceleratedOrbit 12 1494 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1494 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1494) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1494.1, data_12_1494.2] + +/-- Complete interval computation for depth 12, residue 1495. -/ +theorem bounds_12_1495 : exactInterval 12 1495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1495 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1495) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1495 : oddCount 1495 12 = 7 ∧ acceleratedOrbit 12 1495 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1495 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1495) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1495.1, data_12_1495.2] + +/-- Complete interval computation for depth 12, residue 1496. -/ +theorem bounds_12_1496 : exactInterval 12 1496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1496 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1496) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1496 : oddCount 1496 12 = 6 ∧ acceleratedOrbit 12 1496 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1496 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1496) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1496.1, data_12_1496.2] + +/-- Complete interval computation for depth 12, residue 1497. -/ +theorem bounds_12_1497 : exactInterval 12 1497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1497 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1497) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1497 : oddCount 1497 12 = 6 ∧ acceleratedOrbit 12 1497 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1497 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1497) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1497.1, data_12_1497.2] + +/-- Complete interval computation for depth 12, residue 1498. -/ +theorem bounds_12_1498 : exactInterval 12 1498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1498 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1498) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1498 : oddCount 1498 12 = 6 ∧ acceleratedOrbit 12 1498 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1498 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1498) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1498.1, data_12_1498.2] + +/-- Complete interval computation for depth 12, residue 1499. -/ +theorem bounds_12_1499 : exactInterval 12 1499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1499 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1499) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1499 : oddCount 1499 12 = 5 ∧ acceleratedOrbit 12 1499 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1499 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1499) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1499.1, data_12_1499.2] + +/-- Complete interval computation for depth 12, residue 1500. -/ +theorem bounds_12_1500 : exactInterval 12 1500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1500 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1500) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1500 : oddCount 1500 12 = 6 ∧ acceleratedOrbit 12 1500 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1500 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1500) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1500.1, data_12_1500.2] + +/-- Complete interval computation for depth 12, residue 1501. -/ +theorem bounds_12_1501 : exactInterval 12 1501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1501 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1501) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1501 : oddCount 1501 12 = 6 ∧ acceleratedOrbit 12 1501 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1501 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1501) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1501.1, data_12_1501.2] + +/-- Complete interval computation for depth 12, residue 1502. -/ +theorem bounds_12_1502 : exactInterval 12 1502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1502 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1502) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1502 : oddCount 1502 12 = 9 ∧ acceleratedOrbit 12 1502 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1502 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1502) = 3 ^ 9 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1502.1, data_12_1502.2] + +/-- Complete interval computation for depth 12, residue 1503. -/ +theorem bounds_12_1503 : exactInterval 12 1503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1503 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1503) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1503 : oddCount 1503 12 = 9 ∧ acceleratedOrbit 12 1503 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1503 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1503) = 3 ^ 9 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1503.1, data_12_1503.2] + +/-- Complete interval computation for depth 12, residue 1504. -/ +theorem bounds_12_1504 : exactInterval 12 1504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1504 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1504) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1504 : oddCount 1504 12 = 5 ∧ acceleratedOrbit 12 1504 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1504 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1504) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1504.1, data_12_1504.2] + +end Collatz.Research.StoppingAtlas.Batch0298 From 7d2eb3cdf3aa7db9aa6b2f9aee4cebcd2216bbda Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:34 +0530 Subject: [PATCH 0299/1001] proof: certify atlas Batch0299 (12:1505 to 12:1519) --- Collatz/Research/StoppingAtlas/Batch0299.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0299.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0299.lean b/Collatz/Research/StoppingAtlas/Batch0299.lean new file mode 100644 index 00000000..92122713 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0299.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0299 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1505. -/ +theorem bounds_12_1505 : exactInterval 12 1505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1505 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1505) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1505 : oddCount 1505 12 = 7 ∧ acceleratedOrbit 12 1505 = 805 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1505 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1505) = 3 ^ 7 * m + 805 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1505.1, data_12_1505.2] + +/-- Complete interval computation for depth 12, residue 1506. -/ +theorem bounds_12_1506 : exactInterval 12 1506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1506 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1506) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1506 : oddCount 1506 12 = 3 ∧ acceleratedOrbit 12 1506 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1506 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1506) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1506.1, data_12_1506.2] + +/-- Complete interval computation for depth 12, residue 1507. -/ +theorem bounds_12_1507 : exactInterval 12 1507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1507 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1507) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1507 : oddCount 1507 12 = 3 ∧ acceleratedOrbit 12 1507 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1507 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1507) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1507.1, data_12_1507.2] + +/-- Complete interval computation for depth 12, residue 1508. -/ +theorem bounds_12_1508 : exactInterval 12 1508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1508 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1508) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1508 : oddCount 1508 12 = 8 ∧ acceleratedOrbit 12 1508 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1508 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1508) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1508.1, data_12_1508.2] + +/-- Complete interval computation for depth 12, residue 1509. -/ +theorem bounds_12_1509 : exactInterval 12 1509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1509 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1509) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1509 : oddCount 1509 12 = 8 ∧ acceleratedOrbit 12 1509 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1509 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1509) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1509.1, data_12_1509.2] + +/-- Complete interval computation for depth 12, residue 1510. -/ +theorem bounds_12_1510 : exactInterval 12 1510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1510 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1510) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1510 : oddCount 1510 12 = 8 ∧ acceleratedOrbit 12 1510 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1510 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1510) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1510.1, data_12_1510.2] + +/-- Complete interval computation for depth 12, residue 1511. -/ +theorem bounds_12_1511 : exactInterval 12 1511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1511 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1511) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1511 : oddCount 1511 12 = 8 ∧ acceleratedOrbit 12 1511 = 2423 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1511 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1511) = 3 ^ 8 * m + 2423 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1511.1, data_12_1511.2] + +/-- Complete interval computation for depth 12, residue 1512. -/ +theorem bounds_12_1512 : exactInterval 12 1512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1512 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1512) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1512 : oddCount 1512 12 = 5 ∧ acceleratedOrbit 12 1512 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1512 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1512) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1512.1, data_12_1512.2] + +/-- Complete interval computation for depth 12, residue 1513. -/ +theorem bounds_12_1513 : exactInterval 12 1513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1513 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1513) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1513 : oddCount 1513 12 = 9 ∧ acceleratedOrbit 12 1513 = 7280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1513 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1513) = 3 ^ 9 * m + 7280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1513.1, data_12_1513.2] + +/-- Complete interval computation for depth 12, residue 1514. -/ +theorem bounds_12_1514 : exactInterval 12 1514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1514 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1514) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1514 : oddCount 1514 12 = 5 ∧ acceleratedOrbit 12 1514 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1514 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1514) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1514.1, data_12_1514.2] + +/-- Complete interval computation for depth 12, residue 1515. -/ +theorem bounds_12_1515 : exactInterval 12 1515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1515 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1515) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1515 : oddCount 1515 12 = 10 ∧ acceleratedOrbit 12 1515 = 21869 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1515 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1515) = 3 ^ 10 * m + 21869 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1515.1, data_12_1515.2] + +/-- Complete interval computation for depth 12, residue 1516. -/ +theorem bounds_12_1516 : exactInterval 12 1516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1516 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1516) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1516 : oddCount 1516 12 = 6 ∧ acceleratedOrbit 12 1516 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1516 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1516) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1516.1, data_12_1516.2] + +/-- Complete interval computation for depth 12, residue 1517. -/ +theorem bounds_12_1517 : exactInterval 12 1517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1517 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1517) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1517 : oddCount 1517 12 = 6 ∧ acceleratedOrbit 12 1517 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1517 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1517) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1517.1, data_12_1517.2] + +/-- Complete interval computation for depth 12, residue 1518. -/ +theorem bounds_12_1518 : exactInterval 12 1518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1518 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1518) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1518 : oddCount 1518 12 = 6 ∧ acceleratedOrbit 12 1518 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1518 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1518) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1518.1, data_12_1518.2] + +/-- Complete interval computation for depth 12, residue 1519. -/ +theorem bounds_12_1519 : exactInterval 12 1519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1519 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1519) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1519 : oddCount 1519 12 = 8 ∧ acceleratedOrbit 12 1519 = 2435 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1519 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1519) = 3 ^ 8 * m + 2435 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1519.1, data_12_1519.2] + +end Collatz.Research.StoppingAtlas.Batch0299 From f41c32664d2581b290f8f6d80bbf01b91411ee77 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:35 +0530 Subject: [PATCH 0300/1001] proof: certify atlas Batch0300 (12:1520 to 12:1535) --- Collatz/Research/StoppingAtlas/Batch0300.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0300.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0300.lean b/Collatz/Research/StoppingAtlas/Batch0300.lean new file mode 100644 index 00000000..dadd010c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0300.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0300 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1520. -/ +theorem bounds_12_1520 : exactInterval 12 1520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1520 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1520) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1520 : oddCount 1520 12 = 5 ∧ acceleratedOrbit 12 1520 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1520 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1520) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1520.1, data_12_1520.2] + +/-- Complete interval computation for depth 12, residue 1521. -/ +theorem bounds_12_1521 : exactInterval 12 1521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1521 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1521) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1521 : oddCount 1521 12 = 5 ∧ acceleratedOrbit 12 1521 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1521 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1521) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1521.1, data_12_1521.2] + +/-- Complete interval computation for depth 12, residue 1522. -/ +theorem bounds_12_1522 : exactInterval 12 1522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1522 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1522) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1522 : oddCount 1522 12 = 6 ∧ acceleratedOrbit 12 1522 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1522 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1522) = 3 ^ 6 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1522.1, data_12_1522.2] + +/-- Complete interval computation for depth 12, residue 1523. -/ +theorem bounds_12_1523 : exactInterval 12 1523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1523 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1523) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1523 : oddCount 1523 12 = 6 ∧ acceleratedOrbit 12 1523 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1523 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1523) = 3 ^ 6 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1523.1, data_12_1523.2] + +/-- Complete interval computation for depth 12, residue 1524. -/ +theorem bounds_12_1524 : exactInterval 12 1524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1524 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1524) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1524 : oddCount 1524 12 = 5 ∧ acceleratedOrbit 12 1524 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1524 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1524) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1524.1, data_12_1524.2] + +/-- Complete interval computation for depth 12, residue 1525. -/ +theorem bounds_12_1525 : exactInterval 12 1525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1525 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1525) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1525 : oddCount 1525 12 = 5 ∧ acceleratedOrbit 12 1525 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1525 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1525) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1525.1, data_12_1525.2] + +/-- Complete interval computation for depth 12, residue 1526. -/ +theorem bounds_12_1526 : exactInterval 12 1526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1526 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1526) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1526 : oddCount 1526 12 = 8 ∧ acceleratedOrbit 12 1526 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1526 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1526) = 3 ^ 8 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1526.1, data_12_1526.2] + +/-- Complete interval computation for depth 12, residue 1527. -/ +theorem bounds_12_1527 : exactInterval 12 1527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1527 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1527) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1527 : oddCount 1527 12 = 8 ∧ acceleratedOrbit 12 1527 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1527 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1527) = 3 ^ 8 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1527.1, data_12_1527.2] + +/-- Complete interval computation for depth 12, residue 1528. -/ +theorem bounds_12_1528 : exactInterval 12 1528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1528 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1528) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1528 : oddCount 1528 12 = 7 ∧ acceleratedOrbit 12 1528 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1528 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1528) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1528.1, data_12_1528.2] + +/-- Complete interval computation for depth 12, residue 1529. -/ +theorem bounds_12_1529 : exactInterval 12 1529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1529 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1529) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1529 : oddCount 1529 12 = 7 ∧ acceleratedOrbit 12 1529 = 818 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1529 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1529) = 3 ^ 7 * m + 818 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1529.1, data_12_1529.2] + +/-- Complete interval computation for depth 12, residue 1530. -/ +theorem bounds_12_1530 : exactInterval 12 1530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1530 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1530) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1530 : oddCount 1530 12 = 7 ∧ acceleratedOrbit 12 1530 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1530 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1530) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1530.1, data_12_1530.2] + +/-- Complete interval computation for depth 12, residue 1531. -/ +theorem bounds_12_1531 : exactInterval 12 1531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1531 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1531) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1531 : oddCount 1531 12 = 8 ∧ acceleratedOrbit 12 1531 = 2456 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1531 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1531) = 3 ^ 8 * m + 2456 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1531.1, data_12_1531.2] + +/-- Complete interval computation for depth 12, residue 1532. -/ +theorem bounds_12_1532 : exactInterval 12 1532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1532 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1532) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1532 : oddCount 1532 12 = 7 ∧ acceleratedOrbit 12 1532 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1532 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1532) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1532.1, data_12_1532.2] + +/-- Complete interval computation for depth 12, residue 1533. -/ +theorem bounds_12_1533 : exactInterval 12 1533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1533 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1533) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1533 : oddCount 1533 12 = 7 ∧ acceleratedOrbit 12 1533 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1533 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1533) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1533.1, data_12_1533.2] + +/-- Complete interval computation for depth 12, residue 1534. -/ +theorem bounds_12_1534 : exactInterval 12 1534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1534 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1534) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1534 : oddCount 1534 12 = 9 ∧ acceleratedOrbit 12 1534 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1534 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1534) = 3 ^ 9 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1534.1, data_12_1534.2] + +/-- Complete interval computation for depth 12, residue 1535. -/ +theorem bounds_12_1535 : exactInterval 12 1535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1535 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1535) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1535 : oddCount 1535 12 = 9 ∧ acceleratedOrbit 12 1535 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1535 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1535) = 3 ^ 9 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1535.1, data_12_1535.2] + +end Collatz.Research.StoppingAtlas.Batch0300 From ededb7bf927910e575746ca7e203b7ab564983e8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:35 +0530 Subject: [PATCH 0301/1001] proof: certify atlas Batch0301 (12:1536 to 12:1550) --- Collatz/Research/StoppingAtlas/Batch0301.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0301.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0301.lean b/Collatz/Research/StoppingAtlas/Batch0301.lean new file mode 100644 index 00000000..30f44857 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0301.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0301 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1536. -/ +theorem bounds_12_1536 : exactInterval 12 1536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1536 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1536) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1536 : oddCount 1536 12 = 2 ∧ acceleratedOrbit 12 1536 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1536 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1536) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1536.1, data_12_1536.2] + +/-- Complete interval computation for depth 12, residue 1537. -/ +theorem bounds_12_1537 : exactInterval 12 1537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1537 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1537) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1537 : oddCount 1537 12 = 7 ∧ acceleratedOrbit 12 1537 = 823 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1537 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1537) = 3 ^ 7 * m + 823 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1537.1, data_12_1537.2] + +/-- Complete interval computation for depth 12, residue 1538. -/ +theorem bounds_12_1538 : exactInterval 12 1538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1538 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1538) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1538 : oddCount 1538 12 = 5 ∧ acceleratedOrbit 12 1538 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1538 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1538) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1538.1, data_12_1538.2] + +/-- Complete interval computation for depth 12, residue 1539. -/ +theorem bounds_12_1539 : exactInterval 12 1539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1539 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1539) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1539 : oddCount 1539 12 = 5 ∧ acceleratedOrbit 12 1539 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1539 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1539) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1539.1, data_12_1539.2] + +/-- Complete interval computation for depth 12, residue 1540. -/ +theorem bounds_12_1540 : exactInterval 12 1540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1540 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1540) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1540 : oddCount 1540 12 = 5 ∧ acceleratedOrbit 12 1540 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1540 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1540) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1540.1, data_12_1540.2] + +/-- Complete interval computation for depth 12, residue 1541. -/ +theorem bounds_12_1541 : exactInterval 12 1541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1541 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1541) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1541 : oddCount 1541 12 = 5 ∧ acceleratedOrbit 12 1541 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1541 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1541) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1541.1, data_12_1541.2] + +/-- Complete interval computation for depth 12, residue 1542. -/ +theorem bounds_12_1542 : exactInterval 12 1542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1542 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1542) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1542 : oddCount 1542 12 = 5 ∧ acceleratedOrbit 12 1542 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1542 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1542) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1542.1, data_12_1542.2] + +/-- Complete interval computation for depth 12, residue 1543. -/ +theorem bounds_12_1543 : exactInterval 12 1543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1543 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1543) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1543 : oddCount 1543 12 = 6 ∧ acceleratedOrbit 12 1543 = 275 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1543 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1543) = 3 ^ 6 * m + 275 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1543.1, data_12_1543.2] + +/-- Complete interval computation for depth 12, residue 1544. -/ +theorem bounds_12_1544 : exactInterval 12 1544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1544 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1544) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1544 : oddCount 1544 12 = 4 ∧ acceleratedOrbit 12 1544 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1544 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1544) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1544.1, data_12_1544.2] + +/-- Complete interval computation for depth 12, residue 1545. -/ +theorem bounds_12_1545 : exactInterval 12 1545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1545 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1545) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1545 : oddCount 1545 12 = 7 ∧ acceleratedOrbit 12 1545 = 827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1545 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1545) = 3 ^ 7 * m + 827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1545.1, data_12_1545.2] + +/-- Complete interval computation for depth 12, residue 1546. -/ +theorem bounds_12_1546 : exactInterval 12 1546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1546 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1546) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1546 : oddCount 1546 12 = 4 ∧ acceleratedOrbit 12 1546 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1546 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1546) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1546.1, data_12_1546.2] + +/-- Complete interval computation for depth 12, residue 1547. -/ +theorem bounds_12_1547 : exactInterval 12 1547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1547 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1547) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1547 : oddCount 1547 12 = 5 ∧ acceleratedOrbit 12 1547 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1547 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1547) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1547.1, data_12_1547.2] + +/-- Complete interval computation for depth 12, residue 1548. -/ +theorem bounds_12_1548 : exactInterval 12 1548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1548 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1548) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1548 : oddCount 1548 12 = 4 ∧ acceleratedOrbit 12 1548 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1548 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1548) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1548.1, data_12_1548.2] + +/-- Complete interval computation for depth 12, residue 1549. -/ +theorem bounds_12_1549 : exactInterval 12 1549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1549 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1549) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1549 : oddCount 1549 12 = 4 ∧ acceleratedOrbit 12 1549 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1549 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1549) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1549.1, data_12_1549.2] + +/-- Complete interval computation for depth 12, residue 1550. -/ +theorem bounds_12_1550 : exactInterval 12 1550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1550 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1550) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1550 : oddCount 1550 12 = 7 ∧ acceleratedOrbit 12 1550 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1550 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1550) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1550.1, data_12_1550.2] + +end Collatz.Research.StoppingAtlas.Batch0301 From ec980bf915a6873acd6a8b3ed837d58e8a982dc5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:35 +0530 Subject: [PATCH 0302/1001] proof: certify atlas Batch0302 (12:1551 to 12:1565) --- Collatz/Research/StoppingAtlas/Batch0302.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0302.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0302.lean b/Collatz/Research/StoppingAtlas/Batch0302.lean new file mode 100644 index 00000000..c0fdb4c4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0302.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0302 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1551. -/ +theorem bounds_12_1551 : exactInterval 12 1551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1551 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1551) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1551 : oddCount 1551 12 = 7 ∧ acceleratedOrbit 12 1551 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1551 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1551) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1551.1, data_12_1551.2] + +/-- Complete interval computation for depth 12, residue 1552. -/ +theorem bounds_12_1552 : exactInterval 12 1552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1552 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1552) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1552 : oddCount 1552 12 = 5 ∧ acceleratedOrbit 12 1552 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1552 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1552) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1552.1, data_12_1552.2] + +/-- Complete interval computation for depth 12, residue 1553. -/ +theorem bounds_12_1553 : exactInterval 12 1553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1553 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1553) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1553 : oddCount 1553 12 = 4 ∧ acceleratedOrbit 12 1553 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1553 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1553) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1553.1, data_12_1553.2] + +/-- Complete interval computation for depth 12, residue 1554. -/ +theorem bounds_12_1554 : exactInterval 12 1554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1554 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1554) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1554 : oddCount 1554 12 = 7 ∧ acceleratedOrbit 12 1554 = 832 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1554 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1554) = 3 ^ 7 * m + 832 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1554.1, data_12_1554.2] + +/-- Complete interval computation for depth 12, residue 1555. -/ +theorem bounds_12_1555 : exactInterval 12 1555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1555 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1555) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1555 : oddCount 1555 12 = 7 ∧ acceleratedOrbit 12 1555 = 832 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1555 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1555) = 3 ^ 7 * m + 832 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1555.1, data_12_1555.2] + +/-- Complete interval computation for depth 12, residue 1556. -/ +theorem bounds_12_1556 : exactInterval 12 1556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1556 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1556) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1556 : oddCount 1556 12 = 5 ∧ acceleratedOrbit 12 1556 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1556 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1556) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1556.1, data_12_1556.2] + +/-- Complete interval computation for depth 12, residue 1557. -/ +theorem bounds_12_1557 : exactInterval 12 1557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1557 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1557) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1557 : oddCount 1557 12 = 5 ∧ acceleratedOrbit 12 1557 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1557 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1557) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1557.1, data_12_1557.2] + +/-- Complete interval computation for depth 12, residue 1558. -/ +theorem bounds_12_1558 : exactInterval 12 1558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1558 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1558) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1558 : oddCount 1558 12 = 7 ∧ acceleratedOrbit 12 1558 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1558 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1558) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1558.1, data_12_1558.2] + +/-- Complete interval computation for depth 12, residue 1559. -/ +theorem bounds_12_1559 : exactInterval 12 1559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1559 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1559) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1559 : oddCount 1559 12 = 7 ∧ acceleratedOrbit 12 1559 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1559 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1559) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1559.1, data_12_1559.2] + +/-- Complete interval computation for depth 12, residue 1560. -/ +theorem bounds_12_1560 : exactInterval 12 1560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1560 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1560) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1560 : oddCount 1560 12 = 5 ∧ acceleratedOrbit 12 1560 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1560 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1560) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1560.1, data_12_1560.2] + +/-- Complete interval computation for depth 12, residue 1561. -/ +theorem bounds_12_1561 : exactInterval 12 1561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1561 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1561) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1561 : oddCount 1561 12 = 7 ∧ acceleratedOrbit 12 1561 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1561 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1561) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1561.1, data_12_1561.2] + +/-- Complete interval computation for depth 12, residue 1562. -/ +theorem bounds_12_1562 : exactInterval 12 1562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1562 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1562) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1562 : oddCount 1562 12 = 5 ∧ acceleratedOrbit 12 1562 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1562 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1562) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1562.1, data_12_1562.2] + +/-- Complete interval computation for depth 12, residue 1563. -/ +theorem bounds_12_1563 : exactInterval 12 1563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1563 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1563) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1563 : oddCount 1563 12 = 8 ∧ acceleratedOrbit 12 1563 = 2506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1563 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1563) = 3 ^ 8 * m + 2506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1563.1, data_12_1563.2] + +/-- Complete interval computation for depth 12, residue 1564. -/ +theorem bounds_12_1564 : exactInterval 12 1564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1564 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1564) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1564 : oddCount 1564 12 = 4 ∧ acceleratedOrbit 12 1564 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1564 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1564) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1564.1, data_12_1564.2] + +/-- Complete interval computation for depth 12, residue 1565. -/ +theorem bounds_12_1565 : exactInterval 12 1565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1565 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1565) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1565 : oddCount 1565 12 = 4 ∧ acceleratedOrbit 12 1565 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1565 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1565) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1565.1, data_12_1565.2] + +end Collatz.Research.StoppingAtlas.Batch0302 From be1fa65c88192823a8d51d6ce69fa877190c7ce7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:35 +0530 Subject: [PATCH 0303/1001] proof: certify atlas Batch0303 (12:1566 to 12:1581) --- Collatz/Research/StoppingAtlas/Batch0303.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0303.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0303.lean b/Collatz/Research/StoppingAtlas/Batch0303.lean new file mode 100644 index 00000000..7e5ab7fe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0303.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0303 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1566. -/ +theorem bounds_12_1566 : exactInterval 12 1566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1566 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1566) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1566 : oddCount 1566 12 = 4 ∧ acceleratedOrbit 12 1566 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1566 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1566) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1566.1, data_12_1566.2] + +/-- Complete interval computation for depth 12, residue 1567. -/ +theorem bounds_12_1567 : exactInterval 12 1567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1567 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1567) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1567 : oddCount 1567 12 = 8 ∧ acceleratedOrbit 12 1567 = 2512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1567 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1567) = 3 ^ 8 * m + 2512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1567.1, data_12_1567.2] + +/-- Complete interval computation for depth 12, residue 1568. -/ +theorem bounds_12_1568 : exactInterval 12 1568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1568 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1568) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1568 : oddCount 1568 12 = 3 ∧ acceleratedOrbit 12 1568 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1568 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1568) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1568.1, data_12_1568.2] + +/-- Complete interval computation for depth 12, residue 1569. -/ +theorem bounds_12_1569 : exactInterval 12 1569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1569 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1569) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1569 : oddCount 1569 12 = 6 ∧ acceleratedOrbit 12 1569 = 280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1569 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1569) = 3 ^ 6 * m + 280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1569.1, data_12_1569.2] + +/-- Complete interval computation for depth 12, residue 1570. -/ +theorem bounds_12_1570 : exactInterval 12 1570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1570 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1570) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1570 : oddCount 1570 12 = 5 ∧ acceleratedOrbit 12 1570 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1570 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1570) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1570.1, data_12_1570.2] + +/-- Complete interval computation for depth 12, residue 1571. -/ +theorem bounds_12_1571 : exactInterval 12 1571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1571 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1571) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1571 : oddCount 1571 12 = 5 ∧ acceleratedOrbit 12 1571 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1571 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1571) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1571.1, data_12_1571.2] + +/-- Complete interval computation for depth 12, residue 1572. -/ +theorem bounds_12_1572 : exactInterval 12 1572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1572 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1572) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1572 : oddCount 1572 12 = 6 ∧ acceleratedOrbit 12 1572 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1572 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1572) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1572.1, data_12_1572.2] + +/-- Complete interval computation for depth 12, residue 1573. -/ +theorem bounds_12_1573 : exactInterval 12 1573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1573 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1573) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1573 : oddCount 1573 12 = 6 ∧ acceleratedOrbit 12 1573 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1573 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1573) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1573.1, data_12_1573.2] + +/-- Complete interval computation for depth 12, residue 1574. -/ +theorem bounds_12_1574 : exactInterval 12 1574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1574 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1574) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1574 : oddCount 1574 12 = 6 ∧ acceleratedOrbit 12 1574 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1574 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1574) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1574.1, data_12_1574.2] + +/-- Complete interval computation for depth 12, residue 1575. -/ +theorem bounds_12_1575 : exactInterval 12 1575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1575 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1575) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1575 : oddCount 1575 12 = 6 ∧ acceleratedOrbit 12 1575 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1575 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1575) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1575.1, data_12_1575.2] + +/-- Complete interval computation for depth 12, residue 1576. -/ +theorem bounds_12_1576 : exactInterval 12 1576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1576 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1576) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1576 : oddCount 1576 12 = 3 ∧ acceleratedOrbit 12 1576 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1576 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1576) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1576.1, data_12_1576.2] + +/-- Complete interval computation for depth 12, residue 1577. -/ +theorem bounds_12_1577 : exactInterval 12 1577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1577 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1577) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1577 : oddCount 1577 12 = 10 ∧ acceleratedOrbit 12 1577 = 22760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1577 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1577) = 3 ^ 10 * m + 22760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1577.1, data_12_1577.2] + +/-- Complete interval computation for depth 12, residue 1578. -/ +theorem bounds_12_1578 : exactInterval 12 1578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1578 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1578) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1578 : oddCount 1578 12 = 3 ∧ acceleratedOrbit 12 1578 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1578 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1578) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1578.1, data_12_1578.2] + +/-- Complete interval computation for depth 12, residue 1579. -/ +theorem bounds_12_1579 : exactInterval 12 1579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1579 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1579) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1579 : oddCount 1579 12 = 5 ∧ acceleratedOrbit 12 1579 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1579 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1579) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1579.1, data_12_1579.2] + +/-- Complete interval computation for depth 12, residue 1580. -/ +theorem bounds_12_1580 : exactInterval 12 1580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1580 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1580) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1580 : oddCount 1580 12 = 6 ∧ acceleratedOrbit 12 1580 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1580 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1580) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1580.1, data_12_1580.2] + +/-- Complete interval computation for depth 12, residue 1581. -/ +theorem bounds_12_1581 : exactInterval 12 1581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1581 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1581) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1581 : oddCount 1581 12 = 6 ∧ acceleratedOrbit 12 1581 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1581 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1581) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1581.1, data_12_1581.2] + +end Collatz.Research.StoppingAtlas.Batch0303 From 39aca752b764259fe9c4c492f95722a9ab806bbe Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:36 +0530 Subject: [PATCH 0304/1001] proof: certify atlas Batch0304 (12:1582 to 12:1596) --- Collatz/Research/StoppingAtlas/Batch0304.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0304.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0304.lean b/Collatz/Research/StoppingAtlas/Batch0304.lean new file mode 100644 index 00000000..b1fa8f1e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0304.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0304 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1582. -/ +theorem bounds_12_1582 : exactInterval 12 1582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1582 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1582) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1582 : oddCount 1582 12 = 6 ∧ acceleratedOrbit 12 1582 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1582 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1582) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1582.1, data_12_1582.2] + +/-- Complete interval computation for depth 12, residue 1583. -/ +theorem bounds_12_1583 : exactInterval 12 1583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1583 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1583) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1583 : oddCount 1583 12 = 10 ∧ acceleratedOrbit 12 1583 = 22841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1583 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1583) = 3 ^ 10 * m + 22841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1583.1, data_12_1583.2] + +/-- Complete interval computation for depth 12, residue 1584. -/ +theorem bounds_12_1584 : exactInterval 12 1584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1584 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1584) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1584 : oddCount 1584 12 = 3 ∧ acceleratedOrbit 12 1584 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1584 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1584) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1584.1, data_12_1584.2] + +/-- Complete interval computation for depth 12, residue 1585. -/ +theorem bounds_12_1585 : exactInterval 12 1585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1585 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1585) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1585 : oddCount 1585 12 = 7 ∧ acceleratedOrbit 12 1585 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1585 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1585) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1585.1, data_12_1585.2] + +/-- Complete interval computation for depth 12, residue 1586. -/ +theorem bounds_12_1586 : exactInterval 12 1586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1586 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1586) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1586 : oddCount 1586 12 = 7 ∧ acceleratedOrbit 12 1586 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1586 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1586) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1586.1, data_12_1586.2] + +/-- Complete interval computation for depth 12, residue 1587. -/ +theorem bounds_12_1587 : exactInterval 12 1587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1587 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1587) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1587 : oddCount 1587 12 = 7 ∧ acceleratedOrbit 12 1587 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1587 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1587) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1587.1, data_12_1587.2] + +/-- Complete interval computation for depth 12, residue 1588. -/ +theorem bounds_12_1588 : exactInterval 12 1588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1588 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1588) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1588 : oddCount 1588 12 = 3 ∧ acceleratedOrbit 12 1588 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1588 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1588) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1588.1, data_12_1588.2] + +/-- Complete interval computation for depth 12, residue 1589. -/ +theorem bounds_12_1589 : exactInterval 12 1589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1589 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1589) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1589 : oddCount 1589 12 = 3 ∧ acceleratedOrbit 12 1589 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1589 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1589) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1589.1, data_12_1589.2] + +/-- Complete interval computation for depth 12, residue 1590. -/ +theorem bounds_12_1590 : exactInterval 12 1590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1590 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1590) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1590 : oddCount 1590 12 = 9 ∧ acceleratedOrbit 12 1590 = 7654 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1590 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1590) = 3 ^ 9 * m + 7654 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1590.1, data_12_1590.2] + +/-- Complete interval computation for depth 12, residue 1591. -/ +theorem bounds_12_1591 : exactInterval 12 1591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1591 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1591) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1591 : oddCount 1591 12 = 9 ∧ acceleratedOrbit 12 1591 = 7654 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1591 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1591) = 3 ^ 9 * m + 7654 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1591.1, data_12_1591.2] + +/-- Complete interval computation for depth 12, residue 1592. -/ +theorem bounds_12_1592 : exactInterval 12 1592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1592 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1592) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1592 : oddCount 1592 12 = 5 ∧ acceleratedOrbit 12 1592 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1592 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1592) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1592.1, data_12_1592.2] + +/-- Complete interval computation for depth 12, residue 1593. -/ +theorem bounds_12_1593 : exactInterval 12 1593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1593 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1593) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1593 : oddCount 1593 12 = 6 ∧ acceleratedOrbit 12 1593 = 284 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1593 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1593) = 3 ^ 6 * m + 284 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1593.1, data_12_1593.2] + +/-- Complete interval computation for depth 12, residue 1594. -/ +theorem bounds_12_1594 : exactInterval 12 1594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1594 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1594) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1594 : oddCount 1594 12 = 5 ∧ acceleratedOrbit 12 1594 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1594 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1594) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1594.1, data_12_1594.2] + +/-- Complete interval computation for depth 12, residue 1595. -/ +theorem bounds_12_1595 : exactInterval 12 1595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1595 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1595) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1595 : oddCount 1595 12 = 7 ∧ acceleratedOrbit 12 1595 = 854 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1595 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1595) = 3 ^ 7 * m + 854 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1595.1, data_12_1595.2] + +/-- Complete interval computation for depth 12, residue 1596. -/ +theorem bounds_12_1596 : exactInterval 12 1596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1596 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1596) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1596 : oddCount 1596 12 = 5 ∧ acceleratedOrbit 12 1596 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1596 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1596) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1596.1, data_12_1596.2] + +end Collatz.Research.StoppingAtlas.Batch0304 From 518fde94a3283dd71d509032f73085b2fbbcced4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:36 +0530 Subject: [PATCH 0305/1001] proof: certify atlas Batch0305 (12:1597 to 12:1611) --- Collatz/Research/StoppingAtlas/Batch0305.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0305.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0305.lean b/Collatz/Research/StoppingAtlas/Batch0305.lean new file mode 100644 index 00000000..b2724a30 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0305.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0305 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1597. -/ +theorem bounds_12_1597 : exactInterval 12 1597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1597 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1597) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1597 : oddCount 1597 12 = 5 ∧ acceleratedOrbit 12 1597 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1597 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1597) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1597.1, data_12_1597.2] + +/-- Complete interval computation for depth 12, residue 1598. -/ +theorem bounds_12_1598 : exactInterval 12 1598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1598 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1598) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1598 : oddCount 1598 12 = 8 ∧ acceleratedOrbit 12 1598 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1598 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1598) = 3 ^ 8 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1598.1, data_12_1598.2] + +/-- Complete interval computation for depth 12, residue 1599. -/ +theorem bounds_12_1599 : exactInterval 12 1599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1599 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1599) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1599 : oddCount 1599 12 = 8 ∧ acceleratedOrbit 12 1599 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1599 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1599) = 3 ^ 8 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1599.1, data_12_1599.2] + +/-- Complete interval computation for depth 12, residue 1600. -/ +theorem bounds_12_1600 : exactInterval 12 1600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1600 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1600) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1600 : oddCount 1600 12 = 3 ∧ acceleratedOrbit 12 1600 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1600 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1600) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1600.1, data_12_1600.2] + +/-- Complete interval computation for depth 12, residue 1601. -/ +theorem bounds_12_1601 : exactInterval 12 1601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1601 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1601) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1601 : oddCount 1601 12 = 6 ∧ acceleratedOrbit 12 1601 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1601 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1601) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1601.1, data_12_1601.2] + +/-- Complete interval computation for depth 12, residue 1602. -/ +theorem bounds_12_1602 : exactInterval 12 1602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1602 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1602) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1602 : oddCount 1602 12 = 6 ∧ acceleratedOrbit 12 1602 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1602 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1602) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1602.1, data_12_1602.2] + +/-- Complete interval computation for depth 12, residue 1603. -/ +theorem bounds_12_1603 : exactInterval 12 1603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1603 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1603) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1603 : oddCount 1603 12 = 6 ∧ acceleratedOrbit 12 1603 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1603 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1603) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1603.1, data_12_1603.2] + +/-- Complete interval computation for depth 12, residue 1604. -/ +theorem bounds_12_1604 : exactInterval 12 1604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1604 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1604) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1604 : oddCount 1604 12 = 4 ∧ acceleratedOrbit 12 1604 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1604 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1604) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1604.1, data_12_1604.2] + +/-- Complete interval computation for depth 12, residue 1605. -/ +theorem bounds_12_1605 : exactInterval 12 1605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1605 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1605) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1605 : oddCount 1605 12 = 4 ∧ acceleratedOrbit 12 1605 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1605 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1605) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1605.1, data_12_1605.2] + +/-- Complete interval computation for depth 12, residue 1606. -/ +theorem bounds_12_1606 : exactInterval 12 1606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1606 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1606) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1606 : oddCount 1606 12 = 4 ∧ acceleratedOrbit 12 1606 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1606 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1606) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1606.1, data_12_1606.2] + +/-- Complete interval computation for depth 12, residue 1607. -/ +theorem bounds_12_1607 : exactInterval 12 1607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1607 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1607) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1607 : oddCount 1607 12 = 7 ∧ acceleratedOrbit 12 1607 = 859 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1607 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1607) = 3 ^ 7 * m + 859 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1607.1, data_12_1607.2] + +/-- Complete interval computation for depth 12, residue 1608. -/ +theorem bounds_12_1608 : exactInterval 12 1608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1608 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1608) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1608 : oddCount 1608 12 = 4 ∧ acceleratedOrbit 12 1608 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1608 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1608) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1608.1, data_12_1608.2] + +/-- Complete interval computation for depth 12, residue 1609. -/ +theorem bounds_12_1609 : exactInterval 12 1609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1609 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1609) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1609 : oddCount 1609 12 = 8 ∧ acceleratedOrbit 12 1609 = 2582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1609 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1609) = 3 ^ 8 * m + 2582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1609.1, data_12_1609.2] + +/-- Complete interval computation for depth 12, residue 1610. -/ +theorem bounds_12_1610 : exactInterval 12 1610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1610 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1610) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1610 : oddCount 1610 12 = 4 ∧ acceleratedOrbit 12 1610 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1610 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1610) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1610.1, data_12_1610.2] + +/-- Complete interval computation for depth 12, residue 1611. -/ +theorem bounds_12_1611 : exactInterval 12 1611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1611 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1611) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1611 : oddCount 1611 12 = 4 ∧ acceleratedOrbit 12 1611 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1611 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1611) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1611.1, data_12_1611.2] + +end Collatz.Research.StoppingAtlas.Batch0305 From 0a0da0f2bc43f2a45956df8d84f47a9e01c7e115 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:37 +0530 Subject: [PATCH 0306/1001] proof: certify atlas Batch0306 (12:1612 to 12:1627) --- Collatz/Research/StoppingAtlas/Batch0306.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0306.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0306.lean b/Collatz/Research/StoppingAtlas/Batch0306.lean new file mode 100644 index 00000000..7bcddece --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0306.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0306 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1612. -/ +theorem bounds_12_1612 : exactInterval 12 1612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1612 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1612) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1612 : oddCount 1612 12 = 4 ∧ acceleratedOrbit 12 1612 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1612 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1612) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1612.1, data_12_1612.2] + +/-- Complete interval computation for depth 12, residue 1613. -/ +theorem bounds_12_1613 : exactInterval 12 1613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1613 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1613) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1613 : oddCount 1613 12 = 4 ∧ acceleratedOrbit 12 1613 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1613 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1613) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1613.1, data_12_1613.2] + +/-- Complete interval computation for depth 12, residue 1614. -/ +theorem bounds_12_1614 : exactInterval 12 1614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1614 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1614) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1614 : oddCount 1614 12 = 8 ∧ acceleratedOrbit 12 1614 = 2591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1614 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1614) = 3 ^ 8 * m + 2591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1614.1, data_12_1614.2] + +/-- Complete interval computation for depth 12, residue 1615. -/ +theorem bounds_12_1615 : exactInterval 12 1615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1615 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1615) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1615 : oddCount 1615 12 = 8 ∧ acceleratedOrbit 12 1615 = 2591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1615 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1615) = 3 ^ 8 * m + 2591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1615.1, data_12_1615.2] + +/-- Complete interval computation for depth 12, residue 1616. -/ +theorem bounds_12_1616 : exactInterval 12 1616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1616 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1616) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1616 : oddCount 1616 12 = 3 ∧ acceleratedOrbit 12 1616 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1616 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1616) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1616.1, data_12_1616.2] + +/-- Complete interval computation for depth 12, residue 1617. -/ +theorem bounds_12_1617 : exactInterval 12 1617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1617 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1617) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1617 : oddCount 1617 12 = 7 ∧ acceleratedOrbit 12 1617 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1617 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1617) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1617.1, data_12_1617.2] + +/-- Complete interval computation for depth 12, residue 1618. -/ +theorem bounds_12_1618 : exactInterval 12 1618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1618 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1618) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1618 : oddCount 1618 12 = 7 ∧ acceleratedOrbit 12 1618 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1618 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1618) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1618.1, data_12_1618.2] + +/-- Complete interval computation for depth 12, residue 1619. -/ +theorem bounds_12_1619 : exactInterval 12 1619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1619 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1619) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1619 : oddCount 1619 12 = 7 ∧ acceleratedOrbit 12 1619 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1619 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1619) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1619.1, data_12_1619.2] + +/-- Complete interval computation for depth 12, residue 1620. -/ +theorem bounds_12_1620 : exactInterval 12 1620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1620 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1620) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1620 : oddCount 1620 12 = 3 ∧ acceleratedOrbit 12 1620 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1620 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1620) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1620.1, data_12_1620.2] + +/-- Complete interval computation for depth 12, residue 1621. -/ +theorem bounds_12_1621 : exactInterval 12 1621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1621 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1621) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1621 : oddCount 1621 12 = 3 ∧ acceleratedOrbit 12 1621 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1621 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1621) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1621.1, data_12_1621.2] + +/-- Complete interval computation for depth 12, residue 1622. -/ +theorem bounds_12_1622 : exactInterval 12 1622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1622 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1622) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1622 : oddCount 1622 12 = 6 ∧ acceleratedOrbit 12 1622 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1622 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1622) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1622.1, data_12_1622.2] + +/-- Complete interval computation for depth 12, residue 1623. -/ +theorem bounds_12_1623 : exactInterval 12 1623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1623 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1623) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1623 : oddCount 1623 12 = 6 ∧ acceleratedOrbit 12 1623 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1623 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1623) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1623.1, data_12_1623.2] + +/-- Complete interval computation for depth 12, residue 1624. -/ +theorem bounds_12_1624 : exactInterval 12 1624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1624 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1624) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1624 : oddCount 1624 12 = 5 ∧ acceleratedOrbit 12 1624 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1624 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1624) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1624.1, data_12_1624.2] + +/-- Complete interval computation for depth 12, residue 1625. -/ +theorem bounds_12_1625 : exactInterval 12 1625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1625 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1625) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1625 : oddCount 1625 12 = 6 ∧ acceleratedOrbit 12 1625 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1625 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1625) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1625.1, data_12_1625.2] + +/-- Complete interval computation for depth 12, residue 1626. -/ +theorem bounds_12_1626 : exactInterval 12 1626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1626 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1626) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1626 : oddCount 1626 12 = 5 ∧ acceleratedOrbit 12 1626 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1626 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1626) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1626.1, data_12_1626.2] + +/-- Complete interval computation for depth 12, residue 1627. -/ +theorem bounds_12_1627 : exactInterval 12 1627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1627 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1627) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1627 : oddCount 1627 12 = 8 ∧ acceleratedOrbit 12 1627 = 2609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1627 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1627) = 3 ^ 8 * m + 2609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1627.1, data_12_1627.2] + +end Collatz.Research.StoppingAtlas.Batch0306 From 1fe57fae3ebeb4c3c096f3cb8ac8e8d67971b92c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:37 +0530 Subject: [PATCH 0307/1001] proof: certify atlas Batch0307 (12:1628 to 12:1642) --- Collatz/Research/StoppingAtlas/Batch0307.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0307.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0307.lean b/Collatz/Research/StoppingAtlas/Batch0307.lean new file mode 100644 index 00000000..6d5b543d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0307.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0307 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1628. -/ +theorem bounds_12_1628 : exactInterval 12 1628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1628 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1628) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1628 : oddCount 1628 12 = 5 ∧ acceleratedOrbit 12 1628 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1628 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1628) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1628.1, data_12_1628.2] + +/-- Complete interval computation for depth 12, residue 1629. -/ +theorem bounds_12_1629 : exactInterval 12 1629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1629 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1629) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1629 : oddCount 1629 12 = 5 ∧ acceleratedOrbit 12 1629 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1629 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1629) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1629.1, data_12_1629.2] + +/-- Complete interval computation for depth 12, residue 1630. -/ +theorem bounds_12_1630 : exactInterval 12 1630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1630 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1630) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1630 : oddCount 1630 12 = 7 ∧ acceleratedOrbit 12 1630 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1630 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1630) = 3 ^ 7 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1630.1, data_12_1630.2] + +/-- Complete interval computation for depth 12, residue 1631. -/ +theorem bounds_12_1631 : exactInterval 12 1631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1631 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1631) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1631 : oddCount 1631 12 = 7 ∧ acceleratedOrbit 12 1631 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1631 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1631) = 3 ^ 7 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1631.1, data_12_1631.2] + +/-- Complete interval computation for depth 12, residue 1632. -/ +theorem bounds_12_1632 : exactInterval 12 1632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1632 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1632) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1632 : oddCount 1632 12 = 3 ∧ acceleratedOrbit 12 1632 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1632 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1632) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1632.1, data_12_1632.2] + +/-- Complete interval computation for depth 12, residue 1633. -/ +theorem bounds_12_1633 : exactInterval 12 1633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1633 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1633) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1633 : oddCount 1633 12 = 5 ∧ acceleratedOrbit 12 1633 = 97 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1633 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1633) = 3 ^ 5 * m + 97 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1633.1, data_12_1633.2] + +/-- Complete interval computation for depth 12, residue 1634. -/ +theorem bounds_12_1634 : exactInterval 12 1634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1634 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1634) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1634 : oddCount 1634 12 = 5 ∧ acceleratedOrbit 12 1634 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1634 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1634) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1634.1, data_12_1634.2] + +/-- Complete interval computation for depth 12, residue 1635. -/ +theorem bounds_12_1635 : exactInterval 12 1635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1635 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1635) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1635 : oddCount 1635 12 = 5 ∧ acceleratedOrbit 12 1635 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1635 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1635) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1635.1, data_12_1635.2] + +/-- Complete interval computation for depth 12, residue 1636. -/ +theorem bounds_12_1636 : exactInterval 12 1636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1636 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1636) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1636 : oddCount 1636 12 = 5 ∧ acceleratedOrbit 12 1636 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1636 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1636) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1636.1, data_12_1636.2] + +/-- Complete interval computation for depth 12, residue 1637. -/ +theorem bounds_12_1637 : exactInterval 12 1637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1637 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1637) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1637 : oddCount 1637 12 = 5 ∧ acceleratedOrbit 12 1637 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1637 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1637) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1637.1, data_12_1637.2] + +/-- Complete interval computation for depth 12, residue 1638. -/ +theorem bounds_12_1638 : exactInterval 12 1638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1638 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1638) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1638 : oddCount 1638 12 = 5 ∧ acceleratedOrbit 12 1638 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1638 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1638) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1638.1, data_12_1638.2] + +/-- Complete interval computation for depth 12, residue 1639. -/ +theorem bounds_12_1639 : exactInterval 12 1639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1639 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1639) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1639 : oddCount 1639 12 = 9 ∧ acceleratedOrbit 12 1639 = 7883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1639 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1639) = 3 ^ 9 * m + 7883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1639.1, data_12_1639.2] + +/-- Complete interval computation for depth 12, residue 1640. -/ +theorem bounds_12_1640 : exactInterval 12 1640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1640 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1640) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1640 : oddCount 1640 12 = 3 ∧ acceleratedOrbit 12 1640 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1640 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1640) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1640.1, data_12_1640.2] + +/-- Complete interval computation for depth 12, residue 1641. -/ +theorem bounds_12_1641 : exactInterval 12 1641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1641 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1641) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1641 : oddCount 1641 12 = 8 ∧ acceleratedOrbit 12 1641 = 2632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1641 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1641) = 3 ^ 8 * m + 2632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1641.1, data_12_1641.2] + +/-- Complete interval computation for depth 12, residue 1642. -/ +theorem bounds_12_1642 : exactInterval 12 1642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1642 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1642) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1642 : oddCount 1642 12 = 3 ∧ acceleratedOrbit 12 1642 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1642 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1642) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1642.1, data_12_1642.2] + +end Collatz.Research.StoppingAtlas.Batch0307 From 158878eb285b33275a13efd95e436ebfaf26fa0b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:37 +0530 Subject: [PATCH 0308/1001] proof: certify atlas Batch0308 (12:1643 to 12:1657) --- Collatz/Research/StoppingAtlas/Batch0308.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0308.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0308.lean b/Collatz/Research/StoppingAtlas/Batch0308.lean new file mode 100644 index 00000000..6813c8f3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0308.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0308 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1643. -/ +theorem bounds_12_1643 : exactInterval 12 1643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1643 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1643) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1643 : oddCount 1643 12 = 8 ∧ acceleratedOrbit 12 1643 = 2636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1643 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1643) = 3 ^ 8 * m + 2636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1643.1, data_12_1643.2] + +/-- Complete interval computation for depth 12, residue 1644. -/ +theorem bounds_12_1644 : exactInterval 12 1644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1644 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1644) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1644 : oddCount 1644 12 = 7 ∧ acceleratedOrbit 12 1644 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1644 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1644) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1644.1, data_12_1644.2] + +/-- Complete interval computation for depth 12, residue 1645. -/ +theorem bounds_12_1645 : exactInterval 12 1645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1645 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1645) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1645 : oddCount 1645 12 = 7 ∧ acceleratedOrbit 12 1645 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1645 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1645) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1645.1, data_12_1645.2] + +/-- Complete interval computation for depth 12, residue 1646. -/ +theorem bounds_12_1646 : exactInterval 12 1646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1646 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1646) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1646 : oddCount 1646 12 = 7 ∧ acceleratedOrbit 12 1646 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1646 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1646) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1646.1, data_12_1646.2] + +/-- Complete interval computation for depth 12, residue 1647. -/ +theorem bounds_12_1647 : exactInterval 12 1647 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1647 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1647) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1647 : oddCount 1647 12 = 7 ∧ acceleratedOrbit 12 1647 = 880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1647 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1647) = 3 ^ 7 * m + 880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1647.1, data_12_1647.2] + +/-- Complete interval computation for depth 12, residue 1648. -/ +theorem bounds_12_1648 : exactInterval 12 1648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1648 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1648) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1648 : oddCount 1648 12 = 7 ∧ acceleratedOrbit 12 1648 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1648 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1648) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1648.1, data_12_1648.2] + +/-- Complete interval computation for depth 12, residue 1649. -/ +theorem bounds_12_1649 : exactInterval 12 1649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1649 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1649) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1649 : oddCount 1649 12 = 3 ∧ acceleratedOrbit 12 1649 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1649 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1649) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1649.1, data_12_1649.2] + +/-- Complete interval computation for depth 12, residue 1650. -/ +theorem bounds_12_1650 : exactInterval 12 1650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1650 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1650) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1650 : oddCount 1650 12 = 7 ∧ acceleratedOrbit 12 1650 = 884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1650 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1650) = 3 ^ 7 * m + 884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1650.1, data_12_1650.2] + +/-- Complete interval computation for depth 12, residue 1651. -/ +theorem bounds_12_1651 : exactInterval 12 1651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1651 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1651) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1651 : oddCount 1651 12 = 7 ∧ acceleratedOrbit 12 1651 = 884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1651 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1651) = 3 ^ 7 * m + 884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1651.1, data_12_1651.2] + +/-- Complete interval computation for depth 12, residue 1652. -/ +theorem bounds_12_1652 : exactInterval 12 1652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1652 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1652) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1652 : oddCount 1652 12 = 7 ∧ acceleratedOrbit 12 1652 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1652 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1652) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1652.1, data_12_1652.2] + +/-- Complete interval computation for depth 12, residue 1653. -/ +theorem bounds_12_1653 : exactInterval 12 1653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1653 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1653) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1653 : oddCount 1653 12 = 7 ∧ acceleratedOrbit 12 1653 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1653 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1653) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1653.1, data_12_1653.2] + +/-- Complete interval computation for depth 12, residue 1654. -/ +theorem bounds_12_1654 : exactInterval 12 1654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1654 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1654) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1654 : oddCount 1654 12 = 6 ∧ acceleratedOrbit 12 1654 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1654 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1654) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1654.1, data_12_1654.2] + +/-- Complete interval computation for depth 12, residue 1655. -/ +theorem bounds_12_1655 : exactInterval 12 1655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1655 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1655) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1655 : oddCount 1655 12 = 6 ∧ acceleratedOrbit 12 1655 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1655 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1655) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1655.1, data_12_1655.2] + +/-- Complete interval computation for depth 12, residue 1656. -/ +theorem bounds_12_1656 : exactInterval 12 1656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1656 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1656) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1656 : oddCount 1656 12 = 7 ∧ acceleratedOrbit 12 1656 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1656 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1656) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1656.1, data_12_1656.2] + +/-- Complete interval computation for depth 12, residue 1657. -/ +theorem bounds_12_1657 : exactInterval 12 1657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1657 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1657) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1657 : oddCount 1657 12 = 7 ∧ acceleratedOrbit 12 1657 = 886 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1657 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1657) = 3 ^ 7 * m + 886 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1657.1, data_12_1657.2] + +end Collatz.Research.StoppingAtlas.Batch0308 From c51063aa4b624cf1eeea27f533a9a61899f24a39 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:37 +0530 Subject: [PATCH 0309/1001] proof: certify atlas Batch0309 (12:1658 to 12:1673) --- Collatz/Research/StoppingAtlas/Batch0309.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0309.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0309.lean b/Collatz/Research/StoppingAtlas/Batch0309.lean new file mode 100644 index 00000000..296eeda1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0309.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0309 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1658. -/ +theorem bounds_12_1658 : exactInterval 12 1658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1658 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1658) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1658 : oddCount 1658 12 = 7 ∧ acceleratedOrbit 12 1658 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1658 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1658) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1658.1, data_12_1658.2] + +/-- Complete interval computation for depth 12, residue 1659. -/ +theorem bounds_12_1659 : exactInterval 12 1659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1659 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1659) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1659 : oddCount 1659 12 = 6 ∧ acceleratedOrbit 12 1659 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1659 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1659) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1659.1, data_12_1659.2] + +/-- Complete interval computation for depth 12, residue 1660. -/ +theorem bounds_12_1660 : exactInterval 12 1660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1660 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1660) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1660 : oddCount 1660 12 = 8 ∧ acceleratedOrbit 12 1660 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1660 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1660) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1660.1, data_12_1660.2] + +/-- Complete interval computation for depth 12, residue 1661. -/ +theorem bounds_12_1661 : exactInterval 12 1661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1661 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1661) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1661 : oddCount 1661 12 = 8 ∧ acceleratedOrbit 12 1661 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1661 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1661) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1661.1, data_12_1661.2] + +/-- Complete interval computation for depth 12, residue 1662. -/ +theorem bounds_12_1662 : exactInterval 12 1662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1662 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1662) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1662 : oddCount 1662 12 = 8 ∧ acceleratedOrbit 12 1662 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1662 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1662) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1662.1, data_12_1662.2] + +/-- Complete interval computation for depth 12, residue 1663. -/ +theorem bounds_12_1663 : exactInterval 12 1663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1663 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1663) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1663 : oddCount 1663 12 = 10 ∧ acceleratedOrbit 12 1663 = 23989 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1663 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1663) = 3 ^ 10 * m + 23989 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1663.1, data_12_1663.2] + +/-- Complete interval computation for depth 12, residue 1664. -/ +theorem bounds_12_1664 : exactInterval 12 1664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1664 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1664) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1664 : oddCount 1664 12 = 2 ∧ acceleratedOrbit 12 1664 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1664 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1664) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1664.1, data_12_1664.2] + +/-- Complete interval computation for depth 12, residue 1665. -/ +theorem bounds_12_1665 : exactInterval 12 1665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1665 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1665) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1665 : oddCount 1665 12 = 9 ∧ acceleratedOrbit 12 1665 = 8018 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1665 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1665) = 3 ^ 9 * m + 8018 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1665.1, data_12_1665.2] + +/-- Complete interval computation for depth 12, residue 1666. -/ +theorem bounds_12_1666 : exactInterval 12 1666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1666 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1666) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1666 : oddCount 1666 12 = 3 ∧ acceleratedOrbit 12 1666 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1666 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1666) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1666.1, data_12_1666.2] + +/-- Complete interval computation for depth 12, residue 1667. -/ +theorem bounds_12_1667 : exactInterval 12 1667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1667 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1667) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1667 : oddCount 1667 12 = 3 ∧ acceleratedOrbit 12 1667 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1667 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1667) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1667.1, data_12_1667.2] + +/-- Complete interval computation for depth 12, residue 1668. -/ +theorem bounds_12_1668 : exactInterval 12 1668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1668 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1668) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1668 : oddCount 1668 12 = 6 ∧ acceleratedOrbit 12 1668 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1668 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1668) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1668.1, data_12_1668.2] + +/-- Complete interval computation for depth 12, residue 1669. -/ +theorem bounds_12_1669 : exactInterval 12 1669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1669 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1669) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1669 : oddCount 1669 12 = 6 ∧ acceleratedOrbit 12 1669 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1669 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1669) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1669.1, data_12_1669.2] + +/-- Complete interval computation for depth 12, residue 1670. -/ +theorem bounds_12_1670 : exactInterval 12 1670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1670 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1670) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1670 : oddCount 1670 12 = 6 ∧ acceleratedOrbit 12 1670 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1670 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1670) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1670.1, data_12_1670.2] + +/-- Complete interval computation for depth 12, residue 1671. -/ +theorem bounds_12_1671 : exactInterval 12 1671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1671 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1671) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1671 : oddCount 1671 12 = 6 ∧ acceleratedOrbit 12 1671 = 298 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1671 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1671) = 3 ^ 6 * m + 298 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1671.1, data_12_1671.2] + +/-- Complete interval computation for depth 12, residue 1672. -/ +theorem bounds_12_1672 : exactInterval 12 1672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1672 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1672) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1672 : oddCount 1672 12 = 5 ∧ acceleratedOrbit 12 1672 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1672 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1672) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1672.1, data_12_1672.2] + +/-- Complete interval computation for depth 12, residue 1673. -/ +theorem bounds_12_1673 : exactInterval 12 1673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1673 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1673) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1673 : oddCount 1673 12 = 8 ∧ acceleratedOrbit 12 1673 = 2683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1673 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1673) = 3 ^ 8 * m + 2683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1673.1, data_12_1673.2] + +end Collatz.Research.StoppingAtlas.Batch0309 From 3c10f16b8e2f06b148fb8c85ce7c97e770df1e38 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:38 +0530 Subject: [PATCH 0310/1001] proof: certify atlas Batch0310 (12:1674 to 12:1688) --- Collatz/Research/StoppingAtlas/Batch0310.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0310.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0310.lean b/Collatz/Research/StoppingAtlas/Batch0310.lean new file mode 100644 index 00000000..ddbee791 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0310.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0310 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1674. -/ +theorem bounds_12_1674 : exactInterval 12 1674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1674 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1674) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1674 : oddCount 1674 12 = 5 ∧ acceleratedOrbit 12 1674 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1674 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1674) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1674.1, data_12_1674.2] + +/-- Complete interval computation for depth 12, residue 1675. -/ +theorem bounds_12_1675 : exactInterval 12 1675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1675 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1675) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1675 : oddCount 1675 12 = 6 ∧ acceleratedOrbit 12 1675 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1675 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1675) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1675.1, data_12_1675.2] + +/-- Complete interval computation for depth 12, residue 1676. -/ +theorem bounds_12_1676 : exactInterval 12 1676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1676 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1676) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1676 : oddCount 1676 12 = 5 ∧ acceleratedOrbit 12 1676 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1676 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1676) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1676.1, data_12_1676.2] + +/-- Complete interval computation for depth 12, residue 1677. -/ +theorem bounds_12_1677 : exactInterval 12 1677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1677 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1677) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1677 : oddCount 1677 12 = 5 ∧ acceleratedOrbit 12 1677 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1677 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1677) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1677.1, data_12_1677.2] + +/-- Complete interval computation for depth 12, residue 1678. -/ +theorem bounds_12_1678 : exactInterval 12 1678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1678 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1678) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1678 : oddCount 1678 12 = 8 ∧ acceleratedOrbit 12 1678 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1678 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1678) = 3 ^ 8 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1678.1, data_12_1678.2] + +/-- Complete interval computation for depth 12, residue 1679. -/ +theorem bounds_12_1679 : exactInterval 12 1679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1679 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1679) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1679 : oddCount 1679 12 = 8 ∧ acceleratedOrbit 12 1679 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1679 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1679) = 3 ^ 8 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1679.1, data_12_1679.2] + +/-- Complete interval computation for depth 12, residue 1680. -/ +theorem bounds_12_1680 : exactInterval 12 1680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1680 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1680) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1680 : oddCount 1680 12 = 5 ∧ acceleratedOrbit 12 1680 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1680 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1680) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1680.1, data_12_1680.2] + +/-- Complete interval computation for depth 12, residue 1681. -/ +theorem bounds_12_1681 : exactInterval 12 1681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1681 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1681) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1681 : oddCount 1681 12 = 5 ∧ acceleratedOrbit 12 1681 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1681 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1681) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1681.1, data_12_1681.2] + +/-- Complete interval computation for depth 12, residue 1682. -/ +theorem bounds_12_1682 : exactInterval 12 1682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1682 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1682) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1682 : oddCount 1682 12 = 5 ∧ acceleratedOrbit 12 1682 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1682 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1682) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1682.1, data_12_1682.2] + +/-- Complete interval computation for depth 12, residue 1683. -/ +theorem bounds_12_1683 : exactInterval 12 1683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1683 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1683) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1683 : oddCount 1683 12 = 5 ∧ acceleratedOrbit 12 1683 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1683 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1683) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1683.1, data_12_1683.2] + +/-- Complete interval computation for depth 12, residue 1684. -/ +theorem bounds_12_1684 : exactInterval 12 1684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1684 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1684) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1684 : oddCount 1684 12 = 5 ∧ acceleratedOrbit 12 1684 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1684 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1684) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1684.1, data_12_1684.2] + +/-- Complete interval computation for depth 12, residue 1685. -/ +theorem bounds_12_1685 : exactInterval 12 1685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1685 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1685) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1685 : oddCount 1685 12 = 5 ∧ acceleratedOrbit 12 1685 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1685 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1685) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1685.1, data_12_1685.2] + +/-- Complete interval computation for depth 12, residue 1686. -/ +theorem bounds_12_1686 : exactInterval 12 1686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1686 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1686) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1686 : oddCount 1686 12 = 5 ∧ acceleratedOrbit 12 1686 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1686 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1686) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1686.1, data_12_1686.2] + +/-- Complete interval computation for depth 12, residue 1687. -/ +theorem bounds_12_1687 : exactInterval 12 1687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1687 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1687) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1687 : oddCount 1687 12 = 5 ∧ acceleratedOrbit 12 1687 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1687 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1687) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1687.1, data_12_1687.2] + +/-- Complete interval computation for depth 12, residue 1688. -/ +theorem bounds_12_1688 : exactInterval 12 1688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1688 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1688) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1688 : oddCount 1688 12 = 5 ∧ acceleratedOrbit 12 1688 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1688 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1688) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1688.1, data_12_1688.2] + +end Collatz.Research.StoppingAtlas.Batch0310 From f9436dbc7236dc9531e3a7baf245d502f25f2181 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:38 +0530 Subject: [PATCH 0311/1001] proof: certify atlas Batch0311 (12:1689 to 12:1703) --- Collatz/Research/StoppingAtlas/Batch0311.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0311.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0311.lean b/Collatz/Research/StoppingAtlas/Batch0311.lean new file mode 100644 index 00000000..e1b6c460 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0311.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0311 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1689. -/ +theorem bounds_12_1689 : exactInterval 12 1689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1689 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1689) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1689 : oddCount 1689 12 = 7 ∧ acceleratedOrbit 12 1689 = 904 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1689 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1689) = 3 ^ 7 * m + 904 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1689.1, data_12_1689.2] + +/-- Complete interval computation for depth 12, residue 1690. -/ +theorem bounds_12_1690 : exactInterval 12 1690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1690 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1690) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1690 : oddCount 1690 12 = 5 ∧ acceleratedOrbit 12 1690 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1690 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1690) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1690.1, data_12_1690.2] + +/-- Complete interval computation for depth 12, residue 1691. -/ +theorem bounds_12_1691 : exactInterval 12 1691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1691 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1691) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1691 : oddCount 1691 12 = 8 ∧ acceleratedOrbit 12 1691 = 2711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1691 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1691) = 3 ^ 8 * m + 2711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1691.1, data_12_1691.2] + +/-- Complete interval computation for depth 12, residue 1692. -/ +theorem bounds_12_1692 : exactInterval 12 1692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1692 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1692) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1692 : oddCount 1692 12 = 6 ∧ acceleratedOrbit 12 1692 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1692 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1692) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1692.1, data_12_1692.2] + +/-- Complete interval computation for depth 12, residue 1693. -/ +theorem bounds_12_1693 : exactInterval 12 1693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1693 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1693) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1693 : oddCount 1693 12 = 6 ∧ acceleratedOrbit 12 1693 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1693 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1693) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1693.1, data_12_1693.2] + +/-- Complete interval computation for depth 12, residue 1694. -/ +theorem bounds_12_1694 : exactInterval 12 1694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1694 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1694) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1694 : oddCount 1694 12 = 6 ∧ acceleratedOrbit 12 1694 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1694 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1694) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1694.1, data_12_1694.2] + +/-- Complete interval computation for depth 12, residue 1695. -/ +theorem bounds_12_1695 : exactInterval 12 1695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1695 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1695) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1695 : oddCount 1695 12 = 10 ∧ acceleratedOrbit 12 1695 = 24452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1695 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1695) = 3 ^ 10 * m + 24452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1695.1, data_12_1695.2] + +/-- Complete interval computation for depth 12, residue 1696. -/ +theorem bounds_12_1696 : exactInterval 12 1696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1696 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1696) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1696 : oddCount 1696 12 = 2 ∧ acceleratedOrbit 12 1696 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1696 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1696) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1696.1, data_12_1696.2] + +/-- Complete interval computation for depth 12, residue 1697. -/ +theorem bounds_12_1697 : exactInterval 12 1697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1697 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1697) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1697 : oddCount 1697 12 = 7 ∧ acceleratedOrbit 12 1697 = 908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1697 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1697) = 3 ^ 7 * m + 908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1697.1, data_12_1697.2] + +/-- Complete interval computation for depth 12, residue 1698. -/ +theorem bounds_12_1698 : exactInterval 12 1698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1698 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1698) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1698 : oddCount 1698 12 = 7 ∧ acceleratedOrbit 12 1698 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1698 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1698) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1698.1, data_12_1698.2] + +/-- Complete interval computation for depth 12, residue 1699. -/ +theorem bounds_12_1699 : exactInterval 12 1699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1699 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1699) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1699 : oddCount 1699 12 = 7 ∧ acceleratedOrbit 12 1699 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1699 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1699) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1699.1, data_12_1699.2] + +/-- Complete interval computation for depth 12, residue 1700. -/ +theorem bounds_12_1700 : exactInterval 12 1700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1700 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1700) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1700 : oddCount 1700 12 = 7 ∧ acceleratedOrbit 12 1700 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1700 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1700) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1700.1, data_12_1700.2] + +/-- Complete interval computation for depth 12, residue 1701. -/ +theorem bounds_12_1701 : exactInterval 12 1701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1701 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1701) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1701 : oddCount 1701 12 = 7 ∧ acceleratedOrbit 12 1701 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1701 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1701) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1701.1, data_12_1701.2] + +/-- Complete interval computation for depth 12, residue 1702. -/ +theorem bounds_12_1702 : exactInterval 12 1702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1702 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1702) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1702 : oddCount 1702 12 = 7 ∧ acceleratedOrbit 12 1702 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1702 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1702) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1702.1, data_12_1702.2] + +/-- Complete interval computation for depth 12, residue 1703. -/ +theorem bounds_12_1703 : exactInterval 12 1703 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1703 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1703) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1703 : oddCount 1703 12 = 7 ∧ acceleratedOrbit 12 1703 = 910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1703 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1703) = 3 ^ 7 * m + 910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1703.1, data_12_1703.2] + +end Collatz.Research.StoppingAtlas.Batch0311 From bc3a60a66184b26db711b5e5c81612019f248dea Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:38 +0530 Subject: [PATCH 0312/1001] proof: certify atlas Batch0312 (12:1704 to 12:1719) --- Collatz/Research/StoppingAtlas/Batch0312.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0312.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0312.lean b/Collatz/Research/StoppingAtlas/Batch0312.lean new file mode 100644 index 00000000..3212bbe3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0312.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0312 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1704. -/ +theorem bounds_12_1704 : exactInterval 12 1704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1704 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1704) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1704 : oddCount 1704 12 = 2 ∧ acceleratedOrbit 12 1704 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1704 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1704) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1704.1, data_12_1704.2] + +/-- Complete interval computation for depth 12, residue 1705. -/ +theorem bounds_12_1705 : exactInterval 12 1705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1705 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1705) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1705 : oddCount 1705 12 = 9 ∧ acceleratedOrbit 12 1705 = 8201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1705 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1705) = 3 ^ 9 * m + 8201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1705.1, data_12_1705.2] + +/-- Complete interval computation for depth 12, residue 1706. -/ +theorem bounds_12_1706 : exactInterval 12 1706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1706 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1706) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1706 : oddCount 1706 12 = 2 ∧ acceleratedOrbit 12 1706 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1706 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1706) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1706.1, data_12_1706.2] + +/-- Complete interval computation for depth 12, residue 1707. -/ +theorem bounds_12_1707 : exactInterval 12 1707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1707 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1707) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1707 : oddCount 1707 12 = 7 ∧ acceleratedOrbit 12 1707 = 913 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1707 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1707) = 3 ^ 7 * m + 913 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1707.1, data_12_1707.2] + +/-- Complete interval computation for depth 12, residue 1708. -/ +theorem bounds_12_1708 : exactInterval 12 1708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1708 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1708) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1708 : oddCount 1708 12 = 7 ∧ acceleratedOrbit 12 1708 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1708 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1708) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1708.1, data_12_1708.2] + +/-- Complete interval computation for depth 12, residue 1709. -/ +theorem bounds_12_1709 : exactInterval 12 1709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1709 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1709) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1709 : oddCount 1709 12 = 7 ∧ acceleratedOrbit 12 1709 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1709 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1709) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1709.1, data_12_1709.2] + +/-- Complete interval computation for depth 12, residue 1710. -/ +theorem bounds_12_1710 : exactInterval 12 1710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1710 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1710) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1710 : oddCount 1710 12 = 7 ∧ acceleratedOrbit 12 1710 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1710 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1710) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1710.1, data_12_1710.2] + +/-- Complete interval computation for depth 12, residue 1711. -/ +theorem bounds_12_1711 : exactInterval 12 1711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1711 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1711) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1711 : oddCount 1711 12 = 8 ∧ acceleratedOrbit 12 1711 = 2744 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1711 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1711) = 3 ^ 8 * m + 2744 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1711.1, data_12_1711.2] + +/-- Complete interval computation for depth 12, residue 1712. -/ +theorem bounds_12_1712 : exactInterval 12 1712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1712 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1712) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1712 : oddCount 1712 12 = 5 ∧ acceleratedOrbit 12 1712 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1712 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1712) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1712.1, data_12_1712.2] + +/-- Complete interval computation for depth 12, residue 1713. -/ +theorem bounds_12_1713 : exactInterval 12 1713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1713 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1713) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1713 : oddCount 1713 12 = 4 ∧ acceleratedOrbit 12 1713 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1713 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1713) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1713.1, data_12_1713.2] + +/-- Complete interval computation for depth 12, residue 1714. -/ +theorem bounds_12_1714 : exactInterval 12 1714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1714 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1714) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1714 : oddCount 1714 12 = 4 ∧ acceleratedOrbit 12 1714 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1714 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1714) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1714.1, data_12_1714.2] + +/-- Complete interval computation for depth 12, residue 1715. -/ +theorem bounds_12_1715 : exactInterval 12 1715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1715 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1715) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1715 : oddCount 1715 12 = 4 ∧ acceleratedOrbit 12 1715 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1715 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1715) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1715.1, data_12_1715.2] + +/-- Complete interval computation for depth 12, residue 1716. -/ +theorem bounds_12_1716 : exactInterval 12 1716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1716 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1716) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1716 : oddCount 1716 12 = 5 ∧ acceleratedOrbit 12 1716 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1716 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1716) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1716.1, data_12_1716.2] + +/-- Complete interval computation for depth 12, residue 1717. -/ +theorem bounds_12_1717 : exactInterval 12 1717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1717 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1717) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1717 : oddCount 1717 12 = 5 ∧ acceleratedOrbit 12 1717 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1717 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1717) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1717.1, data_12_1717.2] + +/-- Complete interval computation for depth 12, residue 1718. -/ +theorem bounds_12_1718 : exactInterval 12 1718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1718 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1718) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1718 : oddCount 1718 12 = 7 ∧ acceleratedOrbit 12 1718 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1718 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1718) = 3 ^ 7 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1718.1, data_12_1718.2] + +/-- Complete interval computation for depth 12, residue 1719. -/ +theorem bounds_12_1719 : exactInterval 12 1719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1719 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1719) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1719 : oddCount 1719 12 = 7 ∧ acceleratedOrbit 12 1719 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1719 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1719) = 3 ^ 7 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1719.1, data_12_1719.2] + +end Collatz.Research.StoppingAtlas.Batch0312 From 2810896e6b3e0a4460714cdc856bff44baf446bc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:39 +0530 Subject: [PATCH 0313/1001] proof: certify atlas Batch0313 (12:1720 to 12:1734) --- Collatz/Research/StoppingAtlas/Batch0313.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0313.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0313.lean b/Collatz/Research/StoppingAtlas/Batch0313.lean new file mode 100644 index 00000000..cc2faa09 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0313.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0313 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1720. -/ +theorem bounds_12_1720 : exactInterval 12 1720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1720 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1720) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1720 : oddCount 1720 12 = 5 ∧ acceleratedOrbit 12 1720 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1720 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1720) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1720.1, data_12_1720.2] + +/-- Complete interval computation for depth 12, residue 1721. -/ +theorem bounds_12_1721 : exactInterval 12 1721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1721 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1721) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1721 : oddCount 1721 12 = 6 ∧ acceleratedOrbit 12 1721 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1721 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1721) = 3 ^ 6 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1721.1, data_12_1721.2] + +/-- Complete interval computation for depth 12, residue 1722. -/ +theorem bounds_12_1722 : exactInterval 12 1722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1722 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1722) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1722 : oddCount 1722 12 = 5 ∧ acceleratedOrbit 12 1722 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1722 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1722) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1722.1, data_12_1722.2] + +/-- Complete interval computation for depth 12, residue 1723. -/ +theorem bounds_12_1723 : exactInterval 12 1723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1723 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1723) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1723 : oddCount 1723 12 = 6 ∧ acceleratedOrbit 12 1723 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1723 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1723) = 3 ^ 6 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1723.1, data_12_1723.2] + +/-- Complete interval computation for depth 12, residue 1724. -/ +theorem bounds_12_1724 : exactInterval 12 1724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1724 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1724) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1724 : oddCount 1724 12 = 6 ∧ acceleratedOrbit 12 1724 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1724 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1724) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1724.1, data_12_1724.2] + +/-- Complete interval computation for depth 12, residue 1725. -/ +theorem bounds_12_1725 : exactInterval 12 1725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1725 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1725) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1725 : oddCount 1725 12 = 6 ∧ acceleratedOrbit 12 1725 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1725 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1725) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1725.1, data_12_1725.2] + +/-- Complete interval computation for depth 12, residue 1726. -/ +theorem bounds_12_1726 : exactInterval 12 1726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1726 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1726) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1726 : oddCount 1726 12 = 6 ∧ acceleratedOrbit 12 1726 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1726 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1726) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1726.1, data_12_1726.2] + +/-- Complete interval computation for depth 12, residue 1727. -/ +theorem bounds_12_1727 : exactInterval 12 1727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1727 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1727) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1727 : oddCount 1727 12 = 8 ∧ acceleratedOrbit 12 1727 = 2768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1727 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1727) = 3 ^ 8 * m + 2768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1727.1, data_12_1727.2] + +/-- Complete interval computation for depth 12, residue 1728. -/ +theorem bounds_12_1728 : exactInterval 12 1728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1728 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1728) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1728 : oddCount 1728 12 = 5 ∧ acceleratedOrbit 12 1728 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1728 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1728) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1728.1, data_12_1728.2] + +/-- Complete interval computation for depth 12, residue 1729. -/ +theorem bounds_12_1729 : exactInterval 12 1729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1729 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1729) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1729 : oddCount 1729 12 = 5 ∧ acceleratedOrbit 12 1729 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1729 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1729) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1729.1, data_12_1729.2] + +/-- Complete interval computation for depth 12, residue 1730. -/ +theorem bounds_12_1730 : exactInterval 12 1730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1730 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1730) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1730 : oddCount 1730 12 = 8 ∧ acceleratedOrbit 12 1730 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1730 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1730) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1730.1, data_12_1730.2] + +/-- Complete interval computation for depth 12, residue 1731. -/ +theorem bounds_12_1731 : exactInterval 12 1731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1731 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1731) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1731 : oddCount 1731 12 = 8 ∧ acceleratedOrbit 12 1731 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1731 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1731) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1731.1, data_12_1731.2] + +/-- Complete interval computation for depth 12, residue 1732. -/ +theorem bounds_12_1732 : exactInterval 12 1732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1732 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1732) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1732 : oddCount 1732 12 = 4 ∧ acceleratedOrbit 12 1732 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1732 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1732) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1732.1, data_12_1732.2] + +/-- Complete interval computation for depth 12, residue 1733. -/ +theorem bounds_12_1733 : exactInterval 12 1733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1733 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1733) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1733 : oddCount 1733 12 = 4 ∧ acceleratedOrbit 12 1733 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1733 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1733) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1733.1, data_12_1733.2] + +/-- Complete interval computation for depth 12, residue 1734. -/ +theorem bounds_12_1734 : exactInterval 12 1734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1734 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1734) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1734 : oddCount 1734 12 = 4 ∧ acceleratedOrbit 12 1734 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1734 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1734) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1734.1, data_12_1734.2] + +end Collatz.Research.StoppingAtlas.Batch0313 From fa9d4f51a1f98f5a5e6add879bb4ad51600db44b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:39 +0530 Subject: [PATCH 0314/1001] proof: certify atlas Batch0314 (12:1735 to 12:1750) --- Collatz/Research/StoppingAtlas/Batch0314.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0314.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0314.lean b/Collatz/Research/StoppingAtlas/Batch0314.lean new file mode 100644 index 00000000..c063bc8b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0314.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0314 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1735. -/ +theorem bounds_12_1735 : exactInterval 12 1735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1735 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1735) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1735 : oddCount 1735 12 = 5 ∧ acceleratedOrbit 12 1735 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1735 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1735) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1735.1, data_12_1735.2] + +/-- Complete interval computation for depth 12, residue 1736. -/ +theorem bounds_12_1736 : exactInterval 12 1736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1736 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1736) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1736 : oddCount 1736 12 = 4 ∧ acceleratedOrbit 12 1736 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1736 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1736) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1736.1, data_12_1736.2] + +/-- Complete interval computation for depth 12, residue 1737. -/ +theorem bounds_12_1737 : exactInterval 12 1737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1737 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1737) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1737 : oddCount 1737 12 = 6 ∧ acceleratedOrbit 12 1737 = 310 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1737 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1737) = 3 ^ 6 * m + 310 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1737.1, data_12_1737.2] + +/-- Complete interval computation for depth 12, residue 1738. -/ +theorem bounds_12_1738 : exactInterval 12 1738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1738 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1738) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1738 : oddCount 1738 12 = 4 ∧ acceleratedOrbit 12 1738 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1738 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1738) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1738.1, data_12_1738.2] + +/-- Complete interval computation for depth 12, residue 1739. -/ +theorem bounds_12_1739 : exactInterval 12 1739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1739 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1739) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1739 : oddCount 1739 12 = 7 ∧ acceleratedOrbit 12 1739 = 931 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1739 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1739) = 3 ^ 7 * m + 931 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1739.1, data_12_1739.2] + +/-- Complete interval computation for depth 12, residue 1740. -/ +theorem bounds_12_1740 : exactInterval 12 1740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1740 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1740) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1740 : oddCount 1740 12 = 4 ∧ acceleratedOrbit 12 1740 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1740 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1740) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1740.1, data_12_1740.2] + +/-- Complete interval computation for depth 12, residue 1741. -/ +theorem bounds_12_1741 : exactInterval 12 1741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1741 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1741) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1741 : oddCount 1741 12 = 4 ∧ acceleratedOrbit 12 1741 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1741 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1741) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1741.1, data_12_1741.2] + +/-- Complete interval computation for depth 12, residue 1742. -/ +theorem bounds_12_1742 : exactInterval 12 1742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1742 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1742) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1742 : oddCount 1742 12 = 9 ∧ acceleratedOrbit 12 1742 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1742 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1742) = 3 ^ 9 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1742.1, data_12_1742.2] + +/-- Complete interval computation for depth 12, residue 1743. -/ +theorem bounds_12_1743 : exactInterval 12 1743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1743 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1743) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1743 : oddCount 1743 12 = 9 ∧ acceleratedOrbit 12 1743 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1743 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1743) = 3 ^ 9 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1743.1, data_12_1743.2] + +/-- Complete interval computation for depth 12, residue 1744. -/ +theorem bounds_12_1744 : exactInterval 12 1744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1744 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1744) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1744 : oddCount 1744 12 = 5 ∧ acceleratedOrbit 12 1744 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1744 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1744) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1744.1, data_12_1744.2] + +/-- Complete interval computation for depth 12, residue 1745. -/ +theorem bounds_12_1745 : exactInterval 12 1745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1745 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1745) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1745 : oddCount 1745 12 = 7 ∧ acceleratedOrbit 12 1745 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1745 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1745) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1745.1, data_12_1745.2] + +/-- Complete interval computation for depth 12, residue 1746. -/ +theorem bounds_12_1746 : exactInterval 12 1746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1746 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1746) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1746 : oddCount 1746 12 = 7 ∧ acceleratedOrbit 12 1746 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1746 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1746) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1746.1, data_12_1746.2] + +/-- Complete interval computation for depth 12, residue 1747. -/ +theorem bounds_12_1747 : exactInterval 12 1747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1747 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1747) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1747 : oddCount 1747 12 = 7 ∧ acceleratedOrbit 12 1747 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1747 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1747) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1747.1, data_12_1747.2] + +/-- Complete interval computation for depth 12, residue 1748. -/ +theorem bounds_12_1748 : exactInterval 12 1748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1748 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1748) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1748 : oddCount 1748 12 = 5 ∧ acceleratedOrbit 12 1748 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1748 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1748) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1748.1, data_12_1748.2] + +/-- Complete interval computation for depth 12, residue 1749. -/ +theorem bounds_12_1749 : exactInterval 12 1749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1749 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1749) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1749 : oddCount 1749 12 = 5 ∧ acceleratedOrbit 12 1749 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1749 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1749) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1749.1, data_12_1749.2] + +/-- Complete interval computation for depth 12, residue 1750. -/ +theorem bounds_12_1750 : exactInterval 12 1750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1750 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1750) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1750 : oddCount 1750 12 = 5 ∧ acceleratedOrbit 12 1750 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1750 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1750) = 3 ^ 5 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1750.1, data_12_1750.2] + +end Collatz.Research.StoppingAtlas.Batch0314 From 7db09c05e1758c444f5a781b2bbff2bcb8e00484 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:40 +0530 Subject: [PATCH 0315/1001] proof: certify atlas Batch0315 (12:1751 to 12:1765) --- Collatz/Research/StoppingAtlas/Batch0315.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0315.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0315.lean b/Collatz/Research/StoppingAtlas/Batch0315.lean new file mode 100644 index 00000000..93ec2167 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0315.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0315 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1751. -/ +theorem bounds_12_1751 : exactInterval 12 1751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1751 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1751) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1751 : oddCount 1751 12 = 5 ∧ acceleratedOrbit 12 1751 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1751 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1751) = 3 ^ 5 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1751.1, data_12_1751.2] + +/-- Complete interval computation for depth 12, residue 1752. -/ +theorem bounds_12_1752 : exactInterval 12 1752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1752 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1752) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1752 : oddCount 1752 12 = 6 ∧ acceleratedOrbit 12 1752 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1752 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1752) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1752.1, data_12_1752.2] + +/-- Complete interval computation for depth 12, residue 1753. -/ +theorem bounds_12_1753 : exactInterval 12 1753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1753 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1753) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1753 : oddCount 1753 12 = 6 ∧ acceleratedOrbit 12 1753 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1753 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1753) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1753.1, data_12_1753.2] + +/-- Complete interval computation for depth 12, residue 1754. -/ +theorem bounds_12_1754 : exactInterval 12 1754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1754 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1754) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1754 : oddCount 1754 12 = 6 ∧ acceleratedOrbit 12 1754 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1754 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1754) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1754.1, data_12_1754.2] + +/-- Complete interval computation for depth 12, residue 1755. -/ +theorem bounds_12_1755 : exactInterval 12 1755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1755 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1755) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1755 : oddCount 1755 12 = 7 ∧ acceleratedOrbit 12 1755 = 938 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1755 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1755) = 3 ^ 7 * m + 938 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1755.1, data_12_1755.2] + +/-- Complete interval computation for depth 12, residue 1756. -/ +theorem bounds_12_1756 : exactInterval 12 1756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1756 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1756) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1756 : oddCount 1756 12 = 6 ∧ acceleratedOrbit 12 1756 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1756 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1756) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1756.1, data_12_1756.2] + +/-- Complete interval computation for depth 12, residue 1757. -/ +theorem bounds_12_1757 : exactInterval 12 1757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1757 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1757) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1757 : oddCount 1757 12 = 6 ∧ acceleratedOrbit 12 1757 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1757 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1757) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1757.1, data_12_1757.2] + +/-- Complete interval computation for depth 12, residue 1758. -/ +theorem bounds_12_1758 : exactInterval 12 1758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1758 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1758) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1758 : oddCount 1758 12 = 7 ∧ acceleratedOrbit 12 1758 = 940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1758 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1758) = 3 ^ 7 * m + 940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1758.1, data_12_1758.2] + +/-- Complete interval computation for depth 12, residue 1759. -/ +theorem bounds_12_1759 : exactInterval 12 1759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1759 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1759) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1759 : oddCount 1759 12 = 7 ∧ acceleratedOrbit 12 1759 = 940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1759 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1759) = 3 ^ 7 * m + 940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1759.1, data_12_1759.2] + +/-- Complete interval computation for depth 12, residue 1760. -/ +theorem bounds_12_1760 : exactInterval 12 1760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1760 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1760) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1760 : oddCount 1760 12 = 5 ∧ acceleratedOrbit 12 1760 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1760 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1760) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1760.1, data_12_1760.2] + +/-- Complete interval computation for depth 12, residue 1761. -/ +theorem bounds_12_1761 : exactInterval 12 1761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1761 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1761) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1761 : oddCount 1761 12 = 8 ∧ acceleratedOrbit 12 1761 = 2825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1761 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1761) = 3 ^ 8 * m + 2825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1761.1, data_12_1761.2] + +/-- Complete interval computation for depth 12, residue 1762. -/ +theorem bounds_12_1762 : exactInterval 12 1762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1762 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1762) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1762 : oddCount 1762 12 = 5 ∧ acceleratedOrbit 12 1762 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1762 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1762) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1762.1, data_12_1762.2] + +/-- Complete interval computation for depth 12, residue 1763. -/ +theorem bounds_12_1763 : exactInterval 12 1763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1763 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1763) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1763 : oddCount 1763 12 = 5 ∧ acceleratedOrbit 12 1763 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1763 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1763) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1763.1, data_12_1763.2] + +/-- Complete interval computation for depth 12, residue 1764. -/ +theorem bounds_12_1764 : exactInterval 12 1764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1764 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1764) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1764 : oddCount 1764 12 = 4 ∧ acceleratedOrbit 12 1764 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1764 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1764) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1764.1, data_12_1764.2] + +/-- Complete interval computation for depth 12, residue 1765. -/ +theorem bounds_12_1765 : exactInterval 12 1765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1765 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1765) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1765 : oddCount 1765 12 = 4 ∧ acceleratedOrbit 12 1765 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1765 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1765) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1765.1, data_12_1765.2] + +end Collatz.Research.StoppingAtlas.Batch0315 From b1a5407e95593f782e8abe71643f5542f8ed5dad Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:40 +0530 Subject: [PATCH 0316/1001] proof: certify atlas Batch0316 (12:1766 to 12:1780) --- Collatz/Research/StoppingAtlas/Batch0316.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0316.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0316.lean b/Collatz/Research/StoppingAtlas/Batch0316.lean new file mode 100644 index 00000000..7bf1caf3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0316.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0316 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1766. -/ +theorem bounds_12_1766 : exactInterval 12 1766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1766 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1766) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1766 : oddCount 1766 12 = 4 ∧ acceleratedOrbit 12 1766 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1766 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1766) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1766.1, data_12_1766.2] + +/-- Complete interval computation for depth 12, residue 1767. -/ +theorem bounds_12_1767 : exactInterval 12 1767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1767 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1767) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1767 : oddCount 1767 12 = 9 ∧ acceleratedOrbit 12 1767 = 8498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1767 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1767) = 3 ^ 9 * m + 8498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1767.1, data_12_1767.2] + +/-- Complete interval computation for depth 12, residue 1768. -/ +theorem bounds_12_1768 : exactInterval 12 1768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1768 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1768) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1768 : oddCount 1768 12 = 5 ∧ acceleratedOrbit 12 1768 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1768 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1768) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1768.1, data_12_1768.2] + +/-- Complete interval computation for depth 12, residue 1769. -/ +theorem bounds_12_1769 : exactInterval 12 1769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1769 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1769) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1769 : oddCount 1769 12 = 8 ∧ acceleratedOrbit 12 1769 = 2837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1769 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1769) = 3 ^ 8 * m + 2837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1769.1, data_12_1769.2] + +/-- Complete interval computation for depth 12, residue 1770. -/ +theorem bounds_12_1770 : exactInterval 12 1770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1770 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1770) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1770 : oddCount 1770 12 = 5 ∧ acceleratedOrbit 12 1770 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1770 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1770) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1770.1, data_12_1770.2] + +/-- Complete interval computation for depth 12, residue 1771. -/ +theorem bounds_12_1771 : exactInterval 12 1771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1771 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1771) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1771 : oddCount 1771 12 = 7 ∧ acceleratedOrbit 12 1771 = 947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1771 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1771) = 3 ^ 7 * m + 947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1771.1, data_12_1771.2] + +/-- Complete interval computation for depth 12, residue 1772. -/ +theorem bounds_12_1772 : exactInterval 12 1772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1772 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1772) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1772 : oddCount 1772 12 = 6 ∧ acceleratedOrbit 12 1772 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1772 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1772) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1772.1, data_12_1772.2] + +/-- Complete interval computation for depth 12, residue 1773. -/ +theorem bounds_12_1773 : exactInterval 12 1773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1773 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1773) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1773 : oddCount 1773 12 = 6 ∧ acceleratedOrbit 12 1773 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1773 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1773) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1773.1, data_12_1773.2] + +/-- Complete interval computation for depth 12, residue 1774. -/ +theorem bounds_12_1774 : exactInterval 12 1774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1774 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1774) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1774 : oddCount 1774 12 = 6 ∧ acceleratedOrbit 12 1774 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1774 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1774) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1774.1, data_12_1774.2] + +/-- Complete interval computation for depth 12, residue 1775. -/ +theorem bounds_12_1775 : exactInterval 12 1775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1775 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1775) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1775 : oddCount 1775 12 = 8 ∧ acceleratedOrbit 12 1775 = 2845 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1775 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1775) = 3 ^ 8 * m + 2845 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1775.1, data_12_1775.2] + +/-- Complete interval computation for depth 12, residue 1776. -/ +theorem bounds_12_1776 : exactInterval 12 1776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1776 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1776) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1776 : oddCount 1776 12 = 6 ∧ acceleratedOrbit 12 1776 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1776 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1776) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1776.1, data_12_1776.2] + +/-- Complete interval computation for depth 12, residue 1777. -/ +theorem bounds_12_1777 : exactInterval 12 1777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1777 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1777) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1777 : oddCount 1777 12 = 5 ∧ acceleratedOrbit 12 1777 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1777 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1777) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1777.1, data_12_1777.2] + +/-- Complete interval computation for depth 12, residue 1778. -/ +theorem bounds_12_1778 : exactInterval 12 1778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1778 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1778) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1778 : oddCount 1778 12 = 8 ∧ acceleratedOrbit 12 1778 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1778 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1778) = 3 ^ 8 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1778.1, data_12_1778.2] + +/-- Complete interval computation for depth 12, residue 1779. -/ +theorem bounds_12_1779 : exactInterval 12 1779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1779 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1779) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1779 : oddCount 1779 12 = 8 ∧ acceleratedOrbit 12 1779 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1779 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1779) = 3 ^ 8 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1779.1, data_12_1779.2] + +/-- Complete interval computation for depth 12, residue 1780. -/ +theorem bounds_12_1780 : exactInterval 12 1780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1780 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1780) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1780 : oddCount 1780 12 = 6 ∧ acceleratedOrbit 12 1780 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1780 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1780) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1780.1, data_12_1780.2] + +end Collatz.Research.StoppingAtlas.Batch0316 From ed98dde2ea2be51d507b52dcf3e4e7bd28691976 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:40 +0530 Subject: [PATCH 0317/1001] proof: certify atlas Batch0317 (12:1781 to 12:1796) --- Collatz/Research/StoppingAtlas/Batch0317.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0317.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0317.lean b/Collatz/Research/StoppingAtlas/Batch0317.lean new file mode 100644 index 00000000..b525ab25 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0317.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0317 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1781. -/ +theorem bounds_12_1781 : exactInterval 12 1781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1781 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1781) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1781 : oddCount 1781 12 = 6 ∧ acceleratedOrbit 12 1781 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1781 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1781) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1781.1, data_12_1781.2] + +/-- Complete interval computation for depth 12, residue 1782. -/ +theorem bounds_12_1782 : exactInterval 12 1782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1782 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1782) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1782 : oddCount 1782 12 = 8 ∧ acceleratedOrbit 12 1782 = 2861 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1782 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1782) = 3 ^ 8 * m + 2861 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1782.1, data_12_1782.2] + +/-- Complete interval computation for depth 12, residue 1783. -/ +theorem bounds_12_1783 : exactInterval 12 1783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1783 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1783) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1783 : oddCount 1783 12 = 8 ∧ acceleratedOrbit 12 1783 = 2861 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1783 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1783) = 3 ^ 8 * m + 2861 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1783.1, data_12_1783.2] + +/-- Complete interval computation for depth 12, residue 1784. -/ +theorem bounds_12_1784 : exactInterval 12 1784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1784 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1784) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1784 : oddCount 1784 12 = 6 ∧ acceleratedOrbit 12 1784 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1784 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1784) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1784.1, data_12_1784.2] + +/-- Complete interval computation for depth 12, residue 1785. -/ +theorem bounds_12_1785 : exactInterval 12 1785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1785 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1785) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1785 : oddCount 1785 12 = 5 ∧ acceleratedOrbit 12 1785 = 106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1785 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1785) = 3 ^ 5 * m + 106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1785.1, data_12_1785.2] + +/-- Complete interval computation for depth 12, residue 1786. -/ +theorem bounds_12_1786 : exactInterval 12 1786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1786 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1786) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1786 : oddCount 1786 12 = 6 ∧ acceleratedOrbit 12 1786 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1786 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1786) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1786.1, data_12_1786.2] + +/-- Complete interval computation for depth 12, residue 1787. -/ +theorem bounds_12_1787 : exactInterval 12 1787 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1787 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1787) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1787 : oddCount 1787 12 = 7 ∧ acceleratedOrbit 12 1787 = 955 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1787 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1787) = 3 ^ 7 * m + 955 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1787.1, data_12_1787.2] + +/-- Complete interval computation for depth 12, residue 1788. -/ +theorem bounds_12_1788 : exactInterval 12 1788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1788 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1788) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1788 : oddCount 1788 12 = 9 ∧ acceleratedOrbit 12 1788 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1788 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1788) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1788.1, data_12_1788.2] + +/-- Complete interval computation for depth 12, residue 1789. -/ +theorem bounds_12_1789 : exactInterval 12 1789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1789 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1789) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1789 : oddCount 1789 12 = 9 ∧ acceleratedOrbit 12 1789 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1789 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1789) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1789.1, data_12_1789.2] + +/-- Complete interval computation for depth 12, residue 1790. -/ +theorem bounds_12_1790 : exactInterval 12 1790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1790 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1790) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1790 : oddCount 1790 12 = 9 ∧ acceleratedOrbit 12 1790 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1790 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1790) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1790.1, data_12_1790.2] + +/-- Complete interval computation for depth 12, residue 1791. -/ +theorem bounds_12_1791 : exactInterval 12 1791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1791 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1791) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1791 : oddCount 1791 12 = 10 ∧ acceleratedOrbit 12 1791 = 25834 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1791 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1791) = 3 ^ 10 * m + 25834 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1791.1, data_12_1791.2] + +/-- Complete interval computation for depth 12, residue 1792. -/ +theorem bounds_12_1792 : exactInterval 12 1792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1792 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1792) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1792 : oddCount 1792 12 = 3 ∧ acceleratedOrbit 12 1792 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1792 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1792) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1792.1, data_12_1792.2] + +/-- Complete interval computation for depth 12, residue 1793. -/ +theorem bounds_12_1793 : exactInterval 12 1793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1793 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1793) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1793 : oddCount 1793 12 = 5 ∧ acceleratedOrbit 12 1793 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1793 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1793) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1793.1, data_12_1793.2] + +/-- Complete interval computation for depth 12, residue 1794. -/ +theorem bounds_12_1794 : exactInterval 12 1794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1794 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1794) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1794 : oddCount 1794 12 = 7 ∧ acceleratedOrbit 12 1794 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1794 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1794) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1794.1, data_12_1794.2] + +/-- Complete interval computation for depth 12, residue 1795. -/ +theorem bounds_12_1795 : exactInterval 12 1795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1795 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1795) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1795 : oddCount 1795 12 = 7 ∧ acceleratedOrbit 12 1795 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1795 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1795) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1795.1, data_12_1795.2] + +/-- Complete interval computation for depth 12, residue 1796. -/ +theorem bounds_12_1796 : exactInterval 12 1796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1796 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1796) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1796 : oddCount 1796 12 = 6 ∧ acceleratedOrbit 12 1796 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1796 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1796) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1796.1, data_12_1796.2] + +end Collatz.Research.StoppingAtlas.Batch0317 From bb38de1fd085eb1ee45b1c1027e1bb22395dee89 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:41 +0530 Subject: [PATCH 0318/1001] proof: certify atlas Batch0318 (12:1797 to 12:1811) --- Collatz/Research/StoppingAtlas/Batch0318.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0318.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0318.lean b/Collatz/Research/StoppingAtlas/Batch0318.lean new file mode 100644 index 00000000..19f819e4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0318.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0318 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1797. -/ +theorem bounds_12_1797 : exactInterval 12 1797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1797 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1797) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1797 : oddCount 1797 12 = 6 ∧ acceleratedOrbit 12 1797 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1797 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1797) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1797.1, data_12_1797.2] + +/-- Complete interval computation for depth 12, residue 1798. -/ +theorem bounds_12_1798 : exactInterval 12 1798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1798 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1798) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1798 : oddCount 1798 12 = 6 ∧ acceleratedOrbit 12 1798 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1798 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1798) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1798.1, data_12_1798.2] + +/-- Complete interval computation for depth 12, residue 1799. -/ +theorem bounds_12_1799 : exactInterval 12 1799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1799 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1799) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1799 : oddCount 1799 12 = 7 ∧ acceleratedOrbit 12 1799 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1799 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1799) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1799.1, data_12_1799.2] + +/-- Complete interval computation for depth 12, residue 1800. -/ +theorem bounds_12_1800 : exactInterval 12 1800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1800 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1800) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1800 : oddCount 1800 12 = 7 ∧ acceleratedOrbit 12 1800 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1800 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1800) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1800.1, data_12_1800.2] + +/-- Complete interval computation for depth 12, residue 1801. -/ +theorem bounds_12_1801 : exactInterval 12 1801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1801 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1801) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1801 : oddCount 1801 12 = 9 ∧ acceleratedOrbit 12 1801 = 8666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1801 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1801) = 3 ^ 9 * m + 8666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1801.1, data_12_1801.2] + +/-- Complete interval computation for depth 12, residue 1802. -/ +theorem bounds_12_1802 : exactInterval 12 1802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1802 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1802) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1802 : oddCount 1802 12 = 7 ∧ acceleratedOrbit 12 1802 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1802 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1802) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1802.1, data_12_1802.2] + +/-- Complete interval computation for depth 12, residue 1803. -/ +theorem bounds_12_1803 : exactInterval 12 1803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1803 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1803) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1803 : oddCount 1803 12 = 7 ∧ acceleratedOrbit 12 1803 = 965 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1803 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1803) = 3 ^ 7 * m + 965 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1803.1, data_12_1803.2] + +/-- Complete interval computation for depth 12, residue 1804. -/ +theorem bounds_12_1804 : exactInterval 12 1804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1804 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1804) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1804 : oddCount 1804 12 = 7 ∧ acceleratedOrbit 12 1804 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1804 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1804) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1804.1, data_12_1804.2] + +/-- Complete interval computation for depth 12, residue 1805. -/ +theorem bounds_12_1805 : exactInterval 12 1805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1805 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1805) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1805 : oddCount 1805 12 = 7 ∧ acceleratedOrbit 12 1805 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1805 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1805) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1805.1, data_12_1805.2] + +/-- Complete interval computation for depth 12, residue 1806. -/ +theorem bounds_12_1806 : exactInterval 12 1806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1806 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1806) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1806 : oddCount 1806 12 = 6 ∧ acceleratedOrbit 12 1806 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1806 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1806) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1806.1, data_12_1806.2] + +/-- Complete interval computation for depth 12, residue 1807. -/ +theorem bounds_12_1807 : exactInterval 12 1807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1807 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1807) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1807 : oddCount 1807 12 = 6 ∧ acceleratedOrbit 12 1807 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1807 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1807) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1807.1, data_12_1807.2] + +/-- Complete interval computation for depth 12, residue 1808. -/ +theorem bounds_12_1808 : exactInterval 12 1808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1808 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1808) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1808 : oddCount 1808 12 = 2 ∧ acceleratedOrbit 12 1808 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1808 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1808) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1808.1, data_12_1808.2] + +/-- Complete interval computation for depth 12, residue 1809. -/ +theorem bounds_12_1809 : exactInterval 12 1809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1809 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1809) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1809 : oddCount 1809 12 = 7 ∧ acceleratedOrbit 12 1809 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1809 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1809) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1809.1, data_12_1809.2] + +/-- Complete interval computation for depth 12, residue 1810. -/ +theorem bounds_12_1810 : exactInterval 12 1810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1810 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1810) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1810 : oddCount 1810 12 = 8 ∧ acceleratedOrbit 12 1810 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1810 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1810) = 3 ^ 8 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1810.1, data_12_1810.2] + +/-- Complete interval computation for depth 12, residue 1811. -/ +theorem bounds_12_1811 : exactInterval 12 1811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1811 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1811) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1811 : oddCount 1811 12 = 8 ∧ acceleratedOrbit 12 1811 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1811 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1811) = 3 ^ 8 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1811.1, data_12_1811.2] + +end Collatz.Research.StoppingAtlas.Batch0318 From cc4e712ee3707b55679e4acda596925755b88701 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:41 +0530 Subject: [PATCH 0319/1001] proof: certify atlas Batch0319 (12:1812 to 12:1826) --- Collatz/Research/StoppingAtlas/Batch0319.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0319.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0319.lean b/Collatz/Research/StoppingAtlas/Batch0319.lean new file mode 100644 index 00000000..013e7da1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0319.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0319 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1812. -/ +theorem bounds_12_1812 : exactInterval 12 1812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1812 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1812) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1812 : oddCount 1812 12 = 2 ∧ acceleratedOrbit 12 1812 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1812 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1812) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1812.1, data_12_1812.2] + +/-- Complete interval computation for depth 12, residue 1813. -/ +theorem bounds_12_1813 : exactInterval 12 1813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1813 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1813) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1813 : oddCount 1813 12 = 2 ∧ acceleratedOrbit 12 1813 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1813 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1813) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1813.1, data_12_1813.2] + +/-- Complete interval computation for depth 12, residue 1814. -/ +theorem bounds_12_1814 : exactInterval 12 1814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1814 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1814) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1814 : oddCount 1814 12 = 8 ∧ acceleratedOrbit 12 1814 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1814 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1814) = 3 ^ 8 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1814.1, data_12_1814.2] + +/-- Complete interval computation for depth 12, residue 1815. -/ +theorem bounds_12_1815 : exactInterval 12 1815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1815 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1815) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1815 : oddCount 1815 12 = 8 ∧ acceleratedOrbit 12 1815 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1815 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1815) = 3 ^ 8 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1815.1, data_12_1815.2] + +/-- Complete interval computation for depth 12, residue 1816. -/ +theorem bounds_12_1816 : exactInterval 12 1816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1816 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1816) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1816 : oddCount 1816 12 = 2 ∧ acceleratedOrbit 12 1816 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1816 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1816) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1816.1, data_12_1816.2] + +/-- Complete interval computation for depth 12, residue 1817. -/ +theorem bounds_12_1817 : exactInterval 12 1817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1817 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1817) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1817 : oddCount 1817 12 = 9 ∧ acceleratedOrbit 12 1817 = 8747 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1817 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1817) = 3 ^ 9 * m + 8747 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1817.1, data_12_1817.2] + +/-- Complete interval computation for depth 12, residue 1818. -/ +theorem bounds_12_1818 : exactInterval 12 1818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1818 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1818) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1818 : oddCount 1818 12 = 2 ∧ acceleratedOrbit 12 1818 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1818 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1818) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1818.1, data_12_1818.2] + +/-- Complete interval computation for depth 12, residue 1819. -/ +theorem bounds_12_1819 : exactInterval 12 1819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1819 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1819) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1819 : oddCount 1819 12 = 11 ∧ acceleratedOrbit 12 1819 = 78731 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1819 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1819) = 3 ^ 11 * m + 78731 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1819.1, data_12_1819.2] + +/-- Complete interval computation for depth 12, residue 1820. -/ +theorem bounds_12_1820 : exactInterval 12 1820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1820 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1820) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1820 : oddCount 1820 12 = 6 ∧ acceleratedOrbit 12 1820 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1820 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1820) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1820.1, data_12_1820.2] + +/-- Complete interval computation for depth 12, residue 1821. -/ +theorem bounds_12_1821 : exactInterval 12 1821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1821 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1821) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1821 : oddCount 1821 12 = 6 ∧ acceleratedOrbit 12 1821 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1821 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1821) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1821.1, data_12_1821.2] + +/-- Complete interval computation for depth 12, residue 1822. -/ +theorem bounds_12_1822 : exactInterval 12 1822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1822 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1822) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1822 : oddCount 1822 12 = 6 ∧ acceleratedOrbit 12 1822 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1822 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1822) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1822.1, data_12_1822.2] + +/-- Complete interval computation for depth 12, residue 1823. -/ +theorem bounds_12_1823 : exactInterval 12 1823 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1823 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1823) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1823 : oddCount 1823 12 = 7 ∧ acceleratedOrbit 12 1823 = 974 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1823 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1823) = 3 ^ 7 * m + 974 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1823.1, data_12_1823.2] + +/-- Complete interval computation for depth 12, residue 1824. -/ +theorem bounds_12_1824 : exactInterval 12 1824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1824 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1824) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1824 : oddCount 1824 12 = 4 ∧ acceleratedOrbit 12 1824 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1824 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1824) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1824.1, data_12_1824.2] + +/-- Complete interval computation for depth 12, residue 1825. -/ +theorem bounds_12_1825 : exactInterval 12 1825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1825 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1825) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1825 : oddCount 1825 12 = 6 ∧ acceleratedOrbit 12 1825 = 326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1825 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1825) = 3 ^ 6 * m + 326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1825.1, data_12_1825.2] + +/-- Complete interval computation for depth 12, residue 1826. -/ +theorem bounds_12_1826 : exactInterval 12 1826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1826 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1826) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1826 : oddCount 1826 12 = 5 ∧ acceleratedOrbit 12 1826 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1826 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1826) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1826.1, data_12_1826.2] + +end Collatz.Research.StoppingAtlas.Batch0319 From c7238a1072ed6945cb4feaf713bc9321a78e3ebe Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:41 +0530 Subject: [PATCH 0320/1001] proof: certify atlas Batch0320 (12:1827 to 12:1842) --- Collatz/Research/StoppingAtlas/Batch0320.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0320.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0320.lean b/Collatz/Research/StoppingAtlas/Batch0320.lean new file mode 100644 index 00000000..deb4d7e2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0320.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0320 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1827. -/ +theorem bounds_12_1827 : exactInterval 12 1827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1827 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1827) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1827 : oddCount 1827 12 = 5 ∧ acceleratedOrbit 12 1827 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1827 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1827) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1827.1, data_12_1827.2] + +/-- Complete interval computation for depth 12, residue 1828. -/ +theorem bounds_12_1828 : exactInterval 12 1828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1828 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1828) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1828 : oddCount 1828 12 = 5 ∧ acceleratedOrbit 12 1828 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1828 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1828) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1828.1, data_12_1828.2] + +/-- Complete interval computation for depth 12, residue 1829. -/ +theorem bounds_12_1829 : exactInterval 12 1829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1829 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1829) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1829 : oddCount 1829 12 = 5 ∧ acceleratedOrbit 12 1829 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1829 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1829) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1829.1, data_12_1829.2] + +/-- Complete interval computation for depth 12, residue 1830. -/ +theorem bounds_12_1830 : exactInterval 12 1830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1830 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1830) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1830 : oddCount 1830 12 = 5 ∧ acceleratedOrbit 12 1830 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1830 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1830) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1830.1, data_12_1830.2] + +/-- Complete interval computation for depth 12, residue 1831. -/ +theorem bounds_12_1831 : exactInterval 12 1831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1831 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1831) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1831 : oddCount 1831 12 = 8 ∧ acceleratedOrbit 12 1831 = 2936 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1831 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1831) = 3 ^ 8 * m + 2936 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1831.1, data_12_1831.2] + +/-- Complete interval computation for depth 12, residue 1832. -/ +theorem bounds_12_1832 : exactInterval 12 1832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1832 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1832) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1832 : oddCount 1832 12 = 4 ∧ acceleratedOrbit 12 1832 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1832 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1832) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1832.1, data_12_1832.2] + +/-- Complete interval computation for depth 12, residue 1833. -/ +theorem bounds_12_1833 : exactInterval 12 1833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1833 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1833) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1833 : oddCount 1833 12 = 7 ∧ acceleratedOrbit 12 1833 = 980 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1833 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1833) = 3 ^ 7 * m + 980 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1833.1, data_12_1833.2] + +/-- Complete interval computation for depth 12, residue 1834. -/ +theorem bounds_12_1834 : exactInterval 12 1834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1834 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1834) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1834 : oddCount 1834 12 = 4 ∧ acceleratedOrbit 12 1834 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1834 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1834) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1834.1, data_12_1834.2] + +/-- Complete interval computation for depth 12, residue 1835. -/ +theorem bounds_12_1835 : exactInterval 12 1835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1835 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1835) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1835 : oddCount 1835 12 = 5 ∧ acceleratedOrbit 12 1835 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1835 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1835) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1835.1, data_12_1835.2] + +/-- Complete interval computation for depth 12, residue 1836. -/ +theorem bounds_12_1836 : exactInterval 12 1836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1836 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1836) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1836 : oddCount 1836 12 = 5 ∧ acceleratedOrbit 12 1836 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1836 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1836) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1836.1, data_12_1836.2] + +/-- Complete interval computation for depth 12, residue 1837. -/ +theorem bounds_12_1837 : exactInterval 12 1837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1837 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1837) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1837 : oddCount 1837 12 = 5 ∧ acceleratedOrbit 12 1837 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1837 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1837) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1837.1, data_12_1837.2] + +/-- Complete interval computation for depth 12, residue 1838. -/ +theorem bounds_12_1838 : exactInterval 12 1838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1838 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1838) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1838 : oddCount 1838 12 = 5 ∧ acceleratedOrbit 12 1838 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1838 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1838) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1838.1, data_12_1838.2] + +/-- Complete interval computation for depth 12, residue 1839. -/ +theorem bounds_12_1839 : exactInterval 12 1839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1839 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1839) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1839 : oddCount 1839 12 = 7 ∧ acceleratedOrbit 12 1839 = 983 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1839 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1839) = 3 ^ 7 * m + 983 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1839.1, data_12_1839.2] + +/-- Complete interval computation for depth 12, residue 1840. -/ +theorem bounds_12_1840 : exactInterval 12 1840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1840 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1840) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1840 : oddCount 1840 12 = 4 ∧ acceleratedOrbit 12 1840 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1840 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1840) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1840.1, data_12_1840.2] + +/-- Complete interval computation for depth 12, residue 1841. -/ +theorem bounds_12_1841 : exactInterval 12 1841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1841 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1841) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1841 : oddCount 1841 12 = 5 ∧ acceleratedOrbit 12 1841 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1841 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1841) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1841.1, data_12_1841.2] + +/-- Complete interval computation for depth 12, residue 1842. -/ +theorem bounds_12_1842 : exactInterval 12 1842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1842 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1842) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1842 : oddCount 1842 12 = 5 ∧ acceleratedOrbit 12 1842 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1842 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1842) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1842.1, data_12_1842.2] + +end Collatz.Research.StoppingAtlas.Batch0320 From 3351e05fc0135b4b0de845611c6fa90cc7e147be Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:41 +0530 Subject: [PATCH 0321/1001] proof: certify atlas Batch0321 (12:1843 to 12:1857) --- Collatz/Research/StoppingAtlas/Batch0321.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0321.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0321.lean b/Collatz/Research/StoppingAtlas/Batch0321.lean new file mode 100644 index 00000000..e4b34a8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0321.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0321 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1843. -/ +theorem bounds_12_1843 : exactInterval 12 1843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1843 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1843) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1843 : oddCount 1843 12 = 5 ∧ acceleratedOrbit 12 1843 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1843 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1843) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1843.1, data_12_1843.2] + +/-- Complete interval computation for depth 12, residue 1844. -/ +theorem bounds_12_1844 : exactInterval 12 1844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1844 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1844) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1844 : oddCount 1844 12 = 4 ∧ acceleratedOrbit 12 1844 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1844 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1844) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1844.1, data_12_1844.2] + +/-- Complete interval computation for depth 12, residue 1845. -/ +theorem bounds_12_1845 : exactInterval 12 1845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1845 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1845) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1845 : oddCount 1845 12 = 4 ∧ acceleratedOrbit 12 1845 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1845 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1845) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1845.1, data_12_1845.2] + +/-- Complete interval computation for depth 12, residue 1846. -/ +theorem bounds_12_1846 : exactInterval 12 1846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1846 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1846) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1846 : oddCount 1846 12 = 6 ∧ acceleratedOrbit 12 1846 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1846 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1846) = 3 ^ 6 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1846.1, data_12_1846.2] + +/-- Complete interval computation for depth 12, residue 1847. -/ +theorem bounds_12_1847 : exactInterval 12 1847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1847 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1847) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1847 : oddCount 1847 12 = 6 ∧ acceleratedOrbit 12 1847 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1847 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1847) = 3 ^ 6 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1847.1, data_12_1847.2] + +/-- Complete interval computation for depth 12, residue 1848. -/ +theorem bounds_12_1848 : exactInterval 12 1848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1848 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1848) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1848 : oddCount 1848 12 = 7 ∧ acceleratedOrbit 12 1848 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1848 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1848) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1848.1, data_12_1848.2] + +/-- Complete interval computation for depth 12, residue 1849. -/ +theorem bounds_12_1849 : exactInterval 12 1849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1849 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1849) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1849 : oddCount 1849 12 = 7 ∧ acceleratedOrbit 12 1849 = 989 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1849 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1849) = 3 ^ 7 * m + 989 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1849.1, data_12_1849.2] + +/-- Complete interval computation for depth 12, residue 1850. -/ +theorem bounds_12_1850 : exactInterval 12 1850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1850 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1850) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1850 : oddCount 1850 12 = 7 ∧ acceleratedOrbit 12 1850 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1850 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1850) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1850.1, data_12_1850.2] + +/-- Complete interval computation for depth 12, residue 1851. -/ +theorem bounds_12_1851 : exactInterval 12 1851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1851 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1851) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1851 : oddCount 1851 12 = 5 ∧ acceleratedOrbit 12 1851 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1851 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1851) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1851.1, data_12_1851.2] + +/-- Complete interval computation for depth 12, residue 1852. -/ +theorem bounds_12_1852 : exactInterval 12 1852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1852 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1852) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1852 : oddCount 1852 12 = 7 ∧ acceleratedOrbit 12 1852 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1852 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1852) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1852.1, data_12_1852.2] + +/-- Complete interval computation for depth 12, residue 1853. -/ +theorem bounds_12_1853 : exactInterval 12 1853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1853 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1853) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1853 : oddCount 1853 12 = 7 ∧ acceleratedOrbit 12 1853 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1853 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1853) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1853.1, data_12_1853.2] + +/-- Complete interval computation for depth 12, residue 1854. -/ +theorem bounds_12_1854 : exactInterval 12 1854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1854 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1854) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1854 : oddCount 1854 12 = 7 ∧ acceleratedOrbit 12 1854 = 991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1854 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1854) = 3 ^ 7 * m + 991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1854.1, data_12_1854.2] + +/-- Complete interval computation for depth 12, residue 1855. -/ +theorem bounds_12_1855 : exactInterval 12 1855 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1855 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1855) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1855 : oddCount 1855 12 = 7 ∧ acceleratedOrbit 12 1855 = 991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1855 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1855) = 3 ^ 7 * m + 991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1855.1, data_12_1855.2] + +/-- Complete interval computation for depth 12, residue 1856. -/ +theorem bounds_12_1856 : exactInterval 12 1856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1856 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1856) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1856 : oddCount 1856 12 = 3 ∧ acceleratedOrbit 12 1856 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1856 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1856) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1856.1, data_12_1856.2] + +/-- Complete interval computation for depth 12, residue 1857. -/ +theorem bounds_12_1857 : exactInterval 12 1857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1857 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1857) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1857 : oddCount 1857 12 = 4 ∧ acceleratedOrbit 12 1857 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1857 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1857) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1857.1, data_12_1857.2] + +end Collatz.Research.StoppingAtlas.Batch0321 From 1d1254d141b4446584a323af96a7676940f07a64 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:42 +0530 Subject: [PATCH 0322/1001] proof: certify atlas Batch0322 (12:1858 to 12:1872) --- Collatz/Research/StoppingAtlas/Batch0322.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0322.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0322.lean b/Collatz/Research/StoppingAtlas/Batch0322.lean new file mode 100644 index 00000000..fd0e240c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0322.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0322 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1858. -/ +theorem bounds_12_1858 : exactInterval 12 1858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1858 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1858) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1858 : oddCount 1858 12 = 6 ∧ acceleratedOrbit 12 1858 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1858 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1858) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1858.1, data_12_1858.2] + +/-- Complete interval computation for depth 12, residue 1859. -/ +theorem bounds_12_1859 : exactInterval 12 1859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1859 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1859) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1859 : oddCount 1859 12 = 6 ∧ acceleratedOrbit 12 1859 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1859 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1859) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1859.1, data_12_1859.2] + +/-- Complete interval computation for depth 12, residue 1860. -/ +theorem bounds_12_1860 : exactInterval 12 1860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1860 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1860) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1860 : oddCount 1860 12 = 4 ∧ acceleratedOrbit 12 1860 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1860 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1860) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1860.1, data_12_1860.2] + +/-- Complete interval computation for depth 12, residue 1861. -/ +theorem bounds_12_1861 : exactInterval 12 1861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1861 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1861) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1861 : oddCount 1861 12 = 4 ∧ acceleratedOrbit 12 1861 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1861 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1861) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1861.1, data_12_1861.2] + +/-- Complete interval computation for depth 12, residue 1862. -/ +theorem bounds_12_1862 : exactInterval 12 1862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1862 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1862) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1862 : oddCount 1862 12 = 4 ∧ acceleratedOrbit 12 1862 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1862 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1862) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1862.1, data_12_1862.2] + +/-- Complete interval computation for depth 12, residue 1863. -/ +theorem bounds_12_1863 : exactInterval 12 1863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1863 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1863) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1863 : oddCount 1863 12 = 8 ∧ acceleratedOrbit 12 1863 = 2987 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1863 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1863) = 3 ^ 8 * m + 2987 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1863.1, data_12_1863.2] + +/-- Complete interval computation for depth 12, residue 1864. -/ +theorem bounds_12_1864 : exactInterval 12 1864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1864 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1864) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1864 : oddCount 1864 12 = 6 ∧ acceleratedOrbit 12 1864 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1864 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1864) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1864.1, data_12_1864.2] + +/-- Complete interval computation for depth 12, residue 1865. -/ +theorem bounds_12_1865 : exactInterval 12 1865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1865 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1865) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1865 : oddCount 1865 12 = 7 ∧ acceleratedOrbit 12 1865 = 998 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1865 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1865) = 3 ^ 7 * m + 998 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1865.1, data_12_1865.2] + +/-- Complete interval computation for depth 12, residue 1866. -/ +theorem bounds_12_1866 : exactInterval 12 1866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1866 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1866) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1866 : oddCount 1866 12 = 6 ∧ acceleratedOrbit 12 1866 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1866 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1866) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1866.1, data_12_1866.2] + +/-- Complete interval computation for depth 12, residue 1867. -/ +theorem bounds_12_1867 : exactInterval 12 1867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1867 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1867) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1867 : oddCount 1867 12 = 4 ∧ acceleratedOrbit 12 1867 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1867 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1867) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1867.1, data_12_1867.2] + +/-- Complete interval computation for depth 12, residue 1868. -/ +theorem bounds_12_1868 : exactInterval 12 1868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1868 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1868) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1868 : oddCount 1868 12 = 6 ∧ acceleratedOrbit 12 1868 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1868 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1868) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1868.1, data_12_1868.2] + +/-- Complete interval computation for depth 12, residue 1869. -/ +theorem bounds_12_1869 : exactInterval 12 1869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1869 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1869) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1869 : oddCount 1869 12 = 6 ∧ acceleratedOrbit 12 1869 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1869 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1869) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1869.1, data_12_1869.2] + +/-- Complete interval computation for depth 12, residue 1870. -/ +theorem bounds_12_1870 : exactInterval 12 1870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1870 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1870) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1870 : oddCount 1870 12 = 7 ∧ acceleratedOrbit 12 1870 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1870 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1870) = 3 ^ 7 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1870.1, data_12_1870.2] + +/-- Complete interval computation for depth 12, residue 1871. -/ +theorem bounds_12_1871 : exactInterval 12 1871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1871 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1871) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1871 : oddCount 1871 12 = 7 ∧ acceleratedOrbit 12 1871 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1871 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1871) = 3 ^ 7 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1871.1, data_12_1871.2] + +/-- Complete interval computation for depth 12, residue 1872. -/ +theorem bounds_12_1872 : exactInterval 12 1872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1872 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1872) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1872 : oddCount 1872 12 = 3 ∧ acceleratedOrbit 12 1872 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1872 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1872) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1872.1, data_12_1872.2] + +end Collatz.Research.StoppingAtlas.Batch0322 From 8816e865e214b7cfc9d57da4bb0fbc688ab91239 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:42 +0530 Subject: [PATCH 0323/1001] proof: certify atlas Batch0323 (12:1873 to 12:1888) --- Collatz/Research/StoppingAtlas/Batch0323.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0323.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0323.lean b/Collatz/Research/StoppingAtlas/Batch0323.lean new file mode 100644 index 00000000..0e345f47 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0323.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0323 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1873. -/ +theorem bounds_12_1873 : exactInterval 12 1873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1873 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1873) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1873 : oddCount 1873 12 = 6 ∧ acceleratedOrbit 12 1873 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1873 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1873) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1873.1, data_12_1873.2] + +/-- Complete interval computation for depth 12, residue 1874. -/ +theorem bounds_12_1874 : exactInterval 12 1874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1874 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1874) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1874 : oddCount 1874 12 = 8 ∧ acceleratedOrbit 12 1874 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1874 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1874) = 3 ^ 8 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1874.1, data_12_1874.2] + +/-- Complete interval computation for depth 12, residue 1875. -/ +theorem bounds_12_1875 : exactInterval 12 1875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1875 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1875) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1875 : oddCount 1875 12 = 8 ∧ acceleratedOrbit 12 1875 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1875 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1875) = 3 ^ 8 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1875.1, data_12_1875.2] + +/-- Complete interval computation for depth 12, residue 1876. -/ +theorem bounds_12_1876 : exactInterval 12 1876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1876 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1876) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1876 : oddCount 1876 12 = 3 ∧ acceleratedOrbit 12 1876 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1876 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1876) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1876.1, data_12_1876.2] + +/-- Complete interval computation for depth 12, residue 1877. -/ +theorem bounds_12_1877 : exactInterval 12 1877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1877 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1877) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1877 : oddCount 1877 12 = 3 ∧ acceleratedOrbit 12 1877 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1877 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1877) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1877.1, data_12_1877.2] + +/-- Complete interval computation for depth 12, residue 1878. -/ +theorem bounds_12_1878 : exactInterval 12 1878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1878 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1878) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1878 : oddCount 1878 12 = 6 ∧ acceleratedOrbit 12 1878 = 335 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1878 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1878) = 3 ^ 6 * m + 335 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1878.1, data_12_1878.2] + +/-- Complete interval computation for depth 12, residue 1879. -/ +theorem bounds_12_1879 : exactInterval 12 1879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1879 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1879) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1879 : oddCount 1879 12 = 6 ∧ acceleratedOrbit 12 1879 = 335 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1879 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1879) = 3 ^ 6 * m + 335 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1879.1, data_12_1879.2] + +/-- Complete interval computation for depth 12, residue 1880. -/ +theorem bounds_12_1880 : exactInterval 12 1880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1880 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1880) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1880 : oddCount 1880 12 = 6 ∧ acceleratedOrbit 12 1880 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1880 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1880) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1880.1, data_12_1880.2] + +/-- Complete interval computation for depth 12, residue 1881. -/ +theorem bounds_12_1881 : exactInterval 12 1881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1881 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1881) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1881 : oddCount 1881 12 = 5 ∧ acceleratedOrbit 12 1881 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1881 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1881) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1881.1, data_12_1881.2] + +/-- Complete interval computation for depth 12, residue 1882. -/ +theorem bounds_12_1882 : exactInterval 12 1882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1882 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1882) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1882 : oddCount 1882 12 = 6 ∧ acceleratedOrbit 12 1882 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1882 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1882) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1882.1, data_12_1882.2] + +/-- Complete interval computation for depth 12, residue 1883. -/ +theorem bounds_12_1883 : exactInterval 12 1883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1883 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1883) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1883 : oddCount 1883 12 = 8 ∧ acceleratedOrbit 12 1883 = 3019 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1883 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1883) = 3 ^ 8 * m + 3019 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1883.1, data_12_1883.2] + +/-- Complete interval computation for depth 12, residue 1884. -/ +theorem bounds_12_1884 : exactInterval 12 1884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1884 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1884) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1884 : oddCount 1884 12 = 6 ∧ acceleratedOrbit 12 1884 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1884 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1884) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1884.1, data_12_1884.2] + +/-- Complete interval computation for depth 12, residue 1885. -/ +theorem bounds_12_1885 : exactInterval 12 1885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1885 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1885) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1885 : oddCount 1885 12 = 6 ∧ acceleratedOrbit 12 1885 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1885 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1885) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1885.1, data_12_1885.2] + +/-- Complete interval computation for depth 12, residue 1886. -/ +theorem bounds_12_1886 : exactInterval 12 1886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1886 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1886) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1886 : oddCount 1886 12 = 5 ∧ acceleratedOrbit 12 1886 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1886 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1886) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1886.1, data_12_1886.2] + +/-- Complete interval computation for depth 12, residue 1887. -/ +theorem bounds_12_1887 : exactInterval 12 1887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1887 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1887) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1887 : oddCount 1887 12 = 5 ∧ acceleratedOrbit 12 1887 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1887 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1887) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1887.1, data_12_1887.2] + +/-- Complete interval computation for depth 12, residue 1888. -/ +theorem bounds_12_1888 : exactInterval 12 1888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1888 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1888) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1888 : oddCount 1888 12 = 4 ∧ acceleratedOrbit 12 1888 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1888 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1888) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1888.1, data_12_1888.2] + +end Collatz.Research.StoppingAtlas.Batch0323 From 131082b039940c74ea86d7a63be924293bfc50b8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:42 +0530 Subject: [PATCH 0324/1001] proof: certify atlas Batch0324 (12:1889 to 12:1903) --- Collatz/Research/StoppingAtlas/Batch0324.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0324.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0324.lean b/Collatz/Research/StoppingAtlas/Batch0324.lean new file mode 100644 index 00000000..4801422c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0324.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0324 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1889. -/ +theorem bounds_12_1889 : exactInterval 12 1889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1889 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1889) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1889 : oddCount 1889 12 = 7 ∧ acceleratedOrbit 12 1889 = 1010 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1889 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1889) = 3 ^ 7 * m + 1010 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1889.1, data_12_1889.2] + +/-- Complete interval computation for depth 12, residue 1890. -/ +theorem bounds_12_1890 : exactInterval 12 1890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1890 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1890) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1890 : oddCount 1890 12 = 4 ∧ acceleratedOrbit 12 1890 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1890 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1890) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1890.1, data_12_1890.2] + +/-- Complete interval computation for depth 12, residue 1891. -/ +theorem bounds_12_1891 : exactInterval 12 1891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1891 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1891) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1891 : oddCount 1891 12 = 4 ∧ acceleratedOrbit 12 1891 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1891 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1891) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1891.1, data_12_1891.2] + +/-- Complete interval computation for depth 12, residue 1892. -/ +theorem bounds_12_1892 : exactInterval 12 1892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1892 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1892) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1892 : oddCount 1892 12 = 4 ∧ acceleratedOrbit 12 1892 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1892 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1892) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1892.1, data_12_1892.2] + +/-- Complete interval computation for depth 12, residue 1893. -/ +theorem bounds_12_1893 : exactInterval 12 1893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1893 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1893) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1893 : oddCount 1893 12 = 4 ∧ acceleratedOrbit 12 1893 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1893 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1893) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1893.1, data_12_1893.2] + +/-- Complete interval computation for depth 12, residue 1894. -/ +theorem bounds_12_1894 : exactInterval 12 1894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1894 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1894) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1894 : oddCount 1894 12 = 4 ∧ acceleratedOrbit 12 1894 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1894 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1894) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1894.1, data_12_1894.2] + +/-- Complete interval computation for depth 12, residue 1895. -/ +theorem bounds_12_1895 : exactInterval 12 1895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1895 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1895) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1895 : oddCount 1895 12 = 10 ∧ acceleratedOrbit 12 1895 = 27337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1895 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1895) = 3 ^ 10 * m + 27337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1895.1, data_12_1895.2] + +/-- Complete interval computation for depth 12, residue 1896. -/ +theorem bounds_12_1896 : exactInterval 12 1896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1896 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1896) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1896 : oddCount 1896 12 = 4 ∧ acceleratedOrbit 12 1896 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1896 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1896) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1896.1, data_12_1896.2] + +/-- Complete interval computation for depth 12, residue 1897. -/ +theorem bounds_12_1897 : exactInterval 12 1897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1897 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1897) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1897 : oddCount 1897 12 = 6 ∧ acceleratedOrbit 12 1897 = 338 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1897 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1897) = 3 ^ 6 * m + 338 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1897.1, data_12_1897.2] + +/-- Complete interval computation for depth 12, residue 1898. -/ +theorem bounds_12_1898 : exactInterval 12 1898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1898 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1898) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1898 : oddCount 1898 12 = 4 ∧ acceleratedOrbit 12 1898 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1898 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1898) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1898.1, data_12_1898.2] + +/-- Complete interval computation for depth 12, residue 1899. -/ +theorem bounds_12_1899 : exactInterval 12 1899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1899 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1899) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1899 : oddCount 1899 12 = 7 ∧ acceleratedOrbit 12 1899 = 1016 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1899 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1899) = 3 ^ 7 * m + 1016 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1899.1, data_12_1899.2] + +/-- Complete interval computation for depth 12, residue 1900. -/ +theorem bounds_12_1900 : exactInterval 12 1900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1900 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1900) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1900 : oddCount 1900 12 = 5 ∧ acceleratedOrbit 12 1900 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1900 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1900) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1900.1, data_12_1900.2] + +/-- Complete interval computation for depth 12, residue 1901. -/ +theorem bounds_12_1901 : exactInterval 12 1901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1901 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1901) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1901 : oddCount 1901 12 = 5 ∧ acceleratedOrbit 12 1901 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1901 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1901) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1901.1, data_12_1901.2] + +/-- Complete interval computation for depth 12, residue 1902. -/ +theorem bounds_12_1902 : exactInterval 12 1902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1902 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1902) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1902 : oddCount 1902 12 = 5 ∧ acceleratedOrbit 12 1902 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1902 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1902) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1902.1, data_12_1902.2] + +/-- Complete interval computation for depth 12, residue 1903. -/ +theorem bounds_12_1903 : exactInterval 12 1903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1903 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1903) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1903 : oddCount 1903 12 = 9 ∧ acceleratedOrbit 12 1903 = 9152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1903 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1903) = 3 ^ 9 * m + 9152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1903.1, data_12_1903.2] + +end Collatz.Research.StoppingAtlas.Batch0324 From 9f1554c4f8fc1c69cd4ec40116f69e0a387037a1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:43 +0530 Subject: [PATCH 0325/1001] proof: certify atlas Batch0325 (12:1904 to 12:1919) --- Collatz/Research/StoppingAtlas/Batch0325.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0325.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0325.lean b/Collatz/Research/StoppingAtlas/Batch0325.lean new file mode 100644 index 00000000..576a5864 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0325.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0325 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1904. -/ +theorem bounds_12_1904 : exactInterval 12 1904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1904 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1904) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1904 : oddCount 1904 12 = 4 ∧ acceleratedOrbit 12 1904 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1904 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1904) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1904.1, data_12_1904.2] + +/-- Complete interval computation for depth 12, residue 1905. -/ +theorem bounds_12_1905 : exactInterval 12 1905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1905 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1905) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1905 : oddCount 1905 12 = 4 ∧ acceleratedOrbit 12 1905 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1905 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1905) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1905.1, data_12_1905.2] + +/-- Complete interval computation for depth 12, residue 1906. -/ +theorem bounds_12_1906 : exactInterval 12 1906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1906 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1906) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1906 : oddCount 1906 12 = 6 ∧ acceleratedOrbit 12 1906 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1906 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1906) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1906.1, data_12_1906.2] + +/-- Complete interval computation for depth 12, residue 1907. -/ +theorem bounds_12_1907 : exactInterval 12 1907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1907 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1907) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1907 : oddCount 1907 12 = 6 ∧ acceleratedOrbit 12 1907 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1907 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1907) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1907.1, data_12_1907.2] + +/-- Complete interval computation for depth 12, residue 1908. -/ +theorem bounds_12_1908 : exactInterval 12 1908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1908 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1908) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1908 : oddCount 1908 12 = 4 ∧ acceleratedOrbit 12 1908 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1908 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1908) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1908.1, data_12_1908.2] + +/-- Complete interval computation for depth 12, residue 1909. -/ +theorem bounds_12_1909 : exactInterval 12 1909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1909 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1909) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1909 : oddCount 1909 12 = 4 ∧ acceleratedOrbit 12 1909 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1909 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1909) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1909.1, data_12_1909.2] + +/-- Complete interval computation for depth 12, residue 1910. -/ +theorem bounds_12_1910 : exactInterval 12 1910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1910 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1910) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1910 : oddCount 1910 12 = 6 ∧ acceleratedOrbit 12 1910 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1910 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1910) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1910.1, data_12_1910.2] + +/-- Complete interval computation for depth 12, residue 1911. -/ +theorem bounds_12_1911 : exactInterval 12 1911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1911 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1911) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1911 : oddCount 1911 12 = 6 ∧ acceleratedOrbit 12 1911 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1911 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1911) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1911.1, data_12_1911.2] + +/-- Complete interval computation for depth 12, residue 1912. -/ +theorem bounds_12_1912 : exactInterval 12 1912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1912 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1912) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1912 : oddCount 1912 12 = 8 ∧ acceleratedOrbit 12 1912 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1912 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1912) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1912.1, data_12_1912.2] + +/-- Complete interval computation for depth 12, residue 1913. -/ +theorem bounds_12_1913 : exactInterval 12 1913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1913 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1913) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1913 : oddCount 1913 12 = 8 ∧ acceleratedOrbit 12 1913 = 3068 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1913 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1913) = 3 ^ 8 * m + 3068 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1913.1, data_12_1913.2] + +/-- Complete interval computation for depth 12, residue 1914. -/ +theorem bounds_12_1914 : exactInterval 12 1914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1914 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1914) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1914 : oddCount 1914 12 = 8 ∧ acceleratedOrbit 12 1914 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1914 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1914) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1914.1, data_12_1914.2] + +/-- Complete interval computation for depth 12, residue 1915. -/ +theorem bounds_12_1915 : exactInterval 12 1915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1915 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1915) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1915 : oddCount 1915 12 = 8 ∧ acceleratedOrbit 12 1915 = 3071 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1915 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1915) = 3 ^ 8 * m + 3071 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1915.1, data_12_1915.2] + +/-- Complete interval computation for depth 12, residue 1916. -/ +theorem bounds_12_1916 : exactInterval 12 1916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1916 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1916) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1916 : oddCount 1916 12 = 8 ∧ acceleratedOrbit 12 1916 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1916 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1916) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1916.1, data_12_1916.2] + +/-- Complete interval computation for depth 12, residue 1917. -/ +theorem bounds_12_1917 : exactInterval 12 1917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1917 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1917) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1917 : oddCount 1917 12 = 8 ∧ acceleratedOrbit 12 1917 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1917 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1917) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1917.1, data_12_1917.2] + +/-- Complete interval computation for depth 12, residue 1918. -/ +theorem bounds_12_1918 : exactInterval 12 1918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1918 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1918) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1918 : oddCount 1918 12 = 9 ∧ acceleratedOrbit 12 1918 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1918 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1918) = 3 ^ 9 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1918.1, data_12_1918.2] + +/-- Complete interval computation for depth 12, residue 1919. -/ +theorem bounds_12_1919 : exactInterval 12 1919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1919 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1919) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1919 : oddCount 1919 12 = 9 ∧ acceleratedOrbit 12 1919 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1919 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1919) = 3 ^ 9 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1919.1, data_12_1919.2] + +end Collatz.Research.StoppingAtlas.Batch0325 From 461fe4f46fdfeb8a696184bb7887f51883585ef3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:43 +0530 Subject: [PATCH 0326/1001] proof: certify atlas Batch0326 (12:1920 to 12:1934) --- Collatz/Research/StoppingAtlas/Batch0326.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0326.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0326.lean b/Collatz/Research/StoppingAtlas/Batch0326.lean new file mode 100644 index 00000000..4035c732 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0326.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0326 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1920. -/ +theorem bounds_12_1920 : exactInterval 12 1920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1920 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1920) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1920 : oddCount 1920 12 = 4 ∧ acceleratedOrbit 12 1920 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1920 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1920) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1920.1, data_12_1920.2] + +/-- Complete interval computation for depth 12, residue 1921. -/ +theorem bounds_12_1921 : exactInterval 12 1921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1921 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1921) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1921 : oddCount 1921 12 = 7 ∧ acceleratedOrbit 12 1921 = 1028 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1921 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1921) = 3 ^ 7 * m + 1028 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1921.1, data_12_1921.2] + +/-- Complete interval computation for depth 12, residue 1922. -/ +theorem bounds_12_1922 : exactInterval 12 1922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1922 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1922) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1922 : oddCount 1922 12 = 6 ∧ acceleratedOrbit 12 1922 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1922 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1922) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1922.1, data_12_1922.2] + +/-- Complete interval computation for depth 12, residue 1923. -/ +theorem bounds_12_1923 : exactInterval 12 1923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1923 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1923) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1923 : oddCount 1923 12 = 6 ∧ acceleratedOrbit 12 1923 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1923 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1923) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1923.1, data_12_1923.2] + +/-- Complete interval computation for depth 12, residue 1924. -/ +theorem bounds_12_1924 : exactInterval 12 1924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1924 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1924) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1924 : oddCount 1924 12 = 6 ∧ acceleratedOrbit 12 1924 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1924 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1924) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1924.1, data_12_1924.2] + +/-- Complete interval computation for depth 12, residue 1925. -/ +theorem bounds_12_1925 : exactInterval 12 1925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1925 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1925) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1925 : oddCount 1925 12 = 6 ∧ acceleratedOrbit 12 1925 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1925 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1925) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1925.1, data_12_1925.2] + +/-- Complete interval computation for depth 12, residue 1926. -/ +theorem bounds_12_1926 : exactInterval 12 1926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1926 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1926) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1926 : oddCount 1926 12 = 6 ∧ acceleratedOrbit 12 1926 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1926 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1926) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1926.1, data_12_1926.2] + +/-- Complete interval computation for depth 12, residue 1927. -/ +theorem bounds_12_1927 : exactInterval 12 1927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1927 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1927) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1927 : oddCount 1927 12 = 6 ∧ acceleratedOrbit 12 1927 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1927 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1927) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1927.1, data_12_1927.2] + +/-- Complete interval computation for depth 12, residue 1928. -/ +theorem bounds_12_1928 : exactInterval 12 1928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1928 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1928) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1928 : oddCount 1928 12 = 3 ∧ acceleratedOrbit 12 1928 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1928 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1928) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1928.1, data_12_1928.2] + +/-- Complete interval computation for depth 12, residue 1929. -/ +theorem bounds_12_1929 : exactInterval 12 1929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1929 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1929) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1929 : oddCount 1929 12 = 7 ∧ acceleratedOrbit 12 1929 = 1031 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1929 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1929) = 3 ^ 7 * m + 1031 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1929.1, data_12_1929.2] + +/-- Complete interval computation for depth 12, residue 1930. -/ +theorem bounds_12_1930 : exactInterval 12 1930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1930 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1930) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1930 : oddCount 1930 12 = 3 ∧ acceleratedOrbit 12 1930 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1930 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1930) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1930.1, data_12_1930.2] + +/-- Complete interval computation for depth 12, residue 1931. -/ +theorem bounds_12_1931 : exactInterval 12 1931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1931 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1931) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1931 : oddCount 1931 12 = 8 ∧ acceleratedOrbit 12 1931 = 3098 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1931 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1931) = 3 ^ 8 * m + 3098 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1931.1, data_12_1931.2] + +/-- Complete interval computation for depth 12, residue 1932. -/ +theorem bounds_12_1932 : exactInterval 12 1932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1932 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1932) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1932 : oddCount 1932 12 = 3 ∧ acceleratedOrbit 12 1932 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1932 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1932) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1932.1, data_12_1932.2] + +/-- Complete interval computation for depth 12, residue 1933. -/ +theorem bounds_12_1933 : exactInterval 12 1933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1933 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1933) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1933 : oddCount 1933 12 = 3 ∧ acceleratedOrbit 12 1933 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1933 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1933) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1933.1, data_12_1933.2] + +/-- Complete interval computation for depth 12, residue 1934. -/ +theorem bounds_12_1934 : exactInterval 12 1934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1934 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1934) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1934 : oddCount 1934 12 = 8 ∧ acceleratedOrbit 12 1934 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1934 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1934) = 3 ^ 8 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1934.1, data_12_1934.2] + +end Collatz.Research.StoppingAtlas.Batch0326 From a1c4a89b470f1843398236c136a90f33a5d93f9b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:43 +0530 Subject: [PATCH 0327/1001] proof: certify atlas Batch0327 (12:1935 to 12:1949) --- Collatz/Research/StoppingAtlas/Batch0327.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0327.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0327.lean b/Collatz/Research/StoppingAtlas/Batch0327.lean new file mode 100644 index 00000000..92518602 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0327.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0327 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1935. -/ +theorem bounds_12_1935 : exactInterval 12 1935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1935 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1935) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1935 : oddCount 1935 12 = 8 ∧ acceleratedOrbit 12 1935 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1935 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1935) = 3 ^ 8 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1935.1, data_12_1935.2] + +/-- Complete interval computation for depth 12, residue 1936. -/ +theorem bounds_12_1936 : exactInterval 12 1936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1936 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1936) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1936 : oddCount 1936 12 = 6 ∧ acceleratedOrbit 12 1936 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1936 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1936) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1936.1, data_12_1936.2] + +/-- Complete interval computation for depth 12, residue 1937. -/ +theorem bounds_12_1937 : exactInterval 12 1937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1937 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1937) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1937 : oddCount 1937 12 = 6 ∧ acceleratedOrbit 12 1937 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1937 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1937) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1937.1, data_12_1937.2] + +/-- Complete interval computation for depth 12, residue 1938. -/ +theorem bounds_12_1938 : exactInterval 12 1938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1938 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1938) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1938 : oddCount 1938 12 = 6 ∧ acceleratedOrbit 12 1938 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1938 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1938) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1938.1, data_12_1938.2] + +/-- Complete interval computation for depth 12, residue 1939. -/ +theorem bounds_12_1939 : exactInterval 12 1939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1939 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1939) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1939 : oddCount 1939 12 = 6 ∧ acceleratedOrbit 12 1939 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1939 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1939) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1939.1, data_12_1939.2] + +/-- Complete interval computation for depth 12, residue 1940. -/ +theorem bounds_12_1940 : exactInterval 12 1940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1940 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1940) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1940 : oddCount 1940 12 = 6 ∧ acceleratedOrbit 12 1940 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1940 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1940) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1940.1, data_12_1940.2] + +/-- Complete interval computation for depth 12, residue 1941. -/ +theorem bounds_12_1941 : exactInterval 12 1941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1941 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1941) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1941 : oddCount 1941 12 = 6 ∧ acceleratedOrbit 12 1941 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1941 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1941) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1941.1, data_12_1941.2] + +/-- Complete interval computation for depth 12, residue 1942. -/ +theorem bounds_12_1942 : exactInterval 12 1942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1942 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1942) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1942 : oddCount 1942 12 = 5 ∧ acceleratedOrbit 12 1942 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1942 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1942) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1942.1, data_12_1942.2] + +/-- Complete interval computation for depth 12, residue 1943. -/ +theorem bounds_12_1943 : exactInterval 12 1943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1943 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1943) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1943 : oddCount 1943 12 = 5 ∧ acceleratedOrbit 12 1943 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1943 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1943) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1943.1, data_12_1943.2] + +/-- Complete interval computation for depth 12, residue 1944. -/ +theorem bounds_12_1944 : exactInterval 12 1944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1944 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1944) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1944 : oddCount 1944 12 = 6 ∧ acceleratedOrbit 12 1944 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1944 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1944) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1944.1, data_12_1944.2] + +/-- Complete interval computation for depth 12, residue 1945. -/ +theorem bounds_12_1945 : exactInterval 12 1945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1945 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1945) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1945 : oddCount 1945 12 = 5 ∧ acceleratedOrbit 12 1945 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1945 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1945) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1945.1, data_12_1945.2] + +/-- Complete interval computation for depth 12, residue 1946. -/ +theorem bounds_12_1946 : exactInterval 12 1946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1946 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1946) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1946 : oddCount 1946 12 = 6 ∧ acceleratedOrbit 12 1946 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1946 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1946) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1946.1, data_12_1946.2] + +/-- Complete interval computation for depth 12, residue 1947. -/ +theorem bounds_12_1947 : exactInterval 12 1947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1947 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1947) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1947 : oddCount 1947 12 = 8 ∧ acceleratedOrbit 12 1947 = 3122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1947 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1947) = 3 ^ 8 * m + 3122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1947.1, data_12_1947.2] + +/-- Complete interval computation for depth 12, residue 1948. -/ +theorem bounds_12_1948 : exactInterval 12 1948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1948 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1948) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1948 : oddCount 1948 12 = 7 ∧ acceleratedOrbit 12 1948 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1948 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1948) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1948.1, data_12_1948.2] + +/-- Complete interval computation for depth 12, residue 1949. -/ +theorem bounds_12_1949 : exactInterval 12 1949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1949 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1949) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1949 : oddCount 1949 12 = 7 ∧ acceleratedOrbit 12 1949 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1949 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1949) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1949.1, data_12_1949.2] + +end Collatz.Research.StoppingAtlas.Batch0327 From 5ff5014e356a7686e32976961c96632125698c01 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:44 +0530 Subject: [PATCH 0328/1001] proof: certify atlas Batch0328 (12:1950 to 12:1965) --- Collatz/Research/StoppingAtlas/Batch0328.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0328.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0328.lean b/Collatz/Research/StoppingAtlas/Batch0328.lean new file mode 100644 index 00000000..0df939dd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0328.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0328 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1950. -/ +theorem bounds_12_1950 : exactInterval 12 1950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1950 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1950) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1950 : oddCount 1950 12 = 7 ∧ acceleratedOrbit 12 1950 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1950 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1950) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1950.1, data_12_1950.2] + +/-- Complete interval computation for depth 12, residue 1951. -/ +theorem bounds_12_1951 : exactInterval 12 1951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1951 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1951) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1951 : oddCount 1951 12 = 8 ∧ acceleratedOrbit 12 1951 = 3127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1951 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1951) = 3 ^ 8 * m + 3127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1951.1, data_12_1951.2] + +/-- Complete interval computation for depth 12, residue 1952. -/ +theorem bounds_12_1952 : exactInterval 12 1952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1952 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1952) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1952 : oddCount 1952 12 = 4 ∧ acceleratedOrbit 12 1952 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1952 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1952) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1952.1, data_12_1952.2] + +/-- Complete interval computation for depth 12, residue 1953. -/ +theorem bounds_12_1953 : exactInterval 12 1953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1953 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1953) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1953 : oddCount 1953 12 = 5 ∧ acceleratedOrbit 12 1953 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1953 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1953) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1953.1, data_12_1953.2] + +/-- Complete interval computation for depth 12, residue 1954. -/ +theorem bounds_12_1954 : exactInterval 12 1954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1954 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1954) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1954 : oddCount 1954 12 = 6 ∧ acceleratedOrbit 12 1954 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1954 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1954) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1954.1, data_12_1954.2] + +/-- Complete interval computation for depth 12, residue 1955. -/ +theorem bounds_12_1955 : exactInterval 12 1955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1955 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1955) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1955 : oddCount 1955 12 = 6 ∧ acceleratedOrbit 12 1955 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1955 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1955) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1955.1, data_12_1955.2] + +/-- Complete interval computation for depth 12, residue 1956. -/ +theorem bounds_12_1956 : exactInterval 12 1956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1956 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1956) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1956 : oddCount 1956 12 = 7 ∧ acceleratedOrbit 12 1956 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1956 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1956) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1956.1, data_12_1956.2] + +/-- Complete interval computation for depth 12, residue 1957. -/ +theorem bounds_12_1957 : exactInterval 12 1957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1957 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1957) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1957 : oddCount 1957 12 = 7 ∧ acceleratedOrbit 12 1957 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1957 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1957) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1957.1, data_12_1957.2] + +/-- Complete interval computation for depth 12, residue 1958. -/ +theorem bounds_12_1958 : exactInterval 12 1958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1958 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1958) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1958 : oddCount 1958 12 = 7 ∧ acceleratedOrbit 12 1958 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1958 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1958) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1958.1, data_12_1958.2] + +/-- Complete interval computation for depth 12, residue 1959. -/ +theorem bounds_12_1959 : exactInterval 12 1959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1959 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1959) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1959 : oddCount 1959 12 = 9 ∧ acceleratedOrbit 12 1959 = 9422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1959 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1959) = 3 ^ 9 * m + 9422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1959.1, data_12_1959.2] + +/-- Complete interval computation for depth 12, residue 1960. -/ +theorem bounds_12_1960 : exactInterval 12 1960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1960 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1960) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1960 : oddCount 1960 12 = 4 ∧ acceleratedOrbit 12 1960 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1960 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1960) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1960.1, data_12_1960.2] + +/-- Complete interval computation for depth 12, residue 1961. -/ +theorem bounds_12_1961 : exactInterval 12 1961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1961 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1961) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1961 : oddCount 1961 12 = 10 ∧ acceleratedOrbit 12 1961 = 28295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1961 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1961) = 3 ^ 10 * m + 28295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1961.1, data_12_1961.2] + +/-- Complete interval computation for depth 12, residue 1962. -/ +theorem bounds_12_1962 : exactInterval 12 1962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1962 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1962) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1962 : oddCount 1962 12 = 4 ∧ acceleratedOrbit 12 1962 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1962 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1962) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1962.1, data_12_1962.2] + +/-- Complete interval computation for depth 12, residue 1963. -/ +theorem bounds_12_1963 : exactInterval 12 1963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1963 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1963) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1963 : oddCount 1963 12 = 8 ∧ acceleratedOrbit 12 1963 = 3149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1963 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1963) = 3 ^ 8 * m + 3149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1963.1, data_12_1963.2] + +/-- Complete interval computation for depth 12, residue 1964. -/ +theorem bounds_12_1964 : exactInterval 12 1964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1964 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1964) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1964 : oddCount 1964 12 = 8 ∧ acceleratedOrbit 12 1964 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1964 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1964) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1964.1, data_12_1964.2] + +/-- Complete interval computation for depth 12, residue 1965. -/ +theorem bounds_12_1965 : exactInterval 12 1965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1965 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1965) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1965 : oddCount 1965 12 = 8 ∧ acceleratedOrbit 12 1965 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1965 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1965) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1965.1, data_12_1965.2] + +end Collatz.Research.StoppingAtlas.Batch0328 From e2c180d5a57a8820542b9d35c1475bb5362b7daa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:44 +0530 Subject: [PATCH 0329/1001] proof: certify atlas Batch0329 (12:1966 to 12:1980) --- Collatz/Research/StoppingAtlas/Batch0329.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0329.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0329.lean b/Collatz/Research/StoppingAtlas/Batch0329.lean new file mode 100644 index 00000000..d866d89a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0329.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0329 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1966. -/ +theorem bounds_12_1966 : exactInterval 12 1966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1966 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1966) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1966 : oddCount 1966 12 = 8 ∧ acceleratedOrbit 12 1966 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1966 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1966) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1966.1, data_12_1966.2] + +/-- Complete interval computation for depth 12, residue 1967. -/ +theorem bounds_12_1967 : exactInterval 12 1967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1967 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1967) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1967 : oddCount 1967 12 = 7 ∧ acceleratedOrbit 12 1967 = 1052 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1967 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1967) = 3 ^ 7 * m + 1052 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1967.1, data_12_1967.2] + +/-- Complete interval computation for depth 12, residue 1968. -/ +theorem bounds_12_1968 : exactInterval 12 1968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1968 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1968) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1968 : oddCount 1968 12 = 5 ∧ acceleratedOrbit 12 1968 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1968 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1968) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1968.1, data_12_1968.2] + +/-- Complete interval computation for depth 12, residue 1969. -/ +theorem bounds_12_1969 : exactInterval 12 1969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1969 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1969) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1969 : oddCount 1969 12 = 3 ∧ acceleratedOrbit 12 1969 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1969 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1969) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1969.1, data_12_1969.2] + +/-- Complete interval computation for depth 12, residue 1970. -/ +theorem bounds_12_1970 : exactInterval 12 1970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1970 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1970) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1970 : oddCount 1970 12 = 3 ∧ acceleratedOrbit 12 1970 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1970 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1970) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1970.1, data_12_1970.2] + +/-- Complete interval computation for depth 12, residue 1971. -/ +theorem bounds_12_1971 : exactInterval 12 1971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1971 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1971) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1971 : oddCount 1971 12 = 3 ∧ acceleratedOrbit 12 1971 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1971 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1971) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1971.1, data_12_1971.2] + +/-- Complete interval computation for depth 12, residue 1972. -/ +theorem bounds_12_1972 : exactInterval 12 1972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1972 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1972) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1972 : oddCount 1972 12 = 5 ∧ acceleratedOrbit 12 1972 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1972 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1972) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1972.1, data_12_1972.2] + +/-- Complete interval computation for depth 12, residue 1973. -/ +theorem bounds_12_1973 : exactInterval 12 1973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1973 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1973) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1973 : oddCount 1973 12 = 5 ∧ acceleratedOrbit 12 1973 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1973 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1973) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1973.1, data_12_1973.2] + +/-- Complete interval computation for depth 12, residue 1974. -/ +theorem bounds_12_1974 : exactInterval 12 1974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1974 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1974) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1974 : oddCount 1974 12 = 6 ∧ acceleratedOrbit 12 1974 = 352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1974 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1974) = 3 ^ 6 * m + 352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1974.1, data_12_1974.2] + +/-- Complete interval computation for depth 12, residue 1975. -/ +theorem bounds_12_1975 : exactInterval 12 1975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1975 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1975) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1975 : oddCount 1975 12 = 6 ∧ acceleratedOrbit 12 1975 = 352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1975 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1975) = 3 ^ 6 * m + 352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1975.1, data_12_1975.2] + +/-- Complete interval computation for depth 12, residue 1976. -/ +theorem bounds_12_1976 : exactInterval 12 1976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1976 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1976) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1976 : oddCount 1976 12 = 5 ∧ acceleratedOrbit 12 1976 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1976 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1976) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1976.1, data_12_1976.2] + +/-- Complete interval computation for depth 12, residue 1977. -/ +theorem bounds_12_1977 : exactInterval 12 1977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1977 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1977) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1977 : oddCount 1977 12 = 6 ∧ acceleratedOrbit 12 1977 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1977 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1977) = 3 ^ 6 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1977.1, data_12_1977.2] + +/-- Complete interval computation for depth 12, residue 1978. -/ +theorem bounds_12_1978 : exactInterval 12 1978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1978 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1978) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1978 : oddCount 1978 12 = 5 ∧ acceleratedOrbit 12 1978 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1978 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1978) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1978.1, data_12_1978.2] + +/-- Complete interval computation for depth 12, residue 1979. -/ +theorem bounds_12_1979 : exactInterval 12 1979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1979 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1979) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1979 : oddCount 1979 12 = 6 ∧ acceleratedOrbit 12 1979 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1979 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1979) = 3 ^ 6 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1979.1, data_12_1979.2] + +/-- Complete interval computation for depth 12, residue 1980. -/ +theorem bounds_12_1980 : exactInterval 12 1980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1980 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1980) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1980 : oddCount 1980 12 = 8 ∧ acceleratedOrbit 12 1980 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1980 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1980) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1980.1, data_12_1980.2] + +end Collatz.Research.StoppingAtlas.Batch0329 From 54b71c837ead2048662d8d2523737c03d5b3e2f1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:44 +0530 Subject: [PATCH 0330/1001] proof: certify atlas Batch0330 (12:1981 to 12:1995) --- Collatz/Research/StoppingAtlas/Batch0330.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0330.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0330.lean b/Collatz/Research/StoppingAtlas/Batch0330.lean new file mode 100644 index 00000000..4705f8e7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0330.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0330 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1981. -/ +theorem bounds_12_1981 : exactInterval 12 1981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1981 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1981) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1981 : oddCount 1981 12 = 8 ∧ acceleratedOrbit 12 1981 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1981 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1981) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1981.1, data_12_1981.2] + +/-- Complete interval computation for depth 12, residue 1982. -/ +theorem bounds_12_1982 : exactInterval 12 1982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1982 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1982) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1982 : oddCount 1982 12 = 8 ∧ acceleratedOrbit 12 1982 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1982 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1982) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1982.1, data_12_1982.2] + +/-- Complete interval computation for depth 12, residue 1983. -/ +theorem bounds_12_1983 : exactInterval 12 1983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1983 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1983) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1983 : oddCount 1983 12 = 8 ∧ acceleratedOrbit 12 1983 = 3178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1983 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1983) = 3 ^ 8 * m + 3178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1983.1, data_12_1983.2] + +/-- Complete interval computation for depth 12, residue 1984. -/ +theorem bounds_12_1984 : exactInterval 12 1984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1984 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1984) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1984 : oddCount 1984 12 = 5 ∧ acceleratedOrbit 12 1984 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1984 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1984) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1984.1, data_12_1984.2] + +/-- Complete interval computation for depth 12, residue 1985. -/ +theorem bounds_12_1985 : exactInterval 12 1985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1985 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1985) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1985 : oddCount 1985 12 = 5 ∧ acceleratedOrbit 12 1985 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1985 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1985) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1985.1, data_12_1985.2] + +/-- Complete interval computation for depth 12, residue 1986. -/ +theorem bounds_12_1986 : exactInterval 12 1986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1986 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1986) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1986 : oddCount 1986 12 = 7 ∧ acceleratedOrbit 12 1986 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1986 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1986) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1986.1, data_12_1986.2] + +/-- Complete interval computation for depth 12, residue 1987. -/ +theorem bounds_12_1987 : exactInterval 12 1987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1987 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1987) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1987 : oddCount 1987 12 = 7 ∧ acceleratedOrbit 12 1987 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1987 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1987) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1987.1, data_12_1987.2] + +/-- Complete interval computation for depth 12, residue 1988. -/ +theorem bounds_12_1988 : exactInterval 12 1988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1988 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1988) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1988 : oddCount 1988 12 = 4 ∧ acceleratedOrbit 12 1988 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1988 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1988) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1988.1, data_12_1988.2] + +/-- Complete interval computation for depth 12, residue 1989. -/ +theorem bounds_12_1989 : exactInterval 12 1989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1989 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1989) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1989 : oddCount 1989 12 = 4 ∧ acceleratedOrbit 12 1989 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1989 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1989) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1989.1, data_12_1989.2] + +/-- Complete interval computation for depth 12, residue 1990. -/ +theorem bounds_12_1990 : exactInterval 12 1990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1990 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1990) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1990 : oddCount 1990 12 = 4 ∧ acceleratedOrbit 12 1990 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1990 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1990) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1990.1, data_12_1990.2] + +/-- Complete interval computation for depth 12, residue 1991. -/ +theorem bounds_12_1991 : exactInterval 12 1991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1991 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1991) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1991 : oddCount 1991 12 = 7 ∧ acceleratedOrbit 12 1991 = 1064 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1991 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1991) = 3 ^ 7 * m + 1064 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1991.1, data_12_1991.2] + +/-- Complete interval computation for depth 12, residue 1992. -/ +theorem bounds_12_1992 : exactInterval 12 1992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1992 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1992) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1992 : oddCount 1992 12 = 5 ∧ acceleratedOrbit 12 1992 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1992 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1992) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1992.1, data_12_1992.2] + +/-- Complete interval computation for depth 12, residue 1993. -/ +theorem bounds_12_1993 : exactInterval 12 1993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1993 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1993) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1993 : oddCount 1993 12 = 7 ∧ acceleratedOrbit 12 1993 = 1066 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1993 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1993) = 3 ^ 7 * m + 1066 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1993.1, data_12_1993.2] + +/-- Complete interval computation for depth 12, residue 1994. -/ +theorem bounds_12_1994 : exactInterval 12 1994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1994 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1994) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1994 : oddCount 1994 12 = 5 ∧ acceleratedOrbit 12 1994 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1994 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1994) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1994.1, data_12_1994.2] + +/-- Complete interval computation for depth 12, residue 1995. -/ +theorem bounds_12_1995 : exactInterval 12 1995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1995 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1995) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1995 : oddCount 1995 12 = 5 ∧ acceleratedOrbit 12 1995 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1995 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1995) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1995.1, data_12_1995.2] + +end Collatz.Research.StoppingAtlas.Batch0330 From bd274f913d1f0a3f0978998d681fa78b1724d865 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:45 +0530 Subject: [PATCH 0331/1001] proof: certify atlas Batch0331 (12:1996 to 12:2011) --- Collatz/Research/StoppingAtlas/Batch0331.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0331.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0331.lean b/Collatz/Research/StoppingAtlas/Batch0331.lean new file mode 100644 index 00000000..968a4eb5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0331.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0331 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 1996. -/ +theorem bounds_12_1996 : exactInterval 12 1996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1996 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1996) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1996 : oddCount 1996 12 = 5 ∧ acceleratedOrbit 12 1996 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1996 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1996) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1996.1, data_12_1996.2] + +/-- Complete interval computation for depth 12, residue 1997. -/ +theorem bounds_12_1997 : exactInterval 12 1997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1997 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1997) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1997 : oddCount 1997 12 = 5 ∧ acceleratedOrbit 12 1997 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1997 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1997) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1997.1, data_12_1997.2] + +/-- Complete interval computation for depth 12, residue 1998. -/ +theorem bounds_12_1998 : exactInterval 12 1998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1998 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1998) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1998 : oddCount 1998 12 = 6 ∧ acceleratedOrbit 12 1998 = 356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1998 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1998) = 3 ^ 6 * m + 356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1998.1, data_12_1998.2] + +/-- Complete interval computation for depth 12, residue 1999. -/ +theorem bounds_12_1999 : exactInterval 12 1999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_1999 (m : Nat) : + stoppingTime (2 ^ 12 * m + 1999) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_1999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_1999 : oddCount 1999 12 = 6 ∧ acceleratedOrbit 12 1999 = 356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_1999 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 1999) = 3 ^ 6 * m + 356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_1999.1, data_12_1999.2] + +/-- Complete interval computation for depth 12, residue 2000. -/ +theorem bounds_12_2000 : exactInterval 12 2000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2000 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2000) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2000 : oddCount 2000 12 = 5 ∧ acceleratedOrbit 12 2000 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2000 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2000) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2000.1, data_12_2000.2] + +/-- Complete interval computation for depth 12, residue 2001. -/ +theorem bounds_12_2001 : exactInterval 12 2001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2001 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2001) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2001 : oddCount 2001 12 = 5 ∧ acceleratedOrbit 12 2001 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2001 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2001) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2001.1, data_12_2001.2] + +/-- Complete interval computation for depth 12, residue 2002. -/ +theorem bounds_12_2002 : exactInterval 12 2002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2002 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2002) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2002 : oddCount 2002 12 = 9 ∧ acceleratedOrbit 12 2002 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2002 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2002) = 3 ^ 9 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2002.1, data_12_2002.2] + +/-- Complete interval computation for depth 12, residue 2003. -/ +theorem bounds_12_2003 : exactInterval 12 2003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2003 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2003) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2003 : oddCount 2003 12 = 9 ∧ acceleratedOrbit 12 2003 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2003 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2003) = 3 ^ 9 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2003.1, data_12_2003.2] + +/-- Complete interval computation for depth 12, residue 2004. -/ +theorem bounds_12_2004 : exactInterval 12 2004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2004 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2004) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2004 : oddCount 2004 12 = 5 ∧ acceleratedOrbit 12 2004 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2004 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2004) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2004.1, data_12_2004.2] + +/-- Complete interval computation for depth 12, residue 2005. -/ +theorem bounds_12_2005 : exactInterval 12 2005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2005 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2005) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2005 : oddCount 2005 12 = 5 ∧ acceleratedOrbit 12 2005 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2005 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2005) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2005.1, data_12_2005.2] + +/-- Complete interval computation for depth 12, residue 2006. -/ +theorem bounds_12_2006 : exactInterval 12 2006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2006 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2006) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2006 : oddCount 2006 12 = 7 ∧ acceleratedOrbit 12 2006 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2006 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2006) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2006.1, data_12_2006.2] + +/-- Complete interval computation for depth 12, residue 2007. -/ +theorem bounds_12_2007 : exactInterval 12 2007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2007 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2007) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2007 : oddCount 2007 12 = 7 ∧ acceleratedOrbit 12 2007 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2007 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2007) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2007.1, data_12_2007.2] + +/-- Complete interval computation for depth 12, residue 2008. -/ +theorem bounds_12_2008 : exactInterval 12 2008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2008 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2008) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2008 : oddCount 2008 12 = 7 ∧ acceleratedOrbit 12 2008 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2008 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2008) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2008.1, data_12_2008.2] + +/-- Complete interval computation for depth 12, residue 2009. -/ +theorem bounds_12_2009 : exactInterval 12 2009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2009 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2009) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2009 : oddCount 2009 12 = 4 ∧ acceleratedOrbit 12 2009 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2009 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2009) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2009.1, data_12_2009.2] + +/-- Complete interval computation for depth 12, residue 2010. -/ +theorem bounds_12_2010 : exactInterval 12 2010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2010 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2010) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2010 : oddCount 2010 12 = 7 ∧ acceleratedOrbit 12 2010 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2010 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2010) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2010.1, data_12_2010.2] + +/-- Complete interval computation for depth 12, residue 2011. -/ +theorem bounds_12_2011 : exactInterval 12 2011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2011 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2011) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2011 : oddCount 2011 12 = 7 ∧ acceleratedOrbit 12 2011 = 1075 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2011 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2011) = 3 ^ 7 * m + 1075 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2011.1, data_12_2011.2] + +end Collatz.Research.StoppingAtlas.Batch0331 From dc1b5c59dfce5a4fee6dcbc2078150e25eb8b3fe Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:45 +0530 Subject: [PATCH 0332/1001] proof: certify atlas Batch0332 (12:2012 to 12:2026) --- Collatz/Research/StoppingAtlas/Batch0332.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0332.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0332.lean b/Collatz/Research/StoppingAtlas/Batch0332.lean new file mode 100644 index 00000000..1de7a25c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0332.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0332 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2012. -/ +theorem bounds_12_2012 : exactInterval 12 2012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2012 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2012) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2012 : oddCount 2012 12 = 7 ∧ acceleratedOrbit 12 2012 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2012 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2012) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2012.1, data_12_2012.2] + +/-- Complete interval computation for depth 12, residue 2013. -/ +theorem bounds_12_2013 : exactInterval 12 2013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2013 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2013) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2013 : oddCount 2013 12 = 7 ∧ acceleratedOrbit 12 2013 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2013 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2013) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2013.1, data_12_2013.2] + +/-- Complete interval computation for depth 12, residue 2014. -/ +theorem bounds_12_2014 : exactInterval 12 2014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2014 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2014) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2014 : oddCount 2014 12 = 8 ∧ acceleratedOrbit 12 2014 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2014 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2014) = 3 ^ 8 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2014.1, data_12_2014.2] + +/-- Complete interval computation for depth 12, residue 2015. -/ +theorem bounds_12_2015 : exactInterval 12 2015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2015 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2015) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2015 : oddCount 2015 12 = 8 ∧ acceleratedOrbit 12 2015 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2015 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2015) = 3 ^ 8 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2015.1, data_12_2015.2] + +/-- Complete interval computation for depth 12, residue 2016. -/ +theorem bounds_12_2016 : exactInterval 12 2016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2016 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2016) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2016 : oddCount 2016 12 = 6 ∧ acceleratedOrbit 12 2016 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2016 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2016) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2016.1, data_12_2016.2] + +/-- Complete interval computation for depth 12, residue 2017. -/ +theorem bounds_12_2017 : exactInterval 12 2017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2017 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2017) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2017 : oddCount 2017 12 = 8 ∧ acceleratedOrbit 12 2017 = 3235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2017 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2017) = 3 ^ 8 * m + 3235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2017.1, data_12_2017.2] + +/-- Complete interval computation for depth 12, residue 2018. -/ +theorem bounds_12_2018 : exactInterval 12 2018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2018 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2018) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2018 : oddCount 2018 12 = 5 ∧ acceleratedOrbit 12 2018 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2018 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2018) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2018.1, data_12_2018.2] + +/-- Complete interval computation for depth 12, residue 2019. -/ +theorem bounds_12_2019 : exactInterval 12 2019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2019 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2019) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2019 : oddCount 2019 12 = 5 ∧ acceleratedOrbit 12 2019 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2019 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2019) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2019.1, data_12_2019.2] + +/-- Complete interval computation for depth 12, residue 2020. -/ +theorem bounds_12_2020 : exactInterval 12 2020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2020 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2020) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2020 : oddCount 2020 12 = 6 ∧ acceleratedOrbit 12 2020 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2020 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2020) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2020.1, data_12_2020.2] + +/-- Complete interval computation for depth 12, residue 2021. -/ +theorem bounds_12_2021 : exactInterval 12 2021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2021 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2021) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2021 : oddCount 2021 12 = 6 ∧ acceleratedOrbit 12 2021 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2021 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2021) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2021.1, data_12_2021.2] + +/-- Complete interval computation for depth 12, residue 2022. -/ +theorem bounds_12_2022 : exactInterval 12 2022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2022 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2022) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2022 : oddCount 2022 12 = 6 ∧ acceleratedOrbit 12 2022 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2022 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2022) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2022.1, data_12_2022.2] + +/-- Complete interval computation for depth 12, residue 2023. -/ +theorem bounds_12_2023 : exactInterval 12 2023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2023 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2023) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2023 : oddCount 2023 12 = 7 ∧ acceleratedOrbit 12 2023 = 1081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2023 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2023) = 3 ^ 7 * m + 1081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2023.1, data_12_2023.2] + +/-- Complete interval computation for depth 12, residue 2024. -/ +theorem bounds_12_2024 : exactInterval 12 2024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2024 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2024) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2024 : oddCount 2024 12 = 6 ∧ acceleratedOrbit 12 2024 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2024 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2024) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2024.1, data_12_2024.2] + +/-- Complete interval computation for depth 12, residue 2025. -/ +theorem bounds_12_2025 : exactInterval 12 2025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2025 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2025) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2025 : oddCount 2025 12 = 9 ∧ acceleratedOrbit 12 2025 = 9740 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2025 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2025) = 3 ^ 9 * m + 9740 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2025.1, data_12_2025.2] + +/-- Complete interval computation for depth 12, residue 2026. -/ +theorem bounds_12_2026 : exactInterval 12 2026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2026 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2026) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2026 : oddCount 2026 12 = 6 ∧ acceleratedOrbit 12 2026 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2026 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2026) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2026.1, data_12_2026.2] + +end Collatz.Research.StoppingAtlas.Batch0332 From 42fcb9e8deeb65870153b890878e6e3f3087447d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:45 +0530 Subject: [PATCH 0333/1001] proof: certify atlas Batch0333 (12:2027 to 12:2041) --- Collatz/Research/StoppingAtlas/Batch0333.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0333.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0333.lean b/Collatz/Research/StoppingAtlas/Batch0333.lean new file mode 100644 index 00000000..087d49fe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0333.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0333 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2027. -/ +theorem bounds_12_2027 : exactInterval 12 2027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2027 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2027) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2027 : oddCount 2027 12 = 8 ∧ acceleratedOrbit 12 2027 = 3250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2027 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2027) = 3 ^ 8 * m + 3250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2027.1, data_12_2027.2] + +/-- Complete interval computation for depth 12, residue 2028. -/ +theorem bounds_12_2028 : exactInterval 12 2028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2028 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2028) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2028 : oddCount 2028 12 = 6 ∧ acceleratedOrbit 12 2028 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2028 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2028) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2028.1, data_12_2028.2] + +/-- Complete interval computation for depth 12, residue 2029. -/ +theorem bounds_12_2029 : exactInterval 12 2029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2029 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2029) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2029 : oddCount 2029 12 = 6 ∧ acceleratedOrbit 12 2029 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2029 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2029) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2029.1, data_12_2029.2] + +/-- Complete interval computation for depth 12, residue 2030. -/ +theorem bounds_12_2030 : exactInterval 12 2030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2030 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2030) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2030 : oddCount 2030 12 = 6 ∧ acceleratedOrbit 12 2030 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2030 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2030) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2030.1, data_12_2030.2] + +/-- Complete interval computation for depth 12, residue 2031. -/ +theorem bounds_12_2031 : exactInterval 12 2031 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2031 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2031) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2031 : oddCount 2031 12 = 7 ∧ acceleratedOrbit 12 2031 = 1085 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2031 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2031) = 3 ^ 7 * m + 1085 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2031.1, data_12_2031.2] + +/-- Complete interval computation for depth 12, residue 2032. -/ +theorem bounds_12_2032 : exactInterval 12 2032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2032 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2032) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2032 : oddCount 2032 12 = 7 ∧ acceleratedOrbit 12 2032 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2032 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2032) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2032.1, data_12_2032.2] + +/-- Complete interval computation for depth 12, residue 2033. -/ +theorem bounds_12_2033 : exactInterval 12 2033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2033 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2033) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2033 : oddCount 2033 12 = 6 ∧ acceleratedOrbit 12 2033 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2033 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2033) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2033.1, data_12_2033.2] + +/-- Complete interval computation for depth 12, residue 2034. -/ +theorem bounds_12_2034 : exactInterval 12 2034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2034 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2034) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2034 : oddCount 2034 12 = 8 ∧ acceleratedOrbit 12 2034 = 3266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2034 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2034) = 3 ^ 8 * m + 3266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2034.1, data_12_2034.2] + +/-- Complete interval computation for depth 12, residue 2035. -/ +theorem bounds_12_2035 : exactInterval 12 2035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2035 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2035) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2035 : oddCount 2035 12 = 8 ∧ acceleratedOrbit 12 2035 = 3266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2035 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2035) = 3 ^ 8 * m + 3266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2035.1, data_12_2035.2] + +/-- Complete interval computation for depth 12, residue 2036. -/ +theorem bounds_12_2036 : exactInterval 12 2036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2036 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2036) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2036 : oddCount 2036 12 = 7 ∧ acceleratedOrbit 12 2036 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2036 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2036) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2036.1, data_12_2036.2] + +/-- Complete interval computation for depth 12, residue 2037. -/ +theorem bounds_12_2037 : exactInterval 12 2037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2037 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2037) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2037 : oddCount 2037 12 = 7 ∧ acceleratedOrbit 12 2037 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2037 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2037) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2037.1, data_12_2037.2] + +/-- Complete interval computation for depth 12, residue 2038. -/ +theorem bounds_12_2038 : exactInterval 12 2038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2038 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2038) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2038 : oddCount 2038 12 = 7 ∧ acceleratedOrbit 12 2038 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2038 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2038) = 3 ^ 7 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2038.1, data_12_2038.2] + +/-- Complete interval computation for depth 12, residue 2039. -/ +theorem bounds_12_2039 : exactInterval 12 2039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2039 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2039) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2039 : oddCount 2039 12 = 7 ∧ acceleratedOrbit 12 2039 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2039 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2039) = 3 ^ 7 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2039.1, data_12_2039.2] + +/-- Complete interval computation for depth 12, residue 2040. -/ +theorem bounds_12_2040 : exactInterval 12 2040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2040 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2040) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2040 : oddCount 2040 12 = 8 ∧ acceleratedOrbit 12 2040 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2040 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2040) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2040.1, data_12_2040.2] + +/-- Complete interval computation for depth 12, residue 2041. -/ +theorem bounds_12_2041 : exactInterval 12 2041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2041 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2041) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2041 : oddCount 2041 12 = 7 ∧ acceleratedOrbit 12 2041 = 1091 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2041 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2041) = 3 ^ 7 * m + 1091 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2041.1, data_12_2041.2] + +end Collatz.Research.StoppingAtlas.Batch0333 From 9010864962a4cff54a16283bcb148f79a5f0c7c1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:46 +0530 Subject: [PATCH 0334/1001] proof: certify atlas Batch0334 (12:2042 to 12:2057) --- Collatz/Research/StoppingAtlas/Batch0334.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0334.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0334.lean b/Collatz/Research/StoppingAtlas/Batch0334.lean new file mode 100644 index 00000000..409056db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0334.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0334 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2042. -/ +theorem bounds_12_2042 : exactInterval 12 2042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2042 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2042) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2042 : oddCount 2042 12 = 8 ∧ acceleratedOrbit 12 2042 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2042 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2042) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2042.1, data_12_2042.2] + +/-- Complete interval computation for depth 12, residue 2043. -/ +theorem bounds_12_2043 : exactInterval 12 2043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2043 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2043) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2043 : oddCount 2043 12 = 9 ∧ acceleratedOrbit 12 2043 = 9827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2043 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2043) = 3 ^ 9 * m + 9827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2043.1, data_12_2043.2] + +/-- Complete interval computation for depth 12, residue 2044. -/ +theorem bounds_12_2044 : exactInterval 12 2044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2044 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2044) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2044 : oddCount 2044 12 = 9 ∧ acceleratedOrbit 12 2044 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2044 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2044) = 3 ^ 9 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2044.1, data_12_2044.2] + +/-- Complete interval computation for depth 12, residue 2045. -/ +theorem bounds_12_2045 : exactInterval 12 2045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2045 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2045) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2045 : oddCount 2045 12 = 9 ∧ acceleratedOrbit 12 2045 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2045 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2045) = 3 ^ 9 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2045.1, data_12_2045.2] + +/-- Complete interval computation for depth 12, residue 2046. -/ +theorem bounds_12_2046 : exactInterval 12 2046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2046 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2046) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2046 : oddCount 2046 12 = 10 ∧ acceleratedOrbit 12 2046 = 29524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2046 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2046) = 3 ^ 10 * m + 29524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2046.1, data_12_2046.2] + +/-- Complete interval computation for depth 12, residue 2047. -/ +theorem bounds_12_2047 : exactInterval 12 2047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2047 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2047) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2047 : oddCount 2047 12 = 11 ∧ acceleratedOrbit 12 2047 = 88573 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2047 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2047) = 3 ^ 11 * m + 88573 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2047.1, data_12_2047.2] + +/-- Complete interval computation for depth 12, residue 2048. -/ +theorem bounds_12_2048 : exactInterval 12 2048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2048 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2048) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2048 : oddCount 2048 12 = 1 ∧ acceleratedOrbit 12 2048 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2048 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2048) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2048.1, data_12_2048.2] + +/-- Complete interval computation for depth 12, residue 2049. -/ +theorem bounds_12_2049 : exactInterval 12 2049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2049 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2049) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2049 : oddCount 2049 12 = 7 ∧ acceleratedOrbit 12 2049 = 1097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2049 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2049) = 3 ^ 7 * m + 1097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2049.1, data_12_2049.2] + +/-- Complete interval computation for depth 12, residue 2050. -/ +theorem bounds_12_2050 : exactInterval 12 2050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2050 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2050) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2050 : oddCount 2050 12 = 5 ∧ acceleratedOrbit 12 2050 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2050 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2050) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2050.1, data_12_2050.2] + +/-- Complete interval computation for depth 12, residue 2051. -/ +theorem bounds_12_2051 : exactInterval 12 2051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2051 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2051) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2051 : oddCount 2051 12 = 5 ∧ acceleratedOrbit 12 2051 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2051 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2051) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2051.1, data_12_2051.2] + +/-- Complete interval computation for depth 12, residue 2052. -/ +theorem bounds_12_2052 : exactInterval 12 2052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2052 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2052) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2052 : oddCount 2052 12 = 6 ∧ acceleratedOrbit 12 2052 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2052 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2052) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2052.1, data_12_2052.2] + +/-- Complete interval computation for depth 12, residue 2053. -/ +theorem bounds_12_2053 : exactInterval 12 2053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2053 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2053) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2053 : oddCount 2053 12 = 6 ∧ acceleratedOrbit 12 2053 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2053 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2053) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2053.1, data_12_2053.2] + +/-- Complete interval computation for depth 12, residue 2054. -/ +theorem bounds_12_2054 : exactInterval 12 2054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2054 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2054) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2054 : oddCount 2054 12 = 6 ∧ acceleratedOrbit 12 2054 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2054 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2054) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2054.1, data_12_2054.2] + +/-- Complete interval computation for depth 12, residue 2055. -/ +theorem bounds_12_2055 : exactInterval 12 2055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2055 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2055) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2055 : oddCount 2055 12 = 5 ∧ acceleratedOrbit 12 2055 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2055 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2055) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2055.1, data_12_2055.2] + +/-- Complete interval computation for depth 12, residue 2056. -/ +theorem bounds_12_2056 : exactInterval 12 2056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2056 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2056) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2056 : oddCount 2056 12 = 4 ∧ acceleratedOrbit 12 2056 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2056 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2056) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2056.1, data_12_2056.2] + +/-- Complete interval computation for depth 12, residue 2057. -/ +theorem bounds_12_2057 : exactInterval 12 2057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2057 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2057) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2057 : oddCount 2057 12 = 7 ∧ acceleratedOrbit 12 2057 = 1100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2057 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2057) = 3 ^ 7 * m + 1100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2057.1, data_12_2057.2] + +end Collatz.Research.StoppingAtlas.Batch0334 From c8c1b809fd759015ade0e1dc49357942caac92e6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:46 +0530 Subject: [PATCH 0335/1001] proof: certify atlas Batch0335 (12:2058 to 12:2072) --- Collatz/Research/StoppingAtlas/Batch0335.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0335.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0335.lean b/Collatz/Research/StoppingAtlas/Batch0335.lean new file mode 100644 index 00000000..9b63041f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0335.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0335 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2058. -/ +theorem bounds_12_2058 : exactInterval 12 2058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2058 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2058) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2058 : oddCount 2058 12 = 4 ∧ acceleratedOrbit 12 2058 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2058 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2058) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2058.1, data_12_2058.2] + +/-- Complete interval computation for depth 12, residue 2059. -/ +theorem bounds_12_2059 : exactInterval 12 2059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2059 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2059) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2059 : oddCount 2059 12 = 6 ∧ acceleratedOrbit 12 2059 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2059 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2059) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2059.1, data_12_2059.2] + +/-- Complete interval computation for depth 12, residue 2060. -/ +theorem bounds_12_2060 : exactInterval 12 2060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2060 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2060) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2060 : oddCount 2060 12 = 4 ∧ acceleratedOrbit 12 2060 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2060 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2060) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2060.1, data_12_2060.2] + +/-- Complete interval computation for depth 12, residue 2061. -/ +theorem bounds_12_2061 : exactInterval 12 2061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2061 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2061) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2061 : oddCount 2061 12 = 4 ∧ acceleratedOrbit 12 2061 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2061 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2061) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2061.1, data_12_2061.2] + +/-- Complete interval computation for depth 12, residue 2062. -/ +theorem bounds_12_2062 : exactInterval 12 2062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2062 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2062) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2062 : oddCount 2062 12 = 6 ∧ acceleratedOrbit 12 2062 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2062 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2062) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2062.1, data_12_2062.2] + +/-- Complete interval computation for depth 12, residue 2063. -/ +theorem bounds_12_2063 : exactInterval 12 2063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2063 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2063) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2063 : oddCount 2063 12 = 6 ∧ acceleratedOrbit 12 2063 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2063 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2063) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2063.1, data_12_2063.2] + +/-- Complete interval computation for depth 12, residue 2064. -/ +theorem bounds_12_2064 : exactInterval 12 2064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2064 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2064) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2064 : oddCount 2064 12 = 5 ∧ acceleratedOrbit 12 2064 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2064 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2064) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2064.1, data_12_2064.2] + +/-- Complete interval computation for depth 12, residue 2065. -/ +theorem bounds_12_2065 : exactInterval 12 2065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2065 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2065) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2065 : oddCount 2065 12 = 4 ∧ acceleratedOrbit 12 2065 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2065 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2065) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2065.1, data_12_2065.2] + +/-- Complete interval computation for depth 12, residue 2066. -/ +theorem bounds_12_2066 : exactInterval 12 2066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2066 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2066) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2066 : oddCount 2066 12 = 7 ∧ acceleratedOrbit 12 2066 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2066 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2066) = 3 ^ 7 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2066.1, data_12_2066.2] + +/-- Complete interval computation for depth 12, residue 2067. -/ +theorem bounds_12_2067 : exactInterval 12 2067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2067 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2067) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2067 : oddCount 2067 12 = 7 ∧ acceleratedOrbit 12 2067 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2067 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2067) = 3 ^ 7 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2067.1, data_12_2067.2] + +/-- Complete interval computation for depth 12, residue 2068. -/ +theorem bounds_12_2068 : exactInterval 12 2068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2068 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2068) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2068 : oddCount 2068 12 = 5 ∧ acceleratedOrbit 12 2068 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2068 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2068) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2068.1, data_12_2068.2] + +/-- Complete interval computation for depth 12, residue 2069. -/ +theorem bounds_12_2069 : exactInterval 12 2069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2069 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2069) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2069 : oddCount 2069 12 = 5 ∧ acceleratedOrbit 12 2069 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2069 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2069) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2069.1, data_12_2069.2] + +/-- Complete interval computation for depth 12, residue 2070. -/ +theorem bounds_12_2070 : exactInterval 12 2070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2070 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2070) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2070 : oddCount 2070 12 = 4 ∧ acceleratedOrbit 12 2070 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2070 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2070) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2070.1, data_12_2070.2] + +/-- Complete interval computation for depth 12, residue 2071. -/ +theorem bounds_12_2071 : exactInterval 12 2071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2071 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2071) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2071 : oddCount 2071 12 = 4 ∧ acceleratedOrbit 12 2071 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2071 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2071) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2071.1, data_12_2071.2] + +/-- Complete interval computation for depth 12, residue 2072. -/ +theorem bounds_12_2072 : exactInterval 12 2072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2072 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2072) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2072 : oddCount 2072 12 = 5 ∧ acceleratedOrbit 12 2072 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2072 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2072) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2072.1, data_12_2072.2] + +end Collatz.Research.StoppingAtlas.Batch0335 From 6b41a10a9e009c633ec121707229d8f163a4cc67 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:46 +0530 Subject: [PATCH 0336/1001] proof: certify atlas Batch0336 (12:2073 to 12:2087) --- Collatz/Research/StoppingAtlas/Batch0336.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0336.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0336.lean b/Collatz/Research/StoppingAtlas/Batch0336.lean new file mode 100644 index 00000000..b46ceea4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0336.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0336 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2073. -/ +theorem bounds_12_2073 : exactInterval 12 2073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2073 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2073) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2073 : oddCount 2073 12 = 7 ∧ acceleratedOrbit 12 2073 = 1109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2073 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2073) = 3 ^ 7 * m + 1109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2073.1, data_12_2073.2] + +/-- Complete interval computation for depth 12, residue 2074. -/ +theorem bounds_12_2074 : exactInterval 12 2074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2074 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2074) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2074 : oddCount 2074 12 = 5 ∧ acceleratedOrbit 12 2074 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2074 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2074) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2074.1, data_12_2074.2] + +/-- Complete interval computation for depth 12, residue 2075. -/ +theorem bounds_12_2075 : exactInterval 12 2075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2075 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2075) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2075 : oddCount 2075 12 = 8 ∧ acceleratedOrbit 12 2075 = 3326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2075 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2075) = 3 ^ 8 * m + 3326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2075.1, data_12_2075.2] + +/-- Complete interval computation for depth 12, residue 2076. -/ +theorem bounds_12_2076 : exactInterval 12 2076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2076 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2076) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2076 : oddCount 2076 12 = 6 ∧ acceleratedOrbit 12 2076 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2076 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2076) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2076.1, data_12_2076.2] + +/-- Complete interval computation for depth 12, residue 2077. -/ +theorem bounds_12_2077 : exactInterval 12 2077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2077 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2077) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2077 : oddCount 2077 12 = 6 ∧ acceleratedOrbit 12 2077 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2077 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2077) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2077.1, data_12_2077.2] + +/-- Complete interval computation for depth 12, residue 2078. -/ +theorem bounds_12_2078 : exactInterval 12 2078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2078 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2078) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2078 : oddCount 2078 12 = 6 ∧ acceleratedOrbit 12 2078 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2078 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2078) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2078.1, data_12_2078.2] + +/-- Complete interval computation for depth 12, residue 2079. -/ +theorem bounds_12_2079 : exactInterval 12 2079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2079 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2079) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2079 : oddCount 2079 12 = 8 ∧ acceleratedOrbit 12 2079 = 3332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2079 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2079) = 3 ^ 8 * m + 3332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2079.1, data_12_2079.2] + +/-- Complete interval computation for depth 12, residue 2080. -/ +theorem bounds_12_2080 : exactInterval 12 2080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2080 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2080) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2080 : oddCount 2080 12 = 3 ∧ acceleratedOrbit 12 2080 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2080 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2080) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2080.1, data_12_2080.2] + +/-- Complete interval computation for depth 12, residue 2081. -/ +theorem bounds_12_2081 : exactInterval 12 2081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2081 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2081) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2081 : oddCount 2081 12 = 6 ∧ acceleratedOrbit 12 2081 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2081 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2081) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2081.1, data_12_2081.2] + +/-- Complete interval computation for depth 12, residue 2082. -/ +theorem bounds_12_2082 : exactInterval 12 2082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2082 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2082) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2082 : oddCount 2082 12 = 5 ∧ acceleratedOrbit 12 2082 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2082 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2082) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2082.1, data_12_2082.2] + +/-- Complete interval computation for depth 12, residue 2083. -/ +theorem bounds_12_2083 : exactInterval 12 2083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2083 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2083) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2083 : oddCount 2083 12 = 5 ∧ acceleratedOrbit 12 2083 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2083 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2083) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2083.1, data_12_2083.2] + +/-- Complete interval computation for depth 12, residue 2084. -/ +theorem bounds_12_2084 : exactInterval 12 2084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2084 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2084) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2084 : oddCount 2084 12 = 5 ∧ acceleratedOrbit 12 2084 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2084 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2084) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2084.1, data_12_2084.2] + +/-- Complete interval computation for depth 12, residue 2085. -/ +theorem bounds_12_2085 : exactInterval 12 2085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2085 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2085) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2085 : oddCount 2085 12 = 5 ∧ acceleratedOrbit 12 2085 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2085 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2085) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2085.1, data_12_2085.2] + +/-- Complete interval computation for depth 12, residue 2086. -/ +theorem bounds_12_2086 : exactInterval 12 2086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2086 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2086) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2086 : oddCount 2086 12 = 5 ∧ acceleratedOrbit 12 2086 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2086 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2086) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2086.1, data_12_2086.2] + +/-- Complete interval computation for depth 12, residue 2087. -/ +theorem bounds_12_2087 : exactInterval 12 2087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2087 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2087) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2087 : oddCount 2087 12 = 8 ∧ acceleratedOrbit 12 2087 = 3347 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2087 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2087) = 3 ^ 8 * m + 3347 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2087.1, data_12_2087.2] + +end Collatz.Research.StoppingAtlas.Batch0336 From 1c7c4dac3042f8032e780a82f438f5f3b0bc5678 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:46 +0530 Subject: [PATCH 0337/1001] proof: certify atlas Batch0337 (12:2088 to 12:2103) --- Collatz/Research/StoppingAtlas/Batch0337.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0337.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0337.lean b/Collatz/Research/StoppingAtlas/Batch0337.lean new file mode 100644 index 00000000..1a183908 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0337.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0337 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2088. -/ +theorem bounds_12_2088 : exactInterval 12 2088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2088 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2088) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2088 : oddCount 2088 12 = 3 ∧ acceleratedOrbit 12 2088 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2088 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2088) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2088.1, data_12_2088.2] + +/-- Complete interval computation for depth 12, residue 2089. -/ +theorem bounds_12_2089 : exactInterval 12 2089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2089 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2089) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2089 : oddCount 2089 12 = 8 ∧ acceleratedOrbit 12 2089 = 3349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2089 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2089) = 3 ^ 8 * m + 3349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2089.1, data_12_2089.2] + +/-- Complete interval computation for depth 12, residue 2090. -/ +theorem bounds_12_2090 : exactInterval 12 2090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2090 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2090) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2090 : oddCount 2090 12 = 3 ∧ acceleratedOrbit 12 2090 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2090 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2090) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2090.1, data_12_2090.2] + +/-- Complete interval computation for depth 12, residue 2091. -/ +theorem bounds_12_2091 : exactInterval 12 2091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2091 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2091) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2091 : oddCount 2091 12 = 6 ∧ acceleratedOrbit 12 2091 = 373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2091 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2091) = 3 ^ 6 * m + 373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2091.1, data_12_2091.2] + +/-- Complete interval computation for depth 12, residue 2092. -/ +theorem bounds_12_2092 : exactInterval 12 2092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2092 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2092) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2092 : oddCount 2092 12 = 5 ∧ acceleratedOrbit 12 2092 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2092 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2092) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2092.1, data_12_2092.2] + +/-- Complete interval computation for depth 12, residue 2093. -/ +theorem bounds_12_2093 : exactInterval 12 2093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2093 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2093) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2093 : oddCount 2093 12 = 5 ∧ acceleratedOrbit 12 2093 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2093 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2093) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2093.1, data_12_2093.2] + +/-- Complete interval computation for depth 12, residue 2094. -/ +theorem bounds_12_2094 : exactInterval 12 2094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2094 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2094) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2094 : oddCount 2094 12 = 5 ∧ acceleratedOrbit 12 2094 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2094 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2094) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2094.1, data_12_2094.2] + +/-- Complete interval computation for depth 12, residue 2095. -/ +theorem bounds_12_2095 : exactInterval 12 2095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2095 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2095) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2095 : oddCount 2095 12 = 8 ∧ acceleratedOrbit 12 2095 = 3358 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2095 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2095) = 3 ^ 8 * m + 3358 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2095.1, data_12_2095.2] + +/-- Complete interval computation for depth 12, residue 2096. -/ +theorem bounds_12_2096 : exactInterval 12 2096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2096 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2096) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2096 : oddCount 2096 12 = 3 ∧ acceleratedOrbit 12 2096 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2096 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2096) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2096.1, data_12_2096.2] + +/-- Complete interval computation for depth 12, residue 2097. -/ +theorem bounds_12_2097 : exactInterval 12 2097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2097 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2097) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2097 : oddCount 2097 12 = 7 ∧ acceleratedOrbit 12 2097 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2097 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2097) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2097.1, data_12_2097.2] + +/-- Complete interval computation for depth 12, residue 2098. -/ +theorem bounds_12_2098 : exactInterval 12 2098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2098 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2098) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2098 : oddCount 2098 12 = 7 ∧ acceleratedOrbit 12 2098 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2098 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2098) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2098.1, data_12_2098.2] + +/-- Complete interval computation for depth 12, residue 2099. -/ +theorem bounds_12_2099 : exactInterval 12 2099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2099 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2099) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2099 : oddCount 2099 12 = 7 ∧ acceleratedOrbit 12 2099 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2099 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2099) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2099.1, data_12_2099.2] + +/-- Complete interval computation for depth 12, residue 2100. -/ +theorem bounds_12_2100 : exactInterval 12 2100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2100 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2100) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2100 : oddCount 2100 12 = 3 ∧ acceleratedOrbit 12 2100 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2100 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2100) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2100.1, data_12_2100.2] + +/-- Complete interval computation for depth 12, residue 2101. -/ +theorem bounds_12_2101 : exactInterval 12 2101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2101 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2101) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2101 : oddCount 2101 12 = 3 ∧ acceleratedOrbit 12 2101 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2101 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2101) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2101.1, data_12_2101.2] + +/-- Complete interval computation for depth 12, residue 2102. -/ +theorem bounds_12_2102 : exactInterval 12 2102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2102 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2102) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2102 : oddCount 2102 12 = 9 ∧ acceleratedOrbit 12 2102 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2102 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2102) = 3 ^ 9 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2102.1, data_12_2102.2] + +/-- Complete interval computation for depth 12, residue 2103. -/ +theorem bounds_12_2103 : exactInterval 12 2103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2103 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2103) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2103 : oddCount 2103 12 = 9 ∧ acceleratedOrbit 12 2103 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2103 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2103) = 3 ^ 9 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2103.1, data_12_2103.2] + +end Collatz.Research.StoppingAtlas.Batch0337 From 29817281b9c11c1891f12e0572601d969a8dbf5e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:47 +0530 Subject: [PATCH 0338/1001] proof: certify atlas Batch0338 (12:2104 to 12:2118) --- Collatz/Research/StoppingAtlas/Batch0338.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0338.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0338.lean b/Collatz/Research/StoppingAtlas/Batch0338.lean new file mode 100644 index 00000000..1729a254 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0338.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0338 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2104. -/ +theorem bounds_12_2104 : exactInterval 12 2104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2104 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2104) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2104 : oddCount 2104 12 = 6 ∧ acceleratedOrbit 12 2104 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2104 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2104) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2104.1, data_12_2104.2] + +/-- Complete interval computation for depth 12, residue 2105. -/ +theorem bounds_12_2105 : exactInterval 12 2105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2105 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2105) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2105 : oddCount 2105 12 = 5 ∧ acceleratedOrbit 12 2105 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2105 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2105) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2105.1, data_12_2105.2] + +/-- Complete interval computation for depth 12, residue 2106. -/ +theorem bounds_12_2106 : exactInterval 12 2106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2106 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2106) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2106 : oddCount 2106 12 = 6 ∧ acceleratedOrbit 12 2106 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2106 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2106) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2106.1, data_12_2106.2] + +/-- Complete interval computation for depth 12, residue 2107. -/ +theorem bounds_12_2107 : exactInterval 12 2107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2107 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2107) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2107 : oddCount 2107 12 = 7 ∧ acceleratedOrbit 12 2107 = 1127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2107 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2107) = 3 ^ 7 * m + 1127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2107.1, data_12_2107.2] + +/-- Complete interval computation for depth 12, residue 2108. -/ +theorem bounds_12_2108 : exactInterval 12 2108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2108 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2108) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2108 : oddCount 2108 12 = 6 ∧ acceleratedOrbit 12 2108 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2108 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2108) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2108.1, data_12_2108.2] + +/-- Complete interval computation for depth 12, residue 2109. -/ +theorem bounds_12_2109 : exactInterval 12 2109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2109 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2109) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2109 : oddCount 2109 12 = 6 ∧ acceleratedOrbit 12 2109 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2109 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2109) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2109.1, data_12_2109.2] + +/-- Complete interval computation for depth 12, residue 2110. -/ +theorem bounds_12_2110 : exactInterval 12 2110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2110 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2110) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2110 : oddCount 2110 12 = 9 ∧ acceleratedOrbit 12 2110 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2110 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2110) = 3 ^ 9 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2110.1, data_12_2110.2] + +/-- Complete interval computation for depth 12, residue 2111. -/ +theorem bounds_12_2111 : exactInterval 12 2111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2111 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2111) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2111 : oddCount 2111 12 = 9 ∧ acceleratedOrbit 12 2111 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2111 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2111) = 3 ^ 9 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2111.1, data_12_2111.2] + +/-- Complete interval computation for depth 12, residue 2112. -/ +theorem bounds_12_2112 : exactInterval 12 2112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2112 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2112) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2112 : oddCount 2112 12 = 4 ∧ acceleratedOrbit 12 2112 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2112 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2112) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2112.1, data_12_2112.2] + +/-- Complete interval computation for depth 12, residue 2113. -/ +theorem bounds_12_2113 : exactInterval 12 2113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2113 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2113) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2113 : oddCount 2113 12 = 7 ∧ acceleratedOrbit 12 2113 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2113 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2113) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2113.1, data_12_2113.2] + +/-- Complete interval computation for depth 12, residue 2114. -/ +theorem bounds_12_2114 : exactInterval 12 2114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2114 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2114) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2114 : oddCount 2114 12 = 7 ∧ acceleratedOrbit 12 2114 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2114 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2114) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2114.1, data_12_2114.2] + +/-- Complete interval computation for depth 12, residue 2115. -/ +theorem bounds_12_2115 : exactInterval 12 2115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2115 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2115) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2115 : oddCount 2115 12 = 7 ∧ acceleratedOrbit 12 2115 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2115 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2115) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2115.1, data_12_2115.2] + +/-- Complete interval computation for depth 12, residue 2116. -/ +theorem bounds_12_2116 : exactInterval 12 2116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2116 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2116) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2116 : oddCount 2116 12 = 3 ∧ acceleratedOrbit 12 2116 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2116 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2116) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2116.1, data_12_2116.2] + +/-- Complete interval computation for depth 12, residue 2117. -/ +theorem bounds_12_2117 : exactInterval 12 2117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2117 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2117) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2117 : oddCount 2117 12 = 3 ∧ acceleratedOrbit 12 2117 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2117 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2117) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2117.1, data_12_2117.2] + +/-- Complete interval computation for depth 12, residue 2118. -/ +theorem bounds_12_2118 : exactInterval 12 2118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2118 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2118) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2118 : oddCount 2118 12 = 3 ∧ acceleratedOrbit 12 2118 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2118 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2118) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2118.1, data_12_2118.2] + +end Collatz.Research.StoppingAtlas.Batch0338 From 90d0d0ba6fa754e223b364b9b04c97faa2add06d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:47 +0530 Subject: [PATCH 0339/1001] proof: certify atlas Batch0339 (12:2119 to 12:2134) --- Collatz/Research/StoppingAtlas/Batch0339.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0339.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0339.lean b/Collatz/Research/StoppingAtlas/Batch0339.lean new file mode 100644 index 00000000..f0628101 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0339.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0339 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2119. -/ +theorem bounds_12_2119 : exactInterval 12 2119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2119 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2119) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2119 : oddCount 2119 12 = 8 ∧ acceleratedOrbit 12 2119 = 3397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2119 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2119) = 3 ^ 8 * m + 3397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2119.1, data_12_2119.2] + +/-- Complete interval computation for depth 12, residue 2120. -/ +theorem bounds_12_2120 : exactInterval 12 2120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2120 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2120) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2120 : oddCount 2120 12 = 6 ∧ acceleratedOrbit 12 2120 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2120 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2120) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2120.1, data_12_2120.2] + +/-- Complete interval computation for depth 12, residue 2121. -/ +theorem bounds_12_2121 : exactInterval 12 2121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2121 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2121) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2121 : oddCount 2121 12 = 9 ∧ acceleratedOrbit 12 2121 = 10205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2121 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2121) = 3 ^ 9 * m + 10205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2121.1, data_12_2121.2] + +/-- Complete interval computation for depth 12, residue 2122. -/ +theorem bounds_12_2122 : exactInterval 12 2122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2122 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2122) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2122 : oddCount 2122 12 = 6 ∧ acceleratedOrbit 12 2122 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2122 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2122) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2122.1, data_12_2122.2] + +/-- Complete interval computation for depth 12, residue 2123. -/ +theorem bounds_12_2123 : exactInterval 12 2123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2123 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2123) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2123 : oddCount 2123 12 = 3 ∧ acceleratedOrbit 12 2123 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2123 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2123) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2123.1, data_12_2123.2] + +/-- Complete interval computation for depth 12, residue 2124. -/ +theorem bounds_12_2124 : exactInterval 12 2124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2124 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2124) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2124 : oddCount 2124 12 = 6 ∧ acceleratedOrbit 12 2124 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2124 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2124) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2124.1, data_12_2124.2] + +/-- Complete interval computation for depth 12, residue 2125. -/ +theorem bounds_12_2125 : exactInterval 12 2125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2125 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2125) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2125 : oddCount 2125 12 = 6 ∧ acceleratedOrbit 12 2125 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2125 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2125) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2125.1, data_12_2125.2] + +/-- Complete interval computation for depth 12, residue 2126. -/ +theorem bounds_12_2126 : exactInterval 12 2126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2126 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2126) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2126 : oddCount 2126 12 = 6 ∧ acceleratedOrbit 12 2126 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2126 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2126) = 3 ^ 6 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2126.1, data_12_2126.2] + +/-- Complete interval computation for depth 12, residue 2127. -/ +theorem bounds_12_2127 : exactInterval 12 2127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2127 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2127) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2127 : oddCount 2127 12 = 6 ∧ acceleratedOrbit 12 2127 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2127 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2127) = 3 ^ 6 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2127.1, data_12_2127.2] + +/-- Complete interval computation for depth 12, residue 2128. -/ +theorem bounds_12_2128 : exactInterval 12 2128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2128 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2128) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2128 : oddCount 2128 12 = 4 ∧ acceleratedOrbit 12 2128 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2128 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2128) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2128.1, data_12_2128.2] + +/-- Complete interval computation for depth 12, residue 2129. -/ +theorem bounds_12_2129 : exactInterval 12 2129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2129 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2129) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2129 : oddCount 2129 12 = 6 ∧ acceleratedOrbit 12 2129 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2129 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2129) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2129.1, data_12_2129.2] + +/-- Complete interval computation for depth 12, residue 2130. -/ +theorem bounds_12_2130 : exactInterval 12 2130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2130 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2130) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2130 : oddCount 2130 12 = 7 ∧ acceleratedOrbit 12 2130 = 1139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2130 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2130) = 3 ^ 7 * m + 1139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2130.1, data_12_2130.2] + +/-- Complete interval computation for depth 12, residue 2131. -/ +theorem bounds_12_2131 : exactInterval 12 2131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2131 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2131) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2131 : oddCount 2131 12 = 7 ∧ acceleratedOrbit 12 2131 = 1139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2131 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2131) = 3 ^ 7 * m + 1139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2131.1, data_12_2131.2] + +/-- Complete interval computation for depth 12, residue 2132. -/ +theorem bounds_12_2132 : exactInterval 12 2132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2132 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2132) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2132 : oddCount 2132 12 = 4 ∧ acceleratedOrbit 12 2132 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2132 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2132) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2132.1, data_12_2132.2] + +/-- Complete interval computation for depth 12, residue 2133. -/ +theorem bounds_12_2133 : exactInterval 12 2133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2133 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2133) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2133 : oddCount 2133 12 = 4 ∧ acceleratedOrbit 12 2133 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2133 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2133) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2133.1, data_12_2133.2] + +/-- Complete interval computation for depth 12, residue 2134. -/ +theorem bounds_12_2134 : exactInterval 12 2134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2134 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2134) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2134 : oddCount 2134 12 = 5 ∧ acceleratedOrbit 12 2134 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2134 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2134) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2134.1, data_12_2134.2] + +end Collatz.Research.StoppingAtlas.Batch0339 From c9aa654b749c2f932567716a29c0618b10228ad4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:48 +0530 Subject: [PATCH 0340/1001] proof: certify atlas Batch0340 (12:2135 to 12:2149) --- Collatz/Research/StoppingAtlas/Batch0340.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0340.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0340.lean b/Collatz/Research/StoppingAtlas/Batch0340.lean new file mode 100644 index 00000000..ffa9a571 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0340.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0340 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2135. -/ +theorem bounds_12_2135 : exactInterval 12 2135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2135 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2135) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2135 : oddCount 2135 12 = 5 ∧ acceleratedOrbit 12 2135 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2135 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2135) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2135.1, data_12_2135.2] + +/-- Complete interval computation for depth 12, residue 2136. -/ +theorem bounds_12_2136 : exactInterval 12 2136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2136 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2136) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2136 : oddCount 2136 12 = 5 ∧ acceleratedOrbit 12 2136 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2136 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2136) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2136.1, data_12_2136.2] + +/-- Complete interval computation for depth 12, residue 2137. -/ +theorem bounds_12_2137 : exactInterval 12 2137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2137 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2137) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2137 : oddCount 2137 12 = 5 ∧ acceleratedOrbit 12 2137 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2137 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2137) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2137.1, data_12_2137.2] + +/-- Complete interval computation for depth 12, residue 2138. -/ +theorem bounds_12_2138 : exactInterval 12 2138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2138 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2138) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2138 : oddCount 2138 12 = 5 ∧ acceleratedOrbit 12 2138 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2138 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2138) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2138.1, data_12_2138.2] + +/-- Complete interval computation for depth 12, residue 2139. -/ +theorem bounds_12_2139 : exactInterval 12 2139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2139 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2139) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2139 : oddCount 2139 12 = 10 ∧ acceleratedOrbit 12 2139 = 30860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2139 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2139) = 3 ^ 10 * m + 30860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2139.1, data_12_2139.2] + +/-- Complete interval computation for depth 12, residue 2140. -/ +theorem bounds_12_2140 : exactInterval 12 2140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2140 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2140) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2140 : oddCount 2140 12 = 5 ∧ acceleratedOrbit 12 2140 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2140 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2140) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2140.1, data_12_2140.2] + +/-- Complete interval computation for depth 12, residue 2141. -/ +theorem bounds_12_2141 : exactInterval 12 2141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2141 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2141) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2141 : oddCount 2141 12 = 5 ∧ acceleratedOrbit 12 2141 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2141 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2141) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2141.1, data_12_2141.2] + +/-- Complete interval computation for depth 12, residue 2142. -/ +theorem bounds_12_2142 : exactInterval 12 2142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2142 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2142) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2142 : oddCount 2142 12 = 7 ∧ acceleratedOrbit 12 2142 = 1145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2142 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2142) = 3 ^ 7 * m + 1145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2142.1, data_12_2142.2] + +/-- Complete interval computation for depth 12, residue 2143. -/ +theorem bounds_12_2143 : exactInterval 12 2143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2143 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2143) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2143 : oddCount 2143 12 = 7 ∧ acceleratedOrbit 12 2143 = 1145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2143 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2143) = 3 ^ 7 * m + 1145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2143.1, data_12_2143.2] + +/-- Complete interval computation for depth 12, residue 2144. -/ +theorem bounds_12_2144 : exactInterval 12 2144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2144 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2144) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2144 : oddCount 2144 12 = 4 ∧ acceleratedOrbit 12 2144 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2144 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2144) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2144.1, data_12_2144.2] + +/-- Complete interval computation for depth 12, residue 2145. -/ +theorem bounds_12_2145 : exactInterval 12 2145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2145 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2145) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2145 : oddCount 2145 12 = 7 ∧ acceleratedOrbit 12 2145 = 1147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2145 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2145) = 3 ^ 7 * m + 1147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2145.1, data_12_2145.2] + +/-- Complete interval computation for depth 12, residue 2146. -/ +theorem bounds_12_2146 : exactInterval 12 2146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2146 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2146) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2146 : oddCount 2146 12 = 5 ∧ acceleratedOrbit 12 2146 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2146 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2146) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2146.1, data_12_2146.2] + +/-- Complete interval computation for depth 12, residue 2147. -/ +theorem bounds_12_2147 : exactInterval 12 2147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2147 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2147) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2147 : oddCount 2147 12 = 5 ∧ acceleratedOrbit 12 2147 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2147 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2147) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2147.1, data_12_2147.2] + +/-- Complete interval computation for depth 12, residue 2148. -/ +theorem bounds_12_2148 : exactInterval 12 2148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2148 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2148) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2148 : oddCount 2148 12 = 5 ∧ acceleratedOrbit 12 2148 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2148 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2148) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2148.1, data_12_2148.2] + +/-- Complete interval computation for depth 12, residue 2149. -/ +theorem bounds_12_2149 : exactInterval 12 2149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2149 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2149) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2149 : oddCount 2149 12 = 5 ∧ acceleratedOrbit 12 2149 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2149 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2149) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2149.1, data_12_2149.2] + +end Collatz.Research.StoppingAtlas.Batch0340 From 0e7b2cfb372a92dbf49a7ba8dca307e7b87a3f55 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:48 +0530 Subject: [PATCH 0341/1001] proof: certify atlas Batch0341 (12:2150 to 12:2164) --- Collatz/Research/StoppingAtlas/Batch0341.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0341.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0341.lean b/Collatz/Research/StoppingAtlas/Batch0341.lean new file mode 100644 index 00000000..e4c876ce --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0341.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0341 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2150. -/ +theorem bounds_12_2150 : exactInterval 12 2150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2150 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2150) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2150 : oddCount 2150 12 = 5 ∧ acceleratedOrbit 12 2150 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2150 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2150) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2150.1, data_12_2150.2] + +/-- Complete interval computation for depth 12, residue 2151. -/ +theorem bounds_12_2151 : exactInterval 12 2151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2151 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2151) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2151 : oddCount 2151 12 = 9 ∧ acceleratedOrbit 12 2151 = 10343 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2151 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2151) = 3 ^ 9 * m + 10343 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2151.1, data_12_2151.2] + +/-- Complete interval computation for depth 12, residue 2152. -/ +theorem bounds_12_2152 : exactInterval 12 2152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2152 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2152) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2152 : oddCount 2152 12 = 4 ∧ acceleratedOrbit 12 2152 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2152 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2152) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2152.1, data_12_2152.2] + +/-- Complete interval computation for depth 12, residue 2153. -/ +theorem bounds_12_2153 : exactInterval 12 2153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2153 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2153) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2153 : oddCount 2153 12 = 7 ∧ acceleratedOrbit 12 2153 = 1151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2153 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2153) = 3 ^ 7 * m + 1151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2153.1, data_12_2153.2] + +/-- Complete interval computation for depth 12, residue 2154. -/ +theorem bounds_12_2154 : exactInterval 12 2154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2154 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2154) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2154 : oddCount 2154 12 = 4 ∧ acceleratedOrbit 12 2154 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2154 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2154) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2154.1, data_12_2154.2] + +/-- Complete interval computation for depth 12, residue 2155. -/ +theorem bounds_12_2155 : exactInterval 12 2155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2155 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2155) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2155 : oddCount 2155 12 = 9 ∧ acceleratedOrbit 12 2155 = 10367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2155 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2155) = 3 ^ 9 * m + 10367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2155.1, data_12_2155.2] + +/-- Complete interval computation for depth 12, residue 2156. -/ +theorem bounds_12_2156 : exactInterval 12 2156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2156 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2156) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2156 : oddCount 2156 12 = 7 ∧ acceleratedOrbit 12 2156 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2156 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2156) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2156.1, data_12_2156.2] + +/-- Complete interval computation for depth 12, residue 2157. -/ +theorem bounds_12_2157 : exactInterval 12 2157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2157 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2157) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2157 : oddCount 2157 12 = 7 ∧ acceleratedOrbit 12 2157 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2157 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2157) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2157.1, data_12_2157.2] + +/-- Complete interval computation for depth 12, residue 2158. -/ +theorem bounds_12_2158 : exactInterval 12 2158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2158 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2158) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2158 : oddCount 2158 12 = 7 ∧ acceleratedOrbit 12 2158 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2158 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2158) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2158.1, data_12_2158.2] + +/-- Complete interval computation for depth 12, residue 2159. -/ +theorem bounds_12_2159 : exactInterval 12 2159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2159 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2159) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2159 : oddCount 2159 12 = 9 ∧ acceleratedOrbit 12 2159 = 10381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2159 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2159) = 3 ^ 9 * m + 10381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2159.1, data_12_2159.2] + +/-- Complete interval computation for depth 12, residue 2160. -/ +theorem bounds_12_2160 : exactInterval 12 2160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2160 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2160) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2160 : oddCount 2160 12 = 4 ∧ acceleratedOrbit 12 2160 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2160 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2160) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2160.1, data_12_2160.2] + +/-- Complete interval computation for depth 12, residue 2161. -/ +theorem bounds_12_2161 : exactInterval 12 2161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2161 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2161) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2161 : oddCount 2161 12 = 4 ∧ acceleratedOrbit 12 2161 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2161 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2161) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2161.1, data_12_2161.2] + +/-- Complete interval computation for depth 12, residue 2162. -/ +theorem bounds_12_2162 : exactInterval 12 2162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2162 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2162) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2162 : oddCount 2162 12 = 6 ∧ acceleratedOrbit 12 2162 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2162 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2162) = 3 ^ 6 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2162.1, data_12_2162.2] + +/-- Complete interval computation for depth 12, residue 2163. -/ +theorem bounds_12_2163 : exactInterval 12 2163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2163 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2163) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2163 : oddCount 2163 12 = 6 ∧ acceleratedOrbit 12 2163 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2163 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2163) = 3 ^ 6 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2163.1, data_12_2163.2] + +/-- Complete interval computation for depth 12, residue 2164. -/ +theorem bounds_12_2164 : exactInterval 12 2164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2164 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2164) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2164 : oddCount 2164 12 = 4 ∧ acceleratedOrbit 12 2164 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2164 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2164) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2164.1, data_12_2164.2] + +end Collatz.Research.StoppingAtlas.Batch0341 From 6e9852aca0e7fd11109fa5ab296dfe40b95cee94 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:48 +0530 Subject: [PATCH 0342/1001] proof: certify atlas Batch0342 (12:2165 to 12:2180) --- Collatz/Research/StoppingAtlas/Batch0342.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0342.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0342.lean b/Collatz/Research/StoppingAtlas/Batch0342.lean new file mode 100644 index 00000000..3bd96fa0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0342.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0342 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2165. -/ +theorem bounds_12_2165 : exactInterval 12 2165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2165 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2165) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2165 : oddCount 2165 12 = 4 ∧ acceleratedOrbit 12 2165 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2165 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2165) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2165.1, data_12_2165.2] + +/-- Complete interval computation for depth 12, residue 2166. -/ +theorem bounds_12_2166 : exactInterval 12 2166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2166 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2166) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2166 : oddCount 2166 12 = 7 ∧ acceleratedOrbit 12 2166 = 1160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2166 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2166) = 3 ^ 7 * m + 1160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2166.1, data_12_2166.2] + +/-- Complete interval computation for depth 12, residue 2167. -/ +theorem bounds_12_2167 : exactInterval 12 2167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2167 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2167) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2167 : oddCount 2167 12 = 7 ∧ acceleratedOrbit 12 2167 = 1160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2167 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2167) = 3 ^ 7 * m + 1160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2167.1, data_12_2167.2] + +/-- Complete interval computation for depth 12, residue 2168. -/ +theorem bounds_12_2168 : exactInterval 12 2168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2168 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2168) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2168 : oddCount 2168 12 = 4 ∧ acceleratedOrbit 12 2168 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2168 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2168) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2168.1, data_12_2168.2] + +/-- Complete interval computation for depth 12, residue 2169. -/ +theorem bounds_12_2169 : exactInterval 12 2169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2169 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2169) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2169 : oddCount 2169 12 = 8 ∧ acceleratedOrbit 12 2169 = 3478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2169 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2169) = 3 ^ 8 * m + 3478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2169.1, data_12_2169.2] + +/-- Complete interval computation for depth 12, residue 2170. -/ +theorem bounds_12_2170 : exactInterval 12 2170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2170 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2170) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2170 : oddCount 2170 12 = 4 ∧ acceleratedOrbit 12 2170 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2170 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2170) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2170.1, data_12_2170.2] + +/-- Complete interval computation for depth 12, residue 2171. -/ +theorem bounds_12_2171 : exactInterval 12 2171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2171 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2171) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2171 : oddCount 2171 12 = 8 ∧ acceleratedOrbit 12 2171 = 3482 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2171 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2171) = 3 ^ 8 * m + 3482 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2171.1, data_12_2171.2] + +/-- Complete interval computation for depth 12, residue 2172. -/ +theorem bounds_12_2172 : exactInterval 12 2172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2172 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2172) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2172 : oddCount 2172 12 = 7 ∧ acceleratedOrbit 12 2172 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2172 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2172) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2172.1, data_12_2172.2] + +/-- Complete interval computation for depth 12, residue 2173. -/ +theorem bounds_12_2173 : exactInterval 12 2173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2173 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2173) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2173 : oddCount 2173 12 = 7 ∧ acceleratedOrbit 12 2173 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2173 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2173) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2173.1, data_12_2173.2] + +/-- Complete interval computation for depth 12, residue 2174. -/ +theorem bounds_12_2174 : exactInterval 12 2174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2174 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2174) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2174 : oddCount 2174 12 = 7 ∧ acceleratedOrbit 12 2174 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2174 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2174) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2174.1, data_12_2174.2] + +/-- Complete interval computation for depth 12, residue 2175. -/ +theorem bounds_12_2175 : exactInterval 12 2175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2175 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2175) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2175 : oddCount 2175 12 = 9 ∧ acceleratedOrbit 12 2175 = 10457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2175 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2175) = 3 ^ 9 * m + 10457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2175.1, data_12_2175.2] + +/-- Complete interval computation for depth 12, residue 2176. -/ +theorem bounds_12_2176 : exactInterval 12 2176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2176 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2176) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2176 : oddCount 2176 12 = 2 ∧ acceleratedOrbit 12 2176 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2176 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2176) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2176.1, data_12_2176.2] + +/-- Complete interval computation for depth 12, residue 2177. -/ +theorem bounds_12_2177 : exactInterval 12 2177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2177 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2177) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2177 : oddCount 2177 12 = 6 ∧ acceleratedOrbit 12 2177 = 388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2177 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2177) = 3 ^ 6 * m + 388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2177.1, data_12_2177.2] + +/-- Complete interval computation for depth 12, residue 2178. -/ +theorem bounds_12_2178 : exactInterval 12 2178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2178 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2178) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2178 : oddCount 2178 12 = 5 ∧ acceleratedOrbit 12 2178 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2178 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2178) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2178.1, data_12_2178.2] + +/-- Complete interval computation for depth 12, residue 2179. -/ +theorem bounds_12_2179 : exactInterval 12 2179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2179 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2179) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2179 : oddCount 2179 12 = 5 ∧ acceleratedOrbit 12 2179 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2179 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2179) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2179.1, data_12_2179.2] + +/-- Complete interval computation for depth 12, residue 2180. -/ +theorem bounds_12_2180 : exactInterval 12 2180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2180 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2180) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2180 : oddCount 2180 12 = 5 ∧ acceleratedOrbit 12 2180 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2180 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2180) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2180.1, data_12_2180.2] + +end Collatz.Research.StoppingAtlas.Batch0342 From 9b3b710279fd916b43a6a83ebc419fc520e84367 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:49 +0530 Subject: [PATCH 0343/1001] proof: certify atlas Batch0343 (12:2181 to 12:2195) --- Collatz/Research/StoppingAtlas/Batch0343.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0343.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0343.lean b/Collatz/Research/StoppingAtlas/Batch0343.lean new file mode 100644 index 00000000..3af9983d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0343.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0343 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2181. -/ +theorem bounds_12_2181 : exactInterval 12 2181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2181 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2181) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2181 : oddCount 2181 12 = 5 ∧ acceleratedOrbit 12 2181 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2181 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2181) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2181.1, data_12_2181.2] + +/-- Complete interval computation for depth 12, residue 2182. -/ +theorem bounds_12_2182 : exactInterval 12 2182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2182 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2182) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2182 : oddCount 2182 12 = 5 ∧ acceleratedOrbit 12 2182 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2182 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2182) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2182.1, data_12_2182.2] + +/-- Complete interval computation for depth 12, residue 2183. -/ +theorem bounds_12_2183 : exactInterval 12 2183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2183 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2183) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2183 : oddCount 2183 12 = 6 ∧ acceleratedOrbit 12 2183 = 389 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2183 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2183) = 3 ^ 6 * m + 389 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2183.1, data_12_2183.2] + +/-- Complete interval computation for depth 12, residue 2184. -/ +theorem bounds_12_2184 : exactInterval 12 2184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2184 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2184) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2184 : oddCount 2184 12 = 4 ∧ acceleratedOrbit 12 2184 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2184 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2184) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2184.1, data_12_2184.2] + +/-- Complete interval computation for depth 12, residue 2185. -/ +theorem bounds_12_2185 : exactInterval 12 2185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2185 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2185) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2185 : oddCount 2185 12 = 8 ∧ acceleratedOrbit 12 2185 = 3503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2185 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2185) = 3 ^ 8 * m + 3503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2185.1, data_12_2185.2] + +/-- Complete interval computation for depth 12, residue 2186. -/ +theorem bounds_12_2186 : exactInterval 12 2186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2186 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2186) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2186 : oddCount 2186 12 = 4 ∧ acceleratedOrbit 12 2186 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2186 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2186) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2186.1, data_12_2186.2] + +/-- Complete interval computation for depth 12, residue 2187. -/ +theorem bounds_12_2187 : exactInterval 12 2187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2187 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2187) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2187 : oddCount 2187 12 = 8 ∧ acceleratedOrbit 12 2187 = 3509 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2187 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2187) = 3 ^ 8 * m + 3509 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2187.1, data_12_2187.2] + +/-- Complete interval computation for depth 12, residue 2188. -/ +theorem bounds_12_2188 : exactInterval 12 2188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2188 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2188) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2188 : oddCount 2188 12 = 4 ∧ acceleratedOrbit 12 2188 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2188 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2188) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2188.1, data_12_2188.2] + +/-- Complete interval computation for depth 12, residue 2189. -/ +theorem bounds_12_2189 : exactInterval 12 2189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2189 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2189) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2189 : oddCount 2189 12 = 4 ∧ acceleratedOrbit 12 2189 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2189 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2189) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2189.1, data_12_2189.2] + +/-- Complete interval computation for depth 12, residue 2190. -/ +theorem bounds_12_2190 : exactInterval 12 2190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2190 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2190) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2190 : oddCount 2190 12 = 7 ∧ acceleratedOrbit 12 2190 = 1171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2190 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2190) = 3 ^ 7 * m + 1171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2190.1, data_12_2190.2] + +/-- Complete interval computation for depth 12, residue 2191. -/ +theorem bounds_12_2191 : exactInterval 12 2191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2191 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2191) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2191 : oddCount 2191 12 = 7 ∧ acceleratedOrbit 12 2191 = 1171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2191 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2191) = 3 ^ 7 * m + 1171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2191.1, data_12_2191.2] + +/-- Complete interval computation for depth 12, residue 2192. -/ +theorem bounds_12_2192 : exactInterval 12 2192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2192 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2192) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2192 : oddCount 2192 12 = 6 ∧ acceleratedOrbit 12 2192 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2192 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2192) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2192.1, data_12_2192.2] + +/-- Complete interval computation for depth 12, residue 2193. -/ +theorem bounds_12_2193 : exactInterval 12 2193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2193 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2193) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2193 : oddCount 2193 12 = 7 ∧ acceleratedOrbit 12 2193 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2193 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2193) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2193.1, data_12_2193.2] + +/-- Complete interval computation for depth 12, residue 2194. -/ +theorem bounds_12_2194 : exactInterval 12 2194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2194 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2194) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2194 : oddCount 2194 12 = 7 ∧ acceleratedOrbit 12 2194 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2194 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2194) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2194.1, data_12_2194.2] + +/-- Complete interval computation for depth 12, residue 2195. -/ +theorem bounds_12_2195 : exactInterval 12 2195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2195 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2195) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2195 : oddCount 2195 12 = 7 ∧ acceleratedOrbit 12 2195 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2195 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2195) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2195.1, data_12_2195.2] + +end Collatz.Research.StoppingAtlas.Batch0343 From e0a35ca88b0653d71f1b8fe87733c5e0c52fd3c4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:49 +0530 Subject: [PATCH 0344/1001] proof: certify atlas Batch0344 (12:2196 to 12:2210) --- Collatz/Research/StoppingAtlas/Batch0344.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0344.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0344.lean b/Collatz/Research/StoppingAtlas/Batch0344.lean new file mode 100644 index 00000000..b3796864 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0344.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0344 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2196. -/ +theorem bounds_12_2196 : exactInterval 12 2196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2196 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2196) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2196 : oddCount 2196 12 = 6 ∧ acceleratedOrbit 12 2196 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2196 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2196) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2196.1, data_12_2196.2] + +/-- Complete interval computation for depth 12, residue 2197. -/ +theorem bounds_12_2197 : exactInterval 12 2197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2197 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2197) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2197 : oddCount 2197 12 = 6 ∧ acceleratedOrbit 12 2197 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2197 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2197) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2197.1, data_12_2197.2] + +/-- Complete interval computation for depth 12, residue 2198. -/ +theorem bounds_12_2198 : exactInterval 12 2198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2198 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2198) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2198 : oddCount 2198 12 = 4 ∧ acceleratedOrbit 12 2198 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2198 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2198) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2198.1, data_12_2198.2] + +/-- Complete interval computation for depth 12, residue 2199. -/ +theorem bounds_12_2199 : exactInterval 12 2199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2199 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2199) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2199 : oddCount 2199 12 = 4 ∧ acceleratedOrbit 12 2199 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2199 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2199) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2199.1, data_12_2199.2] + +/-- Complete interval computation for depth 12, residue 2200. -/ +theorem bounds_12_2200 : exactInterval 12 2200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2200 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2200) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2200 : oddCount 2200 12 = 6 ∧ acceleratedOrbit 12 2200 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2200 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2200) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2200.1, data_12_2200.2] + +/-- Complete interval computation for depth 12, residue 2201. -/ +theorem bounds_12_2201 : exactInterval 12 2201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2201 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2201) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2201 : oddCount 2201 12 = 7 ∧ acceleratedOrbit 12 2201 = 1178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2201 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2201) = 3 ^ 7 * m + 1178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2201.1, data_12_2201.2] + +/-- Complete interval computation for depth 12, residue 2202. -/ +theorem bounds_12_2202 : exactInterval 12 2202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2202 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2202) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2202 : oddCount 2202 12 = 6 ∧ acceleratedOrbit 12 2202 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2202 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2202) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2202.1, data_12_2202.2] + +/-- Complete interval computation for depth 12, residue 2203. -/ +theorem bounds_12_2203 : exactInterval 12 2203 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2203 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2203) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2203 : oddCount 2203 12 = 7 ∧ acceleratedOrbit 12 2203 = 1177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2203 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2203) = 3 ^ 7 * m + 1177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2203.1, data_12_2203.2] + +/-- Complete interval computation for depth 12, residue 2204. -/ +theorem bounds_12_2204 : exactInterval 12 2204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2204 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2204) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2204 : oddCount 2204 12 = 5 ∧ acceleratedOrbit 12 2204 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2204 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2204) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2204.1, data_12_2204.2] + +/-- Complete interval computation for depth 12, residue 2205. -/ +theorem bounds_12_2205 : exactInterval 12 2205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2205 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2205) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2205 : oddCount 2205 12 = 5 ∧ acceleratedOrbit 12 2205 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2205 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2205) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2205.1, data_12_2205.2] + +/-- Complete interval computation for depth 12, residue 2206. -/ +theorem bounds_12_2206 : exactInterval 12 2206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2206 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2206) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2206 : oddCount 2206 12 = 5 ∧ acceleratedOrbit 12 2206 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2206 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2206) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2206.1, data_12_2206.2] + +/-- Complete interval computation for depth 12, residue 2207. -/ +theorem bounds_12_2207 : exactInterval 12 2207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2207 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2207) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2207 : oddCount 2207 12 = 11 ∧ acceleratedOrbit 12 2207 = 95498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2207 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2207) = 3 ^ 11 * m + 95498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2207.1, data_12_2207.2] + +/-- Complete interval computation for depth 12, residue 2208. -/ +theorem bounds_12_2208 : exactInterval 12 2208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2208 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2208) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2208 : oddCount 2208 12 = 2 ∧ acceleratedOrbit 12 2208 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2208 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2208) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2208.1, data_12_2208.2] + +/-- Complete interval computation for depth 12, residue 2209. -/ +theorem bounds_12_2209 : exactInterval 12 2209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2209 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2209) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2209 : oddCount 2209 12 = 7 ∧ acceleratedOrbit 12 2209 = 1181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2209 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2209) = 3 ^ 7 * m + 1181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2209.1, data_12_2209.2] + +/-- Complete interval computation for depth 12, residue 2210. -/ +theorem bounds_12_2210 : exactInterval 12 2210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2210 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2210) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2210 : oddCount 2210 12 = 6 ∧ acceleratedOrbit 12 2210 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2210 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2210) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2210.1, data_12_2210.2] + +end Collatz.Research.StoppingAtlas.Batch0344 From 80944e855cd8aa6340c63c44eeea79b4f8f32e04 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:49 +0530 Subject: [PATCH 0345/1001] proof: certify atlas Batch0345 (12:2211 to 12:2226) --- Collatz/Research/StoppingAtlas/Batch0345.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0345.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0345.lean b/Collatz/Research/StoppingAtlas/Batch0345.lean new file mode 100644 index 00000000..bec23dc0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0345.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0345 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2211. -/ +theorem bounds_12_2211 : exactInterval 12 2211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2211 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2211) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2211 : oddCount 2211 12 = 6 ∧ acceleratedOrbit 12 2211 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2211 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2211) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2211.1, data_12_2211.2] + +/-- Complete interval computation for depth 12, residue 2212. -/ +theorem bounds_12_2212 : exactInterval 12 2212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2212 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2212) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2212 : oddCount 2212 12 = 8 ∧ acceleratedOrbit 12 2212 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2212 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2212) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2212.1, data_12_2212.2] + +/-- Complete interval computation for depth 12, residue 2213. -/ +theorem bounds_12_2213 : exactInterval 12 2213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2213 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2213) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2213 : oddCount 2213 12 = 8 ∧ acceleratedOrbit 12 2213 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2213 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2213) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2213.1, data_12_2213.2] + +/-- Complete interval computation for depth 12, residue 2214. -/ +theorem bounds_12_2214 : exactInterval 12 2214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2214 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2214) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2214 : oddCount 2214 12 = 8 ∧ acceleratedOrbit 12 2214 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2214 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2214) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2214.1, data_12_2214.2] + +/-- Complete interval computation for depth 12, residue 2215. -/ +theorem bounds_12_2215 : exactInterval 12 2215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2215 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2215) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2215 : oddCount 2215 12 = 9 ∧ acceleratedOrbit 12 2215 = 10651 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2215 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2215) = 3 ^ 9 * m + 10651 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2215.1, data_12_2215.2] + +/-- Complete interval computation for depth 12, residue 2216. -/ +theorem bounds_12_2216 : exactInterval 12 2216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2216 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2216) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2216 : oddCount 2216 12 = 2 ∧ acceleratedOrbit 12 2216 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2216 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2216) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2216.1, data_12_2216.2] + +/-- Complete interval computation for depth 12, residue 2217. -/ +theorem bounds_12_2217 : exactInterval 12 2217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2217 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2217) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2217 : oddCount 2217 12 = 10 ∧ acceleratedOrbit 12 2217 = 31985 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2217 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2217) = 3 ^ 10 * m + 31985 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2217.1, data_12_2217.2] + +/-- Complete interval computation for depth 12, residue 2218. -/ +theorem bounds_12_2218 : exactInterval 12 2218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2218 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2218) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2218 : oddCount 2218 12 = 2 ∧ acceleratedOrbit 12 2218 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2218 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2218) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2218.1, data_12_2218.2] + +/-- Complete interval computation for depth 12, residue 2219. -/ +theorem bounds_12_2219 : exactInterval 12 2219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2219 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2219) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2219 : oddCount 2219 12 = 7 ∧ acceleratedOrbit 12 2219 = 1187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2219 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2219) = 3 ^ 7 * m + 1187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2219.1, data_12_2219.2] + +/-- Complete interval computation for depth 12, residue 2220. -/ +theorem bounds_12_2220 : exactInterval 12 2220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2220 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2220) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2220 : oddCount 2220 12 = 4 ∧ acceleratedOrbit 12 2220 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2220 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2220) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2220.1, data_12_2220.2] + +/-- Complete interval computation for depth 12, residue 2221. -/ +theorem bounds_12_2221 : exactInterval 12 2221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2221 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2221) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2221 : oddCount 2221 12 = 4 ∧ acceleratedOrbit 12 2221 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2221 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2221) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2221.1, data_12_2221.2] + +/-- Complete interval computation for depth 12, residue 2222. -/ +theorem bounds_12_2222 : exactInterval 12 2222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2222 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2222) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2222 : oddCount 2222 12 = 4 ∧ acceleratedOrbit 12 2222 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2222 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2222) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2222.1, data_12_2222.2] + +/-- Complete interval computation for depth 12, residue 2223. -/ +theorem bounds_12_2223 : exactInterval 12 2223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2223 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2223) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2223 : oddCount 2223 12 = 9 ∧ acceleratedOrbit 12 2223 = 10691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2223 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2223) = 3 ^ 9 * m + 10691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2223.1, data_12_2223.2] + +/-- Complete interval computation for depth 12, residue 2224. -/ +theorem bounds_12_2224 : exactInterval 12 2224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2224 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2224) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2224 : oddCount 2224 12 = 5 ∧ acceleratedOrbit 12 2224 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2224 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2224) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2224.1, data_12_2224.2] + +/-- Complete interval computation for depth 12, residue 2225. -/ +theorem bounds_12_2225 : exactInterval 12 2225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2225 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2225) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2225 : oddCount 2225 12 = 6 ∧ acceleratedOrbit 12 2225 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2225 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2225) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2225.1, data_12_2225.2] + +/-- Complete interval computation for depth 12, residue 2226. -/ +theorem bounds_12_2226 : exactInterval 12 2226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2226 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2226) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2226 : oddCount 2226 12 = 6 ∧ acceleratedOrbit 12 2226 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2226 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2226) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2226.1, data_12_2226.2] + +end Collatz.Research.StoppingAtlas.Batch0345 From b6a95f9aef4ac5af54252518ce993905b0e3f80b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:50 +0530 Subject: [PATCH 0346/1001] proof: certify atlas Batch0346 (12:2227 to 12:2241) --- Collatz/Research/StoppingAtlas/Batch0346.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0346.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0346.lean b/Collatz/Research/StoppingAtlas/Batch0346.lean new file mode 100644 index 00000000..d969bf11 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0346.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0346 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2227. -/ +theorem bounds_12_2227 : exactInterval 12 2227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2227 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2227) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2227 : oddCount 2227 12 = 6 ∧ acceleratedOrbit 12 2227 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2227 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2227) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2227.1, data_12_2227.2] + +/-- Complete interval computation for depth 12, residue 2228. -/ +theorem bounds_12_2228 : exactInterval 12 2228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2228 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2228) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2228 : oddCount 2228 12 = 5 ∧ acceleratedOrbit 12 2228 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2228 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2228) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2228.1, data_12_2228.2] + +/-- Complete interval computation for depth 12, residue 2229. -/ +theorem bounds_12_2229 : exactInterval 12 2229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2229 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2229) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2229 : oddCount 2229 12 = 5 ∧ acceleratedOrbit 12 2229 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2229 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2229) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2229.1, data_12_2229.2] + +/-- Complete interval computation for depth 12, residue 2230. -/ +theorem bounds_12_2230 : exactInterval 12 2230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2230 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2230) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2230 : oddCount 2230 12 = 8 ∧ acceleratedOrbit 12 2230 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2230 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2230) = 3 ^ 8 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2230.1, data_12_2230.2] + +/-- Complete interval computation for depth 12, residue 2231. -/ +theorem bounds_12_2231 : exactInterval 12 2231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2231 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2231) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2231 : oddCount 2231 12 = 8 ∧ acceleratedOrbit 12 2231 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2231 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2231) = 3 ^ 8 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2231.1, data_12_2231.2] + +/-- Complete interval computation for depth 12, residue 2232. -/ +theorem bounds_12_2232 : exactInterval 12 2232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2232 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2232) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2232 : oddCount 2232 12 = 5 ∧ acceleratedOrbit 12 2232 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2232 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2232) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2232.1, data_12_2232.2] + +/-- Complete interval computation for depth 12, residue 2233. -/ +theorem bounds_12_2233 : exactInterval 12 2233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2233 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2233) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2233 : oddCount 2233 12 = 6 ∧ acceleratedOrbit 12 2233 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2233 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2233) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2233.1, data_12_2233.2] + +/-- Complete interval computation for depth 12, residue 2234. -/ +theorem bounds_12_2234 : exactInterval 12 2234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2234 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2234) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2234 : oddCount 2234 12 = 5 ∧ acceleratedOrbit 12 2234 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2234 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2234) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2234.1, data_12_2234.2] + +/-- Complete interval computation for depth 12, residue 2235. -/ +theorem bounds_12_2235 : exactInterval 12 2235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2235 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2235) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2235 : oddCount 2235 12 = 8 ∧ acceleratedOrbit 12 2235 = 3584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2235 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2235) = 3 ^ 8 * m + 3584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2235.1, data_12_2235.2] + +/-- Complete interval computation for depth 12, residue 2236. -/ +theorem bounds_12_2236 : exactInterval 12 2236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2236 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2236) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2236 : oddCount 2236 12 = 8 ∧ acceleratedOrbit 12 2236 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2236 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2236) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2236.1, data_12_2236.2] + +/-- Complete interval computation for depth 12, residue 2237. -/ +theorem bounds_12_2237 : exactInterval 12 2237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2237 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2237) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2237 : oddCount 2237 12 = 8 ∧ acceleratedOrbit 12 2237 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2237 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2237) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2237.1, data_12_2237.2] + +/-- Complete interval computation for depth 12, residue 2238. -/ +theorem bounds_12_2238 : exactInterval 12 2238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2238 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2238) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2238 : oddCount 2238 12 = 8 ∧ acceleratedOrbit 12 2238 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2238 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2238) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2238.1, data_12_2238.2] + +/-- Complete interval computation for depth 12, residue 2239. -/ +theorem bounds_12_2239 : exactInterval 12 2239 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2239 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2239) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2239 : oddCount 2239 12 = 7 ∧ acceleratedOrbit 12 2239 = 1196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2239 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2239) = 3 ^ 7 * m + 1196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2239.1, data_12_2239.2] + +/-- Complete interval computation for depth 12, residue 2240. -/ +theorem bounds_12_2240 : exactInterval 12 2240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2240 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2240) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2240 : oddCount 2240 12 = 2 ∧ acceleratedOrbit 12 2240 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2240 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2240) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2240.1, data_12_2240.2] + +/-- Complete interval computation for depth 12, residue 2241. -/ +theorem bounds_12_2241 : exactInterval 12 2241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2241 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2241) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2241 : oddCount 2241 12 = 6 ∧ acceleratedOrbit 12 2241 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2241 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2241) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2241.1, data_12_2241.2] + +end Collatz.Research.StoppingAtlas.Batch0346 From 6ca9057e5474f08cfe65bd88a47220326e21dd88 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:50 +0530 Subject: [PATCH 0347/1001] proof: certify atlas Batch0347 (12:2242 to 12:2256) --- Collatz/Research/StoppingAtlas/Batch0347.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0347.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0347.lean b/Collatz/Research/StoppingAtlas/Batch0347.lean new file mode 100644 index 00000000..68a61ecb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0347.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0347 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2242. -/ +theorem bounds_12_2242 : exactInterval 12 2242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2242 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2242) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2242 : oddCount 2242 12 = 6 ∧ acceleratedOrbit 12 2242 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2242 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2242) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2242.1, data_12_2242.2] + +/-- Complete interval computation for depth 12, residue 2243. -/ +theorem bounds_12_2243 : exactInterval 12 2243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2243 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2243) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2243 : oddCount 2243 12 = 6 ∧ acceleratedOrbit 12 2243 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2243 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2243) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2243.1, data_12_2243.2] + +/-- Complete interval computation for depth 12, residue 2244. -/ +theorem bounds_12_2244 : exactInterval 12 2244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2244 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2244) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2244 : oddCount 2244 12 = 6 ∧ acceleratedOrbit 12 2244 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2244 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2244) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2244.1, data_12_2244.2] + +/-- Complete interval computation for depth 12, residue 2245. -/ +theorem bounds_12_2245 : exactInterval 12 2245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2245 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2245) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2245 : oddCount 2245 12 = 6 ∧ acceleratedOrbit 12 2245 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2245 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2245) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2245.1, data_12_2245.2] + +/-- Complete interval computation for depth 12, residue 2246. -/ +theorem bounds_12_2246 : exactInterval 12 2246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2246 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2246) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2246 : oddCount 2246 12 = 6 ∧ acceleratedOrbit 12 2246 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2246 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2246) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2246.1, data_12_2246.2] + +/-- Complete interval computation for depth 12, residue 2247. -/ +theorem bounds_12_2247 : exactInterval 12 2247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2247 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2247) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2247 : oddCount 2247 12 = 7 ∧ acceleratedOrbit 12 2247 = 1201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2247 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2247) = 3 ^ 7 * m + 1201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2247.1, data_12_2247.2] + +/-- Complete interval computation for depth 12, residue 2248. -/ +theorem bounds_12_2248 : exactInterval 12 2248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2248 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2248) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2248 : oddCount 2248 12 = 6 ∧ acceleratedOrbit 12 2248 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2248 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2248) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2248.1, data_12_2248.2] + +/-- Complete interval computation for depth 12, residue 2249. -/ +theorem bounds_12_2249 : exactInterval 12 2249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2249 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2249) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2249 : oddCount 2249 12 = 5 ∧ acceleratedOrbit 12 2249 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2249 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2249) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2249.1, data_12_2249.2] + +/-- Complete interval computation for depth 12, residue 2250. -/ +theorem bounds_12_2250 : exactInterval 12 2250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2250 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2250) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2250 : oddCount 2250 12 = 6 ∧ acceleratedOrbit 12 2250 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2250 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2250) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2250.1, data_12_2250.2] + +/-- Complete interval computation for depth 12, residue 2251. -/ +theorem bounds_12_2251 : exactInterval 12 2251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2251 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2251) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2251 : oddCount 2251 12 = 7 ∧ acceleratedOrbit 12 2251 = 1205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2251 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2251) = 3 ^ 7 * m + 1205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2251.1, data_12_2251.2] + +/-- Complete interval computation for depth 12, residue 2252. -/ +theorem bounds_12_2252 : exactInterval 12 2252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2252 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2252) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2252 : oddCount 2252 12 = 6 ∧ acceleratedOrbit 12 2252 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2252 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2252) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2252.1, data_12_2252.2] + +/-- Complete interval computation for depth 12, residue 2253. -/ +theorem bounds_12_2253 : exactInterval 12 2253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2253 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2253) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2253 : oddCount 2253 12 = 6 ∧ acceleratedOrbit 12 2253 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2253 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2253) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2253.1, data_12_2253.2] + +/-- Complete interval computation for depth 12, residue 2254. -/ +theorem bounds_12_2254 : exactInterval 12 2254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2254 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2254) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2254 : oddCount 2254 12 = 9 ∧ acceleratedOrbit 12 2254 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2254 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2254) = 3 ^ 9 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2254.1, data_12_2254.2] + +/-- Complete interval computation for depth 12, residue 2255. -/ +theorem bounds_12_2255 : exactInterval 12 2255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2255 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2255) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2255 : oddCount 2255 12 = 9 ∧ acceleratedOrbit 12 2255 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2255 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2255) = 3 ^ 9 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2255.1, data_12_2255.2] + +/-- Complete interval computation for depth 12, residue 2256. -/ +theorem bounds_12_2256 : exactInterval 12 2256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2256 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2256) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2256 : oddCount 2256 12 = 2 ∧ acceleratedOrbit 12 2256 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2256 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2256) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2256.1, data_12_2256.2] + +end Collatz.Research.StoppingAtlas.Batch0347 From 9cf86793fa6016ecc4880f711baecc786c34482c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:50 +0530 Subject: [PATCH 0348/1001] proof: certify atlas Batch0348 (12:2257 to 12:2272) --- Collatz/Research/StoppingAtlas/Batch0348.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0348.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0348.lean b/Collatz/Research/StoppingAtlas/Batch0348.lean new file mode 100644 index 00000000..0b7dcb68 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0348.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0348 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2257. -/ +theorem bounds_12_2257 : exactInterval 12 2257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2257 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2257) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2257 : oddCount 2257 12 = 7 ∧ acceleratedOrbit 12 2257 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2257 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2257) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2257.1, data_12_2257.2] + +/-- Complete interval computation for depth 12, residue 2258. -/ +theorem bounds_12_2258 : exactInterval 12 2258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2258 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2258) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2258 : oddCount 2258 12 = 7 ∧ acceleratedOrbit 12 2258 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2258 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2258) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2258.1, data_12_2258.2] + +/-- Complete interval computation for depth 12, residue 2259. -/ +theorem bounds_12_2259 : exactInterval 12 2259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2259 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2259) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2259 : oddCount 2259 12 = 7 ∧ acceleratedOrbit 12 2259 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2259 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2259) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2259.1, data_12_2259.2] + +/-- Complete interval computation for depth 12, residue 2260. -/ +theorem bounds_12_2260 : exactInterval 12 2260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2260 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2260) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2260 : oddCount 2260 12 = 2 ∧ acceleratedOrbit 12 2260 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2260 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2260) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2260.1, data_12_2260.2] + +/-- Complete interval computation for depth 12, residue 2261. -/ +theorem bounds_12_2261 : exactInterval 12 2261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2261 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2261) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2261 : oddCount 2261 12 = 2 ∧ acceleratedOrbit 12 2261 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2261 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2261) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2261.1, data_12_2261.2] + +/-- Complete interval computation for depth 12, residue 2262. -/ +theorem bounds_12_2262 : exactInterval 12 2262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2262 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2262) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2262 : oddCount 2262 12 = 7 ∧ acceleratedOrbit 12 2262 = 1210 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2262 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2262) = 3 ^ 7 * m + 1210 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2262.1, data_12_2262.2] + +/-- Complete interval computation for depth 12, residue 2263. -/ +theorem bounds_12_2263 : exactInterval 12 2263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2263 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2263) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2263 : oddCount 2263 12 = 7 ∧ acceleratedOrbit 12 2263 = 1210 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2263 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2263) = 3 ^ 7 * m + 1210 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2263.1, data_12_2263.2] + +/-- Complete interval computation for depth 12, residue 2264. -/ +theorem bounds_12_2264 : exactInterval 12 2264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2264 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2264) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2264 : oddCount 2264 12 = 8 ∧ acceleratedOrbit 12 2264 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2264 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2264) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2264.1, data_12_2264.2] + +/-- Complete interval computation for depth 12, residue 2265. -/ +theorem bounds_12_2265 : exactInterval 12 2265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2265 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2265) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2265 : oddCount 2265 12 = 7 ∧ acceleratedOrbit 12 2265 = 1214 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2265 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2265) = 3 ^ 7 * m + 1214 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2265.1, data_12_2265.2] + +/-- Complete interval computation for depth 12, residue 2266. -/ +theorem bounds_12_2266 : exactInterval 12 2266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2266 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2266) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2266 : oddCount 2266 12 = 8 ∧ acceleratedOrbit 12 2266 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2266 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2266) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2266.1, data_12_2266.2] + +/-- Complete interval computation for depth 12, residue 2267. -/ +theorem bounds_12_2267 : exactInterval 12 2267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2267 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2267) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2267 : oddCount 2267 12 = 8 ∧ acceleratedOrbit 12 2267 = 3635 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2267 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2267) = 3 ^ 8 * m + 3635 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2267.1, data_12_2267.2] + +/-- Complete interval computation for depth 12, residue 2268. -/ +theorem bounds_12_2268 : exactInterval 12 2268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2268 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2268) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2268 : oddCount 2268 12 = 8 ∧ acceleratedOrbit 12 2268 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2268 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2268) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2268.1, data_12_2268.2] + +/-- Complete interval computation for depth 12, residue 2269. -/ +theorem bounds_12_2269 : exactInterval 12 2269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2269 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2269) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2269 : oddCount 2269 12 = 8 ∧ acceleratedOrbit 12 2269 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2269 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2269) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2269.1, data_12_2269.2] + +/-- Complete interval computation for depth 12, residue 2270. -/ +theorem bounds_12_2270 : exactInterval 12 2270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2270 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2270) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2270 : oddCount 2270 12 = 8 ∧ acceleratedOrbit 12 2270 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2270 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2270) = 3 ^ 8 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2270.1, data_12_2270.2] + +/-- Complete interval computation for depth 12, residue 2271. -/ +theorem bounds_12_2271 : exactInterval 12 2271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2271 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2271) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2271 : oddCount 2271 12 = 8 ∧ acceleratedOrbit 12 2271 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2271 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2271) = 3 ^ 8 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2271.1, data_12_2271.2] + +/-- Complete interval computation for depth 12, residue 2272. -/ +theorem bounds_12_2272 : exactInterval 12 2272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2272 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2272) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2272 : oddCount 2272 12 = 5 ∧ acceleratedOrbit 12 2272 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2272 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2272) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2272.1, data_12_2272.2] + +end Collatz.Research.StoppingAtlas.Batch0348 From 2ebfdc0c9ce26da1405f975e62f5df94579b177f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:51 +0530 Subject: [PATCH 0349/1001] proof: certify atlas Batch0349 (12:2273 to 12:2287) --- Collatz/Research/StoppingAtlas/Batch0349.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0349.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0349.lean b/Collatz/Research/StoppingAtlas/Batch0349.lean new file mode 100644 index 00000000..6c2aa02b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0349.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0349 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2273. -/ +theorem bounds_12_2273 : exactInterval 12 2273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2273 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2273) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2273 : oddCount 2273 12 = 10 ∧ acceleratedOrbit 12 2273 = 32804 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2273 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2273) = 3 ^ 10 * m + 32804 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2273.1, data_12_2273.2] + +/-- Complete interval computation for depth 12, residue 2274. -/ +theorem bounds_12_2274 : exactInterval 12 2274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2274 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2274) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2274 : oddCount 2274 12 = 2 ∧ acceleratedOrbit 12 2274 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2274 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2274) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2274.1, data_12_2274.2] + +/-- Complete interval computation for depth 12, residue 2275. -/ +theorem bounds_12_2275 : exactInterval 12 2275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2275 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2275) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2275 : oddCount 2275 12 = 2 ∧ acceleratedOrbit 12 2275 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2275 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2275) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2275.1, data_12_2275.2] + +/-- Complete interval computation for depth 12, residue 2276. -/ +theorem bounds_12_2276 : exactInterval 12 2276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2276 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2276) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2276 : oddCount 2276 12 = 6 ∧ acceleratedOrbit 12 2276 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2276 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2276) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2276.1, data_12_2276.2] + +/-- Complete interval computation for depth 12, residue 2277. -/ +theorem bounds_12_2277 : exactInterval 12 2277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2277 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2277) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2277 : oddCount 2277 12 = 6 ∧ acceleratedOrbit 12 2277 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2277 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2277) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2277.1, data_12_2277.2] + +/-- Complete interval computation for depth 12, residue 2278. -/ +theorem bounds_12_2278 : exactInterval 12 2278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2278 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2278) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2278 : oddCount 2278 12 = 6 ∧ acceleratedOrbit 12 2278 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2278 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2278) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2278.1, data_12_2278.2] + +/-- Complete interval computation for depth 12, residue 2279. -/ +theorem bounds_12_2279 : exactInterval 12 2279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2279 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2279) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2279 : oddCount 2279 12 = 8 ∧ acceleratedOrbit 12 2279 = 3653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2279 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2279) = 3 ^ 8 * m + 3653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2279.1, data_12_2279.2] + +/-- Complete interval computation for depth 12, residue 2280. -/ +theorem bounds_12_2280 : exactInterval 12 2280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2280 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2280) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2280 : oddCount 2280 12 = 5 ∧ acceleratedOrbit 12 2280 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2280 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2280) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2280.1, data_12_2280.2] + +/-- Complete interval computation for depth 12, residue 2281. -/ +theorem bounds_12_2281 : exactInterval 12 2281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2281 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2281) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2281 : oddCount 2281 12 = 7 ∧ acceleratedOrbit 12 2281 = 1219 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2281 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2281) = 3 ^ 7 * m + 1219 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2281.1, data_12_2281.2] + +/-- Complete interval computation for depth 12, residue 2282. -/ +theorem bounds_12_2282 : exactInterval 12 2282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2282 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2282) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2282 : oddCount 2282 12 = 5 ∧ acceleratedOrbit 12 2282 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2282 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2282) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2282.1, data_12_2282.2] + +/-- Complete interval computation for depth 12, residue 2283. -/ +theorem bounds_12_2283 : exactInterval 12 2283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2283 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2283) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2283 : oddCount 2283 12 = 7 ∧ acceleratedOrbit 12 2283 = 1220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2283 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2283) = 3 ^ 7 * m + 1220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2283.1, data_12_2283.2] + +/-- Complete interval computation for depth 12, residue 2284. -/ +theorem bounds_12_2284 : exactInterval 12 2284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2284 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2284) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2284 : oddCount 2284 12 = 5 ∧ acceleratedOrbit 12 2284 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2284 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2284) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2284.1, data_12_2284.2] + +/-- Complete interval computation for depth 12, residue 2285. -/ +theorem bounds_12_2285 : exactInterval 12 2285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2285 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2285) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2285 : oddCount 2285 12 = 5 ∧ acceleratedOrbit 12 2285 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2285 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2285) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2285.1, data_12_2285.2] + +/-- Complete interval computation for depth 12, residue 2286. -/ +theorem bounds_12_2286 : exactInterval 12 2286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2286 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2286) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2286 : oddCount 2286 12 = 5 ∧ acceleratedOrbit 12 2286 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2286 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2286) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2286.1, data_12_2286.2] + +/-- Complete interval computation for depth 12, residue 2287. -/ +theorem bounds_12_2287 : exactInterval 12 2287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2287 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2287) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2287 : oddCount 2287 12 = 10 ∧ acceleratedOrbit 12 2287 = 32987 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2287 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2287) = 3 ^ 10 * m + 32987 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2287.1, data_12_2287.2] + +end Collatz.Research.StoppingAtlas.Batch0349 From 94e72a124e75bddb63c9d95604066c5c1b13d580 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:51 +0530 Subject: [PATCH 0350/1001] proof: certify atlas Batch0350 (12:2288 to 12:2303) --- Collatz/Research/StoppingAtlas/Batch0350.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0350.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0350.lean b/Collatz/Research/StoppingAtlas/Batch0350.lean new file mode 100644 index 00000000..3b880e2f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0350.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0350 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2288. -/ +theorem bounds_12_2288 : exactInterval 12 2288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2288 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2288) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2288 : oddCount 2288 12 = 5 ∧ acceleratedOrbit 12 2288 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2288 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2288) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2288.1, data_12_2288.2] + +/-- Complete interval computation for depth 12, residue 2289. -/ +theorem bounds_12_2289 : exactInterval 12 2289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2289 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2289) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2289 : oddCount 2289 12 = 5 ∧ acceleratedOrbit 12 2289 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2289 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2289) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2289.1, data_12_2289.2] + +/-- Complete interval computation for depth 12, residue 2290. -/ +theorem bounds_12_2290 : exactInterval 12 2290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2290 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2290) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2290 : oddCount 2290 12 = 7 ∧ acceleratedOrbit 12 2290 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2290 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2290) = 3 ^ 7 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2290.1, data_12_2290.2] + +/-- Complete interval computation for depth 12, residue 2291. -/ +theorem bounds_12_2291 : exactInterval 12 2291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2291 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2291) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2291 : oddCount 2291 12 = 7 ∧ acceleratedOrbit 12 2291 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2291 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2291) = 3 ^ 7 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2291.1, data_12_2291.2] + +/-- Complete interval computation for depth 12, residue 2292. -/ +theorem bounds_12_2292 : exactInterval 12 2292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2292 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2292) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2292 : oddCount 2292 12 = 5 ∧ acceleratedOrbit 12 2292 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2292 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2292) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2292.1, data_12_2292.2] + +/-- Complete interval computation for depth 12, residue 2293. -/ +theorem bounds_12_2293 : exactInterval 12 2293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2293 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2293) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2293 : oddCount 2293 12 = 5 ∧ acceleratedOrbit 12 2293 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2293 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2293) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2293.1, data_12_2293.2] + +/-- Complete interval computation for depth 12, residue 2294. -/ +theorem bounds_12_2294 : exactInterval 12 2294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2294 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2294) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2294 : oddCount 2294 12 = 6 ∧ acceleratedOrbit 12 2294 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2294 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2294) = 3 ^ 6 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2294.1, data_12_2294.2] + +/-- Complete interval computation for depth 12, residue 2295. -/ +theorem bounds_12_2295 : exactInterval 12 2295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2295 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2295) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2295 : oddCount 2295 12 = 6 ∧ acceleratedOrbit 12 2295 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2295 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2295) = 3 ^ 6 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2295.1, data_12_2295.2] + +/-- Complete interval computation for depth 12, residue 2296. -/ +theorem bounds_12_2296 : exactInterval 12 2296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2296 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2296) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2296 : oddCount 2296 12 = 6 ∧ acceleratedOrbit 12 2296 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2296 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2296) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2296.1, data_12_2296.2] + +/-- Complete interval computation for depth 12, residue 2297. -/ +theorem bounds_12_2297 : exactInterval 12 2297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2297 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2297) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2297 : oddCount 2297 12 = 7 ∧ acceleratedOrbit 12 2297 = 1228 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2297 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2297) = 3 ^ 7 * m + 1228 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2297.1, data_12_2297.2] + +/-- Complete interval computation for depth 12, residue 2298. -/ +theorem bounds_12_2298 : exactInterval 12 2298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2298 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2298) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2298 : oddCount 2298 12 = 6 ∧ acceleratedOrbit 12 2298 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2298 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2298) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2298.1, data_12_2298.2] + +/-- Complete interval computation for depth 12, residue 2299. -/ +theorem bounds_12_2299 : exactInterval 12 2299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2299 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2299) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2299 : oddCount 2299 12 = 9 ∧ acceleratedOrbit 12 2299 = 11056 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2299 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2299) = 3 ^ 9 * m + 11056 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2299.1, data_12_2299.2] + +/-- Complete interval computation for depth 12, residue 2300. -/ +theorem bounds_12_2300 : exactInterval 12 2300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2300 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2300) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2300 : oddCount 2300 12 = 6 ∧ acceleratedOrbit 12 2300 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2300 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2300) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2300.1, data_12_2300.2] + +/-- Complete interval computation for depth 12, residue 2301. -/ +theorem bounds_12_2301 : exactInterval 12 2301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2301 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2301) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2301 : oddCount 2301 12 = 6 ∧ acceleratedOrbit 12 2301 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2301 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2301) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2301.1, data_12_2301.2] + +/-- Complete interval computation for depth 12, residue 2302. -/ +theorem bounds_12_2302 : exactInterval 12 2302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2302 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2302) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2302 : oddCount 2302 12 = 9 ∧ acceleratedOrbit 12 2302 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2302 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2302) = 3 ^ 9 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2302.1, data_12_2302.2] + +/-- Complete interval computation for depth 12, residue 2303. -/ +theorem bounds_12_2303 : exactInterval 12 2303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2303 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2303) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2303 : oddCount 2303 12 = 9 ∧ acceleratedOrbit 12 2303 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2303 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2303) = 3 ^ 9 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2303.1, data_12_2303.2] + +end Collatz.Research.StoppingAtlas.Batch0350 From fef4db9d30d53846b7b0ab8f2966e039cd1af580 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:51 +0530 Subject: [PATCH 0351/1001] proof: certify atlas Batch0351 (12:2304 to 12:2318) --- Collatz/Research/StoppingAtlas/Batch0351.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0351.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0351.lean b/Collatz/Research/StoppingAtlas/Batch0351.lean new file mode 100644 index 00000000..e1e33724 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0351.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0351 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2304. -/ +theorem bounds_12_2304 : exactInterval 12 2304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2304 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2304) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2304 : oddCount 2304 12 = 3 ∧ acceleratedOrbit 12 2304 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2304 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2304) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2304.1, data_12_2304.2] + +/-- Complete interval computation for depth 12, residue 2305. -/ +theorem bounds_12_2305 : exactInterval 12 2305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2305 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2305) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2305 : oddCount 2305 12 = 5 ∧ acceleratedOrbit 12 2305 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2305 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2305) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2305.1, data_12_2305.2] + +/-- Complete interval computation for depth 12, residue 2306. -/ +theorem bounds_12_2306 : exactInterval 12 2306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2306 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2306) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2306 : oddCount 2306 12 = 7 ∧ acceleratedOrbit 12 2306 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2306 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2306) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2306.1, data_12_2306.2] + +/-- Complete interval computation for depth 12, residue 2307. -/ +theorem bounds_12_2307 : exactInterval 12 2307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2307 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2307) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2307 : oddCount 2307 12 = 7 ∧ acceleratedOrbit 12 2307 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2307 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2307) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2307.1, data_12_2307.2] + +/-- Complete interval computation for depth 12, residue 2308. -/ +theorem bounds_12_2308 : exactInterval 12 2308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2308 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2308) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2308 : oddCount 2308 12 = 4 ∧ acceleratedOrbit 12 2308 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2308 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2308) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2308.1, data_12_2308.2] + +/-- Complete interval computation for depth 12, residue 2309. -/ +theorem bounds_12_2309 : exactInterval 12 2309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2309 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2309) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2309 : oddCount 2309 12 = 4 ∧ acceleratedOrbit 12 2309 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2309 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2309) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2309.1, data_12_2309.2] + +/-- Complete interval computation for depth 12, residue 2310. -/ +theorem bounds_12_2310 : exactInterval 12 2310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2310 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2310) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2310 : oddCount 2310 12 = 4 ∧ acceleratedOrbit 12 2310 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2310 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2310) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2310.1, data_12_2310.2] + +/-- Complete interval computation for depth 12, residue 2311. -/ +theorem bounds_12_2311 : exactInterval 12 2311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2311 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2311) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2311 : oddCount 2311 12 = 7 ∧ acceleratedOrbit 12 2311 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2311 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2311) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2311.1, data_12_2311.2] + +/-- Complete interval computation for depth 12, residue 2312. -/ +theorem bounds_12_2312 : exactInterval 12 2312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2312 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2312) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2312 : oddCount 2312 12 = 4 ∧ acceleratedOrbit 12 2312 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2312 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2312) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2312.1, data_12_2312.2] + +/-- Complete interval computation for depth 12, residue 2313. -/ +theorem bounds_12_2313 : exactInterval 12 2313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2313 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2313) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2313 : oddCount 2313 12 = 6 ∧ acceleratedOrbit 12 2313 = 412 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2313 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2313) = 3 ^ 6 * m + 412 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2313.1, data_12_2313.2] + +/-- Complete interval computation for depth 12, residue 2314. -/ +theorem bounds_12_2314 : exactInterval 12 2314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2314 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2314) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2314 : oddCount 2314 12 = 4 ∧ acceleratedOrbit 12 2314 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2314 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2314) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2314.1, data_12_2314.2] + +/-- Complete interval computation for depth 12, residue 2315. -/ +theorem bounds_12_2315 : exactInterval 12 2315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2315 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2315) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2315 : oddCount 2315 12 = 6 ∧ acceleratedOrbit 12 2315 = 413 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2315 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2315) = 3 ^ 6 * m + 413 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2315.1, data_12_2315.2] + +/-- Complete interval computation for depth 12, residue 2316. -/ +theorem bounds_12_2316 : exactInterval 12 2316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2316 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2316) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2316 : oddCount 2316 12 = 4 ∧ acceleratedOrbit 12 2316 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2316 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2316) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2316.1, data_12_2316.2] + +/-- Complete interval computation for depth 12, residue 2317. -/ +theorem bounds_12_2317 : exactInterval 12 2317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2317 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2317) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2317 : oddCount 2317 12 = 4 ∧ acceleratedOrbit 12 2317 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2317 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2317) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2317.1, data_12_2317.2] + +/-- Complete interval computation for depth 12, residue 2318. -/ +theorem bounds_12_2318 : exactInterval 12 2318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2318 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2318) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2318 : oddCount 2318 12 = 7 ∧ acceleratedOrbit 12 2318 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2318 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2318) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2318.1, data_12_2318.2] + +end Collatz.Research.StoppingAtlas.Batch0351 From 0e423baef49f98c0c01ed8aac9d061bf5c524304 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:52 +0530 Subject: [PATCH 0352/1001] proof: certify atlas Batch0352 (12:2319 to 12:2333) --- Collatz/Research/StoppingAtlas/Batch0352.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0352.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0352.lean b/Collatz/Research/StoppingAtlas/Batch0352.lean new file mode 100644 index 00000000..bf7d125e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0352.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0352 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2319. -/ +theorem bounds_12_2319 : exactInterval 12 2319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2319 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2319) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2319 : oddCount 2319 12 = 7 ∧ acceleratedOrbit 12 2319 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2319 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2319) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2319.1, data_12_2319.2] + +/-- Complete interval computation for depth 12, residue 2320. -/ +theorem bounds_12_2320 : exactInterval 12 2320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2320 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2320) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2320 : oddCount 2320 12 = 4 ∧ acceleratedOrbit 12 2320 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2320 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2320) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2320.1, data_12_2320.2] + +/-- Complete interval computation for depth 12, residue 2321. -/ +theorem bounds_12_2321 : exactInterval 12 2321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2321 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2321) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2321 : oddCount 2321 12 = 4 ∧ acceleratedOrbit 12 2321 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2321 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2321) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2321.1, data_12_2321.2] + +/-- Complete interval computation for depth 12, residue 2322. -/ +theorem bounds_12_2322 : exactInterval 12 2322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2322 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2322) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2322 : oddCount 2322 12 = 9 ∧ acceleratedOrbit 12 2322 = 11177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2322 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2322) = 3 ^ 9 * m + 11177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2322.1, data_12_2322.2] + +/-- Complete interval computation for depth 12, residue 2323. -/ +theorem bounds_12_2323 : exactInterval 12 2323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2323 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2323) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2323 : oddCount 2323 12 = 9 ∧ acceleratedOrbit 12 2323 = 11177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2323 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2323) = 3 ^ 9 * m + 11177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2323.1, data_12_2323.2] + +/-- Complete interval computation for depth 12, residue 2324. -/ +theorem bounds_12_2324 : exactInterval 12 2324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2324 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2324) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2324 : oddCount 2324 12 = 4 ∧ acceleratedOrbit 12 2324 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2324 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2324) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2324.1, data_12_2324.2] + +/-- Complete interval computation for depth 12, residue 2325. -/ +theorem bounds_12_2325 : exactInterval 12 2325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2325 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2325) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2325 : oddCount 2325 12 = 4 ∧ acceleratedOrbit 12 2325 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2325 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2325) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2325.1, data_12_2325.2] + +/-- Complete interval computation for depth 12, residue 2326. -/ +theorem bounds_12_2326 : exactInterval 12 2326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2326 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2326) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2326 : oddCount 2326 12 = 6 ∧ acceleratedOrbit 12 2326 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2326 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2326) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2326.1, data_12_2326.2] + +/-- Complete interval computation for depth 12, residue 2327. -/ +theorem bounds_12_2327 : exactInterval 12 2327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2327 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2327) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2327 : oddCount 2327 12 = 6 ∧ acceleratedOrbit 12 2327 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2327 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2327) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2327.1, data_12_2327.2] + +/-- Complete interval computation for depth 12, residue 2328. -/ +theorem bounds_12_2328 : exactInterval 12 2328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2328 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2328) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2328 : oddCount 2328 12 = 4 ∧ acceleratedOrbit 12 2328 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2328 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2328) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2328.1, data_12_2328.2] + +/-- Complete interval computation for depth 12, residue 2329. -/ +theorem bounds_12_2329 : exactInterval 12 2329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2329 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2329) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2329 : oddCount 2329 12 = 6 ∧ acceleratedOrbit 12 2329 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2329 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2329) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2329.1, data_12_2329.2] + +/-- Complete interval computation for depth 12, residue 2330. -/ +theorem bounds_12_2330 : exactInterval 12 2330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2330 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2330) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2330 : oddCount 2330 12 = 4 ∧ acceleratedOrbit 12 2330 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2330 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2330) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2330.1, data_12_2330.2] + +/-- Complete interval computation for depth 12, residue 2331. -/ +theorem bounds_12_2331 : exactInterval 12 2331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2331 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2331) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2331 : oddCount 2331 12 = 8 ∧ acceleratedOrbit 12 2331 = 3736 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2331 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2331) = 3 ^ 8 * m + 3736 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2331.1, data_12_2331.2] + +/-- Complete interval computation for depth 12, residue 2332. -/ +theorem bounds_12_2332 : exactInterval 12 2332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2332 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2332) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2332 : oddCount 2332 12 = 6 ∧ acceleratedOrbit 12 2332 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2332 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2332) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2332.1, data_12_2332.2] + +/-- Complete interval computation for depth 12, residue 2333. -/ +theorem bounds_12_2333 : exactInterval 12 2333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2333 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2333) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2333 : oddCount 2333 12 = 6 ∧ acceleratedOrbit 12 2333 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2333 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2333) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2333.1, data_12_2333.2] + +end Collatz.Research.StoppingAtlas.Batch0352 From c09039cd22798f31e6787d0727ac50d9c558a5e9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:52 +0530 Subject: [PATCH 0353/1001] proof: certify atlas Batch0353 (12:2334 to 12:2349) --- Collatz/Research/StoppingAtlas/Batch0353.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0353.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0353.lean b/Collatz/Research/StoppingAtlas/Batch0353.lean new file mode 100644 index 00000000..bb37e9e3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0353.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0353 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2334. -/ +theorem bounds_12_2334 : exactInterval 12 2334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2334 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2334) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2334 : oddCount 2334 12 = 6 ∧ acceleratedOrbit 12 2334 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2334 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2334) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2334.1, data_12_2334.2] + +/-- Complete interval computation for depth 12, residue 2335. -/ +theorem bounds_12_2335 : exactInterval 12 2335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2335 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2335) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2335 : oddCount 2335 12 = 8 ∧ acceleratedOrbit 12 2335 = 3743 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2335 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2335) = 3 ^ 8 * m + 3743 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2335.1, data_12_2335.2] + +/-- Complete interval computation for depth 12, residue 2336. -/ +theorem bounds_12_2336 : exactInterval 12 2336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2336 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2336) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2336 : oddCount 2336 12 = 4 ∧ acceleratedOrbit 12 2336 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2336 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2336) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2336.1, data_12_2336.2] + +/-- Complete interval computation for depth 12, residue 2337. -/ +theorem bounds_12_2337 : exactInterval 12 2337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2337 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2337) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2337 : oddCount 2337 12 = 5 ∧ acceleratedOrbit 12 2337 = 139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2337 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2337) = 3 ^ 5 * m + 139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2337.1, data_12_2337.2] + +/-- Complete interval computation for depth 12, residue 2338. -/ +theorem bounds_12_2338 : exactInterval 12 2338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2338 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2338) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2338 : oddCount 2338 12 = 6 ∧ acceleratedOrbit 12 2338 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2338 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2338) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2338.1, data_12_2338.2] + +/-- Complete interval computation for depth 12, residue 2339. -/ +theorem bounds_12_2339 : exactInterval 12 2339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2339 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2339) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2339 : oddCount 2339 12 = 6 ∧ acceleratedOrbit 12 2339 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2339 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2339) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2339.1, data_12_2339.2] + +/-- Complete interval computation for depth 12, residue 2340. -/ +theorem bounds_12_2340 : exactInterval 12 2340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2340 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2340) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2340 : oddCount 2340 12 = 6 ∧ acceleratedOrbit 12 2340 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2340 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2340) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2340.1, data_12_2340.2] + +/-- Complete interval computation for depth 12, residue 2341. -/ +theorem bounds_12_2341 : exactInterval 12 2341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2341 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2341) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2341 : oddCount 2341 12 = 6 ∧ acceleratedOrbit 12 2341 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2341 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2341) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2341.1, data_12_2341.2] + +/-- Complete interval computation for depth 12, residue 2342. -/ +theorem bounds_12_2342 : exactInterval 12 2342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2342 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2342) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2342 : oddCount 2342 12 = 6 ∧ acceleratedOrbit 12 2342 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2342 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2342) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2342.1, data_12_2342.2] + +/-- Complete interval computation for depth 12, residue 2343. -/ +theorem bounds_12_2343 : exactInterval 12 2343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2343 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2343) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2343 : oddCount 2343 12 = 7 ∧ acceleratedOrbit 12 2343 = 1252 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2343 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2343) = 3 ^ 7 * m + 1252 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2343.1, data_12_2343.2] + +/-- Complete interval computation for depth 12, residue 2344. -/ +theorem bounds_12_2344 : exactInterval 12 2344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2344 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2344) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2344 : oddCount 2344 12 = 4 ∧ acceleratedOrbit 12 2344 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2344 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2344) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2344.1, data_12_2344.2] + +/-- Complete interval computation for depth 12, residue 2345. -/ +theorem bounds_12_2345 : exactInterval 12 2345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2345 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2345) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2345 : oddCount 2345 12 = 7 ∧ acceleratedOrbit 12 2345 = 1253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2345 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2345) = 3 ^ 7 * m + 1253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2345.1, data_12_2345.2] + +/-- Complete interval computation for depth 12, residue 2346. -/ +theorem bounds_12_2346 : exactInterval 12 2346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2346 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2346) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2346 : oddCount 2346 12 = 4 ∧ acceleratedOrbit 12 2346 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2346 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2346) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2346.1, data_12_2346.2] + +/-- Complete interval computation for depth 12, residue 2347. -/ +theorem bounds_12_2347 : exactInterval 12 2347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2347 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2347) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2347 : oddCount 2347 12 = 7 ∧ acceleratedOrbit 12 2347 = 1255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2347 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2347) = 3 ^ 7 * m + 1255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2347.1, data_12_2347.2] + +/-- Complete interval computation for depth 12, residue 2348. -/ +theorem bounds_12_2348 : exactInterval 12 2348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2348 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2348) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2348 : oddCount 2348 12 = 4 ∧ acceleratedOrbit 12 2348 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2348 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2348) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2348.1, data_12_2348.2] + +/-- Complete interval computation for depth 12, residue 2349. -/ +theorem bounds_12_2349 : exactInterval 12 2349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2349 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2349) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2349 : oddCount 2349 12 = 4 ∧ acceleratedOrbit 12 2349 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2349 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2349) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2349.1, data_12_2349.2] + +end Collatz.Research.StoppingAtlas.Batch0353 From 43b042708f3b9616e21ccbef7d035582f51a0ff8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:52 +0530 Subject: [PATCH 0354/1001] proof: certify atlas Batch0354 (12:2350 to 12:2364) --- Collatz/Research/StoppingAtlas/Batch0354.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0354.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0354.lean b/Collatz/Research/StoppingAtlas/Batch0354.lean new file mode 100644 index 00000000..49b09167 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0354.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0354 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2350. -/ +theorem bounds_12_2350 : exactInterval 12 2350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2350 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2350) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2350 : oddCount 2350 12 = 4 ∧ acceleratedOrbit 12 2350 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2350 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2350) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2350.1, data_12_2350.2] + +/-- Complete interval computation for depth 12, residue 2351. -/ +theorem bounds_12_2351 : exactInterval 12 2351 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2351 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2351) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2351 : oddCount 2351 12 = 7 ∧ acceleratedOrbit 12 2351 = 1256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2351 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2351) = 3 ^ 7 * m + 1256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2351.1, data_12_2351.2] + +/-- Complete interval computation for depth 12, residue 2352. -/ +theorem bounds_12_2352 : exactInterval 12 2352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2352 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2352) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2352 : oddCount 2352 12 = 4 ∧ acceleratedOrbit 12 2352 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2352 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2352) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2352.1, data_12_2352.2] + +/-- Complete interval computation for depth 12, residue 2353. -/ +theorem bounds_12_2353 : exactInterval 12 2353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2353 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2353) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2353 : oddCount 2353 12 = 5 ∧ acceleratedOrbit 12 2353 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2353 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2353) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2353.1, data_12_2353.2] + +/-- Complete interval computation for depth 12, residue 2354. -/ +theorem bounds_12_2354 : exactInterval 12 2354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2354 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2354) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2354 : oddCount 2354 12 = 5 ∧ acceleratedOrbit 12 2354 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2354 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2354) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2354.1, data_12_2354.2] + +/-- Complete interval computation for depth 12, residue 2355. -/ +theorem bounds_12_2355 : exactInterval 12 2355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2355 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2355) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2355 : oddCount 2355 12 = 5 ∧ acceleratedOrbit 12 2355 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2355 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2355) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2355.1, data_12_2355.2] + +/-- Complete interval computation for depth 12, residue 2356. -/ +theorem bounds_12_2356 : exactInterval 12 2356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2356 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2356) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2356 : oddCount 2356 12 = 4 ∧ acceleratedOrbit 12 2356 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2356 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2356) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2356.1, data_12_2356.2] + +/-- Complete interval computation for depth 12, residue 2357. -/ +theorem bounds_12_2357 : exactInterval 12 2357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2357 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2357) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2357 : oddCount 2357 12 = 4 ∧ acceleratedOrbit 12 2357 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2357 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2357) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2357.1, data_12_2357.2] + +/-- Complete interval computation for depth 12, residue 2358. -/ +theorem bounds_12_2358 : exactInterval 12 2358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2358 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2358) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2358 : oddCount 2358 12 = 8 ∧ acceleratedOrbit 12 2358 = 3782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2358 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2358) = 3 ^ 8 * m + 3782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2358.1, data_12_2358.2] + +/-- Complete interval computation for depth 12, residue 2359. -/ +theorem bounds_12_2359 : exactInterval 12 2359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2359 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2359) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2359 : oddCount 2359 12 = 8 ∧ acceleratedOrbit 12 2359 = 3782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2359 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2359) = 3 ^ 8 * m + 3782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2359.1, data_12_2359.2] + +/-- Complete interval computation for depth 12, residue 2360. -/ +theorem bounds_12_2360 : exactInterval 12 2360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2360 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2360) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2360 : oddCount 2360 12 = 6 ∧ acceleratedOrbit 12 2360 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2360 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2360) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2360.1, data_12_2360.2] + +/-- Complete interval computation for depth 12, residue 2361. -/ +theorem bounds_12_2361 : exactInterval 12 2361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2361 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2361) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2361 : oddCount 2361 12 = 7 ∧ acceleratedOrbit 12 2361 = 1262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2361 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2361) = 3 ^ 7 * m + 1262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2361.1, data_12_2361.2] + +/-- Complete interval computation for depth 12, residue 2362. -/ +theorem bounds_12_2362 : exactInterval 12 2362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2362 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2362) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2362 : oddCount 2362 12 = 6 ∧ acceleratedOrbit 12 2362 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2362 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2362) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2362.1, data_12_2362.2] + +/-- Complete interval computation for depth 12, residue 2363. -/ +theorem bounds_12_2363 : exactInterval 12 2363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2363 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2363) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2363 : oddCount 2363 12 = 6 ∧ acceleratedOrbit 12 2363 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2363 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2363) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2363.1, data_12_2363.2] + +/-- Complete interval computation for depth 12, residue 2364. -/ +theorem bounds_12_2364 : exactInterval 12 2364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2364 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2364) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2364 : oddCount 2364 12 = 6 ∧ acceleratedOrbit 12 2364 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2364 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2364) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2364.1, data_12_2364.2] + +end Collatz.Research.StoppingAtlas.Batch0354 From 98acbff996f0dd148c168c81fec1bea669c3bcfa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:52 +0530 Subject: [PATCH 0355/1001] proof: certify atlas Batch0355 (12:2365 to 12:2379) --- Collatz/Research/StoppingAtlas/Batch0355.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0355.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0355.lean b/Collatz/Research/StoppingAtlas/Batch0355.lean new file mode 100644 index 00000000..f78d7db6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0355.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0355 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2365. -/ +theorem bounds_12_2365 : exactInterval 12 2365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2365 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2365) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2365 : oddCount 2365 12 = 6 ∧ acceleratedOrbit 12 2365 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2365 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2365) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2365.1, data_12_2365.2] + +/-- Complete interval computation for depth 12, residue 2366. -/ +theorem bounds_12_2366 : exactInterval 12 2366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2366 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2366) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2366 : oddCount 2366 12 = 9 ∧ acceleratedOrbit 12 2366 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2366 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2366) = 3 ^ 9 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2366.1, data_12_2366.2] + +/-- Complete interval computation for depth 12, residue 2367. -/ +theorem bounds_12_2367 : exactInterval 12 2367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2367 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2367) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2367 : oddCount 2367 12 = 9 ∧ acceleratedOrbit 12 2367 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2367 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2367) = 3 ^ 9 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2367.1, data_12_2367.2] + +/-- Complete interval computation for depth 12, residue 2368. -/ +theorem bounds_12_2368 : exactInterval 12 2368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2368 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2368) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2368 : oddCount 2368 12 = 3 ∧ acceleratedOrbit 12 2368 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2368 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2368) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2368.1, data_12_2368.2] + +/-- Complete interval computation for depth 12, residue 2369. -/ +theorem bounds_12_2369 : exactInterval 12 2369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2369 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2369) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2369 : oddCount 2369 12 = 4 ∧ acceleratedOrbit 12 2369 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2369 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2369) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2369.1, data_12_2369.2] + +/-- Complete interval computation for depth 12, residue 2370. -/ +theorem bounds_12_2370 : exactInterval 12 2370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2370 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2370) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2370 : oddCount 2370 12 = 8 ∧ acceleratedOrbit 12 2370 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2370 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2370) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2370.1, data_12_2370.2] + +/-- Complete interval computation for depth 12, residue 2371. -/ +theorem bounds_12_2371 : exactInterval 12 2371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2371 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2371) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2371 : oddCount 2371 12 = 8 ∧ acceleratedOrbit 12 2371 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2371 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2371) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2371.1, data_12_2371.2] + +/-- Complete interval computation for depth 12, residue 2372. -/ +theorem bounds_12_2372 : exactInterval 12 2372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2372 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2372) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2372 : oddCount 2372 12 = 6 ∧ acceleratedOrbit 12 2372 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2372 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2372) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2372.1, data_12_2372.2] + +/-- Complete interval computation for depth 12, residue 2373. -/ +theorem bounds_12_2373 : exactInterval 12 2373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2373 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2373) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2373 : oddCount 2373 12 = 6 ∧ acceleratedOrbit 12 2373 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2373 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2373) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2373.1, data_12_2373.2] + +/-- Complete interval computation for depth 12, residue 2374. -/ +theorem bounds_12_2374 : exactInterval 12 2374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2374 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2374) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2374 : oddCount 2374 12 = 6 ∧ acceleratedOrbit 12 2374 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2374 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2374) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2374.1, data_12_2374.2] + +/-- Complete interval computation for depth 12, residue 2375. -/ +theorem bounds_12_2375 : exactInterval 12 2375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2375 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2375) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2375 : oddCount 2375 12 = 10 ∧ acceleratedOrbit 12 2375 = 34262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2375 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2375) = 3 ^ 10 * m + 34262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2375.1, data_12_2375.2] + +/-- Complete interval computation for depth 12, residue 2376. -/ +theorem bounds_12_2376 : exactInterval 12 2376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2376 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2376) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2376 : oddCount 2376 12 = 6 ∧ acceleratedOrbit 12 2376 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2376 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2376) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2376.1, data_12_2376.2] + +/-- Complete interval computation for depth 12, residue 2377. -/ +theorem bounds_12_2377 : exactInterval 12 2377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2377 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2377) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2377 : oddCount 2377 12 = 7 ∧ acceleratedOrbit 12 2377 = 1271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2377 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2377) = 3 ^ 7 * m + 1271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2377.1, data_12_2377.2] + +/-- Complete interval computation for depth 12, residue 2378. -/ +theorem bounds_12_2378 : exactInterval 12 2378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2378 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2378) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2378 : oddCount 2378 12 = 6 ∧ acceleratedOrbit 12 2378 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2378 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2378) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2378.1, data_12_2378.2] + +/-- Complete interval computation for depth 12, residue 2379. -/ +theorem bounds_12_2379 : exactInterval 12 2379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2379 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2379) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2379 : oddCount 2379 12 = 6 ∧ acceleratedOrbit 12 2379 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2379 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2379) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2379.1, data_12_2379.2] + +end Collatz.Research.StoppingAtlas.Batch0355 From 8b39be354a2d45ac194766696b4f376fc5a3ed49 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:53 +0530 Subject: [PATCH 0356/1001] proof: certify atlas Batch0356 (12:2380 to 12:2395) --- Collatz/Research/StoppingAtlas/Batch0356.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0356.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0356.lean b/Collatz/Research/StoppingAtlas/Batch0356.lean new file mode 100644 index 00000000..58a3ef05 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0356.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0356 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2380. -/ +theorem bounds_12_2380 : exactInterval 12 2380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2380 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2380) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2380 : oddCount 2380 12 = 6 ∧ acceleratedOrbit 12 2380 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2380 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2380) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2380.1, data_12_2380.2] + +/-- Complete interval computation for depth 12, residue 2381. -/ +theorem bounds_12_2381 : exactInterval 12 2381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2381 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2381) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2381 : oddCount 2381 12 = 6 ∧ acceleratedOrbit 12 2381 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2381 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2381) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2381.1, data_12_2381.2] + +/-- Complete interval computation for depth 12, residue 2382. -/ +theorem bounds_12_2382 : exactInterval 12 2382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2382 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2382) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2382 : oddCount 2382 12 = 8 ∧ acceleratedOrbit 12 2382 = 3820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2382 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2382) = 3 ^ 8 * m + 3820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2382.1, data_12_2382.2] + +/-- Complete interval computation for depth 12, residue 2383. -/ +theorem bounds_12_2383 : exactInterval 12 2383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2383 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2383) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2383 : oddCount 2383 12 = 8 ∧ acceleratedOrbit 12 2383 = 3820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2383 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2383) = 3 ^ 8 * m + 3820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2383.1, data_12_2383.2] + +/-- Complete interval computation for depth 12, residue 2384. -/ +theorem bounds_12_2384 : exactInterval 12 2384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2384 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2384) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2384 : oddCount 2384 12 = 3 ∧ acceleratedOrbit 12 2384 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2384 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2384) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2384.1, data_12_2384.2] + +/-- Complete interval computation for depth 12, residue 2385. -/ +theorem bounds_12_2385 : exactInterval 12 2385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2385 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2385) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2385 : oddCount 2385 12 = 8 ∧ acceleratedOrbit 12 2385 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2385 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2385) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2385.1, data_12_2385.2] + +/-- Complete interval computation for depth 12, residue 2386. -/ +theorem bounds_12_2386 : exactInterval 12 2386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2386 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2386) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2386 : oddCount 2386 12 = 8 ∧ acceleratedOrbit 12 2386 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2386 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2386) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2386.1, data_12_2386.2] + +/-- Complete interval computation for depth 12, residue 2387. -/ +theorem bounds_12_2387 : exactInterval 12 2387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2387 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2387) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2387 : oddCount 2387 12 = 8 ∧ acceleratedOrbit 12 2387 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2387 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2387) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2387.1, data_12_2387.2] + +/-- Complete interval computation for depth 12, residue 2388. -/ +theorem bounds_12_2388 : exactInterval 12 2388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2388 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2388) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2388 : oddCount 2388 12 = 3 ∧ acceleratedOrbit 12 2388 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2388 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2388) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2388.1, data_12_2388.2] + +/-- Complete interval computation for depth 12, residue 2389. -/ +theorem bounds_12_2389 : exactInterval 12 2389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2389 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2389) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2389 : oddCount 2389 12 = 3 ∧ acceleratedOrbit 12 2389 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2389 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2389) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2389.1, data_12_2389.2] + +/-- Complete interval computation for depth 12, residue 2390. -/ +theorem bounds_12_2390 : exactInterval 12 2390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2390 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2390) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2390 : oddCount 2390 12 = 5 ∧ acceleratedOrbit 12 2390 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2390 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2390) = 3 ^ 5 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2390.1, data_12_2390.2] + +/-- Complete interval computation for depth 12, residue 2391. -/ +theorem bounds_12_2391 : exactInterval 12 2391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2391 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2391) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2391 : oddCount 2391 12 = 5 ∧ acceleratedOrbit 12 2391 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2391 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2391) = 3 ^ 5 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2391.1, data_12_2391.2] + +/-- Complete interval computation for depth 12, residue 2392. -/ +theorem bounds_12_2392 : exactInterval 12 2392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2392 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2392) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2392 : oddCount 2392 12 = 5 ∧ acceleratedOrbit 12 2392 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2392 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2392) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2392.1, data_12_2392.2] + +/-- Complete interval computation for depth 12, residue 2393. -/ +theorem bounds_12_2393 : exactInterval 12 2393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2393 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2393) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2393 : oddCount 2393 12 = 6 ∧ acceleratedOrbit 12 2393 = 427 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2393 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2393) = 3 ^ 6 * m + 427 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2393.1, data_12_2393.2] + +/-- Complete interval computation for depth 12, residue 2394. -/ +theorem bounds_12_2394 : exactInterval 12 2394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2394 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2394) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2394 : oddCount 2394 12 = 5 ∧ acceleratedOrbit 12 2394 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2394 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2394) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2394.1, data_12_2394.2] + +/-- Complete interval computation for depth 12, residue 2395. -/ +theorem bounds_12_2395 : exactInterval 12 2395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2395 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2395) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2395 : oddCount 2395 12 = 7 ∧ acceleratedOrbit 12 2395 = 1280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2395 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2395) = 3 ^ 7 * m + 1280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2395.1, data_12_2395.2] + +end Collatz.Research.StoppingAtlas.Batch0356 From 3a4880f8bf4d7d4f784e44e4d05b2f32765b9379 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:53 +0530 Subject: [PATCH 0357/1001] proof: certify atlas Batch0357 (12:2396 to 12:2410) --- Collatz/Research/StoppingAtlas/Batch0357.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0357.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0357.lean b/Collatz/Research/StoppingAtlas/Batch0357.lean new file mode 100644 index 00000000..8bd15c3c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0357.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0357 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2396. -/ +theorem bounds_12_2396 : exactInterval 12 2396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2396 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2396) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2396 : oddCount 2396 12 = 5 ∧ acceleratedOrbit 12 2396 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2396 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2396) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2396.1, data_12_2396.2] + +/-- Complete interval computation for depth 12, residue 2397. -/ +theorem bounds_12_2397 : exactInterval 12 2397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2397 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2397) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2397 : oddCount 2397 12 = 5 ∧ acceleratedOrbit 12 2397 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2397 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2397) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2397.1, data_12_2397.2] + +/-- Complete interval computation for depth 12, residue 2398. -/ +theorem bounds_12_2398 : exactInterval 12 2398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2398 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2398) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2398 : oddCount 2398 12 = 7 ∧ acceleratedOrbit 12 2398 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2398 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2398) = 3 ^ 7 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2398.1, data_12_2398.2] + +/-- Complete interval computation for depth 12, residue 2399. -/ +theorem bounds_12_2399 : exactInterval 12 2399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2399 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2399) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2399 : oddCount 2399 12 = 7 ∧ acceleratedOrbit 12 2399 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2399 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2399) = 3 ^ 7 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2399.1, data_12_2399.2] + +/-- Complete interval computation for depth 12, residue 2400. -/ +theorem bounds_12_2400 : exactInterval 12 2400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2400 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2400) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2400 : oddCount 2400 12 = 3 ∧ acceleratedOrbit 12 2400 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2400 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2400) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2400.1, data_12_2400.2] + +/-- Complete interval computation for depth 12, residue 2401. -/ +theorem bounds_12_2401 : exactInterval 12 2401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2401 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2401) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2401 : oddCount 2401 12 = 8 ∧ acceleratedOrbit 12 2401 = 3851 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2401 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2401) = 3 ^ 8 * m + 3851 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2401.1, data_12_2401.2] + +/-- Complete interval computation for depth 12, residue 2402. -/ +theorem bounds_12_2402 : exactInterval 12 2402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2402 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2402) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2402 : oddCount 2402 12 = 6 ∧ acceleratedOrbit 12 2402 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2402 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2402) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2402.1, data_12_2402.2] + +/-- Complete interval computation for depth 12, residue 2403. -/ +theorem bounds_12_2403 : exactInterval 12 2403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2403 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2403) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2403 : oddCount 2403 12 = 6 ∧ acceleratedOrbit 12 2403 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2403 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2403) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2403.1, data_12_2403.2] + +/-- Complete interval computation for depth 12, residue 2404. -/ +theorem bounds_12_2404 : exactInterval 12 2404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2404 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2404) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2404 : oddCount 2404 12 = 6 ∧ acceleratedOrbit 12 2404 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2404 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2404) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2404.1, data_12_2404.2] + +/-- Complete interval computation for depth 12, residue 2405. -/ +theorem bounds_12_2405 : exactInterval 12 2405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2405 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2405) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2405 : oddCount 2405 12 = 6 ∧ acceleratedOrbit 12 2405 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2405 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2405) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2405.1, data_12_2405.2] + +/-- Complete interval computation for depth 12, residue 2406. -/ +theorem bounds_12_2406 : exactInterval 12 2406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2406 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2406) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2406 : oddCount 2406 12 = 6 ∧ acceleratedOrbit 12 2406 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2406 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2406) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2406.1, data_12_2406.2] + +/-- Complete interval computation for depth 12, residue 2407. -/ +theorem bounds_12_2407 : exactInterval 12 2407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2407 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2407) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2407 : oddCount 2407 12 = 9 ∧ acceleratedOrbit 12 2407 = 11573 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2407 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2407) = 3 ^ 9 * m + 11573 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2407.1, data_12_2407.2] + +/-- Complete interval computation for depth 12, residue 2408. -/ +theorem bounds_12_2408 : exactInterval 12 2408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2408 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2408) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2408 : oddCount 2408 12 = 3 ∧ acceleratedOrbit 12 2408 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2408 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2408) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2408.1, data_12_2408.2] + +/-- Complete interval computation for depth 12, residue 2409. -/ +theorem bounds_12_2409 : exactInterval 12 2409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2409 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2409) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2409 : oddCount 2409 12 = 5 ∧ acceleratedOrbit 12 2409 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2409 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2409) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2409.1, data_12_2409.2] + +/-- Complete interval computation for depth 12, residue 2410. -/ +theorem bounds_12_2410 : exactInterval 12 2410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2410 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2410) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2410 : oddCount 2410 12 = 3 ∧ acceleratedOrbit 12 2410 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2410 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2410) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2410.1, data_12_2410.2] + +end Collatz.Research.StoppingAtlas.Batch0357 From ecb3f3e601dbdb8a84d930838391cd53703850fd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:54 +0530 Subject: [PATCH 0358/1001] proof: certify atlas Batch0358 (12:2411 to 12:2425) --- Collatz/Research/StoppingAtlas/Batch0358.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0358.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0358.lean b/Collatz/Research/StoppingAtlas/Batch0358.lean new file mode 100644 index 00000000..9216a222 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0358.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0358 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2411. -/ +theorem bounds_12_2411 : exactInterval 12 2411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2411 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2411) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2411 : oddCount 2411 12 = 7 ∧ acceleratedOrbit 12 2411 = 1289 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2411 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2411) = 3 ^ 7 * m + 1289 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2411.1, data_12_2411.2] + +/-- Complete interval computation for depth 12, residue 2412. -/ +theorem bounds_12_2412 : exactInterval 12 2412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2412 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2412) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2412 : oddCount 2412 12 = 7 ∧ acceleratedOrbit 12 2412 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2412 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2412) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2412.1, data_12_2412.2] + +/-- Complete interval computation for depth 12, residue 2413. -/ +theorem bounds_12_2413 : exactInterval 12 2413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2413 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2413) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2413 : oddCount 2413 12 = 7 ∧ acceleratedOrbit 12 2413 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2413 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2413) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2413.1, data_12_2413.2] + +/-- Complete interval computation for depth 12, residue 2414. -/ +theorem bounds_12_2414 : exactInterval 12 2414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2414 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2414) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2414 : oddCount 2414 12 = 7 ∧ acceleratedOrbit 12 2414 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2414 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2414) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2414.1, data_12_2414.2] + +/-- Complete interval computation for depth 12, residue 2415. -/ +theorem bounds_12_2415 : exactInterval 12 2415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2415 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2415) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2415 : oddCount 2415 12 = 6 ∧ acceleratedOrbit 12 2415 = 430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2415 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2415) = 3 ^ 6 * m + 430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2415.1, data_12_2415.2] + +/-- Complete interval computation for depth 12, residue 2416. -/ +theorem bounds_12_2416 : exactInterval 12 2416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2416 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2416) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2416 : oddCount 2416 12 = 3 ∧ acceleratedOrbit 12 2416 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2416 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2416) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2416.1, data_12_2416.2] + +/-- Complete interval computation for depth 12, residue 2417. -/ +theorem bounds_12_2417 : exactInterval 12 2417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2417 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2417) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2417 : oddCount 2417 12 = 3 ∧ acceleratedOrbit 12 2417 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2417 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2417) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2417.1, data_12_2417.2] + +/-- Complete interval computation for depth 12, residue 2418. -/ +theorem bounds_12_2418 : exactInterval 12 2418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2418 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2418) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2418 : oddCount 2418 12 = 7 ∧ acceleratedOrbit 12 2418 = 1295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2418 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2418) = 3 ^ 7 * m + 1295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2418.1, data_12_2418.2] + +/-- Complete interval computation for depth 12, residue 2419. -/ +theorem bounds_12_2419 : exactInterval 12 2419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2419 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2419) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2419 : oddCount 2419 12 = 7 ∧ acceleratedOrbit 12 2419 = 1295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2419 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2419) = 3 ^ 7 * m + 1295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2419.1, data_12_2419.2] + +/-- Complete interval computation for depth 12, residue 2420. -/ +theorem bounds_12_2420 : exactInterval 12 2420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2420 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2420) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2420 : oddCount 2420 12 = 3 ∧ acceleratedOrbit 12 2420 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2420 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2420) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2420.1, data_12_2420.2] + +/-- Complete interval computation for depth 12, residue 2421. -/ +theorem bounds_12_2421 : exactInterval 12 2421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2421 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2421) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2421 : oddCount 2421 12 = 3 ∧ acceleratedOrbit 12 2421 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2421 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2421) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2421.1, data_12_2421.2] + +/-- Complete interval computation for depth 12, residue 2422. -/ +theorem bounds_12_2422 : exactInterval 12 2422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2422 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2422) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2422 : oddCount 2422 12 = 8 ∧ acceleratedOrbit 12 2422 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2422 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2422) = 3 ^ 8 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2422.1, data_12_2422.2] + +/-- Complete interval computation for depth 12, residue 2423. -/ +theorem bounds_12_2423 : exactInterval 12 2423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2423 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2423) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2423 : oddCount 2423 12 = 8 ∧ acceleratedOrbit 12 2423 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2423 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2423) = 3 ^ 8 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2423.1, data_12_2423.2] + +/-- Complete interval computation for depth 12, residue 2424. -/ +theorem bounds_12_2424 : exactInterval 12 2424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2424 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2424) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2424 : oddCount 2424 12 = 6 ∧ acceleratedOrbit 12 2424 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2424 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2424) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2424.1, data_12_2424.2] + +/-- Complete interval computation for depth 12, residue 2425. -/ +theorem bounds_12_2425 : exactInterval 12 2425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2425 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2425) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2425 : oddCount 2425 12 = 10 ∧ acceleratedOrbit 12 2425 = 34991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2425 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2425) = 3 ^ 10 * m + 34991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2425.1, data_12_2425.2] + +end Collatz.Research.StoppingAtlas.Batch0358 From 8948c5ed4f9c164d1bc081ebd44aa1965c274353 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:54 +0530 Subject: [PATCH 0359/1001] proof: certify atlas Batch0359 (12:2426 to 12:2441) --- Collatz/Research/StoppingAtlas/Batch0359.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0359.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0359.lean b/Collatz/Research/StoppingAtlas/Batch0359.lean new file mode 100644 index 00000000..13526075 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0359.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0359 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2426. -/ +theorem bounds_12_2426 : exactInterval 12 2426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2426 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2426) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2426 : oddCount 2426 12 = 6 ∧ acceleratedOrbit 12 2426 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2426 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2426) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2426.1, data_12_2426.2] + +/-- Complete interval computation for depth 12, residue 2427. -/ +theorem bounds_12_2427 : exactInterval 12 2427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2427 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2427) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2427 : oddCount 2427 12 = 7 ∧ acceleratedOrbit 12 2427 = 1297 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2427 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2427) = 3 ^ 7 * m + 1297 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2427.1, data_12_2427.2] + +/-- Complete interval computation for depth 12, residue 2428. -/ +theorem bounds_12_2428 : exactInterval 12 2428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2428 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2428) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2428 : oddCount 2428 12 = 6 ∧ acceleratedOrbit 12 2428 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2428 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2428) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2428.1, data_12_2428.2] + +/-- Complete interval computation for depth 12, residue 2429. -/ +theorem bounds_12_2429 : exactInterval 12 2429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2429 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2429) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2429 : oddCount 2429 12 = 6 ∧ acceleratedOrbit 12 2429 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2429 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2429) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2429.1, data_12_2429.2] + +/-- Complete interval computation for depth 12, residue 2430. -/ +theorem bounds_12_2430 : exactInterval 12 2430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2430 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2430) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2430 : oddCount 2430 12 = 8 ∧ acceleratedOrbit 12 2430 = 3896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2430 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2430) = 3 ^ 8 * m + 3896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2430.1, data_12_2430.2] + +/-- Complete interval computation for depth 12, residue 2431. -/ +theorem bounds_12_2431 : exactInterval 12 2431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2431 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2431) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2431 : oddCount 2431 12 = 8 ∧ acceleratedOrbit 12 2431 = 3896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2431 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2431) = 3 ^ 8 * m + 3896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2431.1, data_12_2431.2] + +/-- Complete interval computation for depth 12, residue 2432. -/ +theorem bounds_12_2432 : exactInterval 12 2432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2432 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2432) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2432 : oddCount 2432 12 = 3 ∧ acceleratedOrbit 12 2432 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2432 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2432) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2432.1, data_12_2432.2] + +/-- Complete interval computation for depth 12, residue 2433. -/ +theorem bounds_12_2433 : exactInterval 12 2433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2433 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2433) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2433 : oddCount 2433 12 = 6 ∧ acceleratedOrbit 12 2433 = 434 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2433 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2433) = 3 ^ 6 * m + 434 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2433.1, data_12_2433.2] + +/-- Complete interval computation for depth 12, residue 2434. -/ +theorem bounds_12_2434 : exactInterval 12 2434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2434 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2434) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2434 : oddCount 2434 12 = 5 ∧ acceleratedOrbit 12 2434 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2434 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2434) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2434.1, data_12_2434.2] + +/-- Complete interval computation for depth 12, residue 2435. -/ +theorem bounds_12_2435 : exactInterval 12 2435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2435 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2435) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2435 : oddCount 2435 12 = 5 ∧ acceleratedOrbit 12 2435 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2435 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2435) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2435.1, data_12_2435.2] + +/-- Complete interval computation for depth 12, residue 2436. -/ +theorem bounds_12_2436 : exactInterval 12 2436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2436 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2436) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2436 : oddCount 2436 12 = 5 ∧ acceleratedOrbit 12 2436 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2436 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2436) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2436.1, data_12_2436.2] + +/-- Complete interval computation for depth 12, residue 2437. -/ +theorem bounds_12_2437 : exactInterval 12 2437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2437 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2437) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2437 : oddCount 2437 12 = 5 ∧ acceleratedOrbit 12 2437 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2437 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2437) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2437.1, data_12_2437.2] + +/-- Complete interval computation for depth 12, residue 2438. -/ +theorem bounds_12_2438 : exactInterval 12 2438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2438 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2438) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2438 : oddCount 2438 12 = 5 ∧ acceleratedOrbit 12 2438 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2438 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2438) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2438.1, data_12_2438.2] + +/-- Complete interval computation for depth 12, residue 2439. -/ +theorem bounds_12_2439 : exactInterval 12 2439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2439 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2439) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2439 : oddCount 2439 12 = 5 ∧ acceleratedOrbit 12 2439 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2439 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2439) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2439.1, data_12_2439.2] + +/-- Complete interval computation for depth 12, residue 2440. -/ +theorem bounds_12_2440 : exactInterval 12 2440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2440 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2440) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2440 : oddCount 2440 12 = 4 ∧ acceleratedOrbit 12 2440 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2440 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2440) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2440.1, data_12_2440.2] + +/-- Complete interval computation for depth 12, residue 2441. -/ +theorem bounds_12_2441 : exactInterval 12 2441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2441 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2441) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2441 : oddCount 2441 12 = 8 ∧ acceleratedOrbit 12 2441 = 3914 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2441 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2441) = 3 ^ 8 * m + 3914 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2441.1, data_12_2441.2] + +end Collatz.Research.StoppingAtlas.Batch0359 From 1387045be638bfde86675e194ad2aa3f06294fcc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:54 +0530 Subject: [PATCH 0360/1001] proof: certify atlas Batch0360 (12:2442 to 12:2456) --- Collatz/Research/StoppingAtlas/Batch0360.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0360.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0360.lean b/Collatz/Research/StoppingAtlas/Batch0360.lean new file mode 100644 index 00000000..a00ec422 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0360.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0360 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2442. -/ +theorem bounds_12_2442 : exactInterval 12 2442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2442 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2442) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2442 : oddCount 2442 12 = 4 ∧ acceleratedOrbit 12 2442 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2442 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2442) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2442.1, data_12_2442.2] + +/-- Complete interval computation for depth 12, residue 2443. -/ +theorem bounds_12_2443 : exactInterval 12 2443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2443 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2443) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2443 : oddCount 2443 12 = 7 ∧ acceleratedOrbit 12 2443 = 1306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2443 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2443) = 3 ^ 7 * m + 1306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2443.1, data_12_2443.2] + +/-- Complete interval computation for depth 12, residue 2444. -/ +theorem bounds_12_2444 : exactInterval 12 2444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2444 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2444) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2444 : oddCount 2444 12 = 4 ∧ acceleratedOrbit 12 2444 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2444 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2444) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2444.1, data_12_2444.2] + +/-- Complete interval computation for depth 12, residue 2445. -/ +theorem bounds_12_2445 : exactInterval 12 2445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2445 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2445) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2445 : oddCount 2445 12 = 4 ∧ acceleratedOrbit 12 2445 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2445 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2445) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2445.1, data_12_2445.2] + +/-- Complete interval computation for depth 12, residue 2446. -/ +theorem bounds_12_2446 : exactInterval 12 2446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2446 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2446) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2446 : oddCount 2446 12 = 6 ∧ acceleratedOrbit 12 2446 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2446 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2446) = 3 ^ 6 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2446.1, data_12_2446.2] + +/-- Complete interval computation for depth 12, residue 2447. -/ +theorem bounds_12_2447 : exactInterval 12 2447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2447 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2447) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2447 : oddCount 2447 12 = 6 ∧ acceleratedOrbit 12 2447 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2447 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2447) = 3 ^ 6 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2447.1, data_12_2447.2] + +/-- Complete interval computation for depth 12, residue 2448. -/ +theorem bounds_12_2448 : exactInterval 12 2448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2448 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2448) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2448 : oddCount 2448 12 = 4 ∧ acceleratedOrbit 12 2448 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2448 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2448) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2448.1, data_12_2448.2] + +/-- Complete interval computation for depth 12, residue 2449. -/ +theorem bounds_12_2449 : exactInterval 12 2449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2449 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2449) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2449 : oddCount 2449 12 = 5 ∧ acceleratedOrbit 12 2449 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2449 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2449) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2449.1, data_12_2449.2] + +/-- Complete interval computation for depth 12, residue 2450. -/ +theorem bounds_12_2450 : exactInterval 12 2450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2450 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2450) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2450 : oddCount 2450 12 = 5 ∧ acceleratedOrbit 12 2450 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2450 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2450) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2450.1, data_12_2450.2] + +/-- Complete interval computation for depth 12, residue 2451. -/ +theorem bounds_12_2451 : exactInterval 12 2451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2451 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2451) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2451 : oddCount 2451 12 = 5 ∧ acceleratedOrbit 12 2451 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2451 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2451) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2451.1, data_12_2451.2] + +/-- Complete interval computation for depth 12, residue 2452. -/ +theorem bounds_12_2452 : exactInterval 12 2452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2452 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2452) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2452 : oddCount 2452 12 = 4 ∧ acceleratedOrbit 12 2452 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2452 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2452) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2452.1, data_12_2452.2] + +/-- Complete interval computation for depth 12, residue 2453. -/ +theorem bounds_12_2453 : exactInterval 12 2453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2453 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2453) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2453 : oddCount 2453 12 = 4 ∧ acceleratedOrbit 12 2453 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2453 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2453) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2453.1, data_12_2453.2] + +/-- Complete interval computation for depth 12, residue 2454. -/ +theorem bounds_12_2454 : exactInterval 12 2454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2454 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2454) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2454 : oddCount 2454 12 = 5 ∧ acceleratedOrbit 12 2454 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2454 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2454) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2454.1, data_12_2454.2] + +/-- Complete interval computation for depth 12, residue 2455. -/ +theorem bounds_12_2455 : exactInterval 12 2455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2455 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2455) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2455 : oddCount 2455 12 = 5 ∧ acceleratedOrbit 12 2455 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2455 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2455) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2455.1, data_12_2455.2] + +/-- Complete interval computation for depth 12, residue 2456. -/ +theorem bounds_12_2456 : exactInterval 12 2456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2456 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2456) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2456 : oddCount 2456 12 = 4 ∧ acceleratedOrbit 12 2456 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2456 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2456) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2456.1, data_12_2456.2] + +end Collatz.Research.StoppingAtlas.Batch0360 From 6d82be54a05437175b3eff300c8345d4ca590843 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:54 +0530 Subject: [PATCH 0361/1001] proof: certify atlas Batch0361 (12:2457 to 12:2471) --- Collatz/Research/StoppingAtlas/Batch0361.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0361.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0361.lean b/Collatz/Research/StoppingAtlas/Batch0361.lean new file mode 100644 index 00000000..50cbaf26 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0361.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0361 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2457. -/ +theorem bounds_12_2457 : exactInterval 12 2457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2457 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2457) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2457 : oddCount 2457 12 = 5 ∧ acceleratedOrbit 12 2457 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2457 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2457) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2457.1, data_12_2457.2] + +/-- Complete interval computation for depth 12, residue 2458. -/ +theorem bounds_12_2458 : exactInterval 12 2458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2458 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2458) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2458 : oddCount 2458 12 = 4 ∧ acceleratedOrbit 12 2458 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2458 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2458) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2458.1, data_12_2458.2] + +/-- Complete interval computation for depth 12, residue 2459. -/ +theorem bounds_12_2459 : exactInterval 12 2459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2459 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2459) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2459 : oddCount 2459 12 = 9 ∧ acceleratedOrbit 12 2459 = 11825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2459 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2459) = 3 ^ 9 * m + 11825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2459.1, data_12_2459.2] + +/-- Complete interval computation for depth 12, residue 2460. -/ +theorem bounds_12_2460 : exactInterval 12 2460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2460 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2460) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2460 : oddCount 2460 12 = 7 ∧ acceleratedOrbit 12 2460 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2460 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2460) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2460.1, data_12_2460.2] + +/-- Complete interval computation for depth 12, residue 2461. -/ +theorem bounds_12_2461 : exactInterval 12 2461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2461 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2461) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2461 : oddCount 2461 12 = 7 ∧ acceleratedOrbit 12 2461 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2461 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2461) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2461.1, data_12_2461.2] + +/-- Complete interval computation for depth 12, residue 2462. -/ +theorem bounds_12_2462 : exactInterval 12 2462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2462 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2462) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2462 : oddCount 2462 12 = 7 ∧ acceleratedOrbit 12 2462 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2462 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2462) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2462.1, data_12_2462.2] + +/-- Complete interval computation for depth 12, residue 2463. -/ +theorem bounds_12_2463 : exactInterval 12 2463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2463 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2463) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2463 : oddCount 2463 12 = 8 ∧ acceleratedOrbit 12 2463 = 3947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2463 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2463) = 3 ^ 8 * m + 3947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2463.1, data_12_2463.2] + +/-- Complete interval computation for depth 12, residue 2464. -/ +theorem bounds_12_2464 : exactInterval 12 2464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2464 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2464) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2464 : oddCount 2464 12 = 3 ∧ acceleratedOrbit 12 2464 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2464 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2464) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2464.1, data_12_2464.2] + +/-- Complete interval computation for depth 12, residue 2465. -/ +theorem bounds_12_2465 : exactInterval 12 2465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2465 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2465) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2465 : oddCount 2465 12 = 7 ∧ acceleratedOrbit 12 2465 = 1318 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2465 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2465) = 3 ^ 7 * m + 1318 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2465.1, data_12_2465.2] + +/-- Complete interval computation for depth 12, residue 2466. -/ +theorem bounds_12_2466 : exactInterval 12 2466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2466 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2466) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2466 : oddCount 2466 12 = 7 ∧ acceleratedOrbit 12 2466 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2466 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2466) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2466.1, data_12_2466.2] + +/-- Complete interval computation for depth 12, residue 2467. -/ +theorem bounds_12_2467 : exactInterval 12 2467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2467 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2467) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2467 : oddCount 2467 12 = 7 ∧ acceleratedOrbit 12 2467 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2467 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2467) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2467.1, data_12_2467.2] + +/-- Complete interval computation for depth 12, residue 2468. -/ +theorem bounds_12_2468 : exactInterval 12 2468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2468 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2468) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2468 : oddCount 2468 12 = 7 ∧ acceleratedOrbit 12 2468 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2468 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2468) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2468.1, data_12_2468.2] + +/-- Complete interval computation for depth 12, residue 2469. -/ +theorem bounds_12_2469 : exactInterval 12 2469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2469 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2469) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2469 : oddCount 2469 12 = 7 ∧ acceleratedOrbit 12 2469 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2469 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2469) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2469.1, data_12_2469.2] + +/-- Complete interval computation for depth 12, residue 2470. -/ +theorem bounds_12_2470 : exactInterval 12 2470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2470 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2470) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2470 : oddCount 2470 12 = 7 ∧ acceleratedOrbit 12 2470 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2470 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2470) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2470.1, data_12_2470.2] + +/-- Complete interval computation for depth 12, residue 2471. -/ +theorem bounds_12_2471 : exactInterval 12 2471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2471 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2471) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2471 : oddCount 2471 12 = 6 ∧ acceleratedOrbit 12 2471 = 440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2471 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2471) = 3 ^ 6 * m + 440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2471.1, data_12_2471.2] + +end Collatz.Research.StoppingAtlas.Batch0361 From b9ea1ce1f4674753bcebfa7c08cb21cb29a3063e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:55 +0530 Subject: [PATCH 0362/1001] proof: certify atlas Batch0362 (12:2472 to 12:2487) --- Collatz/Research/StoppingAtlas/Batch0362.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0362.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0362.lean b/Collatz/Research/StoppingAtlas/Batch0362.lean new file mode 100644 index 00000000..a698934d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0362.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0362 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2472. -/ +theorem bounds_12_2472 : exactInterval 12 2472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2472 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2472) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2472 : oddCount 2472 12 = 3 ∧ acceleratedOrbit 12 2472 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2472 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2472) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2472.1, data_12_2472.2] + +/-- Complete interval computation for depth 12, residue 2473. -/ +theorem bounds_12_2473 : exactInterval 12 2473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2473 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2473) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2473 : oddCount 2473 12 = 8 ∧ acceleratedOrbit 12 2473 = 3964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2473 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2473) = 3 ^ 8 * m + 3964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2473.1, data_12_2473.2] + +/-- Complete interval computation for depth 12, residue 2474. -/ +theorem bounds_12_2474 : exactInterval 12 2474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2474 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2474) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2474 : oddCount 2474 12 = 3 ∧ acceleratedOrbit 12 2474 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2474 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2474) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2474.1, data_12_2474.2] + +/-- Complete interval computation for depth 12, residue 2475. -/ +theorem bounds_12_2475 : exactInterval 12 2475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2475 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2475) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2475 : oddCount 2475 12 = 9 ∧ acceleratedOrbit 12 2475 = 11906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2475 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2475) = 3 ^ 9 * m + 11906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2475.1, data_12_2475.2] + +/-- Complete interval computation for depth 12, residue 2476. -/ +theorem bounds_12_2476 : exactInterval 12 2476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2476 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2476) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2476 : oddCount 2476 12 = 6 ∧ acceleratedOrbit 12 2476 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2476 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2476) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2476.1, data_12_2476.2] + +/-- Complete interval computation for depth 12, residue 2477. -/ +theorem bounds_12_2477 : exactInterval 12 2477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2477 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2477) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2477 : oddCount 2477 12 = 6 ∧ acceleratedOrbit 12 2477 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2477 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2477) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2477.1, data_12_2477.2] + +/-- Complete interval computation for depth 12, residue 2478. -/ +theorem bounds_12_2478 : exactInterval 12 2478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2478 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2478) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2478 : oddCount 2478 12 = 6 ∧ acceleratedOrbit 12 2478 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2478 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2478) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2478.1, data_12_2478.2] + +/-- Complete interval computation for depth 12, residue 2479. -/ +theorem bounds_12_2479 : exactInterval 12 2479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2479 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2479) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2479 : oddCount 2479 12 = 7 ∧ acceleratedOrbit 12 2479 = 1325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2479 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2479) = 3 ^ 7 * m + 1325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2479.1, data_12_2479.2] + +/-- Complete interval computation for depth 12, residue 2480. -/ +theorem bounds_12_2480 : exactInterval 12 2480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2480 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2480) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2480 : oddCount 2480 12 = 6 ∧ acceleratedOrbit 12 2480 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2480 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2480) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2480.1, data_12_2480.2] + +/-- Complete interval computation for depth 12, residue 2481. -/ +theorem bounds_12_2481 : exactInterval 12 2481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2481 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2481) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2481 : oddCount 2481 12 = 5 ∧ acceleratedOrbit 12 2481 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2481 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2481) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2481.1, data_12_2481.2] + +/-- Complete interval computation for depth 12, residue 2482. -/ +theorem bounds_12_2482 : exactInterval 12 2482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2482 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2482) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2482 : oddCount 2482 12 = 5 ∧ acceleratedOrbit 12 2482 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2482 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2482) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2482.1, data_12_2482.2] + +/-- Complete interval computation for depth 12, residue 2483. -/ +theorem bounds_12_2483 : exactInterval 12 2483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2483 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2483) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2483 : oddCount 2483 12 = 5 ∧ acceleratedOrbit 12 2483 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2483 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2483) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2483.1, data_12_2483.2] + +/-- Complete interval computation for depth 12, residue 2484. -/ +theorem bounds_12_2484 : exactInterval 12 2484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2484 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2484) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2484 : oddCount 2484 12 = 6 ∧ acceleratedOrbit 12 2484 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2484 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2484) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2484.1, data_12_2484.2] + +/-- Complete interval computation for depth 12, residue 2485. -/ +theorem bounds_12_2485 : exactInterval 12 2485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2485 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2485) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2485 : oddCount 2485 12 = 6 ∧ acceleratedOrbit 12 2485 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2485 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2485) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2485.1, data_12_2485.2] + +/-- Complete interval computation for depth 12, residue 2486. -/ +theorem bounds_12_2486 : exactInterval 12 2486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2486 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2486) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2486 : oddCount 2486 12 = 6 ∧ acceleratedOrbit 12 2486 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2486 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2486) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2486.1, data_12_2486.2] + +/-- Complete interval computation for depth 12, residue 2487. -/ +theorem bounds_12_2487 : exactInterval 12 2487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2487 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2487) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2487 : oddCount 2487 12 = 6 ∧ acceleratedOrbit 12 2487 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2487 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2487) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2487.1, data_12_2487.2] + +end Collatz.Research.StoppingAtlas.Batch0362 From eb8eedfdb20a02ac403a62866dedb490673b241b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:55 +0530 Subject: [PATCH 0363/1001] proof: certify atlas Batch0363 (12:2488 to 12:2502) --- Collatz/Research/StoppingAtlas/Batch0363.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0363.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0363.lean b/Collatz/Research/StoppingAtlas/Batch0363.lean new file mode 100644 index 00000000..b49d78d0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0363.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0363 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2488. -/ +theorem bounds_12_2488 : exactInterval 12 2488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2488 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2488) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2488 : oddCount 2488 12 = 6 ∧ acceleratedOrbit 12 2488 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2488 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2488) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2488.1, data_12_2488.2] + +/-- Complete interval computation for depth 12, residue 2489. -/ +theorem bounds_12_2489 : exactInterval 12 2489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2489 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2489) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2489 : oddCount 2489 12 = 5 ∧ acceleratedOrbit 12 2489 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2489 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2489) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2489.1, data_12_2489.2] + +/-- Complete interval computation for depth 12, residue 2490. -/ +theorem bounds_12_2490 : exactInterval 12 2490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2490 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2490) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2490 : oddCount 2490 12 = 6 ∧ acceleratedOrbit 12 2490 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2490 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2490) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2490.1, data_12_2490.2] + +/-- Complete interval computation for depth 12, residue 2491. -/ +theorem bounds_12_2491 : exactInterval 12 2491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2491 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2491) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2491 : oddCount 2491 12 = 8 ∧ acceleratedOrbit 12 2491 = 3995 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2491 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2491) = 3 ^ 8 * m + 3995 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2491.1, data_12_2491.2] + +/-- Complete interval computation for depth 12, residue 2492. -/ +theorem bounds_12_2492 : exactInterval 12 2492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2492 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2492) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2492 : oddCount 2492 12 = 7 ∧ acceleratedOrbit 12 2492 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2492 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2492) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2492.1, data_12_2492.2] + +/-- Complete interval computation for depth 12, residue 2493. -/ +theorem bounds_12_2493 : exactInterval 12 2493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2493 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2493) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2493 : oddCount 2493 12 = 7 ∧ acceleratedOrbit 12 2493 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2493 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2493) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2493.1, data_12_2493.2] + +/-- Complete interval computation for depth 12, residue 2494. -/ +theorem bounds_12_2494 : exactInterval 12 2494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2494 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2494) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2494 : oddCount 2494 12 = 7 ∧ acceleratedOrbit 12 2494 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2494 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2494) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2494.1, data_12_2494.2] + +/-- Complete interval computation for depth 12, residue 2495. -/ +theorem bounds_12_2495 : exactInterval 12 2495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2495 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2495) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2495 : oddCount 2495 12 = 10 ∧ acceleratedOrbit 12 2495 = 35984 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2495 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2495) = 3 ^ 10 * m + 35984 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2495.1, data_12_2495.2] + +/-- Complete interval computation for depth 12, residue 2496. -/ +theorem bounds_12_2496 : exactInterval 12 2496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2496 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2496) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2496 : oddCount 2496 12 = 5 ∧ acceleratedOrbit 12 2496 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2496 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2496) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2496.1, data_12_2496.2] + +/-- Complete interval computation for depth 12, residue 2497. -/ +theorem bounds_12_2497 : exactInterval 12 2497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2497 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2497) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2497 : oddCount 2497 12 = 7 ∧ acceleratedOrbit 12 2497 = 1336 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2497 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2497) = 3 ^ 7 * m + 1336 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2497.1, data_12_2497.2] + +/-- Complete interval computation for depth 12, residue 2498. -/ +theorem bounds_12_2498 : exactInterval 12 2498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2498 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2498) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2498 : oddCount 2498 12 = 8 ∧ acceleratedOrbit 12 2498 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2498 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2498) = 3 ^ 8 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2498.1, data_12_2498.2] + +/-- Complete interval computation for depth 12, residue 2499. -/ +theorem bounds_12_2499 : exactInterval 12 2499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2499 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2499) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2499 : oddCount 2499 12 = 8 ∧ acceleratedOrbit 12 2499 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2499 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2499) = 3 ^ 8 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2499.1, data_12_2499.2] + +/-- Complete interval computation for depth 12, residue 2500. -/ +theorem bounds_12_2500 : exactInterval 12 2500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2500 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2500) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2500 : oddCount 2500 12 = 3 ∧ acceleratedOrbit 12 2500 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2500 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2500) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2500.1, data_12_2500.2] + +/-- Complete interval computation for depth 12, residue 2501. -/ +theorem bounds_12_2501 : exactInterval 12 2501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2501 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2501) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2501 : oddCount 2501 12 = 3 ∧ acceleratedOrbit 12 2501 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2501 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2501) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2501.1, data_12_2501.2] + +/-- Complete interval computation for depth 12, residue 2502. -/ +theorem bounds_12_2502 : exactInterval 12 2502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2502 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2502) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2502 : oddCount 2502 12 = 3 ∧ acceleratedOrbit 12 2502 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2502 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2502) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2502.1, data_12_2502.2] + +end Collatz.Research.StoppingAtlas.Batch0363 From 655fb85d2211436c78f82192c10f1bb3ed08533f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:56 +0530 Subject: [PATCH 0364/1001] proof: certify atlas Batch0364 (12:2503 to 12:2518) --- Collatz/Research/StoppingAtlas/Batch0364.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0364.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0364.lean b/Collatz/Research/StoppingAtlas/Batch0364.lean new file mode 100644 index 00000000..4aba7962 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0364.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0364 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2503. -/ +theorem bounds_12_2503 : exactInterval 12 2503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2503 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2503) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2503 : oddCount 2503 12 = 8 ∧ acceleratedOrbit 12 2503 = 4013 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2503 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2503) = 3 ^ 8 * m + 4013 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2503.1, data_12_2503.2] + +/-- Complete interval computation for depth 12, residue 2504. -/ +theorem bounds_12_2504 : exactInterval 12 2504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2504 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2504) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2504 : oddCount 2504 12 = 6 ∧ acceleratedOrbit 12 2504 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2504 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2504) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2504.1, data_12_2504.2] + +/-- Complete interval computation for depth 12, residue 2505. -/ +theorem bounds_12_2505 : exactInterval 12 2505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2505 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2505) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2505 : oddCount 2505 12 = 7 ∧ acceleratedOrbit 12 2505 = 1340 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2505 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2505) = 3 ^ 7 * m + 1340 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2505.1, data_12_2505.2] + +/-- Complete interval computation for depth 12, residue 2506. -/ +theorem bounds_12_2506 : exactInterval 12 2506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2506 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2506) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2506 : oddCount 2506 12 = 6 ∧ acceleratedOrbit 12 2506 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2506 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2506) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2506.1, data_12_2506.2] + +/-- Complete interval computation for depth 12, residue 2507. -/ +theorem bounds_12_2507 : exactInterval 12 2507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2507 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2507) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2507 : oddCount 2507 12 = 5 ∧ acceleratedOrbit 12 2507 = 149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2507 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2507) = 3 ^ 5 * m + 149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2507.1, data_12_2507.2] + +/-- Complete interval computation for depth 12, residue 2508. -/ +theorem bounds_12_2508 : exactInterval 12 2508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2508 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2508) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2508 : oddCount 2508 12 = 6 ∧ acceleratedOrbit 12 2508 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2508 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2508) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2508.1, data_12_2508.2] + +/-- Complete interval computation for depth 12, residue 2509. -/ +theorem bounds_12_2509 : exactInterval 12 2509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2509 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2509) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2509 : oddCount 2509 12 = 6 ∧ acceleratedOrbit 12 2509 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2509 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2509) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2509.1, data_12_2509.2] + +/-- Complete interval computation for depth 12, residue 2510. -/ +theorem bounds_12_2510 : exactInterval 12 2510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2510 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2510) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2510 : oddCount 2510 12 = 8 ∧ acceleratedOrbit 12 2510 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2510 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2510) = 3 ^ 8 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2510.1, data_12_2510.2] + +/-- Complete interval computation for depth 12, residue 2511. -/ +theorem bounds_12_2511 : exactInterval 12 2511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2511 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2511) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2511 : oddCount 2511 12 = 8 ∧ acceleratedOrbit 12 2511 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2511 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2511) = 3 ^ 8 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2511.1, data_12_2511.2] + +/-- Complete interval computation for depth 12, residue 2512. -/ +theorem bounds_12_2512 : exactInterval 12 2512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2512 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2512) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2512 : oddCount 2512 12 = 5 ∧ acceleratedOrbit 12 2512 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2512 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2512) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2512.1, data_12_2512.2] + +/-- Complete interval computation for depth 12, residue 2513. -/ +theorem bounds_12_2513 : exactInterval 12 2513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2513 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2513) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2513 : oddCount 2513 12 = 6 ∧ acceleratedOrbit 12 2513 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2513 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2513) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2513.1, data_12_2513.2] + +/-- Complete interval computation for depth 12, residue 2514. -/ +theorem bounds_12_2514 : exactInterval 12 2514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2514 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2514) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2514 : oddCount 2514 12 = 6 ∧ acceleratedOrbit 12 2514 = 448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2514 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2514) = 3 ^ 6 * m + 448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2514.1, data_12_2514.2] + +/-- Complete interval computation for depth 12, residue 2515. -/ +theorem bounds_12_2515 : exactInterval 12 2515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2515 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2515) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2515 : oddCount 2515 12 = 6 ∧ acceleratedOrbit 12 2515 = 448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2515 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2515) = 3 ^ 6 * m + 448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2515.1, data_12_2515.2] + +/-- Complete interval computation for depth 12, residue 2516. -/ +theorem bounds_12_2516 : exactInterval 12 2516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2516 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2516) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2516 : oddCount 2516 12 = 5 ∧ acceleratedOrbit 12 2516 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2516 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2516) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2516.1, data_12_2516.2] + +/-- Complete interval computation for depth 12, residue 2517. -/ +theorem bounds_12_2517 : exactInterval 12 2517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2517 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2517) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2517 : oddCount 2517 12 = 5 ∧ acceleratedOrbit 12 2517 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2517 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2517) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2517.1, data_12_2517.2] + +/-- Complete interval computation for depth 12, residue 2518. -/ +theorem bounds_12_2518 : exactInterval 12 2518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2518 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2518) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2518 : oddCount 2518 12 = 8 ∧ acceleratedOrbit 12 2518 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2518 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2518) = 3 ^ 8 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2518.1, data_12_2518.2] + +end Collatz.Research.StoppingAtlas.Batch0364 From 3bde1a34899336a8572f77e94523474b25fadfc2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:56 +0530 Subject: [PATCH 0365/1001] proof: certify atlas Batch0365 (12:2519 to 12:2533) --- Collatz/Research/StoppingAtlas/Batch0365.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0365.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0365.lean b/Collatz/Research/StoppingAtlas/Batch0365.lean new file mode 100644 index 00000000..5bf23649 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0365.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0365 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2519. -/ +theorem bounds_12_2519 : exactInterval 12 2519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2519 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2519) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2519 : oddCount 2519 12 = 8 ∧ acceleratedOrbit 12 2519 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2519 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2519) = 3 ^ 8 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2519.1, data_12_2519.2] + +/-- Complete interval computation for depth 12, residue 2520. -/ +theorem bounds_12_2520 : exactInterval 12 2520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2520 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2520) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2520 : oddCount 2520 12 = 4 ∧ acceleratedOrbit 12 2520 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2520 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2520) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2520.1, data_12_2520.2] + +/-- Complete interval computation for depth 12, residue 2521. -/ +theorem bounds_12_2521 : exactInterval 12 2521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2521 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2521) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2521 : oddCount 2521 12 = 4 ∧ acceleratedOrbit 12 2521 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2521 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2521) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2521.1, data_12_2521.2] + +/-- Complete interval computation for depth 12, residue 2522. -/ +theorem bounds_12_2522 : exactInterval 12 2522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2522 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2522) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2522 : oddCount 2522 12 = 4 ∧ acceleratedOrbit 12 2522 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2522 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2522) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2522.1, data_12_2522.2] + +/-- Complete interval computation for depth 12, residue 2523. -/ +theorem bounds_12_2523 : exactInterval 12 2523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2523 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2523) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2523 : oddCount 2523 12 = 7 ∧ acceleratedOrbit 12 2523 = 1349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2523 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2523) = 3 ^ 7 * m + 1349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2523.1, data_12_2523.2] + +/-- Complete interval computation for depth 12, residue 2524. -/ +theorem bounds_12_2524 : exactInterval 12 2524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2524 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2524) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2524 : oddCount 2524 12 = 4 ∧ acceleratedOrbit 12 2524 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2524 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2524) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2524.1, data_12_2524.2] + +/-- Complete interval computation for depth 12, residue 2525. -/ +theorem bounds_12_2525 : exactInterval 12 2525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2525 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2525) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2525 : oddCount 2525 12 = 4 ∧ acceleratedOrbit 12 2525 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2525 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2525) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2525.1, data_12_2525.2] + +/-- Complete interval computation for depth 12, residue 2526. -/ +theorem bounds_12_2526 : exactInterval 12 2526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2526 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2526) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2526 : oddCount 2526 12 = 10 ∧ acceleratedOrbit 12 2526 = 36449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2526 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2526) = 3 ^ 10 * m + 36449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2526.1, data_12_2526.2] + +/-- Complete interval computation for depth 12, residue 2527. -/ +theorem bounds_12_2527 : exactInterval 12 2527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2527 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2527) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2527 : oddCount 2527 12 = 10 ∧ acceleratedOrbit 12 2527 = 36449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2527 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2527) = 3 ^ 10 * m + 36449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2527.1, data_12_2527.2] + +/-- Complete interval computation for depth 12, residue 2528. -/ +theorem bounds_12_2528 : exactInterval 12 2528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2528 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2528) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2528 : oddCount 2528 12 = 5 ∧ acceleratedOrbit 12 2528 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2528 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2528) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2528.1, data_12_2528.2] + +/-- Complete interval computation for depth 12, residue 2529. -/ +theorem bounds_12_2529 : exactInterval 12 2529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2529 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2529) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2529 : oddCount 2529 12 = 7 ∧ acceleratedOrbit 12 2529 = 1352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2529 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2529) = 3 ^ 7 * m + 1352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2529.1, data_12_2529.2] + +/-- Complete interval computation for depth 12, residue 2530. -/ +theorem bounds_12_2530 : exactInterval 12 2530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2530 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2530) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2530 : oddCount 2530 12 = 5 ∧ acceleratedOrbit 12 2530 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2530 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2530) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2530.1, data_12_2530.2] + +/-- Complete interval computation for depth 12, residue 2531. -/ +theorem bounds_12_2531 : exactInterval 12 2531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2531 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2531) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2531 : oddCount 2531 12 = 5 ∧ acceleratedOrbit 12 2531 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2531 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2531) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2531.1, data_12_2531.2] + +/-- Complete interval computation for depth 12, residue 2532. -/ +theorem bounds_12_2532 : exactInterval 12 2532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2532 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2532) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2532 : oddCount 2532 12 = 6 ∧ acceleratedOrbit 12 2532 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2532 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2532) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2532.1, data_12_2532.2] + +/-- Complete interval computation for depth 12, residue 2533. -/ +theorem bounds_12_2533 : exactInterval 12 2533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2533 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2533) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2533 : oddCount 2533 12 = 6 ∧ acceleratedOrbit 12 2533 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2533 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2533) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2533.1, data_12_2533.2] + +end Collatz.Research.StoppingAtlas.Batch0365 From d80d7968e3b55d7e00f3b57d144a8d0cc8af5009 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:56 +0530 Subject: [PATCH 0366/1001] proof: certify atlas Batch0366 (12:2534 to 12:2548) --- Collatz/Research/StoppingAtlas/Batch0366.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0366.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0366.lean b/Collatz/Research/StoppingAtlas/Batch0366.lean new file mode 100644 index 00000000..d3df2097 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0366.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0366 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2534. -/ +theorem bounds_12_2534 : exactInterval 12 2534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2534 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2534) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2534 : oddCount 2534 12 = 6 ∧ acceleratedOrbit 12 2534 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2534 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2534) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2534.1, data_12_2534.2] + +/-- Complete interval computation for depth 12, residue 2535. -/ +theorem bounds_12_2535 : exactInterval 12 2535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2535 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2535) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2535 : oddCount 2535 12 = 8 ∧ acceleratedOrbit 12 2535 = 4063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2535 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2535) = 3 ^ 8 * m + 4063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2535.1, data_12_2535.2] + +/-- Complete interval computation for depth 12, residue 2536. -/ +theorem bounds_12_2536 : exactInterval 12 2536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2536 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2536) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2536 : oddCount 2536 12 = 5 ∧ acceleratedOrbit 12 2536 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2536 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2536) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2536.1, data_12_2536.2] + +/-- Complete interval computation for depth 12, residue 2537. -/ +theorem bounds_12_2537 : exactInterval 12 2537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2537 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2537) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2537 : oddCount 2537 12 = 8 ∧ acceleratedOrbit 12 2537 = 4067 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2537 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2537) = 3 ^ 8 * m + 4067 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2537.1, data_12_2537.2] + +/-- Complete interval computation for depth 12, residue 2538. -/ +theorem bounds_12_2538 : exactInterval 12 2538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2538 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2538) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2538 : oddCount 2538 12 = 5 ∧ acceleratedOrbit 12 2538 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2538 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2538) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2538.1, data_12_2538.2] + +/-- Complete interval computation for depth 12, residue 2539. -/ +theorem bounds_12_2539 : exactInterval 12 2539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2539 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2539) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2539 : oddCount 2539 12 = 8 ∧ acceleratedOrbit 12 2539 = 4070 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2539 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2539) = 3 ^ 8 * m + 4070 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2539.1, data_12_2539.2] + +/-- Complete interval computation for depth 12, residue 2540. -/ +theorem bounds_12_2540 : exactInterval 12 2540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2540 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2540) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2540 : oddCount 2540 12 = 5 ∧ acceleratedOrbit 12 2540 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2540 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2540) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2540.1, data_12_2540.2] + +/-- Complete interval computation for depth 12, residue 2541. -/ +theorem bounds_12_2541 : exactInterval 12 2541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2541 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2541) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2541 : oddCount 2541 12 = 5 ∧ acceleratedOrbit 12 2541 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2541 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2541) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2541.1, data_12_2541.2] + +/-- Complete interval computation for depth 12, residue 2542. -/ +theorem bounds_12_2542 : exactInterval 12 2542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2542 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2542) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2542 : oddCount 2542 12 = 5 ∧ acceleratedOrbit 12 2542 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2542 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2542) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2542.1, data_12_2542.2] + +/-- Complete interval computation for depth 12, residue 2543. -/ +theorem bounds_12_2543 : exactInterval 12 2543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2543 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2543) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2543 : oddCount 2543 12 = 9 ∧ acceleratedOrbit 12 2543 = 12226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2543 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2543) = 3 ^ 9 * m + 12226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2543.1, data_12_2543.2] + +/-- Complete interval computation for depth 12, residue 2544. -/ +theorem bounds_12_2544 : exactInterval 12 2544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2544 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2544) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2544 : oddCount 2544 12 = 7 ∧ acceleratedOrbit 12 2544 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2544 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2544) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2544.1, data_12_2544.2] + +/-- Complete interval computation for depth 12, residue 2545. -/ +theorem bounds_12_2545 : exactInterval 12 2545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2545 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2545) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2545 : oddCount 2545 12 = 5 ∧ acceleratedOrbit 12 2545 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2545 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2545) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2545.1, data_12_2545.2] + +/-- Complete interval computation for depth 12, residue 2546. -/ +theorem bounds_12_2546 : exactInterval 12 2546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2546 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2546) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2546 : oddCount 2546 12 = 6 ∧ acceleratedOrbit 12 2546 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2546 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2546) = 3 ^ 6 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2546.1, data_12_2546.2] + +/-- Complete interval computation for depth 12, residue 2547. -/ +theorem bounds_12_2547 : exactInterval 12 2547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2547 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2547) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2547 : oddCount 2547 12 = 6 ∧ acceleratedOrbit 12 2547 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2547 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2547) = 3 ^ 6 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2547.1, data_12_2547.2] + +/-- Complete interval computation for depth 12, residue 2548. -/ +theorem bounds_12_2548 : exactInterval 12 2548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2548 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2548) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2548 : oddCount 2548 12 = 7 ∧ acceleratedOrbit 12 2548 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2548 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2548) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2548.1, data_12_2548.2] + +end Collatz.Research.StoppingAtlas.Batch0366 From db2a275f33f10b4a1b1f9c4927b7274fd9001c16 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:56 +0530 Subject: [PATCH 0367/1001] proof: certify atlas Batch0367 (12:2549 to 12:2564) --- Collatz/Research/StoppingAtlas/Batch0367.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0367.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0367.lean b/Collatz/Research/StoppingAtlas/Batch0367.lean new file mode 100644 index 00000000..72c20adc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0367.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0367 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2549. -/ +theorem bounds_12_2549 : exactInterval 12 2549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2549 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2549) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2549 : oddCount 2549 12 = 7 ∧ acceleratedOrbit 12 2549 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2549 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2549) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2549.1, data_12_2549.2] + +/-- Complete interval computation for depth 12, residue 2550. -/ +theorem bounds_12_2550 : exactInterval 12 2550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2550 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2550) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2550 : oddCount 2550 12 = 8 ∧ acceleratedOrbit 12 2550 = 4090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2550 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2550) = 3 ^ 8 * m + 4090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2550.1, data_12_2550.2] + +/-- Complete interval computation for depth 12, residue 2551. -/ +theorem bounds_12_2551 : exactInterval 12 2551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2551 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2551) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2551 : oddCount 2551 12 = 8 ∧ acceleratedOrbit 12 2551 = 4090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2551 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2551) = 3 ^ 8 * m + 4090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2551.1, data_12_2551.2] + +/-- Complete interval computation for depth 12, residue 2552. -/ +theorem bounds_12_2552 : exactInterval 12 2552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2552 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2552) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2552 : oddCount 2552 12 = 7 ∧ acceleratedOrbit 12 2552 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2552 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2552) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2552.1, data_12_2552.2] + +/-- Complete interval computation for depth 12, residue 2553. -/ +theorem bounds_12_2553 : exactInterval 12 2553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2553 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2553) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2553 : oddCount 2553 12 = 8 ∧ acceleratedOrbit 12 2553 = 4094 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2553 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2553) = 3 ^ 8 * m + 4094 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2553.1, data_12_2553.2] + +/-- Complete interval computation for depth 12, residue 2554. -/ +theorem bounds_12_2554 : exactInterval 12 2554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2554 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2554) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2554 : oddCount 2554 12 = 7 ∧ acceleratedOrbit 12 2554 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2554 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2554) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2554.1, data_12_2554.2] + +/-- Complete interval computation for depth 12, residue 2555. -/ +theorem bounds_12_2555 : exactInterval 12 2555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2555 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2555) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2555 : oddCount 2555 12 = 6 ∧ acceleratedOrbit 12 2555 = 455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2555 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2555) = 3 ^ 6 * m + 455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2555.1, data_12_2555.2] + +/-- Complete interval computation for depth 12, residue 2556. -/ +theorem bounds_12_2556 : exactInterval 12 2556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2556 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2556) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2556 : oddCount 2556 12 = 9 ∧ acceleratedOrbit 12 2556 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2556 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2556) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2556.1, data_12_2556.2] + +/-- Complete interval computation for depth 12, residue 2557. -/ +theorem bounds_12_2557 : exactInterval 12 2557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2557 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2557) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2557 : oddCount 2557 12 = 9 ∧ acceleratedOrbit 12 2557 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2557 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2557) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2557.1, data_12_2557.2] + +/-- Complete interval computation for depth 12, residue 2558. -/ +theorem bounds_12_2558 : exactInterval 12 2558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2558 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2558) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2558 : oddCount 2558 12 = 9 ∧ acceleratedOrbit 12 2558 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2558 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2558) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2558.1, data_12_2558.2] + +/-- Complete interval computation for depth 12, residue 2559. -/ +theorem bounds_12_2559 : exactInterval 12 2559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2559 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2559) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2559 : oddCount 2559 12 = 11 ∧ acceleratedOrbit 12 2559 = 110717 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2559 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2559) = 3 ^ 11 * m + 110717 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2559.1, data_12_2559.2] + +/-- Complete interval computation for depth 12, residue 2560. -/ +theorem bounds_12_2560 : exactInterval 12 2560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2560 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2560) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2560 : oddCount 2560 12 = 1 ∧ acceleratedOrbit 12 2560 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2560 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2560) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2560.1, data_12_2560.2] + +/-- Complete interval computation for depth 12, residue 2561. -/ +theorem bounds_12_2561 : exactInterval 12 2561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2561 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2561) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2561 : oddCount 2561 12 = 7 ∧ acceleratedOrbit 12 2561 = 1370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2561 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2561) = 3 ^ 7 * m + 1370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2561.1, data_12_2561.2] + +/-- Complete interval computation for depth 12, residue 2562. -/ +theorem bounds_12_2562 : exactInterval 12 2562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2562 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2562) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2562 : oddCount 2562 12 = 6 ∧ acceleratedOrbit 12 2562 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2562 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2562) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2562.1, data_12_2562.2] + +/-- Complete interval computation for depth 12, residue 2563. -/ +theorem bounds_12_2563 : exactInterval 12 2563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2563 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2563) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2563 : oddCount 2563 12 = 6 ∧ acceleratedOrbit 12 2563 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2563 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2563) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2563.1, data_12_2563.2] + +/-- Complete interval computation for depth 12, residue 2564. -/ +theorem bounds_12_2564 : exactInterval 12 2564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2564 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2564) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2564 : oddCount 2564 12 = 7 ∧ acceleratedOrbit 12 2564 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2564 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2564) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2564.1, data_12_2564.2] + +end Collatz.Research.StoppingAtlas.Batch0367 From a6ec04bfaa7a3eaa8990197046a612080c136021 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:57 +0530 Subject: [PATCH 0368/1001] proof: certify atlas Batch0368 (12:2565 to 12:2579) --- Collatz/Research/StoppingAtlas/Batch0368.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0368.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0368.lean b/Collatz/Research/StoppingAtlas/Batch0368.lean new file mode 100644 index 00000000..f15f1fa9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0368.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0368 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2565. -/ +theorem bounds_12_2565 : exactInterval 12 2565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2565 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2565) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2565 : oddCount 2565 12 = 7 ∧ acceleratedOrbit 12 2565 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2565 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2565) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2565.1, data_12_2565.2] + +/-- Complete interval computation for depth 12, residue 2566. -/ +theorem bounds_12_2566 : exactInterval 12 2566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2566 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2566) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2566 : oddCount 2566 12 = 7 ∧ acceleratedOrbit 12 2566 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2566 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2566) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2566.1, data_12_2566.2] + +/-- Complete interval computation for depth 12, residue 2567. -/ +theorem bounds_12_2567 : exactInterval 12 2567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2567 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2567) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2567 : oddCount 2567 12 = 7 ∧ acceleratedOrbit 12 2567 = 1372 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2567 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2567) = 3 ^ 7 * m + 1372 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2567.1, data_12_2567.2] + +/-- Complete interval computation for depth 12, residue 2568. -/ +theorem bounds_12_2568 : exactInterval 12 2568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2568 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2568) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2568 : oddCount 2568 12 = 3 ∧ acceleratedOrbit 12 2568 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2568 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2568) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2568.1, data_12_2568.2] + +/-- Complete interval computation for depth 12, residue 2569. -/ +theorem bounds_12_2569 : exactInterval 12 2569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2569 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2569) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2569 : oddCount 2569 12 = 6 ∧ acceleratedOrbit 12 2569 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2569 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2569) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2569.1, data_12_2569.2] + +/-- Complete interval computation for depth 12, residue 2570. -/ +theorem bounds_12_2570 : exactInterval 12 2570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2570 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2570) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2570 : oddCount 2570 12 = 3 ∧ acceleratedOrbit 12 2570 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2570 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2570) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2570.1, data_12_2570.2] + +/-- Complete interval computation for depth 12, residue 2571. -/ +theorem bounds_12_2571 : exactInterval 12 2571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2571 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2571) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2571 : oddCount 2571 12 = 7 ∧ acceleratedOrbit 12 2571 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2571 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2571) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2571.1, data_12_2571.2] + +/-- Complete interval computation for depth 12, residue 2572. -/ +theorem bounds_12_2572 : exactInterval 12 2572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2572 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2572) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2572 : oddCount 2572 12 = 3 ∧ acceleratedOrbit 12 2572 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2572 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2572) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2572.1, data_12_2572.2] + +/-- Complete interval computation for depth 12, residue 2573. -/ +theorem bounds_12_2573 : exactInterval 12 2573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2573 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2573) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2573 : oddCount 2573 12 = 3 ∧ acceleratedOrbit 12 2573 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2573 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2573) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2573.1, data_12_2573.2] + +/-- Complete interval computation for depth 12, residue 2574. -/ +theorem bounds_12_2574 : exactInterval 12 2574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2574 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2574) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2574 : oddCount 2574 12 = 8 ∧ acceleratedOrbit 12 2574 = 4130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2574 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2574) = 3 ^ 8 * m + 4130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2574.1, data_12_2574.2] + +/-- Complete interval computation for depth 12, residue 2575. -/ +theorem bounds_12_2575 : exactInterval 12 2575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2575 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2575) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2575 : oddCount 2575 12 = 8 ∧ acceleratedOrbit 12 2575 = 4130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2575 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2575) = 3 ^ 8 * m + 4130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2575.1, data_12_2575.2] + +/-- Complete interval computation for depth 12, residue 2576. -/ +theorem bounds_12_2576 : exactInterval 12 2576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2576 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2576) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2576 : oddCount 2576 12 = 5 ∧ acceleratedOrbit 12 2576 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2576 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2576) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2576.1, data_12_2576.2] + +/-- Complete interval computation for depth 12, residue 2577. -/ +theorem bounds_12_2577 : exactInterval 12 2577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2577 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2577) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2577 : oddCount 2577 12 = 3 ∧ acceleratedOrbit 12 2577 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2577 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2577) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2577.1, data_12_2577.2] + +/-- Complete interval computation for depth 12, residue 2578. -/ +theorem bounds_12_2578 : exactInterval 12 2578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2578 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2578) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2578 : oddCount 2578 12 = 7 ∧ acceleratedOrbit 12 2578 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2578 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2578) = 3 ^ 7 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2578.1, data_12_2578.2] + +/-- Complete interval computation for depth 12, residue 2579. -/ +theorem bounds_12_2579 : exactInterval 12 2579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2579 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2579) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2579 : oddCount 2579 12 = 7 ∧ acceleratedOrbit 12 2579 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2579 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2579) = 3 ^ 7 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2579.1, data_12_2579.2] + +end Collatz.Research.StoppingAtlas.Batch0368 From 10650fa1f95dd25587f66ae687cddfe47f27119c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:57 +0530 Subject: [PATCH 0369/1001] proof: certify atlas Batch0369 (12:2580 to 12:2594) --- Collatz/Research/StoppingAtlas/Batch0369.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0369.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0369.lean b/Collatz/Research/StoppingAtlas/Batch0369.lean new file mode 100644 index 00000000..b5a3db96 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0369.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0369 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2580. -/ +theorem bounds_12_2580 : exactInterval 12 2580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2580 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2580) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2580 : oddCount 2580 12 = 5 ∧ acceleratedOrbit 12 2580 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2580 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2580) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2580.1, data_12_2580.2] + +/-- Complete interval computation for depth 12, residue 2581. -/ +theorem bounds_12_2581 : exactInterval 12 2581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2581 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2581) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2581 : oddCount 2581 12 = 5 ∧ acceleratedOrbit 12 2581 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2581 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2581) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2581.1, data_12_2581.2] + +/-- Complete interval computation for depth 12, residue 2582. -/ +theorem bounds_12_2582 : exactInterval 12 2582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2582 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2582) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2582 : oddCount 2582 12 = 6 ∧ acceleratedOrbit 12 2582 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2582 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2582) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2582.1, data_12_2582.2] + +/-- Complete interval computation for depth 12, residue 2583. -/ +theorem bounds_12_2583 : exactInterval 12 2583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2583 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2583) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2583 : oddCount 2583 12 = 6 ∧ acceleratedOrbit 12 2583 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2583 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2583) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2583.1, data_12_2583.2] + +/-- Complete interval computation for depth 12, residue 2584. -/ +theorem bounds_12_2584 : exactInterval 12 2584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2584 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2584) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2584 : oddCount 2584 12 = 5 ∧ acceleratedOrbit 12 2584 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2584 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2584) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2584.1, data_12_2584.2] + +/-- Complete interval computation for depth 12, residue 2585. -/ +theorem bounds_12_2585 : exactInterval 12 2585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2585 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2585) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2585 : oddCount 2585 12 = 6 ∧ acceleratedOrbit 12 2585 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2585 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2585) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2585.1, data_12_2585.2] + +/-- Complete interval computation for depth 12, residue 2586. -/ +theorem bounds_12_2586 : exactInterval 12 2586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2586 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2586) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2586 : oddCount 2586 12 = 5 ∧ acceleratedOrbit 12 2586 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2586 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2586) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2586.1, data_12_2586.2] + +/-- Complete interval computation for depth 12, residue 2587. -/ +theorem bounds_12_2587 : exactInterval 12 2587 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2587 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2587) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2587 : oddCount 2587 12 = 7 ∧ acceleratedOrbit 12 2587 = 1382 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2587 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2587) = 3 ^ 7 * m + 1382 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2587.1, data_12_2587.2] + +/-- Complete interval computation for depth 12, residue 2588. -/ +theorem bounds_12_2588 : exactInterval 12 2588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2588 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2588) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2588 : oddCount 2588 12 = 5 ∧ acceleratedOrbit 12 2588 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2588 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2588) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2588.1, data_12_2588.2] + +/-- Complete interval computation for depth 12, residue 2589. -/ +theorem bounds_12_2589 : exactInterval 12 2589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2589 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2589) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2589 : oddCount 2589 12 = 5 ∧ acceleratedOrbit 12 2589 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2589 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2589) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2589.1, data_12_2589.2] + +/-- Complete interval computation for depth 12, residue 2590. -/ +theorem bounds_12_2590 : exactInterval 12 2590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2590 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2590) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2590 : oddCount 2590 12 = 5 ∧ acceleratedOrbit 12 2590 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2590 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2590) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2590.1, data_12_2590.2] + +/-- Complete interval computation for depth 12, residue 2591. -/ +theorem bounds_12_2591 : exactInterval 12 2591 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2591 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2591) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2591 : oddCount 2591 12 = 7 ∧ acceleratedOrbit 12 2591 = 1384 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2591 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2591) = 3 ^ 7 * m + 1384 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2591.1, data_12_2591.2] + +/-- Complete interval computation for depth 12, residue 2592. -/ +theorem bounds_12_2592 : exactInterval 12 2592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2592 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2592) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2592 : oddCount 2592 12 = 4 ∧ acceleratedOrbit 12 2592 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2592 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2592) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2592.1, data_12_2592.2] + +/-- Complete interval computation for depth 12, residue 2593. -/ +theorem bounds_12_2593 : exactInterval 12 2593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2593 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2593) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2593 : oddCount 2593 12 = 5 ∧ acceleratedOrbit 12 2593 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2593 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2593) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2593.1, data_12_2593.2] + +/-- Complete interval computation for depth 12, residue 2594. -/ +theorem bounds_12_2594 : exactInterval 12 2594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2594 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2594) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2594 : oddCount 2594 12 = 5 ∧ acceleratedOrbit 12 2594 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2594 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2594) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2594.1, data_12_2594.2] + +end Collatz.Research.StoppingAtlas.Batch0369 From 20261c2423fe6415a390e2cbd426db1a92d340ef Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:58 +0530 Subject: [PATCH 0370/1001] proof: certify atlas Batch0370 (12:2595 to 12:2610) --- Collatz/Research/StoppingAtlas/Batch0370.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0370.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0370.lean b/Collatz/Research/StoppingAtlas/Batch0370.lean new file mode 100644 index 00000000..eb993091 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0370.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0370 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2595. -/ +theorem bounds_12_2595 : exactInterval 12 2595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2595 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2595) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2595 : oddCount 2595 12 = 5 ∧ acceleratedOrbit 12 2595 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2595 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2595) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2595.1, data_12_2595.2] + +/-- Complete interval computation for depth 12, residue 2596. -/ +theorem bounds_12_2596 : exactInterval 12 2596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2596 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2596) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2596 : oddCount 2596 12 = 7 ∧ acceleratedOrbit 12 2596 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2596 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2596) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2596.1, data_12_2596.2] + +/-- Complete interval computation for depth 12, residue 2597. -/ +theorem bounds_12_2597 : exactInterval 12 2597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2597 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2597) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2597 : oddCount 2597 12 = 7 ∧ acceleratedOrbit 12 2597 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2597 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2597) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2597.1, data_12_2597.2] + +/-- Complete interval computation for depth 12, residue 2598. -/ +theorem bounds_12_2598 : exactInterval 12 2598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2598 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2598) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2598 : oddCount 2598 12 = 7 ∧ acceleratedOrbit 12 2598 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2598 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2598) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2598.1, data_12_2598.2] + +/-- Complete interval computation for depth 12, residue 2599. -/ +theorem bounds_12_2599 : exactInterval 12 2599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2599 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2599) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2599 : oddCount 2599 12 = 6 ∧ acceleratedOrbit 12 2599 = 463 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2599 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2599) = 3 ^ 6 * m + 463 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2599.1, data_12_2599.2] + +/-- Complete interval computation for depth 12, residue 2600. -/ +theorem bounds_12_2600 : exactInterval 12 2600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2600 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2600) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2600 : oddCount 2600 12 = 4 ∧ acceleratedOrbit 12 2600 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2600 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2600) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2600.1, data_12_2600.2] + +/-- Complete interval computation for depth 12, residue 2601. -/ +theorem bounds_12_2601 : exactInterval 12 2601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2601 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2601) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2601 : oddCount 2601 12 = 8 ∧ acceleratedOrbit 12 2601 = 4169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2601 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2601) = 3 ^ 8 * m + 4169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2601.1, data_12_2601.2] + +/-- Complete interval computation for depth 12, residue 2602. -/ +theorem bounds_12_2602 : exactInterval 12 2602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2602 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2602) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2602 : oddCount 2602 12 = 4 ∧ acceleratedOrbit 12 2602 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2602 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2602) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2602.1, data_12_2602.2] + +/-- Complete interval computation for depth 12, residue 2603. -/ +theorem bounds_12_2603 : exactInterval 12 2603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2603 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2603) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2603 : oddCount 2603 12 = 5 ∧ acceleratedOrbit 12 2603 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2603 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2603) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2603.1, data_12_2603.2] + +/-- Complete interval computation for depth 12, residue 2604. -/ +theorem bounds_12_2604 : exactInterval 12 2604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2604 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2604) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2604 : oddCount 2604 12 = 5 ∧ acceleratedOrbit 12 2604 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2604 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2604) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2604.1, data_12_2604.2] + +/-- Complete interval computation for depth 12, residue 2605. -/ +theorem bounds_12_2605 : exactInterval 12 2605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2605 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2605) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2605 : oddCount 2605 12 = 5 ∧ acceleratedOrbit 12 2605 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2605 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2605) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2605.1, data_12_2605.2] + +/-- Complete interval computation for depth 12, residue 2606. -/ +theorem bounds_12_2606 : exactInterval 12 2606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2606 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2606) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2606 : oddCount 2606 12 = 5 ∧ acceleratedOrbit 12 2606 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2606 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2606) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2606.1, data_12_2606.2] + +/-- Complete interval computation for depth 12, residue 2607. -/ +theorem bounds_12_2607 : exactInterval 12 2607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2607 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2607) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2607 : oddCount 2607 12 = 8 ∧ acceleratedOrbit 12 2607 = 4178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2607 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2607) = 3 ^ 8 * m + 4178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2607.1, data_12_2607.2] + +/-- Complete interval computation for depth 12, residue 2608. -/ +theorem bounds_12_2608 : exactInterval 12 2608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2608 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2608) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2608 : oddCount 2608 12 = 4 ∧ acceleratedOrbit 12 2608 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2608 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2608) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2608.1, data_12_2608.2] + +/-- Complete interval computation for depth 12, residue 2609. -/ +theorem bounds_12_2609 : exactInterval 12 2609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2609 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2609) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2609 : oddCount 2609 12 = 7 ∧ acceleratedOrbit 12 2609 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2609 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2609) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2609.1, data_12_2609.2] + +/-- Complete interval computation for depth 12, residue 2610. -/ +theorem bounds_12_2610 : exactInterval 12 2610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2610 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2610) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2610 : oddCount 2610 12 = 7 ∧ acceleratedOrbit 12 2610 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2610 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2610) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2610.1, data_12_2610.2] + +end Collatz.Research.StoppingAtlas.Batch0370 From bfbe37ca4a0445c7b30e93a204ee39398781dade Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:58 +0530 Subject: [PATCH 0371/1001] proof: certify atlas Batch0371 (12:2611 to 12:2625) --- Collatz/Research/StoppingAtlas/Batch0371.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0371.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0371.lean b/Collatz/Research/StoppingAtlas/Batch0371.lean new file mode 100644 index 00000000..fe7bbb76 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0371.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0371 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2611. -/ +theorem bounds_12_2611 : exactInterval 12 2611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2611 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2611) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2611 : oddCount 2611 12 = 7 ∧ acceleratedOrbit 12 2611 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2611 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2611) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2611.1, data_12_2611.2] + +/-- Complete interval computation for depth 12, residue 2612. -/ +theorem bounds_12_2612 : exactInterval 12 2612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2612 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2612) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2612 : oddCount 2612 12 = 4 ∧ acceleratedOrbit 12 2612 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2612 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2612) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2612.1, data_12_2612.2] + +/-- Complete interval computation for depth 12, residue 2613. -/ +theorem bounds_12_2613 : exactInterval 12 2613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2613 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2613) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2613 : oddCount 2613 12 = 4 ∧ acceleratedOrbit 12 2613 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2613 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2613) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2613.1, data_12_2613.2] + +/-- Complete interval computation for depth 12, residue 2614. -/ +theorem bounds_12_2614 : exactInterval 12 2614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2614 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2614) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2614 : oddCount 2614 12 = 9 ∧ acceleratedOrbit 12 2614 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2614 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2614) = 3 ^ 9 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2614.1, data_12_2614.2] + +/-- Complete interval computation for depth 12, residue 2615. -/ +theorem bounds_12_2615 : exactInterval 12 2615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2615 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2615) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2615 : oddCount 2615 12 = 9 ∧ acceleratedOrbit 12 2615 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2615 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2615) = 3 ^ 9 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2615.1, data_12_2615.2] + +/-- Complete interval computation for depth 12, residue 2616. -/ +theorem bounds_12_2616 : exactInterval 12 2616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2616 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2616) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2616 : oddCount 2616 12 = 7 ∧ acceleratedOrbit 12 2616 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2616 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2616) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2616.1, data_12_2616.2] + +/-- Complete interval computation for depth 12, residue 2617. -/ +theorem bounds_12_2617 : exactInterval 12 2617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2617 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2617) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2617 : oddCount 2617 12 = 7 ∧ acceleratedOrbit 12 2617 = 1399 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2617 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2617) = 3 ^ 7 * m + 1399 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2617.1, data_12_2617.2] + +/-- Complete interval computation for depth 12, residue 2618. -/ +theorem bounds_12_2618 : exactInterval 12 2618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2618 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2618) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2618 : oddCount 2618 12 = 7 ∧ acceleratedOrbit 12 2618 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2618 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2618) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2618.1, data_12_2618.2] + +/-- Complete interval computation for depth 12, residue 2619. -/ +theorem bounds_12_2619 : exactInterval 12 2619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2619 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2619) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2619 : oddCount 2619 12 = 6 ∧ acceleratedOrbit 12 2619 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2619 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2619) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2619.1, data_12_2619.2] + +/-- Complete interval computation for depth 12, residue 2620. -/ +theorem bounds_12_2620 : exactInterval 12 2620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2620 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2620) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2620 : oddCount 2620 12 = 7 ∧ acceleratedOrbit 12 2620 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2620 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2620) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2620.1, data_12_2620.2] + +/-- Complete interval computation for depth 12, residue 2621. -/ +theorem bounds_12_2621 : exactInterval 12 2621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2621 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2621) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2621 : oddCount 2621 12 = 7 ∧ acceleratedOrbit 12 2621 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2621 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2621) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2621.1, data_12_2621.2] + +/-- Complete interval computation for depth 12, residue 2622. -/ +theorem bounds_12_2622 : exactInterval 12 2622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2622 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2622) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2622 : oddCount 2622 12 = 6 ∧ acceleratedOrbit 12 2622 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2622 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2622) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2622.1, data_12_2622.2] + +/-- Complete interval computation for depth 12, residue 2623. -/ +theorem bounds_12_2623 : exactInterval 12 2623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2623 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2623) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2623 : oddCount 2623 12 = 6 ∧ acceleratedOrbit 12 2623 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2623 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2623) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2623.1, data_12_2623.2] + +/-- Complete interval computation for depth 12, residue 2624. -/ +theorem bounds_12_2624 : exactInterval 12 2624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2624 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2624) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2624 : oddCount 2624 12 = 5 ∧ acceleratedOrbit 12 2624 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2624 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2624) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2624.1, data_12_2624.2] + +/-- Complete interval computation for depth 12, residue 2625. -/ +theorem bounds_12_2625 : exactInterval 12 2625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2625 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2625) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2625 : oddCount 2625 12 = 4 ∧ acceleratedOrbit 12 2625 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2625 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2625) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2625.1, data_12_2625.2] + +end Collatz.Research.StoppingAtlas.Batch0371 From 6bb6c5036f60f5a12a42396b52347f8fc1b64ba0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:58 +0530 Subject: [PATCH 0372/1001] proof: certify atlas Batch0372 (12:2626 to 12:2640) --- Collatz/Research/StoppingAtlas/Batch0372.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0372.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0372.lean b/Collatz/Research/StoppingAtlas/Batch0372.lean new file mode 100644 index 00000000..88d042d2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0372.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0372 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2626. -/ +theorem bounds_12_2626 : exactInterval 12 2626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2626 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2626) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2626 : oddCount 2626 12 = 4 ∧ acceleratedOrbit 12 2626 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2626 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2626) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2626.1, data_12_2626.2] + +/-- Complete interval computation for depth 12, residue 2627. -/ +theorem bounds_12_2627 : exactInterval 12 2627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2627 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2627) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2627 : oddCount 2627 12 = 4 ∧ acceleratedOrbit 12 2627 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2627 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2627) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2627.1, data_12_2627.2] + +/-- Complete interval computation for depth 12, residue 2628. -/ +theorem bounds_12_2628 : exactInterval 12 2628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2628 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2628) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2628 : oddCount 2628 12 = 5 ∧ acceleratedOrbit 12 2628 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2628 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2628) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2628.1, data_12_2628.2] + +/-- Complete interval computation for depth 12, residue 2629. -/ +theorem bounds_12_2629 : exactInterval 12 2629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2629 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2629) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2629 : oddCount 2629 12 = 5 ∧ acceleratedOrbit 12 2629 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2629 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2629) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2629.1, data_12_2629.2] + +/-- Complete interval computation for depth 12, residue 2630. -/ +theorem bounds_12_2630 : exactInterval 12 2630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2630 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2630) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2630 : oddCount 2630 12 = 5 ∧ acceleratedOrbit 12 2630 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2630 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2630) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2630.1, data_12_2630.2] + +/-- Complete interval computation for depth 12, residue 2631. -/ +theorem bounds_12_2631 : exactInterval 12 2631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2631 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2631) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2631 : oddCount 2631 12 = 7 ∧ acceleratedOrbit 12 2631 = 1406 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2631 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2631) = 3 ^ 7 * m + 1406 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2631.1, data_12_2631.2] + +/-- Complete interval computation for depth 12, residue 2632. -/ +theorem bounds_12_2632 : exactInterval 12 2632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2632 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2632) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2632 : oddCount 2632 12 = 5 ∧ acceleratedOrbit 12 2632 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2632 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2632) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2632.1, data_12_2632.2] + +/-- Complete interval computation for depth 12, residue 2633. -/ +theorem bounds_12_2633 : exactInterval 12 2633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2633 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2633) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2633 : oddCount 2633 12 = 6 ∧ acceleratedOrbit 12 2633 = 469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2633 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2633) = 3 ^ 6 * m + 469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2633.1, data_12_2633.2] + +/-- Complete interval computation for depth 12, residue 2634. -/ +theorem bounds_12_2634 : exactInterval 12 2634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2634 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2634) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2634 : oddCount 2634 12 = 5 ∧ acceleratedOrbit 12 2634 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2634 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2634) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2634.1, data_12_2634.2] + +/-- Complete interval computation for depth 12, residue 2635. -/ +theorem bounds_12_2635 : exactInterval 12 2635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2635 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2635) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2635 : oddCount 2635 12 = 5 ∧ acceleratedOrbit 12 2635 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2635 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2635) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2635.1, data_12_2635.2] + +/-- Complete interval computation for depth 12, residue 2636. -/ +theorem bounds_12_2636 : exactInterval 12 2636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2636 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2636) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2636 : oddCount 2636 12 = 5 ∧ acceleratedOrbit 12 2636 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2636 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2636) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2636.1, data_12_2636.2] + +/-- Complete interval computation for depth 12, residue 2637. -/ +theorem bounds_12_2637 : exactInterval 12 2637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2637 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2637) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2637 : oddCount 2637 12 = 5 ∧ acceleratedOrbit 12 2637 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2637 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2637) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2637.1, data_12_2637.2] + +/-- Complete interval computation for depth 12, residue 2638. -/ +theorem bounds_12_2638 : exactInterval 12 2638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2638 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2638) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2638 : oddCount 2638 12 = 6 ∧ acceleratedOrbit 12 2638 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2638 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2638) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2638.1, data_12_2638.2] + +/-- Complete interval computation for depth 12, residue 2639. -/ +theorem bounds_12_2639 : exactInterval 12 2639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2639 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2639) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2639 : oddCount 2639 12 = 6 ∧ acceleratedOrbit 12 2639 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2639 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2639) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2639.1, data_12_2639.2] + +/-- Complete interval computation for depth 12, residue 2640. -/ +theorem bounds_12_2640 : exactInterval 12 2640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2640 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2640) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2640 : oddCount 2640 12 = 5 ∧ acceleratedOrbit 12 2640 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2640 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2640) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2640.1, data_12_2640.2] + +end Collatz.Research.StoppingAtlas.Batch0372 From 498836d73f5fde85cfdcdb253abf11376784bd57 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:58 +0530 Subject: [PATCH 0373/1001] proof: certify atlas Batch0373 (12:2641 to 12:2656) --- Collatz/Research/StoppingAtlas/Batch0373.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0373.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0373.lean b/Collatz/Research/StoppingAtlas/Batch0373.lean new file mode 100644 index 00000000..1a5e1fa3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0373.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0373 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2641. -/ +theorem bounds_12_2641 : exactInterval 12 2641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2641 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2641) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2641 : oddCount 2641 12 = 8 ∧ acceleratedOrbit 12 2641 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2641 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2641) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2641.1, data_12_2641.2] + +/-- Complete interval computation for depth 12, residue 2642. -/ +theorem bounds_12_2642 : exactInterval 12 2642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2642 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2642) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2642 : oddCount 2642 12 = 8 ∧ acceleratedOrbit 12 2642 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2642 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2642) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2642.1, data_12_2642.2] + +/-- Complete interval computation for depth 12, residue 2643. -/ +theorem bounds_12_2643 : exactInterval 12 2643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2643 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2643) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2643 : oddCount 2643 12 = 8 ∧ acceleratedOrbit 12 2643 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2643 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2643) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2643.1, data_12_2643.2] + +/-- Complete interval computation for depth 12, residue 2644. -/ +theorem bounds_12_2644 : exactInterval 12 2644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2644 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2644) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2644 : oddCount 2644 12 = 5 ∧ acceleratedOrbit 12 2644 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2644 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2644) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2644.1, data_12_2644.2] + +/-- Complete interval computation for depth 12, residue 2645. -/ +theorem bounds_12_2645 : exactInterval 12 2645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2645 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2645) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2645 : oddCount 2645 12 = 5 ∧ acceleratedOrbit 12 2645 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2645 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2645) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2645.1, data_12_2645.2] + +/-- Complete interval computation for depth 12, residue 2646. -/ +theorem bounds_12_2646 : exactInterval 12 2646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2646 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2646) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2646 : oddCount 2646 12 = 6 ∧ acceleratedOrbit 12 2646 = 472 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2646 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2646) = 3 ^ 6 * m + 472 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2646.1, data_12_2646.2] + +/-- Complete interval computation for depth 12, residue 2647. -/ +theorem bounds_12_2647 : exactInterval 12 2647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2647 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2647) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2647 : oddCount 2647 12 = 6 ∧ acceleratedOrbit 12 2647 = 472 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2647 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2647) = 3 ^ 6 * m + 472 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2647.1, data_12_2647.2] + +/-- Complete interval computation for depth 12, residue 2648. -/ +theorem bounds_12_2648 : exactInterval 12 2648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2648 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2648) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2648 : oddCount 2648 12 = 4 ∧ acceleratedOrbit 12 2648 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2648 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2648) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2648.1, data_12_2648.2] + +/-- Complete interval computation for depth 12, residue 2649. -/ +theorem bounds_12_2649 : exactInterval 12 2649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2649 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2649) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2649 : oddCount 2649 12 = 7 ∧ acceleratedOrbit 12 2649 = 1417 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2649 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2649) = 3 ^ 7 * m + 1417 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2649.1, data_12_2649.2] + +/-- Complete interval computation for depth 12, residue 2650. -/ +theorem bounds_12_2650 : exactInterval 12 2650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2650 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2650) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2650 : oddCount 2650 12 = 4 ∧ acceleratedOrbit 12 2650 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2650 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2650) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2650.1, data_12_2650.2] + +/-- Complete interval computation for depth 12, residue 2651. -/ +theorem bounds_12_2651 : exactInterval 12 2651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2651 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2651) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2651 : oddCount 2651 12 = 8 ∧ acceleratedOrbit 12 2651 = 4249 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2651 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2651) = 3 ^ 8 * m + 4249 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2651.1, data_12_2651.2] + +/-- Complete interval computation for depth 12, residue 2652. -/ +theorem bounds_12_2652 : exactInterval 12 2652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2652 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2652) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2652 : oddCount 2652 12 = 4 ∧ acceleratedOrbit 12 2652 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2652 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2652) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2652.1, data_12_2652.2] + +/-- Complete interval computation for depth 12, residue 2653. -/ +theorem bounds_12_2653 : exactInterval 12 2653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2653 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2653) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2653 : oddCount 2653 12 = 4 ∧ acceleratedOrbit 12 2653 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2653 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2653) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2653.1, data_12_2653.2] + +/-- Complete interval computation for depth 12, residue 2654. -/ +theorem bounds_12_2654 : exactInterval 12 2654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2654 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2654) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2654 : oddCount 2654 12 = 8 ∧ acceleratedOrbit 12 2654 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2654 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2654) = 3 ^ 8 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2654.1, data_12_2654.2] + +/-- Complete interval computation for depth 12, residue 2655. -/ +theorem bounds_12_2655 : exactInterval 12 2655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2655 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2655) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2655 : oddCount 2655 12 = 8 ∧ acceleratedOrbit 12 2655 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2655 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2655) = 3 ^ 8 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2655.1, data_12_2655.2] + +/-- Complete interval computation for depth 12, residue 2656. -/ +theorem bounds_12_2656 : exactInterval 12 2656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2656 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2656) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2656 : oddCount 2656 12 = 5 ∧ acceleratedOrbit 12 2656 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2656 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2656) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2656.1, data_12_2656.2] + +end Collatz.Research.StoppingAtlas.Batch0373 From 02706408b7e8a6d935015070f86dc847e6afdbd0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:59 +0530 Subject: [PATCH 0374/1001] proof: certify atlas Batch0374 (12:2657 to 12:2671) --- Collatz/Research/StoppingAtlas/Batch0374.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0374.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0374.lean b/Collatz/Research/StoppingAtlas/Batch0374.lean new file mode 100644 index 00000000..8ebac036 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0374.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0374 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2657. -/ +theorem bounds_12_2657 : exactInterval 12 2657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2657 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2657) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2657 : oddCount 2657 12 = 7 ∧ acceleratedOrbit 12 2657 = 1421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2657 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2657) = 3 ^ 7 * m + 1421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2657.1, data_12_2657.2] + +/-- Complete interval computation for depth 12, residue 2658. -/ +theorem bounds_12_2658 : exactInterval 12 2658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2658 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2658) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2658 : oddCount 2658 12 = 6 ∧ acceleratedOrbit 12 2658 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2658 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2658) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2658.1, data_12_2658.2] + +/-- Complete interval computation for depth 12, residue 2659. -/ +theorem bounds_12_2659 : exactInterval 12 2659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2659 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2659) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2659 : oddCount 2659 12 = 6 ∧ acceleratedOrbit 12 2659 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2659 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2659) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2659.1, data_12_2659.2] + +/-- Complete interval computation for depth 12, residue 2660. -/ +theorem bounds_12_2660 : exactInterval 12 2660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2660 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2660) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2660 : oddCount 2660 12 = 6 ∧ acceleratedOrbit 12 2660 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2660 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2660) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2660.1, data_12_2660.2] + +/-- Complete interval computation for depth 12, residue 2661. -/ +theorem bounds_12_2661 : exactInterval 12 2661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2661 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2661) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2661 : oddCount 2661 12 = 6 ∧ acceleratedOrbit 12 2661 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2661 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2661) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2661.1, data_12_2661.2] + +/-- Complete interval computation for depth 12, residue 2662. -/ +theorem bounds_12_2662 : exactInterval 12 2662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2662 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2662) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2662 : oddCount 2662 12 = 6 ∧ acceleratedOrbit 12 2662 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2662 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2662) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2662.1, data_12_2662.2] + +/-- Complete interval computation for depth 12, residue 2663. -/ +theorem bounds_12_2663 : exactInterval 12 2663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2663 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2663) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2663 : oddCount 2663 12 = 8 ∧ acceleratedOrbit 12 2663 = 4268 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2663 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2663) = 3 ^ 8 * m + 4268 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2663.1, data_12_2663.2] + +/-- Complete interval computation for depth 12, residue 2664. -/ +theorem bounds_12_2664 : exactInterval 12 2664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2664 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2664) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2664 : oddCount 2664 12 = 5 ∧ acceleratedOrbit 12 2664 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2664 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2664) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2664.1, data_12_2664.2] + +/-- Complete interval computation for depth 12, residue 2665. -/ +theorem bounds_12_2665 : exactInterval 12 2665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2665 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2665) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2665 : oddCount 2665 12 = 7 ∧ acceleratedOrbit 12 2665 = 1424 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2665 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2665) = 3 ^ 7 * m + 1424 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2665.1, data_12_2665.2] + +/-- Complete interval computation for depth 12, residue 2666. -/ +theorem bounds_12_2666 : exactInterval 12 2666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2666 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2666) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2666 : oddCount 2666 12 = 5 ∧ acceleratedOrbit 12 2666 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2666 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2666) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2666.1, data_12_2666.2] + +/-- Complete interval computation for depth 12, residue 2667. -/ +theorem bounds_12_2667 : exactInterval 12 2667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2667 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2667) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2667 : oddCount 2667 12 = 6 ∧ acceleratedOrbit 12 2667 = 475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2667 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2667) = 3 ^ 6 * m + 475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2667.1, data_12_2667.2] + +/-- Complete interval computation for depth 12, residue 2668. -/ +theorem bounds_12_2668 : exactInterval 12 2668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2668 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2668) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2668 : oddCount 2668 12 = 8 ∧ acceleratedOrbit 12 2668 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2668 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2668) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2668.1, data_12_2668.2] + +/-- Complete interval computation for depth 12, residue 2669. -/ +theorem bounds_12_2669 : exactInterval 12 2669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2669 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2669) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2669 : oddCount 2669 12 = 8 ∧ acceleratedOrbit 12 2669 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2669 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2669) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2669.1, data_12_2669.2] + +/-- Complete interval computation for depth 12, residue 2670. -/ +theorem bounds_12_2670 : exactInterval 12 2670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2670 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2670) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2670 : oddCount 2670 12 = 8 ∧ acceleratedOrbit 12 2670 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2670 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2670) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2670.1, data_12_2670.2] + +/-- Complete interval computation for depth 12, residue 2671. -/ +theorem bounds_12_2671 : exactInterval 12 2671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2671 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2671) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2671 : oddCount 2671 12 = 9 ∧ acceleratedOrbit 12 2671 = 12842 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2671 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2671) = 3 ^ 9 * m + 12842 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2671.1, data_12_2671.2] + +end Collatz.Research.StoppingAtlas.Batch0374 From a5b6c3b52c72bf621fb203936fb08baa092338a3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:59 +0530 Subject: [PATCH 0375/1001] proof: certify atlas Batch0375 (12:2672 to 12:2687) --- Collatz/Research/StoppingAtlas/Batch0375.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0375.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0375.lean b/Collatz/Research/StoppingAtlas/Batch0375.lean new file mode 100644 index 00000000..dc5146dc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0375.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0375 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2672. -/ +theorem bounds_12_2672 : exactInterval 12 2672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2672 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2672) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2672 : oddCount 2672 12 = 6 ∧ acceleratedOrbit 12 2672 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2672 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2672) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2672.1, data_12_2672.2] + +/-- Complete interval computation for depth 12, residue 2673. -/ +theorem bounds_12_2673 : exactInterval 12 2673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2673 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2673) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2673 : oddCount 2673 12 = 5 ∧ acceleratedOrbit 12 2673 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2673 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2673) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2673.1, data_12_2673.2] + +/-- Complete interval computation for depth 12, residue 2674. -/ +theorem bounds_12_2674 : exactInterval 12 2674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2674 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2674) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2674 : oddCount 2674 12 = 8 ∧ acceleratedOrbit 12 2674 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2674 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2674) = 3 ^ 8 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2674.1, data_12_2674.2] + +/-- Complete interval computation for depth 12, residue 2675. -/ +theorem bounds_12_2675 : exactInterval 12 2675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2675 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2675) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2675 : oddCount 2675 12 = 8 ∧ acceleratedOrbit 12 2675 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2675 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2675) = 3 ^ 8 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2675.1, data_12_2675.2] + +/-- Complete interval computation for depth 12, residue 2676. -/ +theorem bounds_12_2676 : exactInterval 12 2676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2676 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2676) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2676 : oddCount 2676 12 = 6 ∧ acceleratedOrbit 12 2676 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2676 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2676) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2676.1, data_12_2676.2] + +/-- Complete interval computation for depth 12, residue 2677. -/ +theorem bounds_12_2677 : exactInterval 12 2677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2677 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2677) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2677 : oddCount 2677 12 = 6 ∧ acceleratedOrbit 12 2677 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2677 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2677) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2677.1, data_12_2677.2] + +/-- Complete interval computation for depth 12, residue 2678. -/ +theorem bounds_12_2678 : exactInterval 12 2678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2678 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2678) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2678 : oddCount 2678 12 = 4 ∧ acceleratedOrbit 12 2678 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2678 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2678) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2678.1, data_12_2678.2] + +/-- Complete interval computation for depth 12, residue 2679. -/ +theorem bounds_12_2679 : exactInterval 12 2679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2679 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2679) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2679 : oddCount 2679 12 = 4 ∧ acceleratedOrbit 12 2679 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2679 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2679) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2679.1, data_12_2679.2] + +/-- Complete interval computation for depth 12, residue 2680. -/ +theorem bounds_12_2680 : exactInterval 12 2680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2680 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2680) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2680 : oddCount 2680 12 = 6 ∧ acceleratedOrbit 12 2680 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2680 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2680) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2680.1, data_12_2680.2] + +/-- Complete interval computation for depth 12, residue 2681. -/ +theorem bounds_12_2681 : exactInterval 12 2681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2681 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2681) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2681 : oddCount 2681 12 = 7 ∧ acceleratedOrbit 12 2681 = 1433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2681 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2681) = 3 ^ 7 * m + 1433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2681.1, data_12_2681.2] + +/-- Complete interval computation for depth 12, residue 2682. -/ +theorem bounds_12_2682 : exactInterval 12 2682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2682 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2682) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2682 : oddCount 2682 12 = 6 ∧ acceleratedOrbit 12 2682 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2682 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2682) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2682.1, data_12_2682.2] + +/-- Complete interval computation for depth 12, residue 2683. -/ +theorem bounds_12_2683 : exactInterval 12 2683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2683 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2683) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2683 : oddCount 2683 12 = 6 ∧ acceleratedOrbit 12 2683 = 478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2683 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2683) = 3 ^ 6 * m + 478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2683.1, data_12_2683.2] + +/-- Complete interval computation for depth 12, residue 2684. -/ +theorem bounds_12_2684 : exactInterval 12 2684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2684 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2684) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2684 : oddCount 2684 12 = 8 ∧ acceleratedOrbit 12 2684 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2684 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2684) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2684.1, data_12_2684.2] + +/-- Complete interval computation for depth 12, residue 2685. -/ +theorem bounds_12_2685 : exactInterval 12 2685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2685 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2685) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2685 : oddCount 2685 12 = 8 ∧ acceleratedOrbit 12 2685 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2685 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2685) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2685.1, data_12_2685.2] + +/-- Complete interval computation for depth 12, residue 2686. -/ +theorem bounds_12_2686 : exactInterval 12 2686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2686 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2686) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2686 : oddCount 2686 12 = 8 ∧ acceleratedOrbit 12 2686 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2686 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2686) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2686.1, data_12_2686.2] + +/-- Complete interval computation for depth 12, residue 2687. -/ +theorem bounds_12_2687 : exactInterval 12 2687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2687 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2687) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2687 : oddCount 2687 12 = 9 ∧ acceleratedOrbit 12 2687 = 12917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2687 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2687) = 3 ^ 9 * m + 12917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2687.1, data_12_2687.2] + +end Collatz.Research.StoppingAtlas.Batch0375 From c1d8777f9f70e653b4dd08848ed54886fd99e722 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:23:59 +0530 Subject: [PATCH 0376/1001] proof: certify atlas Batch0376 (12:2688 to 12:2702) --- Collatz/Research/StoppingAtlas/Batch0376.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0376.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0376.lean b/Collatz/Research/StoppingAtlas/Batch0376.lean new file mode 100644 index 00000000..8c0de1b8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0376.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0376 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2688. -/ +theorem bounds_12_2688 : exactInterval 12 2688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2688 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2688) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2688 : oddCount 2688 12 = 1 ∧ acceleratedOrbit 12 2688 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2688 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2688) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2688.1, data_12_2688.2] + +/-- Complete interval computation for depth 12, residue 2689. -/ +theorem bounds_12_2689 : exactInterval 12 2689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2689 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2689) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2689 : oddCount 2689 12 = 8 ∧ acceleratedOrbit 12 2689 = 4313 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2689 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2689) = 3 ^ 8 * m + 4313 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2689.1, data_12_2689.2] + +/-- Complete interval computation for depth 12, residue 2690. -/ +theorem bounds_12_2690 : exactInterval 12 2690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2690 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2690) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2690 : oddCount 2690 12 = 5 ∧ acceleratedOrbit 12 2690 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2690 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2690) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2690.1, data_12_2690.2] + +/-- Complete interval computation for depth 12, residue 2691. -/ +theorem bounds_12_2691 : exactInterval 12 2691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2691 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2691) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2691 : oddCount 2691 12 = 5 ∧ acceleratedOrbit 12 2691 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2691 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2691) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2691.1, data_12_2691.2] + +/-- Complete interval computation for depth 12, residue 2692. -/ +theorem bounds_12_2692 : exactInterval 12 2692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2692 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2692) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2692 : oddCount 2692 12 = 6 ∧ acceleratedOrbit 12 2692 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2692 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2692) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2692.1, data_12_2692.2] + +/-- Complete interval computation for depth 12, residue 2693. -/ +theorem bounds_12_2693 : exactInterval 12 2693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2693 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2693) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2693 : oddCount 2693 12 = 6 ∧ acceleratedOrbit 12 2693 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2693 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2693) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2693.1, data_12_2693.2] + +/-- Complete interval computation for depth 12, residue 2694. -/ +theorem bounds_12_2694 : exactInterval 12 2694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2694 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2694) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2694 : oddCount 2694 12 = 6 ∧ acceleratedOrbit 12 2694 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2694 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2694) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2694.1, data_12_2694.2] + +/-- Complete interval computation for depth 12, residue 2695. -/ +theorem bounds_12_2695 : exactInterval 12 2695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2695 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2695) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2695 : oddCount 2695 12 = 5 ∧ acceleratedOrbit 12 2695 = 160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2695 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2695) = 3 ^ 5 * m + 160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2695.1, data_12_2695.2] + +/-- Complete interval computation for depth 12, residue 2696. -/ +theorem bounds_12_2696 : exactInterval 12 2696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2696 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2696) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2696 : oddCount 2696 12 = 6 ∧ acceleratedOrbit 12 2696 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2696 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2696) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2696.1, data_12_2696.2] + +/-- Complete interval computation for depth 12, residue 2697. -/ +theorem bounds_12_2697 : exactInterval 12 2697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2697 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2697) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2697 : oddCount 2697 12 = 7 ∧ acceleratedOrbit 12 2697 = 1441 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2697 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2697) = 3 ^ 7 * m + 1441 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2697.1, data_12_2697.2] + +/-- Complete interval computation for depth 12, residue 2698. -/ +theorem bounds_12_2698 : exactInterval 12 2698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2698 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2698) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2698 : oddCount 2698 12 = 6 ∧ acceleratedOrbit 12 2698 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2698 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2698) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2698.1, data_12_2698.2] + +/-- Complete interval computation for depth 12, residue 2699. -/ +theorem bounds_12_2699 : exactInterval 12 2699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2699 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2699) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2699 : oddCount 2699 12 = 6 ∧ acceleratedOrbit 12 2699 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2699 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2699) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2699.1, data_12_2699.2] + +/-- Complete interval computation for depth 12, residue 2700. -/ +theorem bounds_12_2700 : exactInterval 12 2700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2700 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2700) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2700 : oddCount 2700 12 = 6 ∧ acceleratedOrbit 12 2700 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2700 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2700) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2700.1, data_12_2700.2] + +/-- Complete interval computation for depth 12, residue 2701. -/ +theorem bounds_12_2701 : exactInterval 12 2701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2701 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2701) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2701 : oddCount 2701 12 = 6 ∧ acceleratedOrbit 12 2701 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2701 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2701) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2701.1, data_12_2701.2] + +/-- Complete interval computation for depth 12, residue 2702. -/ +theorem bounds_12_2702 : exactInterval 12 2702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2702 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2702) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2702 : oddCount 2702 12 = 8 ∧ acceleratedOrbit 12 2702 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2702 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2702) = 3 ^ 8 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2702.1, data_12_2702.2] + +end Collatz.Research.StoppingAtlas.Batch0376 From de443653d59558411a2e8c945c036abbc3e1a0ee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:00 +0530 Subject: [PATCH 0377/1001] proof: certify atlas Batch0377 (12:2703 to 12:2717) --- Collatz/Research/StoppingAtlas/Batch0377.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0377.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0377.lean b/Collatz/Research/StoppingAtlas/Batch0377.lean new file mode 100644 index 00000000..c199b64d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0377.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0377 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2703. -/ +theorem bounds_12_2703 : exactInterval 12 2703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2703 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2703) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2703 : oddCount 2703 12 = 8 ∧ acceleratedOrbit 12 2703 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2703 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2703) = 3 ^ 8 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2703.1, data_12_2703.2] + +/-- Complete interval computation for depth 12, residue 2704. -/ +theorem bounds_12_2704 : exactInterval 12 2704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2704 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2704) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2704 : oddCount 2704 12 = 7 ∧ acceleratedOrbit 12 2704 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2704 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2704) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2704.1, data_12_2704.2] + +/-- Complete interval computation for depth 12, residue 2705. -/ +theorem bounds_12_2705 : exactInterval 12 2705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2705 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2705) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2705 : oddCount 2705 12 = 7 ∧ acceleratedOrbit 12 2705 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2705 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2705) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2705.1, data_12_2705.2] + +/-- Complete interval computation for depth 12, residue 2706. -/ +theorem bounds_12_2706 : exactInterval 12 2706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2706 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2706) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2706 : oddCount 2706 12 = 7 ∧ acceleratedOrbit 12 2706 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2706 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2706) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2706.1, data_12_2706.2] + +/-- Complete interval computation for depth 12, residue 2707. -/ +theorem bounds_12_2707 : exactInterval 12 2707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2707 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2707) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2707 : oddCount 2707 12 = 7 ∧ acceleratedOrbit 12 2707 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2707 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2707) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2707.1, data_12_2707.2] + +/-- Complete interval computation for depth 12, residue 2708. -/ +theorem bounds_12_2708 : exactInterval 12 2708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2708 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2708) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2708 : oddCount 2708 12 = 7 ∧ acceleratedOrbit 12 2708 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2708 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2708) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2708.1, data_12_2708.2] + +/-- Complete interval computation for depth 12, residue 2709. -/ +theorem bounds_12_2709 : exactInterval 12 2709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2709 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2709) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2709 : oddCount 2709 12 = 7 ∧ acceleratedOrbit 12 2709 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2709 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2709) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2709.1, data_12_2709.2] + +/-- Complete interval computation for depth 12, residue 2710. -/ +theorem bounds_12_2710 : exactInterval 12 2710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2710 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2710) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2710 : oddCount 2710 12 = 6 ∧ acceleratedOrbit 12 2710 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2710 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2710) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2710.1, data_12_2710.2] + +/-- Complete interval computation for depth 12, residue 2711. -/ +theorem bounds_12_2711 : exactInterval 12 2711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2711 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2711) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2711 : oddCount 2711 12 = 6 ∧ acceleratedOrbit 12 2711 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2711 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2711) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2711.1, data_12_2711.2] + +/-- Complete interval computation for depth 12, residue 2712. -/ +theorem bounds_12_2712 : exactInterval 12 2712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2712 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2712) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2712 : oddCount 2712 12 = 7 ∧ acceleratedOrbit 12 2712 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2712 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2712) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2712.1, data_12_2712.2] + +/-- Complete interval computation for depth 12, residue 2713. -/ +theorem bounds_12_2713 : exactInterval 12 2713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2713 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2713) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2713 : oddCount 2713 12 = 7 ∧ acceleratedOrbit 12 2713 = 1451 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2713 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2713) = 3 ^ 7 * m + 1451 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2713.1, data_12_2713.2] + +/-- Complete interval computation for depth 12, residue 2714. -/ +theorem bounds_12_2714 : exactInterval 12 2714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2714 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2714) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2714 : oddCount 2714 12 = 7 ∧ acceleratedOrbit 12 2714 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2714 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2714) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2714.1, data_12_2714.2] + +/-- Complete interval computation for depth 12, residue 2715. -/ +theorem bounds_12_2715 : exactInterval 12 2715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2715 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2715) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2715 : oddCount 2715 12 = 9 ∧ acceleratedOrbit 12 2715 = 13054 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2715 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2715) = 3 ^ 9 * m + 13054 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2715.1, data_12_2715.2] + +/-- Complete interval computation for depth 12, residue 2716. -/ +theorem bounds_12_2716 : exactInterval 12 2716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2716 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2716) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2716 : oddCount 2716 12 = 7 ∧ acceleratedOrbit 12 2716 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2716 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2716) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2716.1, data_12_2716.2] + +/-- Complete interval computation for depth 12, residue 2717. -/ +theorem bounds_12_2717 : exactInterval 12 2717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2717 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2717) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2717 : oddCount 2717 12 = 7 ∧ acceleratedOrbit 12 2717 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2717 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2717) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2717.1, data_12_2717.2] + +end Collatz.Research.StoppingAtlas.Batch0377 From 06197a7ad1b7c870ea4fa41412eff74028d2f377 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:00 +0530 Subject: [PATCH 0378/1001] proof: certify atlas Batch0378 (12:2718 to 12:2733) --- Collatz/Research/StoppingAtlas/Batch0378.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0378.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0378.lean b/Collatz/Research/StoppingAtlas/Batch0378.lean new file mode 100644 index 00000000..25632ccd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0378.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0378 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2718. -/ +theorem bounds_12_2718 : exactInterval 12 2718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2718 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2718) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2718 : oddCount 2718 12 = 7 ∧ acceleratedOrbit 12 2718 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2718 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2718) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2718.1, data_12_2718.2] + +/-- Complete interval computation for depth 12, residue 2719. -/ +theorem bounds_12_2719 : exactInterval 12 2719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2719 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2719) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2719 : oddCount 2719 12 = 8 ∧ acceleratedOrbit 12 2719 = 4357 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2719 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2719) = 3 ^ 8 * m + 4357 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2719.1, data_12_2719.2] + +/-- Complete interval computation for depth 12, residue 2720. -/ +theorem bounds_12_2720 : exactInterval 12 2720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2720 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2720) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2720 : oddCount 2720 12 = 1 ∧ acceleratedOrbit 12 2720 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2720 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2720) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2720.1, data_12_2720.2] + +/-- Complete interval computation for depth 12, residue 2721. -/ +theorem bounds_12_2721 : exactInterval 12 2721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2721 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2721) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2721 : oddCount 2721 12 = 8 ∧ acceleratedOrbit 12 2721 = 4364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2721 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2721) = 3 ^ 8 * m + 4364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2721.1, data_12_2721.2] + +/-- Complete interval computation for depth 12, residue 2722. -/ +theorem bounds_12_2722 : exactInterval 12 2722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2722 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2722) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2722 : oddCount 2722 12 = 8 ∧ acceleratedOrbit 12 2722 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2722 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2722) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2722.1, data_12_2722.2] + +/-- Complete interval computation for depth 12, residue 2723. -/ +theorem bounds_12_2723 : exactInterval 12 2723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2723 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2723) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2723 : oddCount 2723 12 = 8 ∧ acceleratedOrbit 12 2723 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2723 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2723) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2723.1, data_12_2723.2] + +/-- Complete interval computation for depth 12, residue 2724. -/ +theorem bounds_12_2724 : exactInterval 12 2724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2724 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2724) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2724 : oddCount 2724 12 = 9 ∧ acceleratedOrbit 12 2724 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2724 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2724) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2724.1, data_12_2724.2] + +/-- Complete interval computation for depth 12, residue 2725. -/ +theorem bounds_12_2725 : exactInterval 12 2725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2725 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2725) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2725 : oddCount 2725 12 = 9 ∧ acceleratedOrbit 12 2725 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2725 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2725) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2725.1, data_12_2725.2] + +/-- Complete interval computation for depth 12, residue 2726. -/ +theorem bounds_12_2726 : exactInterval 12 2726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2726 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2726) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2726 : oddCount 2726 12 = 9 ∧ acceleratedOrbit 12 2726 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2726 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2726) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2726.1, data_12_2726.2] + +/-- Complete interval computation for depth 12, residue 2727. -/ +theorem bounds_12_2727 : exactInterval 12 2727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2727 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2727) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2727 : oddCount 2727 12 = 9 ∧ acceleratedOrbit 12 2727 = 13112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2727 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2727) = 3 ^ 9 * m + 13112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2727.1, data_12_2727.2] + +/-- Complete interval computation for depth 12, residue 2728. -/ +theorem bounds_12_2728 : exactInterval 12 2728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2728 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2728) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2728 : oddCount 2728 12 = 1 ∧ acceleratedOrbit 12 2728 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2728 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2728) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2728.1, data_12_2728.2] + +/-- Complete interval computation for depth 12, residue 2729. -/ +theorem bounds_12_2729 : exactInterval 12 2729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2729 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2729) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2729 : oddCount 2729 12 = 11 ∧ acceleratedOrbit 12 2729 = 118097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2729 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2729) = 3 ^ 11 * m + 118097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2729.1, data_12_2729.2] + +/-- Complete interval computation for depth 12, residue 2730. -/ +theorem bounds_12_2730 : exactInterval 12 2730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2730 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2730) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2730 : oddCount 2730 12 = 1 ∧ acceleratedOrbit 12 2730 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2730 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2730) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2730.1, data_12_2730.2] + +/-- Complete interval computation for depth 12, residue 2731. -/ +theorem bounds_12_2731 : exactInterval 12 2731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2731 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2731) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2731 : oddCount 2731 12 = 7 ∧ acceleratedOrbit 12 2731 = 1460 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2731 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2731) = 3 ^ 7 * m + 1460 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2731.1, data_12_2731.2] + +/-- Complete interval computation for depth 12, residue 2732. -/ +theorem bounds_12_2732 : exactInterval 12 2732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2732 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2732) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2732 : oddCount 2732 12 = 6 ∧ acceleratedOrbit 12 2732 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2732 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2732) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2732.1, data_12_2732.2] + +/-- Complete interval computation for depth 12, residue 2733. -/ +theorem bounds_12_2733 : exactInterval 12 2733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2733 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2733) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2733 : oddCount 2733 12 = 6 ∧ acceleratedOrbit 12 2733 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2733 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2733) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2733.1, data_12_2733.2] + +end Collatz.Research.StoppingAtlas.Batch0378 From 315aaaf1aaafc54b92363c7c5835c9a62aee1271 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:00 +0530 Subject: [PATCH 0379/1001] proof: certify atlas Batch0379 (12:2734 to 12:2748) --- Collatz/Research/StoppingAtlas/Batch0379.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0379.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0379.lean b/Collatz/Research/StoppingAtlas/Batch0379.lean new file mode 100644 index 00000000..011f231c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0379.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0379 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2734. -/ +theorem bounds_12_2734 : exactInterval 12 2734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2734 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2734) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2734 : oddCount 2734 12 = 6 ∧ acceleratedOrbit 12 2734 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2734 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2734) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2734.1, data_12_2734.2] + +/-- Complete interval computation for depth 12, residue 2735. -/ +theorem bounds_12_2735 : exactInterval 12 2735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2735 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2735) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2735 : oddCount 2735 12 = 6 ∧ acceleratedOrbit 12 2735 = 487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2735 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2735) = 3 ^ 6 * m + 487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2735.1, data_12_2735.2] + +/-- Complete interval computation for depth 12, residue 2736. -/ +theorem bounds_12_2736 : exactInterval 12 2736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2736 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2736) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2736 : oddCount 2736 12 = 5 ∧ acceleratedOrbit 12 2736 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2736 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2736) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2736.1, data_12_2736.2] + +/-- Complete interval computation for depth 12, residue 2737. -/ +theorem bounds_12_2737 : exactInterval 12 2737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2737 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2737) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2737 : oddCount 2737 12 = 5 ∧ acceleratedOrbit 12 2737 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2737 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2737) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2737.1, data_12_2737.2] + +/-- Complete interval computation for depth 12, residue 2738. -/ +theorem bounds_12_2738 : exactInterval 12 2738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2738 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2738) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2738 : oddCount 2738 12 = 5 ∧ acceleratedOrbit 12 2738 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2738 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2738) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2738.1, data_12_2738.2] + +/-- Complete interval computation for depth 12, residue 2739. -/ +theorem bounds_12_2739 : exactInterval 12 2739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2739 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2739) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2739 : oddCount 2739 12 = 5 ∧ acceleratedOrbit 12 2739 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2739 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2739) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2739.1, data_12_2739.2] + +/-- Complete interval computation for depth 12, residue 2740. -/ +theorem bounds_12_2740 : exactInterval 12 2740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2740 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2740) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2740 : oddCount 2740 12 = 5 ∧ acceleratedOrbit 12 2740 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2740 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2740) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2740.1, data_12_2740.2] + +/-- Complete interval computation for depth 12, residue 2741. -/ +theorem bounds_12_2741 : exactInterval 12 2741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2741 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2741) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2741 : oddCount 2741 12 = 5 ∧ acceleratedOrbit 12 2741 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2741 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2741) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2741.1, data_12_2741.2] + +/-- Complete interval computation for depth 12, residue 2742. -/ +theorem bounds_12_2742 : exactInterval 12 2742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2742 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2742) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2742 : oddCount 2742 12 = 7 ∧ acceleratedOrbit 12 2742 = 1466 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2742 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2742) = 3 ^ 7 * m + 1466 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2742.1, data_12_2742.2] + +/-- Complete interval computation for depth 12, residue 2743. -/ +theorem bounds_12_2743 : exactInterval 12 2743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2743 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2743) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2743 : oddCount 2743 12 = 7 ∧ acceleratedOrbit 12 2743 = 1466 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2743 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2743) = 3 ^ 7 * m + 1466 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2743.1, data_12_2743.2] + +/-- Complete interval computation for depth 12, residue 2744. -/ +theorem bounds_12_2744 : exactInterval 12 2744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2744 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2744) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2744 : oddCount 2744 12 = 5 ∧ acceleratedOrbit 12 2744 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2744 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2744) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2744.1, data_12_2744.2] + +/-- Complete interval computation for depth 12, residue 2745. -/ +theorem bounds_12_2745 : exactInterval 12 2745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2745 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2745) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2745 : oddCount 2745 12 = 5 ∧ acceleratedOrbit 12 2745 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2745 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2745) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2745.1, data_12_2745.2] + +/-- Complete interval computation for depth 12, residue 2746. -/ +theorem bounds_12_2746 : exactInterval 12 2746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2746 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2746) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2746 : oddCount 2746 12 = 5 ∧ acceleratedOrbit 12 2746 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2746 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2746) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2746.1, data_12_2746.2] + +/-- Complete interval computation for depth 12, residue 2747. -/ +theorem bounds_12_2747 : exactInterval 12 2747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2747 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2747) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2747 : oddCount 2747 12 = 7 ∧ acceleratedOrbit 12 2747 = 1468 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2747 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2747) = 3 ^ 7 * m + 1468 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2747.1, data_12_2747.2] + +/-- Complete interval computation for depth 12, residue 2748. -/ +theorem bounds_12_2748 : exactInterval 12 2748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2748 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2748) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2748 : oddCount 2748 12 = 6 ∧ acceleratedOrbit 12 2748 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2748 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2748) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2748.1, data_12_2748.2] + +end Collatz.Research.StoppingAtlas.Batch0379 From e95d1a31c4cfe8c9d53979a2e0e291f06a99ec42 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:01 +0530 Subject: [PATCH 0380/1001] proof: certify atlas Batch0380 (12:2749 to 12:2763) --- Collatz/Research/StoppingAtlas/Batch0380.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0380.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0380.lean b/Collatz/Research/StoppingAtlas/Batch0380.lean new file mode 100644 index 00000000..f10361f3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0380.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0380 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2749. -/ +theorem bounds_12_2749 : exactInterval 12 2749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2749 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2749) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2749 : oddCount 2749 12 = 6 ∧ acceleratedOrbit 12 2749 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2749 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2749) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2749.1, data_12_2749.2] + +/-- Complete interval computation for depth 12, residue 2750. -/ +theorem bounds_12_2750 : exactInterval 12 2750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2750 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2750) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2750 : oddCount 2750 12 = 6 ∧ acceleratedOrbit 12 2750 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2750 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2750) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2750.1, data_12_2750.2] + +/-- Complete interval computation for depth 12, residue 2751. -/ +theorem bounds_12_2751 : exactInterval 12 2751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2751 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2751) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2751 : oddCount 2751 12 = 9 ∧ acceleratedOrbit 12 2751 = 13225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2751 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2751) = 3 ^ 9 * m + 13225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2751.1, data_12_2751.2] + +/-- Complete interval computation for depth 12, residue 2752. -/ +theorem bounds_12_2752 : exactInterval 12 2752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2752 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2752) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2752 : oddCount 2752 12 = 4 ∧ acceleratedOrbit 12 2752 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2752 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2752) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2752.1, data_12_2752.2] + +/-- Complete interval computation for depth 12, residue 2753. -/ +theorem bounds_12_2753 : exactInterval 12 2753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2753 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2753) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2753 : oddCount 2753 12 = 5 ∧ acceleratedOrbit 12 2753 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2753 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2753) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2753.1, data_12_2753.2] + +/-- Complete interval computation for depth 12, residue 2754. -/ +theorem bounds_12_2754 : exactInterval 12 2754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2754 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2754) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2754 : oddCount 2754 12 = 6 ∧ acceleratedOrbit 12 2754 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2754 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2754) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2754.1, data_12_2754.2] + +/-- Complete interval computation for depth 12, residue 2755. -/ +theorem bounds_12_2755 : exactInterval 12 2755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2755 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2755) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2755 : oddCount 2755 12 = 6 ∧ acceleratedOrbit 12 2755 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2755 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2755) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2755.1, data_12_2755.2] + +/-- Complete interval computation for depth 12, residue 2756. -/ +theorem bounds_12_2756 : exactInterval 12 2756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2756 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2756) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2756 : oddCount 2756 12 = 4 ∧ acceleratedOrbit 12 2756 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2756 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2756) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2756.1, data_12_2756.2] + +/-- Complete interval computation for depth 12, residue 2757. -/ +theorem bounds_12_2757 : exactInterval 12 2757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2757 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2757) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2757 : oddCount 2757 12 = 4 ∧ acceleratedOrbit 12 2757 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2757 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2757) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2757.1, data_12_2757.2] + +/-- Complete interval computation for depth 12, residue 2758. -/ +theorem bounds_12_2758 : exactInterval 12 2758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2758 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2758) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2758 : oddCount 2758 12 = 4 ∧ acceleratedOrbit 12 2758 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2758 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2758) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2758.1, data_12_2758.2] + +/-- Complete interval computation for depth 12, residue 2759. -/ +theorem bounds_12_2759 : exactInterval 12 2759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2759 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2759) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2759 : oddCount 2759 12 = 7 ∧ acceleratedOrbit 12 2759 = 1475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2759 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2759) = 3 ^ 7 * m + 1475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2759.1, data_12_2759.2] + +/-- Complete interval computation for depth 12, residue 2760. -/ +theorem bounds_12_2760 : exactInterval 12 2760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2760 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2760) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2760 : oddCount 2760 12 = 4 ∧ acceleratedOrbit 12 2760 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2760 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2760) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2760.1, data_12_2760.2] + +/-- Complete interval computation for depth 12, residue 2761. -/ +theorem bounds_12_2761 : exactInterval 12 2761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2761 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2761) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2761 : oddCount 2761 12 = 5 ∧ acceleratedOrbit 12 2761 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2761 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2761) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2761.1, data_12_2761.2] + +/-- Complete interval computation for depth 12, residue 2762. -/ +theorem bounds_12_2762 : exactInterval 12 2762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2762 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2762) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2762 : oddCount 2762 12 = 4 ∧ acceleratedOrbit 12 2762 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2762 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2762) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2762.1, data_12_2762.2] + +/-- Complete interval computation for depth 12, residue 2763. -/ +theorem bounds_12_2763 : exactInterval 12 2763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2763 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2763) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2763 : oddCount 2763 12 = 7 ∧ acceleratedOrbit 12 2763 = 1478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2763 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2763) = 3 ^ 7 * m + 1478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2763.1, data_12_2763.2] + +end Collatz.Research.StoppingAtlas.Batch0380 From 6f976da66fe5e984e15131180f141f15ba43af69 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:01 +0530 Subject: [PATCH 0381/1001] proof: certify atlas Batch0381 (12:2764 to 12:2779) --- Collatz/Research/StoppingAtlas/Batch0381.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0381.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0381.lean b/Collatz/Research/StoppingAtlas/Batch0381.lean new file mode 100644 index 00000000..7201da3d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0381.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0381 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2764. -/ +theorem bounds_12_2764 : exactInterval 12 2764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2764 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2764) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2764 : oddCount 2764 12 = 4 ∧ acceleratedOrbit 12 2764 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2764 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2764) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2764.1, data_12_2764.2] + +/-- Complete interval computation for depth 12, residue 2765. -/ +theorem bounds_12_2765 : exactInterval 12 2765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2765 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2765) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2765 : oddCount 2765 12 = 4 ∧ acceleratedOrbit 12 2765 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2765 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2765) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2765.1, data_12_2765.2] + +/-- Complete interval computation for depth 12, residue 2766. -/ +theorem bounds_12_2766 : exactInterval 12 2766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2766 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2766) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2766 : oddCount 2766 12 = 9 ∧ acceleratedOrbit 12 2766 = 13304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2766 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2766) = 3 ^ 9 * m + 13304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2766.1, data_12_2766.2] + +/-- Complete interval computation for depth 12, residue 2767. -/ +theorem bounds_12_2767 : exactInterval 12 2767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2767 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2767) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2767 : oddCount 2767 12 = 9 ∧ acceleratedOrbit 12 2767 = 13304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2767 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2767) = 3 ^ 9 * m + 13304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2767.1, data_12_2767.2] + +/-- Complete interval computation for depth 12, residue 2768. -/ +theorem bounds_12_2768 : exactInterval 12 2768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2768 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2768) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2768 : oddCount 2768 12 = 4 ∧ acceleratedOrbit 12 2768 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2768 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2768) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2768.1, data_12_2768.2] + +/-- Complete interval computation for depth 12, residue 2769. -/ +theorem bounds_12_2769 : exactInterval 12 2769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2769 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2769) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2769 : oddCount 2769 12 = 6 ∧ acceleratedOrbit 12 2769 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2769 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2769) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2769.1, data_12_2769.2] + +/-- Complete interval computation for depth 12, residue 2770. -/ +theorem bounds_12_2770 : exactInterval 12 2770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2770 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2770) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2770 : oddCount 2770 12 = 6 ∧ acceleratedOrbit 12 2770 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2770 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2770) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2770.1, data_12_2770.2] + +/-- Complete interval computation for depth 12, residue 2771. -/ +theorem bounds_12_2771 : exactInterval 12 2771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2771 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2771) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2771 : oddCount 2771 12 = 6 ∧ acceleratedOrbit 12 2771 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2771 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2771) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2771.1, data_12_2771.2] + +/-- Complete interval computation for depth 12, residue 2772. -/ +theorem bounds_12_2772 : exactInterval 12 2772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2772 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2772) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2772 : oddCount 2772 12 = 4 ∧ acceleratedOrbit 12 2772 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2772 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2772) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2772.1, data_12_2772.2] + +/-- Complete interval computation for depth 12, residue 2773. -/ +theorem bounds_12_2773 : exactInterval 12 2773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2773 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2773) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2773 : oddCount 2773 12 = 4 ∧ acceleratedOrbit 12 2773 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2773 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2773) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2773.1, data_12_2773.2] + +/-- Complete interval computation for depth 12, residue 2774. -/ +theorem bounds_12_2774 : exactInterval 12 2774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2774 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2774) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2774 : oddCount 2774 12 = 7 ∧ acceleratedOrbit 12 2774 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2774 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2774) = 3 ^ 7 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2774.1, data_12_2774.2] + +/-- Complete interval computation for depth 12, residue 2775. -/ +theorem bounds_12_2775 : exactInterval 12 2775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2775 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2775) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2775 : oddCount 2775 12 = 7 ∧ acceleratedOrbit 12 2775 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2775 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2775) = 3 ^ 7 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2775.1, data_12_2775.2] + +/-- Complete interval computation for depth 12, residue 2776. -/ +theorem bounds_12_2776 : exactInterval 12 2776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2776 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2776) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2776 : oddCount 2776 12 = 6 ∧ acceleratedOrbit 12 2776 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2776 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2776) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2776.1, data_12_2776.2] + +/-- Complete interval computation for depth 12, residue 2777. -/ +theorem bounds_12_2777 : exactInterval 12 2777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2777 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2777) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2777 : oddCount 2777 12 = 4 ∧ acceleratedOrbit 12 2777 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2777 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2777) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2777.1, data_12_2777.2] + +/-- Complete interval computation for depth 12, residue 2778. -/ +theorem bounds_12_2778 : exactInterval 12 2778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2778 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2778) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2778 : oddCount 2778 12 = 6 ∧ acceleratedOrbit 12 2778 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2778 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2778) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2778.1, data_12_2778.2] + +/-- Complete interval computation for depth 12, residue 2779. -/ +theorem bounds_12_2779 : exactInterval 12 2779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2779 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2779) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2779 : oddCount 2779 12 = 9 ∧ acceleratedOrbit 12 2779 = 13364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2779 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2779) = 3 ^ 9 * m + 13364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2779.1, data_12_2779.2] + +end Collatz.Research.StoppingAtlas.Batch0381 From 05c462c3d91ef4d24ea21ab939c22015ce8af4b8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:01 +0530 Subject: [PATCH 0382/1001] proof: certify atlas Batch0382 (12:2780 to 12:2794) --- Collatz/Research/StoppingAtlas/Batch0382.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0382.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0382.lean b/Collatz/Research/StoppingAtlas/Batch0382.lean new file mode 100644 index 00000000..c8c61a19 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0382.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0382 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2780. -/ +theorem bounds_12_2780 : exactInterval 12 2780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2780 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2780) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2780 : oddCount 2780 12 = 6 ∧ acceleratedOrbit 12 2780 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2780 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2780) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2780.1, data_12_2780.2] + +/-- Complete interval computation for depth 12, residue 2781. -/ +theorem bounds_12_2781 : exactInterval 12 2781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2781 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2781) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2781 : oddCount 2781 12 = 6 ∧ acceleratedOrbit 12 2781 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2781 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2781) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2781.1, data_12_2781.2] + +/-- Complete interval computation for depth 12, residue 2782. -/ +theorem bounds_12_2782 : exactInterval 12 2782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2782 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2782) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2782 : oddCount 2782 12 = 7 ∧ acceleratedOrbit 12 2782 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2782 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2782) = 3 ^ 7 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2782.1, data_12_2782.2] + +/-- Complete interval computation for depth 12, residue 2783. -/ +theorem bounds_12_2783 : exactInterval 12 2783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2783 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2783) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2783 : oddCount 2783 12 = 7 ∧ acceleratedOrbit 12 2783 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2783 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2783) = 3 ^ 7 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2783.1, data_12_2783.2] + +/-- Complete interval computation for depth 12, residue 2784. -/ +theorem bounds_12_2784 : exactInterval 12 2784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2784 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2784) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2784 : oddCount 2784 12 = 4 ∧ acceleratedOrbit 12 2784 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2784 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2784) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2784.1, data_12_2784.2] + +/-- Complete interval computation for depth 12, residue 2785. -/ +theorem bounds_12_2785 : exactInterval 12 2785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2785 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2785) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2785 : oddCount 2785 12 = 8 ∧ acceleratedOrbit 12 2785 = 4465 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2785 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2785) = 3 ^ 8 * m + 4465 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2785.1, data_12_2785.2] + +/-- Complete interval computation for depth 12, residue 2786. -/ +theorem bounds_12_2786 : exactInterval 12 2786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2786 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2786) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2786 : oddCount 2786 12 = 4 ∧ acceleratedOrbit 12 2786 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2786 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2786) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2786.1, data_12_2786.2] + +/-- Complete interval computation for depth 12, residue 2787. -/ +theorem bounds_12_2787 : exactInterval 12 2787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2787 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2787) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2787 : oddCount 2787 12 = 4 ∧ acceleratedOrbit 12 2787 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2787 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2787) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2787.1, data_12_2787.2] + +/-- Complete interval computation for depth 12, residue 2788. -/ +theorem bounds_12_2788 : exactInterval 12 2788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2788 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2788) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2788 : oddCount 2788 12 = 5 ∧ acceleratedOrbit 12 2788 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2788 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2788) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2788.1, data_12_2788.2] + +/-- Complete interval computation for depth 12, residue 2789. -/ +theorem bounds_12_2789 : exactInterval 12 2789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2789 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2789) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2789 : oddCount 2789 12 = 5 ∧ acceleratedOrbit 12 2789 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2789 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2789) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2789.1, data_12_2789.2] + +/-- Complete interval computation for depth 12, residue 2790. -/ +theorem bounds_12_2790 : exactInterval 12 2790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2790 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2790) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2790 : oddCount 2790 12 = 5 ∧ acceleratedOrbit 12 2790 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2790 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2790) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2790.1, data_12_2790.2] + +/-- Complete interval computation for depth 12, residue 2791. -/ +theorem bounds_12_2791 : exactInterval 12 2791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2791 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2791) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2791 : oddCount 2791 12 = 10 ∧ acceleratedOrbit 12 2791 = 40256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2791 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2791) = 3 ^ 10 * m + 40256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2791.1, data_12_2791.2] + +/-- Complete interval computation for depth 12, residue 2792. -/ +theorem bounds_12_2792 : exactInterval 12 2792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2792 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2792) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2792 : oddCount 2792 12 = 4 ∧ acceleratedOrbit 12 2792 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2792 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2792) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2792.1, data_12_2792.2] + +/-- Complete interval computation for depth 12, residue 2793. -/ +theorem bounds_12_2793 : exactInterval 12 2793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2793 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2793) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2793 : oddCount 2793 12 = 8 ∧ acceleratedOrbit 12 2793 = 4477 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2793 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2793) = 3 ^ 8 * m + 4477 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2793.1, data_12_2793.2] + +/-- Complete interval computation for depth 12, residue 2794. -/ +theorem bounds_12_2794 : exactInterval 12 2794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2794 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2794) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2794 : oddCount 2794 12 = 4 ∧ acceleratedOrbit 12 2794 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2794 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2794) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2794.1, data_12_2794.2] + +end Collatz.Research.StoppingAtlas.Batch0382 From 64713e9657c0623297791d1297dafbca909f2683 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:02 +0530 Subject: [PATCH 0383/1001] proof: certify atlas Batch0383 (12:2795 to 12:2809) --- Collatz/Research/StoppingAtlas/Batch0383.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0383.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0383.lean b/Collatz/Research/StoppingAtlas/Batch0383.lean new file mode 100644 index 00000000..8cc04631 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0383.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0383 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2795. -/ +theorem bounds_12_2795 : exactInterval 12 2795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2795 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2795) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2795 : oddCount 2795 12 = 8 ∧ acceleratedOrbit 12 2795 = 4481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2795 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2795) = 3 ^ 8 * m + 4481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2795.1, data_12_2795.2] + +/-- Complete interval computation for depth 12, residue 2796. -/ +theorem bounds_12_2796 : exactInterval 12 2796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2796 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2796) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2796 : oddCount 2796 12 = 6 ∧ acceleratedOrbit 12 2796 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2796 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2796) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2796.1, data_12_2796.2] + +/-- Complete interval computation for depth 12, residue 2797. -/ +theorem bounds_12_2797 : exactInterval 12 2797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2797 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2797) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2797 : oddCount 2797 12 = 6 ∧ acceleratedOrbit 12 2797 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2797 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2797) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2797.1, data_12_2797.2] + +/-- Complete interval computation for depth 12, residue 2798. -/ +theorem bounds_12_2798 : exactInterval 12 2798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2798 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2798) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2798 : oddCount 2798 12 = 6 ∧ acceleratedOrbit 12 2798 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2798 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2798) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2798.1, data_12_2798.2] + +/-- Complete interval computation for depth 12, residue 2799. -/ +theorem bounds_12_2799 : exactInterval 12 2799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2799 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2799) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2799 : oddCount 2799 12 = 9 ∧ acceleratedOrbit 12 2799 = 13456 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2799 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2799) = 3 ^ 9 * m + 13456 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2799.1, data_12_2799.2] + +/-- Complete interval computation for depth 12, residue 2800. -/ +theorem bounds_12_2800 : exactInterval 12 2800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2800 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2800) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2800 : oddCount 2800 12 = 5 ∧ acceleratedOrbit 12 2800 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2800 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2800) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2800.1, data_12_2800.2] + +/-- Complete interval computation for depth 12, residue 2801. -/ +theorem bounds_12_2801 : exactInterval 12 2801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2801 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2801) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2801 : oddCount 2801 12 = 4 ∧ acceleratedOrbit 12 2801 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2801 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2801) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2801.1, data_12_2801.2] + +/-- Complete interval computation for depth 12, residue 2802. -/ +theorem bounds_12_2802 : exactInterval 12 2802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2802 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2802) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2802 : oddCount 2802 12 = 8 ∧ acceleratedOrbit 12 2802 = 4495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2802 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2802) = 3 ^ 8 * m + 4495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2802.1, data_12_2802.2] + +/-- Complete interval computation for depth 12, residue 2803. -/ +theorem bounds_12_2803 : exactInterval 12 2803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2803 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2803) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2803 : oddCount 2803 12 = 8 ∧ acceleratedOrbit 12 2803 = 4495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2803 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2803) = 3 ^ 8 * m + 4495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2803.1, data_12_2803.2] + +/-- Complete interval computation for depth 12, residue 2804. -/ +theorem bounds_12_2804 : exactInterval 12 2804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2804 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2804) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2804 : oddCount 2804 12 = 5 ∧ acceleratedOrbit 12 2804 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2804 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2804) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2804.1, data_12_2804.2] + +/-- Complete interval computation for depth 12, residue 2805. -/ +theorem bounds_12_2805 : exactInterval 12 2805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2805 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2805) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2805 : oddCount 2805 12 = 5 ∧ acceleratedOrbit 12 2805 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2805 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2805) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2805.1, data_12_2805.2] + +/-- Complete interval computation for depth 12, residue 2806. -/ +theorem bounds_12_2806 : exactInterval 12 2806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2806 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2806) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2806 : oddCount 2806 12 = 6 ∧ acceleratedOrbit 12 2806 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2806 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2806) = 3 ^ 6 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2806.1, data_12_2806.2] + +/-- Complete interval computation for depth 12, residue 2807. -/ +theorem bounds_12_2807 : exactInterval 12 2807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2807 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2807) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2807 : oddCount 2807 12 = 6 ∧ acceleratedOrbit 12 2807 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2807 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2807) = 3 ^ 6 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2807.1, data_12_2807.2] + +/-- Complete interval computation for depth 12, residue 2808. -/ +theorem bounds_12_2808 : exactInterval 12 2808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2808 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2808) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2808 : oddCount 2808 12 = 5 ∧ acceleratedOrbit 12 2808 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2808 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2808) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2808.1, data_12_2808.2] + +/-- Complete interval computation for depth 12, residue 2809. -/ +theorem bounds_12_2809 : exactInterval 12 2809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2809 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2809) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2809 : oddCount 2809 12 = 7 ∧ acceleratedOrbit 12 2809 = 1502 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2809 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2809) = 3 ^ 7 * m + 1502 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2809.1, data_12_2809.2] + +end Collatz.Research.StoppingAtlas.Batch0383 From acff24dfa391f0e6218811130badf9f8cf6c6cb6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:02 +0530 Subject: [PATCH 0384/1001] proof: certify atlas Batch0384 (12:2810 to 12:2825) --- Collatz/Research/StoppingAtlas/Batch0384.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0384.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0384.lean b/Collatz/Research/StoppingAtlas/Batch0384.lean new file mode 100644 index 00000000..ab3b69c7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0384.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0384 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2810. -/ +theorem bounds_12_2810 : exactInterval 12 2810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2810 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2810) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2810 : oddCount 2810 12 = 5 ∧ acceleratedOrbit 12 2810 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2810 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2810) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2810.1, data_12_2810.2] + +/-- Complete interval computation for depth 12, residue 2811. -/ +theorem bounds_12_2811 : exactInterval 12 2811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2811 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2811) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2811 : oddCount 2811 12 = 9 ∧ acceleratedOrbit 12 2811 = 13517 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2811 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2811) = 3 ^ 9 * m + 13517 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2811.1, data_12_2811.2] + +/-- Complete interval computation for depth 12, residue 2812. -/ +theorem bounds_12_2812 : exactInterval 12 2812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2812 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2812) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2812 : oddCount 2812 12 = 8 ∧ acceleratedOrbit 12 2812 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2812 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2812) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2812.1, data_12_2812.2] + +/-- Complete interval computation for depth 12, residue 2813. -/ +theorem bounds_12_2813 : exactInterval 12 2813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2813 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2813) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2813 : oddCount 2813 12 = 8 ∧ acceleratedOrbit 12 2813 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2813 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2813) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2813.1, data_12_2813.2] + +/-- Complete interval computation for depth 12, residue 2814. -/ +theorem bounds_12_2814 : exactInterval 12 2814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2814 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2814) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2814 : oddCount 2814 12 = 8 ∧ acceleratedOrbit 12 2814 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2814 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2814) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2814.1, data_12_2814.2] + +/-- Complete interval computation for depth 12, residue 2815. -/ +theorem bounds_12_2815 : exactInterval 12 2815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2815 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2815) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2815 : oddCount 2815 12 = 9 ∧ acceleratedOrbit 12 2815 = 13532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2815 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2815) = 3 ^ 9 * m + 13532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2815.1, data_12_2815.2] + +/-- Complete interval computation for depth 12, residue 2816. -/ +theorem bounds_12_2816 : exactInterval 12 2816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2816 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2816) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2816 : oddCount 2816 12 = 3 ∧ acceleratedOrbit 12 2816 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2816 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2816) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2816.1, data_12_2816.2] + +/-- Complete interval computation for depth 12, residue 2817. -/ +theorem bounds_12_2817 : exactInterval 12 2817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2817 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2817) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2817 : oddCount 2817 12 = 6 ∧ acceleratedOrbit 12 2817 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2817 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2817) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2817.1, data_12_2817.2] + +/-- Complete interval computation for depth 12, residue 2818. -/ +theorem bounds_12_2818 : exactInterval 12 2818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2818 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2818) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2818 : oddCount 2818 12 = 6 ∧ acceleratedOrbit 12 2818 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2818 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2818) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2818.1, data_12_2818.2] + +/-- Complete interval computation for depth 12, residue 2819. -/ +theorem bounds_12_2819 : exactInterval 12 2819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2819 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2819) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2819 : oddCount 2819 12 = 6 ∧ acceleratedOrbit 12 2819 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2819 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2819) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2819.1, data_12_2819.2] + +/-- Complete interval computation for depth 12, residue 2820. -/ +theorem bounds_12_2820 : exactInterval 12 2820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2820 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2820) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2820 : oddCount 2820 12 = 4 ∧ acceleratedOrbit 12 2820 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2820 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2820) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2820.1, data_12_2820.2] + +/-- Complete interval computation for depth 12, residue 2821. -/ +theorem bounds_12_2821 : exactInterval 12 2821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2821 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2821) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2821 : oddCount 2821 12 = 4 ∧ acceleratedOrbit 12 2821 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2821 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2821) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2821.1, data_12_2821.2] + +/-- Complete interval computation for depth 12, residue 2822. -/ +theorem bounds_12_2822 : exactInterval 12 2822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2822 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2822) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2822 : oddCount 2822 12 = 4 ∧ acceleratedOrbit 12 2822 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2822 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2822) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2822.1, data_12_2822.2] + +/-- Complete interval computation for depth 12, residue 2823. -/ +theorem bounds_12_2823 : exactInterval 12 2823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2823 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2823) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2823 : oddCount 2823 12 = 8 ∧ acceleratedOrbit 12 2823 = 4526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2823 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2823) = 3 ^ 8 * m + 4526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2823.1, data_12_2823.2] + +/-- Complete interval computation for depth 12, residue 2824. -/ +theorem bounds_12_2824 : exactInterval 12 2824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2824 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2824) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2824 : oddCount 2824 12 = 6 ∧ acceleratedOrbit 12 2824 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2824 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2824) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2824.1, data_12_2824.2] + +/-- Complete interval computation for depth 12, residue 2825. -/ +theorem bounds_12_2825 : exactInterval 12 2825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2825 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2825) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2825 : oddCount 2825 12 = 8 ∧ acceleratedOrbit 12 2825 = 4529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2825 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2825) = 3 ^ 8 * m + 4529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2825.1, data_12_2825.2] + +end Collatz.Research.StoppingAtlas.Batch0384 From 73b9f1266869e063aff6f154dc89528c9b9c89fd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:02 +0530 Subject: [PATCH 0385/1001] proof: certify atlas Batch0385 (12:2826 to 12:2840) --- Collatz/Research/StoppingAtlas/Batch0385.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0385.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0385.lean b/Collatz/Research/StoppingAtlas/Batch0385.lean new file mode 100644 index 00000000..3e58b431 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0385.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0385 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2826. -/ +theorem bounds_12_2826 : exactInterval 12 2826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2826 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2826) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2826 : oddCount 2826 12 = 6 ∧ acceleratedOrbit 12 2826 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2826 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2826) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2826.1, data_12_2826.2] + +/-- Complete interval computation for depth 12, residue 2827. -/ +theorem bounds_12_2827 : exactInterval 12 2827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2827 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2827) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2827 : oddCount 2827 12 = 8 ∧ acceleratedOrbit 12 2827 = 4535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2827 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2827) = 3 ^ 8 * m + 4535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2827.1, data_12_2827.2] + +/-- Complete interval computation for depth 12, residue 2828. -/ +theorem bounds_12_2828 : exactInterval 12 2828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2828 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2828) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2828 : oddCount 2828 12 = 6 ∧ acceleratedOrbit 12 2828 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2828 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2828) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2828.1, data_12_2828.2] + +/-- Complete interval computation for depth 12, residue 2829. -/ +theorem bounds_12_2829 : exactInterval 12 2829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2829 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2829) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2829 : oddCount 2829 12 = 6 ∧ acceleratedOrbit 12 2829 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2829 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2829) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2829.1, data_12_2829.2] + +/-- Complete interval computation for depth 12, residue 2830. -/ +theorem bounds_12_2830 : exactInterval 12 2830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2830 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2830) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2830 : oddCount 2830 12 = 4 ∧ acceleratedOrbit 12 2830 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2830 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2830) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2830.1, data_12_2830.2] + +/-- Complete interval computation for depth 12, residue 2831. -/ +theorem bounds_12_2831 : exactInterval 12 2831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2831 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2831) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2831 : oddCount 2831 12 = 4 ∧ acceleratedOrbit 12 2831 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2831 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2831) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2831.1, data_12_2831.2] + +/-- Complete interval computation for depth 12, residue 2832. -/ +theorem bounds_12_2832 : exactInterval 12 2832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2832 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2832) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2832 : oddCount 2832 12 = 3 ∧ acceleratedOrbit 12 2832 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2832 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2832) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2832.1, data_12_2832.2] + +/-- Complete interval computation for depth 12, residue 2833. -/ +theorem bounds_12_2833 : exactInterval 12 2833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2833 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2833) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2833 : oddCount 2833 12 = 6 ∧ acceleratedOrbit 12 2833 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2833 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2833) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2833.1, data_12_2833.2] + +/-- Complete interval computation for depth 12, residue 2834. -/ +theorem bounds_12_2834 : exactInterval 12 2834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2834 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2834) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2834 : oddCount 2834 12 = 6 ∧ acceleratedOrbit 12 2834 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2834 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2834) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2834.1, data_12_2834.2] + +/-- Complete interval computation for depth 12, residue 2835. -/ +theorem bounds_12_2835 : exactInterval 12 2835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2835 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2835) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2835 : oddCount 2835 12 = 6 ∧ acceleratedOrbit 12 2835 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2835 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2835) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2835.1, data_12_2835.2] + +/-- Complete interval computation for depth 12, residue 2836. -/ +theorem bounds_12_2836 : exactInterval 12 2836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2836 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2836) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2836 : oddCount 2836 12 = 3 ∧ acceleratedOrbit 12 2836 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2836 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2836) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2836.1, data_12_2836.2] + +/-- Complete interval computation for depth 12, residue 2837. -/ +theorem bounds_12_2837 : exactInterval 12 2837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2837 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2837) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2837 : oddCount 2837 12 = 3 ∧ acceleratedOrbit 12 2837 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2837 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2837) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2837.1, data_12_2837.2] + +/-- Complete interval computation for depth 12, residue 2838. -/ +theorem bounds_12_2838 : exactInterval 12 2838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2838 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2838) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2838 : oddCount 2838 12 = 6 ∧ acceleratedOrbit 12 2838 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2838 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2838) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2838.1, data_12_2838.2] + +/-- Complete interval computation for depth 12, residue 2839. -/ +theorem bounds_12_2839 : exactInterval 12 2839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2839 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2839) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2839 : oddCount 2839 12 = 6 ∧ acceleratedOrbit 12 2839 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2839 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2839) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2839.1, data_12_2839.2] + +/-- Complete interval computation for depth 12, residue 2840. -/ +theorem bounds_12_2840 : exactInterval 12 2840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2840 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2840) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2840 : oddCount 2840 12 = 3 ∧ acceleratedOrbit 12 2840 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2840 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2840) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2840.1, data_12_2840.2] + +end Collatz.Research.StoppingAtlas.Batch0385 From 33386012843bc88385c3f3ffd3054142e1766995 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:03 +0530 Subject: [PATCH 0386/1001] proof: certify atlas Batch0386 (12:2841 to 12:2855) --- Collatz/Research/StoppingAtlas/Batch0386.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0386.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0386.lean b/Collatz/Research/StoppingAtlas/Batch0386.lean new file mode 100644 index 00000000..4a7e6af0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0386.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0386 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2841. -/ +theorem bounds_12_2841 : exactInterval 12 2841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2841 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2841) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2841 : oddCount 2841 12 = 8 ∧ acceleratedOrbit 12 2841 = 4556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2841 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2841) = 3 ^ 8 * m + 4556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2841.1, data_12_2841.2] + +/-- Complete interval computation for depth 12, residue 2842. -/ +theorem bounds_12_2842 : exactInterval 12 2842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2842 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2842) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2842 : oddCount 2842 12 = 3 ∧ acceleratedOrbit 12 2842 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2842 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2842) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2842.1, data_12_2842.2] + +/-- Complete interval computation for depth 12, residue 2843. -/ +theorem bounds_12_2843 : exactInterval 12 2843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2843 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2843) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2843 : oddCount 2843 12 = 10 ∧ acceleratedOrbit 12 2843 = 41006 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2843 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2843) = 3 ^ 10 * m + 41006 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2843.1, data_12_2843.2] + +/-- Complete interval computation for depth 12, residue 2844. -/ +theorem bounds_12_2844 : exactInterval 12 2844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2844 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2844) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2844 : oddCount 2844 12 = 5 ∧ acceleratedOrbit 12 2844 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2844 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2844) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2844.1, data_12_2844.2] + +/-- Complete interval computation for depth 12, residue 2845. -/ +theorem bounds_12_2845 : exactInterval 12 2845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2845 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2845) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2845 : oddCount 2845 12 = 5 ∧ acceleratedOrbit 12 2845 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2845 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2845) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2845.1, data_12_2845.2] + +/-- Complete interval computation for depth 12, residue 2846. -/ +theorem bounds_12_2846 : exactInterval 12 2846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2846 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2846) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2846 : oddCount 2846 12 = 5 ∧ acceleratedOrbit 12 2846 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2846 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2846) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2846.1, data_12_2846.2] + +/-- Complete interval computation for depth 12, residue 2847. -/ +theorem bounds_12_2847 : exactInterval 12 2847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2847 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2847) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2847 : oddCount 2847 12 = 9 ∧ acceleratedOrbit 12 2847 = 13688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2847 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2847) = 3 ^ 9 * m + 13688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2847.1, data_12_2847.2] + +/-- Complete interval computation for depth 12, residue 2848. -/ +theorem bounds_12_2848 : exactInterval 12 2848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2848 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2848) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2848 : oddCount 2848 12 = 3 ∧ acceleratedOrbit 12 2848 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2848 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2848) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2848.1, data_12_2848.2] + +/-- Complete interval computation for depth 12, residue 2849. -/ +theorem bounds_12_2849 : exactInterval 12 2849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2849 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2849) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2849 : oddCount 2849 12 = 6 ∧ acceleratedOrbit 12 2849 = 508 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2849 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2849) = 3 ^ 6 * m + 508 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2849.1, data_12_2849.2] + +/-- Complete interval computation for depth 12, residue 2850. -/ +theorem bounds_12_2850 : exactInterval 12 2850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2850 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2850) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2850 : oddCount 2850 12 = 5 ∧ acceleratedOrbit 12 2850 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2850 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2850) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2850.1, data_12_2850.2] + +/-- Complete interval computation for depth 12, residue 2851. -/ +theorem bounds_12_2851 : exactInterval 12 2851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2851 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2851) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2851 : oddCount 2851 12 = 5 ∧ acceleratedOrbit 12 2851 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2851 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2851) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2851.1, data_12_2851.2] + +/-- Complete interval computation for depth 12, residue 2852. -/ +theorem bounds_12_2852 : exactInterval 12 2852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2852 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2852) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2852 : oddCount 2852 12 = 5 ∧ acceleratedOrbit 12 2852 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2852 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2852) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2852.1, data_12_2852.2] + +/-- Complete interval computation for depth 12, residue 2853. -/ +theorem bounds_12_2853 : exactInterval 12 2853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2853 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2853) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2853 : oddCount 2853 12 = 5 ∧ acceleratedOrbit 12 2853 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2853 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2853) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2853.1, data_12_2853.2] + +/-- Complete interval computation for depth 12, residue 2854. -/ +theorem bounds_12_2854 : exactInterval 12 2854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2854 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2854) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2854 : oddCount 2854 12 = 5 ∧ acceleratedOrbit 12 2854 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2854 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2854) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2854.1, data_12_2854.2] + +/-- Complete interval computation for depth 12, residue 2855. -/ +theorem bounds_12_2855 : exactInterval 12 2855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2855 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2855) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2855 : oddCount 2855 12 = 8 ∧ acceleratedOrbit 12 2855 = 4576 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2855 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2855) = 3 ^ 8 * m + 4576 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2855.1, data_12_2855.2] + +end Collatz.Research.StoppingAtlas.Batch0386 From 4088ebc66e0b606a32ee8c3af4ea4b8194b8e443 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:03 +0530 Subject: [PATCH 0387/1001] proof: certify atlas Batch0387 (12:2856 to 12:2871) --- Collatz/Research/StoppingAtlas/Batch0387.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0387.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0387.lean b/Collatz/Research/StoppingAtlas/Batch0387.lean new file mode 100644 index 00000000..1f07452c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0387.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0387 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2856. -/ +theorem bounds_12_2856 : exactInterval 12 2856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2856 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2856) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2856 : oddCount 2856 12 = 3 ∧ acceleratedOrbit 12 2856 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2856 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2856) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2856.1, data_12_2856.2] + +/-- Complete interval computation for depth 12, residue 2857. -/ +theorem bounds_12_2857 : exactInterval 12 2857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2857 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2857) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2857 : oddCount 2857 12 = 8 ∧ acceleratedOrbit 12 2857 = 4580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2857 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2857) = 3 ^ 8 * m + 4580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2857.1, data_12_2857.2] + +/-- Complete interval computation for depth 12, residue 2858. -/ +theorem bounds_12_2858 : exactInterval 12 2858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2858 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2858) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2858 : oddCount 2858 12 = 3 ∧ acceleratedOrbit 12 2858 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2858 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2858) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2858.1, data_12_2858.2] + +/-- Complete interval computation for depth 12, residue 2859. -/ +theorem bounds_12_2859 : exactInterval 12 2859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2859 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2859) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2859 : oddCount 2859 12 = 7 ∧ acceleratedOrbit 12 2859 = 1529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2859 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2859) = 3 ^ 7 * m + 1529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2859.1, data_12_2859.2] + +/-- Complete interval computation for depth 12, residue 2860. -/ +theorem bounds_12_2860 : exactInterval 12 2860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2860 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2860) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2860 : oddCount 2860 12 = 6 ∧ acceleratedOrbit 12 2860 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2860 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2860) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2860.1, data_12_2860.2] + +/-- Complete interval computation for depth 12, residue 2861. -/ +theorem bounds_12_2861 : exactInterval 12 2861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2861 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2861) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2861 : oddCount 2861 12 = 6 ∧ acceleratedOrbit 12 2861 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2861 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2861) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2861.1, data_12_2861.2] + +/-- Complete interval computation for depth 12, residue 2862. -/ +theorem bounds_12_2862 : exactInterval 12 2862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2862 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2862) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2862 : oddCount 2862 12 = 6 ∧ acceleratedOrbit 12 2862 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2862 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2862) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2862.1, data_12_2862.2] + +/-- Complete interval computation for depth 12, residue 2863. -/ +theorem bounds_12_2863 : exactInterval 12 2863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2863 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2863) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2863 : oddCount 2863 12 = 8 ∧ acceleratedOrbit 12 2863 = 4589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2863 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2863) = 3 ^ 8 * m + 4589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2863.1, data_12_2863.2] + +/-- Complete interval computation for depth 12, residue 2864. -/ +theorem bounds_12_2864 : exactInterval 12 2864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2864 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2864) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2864 : oddCount 2864 12 = 3 ∧ acceleratedOrbit 12 2864 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2864 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2864) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2864.1, data_12_2864.2] + +/-- Complete interval computation for depth 12, residue 2865. -/ +theorem bounds_12_2865 : exactInterval 12 2865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2865 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2865) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2865 : oddCount 2865 12 = 6 ∧ acceleratedOrbit 12 2865 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2865 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2865) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2865.1, data_12_2865.2] + +/-- Complete interval computation for depth 12, residue 2866. -/ +theorem bounds_12_2866 : exactInterval 12 2866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2866 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2866) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2866 : oddCount 2866 12 = 6 ∧ acceleratedOrbit 12 2866 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2866 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2866) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2866.1, data_12_2866.2] + +/-- Complete interval computation for depth 12, residue 2867. -/ +theorem bounds_12_2867 : exactInterval 12 2867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2867 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2867) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2867 : oddCount 2867 12 = 6 ∧ acceleratedOrbit 12 2867 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2867 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2867) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2867.1, data_12_2867.2] + +/-- Complete interval computation for depth 12, residue 2868. -/ +theorem bounds_12_2868 : exactInterval 12 2868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2868 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2868) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2868 : oddCount 2868 12 = 3 ∧ acceleratedOrbit 12 2868 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2868 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2868) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2868.1, data_12_2868.2] + +/-- Complete interval computation for depth 12, residue 2869. -/ +theorem bounds_12_2869 : exactInterval 12 2869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2869 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2869) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2869 : oddCount 2869 12 = 3 ∧ acceleratedOrbit 12 2869 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2869 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2869) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2869.1, data_12_2869.2] + +/-- Complete interval computation for depth 12, residue 2870. -/ +theorem bounds_12_2870 : exactInterval 12 2870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2870 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2870) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2870 : oddCount 2870 12 = 7 ∧ acceleratedOrbit 12 2870 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2870 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2870) = 3 ^ 7 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2870.1, data_12_2870.2] + +/-- Complete interval computation for depth 12, residue 2871. -/ +theorem bounds_12_2871 : exactInterval 12 2871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2871 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2871) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2871 : oddCount 2871 12 = 7 ∧ acceleratedOrbit 12 2871 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2871 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2871) = 3 ^ 7 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2871.1, data_12_2871.2] + +end Collatz.Research.StoppingAtlas.Batch0387 From c2dffc08430dc7f253cc4b178b66336f10d38a44 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:03 +0530 Subject: [PATCH 0388/1001] proof: certify atlas Batch0388 (12:2872 to 12:2886) --- Collatz/Research/StoppingAtlas/Batch0388.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0388.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0388.lean b/Collatz/Research/StoppingAtlas/Batch0388.lean new file mode 100644 index 00000000..642685b8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0388.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0388 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2872. -/ +theorem bounds_12_2872 : exactInterval 12 2872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2872 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2872) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2872 : oddCount 2872 12 = 8 ∧ acceleratedOrbit 12 2872 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2872 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2872) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2872.1, data_12_2872.2] + +/-- Complete interval computation for depth 12, residue 2873. -/ +theorem bounds_12_2873 : exactInterval 12 2873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2873 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2873) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2873 : oddCount 2873 12 = 8 ∧ acceleratedOrbit 12 2873 = 4607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2873 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2873) = 3 ^ 8 * m + 4607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2873.1, data_12_2873.2] + +/-- Complete interval computation for depth 12, residue 2874. -/ +theorem bounds_12_2874 : exactInterval 12 2874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2874 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2874) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2874 : oddCount 2874 12 = 8 ∧ acceleratedOrbit 12 2874 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2874 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2874) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2874.1, data_12_2874.2] + +/-- Complete interval computation for depth 12, residue 2875. -/ +theorem bounds_12_2875 : exactInterval 12 2875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2875 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2875) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2875 : oddCount 2875 12 = 7 ∧ acceleratedOrbit 12 2875 = 1538 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2875 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2875) = 3 ^ 7 * m + 1538 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2875.1, data_12_2875.2] + +/-- Complete interval computation for depth 12, residue 2876. -/ +theorem bounds_12_2876 : exactInterval 12 2876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2876 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2876) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2876 : oddCount 2876 12 = 8 ∧ acceleratedOrbit 12 2876 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2876 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2876) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2876.1, data_12_2876.2] + +/-- Complete interval computation for depth 12, residue 2877. -/ +theorem bounds_12_2877 : exactInterval 12 2877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2877 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2877) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2877 : oddCount 2877 12 = 8 ∧ acceleratedOrbit 12 2877 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2877 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2877) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2877.1, data_12_2877.2] + +/-- Complete interval computation for depth 12, residue 2878. -/ +theorem bounds_12_2878 : exactInterval 12 2878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2878 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2878) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2878 : oddCount 2878 12 = 9 ∧ acceleratedOrbit 12 2878 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2878 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2878) = 3 ^ 9 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2878.1, data_12_2878.2] + +/-- Complete interval computation for depth 12, residue 2879. -/ +theorem bounds_12_2879 : exactInterval 12 2879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2879 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2879) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2879 : oddCount 2879 12 = 9 ∧ acceleratedOrbit 12 2879 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2879 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2879) = 3 ^ 9 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2879.1, data_12_2879.2] + +/-- Complete interval computation for depth 12, residue 2880. -/ +theorem bounds_12_2880 : exactInterval 12 2880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2880 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2880) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2880 : oddCount 2880 12 = 3 ∧ acceleratedOrbit 12 2880 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2880 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2880) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2880.1, data_12_2880.2] + +/-- Complete interval computation for depth 12, residue 2881. -/ +theorem bounds_12_2881 : exactInterval 12 2881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2881 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2881) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2881 : oddCount 2881 12 = 3 ∧ acceleratedOrbit 12 2881 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2881 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2881) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2881.1, data_12_2881.2] + +/-- Complete interval computation for depth 12, residue 2882. -/ +theorem bounds_12_2882 : exactInterval 12 2882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2882 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2882) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2882 : oddCount 2882 12 = 6 ∧ acceleratedOrbit 12 2882 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2882 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2882) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2882.1, data_12_2882.2] + +/-- Complete interval computation for depth 12, residue 2883. -/ +theorem bounds_12_2883 : exactInterval 12 2883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2883 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2883) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2883 : oddCount 2883 12 = 6 ∧ acceleratedOrbit 12 2883 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2883 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2883) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2883.1, data_12_2883.2] + +/-- Complete interval computation for depth 12, residue 2884. -/ +theorem bounds_12_2884 : exactInterval 12 2884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2884 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2884) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2884 : oddCount 2884 12 = 5 ∧ acceleratedOrbit 12 2884 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2884 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2884) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2884.1, data_12_2884.2] + +/-- Complete interval computation for depth 12, residue 2885. -/ +theorem bounds_12_2885 : exactInterval 12 2885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2885 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2885) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2885 : oddCount 2885 12 = 5 ∧ acceleratedOrbit 12 2885 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2885 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2885) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2885.1, data_12_2885.2] + +/-- Complete interval computation for depth 12, residue 2886. -/ +theorem bounds_12_2886 : exactInterval 12 2886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2886 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2886) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2886 : oddCount 2886 12 = 5 ∧ acceleratedOrbit 12 2886 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2886 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2886) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2886.1, data_12_2886.2] + +end Collatz.Research.StoppingAtlas.Batch0388 From 4514f0ed9ade9a3615661e62a49c13fbfcc7951a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:04 +0530 Subject: [PATCH 0389/1001] proof: certify atlas Batch0389 (12:2887 to 12:2902) --- Collatz/Research/StoppingAtlas/Batch0389.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0389.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0389.lean b/Collatz/Research/StoppingAtlas/Batch0389.lean new file mode 100644 index 00000000..184eb778 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0389.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0389 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2887. -/ +theorem bounds_12_2887 : exactInterval 12 2887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2887 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2887) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2887 : oddCount 2887 12 = 8 ∧ acceleratedOrbit 12 2887 = 4627 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2887 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2887) = 3 ^ 8 * m + 4627 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2887.1, data_12_2887.2] + +/-- Complete interval computation for depth 12, residue 2888. -/ +theorem bounds_12_2888 : exactInterval 12 2888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2888 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2888) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2888 : oddCount 2888 12 = 5 ∧ acceleratedOrbit 12 2888 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2888 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2888) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2888.1, data_12_2888.2] + +/-- Complete interval computation for depth 12, residue 2889. -/ +theorem bounds_12_2889 : exactInterval 12 2889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2889 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2889) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2889 : oddCount 2889 12 = 6 ∧ acceleratedOrbit 12 2889 = 515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2889 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2889) = 3 ^ 6 * m + 515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2889.1, data_12_2889.2] + +/-- Complete interval computation for depth 12, residue 2890. -/ +theorem bounds_12_2890 : exactInterval 12 2890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2890 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2890) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2890 : oddCount 2890 12 = 5 ∧ acceleratedOrbit 12 2890 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2890 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2890) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2890.1, data_12_2890.2] + +/-- Complete interval computation for depth 12, residue 2891. -/ +theorem bounds_12_2891 : exactInterval 12 2891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2891 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2891) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2891 : oddCount 2891 12 = 5 ∧ acceleratedOrbit 12 2891 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2891 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2891) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2891.1, data_12_2891.2] + +/-- Complete interval computation for depth 12, residue 2892. -/ +theorem bounds_12_2892 : exactInterval 12 2892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2892 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2892) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2892 : oddCount 2892 12 = 5 ∧ acceleratedOrbit 12 2892 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2892 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2892) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2892.1, data_12_2892.2] + +/-- Complete interval computation for depth 12, residue 2893. -/ +theorem bounds_12_2893 : exactInterval 12 2893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2893 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2893) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2893 : oddCount 2893 12 = 5 ∧ acceleratedOrbit 12 2893 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2893 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2893) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2893.1, data_12_2893.2] + +/-- Complete interval computation for depth 12, residue 2894. -/ +theorem bounds_12_2894 : exactInterval 12 2894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2894 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2894) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2894 : oddCount 2894 12 = 7 ∧ acceleratedOrbit 12 2894 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2894 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2894) = 3 ^ 7 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2894.1, data_12_2894.2] + +/-- Complete interval computation for depth 12, residue 2895. -/ +theorem bounds_12_2895 : exactInterval 12 2895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2895 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2895) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2895 : oddCount 2895 12 = 7 ∧ acceleratedOrbit 12 2895 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2895 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2895) = 3 ^ 7 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2895.1, data_12_2895.2] + +/-- Complete interval computation for depth 12, residue 2896. -/ +theorem bounds_12_2896 : exactInterval 12 2896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2896 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2896) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2896 : oddCount 2896 12 = 3 ∧ acceleratedOrbit 12 2896 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2896 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2896) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2896.1, data_12_2896.2] + +/-- Complete interval computation for depth 12, residue 2897. -/ +theorem bounds_12_2897 : exactInterval 12 2897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2897 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2897) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2897 : oddCount 2897 12 = 7 ∧ acceleratedOrbit 12 2897 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2897 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2897) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2897.1, data_12_2897.2] + +/-- Complete interval computation for depth 12, residue 2898. -/ +theorem bounds_12_2898 : exactInterval 12 2898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2898 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2898) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2898 : oddCount 2898 12 = 7 ∧ acceleratedOrbit 12 2898 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2898 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2898) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2898.1, data_12_2898.2] + +/-- Complete interval computation for depth 12, residue 2899. -/ +theorem bounds_12_2899 : exactInterval 12 2899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2899 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2899) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2899 : oddCount 2899 12 = 7 ∧ acceleratedOrbit 12 2899 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2899 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2899) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2899.1, data_12_2899.2] + +/-- Complete interval computation for depth 12, residue 2900. -/ +theorem bounds_12_2900 : exactInterval 12 2900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2900 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2900) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2900 : oddCount 2900 12 = 3 ∧ acceleratedOrbit 12 2900 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2900 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2900) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2900.1, data_12_2900.2] + +/-- Complete interval computation for depth 12, residue 2901. -/ +theorem bounds_12_2901 : exactInterval 12 2901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2901 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2901) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2901 : oddCount 2901 12 = 3 ∧ acceleratedOrbit 12 2901 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2901 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2901) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2901.1, data_12_2901.2] + +/-- Complete interval computation for depth 12, residue 2902. -/ +theorem bounds_12_2902 : exactInterval 12 2902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2902 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2902) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2902 : oddCount 2902 12 = 7 ∧ acceleratedOrbit 12 2902 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2902 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2902) = 3 ^ 7 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2902.1, data_12_2902.2] + +end Collatz.Research.StoppingAtlas.Batch0389 From 0f1ce7c05f989d03713487c998b8608ca63e338e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:04 +0530 Subject: [PATCH 0390/1001] proof: certify atlas Batch0390 (12:2903 to 12:2917) --- Collatz/Research/StoppingAtlas/Batch0390.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0390.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0390.lean b/Collatz/Research/StoppingAtlas/Batch0390.lean new file mode 100644 index 00000000..c4c0b4e8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0390.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0390 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2903. -/ +theorem bounds_12_2903 : exactInterval 12 2903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2903 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2903) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2903 : oddCount 2903 12 = 7 ∧ acceleratedOrbit 12 2903 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2903 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2903) = 3 ^ 7 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2903.1, data_12_2903.2] + +/-- Complete interval computation for depth 12, residue 2904. -/ +theorem bounds_12_2904 : exactInterval 12 2904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2904 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2904) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2904 : oddCount 2904 12 = 5 ∧ acceleratedOrbit 12 2904 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2904 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2904) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2904.1, data_12_2904.2] + +/-- Complete interval computation for depth 12, residue 2905. -/ +theorem bounds_12_2905 : exactInterval 12 2905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2905 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2905) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2905 : oddCount 2905 12 = 5 ∧ acceleratedOrbit 12 2905 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2905 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2905) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2905.1, data_12_2905.2] + +/-- Complete interval computation for depth 12, residue 2906. -/ +theorem bounds_12_2906 : exactInterval 12 2906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2906 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2906) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2906 : oddCount 2906 12 = 5 ∧ acceleratedOrbit 12 2906 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2906 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2906) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2906.1, data_12_2906.2] + +/-- Complete interval computation for depth 12, residue 2907. -/ +theorem bounds_12_2907 : exactInterval 12 2907 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2907 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2907) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2907 : oddCount 2907 12 = 7 ∧ acceleratedOrbit 12 2907 = 1553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2907 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2907) = 3 ^ 7 * m + 1553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2907.1, data_12_2907.2] + +/-- Complete interval computation for depth 12, residue 2908. -/ +theorem bounds_12_2908 : exactInterval 12 2908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2908 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2908) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2908 : oddCount 2908 12 = 5 ∧ acceleratedOrbit 12 2908 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2908 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2908) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2908.1, data_12_2908.2] + +/-- Complete interval computation for depth 12, residue 2909. -/ +theorem bounds_12_2909 : exactInterval 12 2909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2909 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2909) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2909 : oddCount 2909 12 = 5 ∧ acceleratedOrbit 12 2909 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2909 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2909) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2909.1, data_12_2909.2] + +/-- Complete interval computation for depth 12, residue 2910. -/ +theorem bounds_12_2910 : exactInterval 12 2910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2910 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2910) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2910 : oddCount 2910 12 = 7 ∧ acceleratedOrbit 12 2910 = 1556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2910 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2910) = 3 ^ 7 * m + 1556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2910.1, data_12_2910.2] + +/-- Complete interval computation for depth 12, residue 2911. -/ +theorem bounds_12_2911 : exactInterval 12 2911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2911 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2911) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2911 : oddCount 2911 12 = 7 ∧ acceleratedOrbit 12 2911 = 1556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2911 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2911) = 3 ^ 7 * m + 1556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2911.1, data_12_2911.2] + +/-- Complete interval computation for depth 12, residue 2912. -/ +theorem bounds_12_2912 : exactInterval 12 2912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2912 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2912) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2912 : oddCount 2912 12 = 5 ∧ acceleratedOrbit 12 2912 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2912 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2912) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2912.1, data_12_2912.2] + +/-- Complete interval computation for depth 12, residue 2913. -/ +theorem bounds_12_2913 : exactInterval 12 2913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2913 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2913) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2913 : oddCount 2913 12 = 9 ∧ acceleratedOrbit 12 2913 = 14012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2913 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2913) = 3 ^ 9 * m + 14012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2913.1, data_12_2913.2] + +/-- Complete interval computation for depth 12, residue 2914. -/ +theorem bounds_12_2914 : exactInterval 12 2914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2914 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2914) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2914 : oddCount 2914 12 = 4 ∧ acceleratedOrbit 12 2914 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2914 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2914) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2914.1, data_12_2914.2] + +/-- Complete interval computation for depth 12, residue 2915. -/ +theorem bounds_12_2915 : exactInterval 12 2915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2915 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2915) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2915 : oddCount 2915 12 = 4 ∧ acceleratedOrbit 12 2915 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2915 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2915) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2915.1, data_12_2915.2] + +/-- Complete interval computation for depth 12, residue 2916. -/ +theorem bounds_12_2916 : exactInterval 12 2916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2916 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2916) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2916 : oddCount 2916 12 = 4 ∧ acceleratedOrbit 12 2916 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2916 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2916) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2916.1, data_12_2916.2] + +/-- Complete interval computation for depth 12, residue 2917. -/ +theorem bounds_12_2917 : exactInterval 12 2917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2917 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2917) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2917 : oddCount 2917 12 = 4 ∧ acceleratedOrbit 12 2917 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2917 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2917) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2917.1, data_12_2917.2] + +end Collatz.Research.StoppingAtlas.Batch0390 From f1ed9bb4d9856e4ad8b06953876f1d3259bbaa21 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:04 +0530 Subject: [PATCH 0391/1001] proof: certify atlas Batch0391 (12:2918 to 12:2932) --- Collatz/Research/StoppingAtlas/Batch0391.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0391.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0391.lean b/Collatz/Research/StoppingAtlas/Batch0391.lean new file mode 100644 index 00000000..1644a55a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0391.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0391 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2918. -/ +theorem bounds_12_2918 : exactInterval 12 2918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2918 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2918) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2918 : oddCount 2918 12 = 4 ∧ acceleratedOrbit 12 2918 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2918 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2918) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2918.1, data_12_2918.2] + +/-- Complete interval computation for depth 12, residue 2919. -/ +theorem bounds_12_2919 : exactInterval 12 2919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2919 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2919) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2919 : oddCount 2919 12 = 9 ∧ acceleratedOrbit 12 2919 = 14033 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2919 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2919) = 3 ^ 9 * m + 14033 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2919.1, data_12_2919.2] + +/-- Complete interval computation for depth 12, residue 2920. -/ +theorem bounds_12_2920 : exactInterval 12 2920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2920 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2920) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2920 : oddCount 2920 12 = 5 ∧ acceleratedOrbit 12 2920 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2920 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2920) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2920.1, data_12_2920.2] + +/-- Complete interval computation for depth 12, residue 2921. -/ +theorem bounds_12_2921 : exactInterval 12 2921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2921 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2921) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2921 : oddCount 2921 12 = 7 ∧ acceleratedOrbit 12 2921 = 1561 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2921 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2921) = 3 ^ 7 * m + 1561 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2921.1, data_12_2921.2] + +/-- Complete interval computation for depth 12, residue 2922. -/ +theorem bounds_12_2922 : exactInterval 12 2922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2922 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2922) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2922 : oddCount 2922 12 = 5 ∧ acceleratedOrbit 12 2922 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2922 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2922) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2922.1, data_12_2922.2] + +/-- Complete interval computation for depth 12, residue 2923. -/ +theorem bounds_12_2923 : exactInterval 12 2923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2923 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2923) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2923 : oddCount 2923 12 = 6 ∧ acceleratedOrbit 12 2923 = 521 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2923 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2923) = 3 ^ 6 * m + 521 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2923.1, data_12_2923.2] + +/-- Complete interval computation for depth 12, residue 2924. -/ +theorem bounds_12_2924 : exactInterval 12 2924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2924 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2924) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2924 : oddCount 2924 12 = 7 ∧ acceleratedOrbit 12 2924 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2924 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2924) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2924.1, data_12_2924.2] + +/-- Complete interval computation for depth 12, residue 2925. -/ +theorem bounds_12_2925 : exactInterval 12 2925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2925 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2925) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2925 : oddCount 2925 12 = 7 ∧ acceleratedOrbit 12 2925 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2925 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2925) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2925.1, data_12_2925.2] + +/-- Complete interval computation for depth 12, residue 2926. -/ +theorem bounds_12_2926 : exactInterval 12 2926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2926 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2926) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2926 : oddCount 2926 12 = 7 ∧ acceleratedOrbit 12 2926 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2926 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2926) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2926.1, data_12_2926.2] + +/-- Complete interval computation for depth 12, residue 2927. -/ +theorem bounds_12_2927 : exactInterval 12 2927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2927 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2927) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2927 : oddCount 2927 12 = 8 ∧ acceleratedOrbit 12 2927 = 4691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2927 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2927) = 3 ^ 8 * m + 4691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2927.1, data_12_2927.2] + +/-- Complete interval computation for depth 12, residue 2928. -/ +theorem bounds_12_2928 : exactInterval 12 2928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2928 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2928) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2928 : oddCount 2928 12 = 5 ∧ acceleratedOrbit 12 2928 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2928 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2928) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2928.1, data_12_2928.2] + +/-- Complete interval computation for depth 12, residue 2929. -/ +theorem bounds_12_2929 : exactInterval 12 2929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2929 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2929) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2929 : oddCount 2929 12 = 5 ∧ acceleratedOrbit 12 2929 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2929 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2929) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2929.1, data_12_2929.2] + +/-- Complete interval computation for depth 12, residue 2930. -/ +theorem bounds_12_2930 : exactInterval 12 2930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2930 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2930) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2930 : oddCount 2930 12 = 4 ∧ acceleratedOrbit 12 2930 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2930 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2930) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2930.1, data_12_2930.2] + +/-- Complete interval computation for depth 12, residue 2931. -/ +theorem bounds_12_2931 : exactInterval 12 2931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2931 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2931) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2931 : oddCount 2931 12 = 4 ∧ acceleratedOrbit 12 2931 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2931 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2931) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2931.1, data_12_2931.2] + +/-- Complete interval computation for depth 12, residue 2932. -/ +theorem bounds_12_2932 : exactInterval 12 2932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2932 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2932) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2932 : oddCount 2932 12 = 5 ∧ acceleratedOrbit 12 2932 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2932 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2932) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2932.1, data_12_2932.2] + +end Collatz.Research.StoppingAtlas.Batch0391 From 9f678bed5a109944970eabd8e794f34fef452bfb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:05 +0530 Subject: [PATCH 0392/1001] proof: certify atlas Batch0392 (12:2933 to 12:2948) --- Collatz/Research/StoppingAtlas/Batch0392.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0392.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0392.lean b/Collatz/Research/StoppingAtlas/Batch0392.lean new file mode 100644 index 00000000..b4dcb77d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0392.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0392 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2933. -/ +theorem bounds_12_2933 : exactInterval 12 2933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2933 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2933) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2933 : oddCount 2933 12 = 5 ∧ acceleratedOrbit 12 2933 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2933 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2933) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2933.1, data_12_2933.2] + +/-- Complete interval computation for depth 12, residue 2934. -/ +theorem bounds_12_2934 : exactInterval 12 2934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2934 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2934) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2934 : oddCount 2934 12 = 6 ∧ acceleratedOrbit 12 2934 = 523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2934 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2934) = 3 ^ 6 * m + 523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2934.1, data_12_2934.2] + +/-- Complete interval computation for depth 12, residue 2935. -/ +theorem bounds_12_2935 : exactInterval 12 2935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2935 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2935) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2935 : oddCount 2935 12 = 6 ∧ acceleratedOrbit 12 2935 = 523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2935 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2935) = 3 ^ 6 * m + 523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2935.1, data_12_2935.2] + +/-- Complete interval computation for depth 12, residue 2936. -/ +theorem bounds_12_2936 : exactInterval 12 2936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2936 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2936) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2936 : oddCount 2936 12 = 6 ∧ acceleratedOrbit 12 2936 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2936 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2936) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2936.1, data_12_2936.2] + +/-- Complete interval computation for depth 12, residue 2937. -/ +theorem bounds_12_2937 : exactInterval 12 2937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2937 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2937) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2937 : oddCount 2937 12 = 8 ∧ acceleratedOrbit 12 2937 = 4708 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2937 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2937) = 3 ^ 8 * m + 4708 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2937.1, data_12_2937.2] + +/-- Complete interval computation for depth 12, residue 2938. -/ +theorem bounds_12_2938 : exactInterval 12 2938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2938 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2938) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2938 : oddCount 2938 12 = 6 ∧ acceleratedOrbit 12 2938 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2938 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2938) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2938.1, data_12_2938.2] + +/-- Complete interval computation for depth 12, residue 2939. -/ +theorem bounds_12_2939 : exactInterval 12 2939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2939 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2939) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2939 : oddCount 2939 12 = 8 ∧ acceleratedOrbit 12 2939 = 4711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2939 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2939) = 3 ^ 8 * m + 4711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2939.1, data_12_2939.2] + +/-- Complete interval computation for depth 12, residue 2940. -/ +theorem bounds_12_2940 : exactInterval 12 2940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2940 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2940) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2940 : oddCount 2940 12 = 6 ∧ acceleratedOrbit 12 2940 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2940 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2940) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2940.1, data_12_2940.2] + +/-- Complete interval computation for depth 12, residue 2941. -/ +theorem bounds_12_2941 : exactInterval 12 2941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2941 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2941) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2941 : oddCount 2941 12 = 6 ∧ acceleratedOrbit 12 2941 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2941 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2941) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2941.1, data_12_2941.2] + +/-- Complete interval computation for depth 12, residue 2942. -/ +theorem bounds_12_2942 : exactInterval 12 2942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2942 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2942) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2942 : oddCount 2942 12 = 10 ∧ acceleratedOrbit 12 2942 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2942 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2942) = 3 ^ 10 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2942.1, data_12_2942.2] + +/-- Complete interval computation for depth 12, residue 2943. -/ +theorem bounds_12_2943 : exactInterval 12 2943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2943 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2943) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2943 : oddCount 2943 12 = 10 ∧ acceleratedOrbit 12 2943 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2943 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2943) = 3 ^ 10 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2943.1, data_12_2943.2] + +/-- Complete interval computation for depth 12, residue 2944. -/ +theorem bounds_12_2944 : exactInterval 12 2944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2944 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2944) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2944 : oddCount 2944 12 = 3 ∧ acceleratedOrbit 12 2944 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2944 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2944) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2944.1, data_12_2944.2] + +/-- Complete interval computation for depth 12, residue 2945. -/ +theorem bounds_12_2945 : exactInterval 12 2945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2945 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2945) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2945 : oddCount 2945 12 = 8 ∧ acceleratedOrbit 12 2945 = 4724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2945 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2945) = 3 ^ 8 * m + 4724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2945.1, data_12_2945.2] + +/-- Complete interval computation for depth 12, residue 2946. -/ +theorem bounds_12_2946 : exactInterval 12 2946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2946 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2946) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2946 : oddCount 2946 12 = 6 ∧ acceleratedOrbit 12 2946 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2946 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2946) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2946.1, data_12_2946.2] + +/-- Complete interval computation for depth 12, residue 2947. -/ +theorem bounds_12_2947 : exactInterval 12 2947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2947 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2947) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2947 : oddCount 2947 12 = 6 ∧ acceleratedOrbit 12 2947 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2947 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2947) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2947.1, data_12_2947.2] + +/-- Complete interval computation for depth 12, residue 2948. -/ +theorem bounds_12_2948 : exactInterval 12 2948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2948 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2948) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2948 : oddCount 2948 12 = 7 ∧ acceleratedOrbit 12 2948 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2948 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2948) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2948.1, data_12_2948.2] + +end Collatz.Research.StoppingAtlas.Batch0392 From 4d1fd62d2406c19c993f3130a4d51b115023e076 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:05 +0530 Subject: [PATCH 0393/1001] proof: certify atlas Batch0393 (12:2949 to 12:2963) --- Collatz/Research/StoppingAtlas/Batch0393.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0393.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0393.lean b/Collatz/Research/StoppingAtlas/Batch0393.lean new file mode 100644 index 00000000..ccbdabbe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0393.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0393 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2949. -/ +theorem bounds_12_2949 : exactInterval 12 2949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2949 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2949) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2949 : oddCount 2949 12 = 7 ∧ acceleratedOrbit 12 2949 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2949 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2949) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2949.1, data_12_2949.2] + +/-- Complete interval computation for depth 12, residue 2950. -/ +theorem bounds_12_2950 : exactInterval 12 2950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2950 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2950) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2950 : oddCount 2950 12 = 7 ∧ acceleratedOrbit 12 2950 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2950 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2950) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2950.1, data_12_2950.2] + +/-- Complete interval computation for depth 12, residue 2951. -/ +theorem bounds_12_2951 : exactInterval 12 2951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2951 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2951) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2951 : oddCount 2951 12 = 6 ∧ acceleratedOrbit 12 2951 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2951 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2951) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2951.1, data_12_2951.2] + +/-- Complete interval computation for depth 12, residue 2952. -/ +theorem bounds_12_2952 : exactInterval 12 2952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2952 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2952) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2952 : oddCount 2952 12 = 3 ∧ acceleratedOrbit 12 2952 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2952 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2952) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2952.1, data_12_2952.2] + +/-- Complete interval computation for depth 12, residue 2953. -/ +theorem bounds_12_2953 : exactInterval 12 2953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2953 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2953) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2953 : oddCount 2953 12 = 9 ∧ acceleratedOrbit 12 2953 = 14201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2953 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2953) = 3 ^ 9 * m + 14201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2953.1, data_12_2953.2] + +/-- Complete interval computation for depth 12, residue 2954. -/ +theorem bounds_12_2954 : exactInterval 12 2954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2954 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2954) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2954 : oddCount 2954 12 = 3 ∧ acceleratedOrbit 12 2954 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2954 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2954) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2954.1, data_12_2954.2] + +/-- Complete interval computation for depth 12, residue 2955. -/ +theorem bounds_12_2955 : exactInterval 12 2955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2955 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2955) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2955 : oddCount 2955 12 = 8 ∧ acceleratedOrbit 12 2955 = 4738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2955 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2955) = 3 ^ 8 * m + 4738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2955.1, data_12_2955.2] + +/-- Complete interval computation for depth 12, residue 2956. -/ +theorem bounds_12_2956 : exactInterval 12 2956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2956 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2956) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2956 : oddCount 2956 12 = 3 ∧ acceleratedOrbit 12 2956 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2956 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2956) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2956.1, data_12_2956.2] + +/-- Complete interval computation for depth 12, residue 2957. -/ +theorem bounds_12_2957 : exactInterval 12 2957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2957 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2957) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2957 : oddCount 2957 12 = 3 ∧ acceleratedOrbit 12 2957 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2957 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2957) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2957.1, data_12_2957.2] + +/-- Complete interval computation for depth 12, residue 2958. -/ +theorem bounds_12_2958 : exactInterval 12 2958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2958 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2958) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2958 : oddCount 2958 12 = 6 ∧ acceleratedOrbit 12 2958 = 527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2958 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2958) = 3 ^ 6 * m + 527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2958.1, data_12_2958.2] + +/-- Complete interval computation for depth 12, residue 2959. -/ +theorem bounds_12_2959 : exactInterval 12 2959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2959 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2959) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2959 : oddCount 2959 12 = 6 ∧ acceleratedOrbit 12 2959 = 527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2959 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2959) = 3 ^ 6 * m + 527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2959.1, data_12_2959.2] + +/-- Complete interval computation for depth 12, residue 2960. -/ +theorem bounds_12_2960 : exactInterval 12 2960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2960 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2960) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2960 : oddCount 2960 12 = 4 ∧ acceleratedOrbit 12 2960 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2960 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2960) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2960.1, data_12_2960.2] + +/-- Complete interval computation for depth 12, residue 2961. -/ +theorem bounds_12_2961 : exactInterval 12 2961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2961 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2961) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2961 : oddCount 2961 12 = 5 ∧ acceleratedOrbit 12 2961 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2961 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2961) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2961.1, data_12_2961.2] + +/-- Complete interval computation for depth 12, residue 2962. -/ +theorem bounds_12_2962 : exactInterval 12 2962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2962 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2962) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2962 : oddCount 2962 12 = 5 ∧ acceleratedOrbit 12 2962 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2962 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2962) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2962.1, data_12_2962.2] + +/-- Complete interval computation for depth 12, residue 2963. -/ +theorem bounds_12_2963 : exactInterval 12 2963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2963 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2963) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2963 : oddCount 2963 12 = 5 ∧ acceleratedOrbit 12 2963 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2963 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2963) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2963.1, data_12_2963.2] + +end Collatz.Research.StoppingAtlas.Batch0393 From c04c81ad73f9240ec0552c210aaa9e51841eaad9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:05 +0530 Subject: [PATCH 0394/1001] proof: certify atlas Batch0394 (12:2964 to 12:2978) --- Collatz/Research/StoppingAtlas/Batch0394.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0394.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0394.lean b/Collatz/Research/StoppingAtlas/Batch0394.lean new file mode 100644 index 00000000..a86542d7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0394.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0394 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2964. -/ +theorem bounds_12_2964 : exactInterval 12 2964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2964 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2964) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2964 : oddCount 2964 12 = 4 ∧ acceleratedOrbit 12 2964 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2964 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2964) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2964.1, data_12_2964.2] + +/-- Complete interval computation for depth 12, residue 2965. -/ +theorem bounds_12_2965 : exactInterval 12 2965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2965 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2965) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2965 : oddCount 2965 12 = 4 ∧ acceleratedOrbit 12 2965 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2965 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2965) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2965.1, data_12_2965.2] + +/-- Complete interval computation for depth 12, residue 2966. -/ +theorem bounds_12_2966 : exactInterval 12 2966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2966 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2966) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2966 : oddCount 2966 12 = 6 ∧ acceleratedOrbit 12 2966 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2966 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2966) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2966.1, data_12_2966.2] + +/-- Complete interval computation for depth 12, residue 2967. -/ +theorem bounds_12_2967 : exactInterval 12 2967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2967 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2967) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2967 : oddCount 2967 12 = 6 ∧ acceleratedOrbit 12 2967 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2967 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2967) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2967.1, data_12_2967.2] + +/-- Complete interval computation for depth 12, residue 2968. -/ +theorem bounds_12_2968 : exactInterval 12 2968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2968 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2968) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2968 : oddCount 2968 12 = 4 ∧ acceleratedOrbit 12 2968 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2968 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2968) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2968.1, data_12_2968.2] + +/-- Complete interval computation for depth 12, residue 2969. -/ +theorem bounds_12_2969 : exactInterval 12 2969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2969 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2969) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2969 : oddCount 2969 12 = 6 ∧ acceleratedOrbit 12 2969 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2969 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2969) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2969.1, data_12_2969.2] + +/-- Complete interval computation for depth 12, residue 2970. -/ +theorem bounds_12_2970 : exactInterval 12 2970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2970 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2970) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2970 : oddCount 2970 12 = 4 ∧ acceleratedOrbit 12 2970 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2970 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2970) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2970.1, data_12_2970.2] + +/-- Complete interval computation for depth 12, residue 2971. -/ +theorem bounds_12_2971 : exactInterval 12 2971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2971 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2971) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2971 : oddCount 2971 12 = 6 ∧ acceleratedOrbit 12 2971 = 529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2971 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2971) = 3 ^ 6 * m + 529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2971.1, data_12_2971.2] + +/-- Complete interval computation for depth 12, residue 2972. -/ +theorem bounds_12_2972 : exactInterval 12 2972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2972 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2972) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2972 : oddCount 2972 12 = 8 ∧ acceleratedOrbit 12 2972 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2972 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2972) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2972.1, data_12_2972.2] + +/-- Complete interval computation for depth 12, residue 2973. -/ +theorem bounds_12_2973 : exactInterval 12 2973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2973 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2973) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2973 : oddCount 2973 12 = 8 ∧ acceleratedOrbit 12 2973 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2973 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2973) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2973.1, data_12_2973.2] + +/-- Complete interval computation for depth 12, residue 2974. -/ +theorem bounds_12_2974 : exactInterval 12 2974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2974 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2974) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2974 : oddCount 2974 12 = 8 ∧ acceleratedOrbit 12 2974 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2974 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2974) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2974.1, data_12_2974.2] + +/-- Complete interval computation for depth 12, residue 2975. -/ +theorem bounds_12_2975 : exactInterval 12 2975 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2975 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2975) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2975 : oddCount 2975 12 = 7 ∧ acceleratedOrbit 12 2975 = 1589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2975 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2975) = 3 ^ 7 * m + 1589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2975.1, data_12_2975.2] + +/-- Complete interval computation for depth 12, residue 2976. -/ +theorem bounds_12_2976 : exactInterval 12 2976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2976 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2976) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2976 : oddCount 2976 12 = 3 ∧ acceleratedOrbit 12 2976 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2976 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2976) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2976.1, data_12_2976.2] + +/-- Complete interval computation for depth 12, residue 2977. -/ +theorem bounds_12_2977 : exactInterval 12 2977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2977 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2977) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2977 : oddCount 2977 12 = 7 ∧ acceleratedOrbit 12 2977 = 1592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2977 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2977) = 3 ^ 7 * m + 1592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2977.1, data_12_2977.2] + +/-- Complete interval computation for depth 12, residue 2978. -/ +theorem bounds_12_2978 : exactInterval 12 2978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2978 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2978) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2978 : oddCount 2978 12 = 4 ∧ acceleratedOrbit 12 2978 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2978 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2978) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2978.1, data_12_2978.2] + +end Collatz.Research.StoppingAtlas.Batch0394 From d57da3b1c8a15b8378543a5203cafd9938aaa4bf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:05 +0530 Subject: [PATCH 0395/1001] proof: certify atlas Batch0395 (12:2979 to 12:2994) --- Collatz/Research/StoppingAtlas/Batch0395.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0395.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0395.lean b/Collatz/Research/StoppingAtlas/Batch0395.lean new file mode 100644 index 00000000..1dbfae99 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0395.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0395 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2979. -/ +theorem bounds_12_2979 : exactInterval 12 2979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2979 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2979) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2979 : oddCount 2979 12 = 4 ∧ acceleratedOrbit 12 2979 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2979 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2979) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2979.1, data_12_2979.2] + +/-- Complete interval computation for depth 12, residue 2980. -/ +theorem bounds_12_2980 : exactInterval 12 2980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2980 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2980) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2980 : oddCount 2980 12 = 7 ∧ acceleratedOrbit 12 2980 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2980 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2980) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2980.1, data_12_2980.2] + +/-- Complete interval computation for depth 12, residue 2981. -/ +theorem bounds_12_2981 : exactInterval 12 2981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2981 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2981) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2981 : oddCount 2981 12 = 7 ∧ acceleratedOrbit 12 2981 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2981 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2981) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2981.1, data_12_2981.2] + +/-- Complete interval computation for depth 12, residue 2982. -/ +theorem bounds_12_2982 : exactInterval 12 2982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2982 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2982) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2982 : oddCount 2982 12 = 7 ∧ acceleratedOrbit 12 2982 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2982 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2982) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2982.1, data_12_2982.2] + +/-- Complete interval computation for depth 12, residue 2983. -/ +theorem bounds_12_2983 : exactInterval 12 2983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2983 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2983) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2983 : oddCount 2983 12 = 8 ∧ acceleratedOrbit 12 2983 = 4781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2983 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2983) = 3 ^ 8 * m + 4781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2983.1, data_12_2983.2] + +/-- Complete interval computation for depth 12, residue 2984. -/ +theorem bounds_12_2984 : exactInterval 12 2984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2984 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2984) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2984 : oddCount 2984 12 = 3 ∧ acceleratedOrbit 12 2984 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2984 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2984) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2984.1, data_12_2984.2] + +/-- Complete interval computation for depth 12, residue 2985. -/ +theorem bounds_12_2985 : exactInterval 12 2985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2985 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2985) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2985 : oddCount 2985 12 = 8 ∧ acceleratedOrbit 12 2985 = 4784 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2985 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2985) = 3 ^ 8 * m + 4784 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2985.1, data_12_2985.2] + +/-- Complete interval computation for depth 12, residue 2986. -/ +theorem bounds_12_2986 : exactInterval 12 2986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2986 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2986) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2986 : oddCount 2986 12 = 3 ∧ acceleratedOrbit 12 2986 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2986 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2986) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2986.1, data_12_2986.2] + +/-- Complete interval computation for depth 12, residue 2987. -/ +theorem bounds_12_2987 : exactInterval 12 2987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2987 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2987) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2987 : oddCount 2987 12 = 6 ∧ acceleratedOrbit 12 2987 = 532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2987 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2987) = 3 ^ 6 * m + 532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2987.1, data_12_2987.2] + +/-- Complete interval computation for depth 12, residue 2988. -/ +theorem bounds_12_2988 : exactInterval 12 2988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2988 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2988) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2988 : oddCount 2988 12 = 6 ∧ acceleratedOrbit 12 2988 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2988 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2988) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2988.1, data_12_2988.2] + +/-- Complete interval computation for depth 12, residue 2989. -/ +theorem bounds_12_2989 : exactInterval 12 2989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2989 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2989) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2989 : oddCount 2989 12 = 6 ∧ acceleratedOrbit 12 2989 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2989 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2989) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2989.1, data_12_2989.2] + +/-- Complete interval computation for depth 12, residue 2990. -/ +theorem bounds_12_2990 : exactInterval 12 2990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2990 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2990) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2990 : oddCount 2990 12 = 6 ∧ acceleratedOrbit 12 2990 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2990 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2990) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2990.1, data_12_2990.2] + +/-- Complete interval computation for depth 12, residue 2991. -/ +theorem bounds_12_2991 : exactInterval 12 2991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2991 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2991) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2991 : oddCount 2991 12 = 6 ∧ acceleratedOrbit 12 2991 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2991 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2991) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2991.1, data_12_2991.2] + +/-- Complete interval computation for depth 12, residue 2992. -/ +theorem bounds_12_2992 : exactInterval 12 2992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2992 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2992) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2992 : oddCount 2992 12 = 5 ∧ acceleratedOrbit 12 2992 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2992 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2992) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2992.1, data_12_2992.2] + +/-- Complete interval computation for depth 12, residue 2993. -/ +theorem bounds_12_2993 : exactInterval 12 2993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2993 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2993) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2993 : oddCount 2993 12 = 5 ∧ acceleratedOrbit 12 2993 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2993 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2993) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2993.1, data_12_2993.2] + +/-- Complete interval computation for depth 12, residue 2994. -/ +theorem bounds_12_2994 : exactInterval 12 2994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2994 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2994) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2994 : oddCount 2994 12 = 5 ∧ acceleratedOrbit 12 2994 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2994 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2994) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2994.1, data_12_2994.2] + +end Collatz.Research.StoppingAtlas.Batch0395 From 3ab18c1140eea57ef389cecb46f7b7617966a6e9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:06 +0530 Subject: [PATCH 0396/1001] proof: certify atlas Batch0396 (12:2995 to 12:3009) --- Collatz/Research/StoppingAtlas/Batch0396.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0396.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0396.lean b/Collatz/Research/StoppingAtlas/Batch0396.lean new file mode 100644 index 00000000..e6658cf3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0396.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0396 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 2995. -/ +theorem bounds_12_2995 : exactInterval 12 2995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2995 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2995) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2995 : oddCount 2995 12 = 5 ∧ acceleratedOrbit 12 2995 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2995 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2995) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2995.1, data_12_2995.2] + +/-- Complete interval computation for depth 12, residue 2996. -/ +theorem bounds_12_2996 : exactInterval 12 2996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2996 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2996) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2996 : oddCount 2996 12 = 5 ∧ acceleratedOrbit 12 2996 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2996 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2996) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2996.1, data_12_2996.2] + +/-- Complete interval computation for depth 12, residue 2997. -/ +theorem bounds_12_2997 : exactInterval 12 2997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2997 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2997) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2997 : oddCount 2997 12 = 5 ∧ acceleratedOrbit 12 2997 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2997 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2997) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2997.1, data_12_2997.2] + +/-- Complete interval computation for depth 12, residue 2998. -/ +theorem bounds_12_2998 : exactInterval 12 2998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2998 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2998) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2998 : oddCount 2998 12 = 5 ∧ acceleratedOrbit 12 2998 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2998 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2998) = 3 ^ 5 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2998.1, data_12_2998.2] + +/-- Complete interval computation for depth 12, residue 2999. -/ +theorem bounds_12_2999 : exactInterval 12 2999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_2999 (m : Nat) : + stoppingTime (2 ^ 12 * m + 2999) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_2999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_2999 : oddCount 2999 12 = 5 ∧ acceleratedOrbit 12 2999 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_2999 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 2999) = 3 ^ 5 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_2999.1, data_12_2999.2] + +/-- Complete interval computation for depth 12, residue 3000. -/ +theorem bounds_12_3000 : exactInterval 12 3000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3000 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3000) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3000 : oddCount 3000 12 = 5 ∧ acceleratedOrbit 12 3000 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3000 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3000) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3000.1, data_12_3000.2] + +/-- Complete interval computation for depth 12, residue 3001. -/ +theorem bounds_12_3001 : exactInterval 12 3001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3001 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3001) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3001 : oddCount 3001 12 = 6 ∧ acceleratedOrbit 12 3001 = 535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3001 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3001) = 3 ^ 6 * m + 535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3001.1, data_12_3001.2] + +/-- Complete interval computation for depth 12, residue 3002. -/ +theorem bounds_12_3002 : exactInterval 12 3002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3002 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3002) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3002 : oddCount 3002 12 = 5 ∧ acceleratedOrbit 12 3002 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3002 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3002) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3002.1, data_12_3002.2] + +/-- Complete interval computation for depth 12, residue 3003. -/ +theorem bounds_12_3003 : exactInterval 12 3003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3003 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3003) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3003 : oddCount 3003 12 = 6 ∧ acceleratedOrbit 12 3003 = 535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3003 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3003) = 3 ^ 6 * m + 535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3003.1, data_12_3003.2] + +/-- Complete interval computation for depth 12, residue 3004. -/ +theorem bounds_12_3004 : exactInterval 12 3004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3004 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3004) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3004 : oddCount 3004 12 = 8 ∧ acceleratedOrbit 12 3004 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3004 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3004) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3004.1, data_12_3004.2] + +/-- Complete interval computation for depth 12, residue 3005. -/ +theorem bounds_12_3005 : exactInterval 12 3005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3005 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3005) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3005 : oddCount 3005 12 = 8 ∧ acceleratedOrbit 12 3005 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3005 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3005) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3005.1, data_12_3005.2] + +/-- Complete interval computation for depth 12, residue 3006. -/ +theorem bounds_12_3006 : exactInterval 12 3006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3006 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3006) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3006 : oddCount 3006 12 = 8 ∧ acceleratedOrbit 12 3006 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3006 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3006) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3006.1, data_12_3006.2] + +/-- Complete interval computation for depth 12, residue 3007. -/ +theorem bounds_12_3007 : exactInterval 12 3007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3007 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3007) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3007 : oddCount 3007 12 = 9 ∧ acceleratedOrbit 12 3007 = 14455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3007 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3007) = 3 ^ 9 * m + 14455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3007.1, data_12_3007.2] + +/-- Complete interval computation for depth 12, residue 3008. -/ +theorem bounds_12_3008 : exactInterval 12 3008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3008 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3008) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3008 : oddCount 3008 12 = 5 ∧ acceleratedOrbit 12 3008 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3008 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3008) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3008.1, data_12_3008.2] + +/-- Complete interval computation for depth 12, residue 3009. -/ +theorem bounds_12_3009 : exactInterval 12 3009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3009 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3009) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3009 : oddCount 3009 12 = 7 ∧ acceleratedOrbit 12 3009 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3009 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3009) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3009.1, data_12_3009.2] + +end Collatz.Research.StoppingAtlas.Batch0396 From a49b8b65abf29aa54defa665da2587d5ae99a576 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:06 +0530 Subject: [PATCH 0397/1001] proof: certify atlas Batch0397 (12:3010 to 12:3024) --- Collatz/Research/StoppingAtlas/Batch0397.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0397.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0397.lean b/Collatz/Research/StoppingAtlas/Batch0397.lean new file mode 100644 index 00000000..25209604 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0397.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0397 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3010. -/ +theorem bounds_12_3010 : exactInterval 12 3010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3010 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3010) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3010 : oddCount 3010 12 = 7 ∧ acceleratedOrbit 12 3010 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3010 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3010) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3010.1, data_12_3010.2] + +/-- Complete interval computation for depth 12, residue 3011. -/ +theorem bounds_12_3011 : exactInterval 12 3011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3011 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3011) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3011 : oddCount 3011 12 = 7 ∧ acceleratedOrbit 12 3011 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3011 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3011) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3011.1, data_12_3011.2] + +/-- Complete interval computation for depth 12, residue 3012. -/ +theorem bounds_12_3012 : exactInterval 12 3012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3012 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3012) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3012 : oddCount 3012 12 = 3 ∧ acceleratedOrbit 12 3012 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3012 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3012) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3012.1, data_12_3012.2] + +/-- Complete interval computation for depth 12, residue 3013. -/ +theorem bounds_12_3013 : exactInterval 12 3013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3013 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3013) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3013 : oddCount 3013 12 = 3 ∧ acceleratedOrbit 12 3013 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3013 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3013) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3013.1, data_12_3013.2] + +/-- Complete interval computation for depth 12, residue 3014. -/ +theorem bounds_12_3014 : exactInterval 12 3014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3014 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3014) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3014 : oddCount 3014 12 = 3 ∧ acceleratedOrbit 12 3014 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3014 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3014) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3014.1, data_12_3014.2] + +/-- Complete interval computation for depth 12, residue 3015. -/ +theorem bounds_12_3015 : exactInterval 12 3015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3015 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3015) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3015 : oddCount 3015 12 = 9 ∧ acceleratedOrbit 12 3015 = 14498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3015 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3015) = 3 ^ 9 * m + 14498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3015.1, data_12_3015.2] + +/-- Complete interval computation for depth 12, residue 3016. -/ +theorem bounds_12_3016 : exactInterval 12 3016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3016 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3016) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3016 : oddCount 3016 12 = 7 ∧ acceleratedOrbit 12 3016 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3016 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3016) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3016.1, data_12_3016.2] + +/-- Complete interval computation for depth 12, residue 3017. -/ +theorem bounds_12_3017 : exactInterval 12 3017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3017 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3017) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3017 : oddCount 3017 12 = 7 ∧ acceleratedOrbit 12 3017 = 1613 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3017 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3017) = 3 ^ 7 * m + 1613 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3017.1, data_12_3017.2] + +/-- Complete interval computation for depth 12, residue 3018. -/ +theorem bounds_12_3018 : exactInterval 12 3018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3018 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3018) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3018 : oddCount 3018 12 = 7 ∧ acceleratedOrbit 12 3018 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3018 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3018) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3018.1, data_12_3018.2] + +/-- Complete interval computation for depth 12, residue 3019. -/ +theorem bounds_12_3019 : exactInterval 12 3019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3019 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3019) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3019 : oddCount 3019 12 = 6 ∧ acceleratedOrbit 12 3019 = 539 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3019 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3019) = 3 ^ 6 * m + 539 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3019.1, data_12_3019.2] + +/-- Complete interval computation for depth 12, residue 3020. -/ +theorem bounds_12_3020 : exactInterval 12 3020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3020 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3020) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3020 : oddCount 3020 12 = 7 ∧ acceleratedOrbit 12 3020 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3020 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3020) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3020.1, data_12_3020.2] + +/-- Complete interval computation for depth 12, residue 3021. -/ +theorem bounds_12_3021 : exactInterval 12 3021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3021 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3021) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3021 : oddCount 3021 12 = 7 ∧ acceleratedOrbit 12 3021 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3021 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3021) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3021.1, data_12_3021.2] + +/-- Complete interval computation for depth 12, residue 3022. -/ +theorem bounds_12_3022 : exactInterval 12 3022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3022 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3022) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3022 : oddCount 3022 12 = 7 ∧ acceleratedOrbit 12 3022 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3022 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3022) = 3 ^ 7 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3022.1, data_12_3022.2] + +/-- Complete interval computation for depth 12, residue 3023. -/ +theorem bounds_12_3023 : exactInterval 12 3023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3023 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3023) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3023 : oddCount 3023 12 = 7 ∧ acceleratedOrbit 12 3023 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3023 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3023) = 3 ^ 7 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3023.1, data_12_3023.2] + +/-- Complete interval computation for depth 12, residue 3024. -/ +theorem bounds_12_3024 : exactInterval 12 3024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3024 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3024) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3024 : oddCount 3024 12 = 5 ∧ acceleratedOrbit 12 3024 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3024 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3024) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3024.1, data_12_3024.2] + +end Collatz.Research.StoppingAtlas.Batch0397 From 296a502ffc005704b67da9a4993665809376c908 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:07 +0530 Subject: [PATCH 0398/1001] proof: certify atlas Batch0398 (12:3025 to 12:3040) --- Collatz/Research/StoppingAtlas/Batch0398.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0398.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0398.lean b/Collatz/Research/StoppingAtlas/Batch0398.lean new file mode 100644 index 00000000..e29cc0c3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0398.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0398 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3025. -/ +theorem bounds_12_3025 : exactInterval 12 3025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3025 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3025) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3025 : oddCount 3025 12 = 7 ∧ acceleratedOrbit 12 3025 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3025 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3025) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3025.1, data_12_3025.2] + +/-- Complete interval computation for depth 12, residue 3026. -/ +theorem bounds_12_3026 : exactInterval 12 3026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3026 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3026) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3026 : oddCount 3026 12 = 8 ∧ acceleratedOrbit 12 3026 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3026 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3026) = 3 ^ 8 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3026.1, data_12_3026.2] + +/-- Complete interval computation for depth 12, residue 3027. -/ +theorem bounds_12_3027 : exactInterval 12 3027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3027 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3027) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3027 : oddCount 3027 12 = 8 ∧ acceleratedOrbit 12 3027 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3027 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3027) = 3 ^ 8 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3027.1, data_12_3027.2] + +/-- Complete interval computation for depth 12, residue 3028. -/ +theorem bounds_12_3028 : exactInterval 12 3028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3028 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3028) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3028 : oddCount 3028 12 = 5 ∧ acceleratedOrbit 12 3028 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3028 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3028) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3028.1, data_12_3028.2] + +/-- Complete interval computation for depth 12, residue 3029. -/ +theorem bounds_12_3029 : exactInterval 12 3029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3029 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3029) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3029 : oddCount 3029 12 = 5 ∧ acceleratedOrbit 12 3029 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3029 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3029) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3029.1, data_12_3029.2] + +/-- Complete interval computation for depth 12, residue 3030. -/ +theorem bounds_12_3030 : exactInterval 12 3030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3030 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3030) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3030 : oddCount 3030 12 = 9 ∧ acceleratedOrbit 12 3030 = 14579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3030 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3030) = 3 ^ 9 * m + 14579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3030.1, data_12_3030.2] + +/-- Complete interval computation for depth 12, residue 3031. -/ +theorem bounds_12_3031 : exactInterval 12 3031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3031 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3031) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3031 : oddCount 3031 12 = 9 ∧ acceleratedOrbit 12 3031 = 14579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3031 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3031) = 3 ^ 9 * m + 14579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3031.1, data_12_3031.2] + +/-- Complete interval computation for depth 12, residue 3032. -/ +theorem bounds_12_3032 : exactInterval 12 3032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3032 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3032) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3032 : oddCount 3032 12 = 6 ∧ acceleratedOrbit 12 3032 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3032 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3032) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3032.1, data_12_3032.2] + +/-- Complete interval computation for depth 12, residue 3033. -/ +theorem bounds_12_3033 : exactInterval 12 3033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3033 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3033) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3033 : oddCount 3033 12 = 3 ∧ acceleratedOrbit 12 3033 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3033 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3033) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3033.1, data_12_3033.2] + +/-- Complete interval computation for depth 12, residue 3034. -/ +theorem bounds_12_3034 : exactInterval 12 3034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3034 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3034) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3034 : oddCount 3034 12 = 6 ∧ acceleratedOrbit 12 3034 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3034 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3034) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3034.1, data_12_3034.2] + +/-- Complete interval computation for depth 12, residue 3035. -/ +theorem bounds_12_3035 : exactInterval 12 3035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3035 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3035) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3035 : oddCount 3035 12 = 7 ∧ acceleratedOrbit 12 3035 = 1622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3035 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3035) = 3 ^ 7 * m + 1622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3035.1, data_12_3035.2] + +/-- Complete interval computation for depth 12, residue 3036. -/ +theorem bounds_12_3036 : exactInterval 12 3036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3036 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3036) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3036 : oddCount 3036 12 = 6 ∧ acceleratedOrbit 12 3036 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3036 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3036) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3036.1, data_12_3036.2] + +/-- Complete interval computation for depth 12, residue 3037. -/ +theorem bounds_12_3037 : exactInterval 12 3037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3037 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3037) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3037 : oddCount 3037 12 = 6 ∧ acceleratedOrbit 12 3037 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3037 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3037) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3037.1, data_12_3037.2] + +/-- Complete interval computation for depth 12, residue 3038. -/ +theorem bounds_12_3038 : exactInterval 12 3038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3038 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3038) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3038 : oddCount 3038 12 = 8 ∧ acceleratedOrbit 12 3038 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3038 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3038) = 3 ^ 8 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3038.1, data_12_3038.2] + +/-- Complete interval computation for depth 12, residue 3039. -/ +theorem bounds_12_3039 : exactInterval 12 3039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3039 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3039) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3039 : oddCount 3039 12 = 8 ∧ acceleratedOrbit 12 3039 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3039 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3039) = 3 ^ 8 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3039.1, data_12_3039.2] + +/-- Complete interval computation for depth 12, residue 3040. -/ +theorem bounds_12_3040 : exactInterval 12 3040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3040 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3040) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3040 : oddCount 3040 12 = 5 ∧ acceleratedOrbit 12 3040 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3040 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3040) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3040.1, data_12_3040.2] + +end Collatz.Research.StoppingAtlas.Batch0398 From 008b20148d33dcdd53d9436c2d63961c6b61c585 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:07 +0530 Subject: [PATCH 0399/1001] proof: certify atlas Batch0399 (12:3041 to 12:3055) --- Collatz/Research/StoppingAtlas/Batch0399.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0399.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0399.lean b/Collatz/Research/StoppingAtlas/Batch0399.lean new file mode 100644 index 00000000..3682da04 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0399.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0399 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3041. -/ +theorem bounds_12_3041 : exactInterval 12 3041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3041 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3041) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3041 : oddCount 3041 12 = 7 ∧ acceleratedOrbit 12 3041 = 1625 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3041 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3041) = 3 ^ 7 * m + 1625 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3041.1, data_12_3041.2] + +/-- Complete interval computation for depth 12, residue 3042. -/ +theorem bounds_12_3042 : exactInterval 12 3042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3042 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3042) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3042 : oddCount 3042 12 = 5 ∧ acceleratedOrbit 12 3042 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3042 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3042) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3042.1, data_12_3042.2] + +/-- Complete interval computation for depth 12, residue 3043. -/ +theorem bounds_12_3043 : exactInterval 12 3043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3043 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3043) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3043 : oddCount 3043 12 = 5 ∧ acceleratedOrbit 12 3043 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3043 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3043) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3043.1, data_12_3043.2] + +/-- Complete interval computation for depth 12, residue 3044. -/ +theorem bounds_12_3044 : exactInterval 12 3044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3044 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3044) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3044 : oddCount 3044 12 = 5 ∧ acceleratedOrbit 12 3044 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3044 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3044) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3044.1, data_12_3044.2] + +/-- Complete interval computation for depth 12, residue 3045. -/ +theorem bounds_12_3045 : exactInterval 12 3045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3045 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3045) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3045 : oddCount 3045 12 = 5 ∧ acceleratedOrbit 12 3045 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3045 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3045) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3045.1, data_12_3045.2] + +/-- Complete interval computation for depth 12, residue 3046. -/ +theorem bounds_12_3046 : exactInterval 12 3046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3046 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3046) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3046 : oddCount 3046 12 = 5 ∧ acceleratedOrbit 12 3046 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3046 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3046) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3046.1, data_12_3046.2] + +/-- Complete interval computation for depth 12, residue 3047. -/ +theorem bounds_12_3047 : exactInterval 12 3047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3047 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3047) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3047 : oddCount 3047 12 = 7 ∧ acceleratedOrbit 12 3047 = 1628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3047 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3047) = 3 ^ 7 * m + 1628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3047.1, data_12_3047.2] + +/-- Complete interval computation for depth 12, residue 3048. -/ +theorem bounds_12_3048 : exactInterval 12 3048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3048 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3048) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3048 : oddCount 3048 12 = 5 ∧ acceleratedOrbit 12 3048 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3048 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3048) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3048.1, data_12_3048.2] + +/-- Complete interval computation for depth 12, residue 3049. -/ +theorem bounds_12_3049 : exactInterval 12 3049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3049 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3049) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3049 : oddCount 3049 12 = 10 ∧ acceleratedOrbit 12 3049 = 43982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3049 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3049) = 3 ^ 10 * m + 43982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3049.1, data_12_3049.2] + +/-- Complete interval computation for depth 12, residue 3050. -/ +theorem bounds_12_3050 : exactInterval 12 3050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3050 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3050) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3050 : oddCount 3050 12 = 5 ∧ acceleratedOrbit 12 3050 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3050 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3050) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3050.1, data_12_3050.2] + +/-- Complete interval computation for depth 12, residue 3051. -/ +theorem bounds_12_3051 : exactInterval 12 3051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3051 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3051) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3051 : oddCount 3051 12 = 7 ∧ acceleratedOrbit 12 3051 = 1630 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3051 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3051) = 3 ^ 7 * m + 1630 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3051.1, data_12_3051.2] + +/-- Complete interval computation for depth 12, residue 3052. -/ +theorem bounds_12_3052 : exactInterval 12 3052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3052 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3052) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3052 : oddCount 3052 12 = 7 ∧ acceleratedOrbit 12 3052 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3052 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3052) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3052.1, data_12_3052.2] + +/-- Complete interval computation for depth 12, residue 3053. -/ +theorem bounds_12_3053 : exactInterval 12 3053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3053 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3053) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3053 : oddCount 3053 12 = 7 ∧ acceleratedOrbit 12 3053 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3053 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3053) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3053.1, data_12_3053.2] + +/-- Complete interval computation for depth 12, residue 3054. -/ +theorem bounds_12_3054 : exactInterval 12 3054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3054 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3054) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3054 : oddCount 3054 12 = 7 ∧ acceleratedOrbit 12 3054 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3054 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3054) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3054.1, data_12_3054.2] + +/-- Complete interval computation for depth 12, residue 3055. -/ +theorem bounds_12_3055 : exactInterval 12 3055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3055 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3055) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3055 : oddCount 3055 12 = 9 ∧ acceleratedOrbit 12 3055 = 14687 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3055 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3055) = 3 ^ 9 * m + 14687 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3055.1, data_12_3055.2] + +end Collatz.Research.StoppingAtlas.Batch0399 From edfc5fac2562167624668bbfb74a6a0560498f68 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:07 +0530 Subject: [PATCH 0400/1001] proof: certify atlas Batch0400 (12:3056 to 12:3071) --- Collatz/Research/StoppingAtlas/Batch0400.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0400.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0400.lean b/Collatz/Research/StoppingAtlas/Batch0400.lean new file mode 100644 index 00000000..9d3e96f7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0400.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0400 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3056. -/ +theorem bounds_12_3056 : exactInterval 12 3056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3056 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3056) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3056 : oddCount 3056 12 = 7 ∧ acceleratedOrbit 12 3056 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3056 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3056) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3056.1, data_12_3056.2] + +/-- Complete interval computation for depth 12, residue 3057. -/ +theorem bounds_12_3057 : exactInterval 12 3057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3057 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3057) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3057 : oddCount 3057 12 = 5 ∧ acceleratedOrbit 12 3057 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3057 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3057) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3057.1, data_12_3057.2] + +/-- Complete interval computation for depth 12, residue 3058. -/ +theorem bounds_12_3058 : exactInterval 12 3058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3058 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3058) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3058 : oddCount 3058 12 = 6 ∧ acceleratedOrbit 12 3058 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3058 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3058) = 3 ^ 6 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3058.1, data_12_3058.2] + +/-- Complete interval computation for depth 12, residue 3059. -/ +theorem bounds_12_3059 : exactInterval 12 3059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3059 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3059) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3059 : oddCount 3059 12 = 6 ∧ acceleratedOrbit 12 3059 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3059 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3059) = 3 ^ 6 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3059.1, data_12_3059.2] + +/-- Complete interval computation for depth 12, residue 3060. -/ +theorem bounds_12_3060 : exactInterval 12 3060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3060 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3060) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3060 : oddCount 3060 12 = 7 ∧ acceleratedOrbit 12 3060 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3060 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3060) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3060.1, data_12_3060.2] + +/-- Complete interval computation for depth 12, residue 3061. -/ +theorem bounds_12_3061 : exactInterval 12 3061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3061 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3061) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3061 : oddCount 3061 12 = 7 ∧ acceleratedOrbit 12 3061 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3061 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3061) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3061.1, data_12_3061.2] + +/-- Complete interval computation for depth 12, residue 3062. -/ +theorem bounds_12_3062 : exactInterval 12 3062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3062 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3062) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3062 : oddCount 3062 12 = 7 ∧ acceleratedOrbit 12 3062 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3062 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3062) = 3 ^ 7 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3062.1, data_12_3062.2] + +/-- Complete interval computation for depth 12, residue 3063. -/ +theorem bounds_12_3063 : exactInterval 12 3063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3063 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3063) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3063 : oddCount 3063 12 = 7 ∧ acceleratedOrbit 12 3063 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3063 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3063) = 3 ^ 7 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3063.1, data_12_3063.2] + +/-- Complete interval computation for depth 12, residue 3064. -/ +theorem bounds_12_3064 : exactInterval 12 3064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3064 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3064) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3064 : oddCount 3064 12 = 7 ∧ acceleratedOrbit 12 3064 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3064 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3064) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3064.1, data_12_3064.2] + +/-- Complete interval computation for depth 12, residue 3065. -/ +theorem bounds_12_3065 : exactInterval 12 3065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3065 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3065) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3065 : oddCount 3065 12 = 9 ∧ acceleratedOrbit 12 3065 = 14741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3065 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3065) = 3 ^ 9 * m + 14741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3065.1, data_12_3065.2] + +/-- Complete interval computation for depth 12, residue 3066. -/ +theorem bounds_12_3066 : exactInterval 12 3066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3066 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3066) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3066 : oddCount 3066 12 = 7 ∧ acceleratedOrbit 12 3066 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3066 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3066) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3066.1, data_12_3066.2] + +/-- Complete interval computation for depth 12, residue 3067. -/ +theorem bounds_12_3067 : exactInterval 12 3067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3067 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3067) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3067 : oddCount 3067 12 = 8 ∧ acceleratedOrbit 12 3067 = 4916 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3067 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3067) = 3 ^ 8 * m + 4916 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3067.1, data_12_3067.2] + +/-- Complete interval computation for depth 12, residue 3068. -/ +theorem bounds_12_3068 : exactInterval 12 3068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3068 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3068) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3068 : oddCount 3068 12 = 9 ∧ acceleratedOrbit 12 3068 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3068 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3068) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3068.1, data_12_3068.2] + +/-- Complete interval computation for depth 12, residue 3069. -/ +theorem bounds_12_3069 : exactInterval 12 3069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3069 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3069) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3069 : oddCount 3069 12 = 9 ∧ acceleratedOrbit 12 3069 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3069 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3069) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3069.1, data_12_3069.2] + +/-- Complete interval computation for depth 12, residue 3070. -/ +theorem bounds_12_3070 : exactInterval 12 3070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3070 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3070) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3070 : oddCount 3070 12 = 9 ∧ acceleratedOrbit 12 3070 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3070 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3070) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3070.1, data_12_3070.2] + +/-- Complete interval computation for depth 12, residue 3071. -/ +theorem bounds_12_3071 : exactInterval 12 3071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3071 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3071) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3071 : oddCount 3071 12 = 11 ∧ acceleratedOrbit 12 3071 = 132860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3071 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3071) = 3 ^ 11 * m + 132860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3071.1, data_12_3071.2] + +end Collatz.Research.StoppingAtlas.Batch0400 From 8ef181f8393b02681ca0cbbaf09fcbcb338aeb9b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:08 +0530 Subject: [PATCH 0401/1001] proof: certify atlas Batch0401 (12:3072 to 12:3086) --- Collatz/Research/StoppingAtlas/Batch0401.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0401.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0401.lean b/Collatz/Research/StoppingAtlas/Batch0401.lean new file mode 100644 index 00000000..ebb4977e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0401.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0401 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3072. -/ +theorem bounds_12_3072 : exactInterval 12 3072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3072 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3072) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3072 : oddCount 3072 12 = 2 ∧ acceleratedOrbit 12 3072 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3072 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3072) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3072.1, data_12_3072.2] + +/-- Complete interval computation for depth 12, residue 3073. -/ +theorem bounds_12_3073 : exactInterval 12 3073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3073 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3073) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3073 : oddCount 3073 12 = 6 ∧ acceleratedOrbit 12 3073 = 548 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3073 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3073) = 3 ^ 6 * m + 548 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3073.1, data_12_3073.2] + +/-- Complete interval computation for depth 12, residue 3074. -/ +theorem bounds_12_3074 : exactInterval 12 3074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3074 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3074) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3074 : oddCount 3074 12 = 7 ∧ acceleratedOrbit 12 3074 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3074 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3074) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3074.1, data_12_3074.2] + +/-- Complete interval computation for depth 12, residue 3075. -/ +theorem bounds_12_3075 : exactInterval 12 3075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3075 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3075) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3075 : oddCount 3075 12 = 7 ∧ acceleratedOrbit 12 3075 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3075 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3075) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3075.1, data_12_3075.2] + +/-- Complete interval computation for depth 12, residue 3076. -/ +theorem bounds_12_3076 : exactInterval 12 3076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3076 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3076) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3076 : oddCount 3076 12 = 4 ∧ acceleratedOrbit 12 3076 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3076 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3076) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3076.1, data_12_3076.2] + +/-- Complete interval computation for depth 12, residue 3077. -/ +theorem bounds_12_3077 : exactInterval 12 3077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3077 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3077) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3077 : oddCount 3077 12 = 4 ∧ acceleratedOrbit 12 3077 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3077 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3077) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3077.1, data_12_3077.2] + +/-- Complete interval computation for depth 12, residue 3078. -/ +theorem bounds_12_3078 : exactInterval 12 3078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3078 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3078) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3078 : oddCount 3078 12 = 4 ∧ acceleratedOrbit 12 3078 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3078 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3078) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3078.1, data_12_3078.2] + +/-- Complete interval computation for depth 12, residue 3079. -/ +theorem bounds_12_3079 : exactInterval 12 3079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3079 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3079) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3079 : oddCount 3079 12 = 7 ∧ acceleratedOrbit 12 3079 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3079 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3079) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3079.1, data_12_3079.2] + +/-- Complete interval computation for depth 12, residue 3080. -/ +theorem bounds_12_3080 : exactInterval 12 3080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3080 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3080) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3080 : oddCount 3080 12 = 5 ∧ acceleratedOrbit 12 3080 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3080 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3080) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3080.1, data_12_3080.2] + +/-- Complete interval computation for depth 12, residue 3081. -/ +theorem bounds_12_3081 : exactInterval 12 3081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3081 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3081) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3081 : oddCount 3081 12 = 8 ∧ acceleratedOrbit 12 3081 = 4940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3081 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3081) = 3 ^ 8 * m + 4940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3081.1, data_12_3081.2] + +/-- Complete interval computation for depth 12, residue 3082. -/ +theorem bounds_12_3082 : exactInterval 12 3082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3082 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3082) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3082 : oddCount 3082 12 = 5 ∧ acceleratedOrbit 12 3082 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3082 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3082) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3082.1, data_12_3082.2] + +/-- Complete interval computation for depth 12, residue 3083. -/ +theorem bounds_12_3083 : exactInterval 12 3083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3083 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3083) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3083 : oddCount 3083 12 = 4 ∧ acceleratedOrbit 12 3083 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3083 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3083) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3083.1, data_12_3083.2] + +/-- Complete interval computation for depth 12, residue 3084. -/ +theorem bounds_12_3084 : exactInterval 12 3084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3084 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3084) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3084 : oddCount 3084 12 = 5 ∧ acceleratedOrbit 12 3084 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3084 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3084) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3084.1, data_12_3084.2] + +/-- Complete interval computation for depth 12, residue 3085. -/ +theorem bounds_12_3085 : exactInterval 12 3085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3085 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3085) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3085 : oddCount 3085 12 = 5 ∧ acceleratedOrbit 12 3085 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3085 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3085) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3085.1, data_12_3085.2] + +/-- Complete interval computation for depth 12, residue 3086. -/ +theorem bounds_12_3086 : exactInterval 12 3086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3086 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3086) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3086 : oddCount 3086 12 = 6 ∧ acceleratedOrbit 12 3086 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3086 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3086) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3086.1, data_12_3086.2] + +end Collatz.Research.StoppingAtlas.Batch0401 From 21b38c69540b7bc4ce7ebd8a76c6f10611386327 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:08 +0530 Subject: [PATCH 0402/1001] proof: certify atlas Batch0402 (12:3087 to 12:3101) --- Collatz/Research/StoppingAtlas/Batch0402.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0402.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0402.lean b/Collatz/Research/StoppingAtlas/Batch0402.lean new file mode 100644 index 00000000..60c603ce --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0402.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0402 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3087. -/ +theorem bounds_12_3087 : exactInterval 12 3087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3087 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3087) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3087 : oddCount 3087 12 = 6 ∧ acceleratedOrbit 12 3087 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3087 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3087) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3087.1, data_12_3087.2] + +/-- Complete interval computation for depth 12, residue 3088. -/ +theorem bounds_12_3088 : exactInterval 12 3088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3088 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3088) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3088 : oddCount 3088 12 = 4 ∧ acceleratedOrbit 12 3088 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3088 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3088) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3088.1, data_12_3088.2] + +/-- Complete interval computation for depth 12, residue 3089. -/ +theorem bounds_12_3089 : exactInterval 12 3089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3089 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3089) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3089 : oddCount 3089 12 = 5 ∧ acceleratedOrbit 12 3089 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3089 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3089) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3089.1, data_12_3089.2] + +/-- Complete interval computation for depth 12, residue 3090. -/ +theorem bounds_12_3090 : exactInterval 12 3090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3090 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3090) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3090 : oddCount 3090 12 = 6 ∧ acceleratedOrbit 12 3090 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3090 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3090) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3090.1, data_12_3090.2] + +/-- Complete interval computation for depth 12, residue 3091. -/ +theorem bounds_12_3091 : exactInterval 12 3091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3091 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3091) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3091 : oddCount 3091 12 = 6 ∧ acceleratedOrbit 12 3091 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3091 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3091) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3091.1, data_12_3091.2] + +/-- Complete interval computation for depth 12, residue 3092. -/ +theorem bounds_12_3092 : exactInterval 12 3092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3092 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3092) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3092 : oddCount 3092 12 = 4 ∧ acceleratedOrbit 12 3092 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3092 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3092) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3092.1, data_12_3092.2] + +/-- Complete interval computation for depth 12, residue 3093. -/ +theorem bounds_12_3093 : exactInterval 12 3093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3093 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3093) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3093 : oddCount 3093 12 = 4 ∧ acceleratedOrbit 12 3093 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3093 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3093) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3093.1, data_12_3093.2] + +/-- Complete interval computation for depth 12, residue 3094. -/ +theorem bounds_12_3094 : exactInterval 12 3094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3094 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3094) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3094 : oddCount 3094 12 = 5 ∧ acceleratedOrbit 12 3094 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3094 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3094) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3094.1, data_12_3094.2] + +/-- Complete interval computation for depth 12, residue 3095. -/ +theorem bounds_12_3095 : exactInterval 12 3095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3095 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3095) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3095 : oddCount 3095 12 = 5 ∧ acceleratedOrbit 12 3095 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3095 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3095) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3095.1, data_12_3095.2] + +/-- Complete interval computation for depth 12, residue 3096. -/ +theorem bounds_12_3096 : exactInterval 12 3096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3096 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3096) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3096 : oddCount 3096 12 = 4 ∧ acceleratedOrbit 12 3096 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3096 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3096) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3096.1, data_12_3096.2] + +/-- Complete interval computation for depth 12, residue 3097. -/ +theorem bounds_12_3097 : exactInterval 12 3097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3097 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3097) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3097 : oddCount 3097 12 = 8 ∧ acceleratedOrbit 12 3097 = 4967 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3097 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3097) = 3 ^ 8 * m + 4967 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3097.1, data_12_3097.2] + +/-- Complete interval computation for depth 12, residue 3098. -/ +theorem bounds_12_3098 : exactInterval 12 3098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3098 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3098) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3098 : oddCount 3098 12 = 4 ∧ acceleratedOrbit 12 3098 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3098 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3098) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3098.1, data_12_3098.2] + +/-- Complete interval computation for depth 12, residue 3099. -/ +theorem bounds_12_3099 : exactInterval 12 3099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3099 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3099) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3099 : oddCount 3099 12 = 9 ∧ acceleratedOrbit 12 3099 = 14899 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3099 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3099) = 3 ^ 9 * m + 14899 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3099.1, data_12_3099.2] + +/-- Complete interval computation for depth 12, residue 3100. -/ +theorem bounds_12_3100 : exactInterval 12 3100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3100 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3100) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3100 : oddCount 3100 12 = 6 ∧ acceleratedOrbit 12 3100 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3100 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3100) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3100.1, data_12_3100.2] + +/-- Complete interval computation for depth 12, residue 3101. -/ +theorem bounds_12_3101 : exactInterval 12 3101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3101 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3101) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3101 : oddCount 3101 12 = 6 ∧ acceleratedOrbit 12 3101 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3101 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3101) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3101.1, data_12_3101.2] + +end Collatz.Research.StoppingAtlas.Batch0402 From d8cdb333e958de59be5f58bd4bcc470d5f7bce7f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:08 +0530 Subject: [PATCH 0403/1001] proof: certify atlas Batch0403 (12:3102 to 12:3117) --- Collatz/Research/StoppingAtlas/Batch0403.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0403.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0403.lean b/Collatz/Research/StoppingAtlas/Batch0403.lean new file mode 100644 index 00000000..a138d43c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0403.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0403 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3102. -/ +theorem bounds_12_3102 : exactInterval 12 3102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3102 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3102) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3102 : oddCount 3102 12 = 6 ∧ acceleratedOrbit 12 3102 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3102 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3102) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3102.1, data_12_3102.2] + +/-- Complete interval computation for depth 12, residue 3103. -/ +theorem bounds_12_3103 : exactInterval 12 3103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3103 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3103) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3103 : oddCount 3103 12 = 9 ∧ acceleratedOrbit 12 3103 = 14917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3103 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3103) = 3 ^ 9 * m + 14917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3103.1, data_12_3103.2] + +/-- Complete interval computation for depth 12, residue 3104. -/ +theorem bounds_12_3104 : exactInterval 12 3104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3104 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3104) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3104 : oddCount 3104 12 = 5 ∧ acceleratedOrbit 12 3104 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3104 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3104) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3104.1, data_12_3104.2] + +/-- Complete interval computation for depth 12, residue 3105. -/ +theorem bounds_12_3105 : exactInterval 12 3105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3105 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3105) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3105 : oddCount 3105 12 = 7 ∧ acceleratedOrbit 12 3105 = 1660 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3105 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3105) = 3 ^ 7 * m + 1660 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3105.1, data_12_3105.2] + +/-- Complete interval computation for depth 12, residue 3106. -/ +theorem bounds_12_3106 : exactInterval 12 3106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3106 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3106) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3106 : oddCount 3106 12 = 4 ∧ acceleratedOrbit 12 3106 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3106 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3106) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3106.1, data_12_3106.2] + +/-- Complete interval computation for depth 12, residue 3107. -/ +theorem bounds_12_3107 : exactInterval 12 3107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3107 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3107) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3107 : oddCount 3107 12 = 4 ∧ acceleratedOrbit 12 3107 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3107 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3107) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3107.1, data_12_3107.2] + +/-- Complete interval computation for depth 12, residue 3108. -/ +theorem bounds_12_3108 : exactInterval 12 3108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3108 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3108) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3108 : oddCount 3108 12 = 7 ∧ acceleratedOrbit 12 3108 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3108 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3108) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3108.1, data_12_3108.2] + +/-- Complete interval computation for depth 12, residue 3109. -/ +theorem bounds_12_3109 : exactInterval 12 3109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3109 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3109) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3109 : oddCount 3109 12 = 7 ∧ acceleratedOrbit 12 3109 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3109 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3109) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3109.1, data_12_3109.2] + +/-- Complete interval computation for depth 12, residue 3110. -/ +theorem bounds_12_3110 : exactInterval 12 3110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3110 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3110) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3110 : oddCount 3110 12 = 7 ∧ acceleratedOrbit 12 3110 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3110 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3110) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3110.1, data_12_3110.2] + +/-- Complete interval computation for depth 12, residue 3111. -/ +theorem bounds_12_3111 : exactInterval 12 3111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3111 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3111) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3111 : oddCount 3111 12 = 6 ∧ acceleratedOrbit 12 3111 = 554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3111 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3111) = 3 ^ 6 * m + 554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3111.1, data_12_3111.2] + +/-- Complete interval computation for depth 12, residue 3112. -/ +theorem bounds_12_3112 : exactInterval 12 3112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3112 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3112) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3112 : oddCount 3112 12 = 5 ∧ acceleratedOrbit 12 3112 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3112 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3112) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3112.1, data_12_3112.2] + +/-- Complete interval computation for depth 12, residue 3113. -/ +theorem bounds_12_3113 : exactInterval 12 3113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3113 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3113) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3113 : oddCount 3113 12 = 7 ∧ acceleratedOrbit 12 3113 = 1663 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3113 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3113) = 3 ^ 7 * m + 1663 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3113.1, data_12_3113.2] + +/-- Complete interval computation for depth 12, residue 3114. -/ +theorem bounds_12_3114 : exactInterval 12 3114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3114 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3114) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3114 : oddCount 3114 12 = 5 ∧ acceleratedOrbit 12 3114 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3114 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3114) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3114.1, data_12_3114.2] + +/-- Complete interval computation for depth 12, residue 3115. -/ +theorem bounds_12_3115 : exactInterval 12 3115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3115 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3115) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3115 : oddCount 3115 12 = 5 ∧ acceleratedOrbit 12 3115 = 185 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3115 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3115) = 3 ^ 5 * m + 185 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3115.1, data_12_3115.2] + +/-- Complete interval computation for depth 12, residue 3116. -/ +theorem bounds_12_3116 : exactInterval 12 3116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3116 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3116) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3116 : oddCount 3116 12 = 6 ∧ acceleratedOrbit 12 3116 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3116 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3116) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3116.1, data_12_3116.2] + +/-- Complete interval computation for depth 12, residue 3117. -/ +theorem bounds_12_3117 : exactInterval 12 3117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3117 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3117) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3117 : oddCount 3117 12 = 6 ∧ acceleratedOrbit 12 3117 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3117 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3117) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3117.1, data_12_3117.2] + +end Collatz.Research.StoppingAtlas.Batch0403 From 428b771661bbf32bda926766812d4de4632b53bc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:09 +0530 Subject: [PATCH 0404/1001] proof: certify atlas Batch0404 (12:3118 to 12:3132) --- Collatz/Research/StoppingAtlas/Batch0404.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0404.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0404.lean b/Collatz/Research/StoppingAtlas/Batch0404.lean new file mode 100644 index 00000000..06fc8e7d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0404.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0404 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3118. -/ +theorem bounds_12_3118 : exactInterval 12 3118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3118 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3118) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3118 : oddCount 3118 12 = 6 ∧ acceleratedOrbit 12 3118 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3118 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3118) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3118.1, data_12_3118.2] + +/-- Complete interval computation for depth 12, residue 3119. -/ +theorem bounds_12_3119 : exactInterval 12 3119 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3119 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3119) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3119 : oddCount 3119 12 = 7 ∧ acceleratedOrbit 12 3119 = 1666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3119 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3119) = 3 ^ 7 * m + 1666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3119.1, data_12_3119.2] + +/-- Complete interval computation for depth 12, residue 3120. -/ +theorem bounds_12_3120 : exactInterval 12 3120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3120 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3120) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3120 : oddCount 3120 12 = 5 ∧ acceleratedOrbit 12 3120 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3120 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3120) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3120.1, data_12_3120.2] + +/-- Complete interval computation for depth 12, residue 3121. -/ +theorem bounds_12_3121 : exactInterval 12 3121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3121 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3121) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3121 : oddCount 3121 12 = 6 ∧ acceleratedOrbit 12 3121 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3121 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3121) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3121.1, data_12_3121.2] + +/-- Complete interval computation for depth 12, residue 3122. -/ +theorem bounds_12_3122 : exactInterval 12 3122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3122 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3122) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3122 : oddCount 3122 12 = 6 ∧ acceleratedOrbit 12 3122 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3122 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3122) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3122.1, data_12_3122.2] + +/-- Complete interval computation for depth 12, residue 3123. -/ +theorem bounds_12_3123 : exactInterval 12 3123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3123 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3123) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3123 : oddCount 3123 12 = 6 ∧ acceleratedOrbit 12 3123 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3123 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3123) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3123.1, data_12_3123.2] + +/-- Complete interval computation for depth 12, residue 3124. -/ +theorem bounds_12_3124 : exactInterval 12 3124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3124 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3124) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3124 : oddCount 3124 12 = 5 ∧ acceleratedOrbit 12 3124 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3124 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3124) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3124.1, data_12_3124.2] + +/-- Complete interval computation for depth 12, residue 3125. -/ +theorem bounds_12_3125 : exactInterval 12 3125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3125 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3125) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3125 : oddCount 3125 12 = 5 ∧ acceleratedOrbit 12 3125 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3125 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3125) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3125.1, data_12_3125.2] + +/-- Complete interval computation for depth 12, residue 3126. -/ +theorem bounds_12_3126 : exactInterval 12 3126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3126 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3126) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3126 : oddCount 3126 12 = 8 ∧ acceleratedOrbit 12 3126 = 5012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3126 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3126) = 3 ^ 8 * m + 5012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3126.1, data_12_3126.2] + +/-- Complete interval computation for depth 12, residue 3127. -/ +theorem bounds_12_3127 : exactInterval 12 3127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3127 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3127) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3127 : oddCount 3127 12 = 8 ∧ acceleratedOrbit 12 3127 = 5012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3127 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3127) = 3 ^ 8 * m + 5012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3127.1, data_12_3127.2] + +/-- Complete interval computation for depth 12, residue 3128. -/ +theorem bounds_12_3128 : exactInterval 12 3128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3128 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3128) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3128 : oddCount 3128 12 = 4 ∧ acceleratedOrbit 12 3128 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3128 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3128) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3128.1, data_12_3128.2] + +/-- Complete interval computation for depth 12, residue 3129. -/ +theorem bounds_12_3129 : exactInterval 12 3129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3129 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3129) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3129 : oddCount 3129 12 = 7 ∧ acceleratedOrbit 12 3129 = 1673 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3129 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3129) = 3 ^ 7 * m + 1673 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3129.1, data_12_3129.2] + +/-- Complete interval computation for depth 12, residue 3130. -/ +theorem bounds_12_3130 : exactInterval 12 3130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3130 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3130) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3130 : oddCount 3130 12 = 4 ∧ acceleratedOrbit 12 3130 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3130 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3130) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3130.1, data_12_3130.2] + +/-- Complete interval computation for depth 12, residue 3131. -/ +theorem bounds_12_3131 : exactInterval 12 3131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3131 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3131) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3131 : oddCount 3131 12 = 8 ∧ acceleratedOrbit 12 3131 = 5021 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3131 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3131) = 3 ^ 8 * m + 5021 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3131.1, data_12_3131.2] + +/-- Complete interval computation for depth 12, residue 3132. -/ +theorem bounds_12_3132 : exactInterval 12 3132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3132 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3132) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3132 : oddCount 3132 12 = 4 ∧ acceleratedOrbit 12 3132 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3132 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3132) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3132.1, data_12_3132.2] + +end Collatz.Research.StoppingAtlas.Batch0404 From 9689dcabd6ffdad843f799d42f47c263ddc18ac4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:09 +0530 Subject: [PATCH 0405/1001] proof: certify atlas Batch0405 (12:3133 to 12:3147) --- Collatz/Research/StoppingAtlas/Batch0405.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0405.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0405.lean b/Collatz/Research/StoppingAtlas/Batch0405.lean new file mode 100644 index 00000000..d51b06a2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0405.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0405 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3133. -/ +theorem bounds_12_3133 : exactInterval 12 3133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3133 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3133) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3133 : oddCount 3133 12 = 4 ∧ acceleratedOrbit 12 3133 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3133 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3133) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3133.1, data_12_3133.2] + +/-- Complete interval computation for depth 12, residue 3134. -/ +theorem bounds_12_3134 : exactInterval 12 3134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3134 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3134) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3134 : oddCount 3134 12 = 8 ∧ acceleratedOrbit 12 3134 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3134 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3134) = 3 ^ 8 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3134.1, data_12_3134.2] + +/-- Complete interval computation for depth 12, residue 3135. -/ +theorem bounds_12_3135 : exactInterval 12 3135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3135 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3135) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3135 : oddCount 3135 12 = 8 ∧ acceleratedOrbit 12 3135 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3135 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3135) = 3 ^ 8 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3135.1, data_12_3135.2] + +/-- Complete interval computation for depth 12, residue 3136. -/ +theorem bounds_12_3136 : exactInterval 12 3136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3136 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3136) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3136 : oddCount 3136 12 = 2 ∧ acceleratedOrbit 12 3136 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3136 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3136) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3136.1, data_12_3136.2] + +/-- Complete interval computation for depth 12, residue 3137. -/ +theorem bounds_12_3137 : exactInterval 12 3137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3137 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3137) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3137 : oddCount 3137 12 = 6 ∧ acceleratedOrbit 12 3137 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3137 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3137) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3137.1, data_12_3137.2] + +/-- Complete interval computation for depth 12, residue 3138. -/ +theorem bounds_12_3138 : exactInterval 12 3138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3138 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3138) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3138 : oddCount 3138 12 = 6 ∧ acceleratedOrbit 12 3138 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3138 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3138) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3138.1, data_12_3138.2] + +/-- Complete interval computation for depth 12, residue 3139. -/ +theorem bounds_12_3139 : exactInterval 12 3139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3139 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3139) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3139 : oddCount 3139 12 = 6 ∧ acceleratedOrbit 12 3139 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3139 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3139) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3139.1, data_12_3139.2] + +/-- Complete interval computation for depth 12, residue 3140. -/ +theorem bounds_12_3140 : exactInterval 12 3140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3140 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3140) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3140 : oddCount 3140 12 = 5 ∧ acceleratedOrbit 12 3140 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3140 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3140) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3140.1, data_12_3140.2] + +/-- Complete interval computation for depth 12, residue 3141. -/ +theorem bounds_12_3141 : exactInterval 12 3141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3141 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3141) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3141 : oddCount 3141 12 = 5 ∧ acceleratedOrbit 12 3141 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3141 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3141) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3141.1, data_12_3141.2] + +/-- Complete interval computation for depth 12, residue 3142. -/ +theorem bounds_12_3142 : exactInterval 12 3142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3142 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3142) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3142 : oddCount 3142 12 = 5 ∧ acceleratedOrbit 12 3142 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3142 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3142) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3142.1, data_12_3142.2] + +/-- Complete interval computation for depth 12, residue 3143. -/ +theorem bounds_12_3143 : exactInterval 12 3143 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3143 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3143) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3143 : oddCount 3143 12 = 7 ∧ acceleratedOrbit 12 3143 = 1679 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3143 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3143) = 3 ^ 7 * m + 1679 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3143.1, data_12_3143.2] + +/-- Complete interval computation for depth 12, residue 3144. -/ +theorem bounds_12_3144 : exactInterval 12 3144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3144 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3144) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3144 : oddCount 3144 12 = 6 ∧ acceleratedOrbit 12 3144 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3144 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3144) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3144.1, data_12_3144.2] + +/-- Complete interval computation for depth 12, residue 3145. -/ +theorem bounds_12_3145 : exactInterval 12 3145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3145 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3145) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3145 : oddCount 3145 12 = 8 ∧ acceleratedOrbit 12 3145 = 5042 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3145 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3145) = 3 ^ 8 * m + 5042 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3145.1, data_12_3145.2] + +/-- Complete interval computation for depth 12, residue 3146. -/ +theorem bounds_12_3146 : exactInterval 12 3146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3146 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3146) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3146 : oddCount 3146 12 = 6 ∧ acceleratedOrbit 12 3146 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3146 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3146) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3146.1, data_12_3146.2] + +/-- Complete interval computation for depth 12, residue 3147. -/ +theorem bounds_12_3147 : exactInterval 12 3147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3147 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3147) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3147 : oddCount 3147 12 = 5 ∧ acceleratedOrbit 12 3147 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3147 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3147) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3147.1, data_12_3147.2] + +end Collatz.Research.StoppingAtlas.Batch0405 From 5a92454478b9d5c47d6d990f01c3e56598aa567d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:09 +0530 Subject: [PATCH 0406/1001] proof: certify atlas Batch0406 (12:3148 to 12:3163) --- Collatz/Research/StoppingAtlas/Batch0406.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0406.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0406.lean b/Collatz/Research/StoppingAtlas/Batch0406.lean new file mode 100644 index 00000000..516c17df --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0406.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0406 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3148. -/ +theorem bounds_12_3148 : exactInterval 12 3148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3148 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3148) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3148 : oddCount 3148 12 = 6 ∧ acceleratedOrbit 12 3148 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3148 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3148) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3148.1, data_12_3148.2] + +/-- Complete interval computation for depth 12, residue 3149. -/ +theorem bounds_12_3149 : exactInterval 12 3149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3149 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3149) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3149 : oddCount 3149 12 = 6 ∧ acceleratedOrbit 12 3149 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3149 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3149) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3149.1, data_12_3149.2] + +/-- Complete interval computation for depth 12, residue 3150. -/ +theorem bounds_12_3150 : exactInterval 12 3150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3150 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3150) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3150 : oddCount 3150 12 = 5 ∧ acceleratedOrbit 12 3150 = 187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3150 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3150) = 3 ^ 5 * m + 187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3150.1, data_12_3150.2] + +/-- Complete interval computation for depth 12, residue 3151. -/ +theorem bounds_12_3151 : exactInterval 12 3151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3151 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3151) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3151 : oddCount 3151 12 = 5 ∧ acceleratedOrbit 12 3151 = 187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3151 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3151) = 3 ^ 5 * m + 187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3151.1, data_12_3151.2] + +/-- Complete interval computation for depth 12, residue 3152. -/ +theorem bounds_12_3152 : exactInterval 12 3152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3152 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3152) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3152 : oddCount 3152 12 = 2 ∧ acceleratedOrbit 12 3152 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3152 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3152) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3152.1, data_12_3152.2] + +/-- Complete interval computation for depth 12, residue 3153. -/ +theorem bounds_12_3153 : exactInterval 12 3153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3153 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3153) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3153 : oddCount 3153 12 = 6 ∧ acceleratedOrbit 12 3153 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3153 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3153) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3153.1, data_12_3153.2] + +/-- Complete interval computation for depth 12, residue 3154. -/ +theorem bounds_12_3154 : exactInterval 12 3154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3154 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3154) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3154 : oddCount 3154 12 = 9 ∧ acceleratedOrbit 12 3154 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3154 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3154) = 3 ^ 9 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3154.1, data_12_3154.2] + +/-- Complete interval computation for depth 12, residue 3155. -/ +theorem bounds_12_3155 : exactInterval 12 3155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3155 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3155) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3155 : oddCount 3155 12 = 9 ∧ acceleratedOrbit 12 3155 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3155 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3155) = 3 ^ 9 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3155.1, data_12_3155.2] + +/-- Complete interval computation for depth 12, residue 3156. -/ +theorem bounds_12_3156 : exactInterval 12 3156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3156 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3156) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3156 : oddCount 3156 12 = 2 ∧ acceleratedOrbit 12 3156 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3156 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3156) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3156.1, data_12_3156.2] + +/-- Complete interval computation for depth 12, residue 3157. -/ +theorem bounds_12_3157 : exactInterval 12 3157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3157 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3157) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3157 : oddCount 3157 12 = 2 ∧ acceleratedOrbit 12 3157 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3157 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3157) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3157.1, data_12_3157.2] + +/-- Complete interval computation for depth 12, residue 3158. -/ +theorem bounds_12_3158 : exactInterval 12 3158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3158 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3158) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3158 : oddCount 3158 12 = 5 ∧ acceleratedOrbit 12 3158 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3158 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3158) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3158.1, data_12_3158.2] + +/-- Complete interval computation for depth 12, residue 3159. -/ +theorem bounds_12_3159 : exactInterval 12 3159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3159 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3159) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3159 : oddCount 3159 12 = 5 ∧ acceleratedOrbit 12 3159 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3159 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3159) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3159.1, data_12_3159.2] + +/-- Complete interval computation for depth 12, residue 3160. -/ +theorem bounds_12_3160 : exactInterval 12 3160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3160 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3160) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3160 : oddCount 3160 12 = 6 ∧ acceleratedOrbit 12 3160 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3160 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3160) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3160.1, data_12_3160.2] + +/-- Complete interval computation for depth 12, residue 3161. -/ +theorem bounds_12_3161 : exactInterval 12 3161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3161 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3161) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3161 : oddCount 3161 12 = 7 ∧ acceleratedOrbit 12 3161 = 1691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3161 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3161) = 3 ^ 7 * m + 1691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3161.1, data_12_3161.2] + +/-- Complete interval computation for depth 12, residue 3162. -/ +theorem bounds_12_3162 : exactInterval 12 3162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3162 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3162) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3162 : oddCount 3162 12 = 6 ∧ acceleratedOrbit 12 3162 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3162 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3162) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3162.1, data_12_3162.2] + +/-- Complete interval computation for depth 12, residue 3163. -/ +theorem bounds_12_3163 : exactInterval 12 3163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3163 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3163) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3163 : oddCount 3163 12 = 8 ∧ acceleratedOrbit 12 3163 = 5069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3163 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3163) = 3 ^ 8 * m + 5069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3163.1, data_12_3163.2] + +end Collatz.Research.StoppingAtlas.Batch0406 From c462d75e68e2b61343e5d68aadf3a7eb0dd53484 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:09 +0530 Subject: [PATCH 0407/1001] proof: certify atlas Batch0407 (12:3164 to 12:3178) --- Collatz/Research/StoppingAtlas/Batch0407.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0407.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0407.lean b/Collatz/Research/StoppingAtlas/Batch0407.lean new file mode 100644 index 00000000..015935ca --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0407.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0407 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3164. -/ +theorem bounds_12_3164 : exactInterval 12 3164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3164 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3164) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3164 : oddCount 3164 12 = 6 ∧ acceleratedOrbit 12 3164 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3164 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3164) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3164.1, data_12_3164.2] + +/-- Complete interval computation for depth 12, residue 3165. -/ +theorem bounds_12_3165 : exactInterval 12 3165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3165 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3165) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3165 : oddCount 3165 12 = 6 ∧ acceleratedOrbit 12 3165 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3165 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3165) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3165.1, data_12_3165.2] + +/-- Complete interval computation for depth 12, residue 3166. -/ +theorem bounds_12_3166 : exactInterval 12 3166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3166 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3166) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3166 : oddCount 3166 12 = 9 ∧ acceleratedOrbit 12 3166 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3166 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3166) = 3 ^ 9 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3166.1, data_12_3166.2] + +/-- Complete interval computation for depth 12, residue 3167. -/ +theorem bounds_12_3167 : exactInterval 12 3167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3167 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3167) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3167 : oddCount 3167 12 = 9 ∧ acceleratedOrbit 12 3167 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3167 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3167) = 3 ^ 9 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3167.1, data_12_3167.2] + +/-- Complete interval computation for depth 12, residue 3168. -/ +theorem bounds_12_3168 : exactInterval 12 3168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3168 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3168) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3168 : oddCount 3168 12 = 2 ∧ acceleratedOrbit 12 3168 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3168 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3168) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3168.1, data_12_3168.2] + +/-- Complete interval computation for depth 12, residue 3169. -/ +theorem bounds_12_3169 : exactInterval 12 3169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3169 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3169) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3169 : oddCount 3169 12 = 7 ∧ acceleratedOrbit 12 3169 = 1694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3169 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3169) = 3 ^ 7 * m + 1694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3169.1, data_12_3169.2] + +/-- Complete interval computation for depth 12, residue 3170. -/ +theorem bounds_12_3170 : exactInterval 12 3170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3170 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3170) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3170 : oddCount 3170 12 = 7 ∧ acceleratedOrbit 12 3170 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3170 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3170) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3170.1, data_12_3170.2] + +/-- Complete interval computation for depth 12, residue 3171. -/ +theorem bounds_12_3171 : exactInterval 12 3171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3171 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3171) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3171 : oddCount 3171 12 = 7 ∧ acceleratedOrbit 12 3171 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3171 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3171) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3171.1, data_12_3171.2] + +/-- Complete interval computation for depth 12, residue 3172. -/ +theorem bounds_12_3172 : exactInterval 12 3172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3172 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3172) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3172 : oddCount 3172 12 = 7 ∧ acceleratedOrbit 12 3172 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3172 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3172) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3172.1, data_12_3172.2] + +/-- Complete interval computation for depth 12, residue 3173. -/ +theorem bounds_12_3173 : exactInterval 12 3173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3173 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3173) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3173 : oddCount 3173 12 = 7 ∧ acceleratedOrbit 12 3173 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3173 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3173) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3173.1, data_12_3173.2] + +/-- Complete interval computation for depth 12, residue 3174. -/ +theorem bounds_12_3174 : exactInterval 12 3174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3174 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3174) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3174 : oddCount 3174 12 = 7 ∧ acceleratedOrbit 12 3174 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3174 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3174) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3174.1, data_12_3174.2] + +/-- Complete interval computation for depth 12, residue 3175. -/ +theorem bounds_12_3175 : exactInterval 12 3175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3175 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3175) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3175 : oddCount 3175 12 = 10 ∧ acceleratedOrbit 12 3175 = 45791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3175 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3175) = 3 ^ 10 * m + 45791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3175.1, data_12_3175.2] + +/-- Complete interval computation for depth 12, residue 3176. -/ +theorem bounds_12_3176 : exactInterval 12 3176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3176 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3176) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3176 : oddCount 3176 12 = 2 ∧ acceleratedOrbit 12 3176 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3176 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3176) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3176.1, data_12_3176.2] + +/-- Complete interval computation for depth 12, residue 3177. -/ +theorem bounds_12_3177 : exactInterval 12 3177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3177 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3177) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3177 : oddCount 3177 12 = 8 ∧ acceleratedOrbit 12 3177 = 5093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3177 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3177) = 3 ^ 8 * m + 5093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3177.1, data_12_3177.2] + +/-- Complete interval computation for depth 12, residue 3178. -/ +theorem bounds_12_3178 : exactInterval 12 3178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3178 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3178) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3178 : oddCount 3178 12 = 2 ∧ acceleratedOrbit 12 3178 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3178 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3178) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3178.1, data_12_3178.2] + +end Collatz.Research.StoppingAtlas.Batch0407 From 0421e0ea27a27125c90c9fd5ea5454ffede274a9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:10 +0530 Subject: [PATCH 0408/1001] proof: certify atlas Batch0408 (12:3179 to 12:3193) --- Collatz/Research/StoppingAtlas/Batch0408.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0408.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0408.lean b/Collatz/Research/StoppingAtlas/Batch0408.lean new file mode 100644 index 00000000..4b398596 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0408.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0408 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3179. -/ +theorem bounds_12_3179 : exactInterval 12 3179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3179 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3179) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3179 : oddCount 3179 12 = 8 ∧ acceleratedOrbit 12 3179 = 5096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3179 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3179) = 3 ^ 8 * m + 5096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3179.1, data_12_3179.2] + +/-- Complete interval computation for depth 12, residue 3180. -/ +theorem bounds_12_3180 : exactInterval 12 3180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3180 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3180) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3180 : oddCount 3180 12 = 9 ∧ acceleratedOrbit 12 3180 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3180 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3180) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3180.1, data_12_3180.2] + +/-- Complete interval computation for depth 12, residue 3181. -/ +theorem bounds_12_3181 : exactInterval 12 3181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3181 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3181) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3181 : oddCount 3181 12 = 9 ∧ acceleratedOrbit 12 3181 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3181 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3181) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3181.1, data_12_3181.2] + +/-- Complete interval computation for depth 12, residue 3182. -/ +theorem bounds_12_3182 : exactInterval 12 3182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3182 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3182) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3182 : oddCount 3182 12 = 9 ∧ acceleratedOrbit 12 3182 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3182 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3182) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3182.1, data_12_3182.2] + +/-- Complete interval computation for depth 12, residue 3183. -/ +theorem bounds_12_3183 : exactInterval 12 3183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3183 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3183) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3183 : oddCount 3183 12 = 9 ∧ acceleratedOrbit 12 3183 = 15302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3183 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3183) = 3 ^ 9 * m + 15302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3183.1, data_12_3183.2] + +/-- Complete interval computation for depth 12, residue 3184. -/ +theorem bounds_12_3184 : exactInterval 12 3184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3184 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3184) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3184 : oddCount 3184 12 = 5 ∧ acceleratedOrbit 12 3184 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3184 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3184) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3184.1, data_12_3184.2] + +/-- Complete interval computation for depth 12, residue 3185. -/ +theorem bounds_12_3185 : exactInterval 12 3185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3185 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3185) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3185 : oddCount 3185 12 = 2 ∧ acceleratedOrbit 12 3185 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3185 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3185) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3185.1, data_12_3185.2] + +/-- Complete interval computation for depth 12, residue 3186. -/ +theorem bounds_12_3186 : exactInterval 12 3186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3186 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3186) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3186 : oddCount 3186 12 = 6 ∧ acceleratedOrbit 12 3186 = 568 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3186 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3186) = 3 ^ 6 * m + 568 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3186.1, data_12_3186.2] + +/-- Complete interval computation for depth 12, residue 3187. -/ +theorem bounds_12_3187 : exactInterval 12 3187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3187 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3187) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3187 : oddCount 3187 12 = 6 ∧ acceleratedOrbit 12 3187 = 568 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3187 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3187) = 3 ^ 6 * m + 568 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3187.1, data_12_3187.2] + +/-- Complete interval computation for depth 12, residue 3188. -/ +theorem bounds_12_3188 : exactInterval 12 3188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3188 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3188) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3188 : oddCount 3188 12 = 5 ∧ acceleratedOrbit 12 3188 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3188 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3188) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3188.1, data_12_3188.2] + +/-- Complete interval computation for depth 12, residue 3189. -/ +theorem bounds_12_3189 : exactInterval 12 3189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3189 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3189) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3189 : oddCount 3189 12 = 5 ∧ acceleratedOrbit 12 3189 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3189 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3189) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3189.1, data_12_3189.2] + +/-- Complete interval computation for depth 12, residue 3190. -/ +theorem bounds_12_3190 : exactInterval 12 3190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3190 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3190) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3190 : oddCount 3190 12 = 6 ∧ acceleratedOrbit 12 3190 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3190 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3190) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3190.1, data_12_3190.2] + +/-- Complete interval computation for depth 12, residue 3191. -/ +theorem bounds_12_3191 : exactInterval 12 3191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3191 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3191) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3191 : oddCount 3191 12 = 6 ∧ acceleratedOrbit 12 3191 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3191 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3191) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3191.1, data_12_3191.2] + +/-- Complete interval computation for depth 12, residue 3192. -/ +theorem bounds_12_3192 : exactInterval 12 3192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3192 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3192) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3192 : oddCount 3192 12 = 5 ∧ acceleratedOrbit 12 3192 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3192 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3192) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3192.1, data_12_3192.2] + +/-- Complete interval computation for depth 12, residue 3193. -/ +theorem bounds_12_3193 : exactInterval 12 3193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3193 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3193) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3193 : oddCount 3193 12 = 7 ∧ acceleratedOrbit 12 3193 = 1706 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3193 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3193) = 3 ^ 7 * m + 1706 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3193.1, data_12_3193.2] + +end Collatz.Research.StoppingAtlas.Batch0408 From 681d46baeb0b766363d7bbb107922878c1b323f5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:10 +0530 Subject: [PATCH 0409/1001] proof: certify atlas Batch0409 (12:3194 to 12:3209) --- Collatz/Research/StoppingAtlas/Batch0409.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0409.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0409.lean b/Collatz/Research/StoppingAtlas/Batch0409.lean new file mode 100644 index 00000000..966111aa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0409.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0409 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3194. -/ +theorem bounds_12_3194 : exactInterval 12 3194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3194 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3194) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3194 : oddCount 3194 12 = 5 ∧ acceleratedOrbit 12 3194 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3194 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3194) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3194.1, data_12_3194.2] + +/-- Complete interval computation for depth 12, residue 3195. -/ +theorem bounds_12_3195 : exactInterval 12 3195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3195 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3195) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3195 : oddCount 3195 12 = 6 ∧ acceleratedOrbit 12 3195 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3195 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3195) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3195.1, data_12_3195.2] + +/-- Complete interval computation for depth 12, residue 3196. -/ +theorem bounds_12_3196 : exactInterval 12 3196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3196 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3196) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3196 : oddCount 3196 12 = 7 ∧ acceleratedOrbit 12 3196 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3196 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3196) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3196.1, data_12_3196.2] + +/-- Complete interval computation for depth 12, residue 3197. -/ +theorem bounds_12_3197 : exactInterval 12 3197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3197 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3197) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3197 : oddCount 3197 12 = 7 ∧ acceleratedOrbit 12 3197 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3197 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3197) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3197.1, data_12_3197.2] + +/-- Complete interval computation for depth 12, residue 3198. -/ +theorem bounds_12_3198 : exactInterval 12 3198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3198 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3198) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3198 : oddCount 3198 12 = 7 ∧ acceleratedOrbit 12 3198 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3198 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3198) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3198.1, data_12_3198.2] + +/-- Complete interval computation for depth 12, residue 3199. -/ +theorem bounds_12_3199 : exactInterval 12 3199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3199 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3199) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3199 : oddCount 3199 12 = 10 ∧ acceleratedOrbit 12 3199 = 46133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3199 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3199) = 3 ^ 10 * m + 46133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3199.1, data_12_3199.2] + +/-- Complete interval computation for depth 12, residue 3200. -/ +theorem bounds_12_3200 : exactInterval 12 3200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3200 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3200) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3200 : oddCount 3200 12 = 3 ∧ acceleratedOrbit 12 3200 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3200 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3200) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3200.1, data_12_3200.2] + +/-- Complete interval computation for depth 12, residue 3201. -/ +theorem bounds_12_3201 : exactInterval 12 3201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3201 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3201) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3201 : oddCount 3201 12 = 7 ∧ acceleratedOrbit 12 3201 = 1711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3201 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3201) = 3 ^ 7 * m + 1711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3201.1, data_12_3201.2] + +/-- Complete interval computation for depth 12, residue 3202. -/ +theorem bounds_12_3202 : exactInterval 12 3202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3202 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3202) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3202 : oddCount 3202 12 = 5 ∧ acceleratedOrbit 12 3202 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3202 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3202) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3202.1, data_12_3202.2] + +/-- Complete interval computation for depth 12, residue 3203. -/ +theorem bounds_12_3203 : exactInterval 12 3203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3203 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3203) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3203 : oddCount 3203 12 = 5 ∧ acceleratedOrbit 12 3203 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3203 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3203) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3203.1, data_12_3203.2] + +/-- Complete interval computation for depth 12, residue 3204. -/ +theorem bounds_12_3204 : exactInterval 12 3204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3204 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3204) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3204 : oddCount 3204 12 = 5 ∧ acceleratedOrbit 12 3204 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3204 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3204) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3204.1, data_12_3204.2] + +/-- Complete interval computation for depth 12, residue 3205. -/ +theorem bounds_12_3205 : exactInterval 12 3205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3205 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3205) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3205 : oddCount 3205 12 = 5 ∧ acceleratedOrbit 12 3205 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3205 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3205) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3205.1, data_12_3205.2] + +/-- Complete interval computation for depth 12, residue 3206. -/ +theorem bounds_12_3206 : exactInterval 12 3206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3206 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3206) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3206 : oddCount 3206 12 = 5 ∧ acceleratedOrbit 12 3206 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3206 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3206) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3206.1, data_12_3206.2] + +/-- Complete interval computation for depth 12, residue 3207. -/ +theorem bounds_12_3207 : exactInterval 12 3207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3207 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3207) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3207 : oddCount 3207 12 = 7 ∧ acceleratedOrbit 12 3207 = 1714 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3207 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3207) = 3 ^ 7 * m + 1714 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3207.1, data_12_3207.2] + +/-- Complete interval computation for depth 12, residue 3208. -/ +theorem bounds_12_3208 : exactInterval 12 3208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3208 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3208) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3208 : oddCount 3208 12 = 4 ∧ acceleratedOrbit 12 3208 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3208 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3208) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3208.1, data_12_3208.2] + +/-- Complete interval computation for depth 12, residue 3209. -/ +theorem bounds_12_3209 : exactInterval 12 3209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3209 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3209) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3209 : oddCount 3209 12 = 9 ∧ acceleratedOrbit 12 3209 = 15430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3209 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3209) = 3 ^ 9 * m + 15430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3209.1, data_12_3209.2] + +end Collatz.Research.StoppingAtlas.Batch0409 From 9f5d94d8bf30af46fecb4908ccadee89dbbc1bb2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:11 +0530 Subject: [PATCH 0410/1001] proof: certify atlas Batch0410 (12:3210 to 12:3224) --- Collatz/Research/StoppingAtlas/Batch0410.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0410.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0410.lean b/Collatz/Research/StoppingAtlas/Batch0410.lean new file mode 100644 index 00000000..eb904efd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0410.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0410 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3210. -/ +theorem bounds_12_3210 : exactInterval 12 3210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3210 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3210) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3210 : oddCount 3210 12 = 4 ∧ acceleratedOrbit 12 3210 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3210 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3210) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3210.1, data_12_3210.2] + +/-- Complete interval computation for depth 12, residue 3211. -/ +theorem bounds_12_3211 : exactInterval 12 3211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3211 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3211) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3211 : oddCount 3211 12 = 6 ∧ acceleratedOrbit 12 3211 = 572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3211 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3211) = 3 ^ 6 * m + 572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3211.1, data_12_3211.2] + +/-- Complete interval computation for depth 12, residue 3212. -/ +theorem bounds_12_3212 : exactInterval 12 3212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3212 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3212) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3212 : oddCount 3212 12 = 4 ∧ acceleratedOrbit 12 3212 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3212 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3212) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3212.1, data_12_3212.2] + +/-- Complete interval computation for depth 12, residue 3213. -/ +theorem bounds_12_3213 : exactInterval 12 3213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3213 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3213) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3213 : oddCount 3213 12 = 4 ∧ acceleratedOrbit 12 3213 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3213 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3213) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3213.1, data_12_3213.2] + +/-- Complete interval computation for depth 12, residue 3214. -/ +theorem bounds_12_3214 : exactInterval 12 3214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3214 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3214) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3214 : oddCount 3214 12 = 7 ∧ acceleratedOrbit 12 3214 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3214 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3214) = 3 ^ 7 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3214.1, data_12_3214.2] + +/-- Complete interval computation for depth 12, residue 3215. -/ +theorem bounds_12_3215 : exactInterval 12 3215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3215 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3215) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3215 : oddCount 3215 12 = 7 ∧ acceleratedOrbit 12 3215 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3215 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3215) = 3 ^ 7 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3215.1, data_12_3215.2] + +/-- Complete interval computation for depth 12, residue 3216. -/ +theorem bounds_12_3216 : exactInterval 12 3216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3216 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3216) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3216 : oddCount 3216 12 = 4 ∧ acceleratedOrbit 12 3216 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3216 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3216) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3216.1, data_12_3216.2] + +/-- Complete interval computation for depth 12, residue 3217. -/ +theorem bounds_12_3217 : exactInterval 12 3217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3217 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3217) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3217 : oddCount 3217 12 = 7 ∧ acceleratedOrbit 12 3217 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3217 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3217) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3217.1, data_12_3217.2] + +/-- Complete interval computation for depth 12, residue 3218. -/ +theorem bounds_12_3218 : exactInterval 12 3218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3218 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3218) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3218 : oddCount 3218 12 = 7 ∧ acceleratedOrbit 12 3218 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3218 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3218) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3218.1, data_12_3218.2] + +/-- Complete interval computation for depth 12, residue 3219. -/ +theorem bounds_12_3219 : exactInterval 12 3219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3219 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3219) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3219 : oddCount 3219 12 = 7 ∧ acceleratedOrbit 12 3219 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3219 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3219) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3219.1, data_12_3219.2] + +/-- Complete interval computation for depth 12, residue 3220. -/ +theorem bounds_12_3220 : exactInterval 12 3220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3220 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3220) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3220 : oddCount 3220 12 = 4 ∧ acceleratedOrbit 12 3220 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3220 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3220) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3220.1, data_12_3220.2] + +/-- Complete interval computation for depth 12, residue 3221. -/ +theorem bounds_12_3221 : exactInterval 12 3221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3221 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3221) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3221 : oddCount 3221 12 = 4 ∧ acceleratedOrbit 12 3221 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3221 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3221) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3221.1, data_12_3221.2] + +/-- Complete interval computation for depth 12, residue 3222. -/ +theorem bounds_12_3222 : exactInterval 12 3222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3222 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3222) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3222 : oddCount 3222 12 = 4 ∧ acceleratedOrbit 12 3222 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3222 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3222) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3222.1, data_12_3222.2] + +/-- Complete interval computation for depth 12, residue 3223. -/ +theorem bounds_12_3223 : exactInterval 12 3223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3223 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3223) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3223 : oddCount 3223 12 = 4 ∧ acceleratedOrbit 12 3223 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3223 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3223) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3223.1, data_12_3223.2] + +/-- Complete interval computation for depth 12, residue 3224. -/ +theorem bounds_12_3224 : exactInterval 12 3224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3224 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3224) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3224 : oddCount 3224 12 = 4 ∧ acceleratedOrbit 12 3224 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3224 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3224) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3224.1, data_12_3224.2] + +end Collatz.Research.StoppingAtlas.Batch0410 From fbeff78c1443e04c238b305b7c15bc405b90f817 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:11 +0530 Subject: [PATCH 0411/1001] proof: certify atlas Batch0411 (12:3225 to 12:3239) --- Collatz/Research/StoppingAtlas/Batch0411.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0411.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0411.lean b/Collatz/Research/StoppingAtlas/Batch0411.lean new file mode 100644 index 00000000..0996a5e1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0411.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0411 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3225. -/ +theorem bounds_12_3225 : exactInterval 12 3225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3225 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3225) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3225 : oddCount 3225 12 = 6 ∧ acceleratedOrbit 12 3225 = 575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3225 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3225) = 3 ^ 6 * m + 575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3225.1, data_12_3225.2] + +/-- Complete interval computation for depth 12, residue 3226. -/ +theorem bounds_12_3226 : exactInterval 12 3226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3226 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3226) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3226 : oddCount 3226 12 = 4 ∧ acceleratedOrbit 12 3226 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3226 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3226) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3226.1, data_12_3226.2] + +/-- Complete interval computation for depth 12, residue 3227. -/ +theorem bounds_12_3227 : exactInterval 12 3227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3227 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3227) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3227 : oddCount 3227 12 = 9 ∧ acceleratedOrbit 12 3227 = 15515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3227 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3227) = 3 ^ 9 * m + 15515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3227.1, data_12_3227.2] + +/-- Complete interval computation for depth 12, residue 3228. -/ +theorem bounds_12_3228 : exactInterval 12 3228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3228 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3228) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3228 : oddCount 3228 12 = 7 ∧ acceleratedOrbit 12 3228 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3228 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3228) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3228.1, data_12_3228.2] + +/-- Complete interval computation for depth 12, residue 3229. -/ +theorem bounds_12_3229 : exactInterval 12 3229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3229 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3229) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3229 : oddCount 3229 12 = 7 ∧ acceleratedOrbit 12 3229 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3229 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3229) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3229.1, data_12_3229.2] + +/-- Complete interval computation for depth 12, residue 3230. -/ +theorem bounds_12_3230 : exactInterval 12 3230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3230 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3230) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3230 : oddCount 3230 12 = 7 ∧ acceleratedOrbit 12 3230 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3230 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3230) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3230.1, data_12_3230.2] + +/-- Complete interval computation for depth 12, residue 3231. -/ +theorem bounds_12_3231 : exactInterval 12 3231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3231 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3231) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3231 : oddCount 3231 12 = 10 ∧ acceleratedOrbit 12 3231 = 46595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3231 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3231) = 3 ^ 10 * m + 46595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3231.1, data_12_3231.2] + +/-- Complete interval computation for depth 12, residue 3232. -/ +theorem bounds_12_3232 : exactInterval 12 3232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3232 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3232) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3232 : oddCount 3232 12 = 3 ∧ acceleratedOrbit 12 3232 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3232 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3232) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3232.1, data_12_3232.2] + +/-- Complete interval computation for depth 12, residue 3233. -/ +theorem bounds_12_3233 : exactInterval 12 3233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3233 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3233) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3233 : oddCount 3233 12 = 9 ∧ acceleratedOrbit 12 3233 = 15551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3233 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3233) = 3 ^ 9 * m + 15551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3233.1, data_12_3233.2] + +/-- Complete interval computation for depth 12, residue 3234. -/ +theorem bounds_12_3234 : exactInterval 12 3234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3234 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3234) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3234 : oddCount 3234 12 = 6 ∧ acceleratedOrbit 12 3234 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3234 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3234) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3234.1, data_12_3234.2] + +/-- Complete interval computation for depth 12, residue 3235. -/ +theorem bounds_12_3235 : exactInterval 12 3235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3235 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3235) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3235 : oddCount 3235 12 = 6 ∧ acceleratedOrbit 12 3235 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3235 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3235) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3235.1, data_12_3235.2] + +/-- Complete interval computation for depth 12, residue 3236. -/ +theorem bounds_12_3236 : exactInterval 12 3236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3236 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3236) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3236 : oddCount 3236 12 = 6 ∧ acceleratedOrbit 12 3236 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3236 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3236) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3236.1, data_12_3236.2] + +/-- Complete interval computation for depth 12, residue 3237. -/ +theorem bounds_12_3237 : exactInterval 12 3237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3237 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3237) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3237 : oddCount 3237 12 = 6 ∧ acceleratedOrbit 12 3237 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3237 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3237) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3237.1, data_12_3237.2] + +/-- Complete interval computation for depth 12, residue 3238. -/ +theorem bounds_12_3238 : exactInterval 12 3238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3238 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3238) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3238 : oddCount 3238 12 = 6 ∧ acceleratedOrbit 12 3238 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3238 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3238) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3238.1, data_12_3238.2] + +/-- Complete interval computation for depth 12, residue 3239. -/ +theorem bounds_12_3239 : exactInterval 12 3239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3239 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3239) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3239 : oddCount 3239 12 = 9 ∧ acceleratedOrbit 12 3239 = 15572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3239 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3239) = 3 ^ 9 * m + 15572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3239.1, data_12_3239.2] + +end Collatz.Research.StoppingAtlas.Batch0411 From 6e0f74dca5f29a1e45f03521ab61415d0944a680 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:11 +0530 Subject: [PATCH 0412/1001] proof: certify atlas Batch0412 (12:3240 to 12:3255) --- Collatz/Research/StoppingAtlas/Batch0412.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0412.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0412.lean b/Collatz/Research/StoppingAtlas/Batch0412.lean new file mode 100644 index 00000000..d36f4e9c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0412.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0412 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3240. -/ +theorem bounds_12_3240 : exactInterval 12 3240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3240 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3240) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3240 : oddCount 3240 12 = 3 ∧ acceleratedOrbit 12 3240 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3240 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3240) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3240.1, data_12_3240.2] + +/-- Complete interval computation for depth 12, residue 3241. -/ +theorem bounds_12_3241 : exactInterval 12 3241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3241 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3241) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3241 : oddCount 3241 12 = 8 ∧ acceleratedOrbit 12 3241 = 5194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3241 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3241) = 3 ^ 8 * m + 5194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3241.1, data_12_3241.2] + +/-- Complete interval computation for depth 12, residue 3242. -/ +theorem bounds_12_3242 : exactInterval 12 3242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3242 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3242) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3242 : oddCount 3242 12 = 3 ∧ acceleratedOrbit 12 3242 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3242 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3242) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3242.1, data_12_3242.2] + +/-- Complete interval computation for depth 12, residue 3243. -/ +theorem bounds_12_3243 : exactInterval 12 3243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3243 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3243) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3243 : oddCount 3243 12 = 6 ∧ acceleratedOrbit 12 3243 = 578 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3243 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3243) = 3 ^ 6 * m + 578 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3243.1, data_12_3243.2] + +/-- Complete interval computation for depth 12, residue 3244. -/ +theorem bounds_12_3244 : exactInterval 12 3244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3244 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3244) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3244 : oddCount 3244 12 = 5 ∧ acceleratedOrbit 12 3244 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3244 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3244) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3244.1, data_12_3244.2] + +/-- Complete interval computation for depth 12, residue 3245. -/ +theorem bounds_12_3245 : exactInterval 12 3245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3245 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3245) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3245 : oddCount 3245 12 = 5 ∧ acceleratedOrbit 12 3245 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3245 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3245) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3245.1, data_12_3245.2] + +/-- Complete interval computation for depth 12, residue 3246. -/ +theorem bounds_12_3246 : exactInterval 12 3246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3246 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3246) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3246 : oddCount 3246 12 = 5 ∧ acceleratedOrbit 12 3246 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3246 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3246) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3246.1, data_12_3246.2] + +/-- Complete interval computation for depth 12, residue 3247. -/ +theorem bounds_12_3247 : exactInterval 12 3247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3247 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3247) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3247 : oddCount 3247 12 = 8 ∧ acceleratedOrbit 12 3247 = 5204 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3247 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3247) = 3 ^ 8 * m + 5204 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3247.1, data_12_3247.2] + +/-- Complete interval computation for depth 12, residue 3248. -/ +theorem bounds_12_3248 : exactInterval 12 3248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3248 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3248) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3248 : oddCount 3248 12 = 4 ∧ acceleratedOrbit 12 3248 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3248 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3248) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3248.1, data_12_3248.2] + +/-- Complete interval computation for depth 12, residue 3249. -/ +theorem bounds_12_3249 : exactInterval 12 3249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3249 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3249) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3249 : oddCount 3249 12 = 6 ∧ acceleratedOrbit 12 3249 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3249 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3249) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3249.1, data_12_3249.2] + +/-- Complete interval computation for depth 12, residue 3250. -/ +theorem bounds_12_3250 : exactInterval 12 3250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3250 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3250) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3250 : oddCount 3250 12 = 6 ∧ acceleratedOrbit 12 3250 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3250 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3250) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3250.1, data_12_3250.2] + +/-- Complete interval computation for depth 12, residue 3251. -/ +theorem bounds_12_3251 : exactInterval 12 3251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3251 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3251) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3251 : oddCount 3251 12 = 6 ∧ acceleratedOrbit 12 3251 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3251 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3251) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3251.1, data_12_3251.2] + +/-- Complete interval computation for depth 12, residue 3252. -/ +theorem bounds_12_3252 : exactInterval 12 3252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3252 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3252) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3252 : oddCount 3252 12 = 4 ∧ acceleratedOrbit 12 3252 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3252 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3252) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3252.1, data_12_3252.2] + +/-- Complete interval computation for depth 12, residue 3253. -/ +theorem bounds_12_3253 : exactInterval 12 3253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3253 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3253) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3253 : oddCount 3253 12 = 4 ∧ acceleratedOrbit 12 3253 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3253 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3253) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3253.1, data_12_3253.2] + +/-- Complete interval computation for depth 12, residue 3254. -/ +theorem bounds_12_3254 : exactInterval 12 3254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3254 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3254) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3254 : oddCount 3254 12 = 7 ∧ acceleratedOrbit 12 3254 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3254 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3254) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3254.1, data_12_3254.2] + +/-- Complete interval computation for depth 12, residue 3255. -/ +theorem bounds_12_3255 : exactInterval 12 3255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3255 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3255) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3255 : oddCount 3255 12 = 7 ∧ acceleratedOrbit 12 3255 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3255 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3255) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3255.1, data_12_3255.2] + +end Collatz.Research.StoppingAtlas.Batch0412 From a4092397ae9d766dc795d86b49f40e3a7a3e6e48 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:11 +0530 Subject: [PATCH 0413/1001] proof: certify atlas Batch0413 (12:3256 to 12:3270) --- Collatz/Research/StoppingAtlas/Batch0413.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0413.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0413.lean b/Collatz/Research/StoppingAtlas/Batch0413.lean new file mode 100644 index 00000000..ccc7982f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0413.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0413 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3256. -/ +theorem bounds_12_3256 : exactInterval 12 3256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3256 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3256) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3256 : oddCount 3256 12 = 4 ∧ acceleratedOrbit 12 3256 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3256 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3256) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3256.1, data_12_3256.2] + +/-- Complete interval computation for depth 12, residue 3257. -/ +theorem bounds_12_3257 : exactInterval 12 3257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3257 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3257) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3257 : oddCount 3257 12 = 7 ∧ acceleratedOrbit 12 3257 = 1741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3257 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3257) = 3 ^ 7 * m + 1741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3257.1, data_12_3257.2] + +/-- Complete interval computation for depth 12, residue 3258. -/ +theorem bounds_12_3258 : exactInterval 12 3258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3258 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3258) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3258 : oddCount 3258 12 = 4 ∧ acceleratedOrbit 12 3258 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3258 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3258) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3258.1, data_12_3258.2] + +/-- Complete interval computation for depth 12, residue 3259. -/ +theorem bounds_12_3259 : exactInterval 12 3259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3259 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3259) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3259 : oddCount 3259 12 = 8 ∧ acceleratedOrbit 12 3259 = 5224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3259 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3259) = 3 ^ 8 * m + 5224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3259.1, data_12_3259.2] + +/-- Complete interval computation for depth 12, residue 3260. -/ +theorem bounds_12_3260 : exactInterval 12 3260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3260 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3260) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3260 : oddCount 3260 12 = 6 ∧ acceleratedOrbit 12 3260 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3260 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3260) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3260.1, data_12_3260.2] + +/-- Complete interval computation for depth 12, residue 3261. -/ +theorem bounds_12_3261 : exactInterval 12 3261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3261 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3261) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3261 : oddCount 3261 12 = 6 ∧ acceleratedOrbit 12 3261 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3261 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3261) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3261.1, data_12_3261.2] + +/-- Complete interval computation for depth 12, residue 3262. -/ +theorem bounds_12_3262 : exactInterval 12 3262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3262 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3262) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3262 : oddCount 3262 12 = 6 ∧ acceleratedOrbit 12 3262 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3262 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3262) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3262.1, data_12_3262.2] + +/-- Complete interval computation for depth 12, residue 3263. -/ +theorem bounds_12_3263 : exactInterval 12 3263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3263 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3263) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3263 : oddCount 3263 12 = 9 ∧ acceleratedOrbit 12 3263 = 15686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3263 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3263) = 3 ^ 9 * m + 15686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3263.1, data_12_3263.2] + +/-- Complete interval computation for depth 12, residue 3264. -/ +theorem bounds_12_3264 : exactInterval 12 3264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3264 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3264) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3264 : oddCount 3264 12 = 3 ∧ acceleratedOrbit 12 3264 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3264 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3264) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3264.1, data_12_3264.2] + +/-- Complete interval computation for depth 12, residue 3265. -/ +theorem bounds_12_3265 : exactInterval 12 3265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3265 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3265) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3265 : oddCount 3265 12 = 5 ∧ acceleratedOrbit 12 3265 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3265 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3265) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3265.1, data_12_3265.2] + +/-- Complete interval computation for depth 12, residue 3266. -/ +theorem bounds_12_3266 : exactInterval 12 3266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3266 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3266) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3266 : oddCount 3266 12 = 5 ∧ acceleratedOrbit 12 3266 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3266 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3266) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3266.1, data_12_3266.2] + +/-- Complete interval computation for depth 12, residue 3267. -/ +theorem bounds_12_3267 : exactInterval 12 3267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3267 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3267) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3267 : oddCount 3267 12 = 5 ∧ acceleratedOrbit 12 3267 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3267 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3267) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3267.1, data_12_3267.2] + +/-- Complete interval computation for depth 12, residue 3268. -/ +theorem bounds_12_3268 : exactInterval 12 3268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3268 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3268) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3268 : oddCount 3268 12 = 4 ∧ acceleratedOrbit 12 3268 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3268 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3268) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3268.1, data_12_3268.2] + +/-- Complete interval computation for depth 12, residue 3269. -/ +theorem bounds_12_3269 : exactInterval 12 3269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3269 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3269) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3269 : oddCount 3269 12 = 4 ∧ acceleratedOrbit 12 3269 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3269 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3269) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3269.1, data_12_3269.2] + +/-- Complete interval computation for depth 12, residue 3270. -/ +theorem bounds_12_3270 : exactInterval 12 3270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3270 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3270) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3270 : oddCount 3270 12 = 4 ∧ acceleratedOrbit 12 3270 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3270 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3270) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3270.1, data_12_3270.2] + +end Collatz.Research.StoppingAtlas.Batch0413 From 027644322a72fd28a15322d763b7b94faa8bfd7c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:12 +0530 Subject: [PATCH 0414/1001] proof: certify atlas Batch0414 (12:3271 to 12:3286) --- Collatz/Research/StoppingAtlas/Batch0414.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0414.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0414.lean b/Collatz/Research/StoppingAtlas/Batch0414.lean new file mode 100644 index 00000000..90eb50fb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0414.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0414 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3271. -/ +theorem bounds_12_3271 : exactInterval 12 3271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3271 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3271) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3271 : oddCount 3271 12 = 7 ∧ acceleratedOrbit 12 3271 = 1748 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3271 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3271) = 3 ^ 7 * m + 1748 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3271.1, data_12_3271.2] + +/-- Complete interval computation for depth 12, residue 3272. -/ +theorem bounds_12_3272 : exactInterval 12 3272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3272 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3272) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3272 : oddCount 3272 12 = 4 ∧ acceleratedOrbit 12 3272 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3272 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3272) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3272.1, data_12_3272.2] + +/-- Complete interval computation for depth 12, residue 3273. -/ +theorem bounds_12_3273 : exactInterval 12 3273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3273 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3273) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3273 : oddCount 3273 12 = 6 ∧ acceleratedOrbit 12 3273 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3273 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3273) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3273.1, data_12_3273.2] + +/-- Complete interval computation for depth 12, residue 3274. -/ +theorem bounds_12_3274 : exactInterval 12 3274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3274 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3274) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3274 : oddCount 3274 12 = 4 ∧ acceleratedOrbit 12 3274 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3274 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3274) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3274.1, data_12_3274.2] + +/-- Complete interval computation for depth 12, residue 3275. -/ +theorem bounds_12_3275 : exactInterval 12 3275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3275 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3275) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3275 : oddCount 3275 12 = 6 ∧ acceleratedOrbit 12 3275 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3275 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3275) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3275.1, data_12_3275.2] + +/-- Complete interval computation for depth 12, residue 3276. -/ +theorem bounds_12_3276 : exactInterval 12 3276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3276 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3276) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3276 : oddCount 3276 12 = 4 ∧ acceleratedOrbit 12 3276 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3276 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3276) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3276.1, data_12_3276.2] + +/-- Complete interval computation for depth 12, residue 3277. -/ +theorem bounds_12_3277 : exactInterval 12 3277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3277 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3277) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3277 : oddCount 3277 12 = 4 ∧ acceleratedOrbit 12 3277 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3277 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3277) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3277.1, data_12_3277.2] + +/-- Complete interval computation for depth 12, residue 3278. -/ +theorem bounds_12_3278 : exactInterval 12 3278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3278 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3278) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3278 : oddCount 3278 12 = 8 ∧ acceleratedOrbit 12 3278 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3278 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3278) = 3 ^ 8 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3278.1, data_12_3278.2] + +/-- Complete interval computation for depth 12, residue 3279. -/ +theorem bounds_12_3279 : exactInterval 12 3279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3279 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3279) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3279 : oddCount 3279 12 = 8 ∧ acceleratedOrbit 12 3279 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3279 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3279) = 3 ^ 8 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3279.1, data_12_3279.2] + +/-- Complete interval computation for depth 12, residue 3280. -/ +theorem bounds_12_3280 : exactInterval 12 3280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3280 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3280) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3280 : oddCount 3280 12 = 3 ∧ acceleratedOrbit 12 3280 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3280 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3280) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3280.1, data_12_3280.2] + +/-- Complete interval computation for depth 12, residue 3281. -/ +theorem bounds_12_3281 : exactInterval 12 3281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3281 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3281) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3281 : oddCount 3281 12 = 8 ∧ acceleratedOrbit 12 3281 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3281 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3281) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3281.1, data_12_3281.2] + +/-- Complete interval computation for depth 12, residue 3282. -/ +theorem bounds_12_3282 : exactInterval 12 3282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3282 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3282) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3282 : oddCount 3282 12 = 8 ∧ acceleratedOrbit 12 3282 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3282 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3282) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3282.1, data_12_3282.2] + +/-- Complete interval computation for depth 12, residue 3283. -/ +theorem bounds_12_3283 : exactInterval 12 3283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3283 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3283) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3283 : oddCount 3283 12 = 8 ∧ acceleratedOrbit 12 3283 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3283 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3283) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3283.1, data_12_3283.2] + +/-- Complete interval computation for depth 12, residue 3284. -/ +theorem bounds_12_3284 : exactInterval 12 3284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3284 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3284) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3284 : oddCount 3284 12 = 3 ∧ acceleratedOrbit 12 3284 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3284 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3284) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3284.1, data_12_3284.2] + +/-- Complete interval computation for depth 12, residue 3285. -/ +theorem bounds_12_3285 : exactInterval 12 3285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3285 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3285) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3285 : oddCount 3285 12 = 3 ∧ acceleratedOrbit 12 3285 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3285 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3285) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3285.1, data_12_3285.2] + +/-- Complete interval computation for depth 12, residue 3286. -/ +theorem bounds_12_3286 : exactInterval 12 3286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3286 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3286) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3286 : oddCount 3286 12 = 7 ∧ acceleratedOrbit 12 3286 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3286 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3286) = 3 ^ 7 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3286.1, data_12_3286.2] + +end Collatz.Research.StoppingAtlas.Batch0414 From d6869bc9f24a67ecd8557b35efe8b0e37d7b68f1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:12 +0530 Subject: [PATCH 0415/1001] proof: certify atlas Batch0415 (12:3287 to 12:3301) --- Collatz/Research/StoppingAtlas/Batch0415.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0415.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0415.lean b/Collatz/Research/StoppingAtlas/Batch0415.lean new file mode 100644 index 00000000..9599b1eb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0415.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0415 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3287. -/ +theorem bounds_12_3287 : exactInterval 12 3287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3287 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3287) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3287 : oddCount 3287 12 = 7 ∧ acceleratedOrbit 12 3287 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3287 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3287) = 3 ^ 7 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3287.1, data_12_3287.2] + +/-- Complete interval computation for depth 12, residue 3288. -/ +theorem bounds_12_3288 : exactInterval 12 3288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3288 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3288) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3288 : oddCount 3288 12 = 6 ∧ acceleratedOrbit 12 3288 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3288 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3288) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3288.1, data_12_3288.2] + +/-- Complete interval computation for depth 12, residue 3289. -/ +theorem bounds_12_3289 : exactInterval 12 3289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3289 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3289) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3289 : oddCount 3289 12 = 6 ∧ acceleratedOrbit 12 3289 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3289 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3289) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3289.1, data_12_3289.2] + +/-- Complete interval computation for depth 12, residue 3290. -/ +theorem bounds_12_3290 : exactInterval 12 3290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3290 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3290) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3290 : oddCount 3290 12 = 6 ∧ acceleratedOrbit 12 3290 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3290 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3290) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3290.1, data_12_3290.2] + +/-- Complete interval computation for depth 12, residue 3291. -/ +theorem bounds_12_3291 : exactInterval 12 3291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3291 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3291) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3291 : oddCount 3291 12 = 6 ∧ acceleratedOrbit 12 3291 = 586 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3291 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3291) = 3 ^ 6 * m + 586 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3291.1, data_12_3291.2] + +/-- Complete interval computation for depth 12, residue 3292. -/ +theorem bounds_12_3292 : exactInterval 12 3292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3292 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3292) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3292 : oddCount 3292 12 = 6 ∧ acceleratedOrbit 12 3292 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3292 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3292) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3292.1, data_12_3292.2] + +/-- Complete interval computation for depth 12, residue 3293. -/ +theorem bounds_12_3293 : exactInterval 12 3293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3293 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3293) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3293 : oddCount 3293 12 = 6 ∧ acceleratedOrbit 12 3293 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3293 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3293) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3293.1, data_12_3293.2] + +/-- Complete interval computation for depth 12, residue 3294. -/ +theorem bounds_12_3294 : exactInterval 12 3294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3294 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3294) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3294 : oddCount 3294 12 = 7 ∧ acceleratedOrbit 12 3294 = 1760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3294 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3294) = 3 ^ 7 * m + 1760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3294.1, data_12_3294.2] + +/-- Complete interval computation for depth 12, residue 3295. -/ +theorem bounds_12_3295 : exactInterval 12 3295 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3295 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3295) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3295 : oddCount 3295 12 = 7 ∧ acceleratedOrbit 12 3295 = 1760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3295 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3295) = 3 ^ 7 * m + 1760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3295.1, data_12_3295.2] + +/-- Complete interval computation for depth 12, residue 3296. -/ +theorem bounds_12_3296 : exactInterval 12 3296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3296 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3296) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3296 : oddCount 3296 12 = 6 ∧ acceleratedOrbit 12 3296 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3296 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3296) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3296.1, data_12_3296.2] + +/-- Complete interval computation for depth 12, residue 3297. -/ +theorem bounds_12_3297 : exactInterval 12 3297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3297 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3297) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3297 : oddCount 3297 12 = 8 ∧ acceleratedOrbit 12 3297 = 5285 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3297 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3297) = 3 ^ 8 * m + 5285 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3297.1, data_12_3297.2] + +/-- Complete interval computation for depth 12, residue 3298. -/ +theorem bounds_12_3298 : exactInterval 12 3298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3298 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3298) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3298 : oddCount 3298 12 = 3 ∧ acceleratedOrbit 12 3298 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3298 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3298) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3298.1, data_12_3298.2] + +/-- Complete interval computation for depth 12, residue 3299. -/ +theorem bounds_12_3299 : exactInterval 12 3299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3299 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3299) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3299 : oddCount 3299 12 = 3 ∧ acceleratedOrbit 12 3299 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3299 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3299) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3299.1, data_12_3299.2] + +/-- Complete interval computation for depth 12, residue 3300. -/ +theorem bounds_12_3300 : exactInterval 12 3300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3300 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3300) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3300 : oddCount 3300 12 = 6 ∧ acceleratedOrbit 12 3300 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3300 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3300) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3300.1, data_12_3300.2] + +/-- Complete interval computation for depth 12, residue 3301. -/ +theorem bounds_12_3301 : exactInterval 12 3301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3301 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3301) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3301 : oddCount 3301 12 = 6 ∧ acceleratedOrbit 12 3301 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3301 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3301) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3301.1, data_12_3301.2] + +end Collatz.Research.StoppingAtlas.Batch0415 From a96d59902378b0e55884977cb501e1d2048ef949 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:13 +0530 Subject: [PATCH 0416/1001] proof: certify atlas Batch0416 (12:3302 to 12:3316) --- Collatz/Research/StoppingAtlas/Batch0416.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0416.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0416.lean b/Collatz/Research/StoppingAtlas/Batch0416.lean new file mode 100644 index 00000000..987d0b52 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0416.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0416 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3302. -/ +theorem bounds_12_3302 : exactInterval 12 3302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3302 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3302) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3302 : oddCount 3302 12 = 6 ∧ acceleratedOrbit 12 3302 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3302 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3302) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3302.1, data_12_3302.2] + +/-- Complete interval computation for depth 12, residue 3303. -/ +theorem bounds_12_3303 : exactInterval 12 3303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3303 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3303) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3303 : oddCount 3303 12 = 8 ∧ acceleratedOrbit 12 3303 = 5293 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3303 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3303) = 3 ^ 8 * m + 5293 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3303.1, data_12_3303.2] + +/-- Complete interval computation for depth 12, residue 3304. -/ +theorem bounds_12_3304 : exactInterval 12 3304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3304 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3304) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3304 : oddCount 3304 12 = 6 ∧ acceleratedOrbit 12 3304 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3304 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3304) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3304.1, data_12_3304.2] + +/-- Complete interval computation for depth 12, residue 3305. -/ +theorem bounds_12_3305 : exactInterval 12 3305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3305 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3305) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3305 : oddCount 3305 12 = 7 ∧ acceleratedOrbit 12 3305 = 1766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3305 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3305) = 3 ^ 7 * m + 1766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3305.1, data_12_3305.2] + +/-- Complete interval computation for depth 12, residue 3306. -/ +theorem bounds_12_3306 : exactInterval 12 3306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3306 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3306) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3306 : oddCount 3306 12 = 6 ∧ acceleratedOrbit 12 3306 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3306 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3306) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3306.1, data_12_3306.2] + +/-- Complete interval computation for depth 12, residue 3307. -/ +theorem bounds_12_3307 : exactInterval 12 3307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3307 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3307) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3307 : oddCount 3307 12 = 9 ∧ acceleratedOrbit 12 3307 = 15902 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3307 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3307) = 3 ^ 9 * m + 15902 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3307.1, data_12_3307.2] + +/-- Complete interval computation for depth 12, residue 3308. -/ +theorem bounds_12_3308 : exactInterval 12 3308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3308 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3308) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3308 : oddCount 3308 12 = 5 ∧ acceleratedOrbit 12 3308 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3308 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3308) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3308.1, data_12_3308.2] + +/-- Complete interval computation for depth 12, residue 3309. -/ +theorem bounds_12_3309 : exactInterval 12 3309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3309 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3309) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3309 : oddCount 3309 12 = 5 ∧ acceleratedOrbit 12 3309 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3309 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3309) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3309.1, data_12_3309.2] + +/-- Complete interval computation for depth 12, residue 3310. -/ +theorem bounds_12_3310 : exactInterval 12 3310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3310 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3310) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3310 : oddCount 3310 12 = 5 ∧ acceleratedOrbit 12 3310 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3310 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3310) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3310.1, data_12_3310.2] + +/-- Complete interval computation for depth 12, residue 3311. -/ +theorem bounds_12_3311 : exactInterval 12 3311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3311 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3311) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3311 : oddCount 3311 12 = 10 ∧ acceleratedOrbit 12 3311 = 47749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3311 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3311) = 3 ^ 10 * m + 47749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3311.1, data_12_3311.2] + +/-- Complete interval computation for depth 12, residue 3312. -/ +theorem bounds_12_3312 : exactInterval 12 3312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3312 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3312) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3312 : oddCount 3312 12 = 6 ∧ acceleratedOrbit 12 3312 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3312 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3312) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3312.1, data_12_3312.2] + +/-- Complete interval computation for depth 12, residue 3313. -/ +theorem bounds_12_3313 : exactInterval 12 3313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3313 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3313) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3313 : oddCount 3313 12 = 6 ∧ acceleratedOrbit 12 3313 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3313 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3313) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3313.1, data_12_3313.2] + +/-- Complete interval computation for depth 12, residue 3314. -/ +theorem bounds_12_3314 : exactInterval 12 3314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3314 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3314) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3314 : oddCount 3314 12 = 7 ∧ acceleratedOrbit 12 3314 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3314 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3314) = 3 ^ 7 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3314.1, data_12_3314.2] + +/-- Complete interval computation for depth 12, residue 3315. -/ +theorem bounds_12_3315 : exactInterval 12 3315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3315 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3315) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3315 : oddCount 3315 12 = 7 ∧ acceleratedOrbit 12 3315 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3315 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3315) = 3 ^ 7 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3315.1, data_12_3315.2] + +/-- Complete interval computation for depth 12, residue 3316. -/ +theorem bounds_12_3316 : exactInterval 12 3316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3316 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3316) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3316 : oddCount 3316 12 = 6 ∧ acceleratedOrbit 12 3316 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3316 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3316) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3316.1, data_12_3316.2] + +end Collatz.Research.StoppingAtlas.Batch0416 From 04379840a59bebc3ae3fd4496fed24a3d059cf87 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:13 +0530 Subject: [PATCH 0417/1001] proof: certify atlas Batch0417 (12:3317 to 12:3332) --- Collatz/Research/StoppingAtlas/Batch0417.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0417.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0417.lean b/Collatz/Research/StoppingAtlas/Batch0417.lean new file mode 100644 index 00000000..5afb561f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0417.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0417 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3317. -/ +theorem bounds_12_3317 : exactInterval 12 3317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3317 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3317) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3317 : oddCount 3317 12 = 6 ∧ acceleratedOrbit 12 3317 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3317 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3317) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3317.1, data_12_3317.2] + +/-- Complete interval computation for depth 12, residue 3318. -/ +theorem bounds_12_3318 : exactInterval 12 3318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3318 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3318) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3318 : oddCount 3318 12 = 5 ∧ acceleratedOrbit 12 3318 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3318 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3318) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3318.1, data_12_3318.2] + +/-- Complete interval computation for depth 12, residue 3319. -/ +theorem bounds_12_3319 : exactInterval 12 3319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3319 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3319) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3319 : oddCount 3319 12 = 5 ∧ acceleratedOrbit 12 3319 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3319 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3319) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3319.1, data_12_3319.2] + +/-- Complete interval computation for depth 12, residue 3320. -/ +theorem bounds_12_3320 : exactInterval 12 3320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3320 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3320) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3320 : oddCount 3320 12 = 7 ∧ acceleratedOrbit 12 3320 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3320 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3320) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3320.1, data_12_3320.2] + +/-- Complete interval computation for depth 12, residue 3321. -/ +theorem bounds_12_3321 : exactInterval 12 3321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3321 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3321) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3321 : oddCount 3321 12 = 7 ∧ acceleratedOrbit 12 3321 = 1775 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3321 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3321) = 3 ^ 7 * m + 1775 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3321.1, data_12_3321.2] + +/-- Complete interval computation for depth 12, residue 3322. -/ +theorem bounds_12_3322 : exactInterval 12 3322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3322 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3322) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3322 : oddCount 3322 12 = 7 ∧ acceleratedOrbit 12 3322 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3322 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3322) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3322.1, data_12_3322.2] + +/-- Complete interval computation for depth 12, residue 3323. -/ +theorem bounds_12_3323 : exactInterval 12 3323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3323 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3323) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3323 : oddCount 3323 12 = 9 ∧ acceleratedOrbit 12 3323 = 15977 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3323 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3323) = 3 ^ 9 * m + 15977 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3323.1, data_12_3323.2] + +/-- Complete interval computation for depth 12, residue 3324. -/ +theorem bounds_12_3324 : exactInterval 12 3324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3324 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3324) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3324 : oddCount 3324 12 = 7 ∧ acceleratedOrbit 12 3324 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3324 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3324) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3324.1, data_12_3324.2] + +/-- Complete interval computation for depth 12, residue 3325. -/ +theorem bounds_12_3325 : exactInterval 12 3325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3325 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3325) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3325 : oddCount 3325 12 = 7 ∧ acceleratedOrbit 12 3325 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3325 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3325) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3325.1, data_12_3325.2] + +/-- Complete interval computation for depth 12, residue 3326. -/ +theorem bounds_12_3326 : exactInterval 12 3326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3326 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3326) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3326 : oddCount 3326 12 = 10 ∧ acceleratedOrbit 12 3326 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3326 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3326) = 3 ^ 10 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3326.1, data_12_3326.2] + +/-- Complete interval computation for depth 12, residue 3327. -/ +theorem bounds_12_3327 : exactInterval 12 3327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3327 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3327) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3327 : oddCount 3327 12 = 10 ∧ acceleratedOrbit 12 3327 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3327 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3327) = 3 ^ 10 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3327.1, data_12_3327.2] + +/-- Complete interval computation for depth 12, residue 3328. -/ +theorem bounds_12_3328 : exactInterval 12 3328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3328 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3328) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3328 : oddCount 3328 12 = 2 ∧ acceleratedOrbit 12 3328 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3328 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3328) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3328.1, data_12_3328.2] + +/-- Complete interval computation for depth 12, residue 3329. -/ +theorem bounds_12_3329 : exactInterval 12 3329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3329 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3329) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3329 : oddCount 3329 12 = 7 ∧ acceleratedOrbit 12 3329 = 1781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3329 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3329) = 3 ^ 7 * m + 1781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3329.1, data_12_3329.2] + +/-- Complete interval computation for depth 12, residue 3330. -/ +theorem bounds_12_3330 : exactInterval 12 3330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3330 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3330) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3330 : oddCount 3330 12 = 8 ∧ acceleratedOrbit 12 3330 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3330 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3330) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3330.1, data_12_3330.2] + +/-- Complete interval computation for depth 12, residue 3331. -/ +theorem bounds_12_3331 : exactInterval 12 3331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3331 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3331) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3331 : oddCount 3331 12 = 8 ∧ acceleratedOrbit 12 3331 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3331 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3331) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3331.1, data_12_3331.2] + +/-- Complete interval computation for depth 12, residue 3332. -/ +theorem bounds_12_3332 : exactInterval 12 3332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3332 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3332) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3332 : oddCount 3332 12 = 3 ∧ acceleratedOrbit 12 3332 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3332 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3332) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3332.1, data_12_3332.2] + +end Collatz.Research.StoppingAtlas.Batch0417 From 2ef3359bf040188183e4ee5591f0a7953d41e439 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:13 +0530 Subject: [PATCH 0418/1001] proof: certify atlas Batch0418 (12:3333 to 12:3347) --- Collatz/Research/StoppingAtlas/Batch0418.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0418.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0418.lean b/Collatz/Research/StoppingAtlas/Batch0418.lean new file mode 100644 index 00000000..acd07931 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0418.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0418 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3333. -/ +theorem bounds_12_3333 : exactInterval 12 3333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3333 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3333) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3333 : oddCount 3333 12 = 3 ∧ acceleratedOrbit 12 3333 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3333 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3333) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3333.1, data_12_3333.2] + +/-- Complete interval computation for depth 12, residue 3334. -/ +theorem bounds_12_3334 : exactInterval 12 3334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3334 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3334) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3334 : oddCount 3334 12 = 3 ∧ acceleratedOrbit 12 3334 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3334 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3334) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3334.1, data_12_3334.2] + +/-- Complete interval computation for depth 12, residue 3335. -/ +theorem bounds_12_3335 : exactInterval 12 3335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3335 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3335) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3335 : oddCount 3335 12 = 9 ∧ acceleratedOrbit 12 3335 = 16037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3335 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3335) = 3 ^ 9 * m + 16037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3335.1, data_12_3335.2] + +/-- Complete interval computation for depth 12, residue 3336. -/ +theorem bounds_12_3336 : exactInterval 12 3336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3336 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3336) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3336 : oddCount 3336 12 = 5 ∧ acceleratedOrbit 12 3336 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3336 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3336) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3336.1, data_12_3336.2] + +/-- Complete interval computation for depth 12, residue 3337. -/ +theorem bounds_12_3337 : exactInterval 12 3337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3337 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3337) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3337 : oddCount 3337 12 = 7 ∧ acceleratedOrbit 12 3337 = 1783 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3337 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3337) = 3 ^ 7 * m + 1783 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3337.1, data_12_3337.2] + +/-- Complete interval computation for depth 12, residue 3338. -/ +theorem bounds_12_3338 : exactInterval 12 3338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3338 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3338) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3338 : oddCount 3338 12 = 5 ∧ acceleratedOrbit 12 3338 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3338 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3338) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3338.1, data_12_3338.2] + +/-- Complete interval computation for depth 12, residue 3339. -/ +theorem bounds_12_3339 : exactInterval 12 3339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3339 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3339) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3339 : oddCount 3339 12 = 6 ∧ acceleratedOrbit 12 3339 = 595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3339 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3339) = 3 ^ 6 * m + 595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3339.1, data_12_3339.2] + +/-- Complete interval computation for depth 12, residue 3340. -/ +theorem bounds_12_3340 : exactInterval 12 3340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3340 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3340) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3340 : oddCount 3340 12 = 5 ∧ acceleratedOrbit 12 3340 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3340 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3340) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3340.1, data_12_3340.2] + +/-- Complete interval computation for depth 12, residue 3341. -/ +theorem bounds_12_3341 : exactInterval 12 3341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3341 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3341) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3341 : oddCount 3341 12 = 5 ∧ acceleratedOrbit 12 3341 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3341 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3341) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3341.1, data_12_3341.2] + +/-- Complete interval computation for depth 12, residue 3342. -/ +theorem bounds_12_3342 : exactInterval 12 3342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3342 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3342) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3342 : oddCount 3342 12 = 6 ∧ acceleratedOrbit 12 3342 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3342 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3342) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3342.1, data_12_3342.2] + +/-- Complete interval computation for depth 12, residue 3343. -/ +theorem bounds_12_3343 : exactInterval 12 3343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3343 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3343) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3343 : oddCount 3343 12 = 6 ∧ acceleratedOrbit 12 3343 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3343 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3343) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3343.1, data_12_3343.2] + +/-- Complete interval computation for depth 12, residue 3344. -/ +theorem bounds_12_3344 : exactInterval 12 3344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3344 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3344) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3344 : oddCount 3344 12 = 4 ∧ acceleratedOrbit 12 3344 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3344 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3344) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3344.1, data_12_3344.2] + +/-- Complete interval computation for depth 12, residue 3345. -/ +theorem bounds_12_3345 : exactInterval 12 3345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3345 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3345) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3345 : oddCount 3345 12 = 5 ∧ acceleratedOrbit 12 3345 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3345 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3345) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3345.1, data_12_3345.2] + +/-- Complete interval computation for depth 12, residue 3346. -/ +theorem bounds_12_3346 : exactInterval 12 3346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3346 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3346) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3346 : oddCount 3346 12 = 8 ∧ acceleratedOrbit 12 3346 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3346 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3346) = 3 ^ 8 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3346.1, data_12_3346.2] + +/-- Complete interval computation for depth 12, residue 3347. -/ +theorem bounds_12_3347 : exactInterval 12 3347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3347 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3347) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3347 : oddCount 3347 12 = 8 ∧ acceleratedOrbit 12 3347 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3347 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3347) = 3 ^ 8 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3347.1, data_12_3347.2] + +end Collatz.Research.StoppingAtlas.Batch0418 From 2881a0e72ecd4bf448e23e1b0e9fd9daee127769 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:14 +0530 Subject: [PATCH 0419/1001] proof: certify atlas Batch0419 (12:3348 to 12:3362) --- Collatz/Research/StoppingAtlas/Batch0419.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0419.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0419.lean b/Collatz/Research/StoppingAtlas/Batch0419.lean new file mode 100644 index 00000000..4fe93d32 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0419.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0419 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3348. -/ +theorem bounds_12_3348 : exactInterval 12 3348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3348 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3348) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3348 : oddCount 3348 12 = 4 ∧ acceleratedOrbit 12 3348 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3348 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3348) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3348.1, data_12_3348.2] + +/-- Complete interval computation for depth 12, residue 3349. -/ +theorem bounds_12_3349 : exactInterval 12 3349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3349 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3349) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3349 : oddCount 3349 12 = 4 ∧ acceleratedOrbit 12 3349 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3349 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3349) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3349.1, data_12_3349.2] + +/-- Complete interval computation for depth 12, residue 3350. -/ +theorem bounds_12_3350 : exactInterval 12 3350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3350 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3350) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3350 : oddCount 3350 12 = 5 ∧ acceleratedOrbit 12 3350 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3350 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3350) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3350.1, data_12_3350.2] + +/-- Complete interval computation for depth 12, residue 3351. -/ +theorem bounds_12_3351 : exactInterval 12 3351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3351 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3351) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3351 : oddCount 3351 12 = 5 ∧ acceleratedOrbit 12 3351 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3351 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3351) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3351.1, data_12_3351.2] + +/-- Complete interval computation for depth 12, residue 3352. -/ +theorem bounds_12_3352 : exactInterval 12 3352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3352 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3352) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3352 : oddCount 3352 12 = 4 ∧ acceleratedOrbit 12 3352 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3352 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3352) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3352.1, data_12_3352.2] + +/-- Complete interval computation for depth 12, residue 3353. -/ +theorem bounds_12_3353 : exactInterval 12 3353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3353 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3353) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3353 : oddCount 3353 12 = 7 ∧ acceleratedOrbit 12 3353 = 1792 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3353 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3353) = 3 ^ 7 * m + 1792 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3353.1, data_12_3353.2] + +/-- Complete interval computation for depth 12, residue 3354. -/ +theorem bounds_12_3354 : exactInterval 12 3354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3354 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3354) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3354 : oddCount 3354 12 = 4 ∧ acceleratedOrbit 12 3354 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3354 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3354) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3354.1, data_12_3354.2] + +/-- Complete interval computation for depth 12, residue 3355. -/ +theorem bounds_12_3355 : exactInterval 12 3355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3355 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3355) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3355 : oddCount 3355 12 = 9 ∧ acceleratedOrbit 12 3355 = 16129 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3355 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3355) = 3 ^ 9 * m + 16129 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3355.1, data_12_3355.2] + +/-- Complete interval computation for depth 12, residue 3356. -/ +theorem bounds_12_3356 : exactInterval 12 3356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3356 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3356) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3356 : oddCount 3356 12 = 7 ∧ acceleratedOrbit 12 3356 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3356 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3356) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3356.1, data_12_3356.2] + +/-- Complete interval computation for depth 12, residue 3357. -/ +theorem bounds_12_3357 : exactInterval 12 3357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3357 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3357) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3357 : oddCount 3357 12 = 7 ∧ acceleratedOrbit 12 3357 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3357 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3357) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3357.1, data_12_3357.2] + +/-- Complete interval computation for depth 12, residue 3358. -/ +theorem bounds_12_3358 : exactInterval 12 3358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3358 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3358) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3358 : oddCount 3358 12 = 7 ∧ acceleratedOrbit 12 3358 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3358 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3358) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3358.1, data_12_3358.2] + +/-- Complete interval computation for depth 12, residue 3359. -/ +theorem bounds_12_3359 : exactInterval 12 3359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3359 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3359) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3359 : oddCount 3359 12 = 6 ∧ acceleratedOrbit 12 3359 = 598 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3359 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3359) = 3 ^ 6 * m + 598 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3359.1, data_12_3359.2] + +/-- Complete interval computation for depth 12, residue 3360. -/ +theorem bounds_12_3360 : exactInterval 12 3360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3360 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3360) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3360 : oddCount 3360 12 = 5 ∧ acceleratedOrbit 12 3360 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3360 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3360) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3360.1, data_12_3360.2] + +/-- Complete interval computation for depth 12, residue 3361. -/ +theorem bounds_12_3361 : exactInterval 12 3361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3361 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3361) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3361 : oddCount 3361 12 = 5 ∧ acceleratedOrbit 12 3361 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3361 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3361) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3361.1, data_12_3361.2] + +/-- Complete interval computation for depth 12, residue 3362. -/ +theorem bounds_12_3362 : exactInterval 12 3362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3362 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3362) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3362 : oddCount 3362 12 = 5 ∧ acceleratedOrbit 12 3362 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3362 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3362) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3362.1, data_12_3362.2] + +end Collatz.Research.StoppingAtlas.Batch0419 From 3c1e4e9e0c8b8a56e1c01c845fd43494fab7b35e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:14 +0530 Subject: [PATCH 0420/1001] proof: certify atlas Batch0420 (12:3363 to 12:3378) --- Collatz/Research/StoppingAtlas/Batch0420.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0420.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0420.lean b/Collatz/Research/StoppingAtlas/Batch0420.lean new file mode 100644 index 00000000..132d3136 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0420.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0420 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3363. -/ +theorem bounds_12_3363 : exactInterval 12 3363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3363 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3363) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3363 : oddCount 3363 12 = 5 ∧ acceleratedOrbit 12 3363 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3363 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3363) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3363.1, data_12_3363.2] + +/-- Complete interval computation for depth 12, residue 3364. -/ +theorem bounds_12_3364 : exactInterval 12 3364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3364 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3364) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3364 : oddCount 3364 12 = 5 ∧ acceleratedOrbit 12 3364 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3364 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3364) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3364.1, data_12_3364.2] + +/-- Complete interval computation for depth 12, residue 3365. -/ +theorem bounds_12_3365 : exactInterval 12 3365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3365 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3365) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3365 : oddCount 3365 12 = 5 ∧ acceleratedOrbit 12 3365 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3365 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3365) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3365.1, data_12_3365.2] + +/-- Complete interval computation for depth 12, residue 3366. -/ +theorem bounds_12_3366 : exactInterval 12 3366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3366 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3366) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3366 : oddCount 3366 12 = 5 ∧ acceleratedOrbit 12 3366 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3366 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3366) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3366.1, data_12_3366.2] + +/-- Complete interval computation for depth 12, residue 3367. -/ +theorem bounds_12_3367 : exactInterval 12 3367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3367 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3367) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3367 : oddCount 3367 12 = 7 ∧ acceleratedOrbit 12 3367 = 1799 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3367 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3367) = 3 ^ 7 * m + 1799 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3367.1, data_12_3367.2] + +/-- Complete interval computation for depth 12, residue 3368. -/ +theorem bounds_12_3368 : exactInterval 12 3368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3368 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3368) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3368 : oddCount 3368 12 = 5 ∧ acceleratedOrbit 12 3368 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3368 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3368) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3368.1, data_12_3368.2] + +/-- Complete interval computation for depth 12, residue 3369. -/ +theorem bounds_12_3369 : exactInterval 12 3369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3369 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3369) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3369 : oddCount 3369 12 = 9 ∧ acceleratedOrbit 12 3369 = 16199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3369 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3369) = 3 ^ 9 * m + 16199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3369.1, data_12_3369.2] + +/-- Complete interval computation for depth 12, residue 3370. -/ +theorem bounds_12_3370 : exactInterval 12 3370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3370 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3370) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3370 : oddCount 3370 12 = 5 ∧ acceleratedOrbit 12 3370 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3370 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3370) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3370.1, data_12_3370.2] + +/-- Complete interval computation for depth 12, residue 3371. -/ +theorem bounds_12_3371 : exactInterval 12 3371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3371 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3371) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3371 : oddCount 3371 12 = 7 ∧ acceleratedOrbit 12 3371 = 1802 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3371 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3371) = 3 ^ 7 * m + 1802 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3371.1, data_12_3371.2] + +/-- Complete interval computation for depth 12, residue 3372. -/ +theorem bounds_12_3372 : exactInterval 12 3372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3372 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3372) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3372 : oddCount 3372 12 = 4 ∧ acceleratedOrbit 12 3372 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3372 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3372) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3372.1, data_12_3372.2] + +/-- Complete interval computation for depth 12, residue 3373. -/ +theorem bounds_12_3373 : exactInterval 12 3373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3373 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3373) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3373 : oddCount 3373 12 = 4 ∧ acceleratedOrbit 12 3373 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3373 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3373) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3373.1, data_12_3373.2] + +/-- Complete interval computation for depth 12, residue 3374. -/ +theorem bounds_12_3374 : exactInterval 12 3374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3374 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3374) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3374 : oddCount 3374 12 = 4 ∧ acceleratedOrbit 12 3374 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3374 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3374) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3374.1, data_12_3374.2] + +/-- Complete interval computation for depth 12, residue 3375. -/ +theorem bounds_12_3375 : exactInterval 12 3375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3375 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3375) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3375 : oddCount 3375 12 = 9 ∧ acceleratedOrbit 12 3375 = 16226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3375 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3375) = 3 ^ 9 * m + 16226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3375.1, data_12_3375.2] + +/-- Complete interval computation for depth 12, residue 3376. -/ +theorem bounds_12_3376 : exactInterval 12 3376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3376 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3376) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3376 : oddCount 3376 12 = 5 ∧ acceleratedOrbit 12 3376 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3376 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3376) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3376.1, data_12_3376.2] + +/-- Complete interval computation for depth 12, residue 3377. -/ +theorem bounds_12_3377 : exactInterval 12 3377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3377 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3377) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3377 : oddCount 3377 12 = 7 ∧ acceleratedOrbit 12 3377 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3377 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3377) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3377.1, data_12_3377.2] + +/-- Complete interval computation for depth 12, residue 3378. -/ +theorem bounds_12_3378 : exactInterval 12 3378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3378 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3378) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3378 : oddCount 3378 12 = 7 ∧ acceleratedOrbit 12 3378 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3378 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3378) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3378.1, data_12_3378.2] + +end Collatz.Research.StoppingAtlas.Batch0420 From cfd46555f547ec0db3f99eb8386fcc10b9deb056 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:14 +0530 Subject: [PATCH 0421/1001] proof: certify atlas Batch0421 (12:3379 to 12:3393) --- Collatz/Research/StoppingAtlas/Batch0421.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0421.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0421.lean b/Collatz/Research/StoppingAtlas/Batch0421.lean new file mode 100644 index 00000000..b8749806 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0421.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0421 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3379. -/ +theorem bounds_12_3379 : exactInterval 12 3379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3379 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3379) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3379 : oddCount 3379 12 = 7 ∧ acceleratedOrbit 12 3379 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3379 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3379) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3379.1, data_12_3379.2] + +/-- Complete interval computation for depth 12, residue 3380. -/ +theorem bounds_12_3380 : exactInterval 12 3380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3380 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3380) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3380 : oddCount 3380 12 = 5 ∧ acceleratedOrbit 12 3380 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3380 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3380) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3380.1, data_12_3380.2] + +/-- Complete interval computation for depth 12, residue 3381. -/ +theorem bounds_12_3381 : exactInterval 12 3381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3381 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3381) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3381 : oddCount 3381 12 = 5 ∧ acceleratedOrbit 12 3381 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3381 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3381) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3381.1, data_12_3381.2] + +/-- Complete interval computation for depth 12, residue 3382. -/ +theorem bounds_12_3382 : exactInterval 12 3382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3382 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3382) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3382 : oddCount 3382 12 = 8 ∧ acceleratedOrbit 12 3382 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3382 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3382) = 3 ^ 8 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3382.1, data_12_3382.2] + +/-- Complete interval computation for depth 12, residue 3383. -/ +theorem bounds_12_3383 : exactInterval 12 3383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3383 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3383) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3383 : oddCount 3383 12 = 8 ∧ acceleratedOrbit 12 3383 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3383 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3383) = 3 ^ 8 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3383.1, data_12_3383.2] + +/-- Complete interval computation for depth 12, residue 3384. -/ +theorem bounds_12_3384 : exactInterval 12 3384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3384 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3384) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3384 : oddCount 3384 12 = 6 ∧ acceleratedOrbit 12 3384 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3384 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3384) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3384.1, data_12_3384.2] + +/-- Complete interval computation for depth 12, residue 3385. -/ +theorem bounds_12_3385 : exactInterval 12 3385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3385 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3385) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3385 : oddCount 3385 12 = 9 ∧ acceleratedOrbit 12 3385 = 16280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3385 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3385) = 3 ^ 9 * m + 16280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3385.1, data_12_3385.2] + +/-- Complete interval computation for depth 12, residue 3386. -/ +theorem bounds_12_3386 : exactInterval 12 3386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3386 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3386) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3386 : oddCount 3386 12 = 6 ∧ acceleratedOrbit 12 3386 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3386 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3386) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3386.1, data_12_3386.2] + +/-- Complete interval computation for depth 12, residue 3387. -/ +theorem bounds_12_3387 : exactInterval 12 3387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3387 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3387) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3387 : oddCount 3387 12 = 4 ∧ acceleratedOrbit 12 3387 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3387 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3387) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3387.1, data_12_3387.2] + +/-- Complete interval computation for depth 12, residue 3388. -/ +theorem bounds_12_3388 : exactInterval 12 3388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3388 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3388) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3388 : oddCount 3388 12 = 6 ∧ acceleratedOrbit 12 3388 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3388 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3388) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3388.1, data_12_3388.2] + +/-- Complete interval computation for depth 12, residue 3389. -/ +theorem bounds_12_3389 : exactInterval 12 3389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3389 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3389) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3389 : oddCount 3389 12 = 6 ∧ acceleratedOrbit 12 3389 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3389 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3389) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3389.1, data_12_3389.2] + +/-- Complete interval computation for depth 12, residue 3390. -/ +theorem bounds_12_3390 : exactInterval 12 3390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3390 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3390) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3390 : oddCount 3390 12 = 9 ∧ acceleratedOrbit 12 3390 = 16301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3390 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3390) = 3 ^ 9 * m + 16301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3390.1, data_12_3390.2] + +/-- Complete interval computation for depth 12, residue 3391. -/ +theorem bounds_12_3391 : exactInterval 12 3391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3391 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3391) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3391 : oddCount 3391 12 = 9 ∧ acceleratedOrbit 12 3391 = 16301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3391 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3391) = 3 ^ 9 * m + 16301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3391.1, data_12_3391.2] + +/-- Complete interval computation for depth 12, residue 3392. -/ +theorem bounds_12_3392 : exactInterval 12 3392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3392 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3392) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3392 : oddCount 3392 12 = 2 ∧ acceleratedOrbit 12 3392 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3392 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3392) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3392.1, data_12_3392.2] + +/-- Complete interval computation for depth 12, residue 3393. -/ +theorem bounds_12_3393 : exactInterval 12 3393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3393 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3393) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3393 : oddCount 3393 12 = 5 ∧ acceleratedOrbit 12 3393 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3393 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3393) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3393.1, data_12_3393.2] + +end Collatz.Research.StoppingAtlas.Batch0421 From efe7ffb0bd3c8bdcd1e24d2b10ad778d778f0a3f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:15 +0530 Subject: [PATCH 0422/1001] proof: certify atlas Batch0422 (12:3394 to 12:3408) --- Collatz/Research/StoppingAtlas/Batch0422.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0422.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0422.lean b/Collatz/Research/StoppingAtlas/Batch0422.lean new file mode 100644 index 00000000..256a212e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0422.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0422 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3394. -/ +theorem bounds_12_3394 : exactInterval 12 3394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3394 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3394) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3394 : oddCount 3394 12 = 6 ∧ acceleratedOrbit 12 3394 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3394 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3394) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3394.1, data_12_3394.2] + +/-- Complete interval computation for depth 12, residue 3395. -/ +theorem bounds_12_3395 : exactInterval 12 3395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3395 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3395) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3395 : oddCount 3395 12 = 6 ∧ acceleratedOrbit 12 3395 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3395 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3395) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3395.1, data_12_3395.2] + +/-- Complete interval computation for depth 12, residue 3396. -/ +theorem bounds_12_3396 : exactInterval 12 3396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3396 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3396) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3396 : oddCount 3396 12 = 6 ∧ acceleratedOrbit 12 3396 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3396 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3396) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3396.1, data_12_3396.2] + +/-- Complete interval computation for depth 12, residue 3397. -/ +theorem bounds_12_3397 : exactInterval 12 3397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3397 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3397) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3397 : oddCount 3397 12 = 6 ∧ acceleratedOrbit 12 3397 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3397 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3397) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3397.1, data_12_3397.2] + +/-- Complete interval computation for depth 12, residue 3398. -/ +theorem bounds_12_3398 : exactInterval 12 3398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3398 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3398) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3398 : oddCount 3398 12 = 6 ∧ acceleratedOrbit 12 3398 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3398 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3398) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3398.1, data_12_3398.2] + +/-- Complete interval computation for depth 12, residue 3399. -/ +theorem bounds_12_3399 : exactInterval 12 3399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3399 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3399) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3399 : oddCount 3399 12 = 8 ∧ acceleratedOrbit 12 3399 = 5447 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3399 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3399) = 3 ^ 8 * m + 5447 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3399.1, data_12_3399.2] + +/-- Complete interval computation for depth 12, residue 3400. -/ +theorem bounds_12_3400 : exactInterval 12 3400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3400 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3400) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3400 : oddCount 3400 12 = 7 ∧ acceleratedOrbit 12 3400 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3400 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3400) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3400.1, data_12_3400.2] + +/-- Complete interval computation for depth 12, residue 3401. -/ +theorem bounds_12_3401 : exactInterval 12 3401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3401 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3401) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3401 : oddCount 3401 12 = 8 ∧ acceleratedOrbit 12 3401 = 5453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3401 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3401) = 3 ^ 8 * m + 5453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3401.1, data_12_3401.2] + +/-- Complete interval computation for depth 12, residue 3402. -/ +theorem bounds_12_3402 : exactInterval 12 3402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3402 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3402) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3402 : oddCount 3402 12 = 7 ∧ acceleratedOrbit 12 3402 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3402 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3402) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3402.1, data_12_3402.2] + +/-- Complete interval computation for depth 12, residue 3403. -/ +theorem bounds_12_3403 : exactInterval 12 3403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3403 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3403) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3403 : oddCount 3403 12 = 6 ∧ acceleratedOrbit 12 3403 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3403 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3403) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3403.1, data_12_3403.2] + +/-- Complete interval computation for depth 12, residue 3404. -/ +theorem bounds_12_3404 : exactInterval 12 3404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3404 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3404) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3404 : oddCount 3404 12 = 7 ∧ acceleratedOrbit 12 3404 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3404 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3404) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3404.1, data_12_3404.2] + +/-- Complete interval computation for depth 12, residue 3405. -/ +theorem bounds_12_3405 : exactInterval 12 3405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3405 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3405) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3405 : oddCount 3405 12 = 7 ∧ acceleratedOrbit 12 3405 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3405 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3405) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3405.1, data_12_3405.2] + +/-- Complete interval computation for depth 12, residue 3406. -/ +theorem bounds_12_3406 : exactInterval 12 3406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3406 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3406) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3406 : oddCount 3406 12 = 7 ∧ acceleratedOrbit 12 3406 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3406 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3406) = 3 ^ 7 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3406.1, data_12_3406.2] + +/-- Complete interval computation for depth 12, residue 3407. -/ +theorem bounds_12_3407 : exactInterval 12 3407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3407 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3407) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3407 : oddCount 3407 12 = 7 ∧ acceleratedOrbit 12 3407 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3407 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3407) = 3 ^ 7 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3407.1, data_12_3407.2] + +/-- Complete interval computation for depth 12, residue 3408. -/ +theorem bounds_12_3408 : exactInterval 12 3408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3408 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3408) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3408 : oddCount 3408 12 = 2 ∧ acceleratedOrbit 12 3408 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3408 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3408) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3408.1, data_12_3408.2] + +end Collatz.Research.StoppingAtlas.Batch0422 From 2e04da74c50151231e4f223758a0fb936f4f7443 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:15 +0530 Subject: [PATCH 0423/1001] proof: certify atlas Batch0423 (12:3409 to 12:3424) --- Collatz/Research/StoppingAtlas/Batch0423.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0423.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0423.lean b/Collatz/Research/StoppingAtlas/Batch0423.lean new file mode 100644 index 00000000..76150ae2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0423.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0423 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3409. -/ +theorem bounds_12_3409 : exactInterval 12 3409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3409 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3409) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3409 : oddCount 3409 12 = 8 ∧ acceleratedOrbit 12 3409 = 5467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3409 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3409) = 3 ^ 8 * m + 5467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3409.1, data_12_3409.2] + +/-- Complete interval computation for depth 12, residue 3410. -/ +theorem bounds_12_3410 : exactInterval 12 3410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3410 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3410) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3410 : oddCount 3410 12 = 9 ∧ acceleratedOrbit 12 3410 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3410 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3410) = 3 ^ 9 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3410.1, data_12_3410.2] + +/-- Complete interval computation for depth 12, residue 3411. -/ +theorem bounds_12_3411 : exactInterval 12 3411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3411 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3411) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3411 : oddCount 3411 12 = 9 ∧ acceleratedOrbit 12 3411 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3411 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3411) = 3 ^ 9 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3411.1, data_12_3411.2] + +/-- Complete interval computation for depth 12, residue 3412. -/ +theorem bounds_12_3412 : exactInterval 12 3412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3412 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3412) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3412 : oddCount 3412 12 = 2 ∧ acceleratedOrbit 12 3412 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3412 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3412) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3412.1, data_12_3412.2] + +/-- Complete interval computation for depth 12, residue 3413. -/ +theorem bounds_12_3413 : exactInterval 12 3413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3413 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3413) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3413 : oddCount 3413 12 = 2 ∧ acceleratedOrbit 12 3413 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3413 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3413) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3413.1, data_12_3413.2] + +/-- Complete interval computation for depth 12, residue 3414. -/ +theorem bounds_12_3414 : exactInterval 12 3414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3414 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3414) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3414 : oddCount 3414 12 = 7 ∧ acceleratedOrbit 12 3414 = 1826 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3414 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3414) = 3 ^ 7 * m + 1826 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3414.1, data_12_3414.2] + +/-- Complete interval computation for depth 12, residue 3415. -/ +theorem bounds_12_3415 : exactInterval 12 3415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3415 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3415) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3415 : oddCount 3415 12 = 7 ∧ acceleratedOrbit 12 3415 = 1826 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3415 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3415) = 3 ^ 7 * m + 1826 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3415.1, data_12_3415.2] + +/-- Complete interval computation for depth 12, residue 3416. -/ +theorem bounds_12_3416 : exactInterval 12 3416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3416 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3416) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3416 : oddCount 3416 12 = 6 ∧ acceleratedOrbit 12 3416 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3416 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3416) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3416.1, data_12_3416.2] + +/-- Complete interval computation for depth 12, residue 3417. -/ +theorem bounds_12_3417 : exactInterval 12 3417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3417 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3417) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3417 : oddCount 3417 12 = 5 ∧ acceleratedOrbit 12 3417 = 203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3417 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3417) = 3 ^ 5 * m + 203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3417.1, data_12_3417.2] + +/-- Complete interval computation for depth 12, residue 3418. -/ +theorem bounds_12_3418 : exactInterval 12 3418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3418 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3418) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3418 : oddCount 3418 12 = 6 ∧ acceleratedOrbit 12 3418 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3418 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3418) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3418.1, data_12_3418.2] + +/-- Complete interval computation for depth 12, residue 3419. -/ +theorem bounds_12_3419 : exactInterval 12 3419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3419 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3419) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3419 : oddCount 3419 12 = 8 ∧ acceleratedOrbit 12 3419 = 5480 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3419 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3419) = 3 ^ 8 * m + 5480 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3419.1, data_12_3419.2] + +/-- Complete interval computation for depth 12, residue 3420. -/ +theorem bounds_12_3420 : exactInterval 12 3420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3420 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3420) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3420 : oddCount 3420 12 = 6 ∧ acceleratedOrbit 12 3420 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3420 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3420) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3420.1, data_12_3420.2] + +/-- Complete interval computation for depth 12, residue 3421. -/ +theorem bounds_12_3421 : exactInterval 12 3421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3421 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3421) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3421 : oddCount 3421 12 = 6 ∧ acceleratedOrbit 12 3421 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3421 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3421) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3421.1, data_12_3421.2] + +/-- Complete interval computation for depth 12, residue 3422. -/ +theorem bounds_12_3422 : exactInterval 12 3422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3422 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3422) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3422 : oddCount 3422 12 = 7 ∧ acceleratedOrbit 12 3422 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3422 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3422) = 3 ^ 7 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3422.1, data_12_3422.2] + +/-- Complete interval computation for depth 12, residue 3423. -/ +theorem bounds_12_3423 : exactInterval 12 3423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3423 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3423) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3423 : oddCount 3423 12 = 7 ∧ acceleratedOrbit 12 3423 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3423 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3423) = 3 ^ 7 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3423.1, data_12_3423.2] + +/-- Complete interval computation for depth 12, residue 3424. -/ +theorem bounds_12_3424 : exactInterval 12 3424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3424 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3424) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3424 : oddCount 3424 12 = 5 ∧ acceleratedOrbit 12 3424 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3424 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3424) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3424.1, data_12_3424.2] + +end Collatz.Research.StoppingAtlas.Batch0423 From 2d4f06859cd98bbf402eea1d8f49ba13b0da1980 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:15 +0530 Subject: [PATCH 0424/1001] proof: certify atlas Batch0424 (12:3425 to 12:3439) --- Collatz/Research/StoppingAtlas/Batch0424.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0424.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0424.lean b/Collatz/Research/StoppingAtlas/Batch0424.lean new file mode 100644 index 00000000..c0ba8390 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0424.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0424 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3425. -/ +theorem bounds_12_3425 : exactInterval 12 3425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3425 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3425) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3425 : oddCount 3425 12 = 6 ∧ acceleratedOrbit 12 3425 = 610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3425 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3425) = 3 ^ 6 * m + 610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3425.1, data_12_3425.2] + +/-- Complete interval computation for depth 12, residue 3426. -/ +theorem bounds_12_3426 : exactInterval 12 3426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3426 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3426) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3426 : oddCount 3426 12 = 4 ∧ acceleratedOrbit 12 3426 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3426 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3426) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3426.1, data_12_3426.2] + +/-- Complete interval computation for depth 12, residue 3427. -/ +theorem bounds_12_3427 : exactInterval 12 3427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3427 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3427) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3427 : oddCount 3427 12 = 4 ∧ acceleratedOrbit 12 3427 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3427 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3427) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3427.1, data_12_3427.2] + +/-- Complete interval computation for depth 12, residue 3428. -/ +theorem bounds_12_3428 : exactInterval 12 3428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3428 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3428) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3428 : oddCount 3428 12 = 4 ∧ acceleratedOrbit 12 3428 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3428 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3428) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3428.1, data_12_3428.2] + +/-- Complete interval computation for depth 12, residue 3429. -/ +theorem bounds_12_3429 : exactInterval 12 3429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3429 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3429) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3429 : oddCount 3429 12 = 4 ∧ acceleratedOrbit 12 3429 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3429 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3429) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3429.1, data_12_3429.2] + +/-- Complete interval computation for depth 12, residue 3430. -/ +theorem bounds_12_3430 : exactInterval 12 3430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3430 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3430) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3430 : oddCount 3430 12 = 4 ∧ acceleratedOrbit 12 3430 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3430 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3430) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3430.1, data_12_3430.2] + +/-- Complete interval computation for depth 12, residue 3431. -/ +theorem bounds_12_3431 : exactInterval 12 3431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3431 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3431) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3431 : oddCount 3431 12 = 10 ∧ acceleratedOrbit 12 3431 = 49481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3431 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3431) = 3 ^ 10 * m + 49481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3431.1, data_12_3431.2] + +/-- Complete interval computation for depth 12, residue 3432. -/ +theorem bounds_12_3432 : exactInterval 12 3432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3432 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3432) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3432 : oddCount 3432 12 = 5 ∧ acceleratedOrbit 12 3432 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3432 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3432) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3432.1, data_12_3432.2] + +/-- Complete interval computation for depth 12, residue 3433. -/ +theorem bounds_12_3433 : exactInterval 12 3433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3433 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3433) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3433 : oddCount 3433 12 = 7 ∧ acceleratedOrbit 12 3433 = 1835 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3433 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3433) = 3 ^ 7 * m + 1835 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3433.1, data_12_3433.2] + +/-- Complete interval computation for depth 12, residue 3434. -/ +theorem bounds_12_3434 : exactInterval 12 3434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3434 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3434) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3434 : oddCount 3434 12 = 5 ∧ acceleratedOrbit 12 3434 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3434 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3434) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3434.1, data_12_3434.2] + +/-- Complete interval computation for depth 12, residue 3435. -/ +theorem bounds_12_3435 : exactInterval 12 3435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3435 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3435) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3435 : oddCount 3435 12 = 8 ∧ acceleratedOrbit 12 3435 = 5507 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3435 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3435) = 3 ^ 8 * m + 5507 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3435.1, data_12_3435.2] + +/-- Complete interval computation for depth 12, residue 3436. -/ +theorem bounds_12_3436 : exactInterval 12 3436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3436 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3436) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3436 : oddCount 3436 12 = 7 ∧ acceleratedOrbit 12 3436 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3436 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3436) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3436.1, data_12_3436.2] + +/-- Complete interval computation for depth 12, residue 3437. -/ +theorem bounds_12_3437 : exactInterval 12 3437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3437 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3437) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3437 : oddCount 3437 12 = 7 ∧ acceleratedOrbit 12 3437 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3437 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3437) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3437.1, data_12_3437.2] + +/-- Complete interval computation for depth 12, residue 3438. -/ +theorem bounds_12_3438 : exactInterval 12 3438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3438 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3438) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3438 : oddCount 3438 12 = 7 ∧ acceleratedOrbit 12 3438 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3438 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3438) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3438.1, data_12_3438.2] + +/-- Complete interval computation for depth 12, residue 3439. -/ +theorem bounds_12_3439 : exactInterval 12 3439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3439 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3439) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3439 : oddCount 3439 12 = 7 ∧ acceleratedOrbit 12 3439 = 1837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3439 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3439) = 3 ^ 7 * m + 1837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3439.1, data_12_3439.2] + +end Collatz.Research.StoppingAtlas.Batch0424 From b04f2a60906f88f211b6b93aec67e0df8f0eec9c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:15 +0530 Subject: [PATCH 0425/1001] proof: certify atlas Batch0425 (12:3440 to 12:3455) --- Collatz/Research/StoppingAtlas/Batch0425.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0425.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0425.lean b/Collatz/Research/StoppingAtlas/Batch0425.lean new file mode 100644 index 00000000..c91e153d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0425.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0425 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3440. -/ +theorem bounds_12_3440 : exactInterval 12 3440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3440 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3440) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3440 : oddCount 3440 12 = 5 ∧ acceleratedOrbit 12 3440 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3440 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3440) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3440.1, data_12_3440.2] + +/-- Complete interval computation for depth 12, residue 3441. -/ +theorem bounds_12_3441 : exactInterval 12 3441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3441 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3441) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3441 : oddCount 3441 12 = 5 ∧ acceleratedOrbit 12 3441 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3441 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3441) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3441.1, data_12_3441.2] + +/-- Complete interval computation for depth 12, residue 3442. -/ +theorem bounds_12_3442 : exactInterval 12 3442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3442 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3442) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3442 : oddCount 3442 12 = 6 ∧ acceleratedOrbit 12 3442 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3442 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3442) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3442.1, data_12_3442.2] + +/-- Complete interval computation for depth 12, residue 3443. -/ +theorem bounds_12_3443 : exactInterval 12 3443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3443 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3443) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3443 : oddCount 3443 12 = 6 ∧ acceleratedOrbit 12 3443 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3443 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3443) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3443.1, data_12_3443.2] + +/-- Complete interval computation for depth 12, residue 3444. -/ +theorem bounds_12_3444 : exactInterval 12 3444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3444 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3444) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3444 : oddCount 3444 12 = 5 ∧ acceleratedOrbit 12 3444 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3444 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3444) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3444.1, data_12_3444.2] + +/-- Complete interval computation for depth 12, residue 3445. -/ +theorem bounds_12_3445 : exactInterval 12 3445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3445 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3445) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3445 : oddCount 3445 12 = 5 ∧ acceleratedOrbit 12 3445 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3445 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3445) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3445.1, data_12_3445.2] + +/-- Complete interval computation for depth 12, residue 3446. -/ +theorem bounds_12_3446 : exactInterval 12 3446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3446 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3446) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3446 : oddCount 3446 12 = 6 ∧ acceleratedOrbit 12 3446 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3446 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3446) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3446.1, data_12_3446.2] + +/-- Complete interval computation for depth 12, residue 3447. -/ +theorem bounds_12_3447 : exactInterval 12 3447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3447 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3447) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3447 : oddCount 3447 12 = 6 ∧ acceleratedOrbit 12 3447 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3447 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3447) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3447.1, data_12_3447.2] + +/-- Complete interval computation for depth 12, residue 3448. -/ +theorem bounds_12_3448 : exactInterval 12 3448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3448 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3448) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3448 : oddCount 3448 12 = 5 ∧ acceleratedOrbit 12 3448 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3448 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3448) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3448.1, data_12_3448.2] + +/-- Complete interval computation for depth 12, residue 3449. -/ +theorem bounds_12_3449 : exactInterval 12 3449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3449 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3449) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3449 : oddCount 3449 12 = 8 ∧ acceleratedOrbit 12 3449 = 5528 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3449 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3449) = 3 ^ 8 * m + 5528 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3449.1, data_12_3449.2] + +/-- Complete interval computation for depth 12, residue 3450. -/ +theorem bounds_12_3450 : exactInterval 12 3450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3450 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3450) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3450 : oddCount 3450 12 = 5 ∧ acceleratedOrbit 12 3450 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3450 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3450) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3450.1, data_12_3450.2] + +/-- Complete interval computation for depth 12, residue 3451. -/ +theorem bounds_12_3451 : exactInterval 12 3451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3451 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3451) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3451 : oddCount 3451 12 = 7 ∧ acceleratedOrbit 12 3451 = 1844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3451 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3451) = 3 ^ 7 * m + 1844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3451.1, data_12_3451.2] + +/-- Complete interval computation for depth 12, residue 3452. -/ +theorem bounds_12_3452 : exactInterval 12 3452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3452 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3452) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3452 : oddCount 3452 12 = 5 ∧ acceleratedOrbit 12 3452 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3452 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3452) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3452.1, data_12_3452.2] + +/-- Complete interval computation for depth 12, residue 3453. -/ +theorem bounds_12_3453 : exactInterval 12 3453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3453 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3453) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3453 : oddCount 3453 12 = 5 ∧ acceleratedOrbit 12 3453 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3453 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3453) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3453.1, data_12_3453.2] + +/-- Complete interval computation for depth 12, residue 3454. -/ +theorem bounds_12_3454 : exactInterval 12 3454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3454 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3454) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3454 : oddCount 3454 12 = 8 ∧ acceleratedOrbit 12 3454 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3454 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3454) = 3 ^ 8 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3454.1, data_12_3454.2] + +/-- Complete interval computation for depth 12, residue 3455. -/ +theorem bounds_12_3455 : exactInterval 12 3455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3455 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3455) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3455 : oddCount 3455 12 = 8 ∧ acceleratedOrbit 12 3455 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3455 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3455) = 3 ^ 8 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3455.1, data_12_3455.2] + +end Collatz.Research.StoppingAtlas.Batch0425 From d24025683425330125550aabcc6615f2e8b69b50 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:16 +0530 Subject: [PATCH 0426/1001] proof: certify atlas Batch0426 (12:3456 to 12:3470) --- Collatz/Research/StoppingAtlas/Batch0426.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0426.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0426.lean b/Collatz/Research/StoppingAtlas/Batch0426.lean new file mode 100644 index 00000000..3f5f9bc6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0426.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0426 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3456. -/ +theorem bounds_12_3456 : exactInterval 12 3456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3456 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3456) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3456 : oddCount 3456 12 = 4 ∧ acceleratedOrbit 12 3456 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3456 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3456) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3456.1, data_12_3456.2] + +/-- Complete interval computation for depth 12, residue 3457. -/ +theorem bounds_12_3457 : exactInterval 12 3457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3457 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3457) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3457 : oddCount 3457 12 = 6 ∧ acceleratedOrbit 12 3457 = 616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3457 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3457) = 3 ^ 6 * m + 616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3457.1, data_12_3457.2] + +/-- Complete interval computation for depth 12, residue 3458. -/ +theorem bounds_12_3458 : exactInterval 12 3458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3458 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3458) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3458 : oddCount 3458 12 = 5 ∧ acceleratedOrbit 12 3458 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3458 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3458) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3458.1, data_12_3458.2] + +/-- Complete interval computation for depth 12, residue 3459. -/ +theorem bounds_12_3459 : exactInterval 12 3459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3459 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3459) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3459 : oddCount 3459 12 = 5 ∧ acceleratedOrbit 12 3459 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3459 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3459) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3459.1, data_12_3459.2] + +/-- Complete interval computation for depth 12, residue 3460. -/ +theorem bounds_12_3460 : exactInterval 12 3460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3460 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3460) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3460 : oddCount 3460 12 = 7 ∧ acceleratedOrbit 12 3460 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3460 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3460) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3460.1, data_12_3460.2] + +/-- Complete interval computation for depth 12, residue 3461. -/ +theorem bounds_12_3461 : exactInterval 12 3461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3461 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3461) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3461 : oddCount 3461 12 = 7 ∧ acceleratedOrbit 12 3461 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3461 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3461) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3461.1, data_12_3461.2] + +/-- Complete interval computation for depth 12, residue 3462. -/ +theorem bounds_12_3462 : exactInterval 12 3462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3462 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3462) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3462 : oddCount 3462 12 = 7 ∧ acceleratedOrbit 12 3462 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3462 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3462) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3462.1, data_12_3462.2] + +/-- Complete interval computation for depth 12, residue 3463. -/ +theorem bounds_12_3463 : exactInterval 12 3463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3463 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3463) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3463 : oddCount 3463 12 = 5 ∧ acceleratedOrbit 12 3463 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3463 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3463) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3463.1, data_12_3463.2] + +/-- Complete interval computation for depth 12, residue 3464. -/ +theorem bounds_12_3464 : exactInterval 12 3464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3464 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3464) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3464 : oddCount 3464 12 = 3 ∧ acceleratedOrbit 12 3464 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3464 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3464) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3464.1, data_12_3464.2] + +/-- Complete interval computation for depth 12, residue 3465. -/ +theorem bounds_12_3465 : exactInterval 12 3465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3465 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3465) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3465 : oddCount 3465 12 = 6 ∧ acceleratedOrbit 12 3465 = 617 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3465 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3465) = 3 ^ 6 * m + 617 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3465.1, data_12_3465.2] + +/-- Complete interval computation for depth 12, residue 3466. -/ +theorem bounds_12_3466 : exactInterval 12 3466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3466 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3466) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3466 : oddCount 3466 12 = 3 ∧ acceleratedOrbit 12 3466 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3466 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3466) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3466.1, data_12_3466.2] + +/-- Complete interval computation for depth 12, residue 3467. -/ +theorem bounds_12_3467 : exactInterval 12 3467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3467 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3467) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3467 : oddCount 3467 12 = 7 ∧ acceleratedOrbit 12 3467 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3467 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3467) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3467.1, data_12_3467.2] + +/-- Complete interval computation for depth 12, residue 3468. -/ +theorem bounds_12_3468 : exactInterval 12 3468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3468 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3468) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3468 : oddCount 3468 12 = 3 ∧ acceleratedOrbit 12 3468 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3468 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3468) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3468.1, data_12_3468.2] + +/-- Complete interval computation for depth 12, residue 3469. -/ +theorem bounds_12_3469 : exactInterval 12 3469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3469 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3469) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3469 : oddCount 3469 12 = 3 ∧ acceleratedOrbit 12 3469 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3469 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3469) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3469.1, data_12_3469.2] + +/-- Complete interval computation for depth 12, residue 3470. -/ +theorem bounds_12_3470 : exactInterval 12 3470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3470 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3470) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3470 : oddCount 3470 12 = 5 ∧ acceleratedOrbit 12 3470 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3470 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3470) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3470.1, data_12_3470.2] + +end Collatz.Research.StoppingAtlas.Batch0426 From ad46f59b022b56f6c5e94ee3a93952b5544200f6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:16 +0530 Subject: [PATCH 0427/1001] proof: certify atlas Batch0427 (12:3471 to 12:3485) --- Collatz/Research/StoppingAtlas/Batch0427.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0427.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0427.lean b/Collatz/Research/StoppingAtlas/Batch0427.lean new file mode 100644 index 00000000..e98d5d7a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0427.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0427 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3471. -/ +theorem bounds_12_3471 : exactInterval 12 3471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3471 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3471) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3471 : oddCount 3471 12 = 5 ∧ acceleratedOrbit 12 3471 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3471 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3471) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3471.1, data_12_3471.2] + +/-- Complete interval computation for depth 12, residue 3472. -/ +theorem bounds_12_3472 : exactInterval 12 3472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3472 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3472) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3472 : oddCount 3472 12 = 3 ∧ acceleratedOrbit 12 3472 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3472 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3472) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3472.1, data_12_3472.2] + +/-- Complete interval computation for depth 12, residue 3473. -/ +theorem bounds_12_3473 : exactInterval 12 3473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3473 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3473) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3473 : oddCount 3473 12 = 6 ∧ acceleratedOrbit 12 3473 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3473 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3473) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3473.1, data_12_3473.2] + +/-- Complete interval computation for depth 12, residue 3474. -/ +theorem bounds_12_3474 : exactInterval 12 3474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3474 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3474) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3474 : oddCount 3474 12 = 6 ∧ acceleratedOrbit 12 3474 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3474 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3474) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3474.1, data_12_3474.2] + +/-- Complete interval computation for depth 12, residue 3475. -/ +theorem bounds_12_3475 : exactInterval 12 3475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3475 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3475) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3475 : oddCount 3475 12 = 6 ∧ acceleratedOrbit 12 3475 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3475 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3475) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3475.1, data_12_3475.2] + +/-- Complete interval computation for depth 12, residue 3476. -/ +theorem bounds_12_3476 : exactInterval 12 3476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3476 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3476) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3476 : oddCount 3476 12 = 3 ∧ acceleratedOrbit 12 3476 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3476 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3476) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3476.1, data_12_3476.2] + +/-- Complete interval computation for depth 12, residue 3477. -/ +theorem bounds_12_3477 : exactInterval 12 3477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3477 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3477) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3477 : oddCount 3477 12 = 3 ∧ acceleratedOrbit 12 3477 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3477 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3477) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3477.1, data_12_3477.2] + +/-- Complete interval computation for depth 12, residue 3478. -/ +theorem bounds_12_3478 : exactInterval 12 3478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3478 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3478) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3478 : oddCount 3478 12 = 7 ∧ acceleratedOrbit 12 3478 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3478 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3478) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3478.1, data_12_3478.2] + +/-- Complete interval computation for depth 12, residue 3479. -/ +theorem bounds_12_3479 : exactInterval 12 3479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3479 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3479) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3479 : oddCount 3479 12 = 7 ∧ acceleratedOrbit 12 3479 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3479 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3479) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3479.1, data_12_3479.2] + +/-- Complete interval computation for depth 12, residue 3480. -/ +theorem bounds_12_3480 : exactInterval 12 3480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3480 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3480) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3480 : oddCount 3480 12 = 3 ∧ acceleratedOrbit 12 3480 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3480 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3480) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3480.1, data_12_3480.2] + +/-- Complete interval computation for depth 12, residue 3481. -/ +theorem bounds_12_3481 : exactInterval 12 3481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3481 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3481) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3481 : oddCount 3481 12 = 7 ∧ acceleratedOrbit 12 3481 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3481 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3481) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3481.1, data_12_3481.2] + +/-- Complete interval computation for depth 12, residue 3482. -/ +theorem bounds_12_3482 : exactInterval 12 3482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3482 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3482) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3482 : oddCount 3482 12 = 3 ∧ acceleratedOrbit 12 3482 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3482 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3482) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3482.1, data_12_3482.2] + +/-- Complete interval computation for depth 12, residue 3483. -/ +theorem bounds_12_3483 : exactInterval 12 3483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3483 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3483) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3483 : oddCount 3483 12 = 8 ∧ acceleratedOrbit 12 3483 = 5582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3483 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3483) = 3 ^ 8 * m + 5582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3483.1, data_12_3483.2] + +/-- Complete interval computation for depth 12, residue 3484. -/ +theorem bounds_12_3484 : exactInterval 12 3484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3484 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3484) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3484 : oddCount 3484 12 = 9 ∧ acceleratedOrbit 12 3484 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3484 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3484) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3484.1, data_12_3484.2] + +/-- Complete interval computation for depth 12, residue 3485. -/ +theorem bounds_12_3485 : exactInterval 12 3485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3485 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3485) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3485 : oddCount 3485 12 = 9 ∧ acceleratedOrbit 12 3485 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3485 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3485) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3485.1, data_12_3485.2] + +end Collatz.Research.StoppingAtlas.Batch0427 From 0d9df3728790a9478f6e0bfe944e4c78220f5af1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:16 +0530 Subject: [PATCH 0428/1001] proof: certify atlas Batch0428 (12:3486 to 12:3501) --- Collatz/Research/StoppingAtlas/Batch0428.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0428.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0428.lean b/Collatz/Research/StoppingAtlas/Batch0428.lean new file mode 100644 index 00000000..09bb3744 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0428.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0428 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3486. -/ +theorem bounds_12_3486 : exactInterval 12 3486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3486 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3486) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3486 : oddCount 3486 12 = 9 ∧ acceleratedOrbit 12 3486 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3486 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3486) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3486.1, data_12_3486.2] + +/-- Complete interval computation for depth 12, residue 3487. -/ +theorem bounds_12_3487 : exactInterval 12 3487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3487 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3487) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3487 : oddCount 3487 12 = 9 ∧ acceleratedOrbit 12 3487 = 16762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3487 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3487) = 3 ^ 9 * m + 16762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3487.1, data_12_3487.2] + +/-- Complete interval computation for depth 12, residue 3488. -/ +theorem bounds_12_3488 : exactInterval 12 3488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3488 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3488) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3488 : oddCount 3488 12 = 4 ∧ acceleratedOrbit 12 3488 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3488 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3488) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3488.1, data_12_3488.2] + +/-- Complete interval computation for depth 12, residue 3489. -/ +theorem bounds_12_3489 : exactInterval 12 3489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3489 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3489) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3489 : oddCount 3489 12 = 7 ∧ acceleratedOrbit 12 3489 = 1865 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3489 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3489) = 3 ^ 7 * m + 1865 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3489.1, data_12_3489.2] + +/-- Complete interval computation for depth 12, residue 3490. -/ +theorem bounds_12_3490 : exactInterval 12 3490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3490 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3490) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3490 : oddCount 3490 12 = 6 ∧ acceleratedOrbit 12 3490 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3490 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3490) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3490.1, data_12_3490.2] + +/-- Complete interval computation for depth 12, residue 3491. -/ +theorem bounds_12_3491 : exactInterval 12 3491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3491 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3491) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3491 : oddCount 3491 12 = 6 ∧ acceleratedOrbit 12 3491 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3491 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3491) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3491.1, data_12_3491.2] + +/-- Complete interval computation for depth 12, residue 3492. -/ +theorem bounds_12_3492 : exactInterval 12 3492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3492 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3492) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3492 : oddCount 3492 12 = 6 ∧ acceleratedOrbit 12 3492 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3492 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3492) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3492.1, data_12_3492.2] + +/-- Complete interval computation for depth 12, residue 3493. -/ +theorem bounds_12_3493 : exactInterval 12 3493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3493 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3493) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3493 : oddCount 3493 12 = 6 ∧ acceleratedOrbit 12 3493 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3493 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3493) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3493.1, data_12_3493.2] + +/-- Complete interval computation for depth 12, residue 3494. -/ +theorem bounds_12_3494 : exactInterval 12 3494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3494 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3494) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3494 : oddCount 3494 12 = 6 ∧ acceleratedOrbit 12 3494 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3494 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3494) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3494.1, data_12_3494.2] + +/-- Complete interval computation for depth 12, residue 3495. -/ +theorem bounds_12_3495 : exactInterval 12 3495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3495 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3495) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3495 : oddCount 3495 12 = 7 ∧ acceleratedOrbit 12 3495 = 1867 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3495 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3495) = 3 ^ 7 * m + 1867 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3495.1, data_12_3495.2] + +/-- Complete interval computation for depth 12, residue 3496. -/ +theorem bounds_12_3496 : exactInterval 12 3496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3496 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3496) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3496 : oddCount 3496 12 = 4 ∧ acceleratedOrbit 12 3496 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3496 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3496) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3496.1, data_12_3496.2] + +/-- Complete interval computation for depth 12, residue 3497. -/ +theorem bounds_12_3497 : exactInterval 12 3497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3497 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3497) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3497 : oddCount 3497 12 = 7 ∧ acceleratedOrbit 12 3497 = 1868 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3497 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3497) = 3 ^ 7 * m + 1868 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3497.1, data_12_3497.2] + +/-- Complete interval computation for depth 12, residue 3498. -/ +theorem bounds_12_3498 : exactInterval 12 3498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3498 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3498) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3498 : oddCount 3498 12 = 4 ∧ acceleratedOrbit 12 3498 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3498 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3498) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3498.1, data_12_3498.2] + +/-- Complete interval computation for depth 12, residue 3499. -/ +theorem bounds_12_3499 : exactInterval 12 3499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3499 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3499) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3499 : oddCount 3499 12 = 8 ∧ acceleratedOrbit 12 3499 = 5609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3499 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3499) = 3 ^ 8 * m + 5609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3499.1, data_12_3499.2] + +/-- Complete interval computation for depth 12, residue 3500. -/ +theorem bounds_12_3500 : exactInterval 12 3500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3500 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3500) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3500 : oddCount 3500 12 = 5 ∧ acceleratedOrbit 12 3500 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3500 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3500) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3500.1, data_12_3500.2] + +/-- Complete interval computation for depth 12, residue 3501. -/ +theorem bounds_12_3501 : exactInterval 12 3501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3501 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3501) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3501 : oddCount 3501 12 = 5 ∧ acceleratedOrbit 12 3501 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3501 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3501) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3501.1, data_12_3501.2] + +end Collatz.Research.StoppingAtlas.Batch0428 From 57f65604b32bab1b187bf925278e7db9f6200e9e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:17 +0530 Subject: [PATCH 0429/1001] proof: certify atlas Batch0429 (12:3502 to 12:3516) --- Collatz/Research/StoppingAtlas/Batch0429.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0429.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0429.lean b/Collatz/Research/StoppingAtlas/Batch0429.lean new file mode 100644 index 00000000..c59e1cb4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0429.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0429 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3502. -/ +theorem bounds_12_3502 : exactInterval 12 3502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3502 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3502) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3502 : oddCount 3502 12 = 5 ∧ acceleratedOrbit 12 3502 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3502 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3502) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3502.1, data_12_3502.2] + +/-- Complete interval computation for depth 12, residue 3503. -/ +theorem bounds_12_3503 : exactInterval 12 3503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3503 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3503) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3503 : oddCount 3503 12 = 8 ∧ acceleratedOrbit 12 3503 = 5615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3503 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3503) = 3 ^ 8 * m + 5615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3503.1, data_12_3503.2] + +/-- Complete interval computation for depth 12, residue 3504. -/ +theorem bounds_12_3504 : exactInterval 12 3504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3504 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3504) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3504 : oddCount 3504 12 = 5 ∧ acceleratedOrbit 12 3504 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3504 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3504) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3504.1, data_12_3504.2] + +/-- Complete interval computation for depth 12, residue 3505. -/ +theorem bounds_12_3505 : exactInterval 12 3505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3505 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3505) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3505 : oddCount 3505 12 = 5 ∧ acceleratedOrbit 12 3505 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3505 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3505) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3505.1, data_12_3505.2] + +/-- Complete interval computation for depth 12, residue 3506. -/ +theorem bounds_12_3506 : exactInterval 12 3506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3506 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3506) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3506 : oddCount 3506 12 = 5 ∧ acceleratedOrbit 12 3506 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3506 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3506) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3506.1, data_12_3506.2] + +/-- Complete interval computation for depth 12, residue 3507. -/ +theorem bounds_12_3507 : exactInterval 12 3507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3507 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3507) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3507 : oddCount 3507 12 = 5 ∧ acceleratedOrbit 12 3507 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3507 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3507) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3507.1, data_12_3507.2] + +/-- Complete interval computation for depth 12, residue 3508. -/ +theorem bounds_12_3508 : exactInterval 12 3508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3508 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3508) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3508 : oddCount 3508 12 = 5 ∧ acceleratedOrbit 12 3508 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3508 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3508) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3508.1, data_12_3508.2] + +/-- Complete interval computation for depth 12, residue 3509. -/ +theorem bounds_12_3509 : exactInterval 12 3509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3509 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3509) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3509 : oddCount 3509 12 = 5 ∧ acceleratedOrbit 12 3509 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3509 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3509) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3509.1, data_12_3509.2] + +/-- Complete interval computation for depth 12, residue 3510. -/ +theorem bounds_12_3510 : exactInterval 12 3510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3510 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3510) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3510 : oddCount 3510 12 = 7 ∧ acceleratedOrbit 12 3510 = 1876 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3510 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3510) = 3 ^ 7 * m + 1876 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3510.1, data_12_3510.2] + +/-- Complete interval computation for depth 12, residue 3511. -/ +theorem bounds_12_3511 : exactInterval 12 3511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3511 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3511) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3511 : oddCount 3511 12 = 7 ∧ acceleratedOrbit 12 3511 = 1876 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3511 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3511) = 3 ^ 7 * m + 1876 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3511.1, data_12_3511.2] + +/-- Complete interval computation for depth 12, residue 3512. -/ +theorem bounds_12_3512 : exactInterval 12 3512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3512 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3512) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3512 : oddCount 3512 12 = 5 ∧ acceleratedOrbit 12 3512 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3512 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3512) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3512.1, data_12_3512.2] + +/-- Complete interval computation for depth 12, residue 3513. -/ +theorem bounds_12_3513 : exactInterval 12 3513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3513 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3513) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3513 : oddCount 3513 12 = 5 ∧ acceleratedOrbit 12 3513 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3513 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3513) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3513.1, data_12_3513.2] + +/-- Complete interval computation for depth 12, residue 3514. -/ +theorem bounds_12_3514 : exactInterval 12 3514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3514 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3514) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3514 : oddCount 3514 12 = 5 ∧ acceleratedOrbit 12 3514 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3514 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3514) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3514.1, data_12_3514.2] + +/-- Complete interval computation for depth 12, residue 3515. -/ +theorem bounds_12_3515 : exactInterval 12 3515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3515 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3515) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3515 : oddCount 3515 12 = 6 ∧ acceleratedOrbit 12 3515 = 626 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3515 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3515) = 3 ^ 6 * m + 626 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3515.1, data_12_3515.2] + +/-- Complete interval computation for depth 12, residue 3516. -/ +theorem bounds_12_3516 : exactInterval 12 3516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3516 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3516) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3516 : oddCount 3516 12 = 7 ∧ acceleratedOrbit 12 3516 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3516 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3516) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3516.1, data_12_3516.2] + +end Collatz.Research.StoppingAtlas.Batch0429 From 367aaa79fc23cbf1e2441c44cd44141942d9049c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:17 +0530 Subject: [PATCH 0430/1001] proof: certify atlas Batch0430 (12:3517 to 12:3531) --- Collatz/Research/StoppingAtlas/Batch0430.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0430.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0430.lean b/Collatz/Research/StoppingAtlas/Batch0430.lean new file mode 100644 index 00000000..ea8c45cd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0430.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0430 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3517. -/ +theorem bounds_12_3517 : exactInterval 12 3517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3517 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3517) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3517 : oddCount 3517 12 = 7 ∧ acceleratedOrbit 12 3517 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3517 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3517) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3517.1, data_12_3517.2] + +/-- Complete interval computation for depth 12, residue 3518. -/ +theorem bounds_12_3518 : exactInterval 12 3518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3518 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3518) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3518 : oddCount 3518 12 = 7 ∧ acceleratedOrbit 12 3518 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3518 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3518) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3518.1, data_12_3518.2] + +/-- Complete interval computation for depth 12, residue 3519. -/ +theorem bounds_12_3519 : exactInterval 12 3519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3519 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3519) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3519 : oddCount 3519 12 = 10 ∧ acceleratedOrbit 12 3519 = 50746 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3519 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3519) = 3 ^ 10 * m + 50746 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3519.1, data_12_3519.2] + +/-- Complete interval computation for depth 12, residue 3520. -/ +theorem bounds_12_3520 : exactInterval 12 3520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3520 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3520) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3520 : oddCount 3520 12 = 4 ∧ acceleratedOrbit 12 3520 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3520 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3520) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3520.1, data_12_3520.2] + +/-- Complete interval computation for depth 12, residue 3521. -/ +theorem bounds_12_3521 : exactInterval 12 3521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3521 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3521) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3521 : oddCount 3521 12 = 7 ∧ acceleratedOrbit 12 3521 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3521 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3521) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3521.1, data_12_3521.2] + +/-- Complete interval computation for depth 12, residue 3522. -/ +theorem bounds_12_3522 : exactInterval 12 3522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3522 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3522) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3522 : oddCount 3522 12 = 7 ∧ acceleratedOrbit 12 3522 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3522 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3522) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3522.1, data_12_3522.2] + +/-- Complete interval computation for depth 12, residue 3523. -/ +theorem bounds_12_3523 : exactInterval 12 3523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3523 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3523) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3523 : oddCount 3523 12 = 7 ∧ acceleratedOrbit 12 3523 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3523 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3523) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3523.1, data_12_3523.2] + +/-- Complete interval computation for depth 12, residue 3524. -/ +theorem bounds_12_3524 : exactInterval 12 3524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3524 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3524) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3524 : oddCount 3524 12 = 4 ∧ acceleratedOrbit 12 3524 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3524 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3524) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3524.1, data_12_3524.2] + +/-- Complete interval computation for depth 12, residue 3525. -/ +theorem bounds_12_3525 : exactInterval 12 3525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3525 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3525) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3525 : oddCount 3525 12 = 4 ∧ acceleratedOrbit 12 3525 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3525 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3525) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3525.1, data_12_3525.2] + +/-- Complete interval computation for depth 12, residue 3526. -/ +theorem bounds_12_3526 : exactInterval 12 3526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3526 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3526) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3526 : oddCount 3526 12 = 4 ∧ acceleratedOrbit 12 3526 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3526 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3526) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3526.1, data_12_3526.2] + +/-- Complete interval computation for depth 12, residue 3527. -/ +theorem bounds_12_3527 : exactInterval 12 3527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3527 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3527) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3527 : oddCount 3527 12 = 6 ∧ acceleratedOrbit 12 3527 = 628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3527 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3527) = 3 ^ 6 * m + 628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3527.1, data_12_3527.2] + +/-- Complete interval computation for depth 12, residue 3528. -/ +theorem bounds_12_3528 : exactInterval 12 3528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3528 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3528) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3528 : oddCount 3528 12 = 4 ∧ acceleratedOrbit 12 3528 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3528 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3528) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3528.1, data_12_3528.2] + +/-- Complete interval computation for depth 12, residue 3529. -/ +theorem bounds_12_3529 : exactInterval 12 3529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3529 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3529) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3529 : oddCount 3529 12 = 6 ∧ acceleratedOrbit 12 3529 = 629 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3529 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3529) = 3 ^ 6 * m + 629 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3529.1, data_12_3529.2] + +/-- Complete interval computation for depth 12, residue 3530. -/ +theorem bounds_12_3530 : exactInterval 12 3530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3530 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3530) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3530 : oddCount 3530 12 = 4 ∧ acceleratedOrbit 12 3530 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3530 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3530) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3530.1, data_12_3530.2] + +/-- Complete interval computation for depth 12, residue 3531. -/ +theorem bounds_12_3531 : exactInterval 12 3531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3531 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3531) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3531 : oddCount 3531 12 = 7 ∧ acceleratedOrbit 12 3531 = 1889 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3531 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3531) = 3 ^ 7 * m + 1889 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3531.1, data_12_3531.2] + +end Collatz.Research.StoppingAtlas.Batch0430 From 7f95ed8cc9f42c4a3c51e6b20d25bd1c3110980a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:18 +0530 Subject: [PATCH 0431/1001] proof: certify atlas Batch0431 (12:3532 to 12:3547) --- Collatz/Research/StoppingAtlas/Batch0431.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0431.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0431.lean b/Collatz/Research/StoppingAtlas/Batch0431.lean new file mode 100644 index 00000000..a13dec8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0431.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0431 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3532. -/ +theorem bounds_12_3532 : exactInterval 12 3532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3532 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3532) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3532 : oddCount 3532 12 = 4 ∧ acceleratedOrbit 12 3532 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3532 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3532) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3532.1, data_12_3532.2] + +/-- Complete interval computation for depth 12, residue 3533. -/ +theorem bounds_12_3533 : exactInterval 12 3533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3533 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3533) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3533 : oddCount 3533 12 = 4 ∧ acceleratedOrbit 12 3533 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3533 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3533) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3533.1, data_12_3533.2] + +/-- Complete interval computation for depth 12, residue 3534. -/ +theorem bounds_12_3534 : exactInterval 12 3534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3534 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3534) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3534 : oddCount 3534 12 = 8 ∧ acceleratedOrbit 12 3534 = 5665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3534 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3534) = 3 ^ 8 * m + 5665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3534.1, data_12_3534.2] + +/-- Complete interval computation for depth 12, residue 3535. -/ +theorem bounds_12_3535 : exactInterval 12 3535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3535 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3535) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3535 : oddCount 3535 12 = 8 ∧ acceleratedOrbit 12 3535 = 5665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3535 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3535) = 3 ^ 8 * m + 5665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3535.1, data_12_3535.2] + +/-- Complete interval computation for depth 12, residue 3536. -/ +theorem bounds_12_3536 : exactInterval 12 3536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3536 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3536) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3536 : oddCount 3536 12 = 4 ∧ acceleratedOrbit 12 3536 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3536 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3536) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3536.1, data_12_3536.2] + +/-- Complete interval computation for depth 12, residue 3537. -/ +theorem bounds_12_3537 : exactInterval 12 3537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3537 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3537) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3537 : oddCount 3537 12 = 4 ∧ acceleratedOrbit 12 3537 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3537 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3537) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3537.1, data_12_3537.2] + +/-- Complete interval computation for depth 12, residue 3538. -/ +theorem bounds_12_3538 : exactInterval 12 3538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3538 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3538) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3538 : oddCount 3538 12 = 7 ∧ acceleratedOrbit 12 3538 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3538 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3538) = 3 ^ 7 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3538.1, data_12_3538.2] + +/-- Complete interval computation for depth 12, residue 3539. -/ +theorem bounds_12_3539 : exactInterval 12 3539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3539 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3539) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3539 : oddCount 3539 12 = 7 ∧ acceleratedOrbit 12 3539 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3539 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3539) = 3 ^ 7 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3539.1, data_12_3539.2] + +/-- Complete interval computation for depth 12, residue 3540. -/ +theorem bounds_12_3540 : exactInterval 12 3540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3540 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3540) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3540 : oddCount 3540 12 = 4 ∧ acceleratedOrbit 12 3540 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3540 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3540) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3540.1, data_12_3540.2] + +/-- Complete interval computation for depth 12, residue 3541. -/ +theorem bounds_12_3541 : exactInterval 12 3541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3541 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3541) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3541 : oddCount 3541 12 = 4 ∧ acceleratedOrbit 12 3541 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3541 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3541) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3541.1, data_12_3541.2] + +/-- Complete interval computation for depth 12, residue 3542. -/ +theorem bounds_12_3542 : exactInterval 12 3542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3542 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3542) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3542 : oddCount 3542 12 = 6 ∧ acceleratedOrbit 12 3542 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3542 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3542) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3542.1, data_12_3542.2] + +/-- Complete interval computation for depth 12, residue 3543. -/ +theorem bounds_12_3543 : exactInterval 12 3543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3543 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3543) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3543 : oddCount 3543 12 = 6 ∧ acceleratedOrbit 12 3543 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3543 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3543) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3543.1, data_12_3543.2] + +/-- Complete interval computation for depth 12, residue 3544. -/ +theorem bounds_12_3544 : exactInterval 12 3544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3544 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3544) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3544 : oddCount 3544 12 = 5 ∧ acceleratedOrbit 12 3544 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3544 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3544) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3544.1, data_12_3544.2] + +/-- Complete interval computation for depth 12, residue 3545. -/ +theorem bounds_12_3545 : exactInterval 12 3545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3545 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3545) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3545 : oddCount 3545 12 = 5 ∧ acceleratedOrbit 12 3545 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3545 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3545) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3545.1, data_12_3545.2] + +/-- Complete interval computation for depth 12, residue 3546. -/ +theorem bounds_12_3546 : exactInterval 12 3546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3546 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3546) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3546 : oddCount 3546 12 = 5 ∧ acceleratedOrbit 12 3546 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3546 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3546) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3546.1, data_12_3546.2] + +/-- Complete interval computation for depth 12, residue 3547. -/ +theorem bounds_12_3547 : exactInterval 12 3547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3547 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3547) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3547 : oddCount 3547 12 = 6 ∧ acceleratedOrbit 12 3547 = 632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3547 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3547) = 3 ^ 6 * m + 632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3547.1, data_12_3547.2] + +end Collatz.Research.StoppingAtlas.Batch0431 From 95e25c7329235a246bdf58164b845851de4b19e7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:18 +0530 Subject: [PATCH 0432/1001] proof: certify atlas Batch0432 (12:3548 to 12:3562) --- Collatz/Research/StoppingAtlas/Batch0432.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0432.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0432.lean b/Collatz/Research/StoppingAtlas/Batch0432.lean new file mode 100644 index 00000000..a1c23680 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0432.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0432 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3548. -/ +theorem bounds_12_3548 : exactInterval 12 3548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3548 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3548) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3548 : oddCount 3548 12 = 5 ∧ acceleratedOrbit 12 3548 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3548 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3548) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3548.1, data_12_3548.2] + +/-- Complete interval computation for depth 12, residue 3549. -/ +theorem bounds_12_3549 : exactInterval 12 3549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3549 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3549) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3549 : oddCount 3549 12 = 5 ∧ acceleratedOrbit 12 3549 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3549 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3549) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3549.1, data_12_3549.2] + +/-- Complete interval computation for depth 12, residue 3550. -/ +theorem bounds_12_3550 : exactInterval 12 3550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3550 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3550) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3550 : oddCount 3550 12 = 8 ∧ acceleratedOrbit 12 3550 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3550 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3550) = 3 ^ 8 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3550.1, data_12_3550.2] + +/-- Complete interval computation for depth 12, residue 3551. -/ +theorem bounds_12_3551 : exactInterval 12 3551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3551 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3551) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3551 : oddCount 3551 12 = 8 ∧ acceleratedOrbit 12 3551 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3551 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3551) = 3 ^ 8 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3551.1, data_12_3551.2] + +/-- Complete interval computation for depth 12, residue 3552. -/ +theorem bounds_12_3552 : exactInterval 12 3552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3552 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3552) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3552 : oddCount 3552 12 = 6 ∧ acceleratedOrbit 12 3552 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3552 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3552) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3552.1, data_12_3552.2] + +/-- Complete interval computation for depth 12, residue 3553. -/ +theorem bounds_12_3553 : exactInterval 12 3553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3553 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3553) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3553 : oddCount 3553 12 = 8 ∧ acceleratedOrbit 12 3553 = 5696 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3553 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3553) = 3 ^ 8 * m + 5696 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3553.1, data_12_3553.2] + +/-- Complete interval computation for depth 12, residue 3554. -/ +theorem bounds_12_3554 : exactInterval 12 3554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3554 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3554) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3554 : oddCount 3554 12 = 4 ∧ acceleratedOrbit 12 3554 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3554 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3554) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3554.1, data_12_3554.2] + +/-- Complete interval computation for depth 12, residue 3555. -/ +theorem bounds_12_3555 : exactInterval 12 3555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3555 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3555) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3555 : oddCount 3555 12 = 4 ∧ acceleratedOrbit 12 3555 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3555 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3555) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3555.1, data_12_3555.2] + +/-- Complete interval computation for depth 12, residue 3556. -/ +theorem bounds_12_3556 : exactInterval 12 3556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3556 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3556) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3556 : oddCount 3556 12 = 7 ∧ acceleratedOrbit 12 3556 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3556 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3556) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3556.1, data_12_3556.2] + +/-- Complete interval computation for depth 12, residue 3557. -/ +theorem bounds_12_3557 : exactInterval 12 3557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3557 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3557) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3557 : oddCount 3557 12 = 7 ∧ acceleratedOrbit 12 3557 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3557 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3557) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3557.1, data_12_3557.2] + +/-- Complete interval computation for depth 12, residue 3558. -/ +theorem bounds_12_3558 : exactInterval 12 3558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3558 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3558) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3558 : oddCount 3558 12 = 7 ∧ acceleratedOrbit 12 3558 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3558 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3558) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3558.1, data_12_3558.2] + +/-- Complete interval computation for depth 12, residue 3559. -/ +theorem bounds_12_3559 : exactInterval 12 3559 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3559 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3559) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3559 : oddCount 3559 12 = 7 ∧ acceleratedOrbit 12 3559 = 1901 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3559 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3559) = 3 ^ 7 * m + 1901 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3559.1, data_12_3559.2] + +/-- Complete interval computation for depth 12, residue 3560. -/ +theorem bounds_12_3560 : exactInterval 12 3560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3560 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3560) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3560 : oddCount 3560 12 = 6 ∧ acceleratedOrbit 12 3560 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3560 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3560) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3560.1, data_12_3560.2] + +/-- Complete interval computation for depth 12, residue 3561. -/ +theorem bounds_12_3561 : exactInterval 12 3561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3561 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3561) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3561 : oddCount 3561 12 = 8 ∧ acceleratedOrbit 12 3561 = 5707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3561 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3561) = 3 ^ 8 * m + 5707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3561.1, data_12_3561.2] + +/-- Complete interval computation for depth 12, residue 3562. -/ +theorem bounds_12_3562 : exactInterval 12 3562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3562 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3562) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3562 : oddCount 3562 12 = 6 ∧ acceleratedOrbit 12 3562 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3562 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3562) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3562.1, data_12_3562.2] + +end Collatz.Research.StoppingAtlas.Batch0432 From ff3e4b057f57b97e3d4ed4144a692848c12e1658 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:18 +0530 Subject: [PATCH 0433/1001] proof: certify atlas Batch0433 (12:3563 to 12:3577) --- Collatz/Research/StoppingAtlas/Batch0433.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0433.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0433.lean b/Collatz/Research/StoppingAtlas/Batch0433.lean new file mode 100644 index 00000000..39c5170c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0433.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0433 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3563. -/ +theorem bounds_12_3563 : exactInterval 12 3563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3563 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3563) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3563 : oddCount 3563 12 = 9 ∧ acceleratedOrbit 12 3563 = 17131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3563 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3563) = 3 ^ 9 * m + 17131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3563.1, data_12_3563.2] + +/-- Complete interval computation for depth 12, residue 3564. -/ +theorem bounds_12_3564 : exactInterval 12 3564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3564 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3564) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3564 : oddCount 3564 12 = 7 ∧ acceleratedOrbit 12 3564 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3564 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3564) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3564.1, data_12_3564.2] + +/-- Complete interval computation for depth 12, residue 3565. -/ +theorem bounds_12_3565 : exactInterval 12 3565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3565 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3565) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3565 : oddCount 3565 12 = 7 ∧ acceleratedOrbit 12 3565 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3565 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3565) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3565.1, data_12_3565.2] + +/-- Complete interval computation for depth 12, residue 3566. -/ +theorem bounds_12_3566 : exactInterval 12 3566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3566 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3566) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3566 : oddCount 3566 12 = 7 ∧ acceleratedOrbit 12 3566 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3566 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3566) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3566.1, data_12_3566.2] + +/-- Complete interval computation for depth 12, residue 3567. -/ +theorem bounds_12_3567 : exactInterval 12 3567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3567 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3567) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3567 : oddCount 3567 12 = 9 ∧ acceleratedOrbit 12 3567 = 17147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3567 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3567) = 3 ^ 9 * m + 17147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3567.1, data_12_3567.2] + +/-- Complete interval computation for depth 12, residue 3568. -/ +theorem bounds_12_3568 : exactInterval 12 3568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3568 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3568) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3568 : oddCount 3568 12 = 6 ∧ acceleratedOrbit 12 3568 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3568 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3568) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3568.1, data_12_3568.2] + +/-- Complete interval computation for depth 12, residue 3569. -/ +theorem bounds_12_3569 : exactInterval 12 3569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3569 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3569) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3569 : oddCount 3569 12 = 6 ∧ acceleratedOrbit 12 3569 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3569 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3569) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3569.1, data_12_3569.2] + +/-- Complete interval computation for depth 12, residue 3570. -/ +theorem bounds_12_3570 : exactInterval 12 3570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3570 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3570) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3570 : oddCount 3570 12 = 5 ∧ acceleratedOrbit 12 3570 = 212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3570 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3570) = 3 ^ 5 * m + 212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3570.1, data_12_3570.2] + +/-- Complete interval computation for depth 12, residue 3571. -/ +theorem bounds_12_3571 : exactInterval 12 3571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3571 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3571) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3571 : oddCount 3571 12 = 5 ∧ acceleratedOrbit 12 3571 = 212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3571 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3571) = 3 ^ 5 * m + 212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3571.1, data_12_3571.2] + +/-- Complete interval computation for depth 12, residue 3572. -/ +theorem bounds_12_3572 : exactInterval 12 3572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3572 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3572) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3572 : oddCount 3572 12 = 6 ∧ acceleratedOrbit 12 3572 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3572 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3572) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3572.1, data_12_3572.2] + +/-- Complete interval computation for depth 12, residue 3573. -/ +theorem bounds_12_3573 : exactInterval 12 3573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3573 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3573) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3573 : oddCount 3573 12 = 6 ∧ acceleratedOrbit 12 3573 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3573 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3573) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3573.1, data_12_3573.2] + +/-- Complete interval computation for depth 12, residue 3574. -/ +theorem bounds_12_3574 : exactInterval 12 3574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3574 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3574) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3574 : oddCount 3574 12 = 7 ∧ acceleratedOrbit 12 3574 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3574 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3574) = 3 ^ 7 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3574.1, data_12_3574.2] + +/-- Complete interval computation for depth 12, residue 3575. -/ +theorem bounds_12_3575 : exactInterval 12 3575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3575 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3575) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3575 : oddCount 3575 12 = 7 ∧ acceleratedOrbit 12 3575 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3575 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3575) = 3 ^ 7 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3575.1, data_12_3575.2] + +/-- Complete interval computation for depth 12, residue 3576. -/ +theorem bounds_12_3576 : exactInterval 12 3576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3576 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3576) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3576 : oddCount 3576 12 = 8 ∧ acceleratedOrbit 12 3576 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3576 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3576) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3576.1, data_12_3576.2] + +/-- Complete interval computation for depth 12, residue 3577. -/ +theorem bounds_12_3577 : exactInterval 12 3577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3577 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3577) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3577 : oddCount 3577 12 = 6 ∧ acceleratedOrbit 12 3577 = 637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3577 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3577) = 3 ^ 6 * m + 637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3577.1, data_12_3577.2] + +end Collatz.Research.StoppingAtlas.Batch0433 From 4fa0df95c33f5a9a4373569e9c870c104a22a0d0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:19 +0530 Subject: [PATCH 0434/1001] proof: certify atlas Batch0434 (12:3578 to 12:3593) --- Collatz/Research/StoppingAtlas/Batch0434.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0434.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0434.lean b/Collatz/Research/StoppingAtlas/Batch0434.lean new file mode 100644 index 00000000..719736a0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0434.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0434 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3578. -/ +theorem bounds_12_3578 : exactInterval 12 3578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3578 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3578) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3578 : oddCount 3578 12 = 8 ∧ acceleratedOrbit 12 3578 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3578 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3578) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3578.1, data_12_3578.2] + +/-- Complete interval computation for depth 12, residue 3579. -/ +theorem bounds_12_3579 : exactInterval 12 3579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3579 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3579) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3579 : oddCount 3579 12 = 7 ∧ acceleratedOrbit 12 3579 = 1912 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3579 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3579) = 3 ^ 7 * m + 1912 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3579.1, data_12_3579.2] + +/-- Complete interval computation for depth 12, residue 3580. -/ +theorem bounds_12_3580 : exactInterval 12 3580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3580 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3580) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3580 : oddCount 3580 12 = 8 ∧ acceleratedOrbit 12 3580 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3580 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3580) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3580.1, data_12_3580.2] + +/-- Complete interval computation for depth 12, residue 3581. -/ +theorem bounds_12_3581 : exactInterval 12 3581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3581 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3581) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3581 : oddCount 3581 12 = 8 ∧ acceleratedOrbit 12 3581 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3581 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3581) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3581.1, data_12_3581.2] + +/-- Complete interval computation for depth 12, residue 3582. -/ +theorem bounds_12_3582 : exactInterval 12 3582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3582 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3582) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3582 : oddCount 3582 12 = 10 ∧ acceleratedOrbit 12 3582 = 51668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3582 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3582) = 3 ^ 10 * m + 51668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3582.1, data_12_3582.2] + +/-- Complete interval computation for depth 12, residue 3583. -/ +theorem bounds_12_3583 : exactInterval 12 3583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3583 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3583) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3583 : oddCount 3583 12 = 10 ∧ acceleratedOrbit 12 3583 = 51668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3583 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3583) = 3 ^ 10 * m + 51668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3583.1, data_12_3583.2] + +/-- Complete interval computation for depth 12, residue 3584. -/ +theorem bounds_12_3584 : exactInterval 12 3584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3584 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3584) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3584 : oddCount 3584 12 = 3 ∧ acceleratedOrbit 12 3584 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3584 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3584) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3584.1, data_12_3584.2] + +/-- Complete interval computation for depth 12, residue 3585. -/ +theorem bounds_12_3585 : exactInterval 12 3585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3585 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3585) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3585 : oddCount 3585 12 = 8 ∧ acceleratedOrbit 12 3585 = 5750 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3585 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3585) = 3 ^ 8 * m + 5750 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3585.1, data_12_3585.2] + +/-- Complete interval computation for depth 12, residue 3586. -/ +theorem bounds_12_3586 : exactInterval 12 3586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3586 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3586) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3586 : oddCount 3586 12 = 4 ∧ acceleratedOrbit 12 3586 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3586 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3586) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3586.1, data_12_3586.2] + +/-- Complete interval computation for depth 12, residue 3587. -/ +theorem bounds_12_3587 : exactInterval 12 3587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3587 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3587) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3587 : oddCount 3587 12 = 4 ∧ acceleratedOrbit 12 3587 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3587 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3587) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3587.1, data_12_3587.2] + +/-- Complete interval computation for depth 12, residue 3588. -/ +theorem bounds_12_3588 : exactInterval 12 3588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3588 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3588) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3588 : oddCount 3588 12 = 6 ∧ acceleratedOrbit 12 3588 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3588 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3588) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3588.1, data_12_3588.2] + +/-- Complete interval computation for depth 12, residue 3589. -/ +theorem bounds_12_3589 : exactInterval 12 3589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3589 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3589) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3589 : oddCount 3589 12 = 6 ∧ acceleratedOrbit 12 3589 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3589 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3589) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3589.1, data_12_3589.2] + +/-- Complete interval computation for depth 12, residue 3590. -/ +theorem bounds_12_3590 : exactInterval 12 3590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3590 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3590) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3590 : oddCount 3590 12 = 6 ∧ acceleratedOrbit 12 3590 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3590 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3590) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3590.1, data_12_3590.2] + +/-- Complete interval computation for depth 12, residue 3591. -/ +theorem bounds_12_3591 : exactInterval 12 3591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3591 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3591) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3591 : oddCount 3591 12 = 7 ∧ acceleratedOrbit 12 3591 = 1919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3591 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3591) = 3 ^ 7 * m + 1919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3591.1, data_12_3591.2] + +/-- Complete interval computation for depth 12, residue 3592. -/ +theorem bounds_12_3592 : exactInterval 12 3592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3592 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3592) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3592 : oddCount 3592 12 = 5 ∧ acceleratedOrbit 12 3592 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3592 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3592) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3592.1, data_12_3592.2] + +/-- Complete interval computation for depth 12, residue 3593. -/ +theorem bounds_12_3593 : exactInterval 12 3593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3593 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3593) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3593 : oddCount 3593 12 = 6 ∧ acceleratedOrbit 12 3593 = 640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3593 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3593) = 3 ^ 6 * m + 640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3593.1, data_12_3593.2] + +end Collatz.Research.StoppingAtlas.Batch0434 From 5ad577e3089a601690bad17b6697cdf7df0dedcc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:19 +0530 Subject: [PATCH 0435/1001] proof: certify atlas Batch0435 (12:3594 to 12:3608) --- Collatz/Research/StoppingAtlas/Batch0435.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0435.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0435.lean b/Collatz/Research/StoppingAtlas/Batch0435.lean new file mode 100644 index 00000000..37503b90 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0435.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0435 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3594. -/ +theorem bounds_12_3594 : exactInterval 12 3594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3594 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3594) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3594 : oddCount 3594 12 = 5 ∧ acceleratedOrbit 12 3594 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3594 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3594) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3594.1, data_12_3594.2] + +/-- Complete interval computation for depth 12, residue 3595. -/ +theorem bounds_12_3595 : exactInterval 12 3595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3595 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3595) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3595 : oddCount 3595 12 = 6 ∧ acceleratedOrbit 12 3595 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3595 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3595) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3595.1, data_12_3595.2] + +/-- Complete interval computation for depth 12, residue 3596. -/ +theorem bounds_12_3596 : exactInterval 12 3596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3596 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3596) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3596 : oddCount 3596 12 = 5 ∧ acceleratedOrbit 12 3596 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3596 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3596) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3596.1, data_12_3596.2] + +/-- Complete interval computation for depth 12, residue 3597. -/ +theorem bounds_12_3597 : exactInterval 12 3597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3597 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3597) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3597 : oddCount 3597 12 = 5 ∧ acceleratedOrbit 12 3597 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3597 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3597) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3597.1, data_12_3597.2] + +/-- Complete interval computation for depth 12, residue 3598. -/ +theorem bounds_12_3598 : exactInterval 12 3598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3598 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3598) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3598 : oddCount 3598 12 = 6 ∧ acceleratedOrbit 12 3598 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3598 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3598) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3598.1, data_12_3598.2] + +/-- Complete interval computation for depth 12, residue 3599. -/ +theorem bounds_12_3599 : exactInterval 12 3599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3599 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3599) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3599 : oddCount 3599 12 = 6 ∧ acceleratedOrbit 12 3599 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3599 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3599) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3599.1, data_12_3599.2] + +/-- Complete interval computation for depth 12, residue 3600. -/ +theorem bounds_12_3600 : exactInterval 12 3600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3600 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3600) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3600 : oddCount 3600 12 = 6 ∧ acceleratedOrbit 12 3600 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3600 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3600) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3600.1, data_12_3600.2] + +/-- Complete interval computation for depth 12, residue 3601. -/ +theorem bounds_12_3601 : exactInterval 12 3601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3601 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3601) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3601 : oddCount 3601 12 = 5 ∧ acceleratedOrbit 12 3601 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3601 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3601) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3601.1, data_12_3601.2] + +/-- Complete interval computation for depth 12, residue 3602. -/ +theorem bounds_12_3602 : exactInterval 12 3602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3602 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3602) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3602 : oddCount 3602 12 = 8 ∧ acceleratedOrbit 12 3602 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3602 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3602) = 3 ^ 8 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3602.1, data_12_3602.2] + +/-- Complete interval computation for depth 12, residue 3603. -/ +theorem bounds_12_3603 : exactInterval 12 3603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3603 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3603) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3603 : oddCount 3603 12 = 8 ∧ acceleratedOrbit 12 3603 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3603 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3603) = 3 ^ 8 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3603.1, data_12_3603.2] + +/-- Complete interval computation for depth 12, residue 3604. -/ +theorem bounds_12_3604 : exactInterval 12 3604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3604 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3604) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3604 : oddCount 3604 12 = 6 ∧ acceleratedOrbit 12 3604 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3604 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3604) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3604.1, data_12_3604.2] + +/-- Complete interval computation for depth 12, residue 3605. -/ +theorem bounds_12_3605 : exactInterval 12 3605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3605 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3605) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3605 : oddCount 3605 12 = 6 ∧ acceleratedOrbit 12 3605 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3605 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3605) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3605.1, data_12_3605.2] + +/-- Complete interval computation for depth 12, residue 3606. -/ +theorem bounds_12_3606 : exactInterval 12 3606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3606 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3606) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3606 : oddCount 3606 12 = 6 ∧ acceleratedOrbit 12 3606 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3606 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3606) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3606.1, data_12_3606.2] + +/-- Complete interval computation for depth 12, residue 3607. -/ +theorem bounds_12_3607 : exactInterval 12 3607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3607 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3607) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3607 : oddCount 3607 12 = 6 ∧ acceleratedOrbit 12 3607 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3607 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3607) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3607.1, data_12_3607.2] + +/-- Complete interval computation for depth 12, residue 3608. -/ +theorem bounds_12_3608 : exactInterval 12 3608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3608 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3608) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3608 : oddCount 3608 12 = 6 ∧ acceleratedOrbit 12 3608 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3608 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3608) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3608.1, data_12_3608.2] + +end Collatz.Research.StoppingAtlas.Batch0435 From 2a8789666df84f5e5d916986bfb964bec8774a2b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:19 +0530 Subject: [PATCH 0436/1001] proof: certify atlas Batch0436 (12:3609 to 12:3623) --- Collatz/Research/StoppingAtlas/Batch0436.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0436.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0436.lean b/Collatz/Research/StoppingAtlas/Batch0436.lean new file mode 100644 index 00000000..0c904426 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0436.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0436 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3609. -/ +theorem bounds_12_3609 : exactInterval 12 3609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3609 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3609) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3609 : oddCount 3609 12 = 6 ∧ acceleratedOrbit 12 3609 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3609 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3609) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3609.1, data_12_3609.2] + +/-- Complete interval computation for depth 12, residue 3610. -/ +theorem bounds_12_3610 : exactInterval 12 3610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3610 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3610) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3610 : oddCount 3610 12 = 6 ∧ acceleratedOrbit 12 3610 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3610 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3610) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3610.1, data_12_3610.2] + +/-- Complete interval computation for depth 12, residue 3611. -/ +theorem bounds_12_3611 : exactInterval 12 3611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3611 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3611) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3611 : oddCount 3611 12 = 9 ∧ acceleratedOrbit 12 3611 = 17360 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3611 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3611) = 3 ^ 9 * m + 17360 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3611.1, data_12_3611.2] + +/-- Complete interval computation for depth 12, residue 3612. -/ +theorem bounds_12_3612 : exactInterval 12 3612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3612 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3612) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3612 : oddCount 3612 12 = 5 ∧ acceleratedOrbit 12 3612 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3612 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3612) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3612.1, data_12_3612.2] + +/-- Complete interval computation for depth 12, residue 3613. -/ +theorem bounds_12_3613 : exactInterval 12 3613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3613 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3613) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3613 : oddCount 3613 12 = 5 ∧ acceleratedOrbit 12 3613 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3613 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3613) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3613.1, data_12_3613.2] + +/-- Complete interval computation for depth 12, residue 3614. -/ +theorem bounds_12_3614 : exactInterval 12 3614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3614 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3614) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3614 : oddCount 3614 12 = 5 ∧ acceleratedOrbit 12 3614 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3614 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3614) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3614.1, data_12_3614.2] + +/-- Complete interval computation for depth 12, residue 3615. -/ +theorem bounds_12_3615 : exactInterval 12 3615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3615 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3615) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3615 : oddCount 3615 12 = 9 ∧ acceleratedOrbit 12 3615 = 17378 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3615 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3615) = 3 ^ 9 * m + 17378 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3615.1, data_12_3615.2] + +/-- Complete interval computation for depth 12, residue 3616. -/ +theorem bounds_12_3616 : exactInterval 12 3616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3616 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3616) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3616 : oddCount 3616 12 = 2 ∧ acceleratedOrbit 12 3616 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3616 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3616) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3616.1, data_12_3616.2] + +/-- Complete interval computation for depth 12, residue 3617. -/ +theorem bounds_12_3617 : exactInterval 12 3617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3617 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3617) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3617 : oddCount 3617 12 = 7 ∧ acceleratedOrbit 12 3617 = 1934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3617 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3617) = 3 ^ 7 * m + 1934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3617.1, data_12_3617.2] + +/-- Complete interval computation for depth 12, residue 3618. -/ +theorem bounds_12_3618 : exactInterval 12 3618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3618 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3618) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3618 : oddCount 3618 12 = 6 ∧ acceleratedOrbit 12 3618 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3618 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3618) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3618.1, data_12_3618.2] + +/-- Complete interval computation for depth 12, residue 3619. -/ +theorem bounds_12_3619 : exactInterval 12 3619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3619 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3619) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3619 : oddCount 3619 12 = 6 ∧ acceleratedOrbit 12 3619 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3619 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3619) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3619.1, data_12_3619.2] + +/-- Complete interval computation for depth 12, residue 3620. -/ +theorem bounds_12_3620 : exactInterval 12 3620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3620 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3620) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3620 : oddCount 3620 12 = 7 ∧ acceleratedOrbit 12 3620 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3620 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3620) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3620.1, data_12_3620.2] + +/-- Complete interval computation for depth 12, residue 3621. -/ +theorem bounds_12_3621 : exactInterval 12 3621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3621 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3621) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3621 : oddCount 3621 12 = 7 ∧ acceleratedOrbit 12 3621 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3621 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3621) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3621.1, data_12_3621.2] + +/-- Complete interval computation for depth 12, residue 3622. -/ +theorem bounds_12_3622 : exactInterval 12 3622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3622 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3622) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3622 : oddCount 3622 12 = 7 ∧ acceleratedOrbit 12 3622 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3622 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3622) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3622.1, data_12_3622.2] + +/-- Complete interval computation for depth 12, residue 3623. -/ +theorem bounds_12_3623 : exactInterval 12 3623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3623 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3623) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3623 : oddCount 3623 12 = 5 ∧ acceleratedOrbit 12 3623 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3623 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3623) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3623.1, data_12_3623.2] + +end Collatz.Research.StoppingAtlas.Batch0436 From b7ed1a02ec662522e8dff45a12965475f1b9823b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:19 +0530 Subject: [PATCH 0437/1001] proof: certify atlas Batch0437 (12:3624 to 12:3639) --- Collatz/Research/StoppingAtlas/Batch0437.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0437.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0437.lean b/Collatz/Research/StoppingAtlas/Batch0437.lean new file mode 100644 index 00000000..31c6a98c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0437.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0437 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3624. -/ +theorem bounds_12_3624 : exactInterval 12 3624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3624 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3624) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3624 : oddCount 3624 12 = 2 ∧ acceleratedOrbit 12 3624 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3624 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3624) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3624.1, data_12_3624.2] + +/-- Complete interval computation for depth 12, residue 3625. -/ +theorem bounds_12_3625 : exactInterval 12 3625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3625 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3625) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3625 : oddCount 3625 12 = 9 ∧ acceleratedOrbit 12 3625 = 17428 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3625 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3625) = 3 ^ 9 * m + 17428 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3625.1, data_12_3625.2] + +/-- Complete interval computation for depth 12, residue 3626. -/ +theorem bounds_12_3626 : exactInterval 12 3626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3626 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3626) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3626 : oddCount 3626 12 = 2 ∧ acceleratedOrbit 12 3626 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3626 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3626) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3626.1, data_12_3626.2] + +/-- Complete interval computation for depth 12, residue 3627. -/ +theorem bounds_12_3627 : exactInterval 12 3627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3627 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3627) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3627 : oddCount 3627 12 = 6 ∧ acceleratedOrbit 12 3627 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3627 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3627) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3627.1, data_12_3627.2] + +/-- Complete interval computation for depth 12, residue 3628. -/ +theorem bounds_12_3628 : exactInterval 12 3628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3628 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3628) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3628 : oddCount 3628 12 = 7 ∧ acceleratedOrbit 12 3628 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3628 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3628) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3628.1, data_12_3628.2] + +/-- Complete interval computation for depth 12, residue 3629. -/ +theorem bounds_12_3629 : exactInterval 12 3629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3629 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3629) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3629 : oddCount 3629 12 = 7 ∧ acceleratedOrbit 12 3629 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3629 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3629) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3629.1, data_12_3629.2] + +/-- Complete interval computation for depth 12, residue 3630. -/ +theorem bounds_12_3630 : exactInterval 12 3630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3630 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3630) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3630 : oddCount 3630 12 = 7 ∧ acceleratedOrbit 12 3630 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3630 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3630) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3630.1, data_12_3630.2] + +/-- Complete interval computation for depth 12, residue 3631. -/ +theorem bounds_12_3631 : exactInterval 12 3631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3631 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3631) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3631 : oddCount 3631 12 = 9 ∧ acceleratedOrbit 12 3631 = 17455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3631 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3631) = 3 ^ 9 * m + 17455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3631.1, data_12_3631.2] + +/-- Complete interval computation for depth 12, residue 3632. -/ +theorem bounds_12_3632 : exactInterval 12 3632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3632 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3632) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3632 : oddCount 3632 12 = 2 ∧ acceleratedOrbit 12 3632 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3632 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3632) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3632.1, data_12_3632.2] + +/-- Complete interval computation for depth 12, residue 3633. -/ +theorem bounds_12_3633 : exactInterval 12 3633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3633 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3633) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3633 : oddCount 3633 12 = 8 ∧ acceleratedOrbit 12 3633 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3633 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3633) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3633.1, data_12_3633.2] + +/-- Complete interval computation for depth 12, residue 3634. -/ +theorem bounds_12_3634 : exactInterval 12 3634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3634 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3634) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3634 : oddCount 3634 12 = 8 ∧ acceleratedOrbit 12 3634 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3634 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3634) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3634.1, data_12_3634.2] + +/-- Complete interval computation for depth 12, residue 3635. -/ +theorem bounds_12_3635 : exactInterval 12 3635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3635 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3635) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3635 : oddCount 3635 12 = 8 ∧ acceleratedOrbit 12 3635 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3635 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3635) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3635.1, data_12_3635.2] + +/-- Complete interval computation for depth 12, residue 3636. -/ +theorem bounds_12_3636 : exactInterval 12 3636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3636 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3636) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3636 : oddCount 3636 12 = 2 ∧ acceleratedOrbit 12 3636 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3636 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3636) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3636.1, data_12_3636.2] + +/-- Complete interval computation for depth 12, residue 3637. -/ +theorem bounds_12_3637 : exactInterval 12 3637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3637 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3637) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3637 : oddCount 3637 12 = 2 ∧ acceleratedOrbit 12 3637 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3637 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3637) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3637.1, data_12_3637.2] + +/-- Complete interval computation for depth 12, residue 3638. -/ +theorem bounds_12_3638 : exactInterval 12 3638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3638 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3638) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3638 : oddCount 3638 12 = 10 ∧ acceleratedOrbit 12 3638 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3638 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3638) = 3 ^ 10 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3638.1, data_12_3638.2] + +/-- Complete interval computation for depth 12, residue 3639. -/ +theorem bounds_12_3639 : exactInterval 12 3639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3639 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3639) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3639 : oddCount 3639 12 = 10 ∧ acceleratedOrbit 12 3639 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3639 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3639) = 3 ^ 10 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3639.1, data_12_3639.2] + +end Collatz.Research.StoppingAtlas.Batch0437 From 4b28ab3988fbbef6800f9990ddfe978286d73c33 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:20 +0530 Subject: [PATCH 0438/1001] proof: certify atlas Batch0438 (12:3640 to 12:3654) --- Collatz/Research/StoppingAtlas/Batch0438.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0438.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0438.lean b/Collatz/Research/StoppingAtlas/Batch0438.lean new file mode 100644 index 00000000..60c28de2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0438.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0438 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3640. -/ +theorem bounds_12_3640 : exactInterval 12 3640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3640 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3640) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3640 : oddCount 3640 12 = 6 ∧ acceleratedOrbit 12 3640 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3640 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3640) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3640.1, data_12_3640.2] + +/-- Complete interval computation for depth 12, residue 3641. -/ +theorem bounds_12_3641 : exactInterval 12 3641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3641 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3641) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3641 : oddCount 3641 12 = 7 ∧ acceleratedOrbit 12 3641 = 1946 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3641 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3641) = 3 ^ 7 * m + 1946 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3641.1, data_12_3641.2] + +/-- Complete interval computation for depth 12, residue 3642. -/ +theorem bounds_12_3642 : exactInterval 12 3642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3642 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3642) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3642 : oddCount 3642 12 = 6 ∧ acceleratedOrbit 12 3642 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3642 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3642) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3642.1, data_12_3642.2] + +/-- Complete interval computation for depth 12, residue 3643. -/ +theorem bounds_12_3643 : exactInterval 12 3643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3643 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3643) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3643 : oddCount 3643 12 = 6 ∧ acceleratedOrbit 12 3643 = 649 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3643 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3643) = 3 ^ 6 * m + 649 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3643.1, data_12_3643.2] + +/-- Complete interval computation for depth 12, residue 3644. -/ +theorem bounds_12_3644 : exactInterval 12 3644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3644 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3644) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3644 : oddCount 3644 12 = 6 ∧ acceleratedOrbit 12 3644 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3644 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3644) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3644.1, data_12_3644.2] + +/-- Complete interval computation for depth 12, residue 3645. -/ +theorem bounds_12_3645 : exactInterval 12 3645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3645 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3645) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3645 : oddCount 3645 12 = 6 ∧ acceleratedOrbit 12 3645 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3645 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3645) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3645.1, data_12_3645.2] + +/-- Complete interval computation for depth 12, residue 3646. -/ +theorem bounds_12_3646 : exactInterval 12 3646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3646 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3646) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3646 : oddCount 3646 12 = 7 ∧ acceleratedOrbit 12 3646 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3646 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3646) = 3 ^ 7 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3646.1, data_12_3646.2] + +/-- Complete interval computation for depth 12, residue 3647. -/ +theorem bounds_12_3647 : exactInterval 12 3647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3647 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3647) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3647 : oddCount 3647 12 = 7 ∧ acceleratedOrbit 12 3647 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3647 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3647) = 3 ^ 7 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3647.1, data_12_3647.2] + +/-- Complete interval computation for depth 12, residue 3648. -/ +theorem bounds_12_3648 : exactInterval 12 3648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3648 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3648) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3648 : oddCount 3648 12 = 4 ∧ acceleratedOrbit 12 3648 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3648 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3648) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3648.1, data_12_3648.2] + +/-- Complete interval computation for depth 12, residue 3649. -/ +theorem bounds_12_3649 : exactInterval 12 3649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3649 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3649) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3649 : oddCount 3649 12 = 5 ∧ acceleratedOrbit 12 3649 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3649 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3649) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3649.1, data_12_3649.2] + +/-- Complete interval computation for depth 12, residue 3650. -/ +theorem bounds_12_3650 : exactInterval 12 3650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3650 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3650) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3650 : oddCount 3650 12 = 5 ∧ acceleratedOrbit 12 3650 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3650 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3650) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3650.1, data_12_3650.2] + +/-- Complete interval computation for depth 12, residue 3651. -/ +theorem bounds_12_3651 : exactInterval 12 3651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3651 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3651) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3651 : oddCount 3651 12 = 5 ∧ acceleratedOrbit 12 3651 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3651 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3651) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3651.1, data_12_3651.2] + +/-- Complete interval computation for depth 12, residue 3652. -/ +theorem bounds_12_3652 : exactInterval 12 3652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3652 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3652) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3652 : oddCount 3652 12 = 5 ∧ acceleratedOrbit 12 3652 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3652 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3652) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3652.1, data_12_3652.2] + +/-- Complete interval computation for depth 12, residue 3653. -/ +theorem bounds_12_3653 : exactInterval 12 3653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3653 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3653) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3653 : oddCount 3653 12 = 5 ∧ acceleratedOrbit 12 3653 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3653 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3653) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3653.1, data_12_3653.2] + +/-- Complete interval computation for depth 12, residue 3654. -/ +theorem bounds_12_3654 : exactInterval 12 3654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3654 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3654) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3654 : oddCount 3654 12 = 5 ∧ acceleratedOrbit 12 3654 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3654 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3654) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3654.1, data_12_3654.2] + +end Collatz.Research.StoppingAtlas.Batch0438 From 930cb6858b26c09da76f6a26a31ded4362f43eab Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:20 +0530 Subject: [PATCH 0439/1001] proof: certify atlas Batch0439 (12:3655 to 12:3670) --- Collatz/Research/StoppingAtlas/Batch0439.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0439.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0439.lean b/Collatz/Research/StoppingAtlas/Batch0439.lean new file mode 100644 index 00000000..e3be45da --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0439.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0439 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3655. -/ +theorem bounds_12_3655 : exactInterval 12 3655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3655 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3655) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3655 : oddCount 3655 12 = 8 ∧ acceleratedOrbit 12 3655 = 5858 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3655 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3655) = 3 ^ 8 * m + 5858 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3655.1, data_12_3655.2] + +/-- Complete interval computation for depth 12, residue 3656. -/ +theorem bounds_12_3656 : exactInterval 12 3656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3656 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3656) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3656 : oddCount 3656 12 = 5 ∧ acceleratedOrbit 12 3656 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3656 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3656) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3656.1, data_12_3656.2] + +/-- Complete interval computation for depth 12, residue 3657. -/ +theorem bounds_12_3657 : exactInterval 12 3657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3657 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3657) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3657 : oddCount 3657 12 = 7 ∧ acceleratedOrbit 12 3657 = 1954 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3657 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3657) = 3 ^ 7 * m + 1954 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3657.1, data_12_3657.2] + +/-- Complete interval computation for depth 12, residue 3658. -/ +theorem bounds_12_3658 : exactInterval 12 3658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3658 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3658) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3658 : oddCount 3658 12 = 5 ∧ acceleratedOrbit 12 3658 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3658 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3658) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3658.1, data_12_3658.2] + +/-- Complete interval computation for depth 12, residue 3659. -/ +theorem bounds_12_3659 : exactInterval 12 3659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3659 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3659) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3659 : oddCount 3659 12 = 5 ∧ acceleratedOrbit 12 3659 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3659 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3659) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3659.1, data_12_3659.2] + +/-- Complete interval computation for depth 12, residue 3660. -/ +theorem bounds_12_3660 : exactInterval 12 3660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3660 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3660) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3660 : oddCount 3660 12 = 5 ∧ acceleratedOrbit 12 3660 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3660 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3660) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3660.1, data_12_3660.2] + +/-- Complete interval computation for depth 12, residue 3661. -/ +theorem bounds_12_3661 : exactInterval 12 3661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3661 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3661) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3661 : oddCount 3661 12 = 5 ∧ acceleratedOrbit 12 3661 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3661 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3661) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3661.1, data_12_3661.2] + +/-- Complete interval computation for depth 12, residue 3662. -/ +theorem bounds_12_3662 : exactInterval 12 3662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3662 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3662) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3662 : oddCount 3662 12 = 7 ∧ acceleratedOrbit 12 3662 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3662 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3662) = 3 ^ 7 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3662.1, data_12_3662.2] + +/-- Complete interval computation for depth 12, residue 3663. -/ +theorem bounds_12_3663 : exactInterval 12 3663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3663 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3663) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3663 : oddCount 3663 12 = 7 ∧ acceleratedOrbit 12 3663 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3663 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3663) = 3 ^ 7 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3663.1, data_12_3663.2] + +/-- Complete interval computation for depth 12, residue 3664. -/ +theorem bounds_12_3664 : exactInterval 12 3664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3664 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3664) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3664 : oddCount 3664 12 = 4 ∧ acceleratedOrbit 12 3664 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3664 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3664) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3664.1, data_12_3664.2] + +/-- Complete interval computation for depth 12, residue 3665. -/ +theorem bounds_12_3665 : exactInterval 12 3665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3665 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3665) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3665 : oddCount 3665 12 = 6 ∧ acceleratedOrbit 12 3665 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3665 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3665) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3665.1, data_12_3665.2] + +/-- Complete interval computation for depth 12, residue 3666. -/ +theorem bounds_12_3666 : exactInterval 12 3666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3666 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3666) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3666 : oddCount 3666 12 = 6 ∧ acceleratedOrbit 12 3666 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3666 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3666) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3666.1, data_12_3666.2] + +/-- Complete interval computation for depth 12, residue 3667. -/ +theorem bounds_12_3667 : exactInterval 12 3667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3667 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3667) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3667 : oddCount 3667 12 = 6 ∧ acceleratedOrbit 12 3667 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3667 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3667) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3667.1, data_12_3667.2] + +/-- Complete interval computation for depth 12, residue 3668. -/ +theorem bounds_12_3668 : exactInterval 12 3668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3668 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3668) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3668 : oddCount 3668 12 = 4 ∧ acceleratedOrbit 12 3668 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3668 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3668) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3668.1, data_12_3668.2] + +/-- Complete interval computation for depth 12, residue 3669. -/ +theorem bounds_12_3669 : exactInterval 12 3669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3669 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3669) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3669 : oddCount 3669 12 = 4 ∧ acceleratedOrbit 12 3669 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3669 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3669) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3669.1, data_12_3669.2] + +/-- Complete interval computation for depth 12, residue 3670. -/ +theorem bounds_12_3670 : exactInterval 12 3670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3670 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3670) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3670 : oddCount 3670 12 = 5 ∧ acceleratedOrbit 12 3670 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3670 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3670) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3670.1, data_12_3670.2] + +end Collatz.Research.StoppingAtlas.Batch0439 From e6c5e56983edff81746190231d4329d898256018 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:20 +0530 Subject: [PATCH 0440/1001] proof: certify atlas Batch0440 (12:3671 to 12:3685) --- Collatz/Research/StoppingAtlas/Batch0440.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0440.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0440.lean b/Collatz/Research/StoppingAtlas/Batch0440.lean new file mode 100644 index 00000000..e28d3fdc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0440.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0440 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3671. -/ +theorem bounds_12_3671 : exactInterval 12 3671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3671 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3671) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3671 : oddCount 3671 12 = 5 ∧ acceleratedOrbit 12 3671 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3671 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3671) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3671.1, data_12_3671.2] + +/-- Complete interval computation for depth 12, residue 3672. -/ +theorem bounds_12_3672 : exactInterval 12 3672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3672 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3672) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3672 : oddCount 3672 12 = 4 ∧ acceleratedOrbit 12 3672 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3672 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3672) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3672.1, data_12_3672.2] + +/-- Complete interval computation for depth 12, residue 3673. -/ +theorem bounds_12_3673 : exactInterval 12 3673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3673 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3673) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3673 : oddCount 3673 12 = 7 ∧ acceleratedOrbit 12 3673 = 1964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3673 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3673) = 3 ^ 7 * m + 1964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3673.1, data_12_3673.2] + +/-- Complete interval computation for depth 12, residue 3674. -/ +theorem bounds_12_3674 : exactInterval 12 3674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3674 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3674) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3674 : oddCount 3674 12 = 4 ∧ acceleratedOrbit 12 3674 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3674 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3674) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3674.1, data_12_3674.2] + +/-- Complete interval computation for depth 12, residue 3675. -/ +theorem bounds_12_3675 : exactInterval 12 3675 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3675 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3675) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3675 : oddCount 3675 12 = 7 ∧ acceleratedOrbit 12 3675 = 1963 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3675 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3675) = 3 ^ 7 * m + 1963 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3675.1, data_12_3675.2] + +/-- Complete interval computation for depth 12, residue 3676. -/ +theorem bounds_12_3676 : exactInterval 12 3676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3676 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3676) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3676 : oddCount 3676 12 = 4 ∧ acceleratedOrbit 12 3676 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3676 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3676) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3676.1, data_12_3676.2] + +/-- Complete interval computation for depth 12, residue 3677. -/ +theorem bounds_12_3677 : exactInterval 12 3677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3677 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3677) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3677 : oddCount 3677 12 = 4 ∧ acceleratedOrbit 12 3677 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3677 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3677) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3677.1, data_12_3677.2] + +/-- Complete interval computation for depth 12, residue 3678. -/ +theorem bounds_12_3678 : exactInterval 12 3678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3678 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3678) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3678 : oddCount 3678 12 = 6 ∧ acceleratedOrbit 12 3678 = 655 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3678 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3678) = 3 ^ 6 * m + 655 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3678.1, data_12_3678.2] + +/-- Complete interval computation for depth 12, residue 3679. -/ +theorem bounds_12_3679 : exactInterval 12 3679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3679 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3679) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3679 : oddCount 3679 12 = 6 ∧ acceleratedOrbit 12 3679 = 655 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3679 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3679) = 3 ^ 6 * m + 655 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3679.1, data_12_3679.2] + +/-- Complete interval computation for depth 12, residue 3680. -/ +theorem bounds_12_3680 : exactInterval 12 3680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3680 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3680) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3680 : oddCount 3680 12 = 4 ∧ acceleratedOrbit 12 3680 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3680 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3680) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3680.1, data_12_3680.2] + +/-- Complete interval computation for depth 12, residue 3681. -/ +theorem bounds_12_3681 : exactInterval 12 3681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3681 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3681) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3681 : oddCount 3681 12 = 6 ∧ acceleratedOrbit 12 3681 = 656 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3681 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3681) = 3 ^ 6 * m + 656 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3681.1, data_12_3681.2] + +/-- Complete interval computation for depth 12, residue 3682. -/ +theorem bounds_12_3682 : exactInterval 12 3682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3682 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3682) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3682 : oddCount 3682 12 = 4 ∧ acceleratedOrbit 12 3682 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3682 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3682) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3682.1, data_12_3682.2] + +/-- Complete interval computation for depth 12, residue 3683. -/ +theorem bounds_12_3683 : exactInterval 12 3683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3683 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3683) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3683 : oddCount 3683 12 = 4 ∧ acceleratedOrbit 12 3683 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3683 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3683) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3683.1, data_12_3683.2] + +/-- Complete interval computation for depth 12, residue 3684. -/ +theorem bounds_12_3684 : exactInterval 12 3684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3684 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3684) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3684 : oddCount 3684 12 = 4 ∧ acceleratedOrbit 12 3684 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3684 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3684) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3684.1, data_12_3684.2] + +/-- Complete interval computation for depth 12, residue 3685. -/ +theorem bounds_12_3685 : exactInterval 12 3685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3685 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3685) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3685 : oddCount 3685 12 = 4 ∧ acceleratedOrbit 12 3685 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3685 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3685) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3685.1, data_12_3685.2] + +end Collatz.Research.StoppingAtlas.Batch0440 From 9e06d10ef0a30c690f9a9e0019d81b0c646b0dc4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:21 +0530 Subject: [PATCH 0441/1001] proof: certify atlas Batch0441 (12:3686 to 12:3700) --- Collatz/Research/StoppingAtlas/Batch0441.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0441.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0441.lean b/Collatz/Research/StoppingAtlas/Batch0441.lean new file mode 100644 index 00000000..90916824 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0441.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0441 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3686. -/ +theorem bounds_12_3686 : exactInterval 12 3686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3686 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3686) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3686 : oddCount 3686 12 = 4 ∧ acceleratedOrbit 12 3686 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3686 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3686) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3686.1, data_12_3686.2] + +/-- Complete interval computation for depth 12, residue 3687. -/ +theorem bounds_12_3687 : exactInterval 12 3687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3687 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3687) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3687 : oddCount 3687 12 = 8 ∧ acceleratedOrbit 12 3687 = 5908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3687 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3687) = 3 ^ 8 * m + 5908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3687.1, data_12_3687.2] + +/-- Complete interval computation for depth 12, residue 3688. -/ +theorem bounds_12_3688 : exactInterval 12 3688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3688 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3688) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3688 : oddCount 3688 12 = 4 ∧ acceleratedOrbit 12 3688 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3688 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3688) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3688.1, data_12_3688.2] + +/-- Complete interval computation for depth 12, residue 3689. -/ +theorem bounds_12_3689 : exactInterval 12 3689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3689 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3689) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3689 : oddCount 3689 12 = 9 ∧ acceleratedOrbit 12 3689 = 17738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3689 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3689) = 3 ^ 9 * m + 17738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3689.1, data_12_3689.2] + +/-- Complete interval computation for depth 12, residue 3690. -/ +theorem bounds_12_3690 : exactInterval 12 3690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3690 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3690) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3690 : oddCount 3690 12 = 4 ∧ acceleratedOrbit 12 3690 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3690 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3690) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3690.1, data_12_3690.2] + +/-- Complete interval computation for depth 12, residue 3691. -/ +theorem bounds_12_3691 : exactInterval 12 3691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3691 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3691) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3691 : oddCount 3691 12 = 7 ∧ acceleratedOrbit 12 3691 = 1972 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3691 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3691) = 3 ^ 7 * m + 1972 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3691.1, data_12_3691.2] + +/-- Complete interval computation for depth 12, residue 3692. -/ +theorem bounds_12_3692 : exactInterval 12 3692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3692 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3692) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3692 : oddCount 3692 12 = 6 ∧ acceleratedOrbit 12 3692 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3692 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3692) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3692.1, data_12_3692.2] + +/-- Complete interval computation for depth 12, residue 3693. -/ +theorem bounds_12_3693 : exactInterval 12 3693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3693 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3693) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3693 : oddCount 3693 12 = 6 ∧ acceleratedOrbit 12 3693 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3693 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3693) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3693.1, data_12_3693.2] + +/-- Complete interval computation for depth 12, residue 3694. -/ +theorem bounds_12_3694 : exactInterval 12 3694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3694 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3694) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3694 : oddCount 3694 12 = 6 ∧ acceleratedOrbit 12 3694 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3694 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3694) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3694.1, data_12_3694.2] + +/-- Complete interval computation for depth 12, residue 3695. -/ +theorem bounds_12_3695 : exactInterval 12 3695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3695 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3695) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3695 : oddCount 3695 12 = 8 ∧ acceleratedOrbit 12 3695 = 5921 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3695 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3695) = 3 ^ 8 * m + 5921 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3695.1, data_12_3695.2] + +/-- Complete interval computation for depth 12, residue 3696. -/ +theorem bounds_12_3696 : exactInterval 12 3696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3696 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3696) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3696 : oddCount 3696 12 = 6 ∧ acceleratedOrbit 12 3696 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3696 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3696) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3696.1, data_12_3696.2] + +/-- Complete interval computation for depth 12, residue 3697. -/ +theorem bounds_12_3697 : exactInterval 12 3697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3697 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3697) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3697 : oddCount 3697 12 = 4 ∧ acceleratedOrbit 12 3697 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3697 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3697) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3697.1, data_12_3697.2] + +/-- Complete interval computation for depth 12, residue 3698. -/ +theorem bounds_12_3698 : exactInterval 12 3698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3698 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3698) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3698 : oddCount 3698 12 = 6 ∧ acceleratedOrbit 12 3698 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3698 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3698) = 3 ^ 6 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3698.1, data_12_3698.2] + +/-- Complete interval computation for depth 12, residue 3699. -/ +theorem bounds_12_3699 : exactInterval 12 3699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3699 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3699) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3699 : oddCount 3699 12 = 6 ∧ acceleratedOrbit 12 3699 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3699 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3699) = 3 ^ 6 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3699.1, data_12_3699.2] + +/-- Complete interval computation for depth 12, residue 3700. -/ +theorem bounds_12_3700 : exactInterval 12 3700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3700 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3700) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3700 : oddCount 3700 12 = 6 ∧ acceleratedOrbit 12 3700 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3700 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3700) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3700.1, data_12_3700.2] + +end Collatz.Research.StoppingAtlas.Batch0441 From cbae7c82b22a68fb39f91758edddedd0105e9dbb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:21 +0530 Subject: [PATCH 0442/1001] proof: certify atlas Batch0442 (12:3701 to 12:3716) --- Collatz/Research/StoppingAtlas/Batch0442.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0442.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0442.lean b/Collatz/Research/StoppingAtlas/Batch0442.lean new file mode 100644 index 00000000..01eb8ef7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0442.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0442 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3701. -/ +theorem bounds_12_3701 : exactInterval 12 3701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3701 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3701) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3701 : oddCount 3701 12 = 6 ∧ acceleratedOrbit 12 3701 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3701 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3701) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3701.1, data_12_3701.2] + +/-- Complete interval computation for depth 12, residue 3702. -/ +theorem bounds_12_3702 : exactInterval 12 3702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3702 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3702) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3702 : oddCount 3702 12 = 5 ∧ acceleratedOrbit 12 3702 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3702 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3702) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3702.1, data_12_3702.2] + +/-- Complete interval computation for depth 12, residue 3703. -/ +theorem bounds_12_3703 : exactInterval 12 3703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3703 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3703) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3703 : oddCount 3703 12 = 5 ∧ acceleratedOrbit 12 3703 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3703 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3703) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3703.1, data_12_3703.2] + +/-- Complete interval computation for depth 12, residue 3704. -/ +theorem bounds_12_3704 : exactInterval 12 3704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3704 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3704) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3704 : oddCount 3704 12 = 6 ∧ acceleratedOrbit 12 3704 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3704 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3704) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3704.1, data_12_3704.2] + +/-- Complete interval computation for depth 12, residue 3705. -/ +theorem bounds_12_3705 : exactInterval 12 3705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3705 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3705) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3705 : oddCount 3705 12 = 8 ∧ acceleratedOrbit 12 3705 = 5939 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3705 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3705) = 3 ^ 8 * m + 5939 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3705.1, data_12_3705.2] + +/-- Complete interval computation for depth 12, residue 3706. -/ +theorem bounds_12_3706 : exactInterval 12 3706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3706 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3706) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3706 : oddCount 3706 12 = 6 ∧ acceleratedOrbit 12 3706 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3706 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3706) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3706.1, data_12_3706.2] + +/-- Complete interval computation for depth 12, residue 3707. -/ +theorem bounds_12_3707 : exactInterval 12 3707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3707 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3707) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3707 : oddCount 3707 12 = 5 ∧ acceleratedOrbit 12 3707 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3707 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3707) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3707.1, data_12_3707.2] + +/-- Complete interval computation for depth 12, residue 3708. -/ +theorem bounds_12_3708 : exactInterval 12 3708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3708 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3708) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3708 : oddCount 3708 12 = 7 ∧ acceleratedOrbit 12 3708 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3708 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3708) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3708.1, data_12_3708.2] + +/-- Complete interval computation for depth 12, residue 3709. -/ +theorem bounds_12_3709 : exactInterval 12 3709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3709 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3709) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3709 : oddCount 3709 12 = 7 ∧ acceleratedOrbit 12 3709 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3709 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3709) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3709.1, data_12_3709.2] + +/-- Complete interval computation for depth 12, residue 3710. -/ +theorem bounds_12_3710 : exactInterval 12 3710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3710 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3710) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3710 : oddCount 3710 12 = 7 ∧ acceleratedOrbit 12 3710 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3710 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3710) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3710.1, data_12_3710.2] + +/-- Complete interval computation for depth 12, residue 3711. -/ +theorem bounds_12_3711 : exactInterval 12 3711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3711 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3711) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3711 : oddCount 3711 12 = 11 ∧ acceleratedOrbit 12 3711 = 160541 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3711 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3711) = 3 ^ 11 * m + 160541 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3711.1, data_12_3711.2] + +/-- Complete interval computation for depth 12, residue 3712. -/ +theorem bounds_12_3712 : exactInterval 12 3712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3712 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3712) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3712 : oddCount 3712 12 = 3 ∧ acceleratedOrbit 12 3712 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3712 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3712) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3712.1, data_12_3712.2] + +/-- Complete interval computation for depth 12, residue 3713. -/ +theorem bounds_12_3713 : exactInterval 12 3713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3713 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3713) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3713 : oddCount 3713 12 = 8 ∧ acceleratedOrbit 12 3713 = 5953 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3713 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3713) = 3 ^ 8 * m + 5953 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3713.1, data_12_3713.2] + +/-- Complete interval computation for depth 12, residue 3714. -/ +theorem bounds_12_3714 : exactInterval 12 3714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3714 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3714) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3714 : oddCount 3714 12 = 4 ∧ acceleratedOrbit 12 3714 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3714 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3714) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3714.1, data_12_3714.2] + +/-- Complete interval computation for depth 12, residue 3715. -/ +theorem bounds_12_3715 : exactInterval 12 3715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3715 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3715) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3715 : oddCount 3715 12 = 4 ∧ acceleratedOrbit 12 3715 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3715 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3715) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3715.1, data_12_3715.2] + +/-- Complete interval computation for depth 12, residue 3716. -/ +theorem bounds_12_3716 : exactInterval 12 3716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3716 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3716) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3716 : oddCount 3716 12 = 5 ∧ acceleratedOrbit 12 3716 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3716 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3716) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3716.1, data_12_3716.2] + +end Collatz.Research.StoppingAtlas.Batch0442 From cea42cf393c4aa7c693793eadb070d4fdc0e4c6a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:21 +0530 Subject: [PATCH 0443/1001] proof: certify atlas Batch0443 (12:3717 to 12:3731) --- Collatz/Research/StoppingAtlas/Batch0443.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0443.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0443.lean b/Collatz/Research/StoppingAtlas/Batch0443.lean new file mode 100644 index 00000000..550e4a95 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0443.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0443 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3717. -/ +theorem bounds_12_3717 : exactInterval 12 3717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3717 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3717) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3717 : oddCount 3717 12 = 5 ∧ acceleratedOrbit 12 3717 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3717 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3717) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3717.1, data_12_3717.2] + +/-- Complete interval computation for depth 12, residue 3718. -/ +theorem bounds_12_3718 : exactInterval 12 3718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3718 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3718) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3718 : oddCount 3718 12 = 5 ∧ acceleratedOrbit 12 3718 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3718 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3718) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3718.1, data_12_3718.2] + +/-- Complete interval computation for depth 12, residue 3719. -/ +theorem bounds_12_3719 : exactInterval 12 3719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3719 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3719) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3719 : oddCount 3719 12 = 7 ∧ acceleratedOrbit 12 3719 = 1988 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3719 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3719) = 3 ^ 7 * m + 1988 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3719.1, data_12_3719.2] + +/-- Complete interval computation for depth 12, residue 3720. -/ +theorem bounds_12_3720 : exactInterval 12 3720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3720 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3720) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3720 : oddCount 3720 12 = 4 ∧ acceleratedOrbit 12 3720 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3720 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3720) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3720.1, data_12_3720.2] + +/-- Complete interval computation for depth 12, residue 3721. -/ +theorem bounds_12_3721 : exactInterval 12 3721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3721 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3721) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3721 : oddCount 3721 12 = 9 ∧ acceleratedOrbit 12 3721 = 17891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3721 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3721) = 3 ^ 9 * m + 17891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3721.1, data_12_3721.2] + +/-- Complete interval computation for depth 12, residue 3722. -/ +theorem bounds_12_3722 : exactInterval 12 3722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3722 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3722) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3722 : oddCount 3722 12 = 4 ∧ acceleratedOrbit 12 3722 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3722 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3722) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3722.1, data_12_3722.2] + +/-- Complete interval computation for depth 12, residue 3723. -/ +theorem bounds_12_3723 : exactInterval 12 3723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3723 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3723) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3723 : oddCount 3723 12 = 5 ∧ acceleratedOrbit 12 3723 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3723 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3723) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3723.1, data_12_3723.2] + +/-- Complete interval computation for depth 12, residue 3724. -/ +theorem bounds_12_3724 : exactInterval 12 3724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3724 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3724) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3724 : oddCount 3724 12 = 4 ∧ acceleratedOrbit 12 3724 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3724 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3724) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3724.1, data_12_3724.2] + +/-- Complete interval computation for depth 12, residue 3725. -/ +theorem bounds_12_3725 : exactInterval 12 3725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3725 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3725) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3725 : oddCount 3725 12 = 4 ∧ acceleratedOrbit 12 3725 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3725 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3725) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3725.1, data_12_3725.2] + +/-- Complete interval computation for depth 12, residue 3726. -/ +theorem bounds_12_3726 : exactInterval 12 3726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3726 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3726) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3726 : oddCount 3726 12 = 7 ∧ acceleratedOrbit 12 3726 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3726 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3726) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3726.1, data_12_3726.2] + +/-- Complete interval computation for depth 12, residue 3727. -/ +theorem bounds_12_3727 : exactInterval 12 3727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3727 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3727) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3727 : oddCount 3727 12 = 7 ∧ acceleratedOrbit 12 3727 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3727 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3727) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3727.1, data_12_3727.2] + +/-- Complete interval computation for depth 12, residue 3728. -/ +theorem bounds_12_3728 : exactInterval 12 3728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3728 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3728) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3728 : oddCount 3728 12 = 6 ∧ acceleratedOrbit 12 3728 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3728 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3728) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3728.1, data_12_3728.2] + +/-- Complete interval computation for depth 12, residue 3729. -/ +theorem bounds_12_3729 : exactInterval 12 3729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3729 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3729) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3729 : oddCount 3729 12 = 6 ∧ acceleratedOrbit 12 3729 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3729 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3729) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3729.1, data_12_3729.2] + +/-- Complete interval computation for depth 12, residue 3730. -/ +theorem bounds_12_3730 : exactInterval 12 3730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3730 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3730) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3730 : oddCount 3730 12 = 6 ∧ acceleratedOrbit 12 3730 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3730 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3730) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3730.1, data_12_3730.2] + +/-- Complete interval computation for depth 12, residue 3731. -/ +theorem bounds_12_3731 : exactInterval 12 3731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3731 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3731) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3731 : oddCount 3731 12 = 6 ∧ acceleratedOrbit 12 3731 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3731 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3731) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3731.1, data_12_3731.2] + +end Collatz.Research.StoppingAtlas.Batch0443 From 9c9d670b1f3d0469b859a8b9cafb99a2b33a6522 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:22 +0530 Subject: [PATCH 0444/1001] proof: certify atlas Batch0444 (12:3732 to 12:3746) --- Collatz/Research/StoppingAtlas/Batch0444.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0444.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0444.lean b/Collatz/Research/StoppingAtlas/Batch0444.lean new file mode 100644 index 00000000..10433315 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0444.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0444 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3732. -/ +theorem bounds_12_3732 : exactInterval 12 3732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3732 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3732) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3732 : oddCount 3732 12 = 6 ∧ acceleratedOrbit 12 3732 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3732 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3732) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3732.1, data_12_3732.2] + +/-- Complete interval computation for depth 12, residue 3733. -/ +theorem bounds_12_3733 : exactInterval 12 3733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3733 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3733) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3733 : oddCount 3733 12 = 6 ∧ acceleratedOrbit 12 3733 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3733 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3733) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3733.1, data_12_3733.2] + +/-- Complete interval computation for depth 12, residue 3734. -/ +theorem bounds_12_3734 : exactInterval 12 3734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3734 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3734) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3734 : oddCount 3734 12 = 4 ∧ acceleratedOrbit 12 3734 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3734 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3734) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3734.1, data_12_3734.2] + +/-- Complete interval computation for depth 12, residue 3735. -/ +theorem bounds_12_3735 : exactInterval 12 3735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3735 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3735) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3735 : oddCount 3735 12 = 4 ∧ acceleratedOrbit 12 3735 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3735 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3735) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3735.1, data_12_3735.2] + +/-- Complete interval computation for depth 12, residue 3736. -/ +theorem bounds_12_3736 : exactInterval 12 3736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3736 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3736) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3736 : oddCount 3736 12 = 6 ∧ acceleratedOrbit 12 3736 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3736 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3736) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3736.1, data_12_3736.2] + +/-- Complete interval computation for depth 12, residue 3737. -/ +theorem bounds_12_3737 : exactInterval 12 3737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3737 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3737) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3737 : oddCount 3737 12 = 8 ∧ acceleratedOrbit 12 3737 = 5993 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3737 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3737) = 3 ^ 8 * m + 5993 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3737.1, data_12_3737.2] + +/-- Complete interval computation for depth 12, residue 3738. -/ +theorem bounds_12_3738 : exactInterval 12 3738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3738 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3738) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3738 : oddCount 3738 12 = 6 ∧ acceleratedOrbit 12 3738 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3738 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3738) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3738.1, data_12_3738.2] + +/-- Complete interval computation for depth 12, residue 3739. -/ +theorem bounds_12_3739 : exactInterval 12 3739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3739 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3739) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3739 : oddCount 3739 12 = 9 ∧ acceleratedOrbit 12 3739 = 17975 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3739 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3739) = 3 ^ 9 * m + 17975 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3739.1, data_12_3739.2] + +/-- Complete interval computation for depth 12, residue 3740. -/ +theorem bounds_12_3740 : exactInterval 12 3740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3740 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3740) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3740 : oddCount 3740 12 = 7 ∧ acceleratedOrbit 12 3740 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3740 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3740) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3740.1, data_12_3740.2] + +/-- Complete interval computation for depth 12, residue 3741. -/ +theorem bounds_12_3741 : exactInterval 12 3741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3741 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3741) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3741 : oddCount 3741 12 = 7 ∧ acceleratedOrbit 12 3741 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3741 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3741) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3741.1, data_12_3741.2] + +/-- Complete interval computation for depth 12, residue 3742. -/ +theorem bounds_12_3742 : exactInterval 12 3742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3742 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3742) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3742 : oddCount 3742 12 = 7 ∧ acceleratedOrbit 12 3742 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3742 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3742) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3742.1, data_12_3742.2] + +/-- Complete interval computation for depth 12, residue 3743. -/ +theorem bounds_12_3743 : exactInterval 12 3743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3743 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3743) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3743 : oddCount 3743 12 = 9 ∧ acceleratedOrbit 12 3743 = 17992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3743 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3743) = 3 ^ 9 * m + 17992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3743.1, data_12_3743.2] + +/-- Complete interval computation for depth 12, residue 3744. -/ +theorem bounds_12_3744 : exactInterval 12 3744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3744 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3744) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3744 : oddCount 3744 12 = 3 ∧ acceleratedOrbit 12 3744 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3744 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3744) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3744.1, data_12_3744.2] + +/-- Complete interval computation for depth 12, residue 3745. -/ +theorem bounds_12_3745 : exactInterval 12 3745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3745 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3745) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3745 : oddCount 3745 12 = 6 ∧ acceleratedOrbit 12 3745 = 667 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3745 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3745) = 3 ^ 6 * m + 667 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3745.1, data_12_3745.2] + +/-- Complete interval computation for depth 12, residue 3746. -/ +theorem bounds_12_3746 : exactInterval 12 3746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3746 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3746) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3746 : oddCount 3746 12 = 6 ∧ acceleratedOrbit 12 3746 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3746 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3746) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3746.1, data_12_3746.2] + +end Collatz.Research.StoppingAtlas.Batch0444 From 4e55e1130efe17f6b57b4088e9fb8809264e0e41 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:22 +0530 Subject: [PATCH 0445/1001] proof: certify atlas Batch0445 (12:3747 to 12:3762) --- Collatz/Research/StoppingAtlas/Batch0445.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0445.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0445.lean b/Collatz/Research/StoppingAtlas/Batch0445.lean new file mode 100644 index 00000000..629c1aad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0445.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0445 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3747. -/ +theorem bounds_12_3747 : exactInterval 12 3747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3747 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3747) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3747 : oddCount 3747 12 = 6 ∧ acceleratedOrbit 12 3747 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3747 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3747) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3747.1, data_12_3747.2] + +/-- Complete interval computation for depth 12, residue 3748. -/ +theorem bounds_12_3748 : exactInterval 12 3748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3748 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3748) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3748 : oddCount 3748 12 = 8 ∧ acceleratedOrbit 12 3748 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3748 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3748) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3748.1, data_12_3748.2] + +/-- Complete interval computation for depth 12, residue 3749. -/ +theorem bounds_12_3749 : exactInterval 12 3749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3749 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3749) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3749 : oddCount 3749 12 = 8 ∧ acceleratedOrbit 12 3749 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3749 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3749) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3749.1, data_12_3749.2] + +/-- Complete interval computation for depth 12, residue 3750. -/ +theorem bounds_12_3750 : exactInterval 12 3750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3750 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3750) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3750 : oddCount 3750 12 = 8 ∧ acceleratedOrbit 12 3750 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3750 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3750) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3750.1, data_12_3750.2] + +/-- Complete interval computation for depth 12, residue 3751. -/ +theorem bounds_12_3751 : exactInterval 12 3751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3751 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3751) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3751 : oddCount 3751 12 = 8 ∧ acceleratedOrbit 12 3751 = 6011 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3751 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3751) = 3 ^ 8 * m + 6011 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3751.1, data_12_3751.2] + +/-- Complete interval computation for depth 12, residue 3752. -/ +theorem bounds_12_3752 : exactInterval 12 3752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3752 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3752) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3752 : oddCount 3752 12 = 3 ∧ acceleratedOrbit 12 3752 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3752 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3752) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3752.1, data_12_3752.2] + +/-- Complete interval computation for depth 12, residue 3753. -/ +theorem bounds_12_3753 : exactInterval 12 3753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3753 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3753) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3753 : oddCount 3753 12 = 10 ∧ acceleratedOrbit 12 3753 = 54128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3753 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3753) = 3 ^ 10 * m + 54128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3753.1, data_12_3753.2] + +/-- Complete interval computation for depth 12, residue 3754. -/ +theorem bounds_12_3754 : exactInterval 12 3754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3754 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3754) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3754 : oddCount 3754 12 = 3 ∧ acceleratedOrbit 12 3754 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3754 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3754) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3754.1, data_12_3754.2] + +/-- Complete interval computation for depth 12, residue 3755. -/ +theorem bounds_12_3755 : exactInterval 12 3755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3755 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3755) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3755 : oddCount 3755 12 = 8 ∧ acceleratedOrbit 12 3755 = 6020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3755 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3755) = 3 ^ 8 * m + 6020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3755.1, data_12_3755.2] + +/-- Complete interval computation for depth 12, residue 3756. -/ +theorem bounds_12_3756 : exactInterval 12 3756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3756 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3756) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3756 : oddCount 3756 12 = 6 ∧ acceleratedOrbit 12 3756 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3756 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3756) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3756.1, data_12_3756.2] + +/-- Complete interval computation for depth 12, residue 3757. -/ +theorem bounds_12_3757 : exactInterval 12 3757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3757 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3757) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3757 : oddCount 3757 12 = 6 ∧ acceleratedOrbit 12 3757 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3757 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3757) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3757.1, data_12_3757.2] + +/-- Complete interval computation for depth 12, residue 3758. -/ +theorem bounds_12_3758 : exactInterval 12 3758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3758 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3758) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3758 : oddCount 3758 12 = 6 ∧ acceleratedOrbit 12 3758 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3758 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3758) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3758.1, data_12_3758.2] + +/-- Complete interval computation for depth 12, residue 3759. -/ +theorem bounds_12_3759 : exactInterval 12 3759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3759 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3759) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3759 : oddCount 3759 12 = 7 ∧ acceleratedOrbit 12 3759 = 2008 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3759 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3759) = 3 ^ 7 * m + 2008 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3759.1, data_12_3759.2] + +/-- Complete interval computation for depth 12, residue 3760. -/ +theorem bounds_12_3760 : exactInterval 12 3760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3760 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3760) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3760 : oddCount 3760 12 = 6 ∧ acceleratedOrbit 12 3760 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3760 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3760) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3760.1, data_12_3760.2] + +/-- Complete interval computation for depth 12, residue 3761. -/ +theorem bounds_12_3761 : exactInterval 12 3761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3761 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3761) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3761 : oddCount 3761 12 = 5 ∧ acceleratedOrbit 12 3761 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3761 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3761) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3761.1, data_12_3761.2] + +/-- Complete interval computation for depth 12, residue 3762. -/ +theorem bounds_12_3762 : exactInterval 12 3762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3762 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3762) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3762 : oddCount 3762 12 = 5 ∧ acceleratedOrbit 12 3762 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3762 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3762) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3762.1, data_12_3762.2] + +end Collatz.Research.StoppingAtlas.Batch0445 From ac97b62bbee40c0b00ee14d1d1d027a8e5ab3dee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:22 +0530 Subject: [PATCH 0446/1001] proof: certify atlas Batch0446 (12:3763 to 12:3777) --- Collatz/Research/StoppingAtlas/Batch0446.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0446.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0446.lean b/Collatz/Research/StoppingAtlas/Batch0446.lean new file mode 100644 index 00000000..69f980e7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0446.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0446 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3763. -/ +theorem bounds_12_3763 : exactInterval 12 3763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3763 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3763) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3763 : oddCount 3763 12 = 5 ∧ acceleratedOrbit 12 3763 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3763 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3763) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3763.1, data_12_3763.2] + +/-- Complete interval computation for depth 12, residue 3764. -/ +theorem bounds_12_3764 : exactInterval 12 3764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3764 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3764) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3764 : oddCount 3764 12 = 6 ∧ acceleratedOrbit 12 3764 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3764 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3764) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3764.1, data_12_3764.2] + +/-- Complete interval computation for depth 12, residue 3765. -/ +theorem bounds_12_3765 : exactInterval 12 3765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3765 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3765) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3765 : oddCount 3765 12 = 6 ∧ acceleratedOrbit 12 3765 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3765 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3765) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3765.1, data_12_3765.2] + +/-- Complete interval computation for depth 12, residue 3766. -/ +theorem bounds_12_3766 : exactInterval 12 3766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3766 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3766) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3766 : oddCount 3766 12 = 8 ∧ acceleratedOrbit 12 3766 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3766 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3766) = 3 ^ 8 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3766.1, data_12_3766.2] + +/-- Complete interval computation for depth 12, residue 3767. -/ +theorem bounds_12_3767 : exactInterval 12 3767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3767 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3767) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3767 : oddCount 3767 12 = 8 ∧ acceleratedOrbit 12 3767 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3767 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3767) = 3 ^ 8 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3767.1, data_12_3767.2] + +/-- Complete interval computation for depth 12, residue 3768. -/ +theorem bounds_12_3768 : exactInterval 12 3768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3768 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3768) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3768 : oddCount 3768 12 = 6 ∧ acceleratedOrbit 12 3768 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3768 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3768) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3768.1, data_12_3768.2] + +/-- Complete interval computation for depth 12, residue 3769. -/ +theorem bounds_12_3769 : exactInterval 12 3769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3769 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3769) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3769 : oddCount 3769 12 = 7 ∧ acceleratedOrbit 12 3769 = 2015 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3769 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3769) = 3 ^ 7 * m + 2015 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3769.1, data_12_3769.2] + +/-- Complete interval computation for depth 12, residue 3770. -/ +theorem bounds_12_3770 : exactInterval 12 3770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3770 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3770) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3770 : oddCount 3770 12 = 6 ∧ acceleratedOrbit 12 3770 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3770 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3770) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3770.1, data_12_3770.2] + +/-- Complete interval computation for depth 12, residue 3771. -/ +theorem bounds_12_3771 : exactInterval 12 3771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3771 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3771) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3771 : oddCount 3771 12 = 7 ∧ acceleratedOrbit 12 3771 = 2015 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3771 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3771) = 3 ^ 7 * m + 2015 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3771.1, data_12_3771.2] + +/-- Complete interval computation for depth 12, residue 3772. -/ +theorem bounds_12_3772 : exactInterval 12 3772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3772 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3772) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3772 : oddCount 3772 12 = 5 ∧ acceleratedOrbit 12 3772 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3772 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3772) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3772.1, data_12_3772.2] + +/-- Complete interval computation for depth 12, residue 3773. -/ +theorem bounds_12_3773 : exactInterval 12 3773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3773 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3773) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3773 : oddCount 3773 12 = 5 ∧ acceleratedOrbit 12 3773 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3773 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3773) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3773.1, data_12_3773.2] + +/-- Complete interval computation for depth 12, residue 3774. -/ +theorem bounds_12_3774 : exactInterval 12 3774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3774 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3774) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3774 : oddCount 3774 12 = 5 ∧ acceleratedOrbit 12 3774 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3774 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3774) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3774.1, data_12_3774.2] + +/-- Complete interval computation for depth 12, residue 3775. -/ +theorem bounds_12_3775 : exactInterval 12 3775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3775 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3775) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3775 : oddCount 3775 12 = 9 ∧ acceleratedOrbit 12 3775 = 18146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3775 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3775) = 3 ^ 9 * m + 18146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3775.1, data_12_3775.2] + +/-- Complete interval computation for depth 12, residue 3776. -/ +theorem bounds_12_3776 : exactInterval 12 3776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3776 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3776) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3776 : oddCount 3776 12 = 4 ∧ acceleratedOrbit 12 3776 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3776 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3776) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3776.1, data_12_3776.2] + +/-- Complete interval computation for depth 12, residue 3777. -/ +theorem bounds_12_3777 : exactInterval 12 3777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3777 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3777) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3777 : oddCount 3777 12 = 6 ∧ acceleratedOrbit 12 3777 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3777 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3777) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3777.1, data_12_3777.2] + +end Collatz.Research.StoppingAtlas.Batch0446 From cdc50cf8e1e29d1e8fa9d8963ccbecb840c86845 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:23 +0530 Subject: [PATCH 0447/1001] proof: certify atlas Batch0447 (12:3778 to 12:3792) --- Collatz/Research/StoppingAtlas/Batch0447.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0447.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0447.lean b/Collatz/Research/StoppingAtlas/Batch0447.lean new file mode 100644 index 00000000..1fd035c4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0447.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0447 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3778. -/ +theorem bounds_12_3778 : exactInterval 12 3778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3778 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3778) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3778 : oddCount 3778 12 = 7 ∧ acceleratedOrbit 12 3778 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3778 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3778) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3778.1, data_12_3778.2] + +/-- Complete interval computation for depth 12, residue 3779. -/ +theorem bounds_12_3779 : exactInterval 12 3779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3779 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3779) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3779 : oddCount 3779 12 = 7 ∧ acceleratedOrbit 12 3779 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3779 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3779) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3779.1, data_12_3779.2] + +/-- Complete interval computation for depth 12, residue 3780. -/ +theorem bounds_12_3780 : exactInterval 12 3780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3780 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3780) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3780 : oddCount 3780 12 = 3 ∧ acceleratedOrbit 12 3780 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3780 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3780) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3780.1, data_12_3780.2] + +/-- Complete interval computation for depth 12, residue 3781. -/ +theorem bounds_12_3781 : exactInterval 12 3781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3781 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3781) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3781 : oddCount 3781 12 = 3 ∧ acceleratedOrbit 12 3781 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3781 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3781) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3781.1, data_12_3781.2] + +/-- Complete interval computation for depth 12, residue 3782. -/ +theorem bounds_12_3782 : exactInterval 12 3782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3782 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3782) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3782 : oddCount 3782 12 = 3 ∧ acceleratedOrbit 12 3782 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3782 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3782) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3782.1, data_12_3782.2] + +/-- Complete interval computation for depth 12, residue 3783. -/ +theorem bounds_12_3783 : exactInterval 12 3783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3783 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3783) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3783 : oddCount 3783 12 = 6 ∧ acceleratedOrbit 12 3783 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3783 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3783) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3783.1, data_12_3783.2] + +/-- Complete interval computation for depth 12, residue 3784. -/ +theorem bounds_12_3784 : exactInterval 12 3784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3784 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3784) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3784 : oddCount 3784 12 = 3 ∧ acceleratedOrbit 12 3784 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3784 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3784) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3784.1, data_12_3784.2] + +/-- Complete interval computation for depth 12, residue 3785. -/ +theorem bounds_12_3785 : exactInterval 12 3785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3785 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3785) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3785 : oddCount 3785 12 = 7 ∧ acceleratedOrbit 12 3785 = 2024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3785 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3785) = 3 ^ 7 * m + 2024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3785.1, data_12_3785.2] + +/-- Complete interval computation for depth 12, residue 3786. -/ +theorem bounds_12_3786 : exactInterval 12 3786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3786 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3786) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3786 : oddCount 3786 12 = 3 ∧ acceleratedOrbit 12 3786 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3786 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3786) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3786.1, data_12_3786.2] + +/-- Complete interval computation for depth 12, residue 3787. -/ +theorem bounds_12_3787 : exactInterval 12 3787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3787 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3787) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3787 : oddCount 3787 12 = 8 ∧ acceleratedOrbit 12 3787 = 6074 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3787 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3787) = 3 ^ 8 * m + 6074 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3787.1, data_12_3787.2] + +/-- Complete interval computation for depth 12, residue 3788. -/ +theorem bounds_12_3788 : exactInterval 12 3788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3788 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3788) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3788 : oddCount 3788 12 = 3 ∧ acceleratedOrbit 12 3788 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3788 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3788) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3788.1, data_12_3788.2] + +/-- Complete interval computation for depth 12, residue 3789. -/ +theorem bounds_12_3789 : exactInterval 12 3789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3789 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3789) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3789 : oddCount 3789 12 = 3 ∧ acceleratedOrbit 12 3789 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3789 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3789) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3789.1, data_12_3789.2] + +/-- Complete interval computation for depth 12, residue 3790. -/ +theorem bounds_12_3790 : exactInterval 12 3790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3790 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3790) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3790 : oddCount 3790 12 = 10 ∧ acceleratedOrbit 12 3790 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3790 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3790) = 3 ^ 10 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3790.1, data_12_3790.2] + +/-- Complete interval computation for depth 12, residue 3791. -/ +theorem bounds_12_3791 : exactInterval 12 3791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3791 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3791) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3791 : oddCount 3791 12 = 10 ∧ acceleratedOrbit 12 3791 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3791 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3791) = 3 ^ 10 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3791.1, data_12_3791.2] + +/-- Complete interval computation for depth 12, residue 3792. -/ +theorem bounds_12_3792 : exactInterval 12 3792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3792 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3792) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3792 : oddCount 3792 12 = 4 ∧ acceleratedOrbit 12 3792 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3792 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3792) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3792.1, data_12_3792.2] + +end Collatz.Research.StoppingAtlas.Batch0447 From 1cc9a1ffd30438ac7a626e9a1f52f4c3d543126c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:23 +0530 Subject: [PATCH 0448/1001] proof: certify atlas Batch0448 (12:3793 to 12:3808) --- Collatz/Research/StoppingAtlas/Batch0448.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0448.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0448.lean b/Collatz/Research/StoppingAtlas/Batch0448.lean new file mode 100644 index 00000000..829ca2db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0448.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0448 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3793. -/ +theorem bounds_12_3793 : exactInterval 12 3793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3793 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3793) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3793 : oddCount 3793 12 = 6 ∧ acceleratedOrbit 12 3793 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3793 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3793) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3793.1, data_12_3793.2] + +/-- Complete interval computation for depth 12, residue 3794. -/ +theorem bounds_12_3794 : exactInterval 12 3794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3794 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3794) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3794 : oddCount 3794 12 = 6 ∧ acceleratedOrbit 12 3794 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3794 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3794) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3794.1, data_12_3794.2] + +/-- Complete interval computation for depth 12, residue 3795. -/ +theorem bounds_12_3795 : exactInterval 12 3795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3795 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3795) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3795 : oddCount 3795 12 = 6 ∧ acceleratedOrbit 12 3795 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3795 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3795) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3795.1, data_12_3795.2] + +/-- Complete interval computation for depth 12, residue 3796. -/ +theorem bounds_12_3796 : exactInterval 12 3796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3796 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3796) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3796 : oddCount 3796 12 = 4 ∧ acceleratedOrbit 12 3796 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3796 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3796) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3796.1, data_12_3796.2] + +/-- Complete interval computation for depth 12, residue 3797. -/ +theorem bounds_12_3797 : exactInterval 12 3797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3797 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3797) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3797 : oddCount 3797 12 = 4 ∧ acceleratedOrbit 12 3797 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3797 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3797) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3797.1, data_12_3797.2] + +/-- Complete interval computation for depth 12, residue 3798. -/ +theorem bounds_12_3798 : exactInterval 12 3798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3798 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3798) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3798 : oddCount 3798 12 = 6 ∧ acceleratedOrbit 12 3798 = 677 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3798 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3798) = 3 ^ 6 * m + 677 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3798.1, data_12_3798.2] + +/-- Complete interval computation for depth 12, residue 3799. -/ +theorem bounds_12_3799 : exactInterval 12 3799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3799 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3799) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3799 : oddCount 3799 12 = 6 ∧ acceleratedOrbit 12 3799 = 677 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3799 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3799) = 3 ^ 6 * m + 677 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3799.1, data_12_3799.2] + +/-- Complete interval computation for depth 12, residue 3800. -/ +theorem bounds_12_3800 : exactInterval 12 3800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3800 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3800) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3800 : oddCount 3800 12 = 5 ∧ acceleratedOrbit 12 3800 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3800 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3800) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3800.1, data_12_3800.2] + +/-- Complete interval computation for depth 12, residue 3801. -/ +theorem bounds_12_3801 : exactInterval 12 3801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3801 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3801) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3801 : oddCount 3801 12 = 5 ∧ acceleratedOrbit 12 3801 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3801 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3801) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3801.1, data_12_3801.2] + +/-- Complete interval computation for depth 12, residue 3802. -/ +theorem bounds_12_3802 : exactInterval 12 3802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3802 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3802) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3802 : oddCount 3802 12 = 5 ∧ acceleratedOrbit 12 3802 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3802 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3802) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3802.1, data_12_3802.2] + +/-- Complete interval computation for depth 12, residue 3803. -/ +theorem bounds_12_3803 : exactInterval 12 3803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3803 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3803) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3803 : oddCount 3803 12 = 8 ∧ acceleratedOrbit 12 3803 = 6095 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3803 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3803) = 3 ^ 8 * m + 6095 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3803.1, data_12_3803.2] + +/-- Complete interval computation for depth 12, residue 3804. -/ +theorem bounds_12_3804 : exactInterval 12 3804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3804 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3804) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3804 : oddCount 3804 12 = 5 ∧ acceleratedOrbit 12 3804 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3804 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3804) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3804.1, data_12_3804.2] + +/-- Complete interval computation for depth 12, residue 3805. -/ +theorem bounds_12_3805 : exactInterval 12 3805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3805 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3805) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3805 : oddCount 3805 12 = 5 ∧ acceleratedOrbit 12 3805 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3805 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3805) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3805.1, data_12_3805.2] + +/-- Complete interval computation for depth 12, residue 3806. -/ +theorem bounds_12_3806 : exactInterval 12 3806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3806 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3806) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3806 : oddCount 3806 12 = 8 ∧ acceleratedOrbit 12 3806 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3806 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3806) = 3 ^ 8 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3806.1, data_12_3806.2] + +/-- Complete interval computation for depth 12, residue 3807. -/ +theorem bounds_12_3807 : exactInterval 12 3807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3807 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3807) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3807 : oddCount 3807 12 = 8 ∧ acceleratedOrbit 12 3807 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3807 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3807) = 3 ^ 8 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3807.1, data_12_3807.2] + +/-- Complete interval computation for depth 12, residue 3808. -/ +theorem bounds_12_3808 : exactInterval 12 3808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3808 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3808) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3808 : oddCount 3808 12 = 4 ∧ acceleratedOrbit 12 3808 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3808 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3808) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3808.1, data_12_3808.2] + +end Collatz.Research.StoppingAtlas.Batch0448 From 97e051834602242b3393cef751e71feb44432209 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:23 +0530 Subject: [PATCH 0449/1001] proof: certify atlas Batch0449 (12:3809 to 12:3823) --- Collatz/Research/StoppingAtlas/Batch0449.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0449.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0449.lean b/Collatz/Research/StoppingAtlas/Batch0449.lean new file mode 100644 index 00000000..fa6382b7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0449.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0449 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3809. -/ +theorem bounds_12_3809 : exactInterval 12 3809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3809 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3809) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3809 : oddCount 3809 12 = 7 ∧ acceleratedOrbit 12 3809 = 2035 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3809 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3809) = 3 ^ 7 * m + 2035 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3809.1, data_12_3809.2] + +/-- Complete interval computation for depth 12, residue 3810. -/ +theorem bounds_12_3810 : exactInterval 12 3810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3810 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3810) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3810 : oddCount 3810 12 = 4 ∧ acceleratedOrbit 12 3810 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3810 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3810) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3810.1, data_12_3810.2] + +/-- Complete interval computation for depth 12, residue 3811. -/ +theorem bounds_12_3811 : exactInterval 12 3811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3811 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3811) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3811 : oddCount 3811 12 = 4 ∧ acceleratedOrbit 12 3811 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3811 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3811) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3811.1, data_12_3811.2] + +/-- Complete interval computation for depth 12, residue 3812. -/ +theorem bounds_12_3812 : exactInterval 12 3812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3812 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3812) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3812 : oddCount 3812 12 = 5 ∧ acceleratedOrbit 12 3812 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3812 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3812) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3812.1, data_12_3812.2] + +/-- Complete interval computation for depth 12, residue 3813. -/ +theorem bounds_12_3813 : exactInterval 12 3813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3813 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3813) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3813 : oddCount 3813 12 = 5 ∧ acceleratedOrbit 12 3813 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3813 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3813) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3813.1, data_12_3813.2] + +/-- Complete interval computation for depth 12, residue 3814. -/ +theorem bounds_12_3814 : exactInterval 12 3814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3814 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3814) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3814 : oddCount 3814 12 = 5 ∧ acceleratedOrbit 12 3814 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3814 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3814) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3814.1, data_12_3814.2] + +/-- Complete interval computation for depth 12, residue 3815. -/ +theorem bounds_12_3815 : exactInterval 12 3815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3815 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3815) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3815 : oddCount 3815 12 = 8 ∧ acceleratedOrbit 12 3815 = 6113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3815 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3815) = 3 ^ 8 * m + 6113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3815.1, data_12_3815.2] + +/-- Complete interval computation for depth 12, residue 3816. -/ +theorem bounds_12_3816 : exactInterval 12 3816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3816 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3816) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3816 : oddCount 3816 12 = 4 ∧ acceleratedOrbit 12 3816 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3816 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3816) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3816.1, data_12_3816.2] + +/-- Complete interval computation for depth 12, residue 3817. -/ +theorem bounds_12_3817 : exactInterval 12 3817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3817 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3817) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3817 : oddCount 3817 12 = 7 ∧ acceleratedOrbit 12 3817 = 2039 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3817 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3817) = 3 ^ 7 * m + 2039 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3817.1, data_12_3817.2] + +/-- Complete interval computation for depth 12, residue 3818. -/ +theorem bounds_12_3818 : exactInterval 12 3818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3818 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3818) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3818 : oddCount 3818 12 = 4 ∧ acceleratedOrbit 12 3818 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3818 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3818) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3818.1, data_12_3818.2] + +/-- Complete interval computation for depth 12, residue 3819. -/ +theorem bounds_12_3819 : exactInterval 12 3819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3819 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3819) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3819 : oddCount 3819 12 = 6 ∧ acceleratedOrbit 12 3819 = 680 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3819 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3819) = 3 ^ 6 * m + 680 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3819.1, data_12_3819.2] + +/-- Complete interval computation for depth 12, residue 3820. -/ +theorem bounds_12_3820 : exactInterval 12 3820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3820 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3820) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3820 : oddCount 3820 12 = 5 ∧ acceleratedOrbit 12 3820 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3820 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3820) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3820.1, data_12_3820.2] + +/-- Complete interval computation for depth 12, residue 3821. -/ +theorem bounds_12_3821 : exactInterval 12 3821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3821 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3821) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3821 : oddCount 3821 12 = 5 ∧ acceleratedOrbit 12 3821 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3821 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3821) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3821.1, data_12_3821.2] + +/-- Complete interval computation for depth 12, residue 3822. -/ +theorem bounds_12_3822 : exactInterval 12 3822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3822 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3822) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3822 : oddCount 3822 12 = 5 ∧ acceleratedOrbit 12 3822 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3822 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3822) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3822.1, data_12_3822.2] + +/-- Complete interval computation for depth 12, residue 3823. -/ +theorem bounds_12_3823 : exactInterval 12 3823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3823 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3823) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3823 : oddCount 3823 12 = 9 ∧ acceleratedOrbit 12 3823 = 18377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3823 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3823) = 3 ^ 9 * m + 18377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3823.1, data_12_3823.2] + +end Collatz.Research.StoppingAtlas.Batch0449 From 700eb9411d21886d87baf5ccb35ecb0afcb2607f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:24 +0530 Subject: [PATCH 0450/1001] proof: certify atlas Batch0450 (12:3824 to 12:3839) --- Collatz/Research/StoppingAtlas/Batch0450.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0450.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0450.lean b/Collatz/Research/StoppingAtlas/Batch0450.lean new file mode 100644 index 00000000..39bcb78c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0450.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0450 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3824. -/ +theorem bounds_12_3824 : exactInterval 12 3824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3824 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3824) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3824 : oddCount 3824 12 = 7 ∧ acceleratedOrbit 12 3824 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3824 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3824) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3824.1, data_12_3824.2] + +/-- Complete interval computation for depth 12, residue 3825. -/ +theorem bounds_12_3825 : exactInterval 12 3825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3825 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3825) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3825 : oddCount 3825 12 = 4 ∧ acceleratedOrbit 12 3825 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3825 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3825) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3825.1, data_12_3825.2] + +/-- Complete interval computation for depth 12, residue 3826. -/ +theorem bounds_12_3826 : exactInterval 12 3826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3826 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3826) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3826 : oddCount 3826 12 = 7 ∧ acceleratedOrbit 12 3826 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3826 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3826) = 3 ^ 7 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3826.1, data_12_3826.2] + +/-- Complete interval computation for depth 12, residue 3827. -/ +theorem bounds_12_3827 : exactInterval 12 3827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3827 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3827) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3827 : oddCount 3827 12 = 7 ∧ acceleratedOrbit 12 3827 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3827 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3827) = 3 ^ 7 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3827.1, data_12_3827.2] + +/-- Complete interval computation for depth 12, residue 3828. -/ +theorem bounds_12_3828 : exactInterval 12 3828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3828 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3828) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3828 : oddCount 3828 12 = 7 ∧ acceleratedOrbit 12 3828 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3828 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3828) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3828.1, data_12_3828.2] + +/-- Complete interval computation for depth 12, residue 3829. -/ +theorem bounds_12_3829 : exactInterval 12 3829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3829 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3829) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3829 : oddCount 3829 12 = 7 ∧ acceleratedOrbit 12 3829 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3829 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3829) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3829.1, data_12_3829.2] + +/-- Complete interval computation for depth 12, residue 3830. -/ +theorem bounds_12_3830 : exactInterval 12 3830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3830 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3830) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3830 : oddCount 3830 12 = 7 ∧ acceleratedOrbit 12 3830 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3830 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3830) = 3 ^ 7 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3830.1, data_12_3830.2] + +/-- Complete interval computation for depth 12, residue 3831. -/ +theorem bounds_12_3831 : exactInterval 12 3831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3831 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3831) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3831 : oddCount 3831 12 = 7 ∧ acceleratedOrbit 12 3831 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3831 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3831) = 3 ^ 7 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3831.1, data_12_3831.2] + +/-- Complete interval computation for depth 12, residue 3832. -/ +theorem bounds_12_3832 : exactInterval 12 3832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3832 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3832) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3832 : oddCount 3832 12 = 7 ∧ acceleratedOrbit 12 3832 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3832 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3832) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3832.1, data_12_3832.2] + +/-- Complete interval computation for depth 12, residue 3833. -/ +theorem bounds_12_3833 : exactInterval 12 3833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3833 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3833) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3833 : oddCount 3833 12 = 6 ∧ acceleratedOrbit 12 3833 = 683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3833 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3833) = 3 ^ 6 * m + 683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3833.1, data_12_3833.2] + +/-- Complete interval computation for depth 12, residue 3834. -/ +theorem bounds_12_3834 : exactInterval 12 3834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3834 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3834) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3834 : oddCount 3834 12 = 7 ∧ acceleratedOrbit 12 3834 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3834 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3834) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3834.1, data_12_3834.2] + +/-- Complete interval computation for depth 12, residue 3835. -/ +theorem bounds_12_3835 : exactInterval 12 3835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3835 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3835) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3835 : oddCount 3835 12 = 8 ∧ acceleratedOrbit 12 3835 = 6146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3835 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3835) = 3 ^ 8 * m + 6146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3835.1, data_12_3835.2] + +/-- Complete interval computation for depth 12, residue 3836. -/ +theorem bounds_12_3836 : exactInterval 12 3836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3836 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3836) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3836 : oddCount 3836 12 = 8 ∧ acceleratedOrbit 12 3836 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3836 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3836) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3836.1, data_12_3836.2] + +/-- Complete interval computation for depth 12, residue 3837. -/ +theorem bounds_12_3837 : exactInterval 12 3837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3837 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3837) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3837 : oddCount 3837 12 = 8 ∧ acceleratedOrbit 12 3837 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3837 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3837) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3837.1, data_12_3837.2] + +/-- Complete interval computation for depth 12, residue 3838. -/ +theorem bounds_12_3838 : exactInterval 12 3838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3838 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3838) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3838 : oddCount 3838 12 = 8 ∧ acceleratedOrbit 12 3838 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3838 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3838) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3838.1, data_12_3838.2] + +/-- Complete interval computation for depth 12, residue 3839. -/ +theorem bounds_12_3839 : exactInterval 12 3839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3839 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3839) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3839 : oddCount 3839 12 = 11 ∧ acceleratedOrbit 12 3839 = 166076 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3839 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3839) = 3 ^ 11 * m + 166076 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3839.1, data_12_3839.2] + +end Collatz.Research.StoppingAtlas.Batch0450 From e6a923d2d867058bcd2346182edb4402b15e8e5c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:24 +0530 Subject: [PATCH 0451/1001] proof: certify atlas Batch0451 (12:3840 to 12:3854) --- Collatz/Research/StoppingAtlas/Batch0451.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0451.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0451.lean b/Collatz/Research/StoppingAtlas/Batch0451.lean new file mode 100644 index 00000000..0f907eee --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0451.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0451 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3840. -/ +theorem bounds_12_3840 : exactInterval 12 3840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3840 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3840) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3840 : oddCount 3840 12 = 4 ∧ acceleratedOrbit 12 3840 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3840 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3840) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3840.1, data_12_3840.2] + +/-- Complete interval computation for depth 12, residue 3841. -/ +theorem bounds_12_3841 : exactInterval 12 3841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3841 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3841) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3841 : oddCount 3841 12 = 4 ∧ acceleratedOrbit 12 3841 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3841 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3841) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3841.1, data_12_3841.2] + +/-- Complete interval computation for depth 12, residue 3842. -/ +theorem bounds_12_3842 : exactInterval 12 3842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3842 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3842) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3842 : oddCount 3842 12 = 6 ∧ acceleratedOrbit 12 3842 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3842 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3842) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3842.1, data_12_3842.2] + +/-- Complete interval computation for depth 12, residue 3843. -/ +theorem bounds_12_3843 : exactInterval 12 3843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3843 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3843) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3843 : oddCount 3843 12 = 6 ∧ acceleratedOrbit 12 3843 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3843 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3843) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3843.1, data_12_3843.2] + +/-- Complete interval computation for depth 12, residue 3844. -/ +theorem bounds_12_3844 : exactInterval 12 3844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3844 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3844) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3844 : oddCount 3844 12 = 5 ∧ acceleratedOrbit 12 3844 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3844 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3844) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3844.1, data_12_3844.2] + +/-- Complete interval computation for depth 12, residue 3845. -/ +theorem bounds_12_3845 : exactInterval 12 3845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3845 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3845) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3845 : oddCount 3845 12 = 5 ∧ acceleratedOrbit 12 3845 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3845 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3845) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3845.1, data_12_3845.2] + +/-- Complete interval computation for depth 12, residue 3846. -/ +theorem bounds_12_3846 : exactInterval 12 3846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3846 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3846) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3846 : oddCount 3846 12 = 5 ∧ acceleratedOrbit 12 3846 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3846 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3846) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3846.1, data_12_3846.2] + +/-- Complete interval computation for depth 12, residue 3847. -/ +theorem bounds_12_3847 : exactInterval 12 3847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3847 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3847) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3847 : oddCount 3847 12 = 6 ∧ acceleratedOrbit 12 3847 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3847 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3847) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3847.1, data_12_3847.2] + +/-- Complete interval computation for depth 12, residue 3848. -/ +theorem bounds_12_3848 : exactInterval 12 3848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3848 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3848) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3848 : oddCount 3848 12 = 6 ∧ acceleratedOrbit 12 3848 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3848 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3848) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3848.1, data_12_3848.2] + +/-- Complete interval computation for depth 12, residue 3849. -/ +theorem bounds_12_3849 : exactInterval 12 3849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3849 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3849) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3849 : oddCount 3849 12 = 8 ∧ acceleratedOrbit 12 3849 = 6169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3849 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3849) = 3 ^ 8 * m + 6169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3849.1, data_12_3849.2] + +/-- Complete interval computation for depth 12, residue 3850. -/ +theorem bounds_12_3850 : exactInterval 12 3850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3850 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3850) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3850 : oddCount 3850 12 = 6 ∧ acceleratedOrbit 12 3850 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3850 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3850) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3850.1, data_12_3850.2] + +/-- Complete interval computation for depth 12, residue 3851. -/ +theorem bounds_12_3851 : exactInterval 12 3851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3851 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3851) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3851 : oddCount 3851 12 = 6 ∧ acceleratedOrbit 12 3851 = 686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3851 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3851) = 3 ^ 6 * m + 686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3851.1, data_12_3851.2] + +/-- Complete interval computation for depth 12, residue 3852. -/ +theorem bounds_12_3852 : exactInterval 12 3852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3852 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3852) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3852 : oddCount 3852 12 = 6 ∧ acceleratedOrbit 12 3852 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3852 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3852) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3852.1, data_12_3852.2] + +/-- Complete interval computation for depth 12, residue 3853. -/ +theorem bounds_12_3853 : exactInterval 12 3853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3853 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3853) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3853 : oddCount 3853 12 = 6 ∧ acceleratedOrbit 12 3853 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3853 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3853) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3853.1, data_12_3853.2] + +/-- Complete interval computation for depth 12, residue 3854. -/ +theorem bounds_12_3854 : exactInterval 12 3854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3854 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3854) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3854 : oddCount 3854 12 = 5 ∧ acceleratedOrbit 12 3854 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3854 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3854) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3854.1, data_12_3854.2] + +end Collatz.Research.StoppingAtlas.Batch0451 From a8ac7e8e9ae4f5b91715c08179178706c84e98fc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:24 +0530 Subject: [PATCH 0452/1001] proof: certify atlas Batch0452 (12:3855 to 12:3869) --- Collatz/Research/StoppingAtlas/Batch0452.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0452.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0452.lean b/Collatz/Research/StoppingAtlas/Batch0452.lean new file mode 100644 index 00000000..06cf4708 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0452.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0452 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3855. -/ +theorem bounds_12_3855 : exactInterval 12 3855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3855 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3855) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3855 : oddCount 3855 12 = 5 ∧ acceleratedOrbit 12 3855 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3855 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3855) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3855.1, data_12_3855.2] + +/-- Complete interval computation for depth 12, residue 3856. -/ +theorem bounds_12_3856 : exactInterval 12 3856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3856 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3856) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3856 : oddCount 3856 12 = 3 ∧ acceleratedOrbit 12 3856 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3856 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3856) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3856.1, data_12_3856.2] + +/-- Complete interval computation for depth 12, residue 3857. -/ +theorem bounds_12_3857 : exactInterval 12 3857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3857 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3857) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3857 : oddCount 3857 12 = 6 ∧ acceleratedOrbit 12 3857 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3857 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3857) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3857.1, data_12_3857.2] + +/-- Complete interval computation for depth 12, residue 3858. -/ +theorem bounds_12_3858 : exactInterval 12 3858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3858 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3858) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3858 : oddCount 3858 12 = 7 ∧ acceleratedOrbit 12 3858 = 2062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3858 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3858) = 3 ^ 7 * m + 2062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3858.1, data_12_3858.2] + +/-- Complete interval computation for depth 12, residue 3859. -/ +theorem bounds_12_3859 : exactInterval 12 3859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3859 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3859) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3859 : oddCount 3859 12 = 7 ∧ acceleratedOrbit 12 3859 = 2062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3859 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3859) = 3 ^ 7 * m + 2062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3859.1, data_12_3859.2] + +/-- Complete interval computation for depth 12, residue 3860. -/ +theorem bounds_12_3860 : exactInterval 12 3860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3860 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3860) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3860 : oddCount 3860 12 = 3 ∧ acceleratedOrbit 12 3860 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3860 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3860) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3860.1, data_12_3860.2] + +/-- Complete interval computation for depth 12, residue 3861. -/ +theorem bounds_12_3861 : exactInterval 12 3861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3861 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3861) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3861 : oddCount 3861 12 = 3 ∧ acceleratedOrbit 12 3861 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3861 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3861) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3861.1, data_12_3861.2] + +/-- Complete interval computation for depth 12, residue 3862. -/ +theorem bounds_12_3862 : exactInterval 12 3862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3862 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3862) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3862 : oddCount 3862 12 = 7 ∧ acceleratedOrbit 12 3862 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3862 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3862) = 3 ^ 7 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3862.1, data_12_3862.2] + +/-- Complete interval computation for depth 12, residue 3863. -/ +theorem bounds_12_3863 : exactInterval 12 3863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3863 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3863) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3863 : oddCount 3863 12 = 7 ∧ acceleratedOrbit 12 3863 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3863 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3863) = 3 ^ 7 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3863.1, data_12_3863.2] + +/-- Complete interval computation for depth 12, residue 3864. -/ +theorem bounds_12_3864 : exactInterval 12 3864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3864 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3864) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3864 : oddCount 3864 12 = 3 ∧ acceleratedOrbit 12 3864 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3864 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3864) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3864.1, data_12_3864.2] + +/-- Complete interval computation for depth 12, residue 3865. -/ +theorem bounds_12_3865 : exactInterval 12 3865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3865 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3865) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3865 : oddCount 3865 12 = 8 ∧ acceleratedOrbit 12 3865 = 6196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3865 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3865) = 3 ^ 8 * m + 6196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3865.1, data_12_3865.2] + +/-- Complete interval computation for depth 12, residue 3866. -/ +theorem bounds_12_3866 : exactInterval 12 3866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3866 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3866) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3866 : oddCount 3866 12 = 3 ∧ acceleratedOrbit 12 3866 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3866 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3866) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3866.1, data_12_3866.2] + +/-- Complete interval computation for depth 12, residue 3867. -/ +theorem bounds_12_3867 : exactInterval 12 3867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3867 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3867) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3867 : oddCount 3867 12 = 10 ∧ acceleratedOrbit 12 3867 = 55768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3867 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3867) = 3 ^ 10 * m + 55768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3867.1, data_12_3867.2] + +/-- Complete interval computation for depth 12, residue 3868. -/ +theorem bounds_12_3868 : exactInterval 12 3868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3868 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3868) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3868 : oddCount 3868 12 = 7 ∧ acceleratedOrbit 12 3868 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3868 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3868) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3868.1, data_12_3868.2] + +/-- Complete interval computation for depth 12, residue 3869. -/ +theorem bounds_12_3869 : exactInterval 12 3869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3869 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3869) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3869 : oddCount 3869 12 = 7 ∧ acceleratedOrbit 12 3869 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3869 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3869) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3869.1, data_12_3869.2] + +end Collatz.Research.StoppingAtlas.Batch0452 From 20c5c20af44fcbe4a9a2830498c7d5c5fab3cd84 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:25 +0530 Subject: [PATCH 0453/1001] proof: certify atlas Batch0453 (12:3870 to 12:3885) --- Collatz/Research/StoppingAtlas/Batch0453.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0453.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0453.lean b/Collatz/Research/StoppingAtlas/Batch0453.lean new file mode 100644 index 00000000..7e1b50e8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0453.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0453 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3870. -/ +theorem bounds_12_3870 : exactInterval 12 3870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3870 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3870) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3870 : oddCount 3870 12 = 7 ∧ acceleratedOrbit 12 3870 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3870 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3870) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3870.1, data_12_3870.2] + +/-- Complete interval computation for depth 12, residue 3871. -/ +theorem bounds_12_3871 : exactInterval 12 3871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3871 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3871) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3871 : oddCount 3871 12 = 8 ∧ acceleratedOrbit 12 3871 = 6203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3871 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3871) = 3 ^ 8 * m + 6203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3871.1, data_12_3871.2] + +/-- Complete interval computation for depth 12, residue 3872. -/ +theorem bounds_12_3872 : exactInterval 12 3872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3872 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3872) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3872 : oddCount 3872 12 = 5 ∧ acceleratedOrbit 12 3872 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3872 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3872) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3872.1, data_12_3872.2] + +/-- Complete interval computation for depth 12, residue 3873. -/ +theorem bounds_12_3873 : exactInterval 12 3873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3873 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3873) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3873 : oddCount 3873 12 = 5 ∧ acceleratedOrbit 12 3873 = 230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3873 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3873) = 3 ^ 5 * m + 230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3873.1, data_12_3873.2] + +/-- Complete interval computation for depth 12, residue 3874. -/ +theorem bounds_12_3874 : exactInterval 12 3874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3874 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3874) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3874 : oddCount 3874 12 = 6 ∧ acceleratedOrbit 12 3874 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3874 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3874) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3874.1, data_12_3874.2] + +/-- Complete interval computation for depth 12, residue 3875. -/ +theorem bounds_12_3875 : exactInterval 12 3875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3875 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3875) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3875 : oddCount 3875 12 = 6 ∧ acceleratedOrbit 12 3875 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3875 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3875) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3875.1, data_12_3875.2] + +/-- Complete interval computation for depth 12, residue 3876. -/ +theorem bounds_12_3876 : exactInterval 12 3876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3876 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3876) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3876 : oddCount 3876 12 = 6 ∧ acceleratedOrbit 12 3876 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3876 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3876) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3876.1, data_12_3876.2] + +/-- Complete interval computation for depth 12, residue 3877. -/ +theorem bounds_12_3877 : exactInterval 12 3877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3877 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3877) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3877 : oddCount 3877 12 = 6 ∧ acceleratedOrbit 12 3877 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3877 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3877) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3877.1, data_12_3877.2] + +/-- Complete interval computation for depth 12, residue 3878. -/ +theorem bounds_12_3878 : exactInterval 12 3878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3878 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3878) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3878 : oddCount 3878 12 = 6 ∧ acceleratedOrbit 12 3878 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3878 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3878) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3878.1, data_12_3878.2] + +/-- Complete interval computation for depth 12, residue 3879. -/ +theorem bounds_12_3879 : exactInterval 12 3879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3879 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3879) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3879 : oddCount 3879 12 = 7 ∧ acceleratedOrbit 12 3879 = 2072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3879 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3879) = 3 ^ 7 * m + 2072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3879.1, data_12_3879.2] + +/-- Complete interval computation for depth 12, residue 3880. -/ +theorem bounds_12_3880 : exactInterval 12 3880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3880 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3880) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3880 : oddCount 3880 12 = 5 ∧ acceleratedOrbit 12 3880 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3880 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3880) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3880.1, data_12_3880.2] + +/-- Complete interval computation for depth 12, residue 3881. -/ +theorem bounds_12_3881 : exactInterval 12 3881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3881 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3881) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3881 : oddCount 3881 12 = 6 ∧ acceleratedOrbit 12 3881 = 691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3881 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3881) = 3 ^ 6 * m + 691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3881.1, data_12_3881.2] + +/-- Complete interval computation for depth 12, residue 3882. -/ +theorem bounds_12_3882 : exactInterval 12 3882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3882 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3882) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3882 : oddCount 3882 12 = 5 ∧ acceleratedOrbit 12 3882 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3882 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3882) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3882.1, data_12_3882.2] + +/-- Complete interval computation for depth 12, residue 3883. -/ +theorem bounds_12_3883 : exactInterval 12 3883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3883 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3883) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3883 : oddCount 3883 12 = 6 ∧ acceleratedOrbit 12 3883 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3883 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3883) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3883.1, data_12_3883.2] + +/-- Complete interval computation for depth 12, residue 3884. -/ +theorem bounds_12_3884 : exactInterval 12 3884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3884 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3884) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3884 : oddCount 3884 12 = 4 ∧ acceleratedOrbit 12 3884 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3884 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3884) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3884.1, data_12_3884.2] + +/-- Complete interval computation for depth 12, residue 3885. -/ +theorem bounds_12_3885 : exactInterval 12 3885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3885 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3885) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3885 : oddCount 3885 12 = 4 ∧ acceleratedOrbit 12 3885 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3885 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3885) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3885.1, data_12_3885.2] + +end Collatz.Research.StoppingAtlas.Batch0453 From 813ff53a724034a15382f9c583c112ad755f0c51 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:25 +0530 Subject: [PATCH 0454/1001] proof: certify atlas Batch0454 (12:3886 to 12:3900) --- Collatz/Research/StoppingAtlas/Batch0454.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0454.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0454.lean b/Collatz/Research/StoppingAtlas/Batch0454.lean new file mode 100644 index 00000000..f149c274 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0454.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0454 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3886. -/ +theorem bounds_12_3886 : exactInterval 12 3886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3886 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3886) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3886 : oddCount 3886 12 = 4 ∧ acceleratedOrbit 12 3886 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3886 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3886) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3886.1, data_12_3886.2] + +/-- Complete interval computation for depth 12, residue 3887. -/ +theorem bounds_12_3887 : exactInterval 12 3887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3887 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3887) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3887 : oddCount 3887 12 = 6 ∧ acceleratedOrbit 12 3887 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3887 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3887) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3887.1, data_12_3887.2] + +/-- Complete interval computation for depth 12, residue 3888. -/ +theorem bounds_12_3888 : exactInterval 12 3888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3888 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3888) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3888 : oddCount 3888 12 = 5 ∧ acceleratedOrbit 12 3888 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3888 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3888) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3888.1, data_12_3888.2] + +/-- Complete interval computation for depth 12, residue 3889. -/ +theorem bounds_12_3889 : exactInterval 12 3889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3889 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3889) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3889 : oddCount 3889 12 = 4 ∧ acceleratedOrbit 12 3889 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3889 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3889) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3889.1, data_12_3889.2] + +/-- Complete interval computation for depth 12, residue 3890. -/ +theorem bounds_12_3890 : exactInterval 12 3890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3890 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3890) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3890 : oddCount 3890 12 = 4 ∧ acceleratedOrbit 12 3890 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3890 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3890) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3890.1, data_12_3890.2] + +/-- Complete interval computation for depth 12, residue 3891. -/ +theorem bounds_12_3891 : exactInterval 12 3891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3891 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3891) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3891 : oddCount 3891 12 = 4 ∧ acceleratedOrbit 12 3891 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3891 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3891) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3891.1, data_12_3891.2] + +/-- Complete interval computation for depth 12, residue 3892. -/ +theorem bounds_12_3892 : exactInterval 12 3892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3892 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3892) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3892 : oddCount 3892 12 = 5 ∧ acceleratedOrbit 12 3892 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3892 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3892) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3892.1, data_12_3892.2] + +/-- Complete interval computation for depth 12, residue 3893. -/ +theorem bounds_12_3893 : exactInterval 12 3893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3893 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3893) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3893 : oddCount 3893 12 = 5 ∧ acceleratedOrbit 12 3893 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3893 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3893) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3893.1, data_12_3893.2] + +/-- Complete interval computation for depth 12, residue 3894. -/ +theorem bounds_12_3894 : exactInterval 12 3894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3894 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3894) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3894 : oddCount 3894 12 = 7 ∧ acceleratedOrbit 12 3894 = 2081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3894 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3894) = 3 ^ 7 * m + 2081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3894.1, data_12_3894.2] + +/-- Complete interval computation for depth 12, residue 3895. -/ +theorem bounds_12_3895 : exactInterval 12 3895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3895 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3895) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3895 : oddCount 3895 12 = 7 ∧ acceleratedOrbit 12 3895 = 2081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3895 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3895) = 3 ^ 7 * m + 2081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3895.1, data_12_3895.2] + +/-- Complete interval computation for depth 12, residue 3896. -/ +theorem bounds_12_3896 : exactInterval 12 3896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3896 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3896) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3896 : oddCount 3896 12 = 6 ∧ acceleratedOrbit 12 3896 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3896 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3896) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3896.1, data_12_3896.2] + +/-- Complete interval computation for depth 12, residue 3897. -/ +theorem bounds_12_3897 : exactInterval 12 3897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3897 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3897) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3897 : oddCount 3897 12 = 6 ∧ acceleratedOrbit 12 3897 = 694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3897 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3897) = 3 ^ 6 * m + 694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3897.1, data_12_3897.2] + +/-- Complete interval computation for depth 12, residue 3898. -/ +theorem bounds_12_3898 : exactInterval 12 3898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3898 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3898) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3898 : oddCount 3898 12 = 6 ∧ acceleratedOrbit 12 3898 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3898 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3898) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3898.1, data_12_3898.2] + +/-- Complete interval computation for depth 12, residue 3899. -/ +theorem bounds_12_3899 : exactInterval 12 3899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3899 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3899) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3899 : oddCount 3899 12 = 6 ∧ acceleratedOrbit 12 3899 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3899 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3899) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3899.1, data_12_3899.2] + +/-- Complete interval computation for depth 12, residue 3900. -/ +theorem bounds_12_3900 : exactInterval 12 3900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3900 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3900) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3900 : oddCount 3900 12 = 6 ∧ acceleratedOrbit 12 3900 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3900 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3900) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3900.1, data_12_3900.2] + +end Collatz.Research.StoppingAtlas.Batch0454 From ca373134d82ef542b9294ce3b1add8806d1d7a32 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:25 +0530 Subject: [PATCH 0455/1001] proof: certify atlas Batch0455 (12:3901 to 12:3915) --- Collatz/Research/StoppingAtlas/Batch0455.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0455.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0455.lean b/Collatz/Research/StoppingAtlas/Batch0455.lean new file mode 100644 index 00000000..c845776c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0455.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0455 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3901. -/ +theorem bounds_12_3901 : exactInterval 12 3901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3901 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3901) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3901 : oddCount 3901 12 = 6 ∧ acceleratedOrbit 12 3901 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3901 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3901) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3901.1, data_12_3901.2] + +/-- Complete interval computation for depth 12, residue 3902. -/ +theorem bounds_12_3902 : exactInterval 12 3902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3902 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3902) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3902 : oddCount 3902 12 = 8 ∧ acceleratedOrbit 12 3902 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3902 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3902) = 3 ^ 8 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3902.1, data_12_3902.2] + +/-- Complete interval computation for depth 12, residue 3903. -/ +theorem bounds_12_3903 : exactInterval 12 3903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3903 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3903) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3903 : oddCount 3903 12 = 8 ∧ acceleratedOrbit 12 3903 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3903 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3903) = 3 ^ 8 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3903.1, data_12_3903.2] + +/-- Complete interval computation for depth 12, residue 3904. -/ +theorem bounds_12_3904 : exactInterval 12 3904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3904 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3904) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3904 : oddCount 3904 12 = 4 ∧ acceleratedOrbit 12 3904 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3904 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3904) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3904.1, data_12_3904.2] + +/-- Complete interval computation for depth 12, residue 3905. -/ +theorem bounds_12_3905 : exactInterval 12 3905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3905 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3905) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3905 : oddCount 3905 12 = 5 ∧ acceleratedOrbit 12 3905 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3905 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3905) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3905.1, data_12_3905.2] + +/-- Complete interval computation for depth 12, residue 3906. -/ +theorem bounds_12_3906 : exactInterval 12 3906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3906 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3906) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3906 : oddCount 3906 12 = 5 ∧ acceleratedOrbit 12 3906 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3906 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3906) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3906.1, data_12_3906.2] + +/-- Complete interval computation for depth 12, residue 3907. -/ +theorem bounds_12_3907 : exactInterval 12 3907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3907 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3907) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3907 : oddCount 3907 12 = 5 ∧ acceleratedOrbit 12 3907 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3907 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3907) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3907.1, data_12_3907.2] + +/-- Complete interval computation for depth 12, residue 3908. -/ +theorem bounds_12_3908 : exactInterval 12 3908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3908 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3908) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3908 : oddCount 3908 12 = 5 ∧ acceleratedOrbit 12 3908 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3908 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3908) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3908.1, data_12_3908.2] + +/-- Complete interval computation for depth 12, residue 3909. -/ +theorem bounds_12_3909 : exactInterval 12 3909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3909 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3909) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3909 : oddCount 3909 12 = 5 ∧ acceleratedOrbit 12 3909 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3909 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3909) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3909.1, data_12_3909.2] + +/-- Complete interval computation for depth 12, residue 3910. -/ +theorem bounds_12_3910 : exactInterval 12 3910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3910 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3910) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3910 : oddCount 3910 12 = 5 ∧ acceleratedOrbit 12 3910 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3910 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3910) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3910.1, data_12_3910.2] + +/-- Complete interval computation for depth 12, residue 3911. -/ +theorem bounds_12_3911 : exactInterval 12 3911 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3911 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3911) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3911 : oddCount 3911 12 = 7 ∧ acceleratedOrbit 12 3911 = 2089 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3911 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3911) = 3 ^ 7 * m + 2089 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3911.1, data_12_3911.2] + +/-- Complete interval computation for depth 12, residue 3912. -/ +theorem bounds_12_3912 : exactInterval 12 3912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3912 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3912) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3912 : oddCount 3912 12 = 7 ∧ acceleratedOrbit 12 3912 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3912 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3912) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3912.1, data_12_3912.2] + +/-- Complete interval computation for depth 12, residue 3913. -/ +theorem bounds_12_3913 : exactInterval 12 3913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3913 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3913) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3913 : oddCount 3913 12 = 6 ∧ acceleratedOrbit 12 3913 = 697 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3913 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3913) = 3 ^ 6 * m + 697 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3913.1, data_12_3913.2] + +/-- Complete interval computation for depth 12, residue 3914. -/ +theorem bounds_12_3914 : exactInterval 12 3914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3914 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3914) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3914 : oddCount 3914 12 = 7 ∧ acceleratedOrbit 12 3914 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3914 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3914) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3914.1, data_12_3914.2] + +/-- Complete interval computation for depth 12, residue 3915. -/ +theorem bounds_12_3915 : exactInterval 12 3915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3915 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3915) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3915 : oddCount 3915 12 = 5 ∧ acceleratedOrbit 12 3915 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3915 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3915) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3915.1, data_12_3915.2] + +end Collatz.Research.StoppingAtlas.Batch0455 From 75fd8219312a0b985c1c4bd259ffdf173e5a97b8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:26 +0530 Subject: [PATCH 0456/1001] proof: certify atlas Batch0456 (12:3916 to 12:3931) --- Collatz/Research/StoppingAtlas/Batch0456.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0456.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0456.lean b/Collatz/Research/StoppingAtlas/Batch0456.lean new file mode 100644 index 00000000..408b7595 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0456.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0456 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3916. -/ +theorem bounds_12_3916 : exactInterval 12 3916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3916 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3916) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3916 : oddCount 3916 12 = 7 ∧ acceleratedOrbit 12 3916 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3916 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3916) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3916.1, data_12_3916.2] + +/-- Complete interval computation for depth 12, residue 3917. -/ +theorem bounds_12_3917 : exactInterval 12 3917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3917 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3917) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3917 : oddCount 3917 12 = 7 ∧ acceleratedOrbit 12 3917 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3917 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3917) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3917.1, data_12_3917.2] + +/-- Complete interval computation for depth 12, residue 3918. -/ +theorem bounds_12_3918 : exactInterval 12 3918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3918 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3918) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3918 : oddCount 3918 12 = 8 ∧ acceleratedOrbit 12 3918 = 6281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3918 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3918) = 3 ^ 8 * m + 6281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3918.1, data_12_3918.2] + +/-- Complete interval computation for depth 12, residue 3919. -/ +theorem bounds_12_3919 : exactInterval 12 3919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3919 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3919) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3919 : oddCount 3919 12 = 8 ∧ acceleratedOrbit 12 3919 = 6281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3919 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3919) = 3 ^ 8 * m + 6281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3919.1, data_12_3919.2] + +/-- Complete interval computation for depth 12, residue 3920. -/ +theorem bounds_12_3920 : exactInterval 12 3920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3920 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3920) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3920 : oddCount 3920 12 = 4 ∧ acceleratedOrbit 12 3920 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3920 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3920) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3920.1, data_12_3920.2] + +/-- Complete interval computation for depth 12, residue 3921. -/ +theorem bounds_12_3921 : exactInterval 12 3921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3921 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3921) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3921 : oddCount 3921 12 = 7 ∧ acceleratedOrbit 12 3921 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3921 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3921) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3921.1, data_12_3921.2] + +/-- Complete interval computation for depth 12, residue 3922. -/ +theorem bounds_12_3922 : exactInterval 12 3922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3922 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3922) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3922 : oddCount 3922 12 = 9 ∧ acceleratedOrbit 12 3922 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3922 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3922) = 3 ^ 9 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3922.1, data_12_3922.2] + +/-- Complete interval computation for depth 12, residue 3923. -/ +theorem bounds_12_3923 : exactInterval 12 3923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3923 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3923) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3923 : oddCount 3923 12 = 9 ∧ acceleratedOrbit 12 3923 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3923 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3923) = 3 ^ 9 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3923.1, data_12_3923.2] + +/-- Complete interval computation for depth 12, residue 3924. -/ +theorem bounds_12_3924 : exactInterval 12 3924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3924 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3924) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3924 : oddCount 3924 12 = 4 ∧ acceleratedOrbit 12 3924 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3924 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3924) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3924.1, data_12_3924.2] + +/-- Complete interval computation for depth 12, residue 3925. -/ +theorem bounds_12_3925 : exactInterval 12 3925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3925 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3925) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3925 : oddCount 3925 12 = 4 ∧ acceleratedOrbit 12 3925 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3925 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3925) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3925.1, data_12_3925.2] + +/-- Complete interval computation for depth 12, residue 3926. -/ +theorem bounds_12_3926 : exactInterval 12 3926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3926 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3926) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3926 : oddCount 3926 12 = 7 ∧ acceleratedOrbit 12 3926 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3926 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3926) = 3 ^ 7 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3926.1, data_12_3926.2] + +/-- Complete interval computation for depth 12, residue 3927. -/ +theorem bounds_12_3927 : exactInterval 12 3927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3927 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3927) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3927 : oddCount 3927 12 = 7 ∧ acceleratedOrbit 12 3927 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3927 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3927) = 3 ^ 7 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3927.1, data_12_3927.2] + +/-- Complete interval computation for depth 12, residue 3928. -/ +theorem bounds_12_3928 : exactInterval 12 3928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3928 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3928) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3928 : oddCount 3928 12 = 7 ∧ acceleratedOrbit 12 3928 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3928 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3928) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3928.1, data_12_3928.2] + +/-- Complete interval computation for depth 12, residue 3929. -/ +theorem bounds_12_3929 : exactInterval 12 3929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3929 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3929) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3929 : oddCount 3929 12 = 6 ∧ acceleratedOrbit 12 3929 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3929 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3929) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3929.1, data_12_3929.2] + +/-- Complete interval computation for depth 12, residue 3930. -/ +theorem bounds_12_3930 : exactInterval 12 3930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3930 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3930) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3930 : oddCount 3930 12 = 7 ∧ acceleratedOrbit 12 3930 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3930 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3930) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3930.1, data_12_3930.2] + +/-- Complete interval computation for depth 12, residue 3931. -/ +theorem bounds_12_3931 : exactInterval 12 3931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3931 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3931) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3931 : oddCount 3931 12 = 9 ∧ acceleratedOrbit 12 3931 = 18899 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3931 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3931) = 3 ^ 9 * m + 18899 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3931.1, data_12_3931.2] + +end Collatz.Research.StoppingAtlas.Batch0456 From 092b69c9c92be6b3e83b7ba9034ede2da094df57 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:26 +0530 Subject: [PATCH 0457/1001] proof: certify atlas Batch0457 (12:3932 to 12:3946) --- Collatz/Research/StoppingAtlas/Batch0457.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0457.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0457.lean b/Collatz/Research/StoppingAtlas/Batch0457.lean new file mode 100644 index 00000000..3f3ebc9b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0457.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0457 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3932. -/ +theorem bounds_12_3932 : exactInterval 12 3932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3932 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3932) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3932 : oddCount 3932 12 = 7 ∧ acceleratedOrbit 12 3932 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3932 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3932) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3932.1, data_12_3932.2] + +/-- Complete interval computation for depth 12, residue 3933. -/ +theorem bounds_12_3933 : exactInterval 12 3933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3933 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3933) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3933 : oddCount 3933 12 = 7 ∧ acceleratedOrbit 12 3933 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3933 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3933) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3933.1, data_12_3933.2] + +/-- Complete interval computation for depth 12, residue 3934. -/ +theorem bounds_12_3934 : exactInterval 12 3934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3934 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3934) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3934 : oddCount 3934 12 = 6 ∧ acceleratedOrbit 12 3934 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3934 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3934) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3934.1, data_12_3934.2] + +/-- Complete interval computation for depth 12, residue 3935. -/ +theorem bounds_12_3935 : exactInterval 12 3935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3935 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3935) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3935 : oddCount 3935 12 = 6 ∧ acceleratedOrbit 12 3935 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3935 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3935) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3935.1, data_12_3935.2] + +/-- Complete interval computation for depth 12, residue 3936. -/ +theorem bounds_12_3936 : exactInterval 12 3936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3936 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3936) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3936 : oddCount 3936 12 = 5 ∧ acceleratedOrbit 12 3936 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3936 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3936) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3936.1, data_12_3936.2] + +/-- Complete interval computation for depth 12, residue 3937. -/ +theorem bounds_12_3937 : exactInterval 12 3937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3937 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3937) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3937 : oddCount 3937 12 = 8 ∧ acceleratedOrbit 12 3937 = 6311 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3937 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3937) = 3 ^ 8 * m + 6311 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3937.1, data_12_3937.2] + +/-- Complete interval computation for depth 12, residue 3938. -/ +theorem bounds_12_3938 : exactInterval 12 3938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3938 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3938) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3938 : oddCount 3938 12 = 3 ∧ acceleratedOrbit 12 3938 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3938 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3938) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3938.1, data_12_3938.2] + +/-- Complete interval computation for depth 12, residue 3939. -/ +theorem bounds_12_3939 : exactInterval 12 3939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3939 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3939) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3939 : oddCount 3939 12 = 3 ∧ acceleratedOrbit 12 3939 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3939 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3939) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3939.1, data_12_3939.2] + +/-- Complete interval computation for depth 12, residue 3940. -/ +theorem bounds_12_3940 : exactInterval 12 3940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3940 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3940) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3940 : oddCount 3940 12 = 3 ∧ acceleratedOrbit 12 3940 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3940 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3940) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3940.1, data_12_3940.2] + +/-- Complete interval computation for depth 12, residue 3941. -/ +theorem bounds_12_3941 : exactInterval 12 3941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3941 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3941) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3941 : oddCount 3941 12 = 3 ∧ acceleratedOrbit 12 3941 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3941 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3941) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3941.1, data_12_3941.2] + +/-- Complete interval computation for depth 12, residue 3942. -/ +theorem bounds_12_3942 : exactInterval 12 3942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3942 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3942) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3942 : oddCount 3942 12 = 3 ∧ acceleratedOrbit 12 3942 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3942 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3942) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3942.1, data_12_3942.2] + +/-- Complete interval computation for depth 12, residue 3943. -/ +theorem bounds_12_3943 : exactInterval 12 3943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3943 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3943) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3943 : oddCount 3943 12 = 11 ∧ acceleratedOrbit 12 3943 = 170585 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3943 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3943) = 3 ^ 11 * m + 170585 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3943.1, data_12_3943.2] + +/-- Complete interval computation for depth 12, residue 3944. -/ +theorem bounds_12_3944 : exactInterval 12 3944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3944 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3944) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3944 : oddCount 3944 12 = 5 ∧ acceleratedOrbit 12 3944 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3944 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3944) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3944.1, data_12_3944.2] + +/-- Complete interval computation for depth 12, residue 3945. -/ +theorem bounds_12_3945 : exactInterval 12 3945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3945 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3945) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3945 : oddCount 3945 12 = 7 ∧ acceleratedOrbit 12 3945 = 2108 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3945 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3945) = 3 ^ 7 * m + 2108 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3945.1, data_12_3945.2] + +/-- Complete interval computation for depth 12, residue 3946. -/ +theorem bounds_12_3946 : exactInterval 12 3946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3946 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3946) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3946 : oddCount 3946 12 = 5 ∧ acceleratedOrbit 12 3946 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3946 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3946) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3946.1, data_12_3946.2] + +end Collatz.Research.StoppingAtlas.Batch0457 From 3dd08f98846c680d53019807626b4d89f84f2732 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:26 +0530 Subject: [PATCH 0458/1001] proof: certify atlas Batch0458 (12:3947 to 12:3961) --- Collatz/Research/StoppingAtlas/Batch0458.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0458.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0458.lean b/Collatz/Research/StoppingAtlas/Batch0458.lean new file mode 100644 index 00000000..ad293663 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0458.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0458 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3947. -/ +theorem bounds_12_3947 : exactInterval 12 3947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3947 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3947) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3947 : oddCount 3947 12 = 6 ∧ acceleratedOrbit 12 3947 = 703 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3947 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3947) = 3 ^ 6 * m + 703 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3947.1, data_12_3947.2] + +/-- Complete interval computation for depth 12, residue 3948. -/ +theorem bounds_12_3948 : exactInterval 12 3948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3948 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3948) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3948 : oddCount 3948 12 = 6 ∧ acceleratedOrbit 12 3948 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3948 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3948) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3948.1, data_12_3948.2] + +/-- Complete interval computation for depth 12, residue 3949. -/ +theorem bounds_12_3949 : exactInterval 12 3949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3949 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3949) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3949 : oddCount 3949 12 = 6 ∧ acceleratedOrbit 12 3949 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3949 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3949) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3949.1, data_12_3949.2] + +/-- Complete interval computation for depth 12, residue 3950. -/ +theorem bounds_12_3950 : exactInterval 12 3950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3950 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3950) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3950 : oddCount 3950 12 = 6 ∧ acceleratedOrbit 12 3950 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3950 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3950) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3950.1, data_12_3950.2] + +/-- Complete interval computation for depth 12, residue 3951. -/ +theorem bounds_12_3951 : exactInterval 12 3951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3951 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3951) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3951 : oddCount 3951 12 = 8 ∧ acceleratedOrbit 12 3951 = 6331 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3951 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3951) = 3 ^ 8 * m + 6331 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3951.1, data_12_3951.2] + +/-- Complete interval computation for depth 12, residue 3952. -/ +theorem bounds_12_3952 : exactInterval 12 3952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3952 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3952) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3952 : oddCount 3952 12 = 5 ∧ acceleratedOrbit 12 3952 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3952 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3952) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3952.1, data_12_3952.2] + +/-- Complete interval computation for depth 12, residue 3953. -/ +theorem bounds_12_3953 : exactInterval 12 3953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3953 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3953) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3953 : oddCount 3953 12 = 5 ∧ acceleratedOrbit 12 3953 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3953 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3953) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3953.1, data_12_3953.2] + +/-- Complete interval computation for depth 12, residue 3954. -/ +theorem bounds_12_3954 : exactInterval 12 3954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3954 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3954) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3954 : oddCount 3954 12 = 5 ∧ acceleratedOrbit 12 3954 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3954 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3954) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3954.1, data_12_3954.2] + +/-- Complete interval computation for depth 12, residue 3955. -/ +theorem bounds_12_3955 : exactInterval 12 3955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3955 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3955) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3955 : oddCount 3955 12 = 5 ∧ acceleratedOrbit 12 3955 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3955 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3955) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3955.1, data_12_3955.2] + +/-- Complete interval computation for depth 12, residue 3956. -/ +theorem bounds_12_3956 : exactInterval 12 3956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3956 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3956) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3956 : oddCount 3956 12 = 5 ∧ acceleratedOrbit 12 3956 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3956 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3956) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3956.1, data_12_3956.2] + +/-- Complete interval computation for depth 12, residue 3957. -/ +theorem bounds_12_3957 : exactInterval 12 3957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3957 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3957) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3957 : oddCount 3957 12 = 5 ∧ acceleratedOrbit 12 3957 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3957 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3957) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3957.1, data_12_3957.2] + +/-- Complete interval computation for depth 12, residue 3958. -/ +theorem bounds_12_3958 : exactInterval 12 3958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3958 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3958) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3958 : oddCount 3958 12 = 5 ∧ acceleratedOrbit 12 3958 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3958 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3958) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3958.1, data_12_3958.2] + +/-- Complete interval computation for depth 12, residue 3959. -/ +theorem bounds_12_3959 : exactInterval 12 3959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3959 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3959) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3959 : oddCount 3959 12 = 5 ∧ acceleratedOrbit 12 3959 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3959 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3959) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3959.1, data_12_3959.2] + +/-- Complete interval computation for depth 12, residue 3960. -/ +theorem bounds_12_3960 : exactInterval 12 3960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3960 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3960) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3960 : oddCount 3960 12 = 7 ∧ acceleratedOrbit 12 3960 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3960 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3960) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3960.1, data_12_3960.2] + +/-- Complete interval computation for depth 12, residue 3961. -/ +theorem bounds_12_3961 : exactInterval 12 3961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3961 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3961) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3961 : oddCount 3961 12 = 7 ∧ acceleratedOrbit 12 3961 = 2116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3961 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3961) = 3 ^ 7 * m + 2116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3961.1, data_12_3961.2] + +end Collatz.Research.StoppingAtlas.Batch0458 From d8efbc114c21198907776a8b4fa3beb837a00ced Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:27 +0530 Subject: [PATCH 0459/1001] proof: certify atlas Batch0459 (12:3962 to 12:3977) --- Collatz/Research/StoppingAtlas/Batch0459.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0459.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0459.lean b/Collatz/Research/StoppingAtlas/Batch0459.lean new file mode 100644 index 00000000..93033a2e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0459.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0459 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3962. -/ +theorem bounds_12_3962 : exactInterval 12 3962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3962 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3962) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3962 : oddCount 3962 12 = 7 ∧ acceleratedOrbit 12 3962 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3962 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3962) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3962.1, data_12_3962.2] + +/-- Complete interval computation for depth 12, residue 3963. -/ +theorem bounds_12_3963 : exactInterval 12 3963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3963 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3963) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3963 : oddCount 3963 12 = 7 ∧ acceleratedOrbit 12 3963 = 2117 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3963 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3963) = 3 ^ 7 * m + 2117 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3963.1, data_12_3963.2] + +/-- Complete interval computation for depth 12, residue 3964. -/ +theorem bounds_12_3964 : exactInterval 12 3964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3964 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3964) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3964 : oddCount 3964 12 = 7 ∧ acceleratedOrbit 12 3964 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3964 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3964) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3964.1, data_12_3964.2] + +/-- Complete interval computation for depth 12, residue 3965. -/ +theorem bounds_12_3965 : exactInterval 12 3965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3965 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3965) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3965 : oddCount 3965 12 = 7 ∧ acceleratedOrbit 12 3965 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3965 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3965) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3965.1, data_12_3965.2] + +/-- Complete interval computation for depth 12, residue 3966. -/ +theorem bounds_12_3966 : exactInterval 12 3966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3966 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3966) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3966 : oddCount 3966 12 = 8 ∧ acceleratedOrbit 12 3966 = 6356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3966 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3966) = 3 ^ 8 * m + 6356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3966.1, data_12_3966.2] + +/-- Complete interval computation for depth 12, residue 3967. -/ +theorem bounds_12_3967 : exactInterval 12 3967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3967 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3967) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3967 : oddCount 3967 12 = 8 ∧ acceleratedOrbit 12 3967 = 6356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3967 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3967) = 3 ^ 8 * m + 6356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3967.1, data_12_3967.2] + +/-- Complete interval computation for depth 12, residue 3968. -/ +theorem bounds_12_3968 : exactInterval 12 3968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3968 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3968) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3968 : oddCount 3968 12 = 5 ∧ acceleratedOrbit 12 3968 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3968 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3968) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3968.1, data_12_3968.2] + +/-- Complete interval computation for depth 12, residue 3969. -/ +theorem bounds_12_3969 : exactInterval 12 3969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3969 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3969) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3969 : oddCount 3969 12 = 6 ∧ acceleratedOrbit 12 3969 = 707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3969 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3969) = 3 ^ 6 * m + 707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3969.1, data_12_3969.2] + +/-- Complete interval computation for depth 12, residue 3970. -/ +theorem bounds_12_3970 : exactInterval 12 3970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3970 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3970) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3970 : oddCount 3970 12 = 5 ∧ acceleratedOrbit 12 3970 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3970 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3970) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3970.1, data_12_3970.2] + +/-- Complete interval computation for depth 12, residue 3971. -/ +theorem bounds_12_3971 : exactInterval 12 3971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3971 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3971) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3971 : oddCount 3971 12 = 5 ∧ acceleratedOrbit 12 3971 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3971 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3971) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3971.1, data_12_3971.2] + +/-- Complete interval computation for depth 12, residue 3972. -/ +theorem bounds_12_3972 : exactInterval 12 3972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3972 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3972) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3972 : oddCount 3972 12 = 7 ∧ acceleratedOrbit 12 3972 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3972 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3972) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3972.1, data_12_3972.2] + +/-- Complete interval computation for depth 12, residue 3973. -/ +theorem bounds_12_3973 : exactInterval 12 3973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3973 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3973) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3973 : oddCount 3973 12 = 7 ∧ acceleratedOrbit 12 3973 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3973 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3973) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3973.1, data_12_3973.2] + +/-- Complete interval computation for depth 12, residue 3974. -/ +theorem bounds_12_3974 : exactInterval 12 3974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3974 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3974) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3974 : oddCount 3974 12 = 7 ∧ acceleratedOrbit 12 3974 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3974 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3974) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3974.1, data_12_3974.2] + +/-- Complete interval computation for depth 12, residue 3975. -/ +theorem bounds_12_3975 : exactInterval 12 3975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3975 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3975) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3975 : oddCount 3975 12 = 5 ∧ acceleratedOrbit 12 3975 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3975 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3975) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3975.1, data_12_3975.2] + +/-- Complete interval computation for depth 12, residue 3976. -/ +theorem bounds_12_3976 : exactInterval 12 3976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3976 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3976) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3976 : oddCount 3976 12 = 4 ∧ acceleratedOrbit 12 3976 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3976 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3976) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3976.1, data_12_3976.2] + +/-- Complete interval computation for depth 12, residue 3977. -/ +theorem bounds_12_3977 : exactInterval 12 3977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3977 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3977) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3977 : oddCount 3977 12 = 8 ∧ acceleratedOrbit 12 3977 = 6374 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3977 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3977) = 3 ^ 8 * m + 6374 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3977.1, data_12_3977.2] + +end Collatz.Research.StoppingAtlas.Batch0459 From 1107585973924d4a129c062438ad4e1891667759 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:27 +0530 Subject: [PATCH 0460/1001] proof: certify atlas Batch0460 (12:3978 to 12:3992) --- Collatz/Research/StoppingAtlas/Batch0460.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0460.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0460.lean b/Collatz/Research/StoppingAtlas/Batch0460.lean new file mode 100644 index 00000000..fb744921 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0460.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0460 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3978. -/ +theorem bounds_12_3978 : exactInterval 12 3978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3978 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3978) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3978 : oddCount 3978 12 = 4 ∧ acceleratedOrbit 12 3978 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3978 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3978) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3978.1, data_12_3978.2] + +/-- Complete interval computation for depth 12, residue 3979. -/ +theorem bounds_12_3979 : exactInterval 12 3979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3979 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3979) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3979 : oddCount 3979 12 = 7 ∧ acceleratedOrbit 12 3979 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3979 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3979) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3979.1, data_12_3979.2] + +/-- Complete interval computation for depth 12, residue 3980. -/ +theorem bounds_12_3980 : exactInterval 12 3980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3980 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3980) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3980 : oddCount 3980 12 = 4 ∧ acceleratedOrbit 12 3980 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3980 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3980) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3980.1, data_12_3980.2] + +/-- Complete interval computation for depth 12, residue 3981. -/ +theorem bounds_12_3981 : exactInterval 12 3981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3981 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3981) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3981 : oddCount 3981 12 = 4 ∧ acceleratedOrbit 12 3981 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3981 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3981) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3981.1, data_12_3981.2] + +/-- Complete interval computation for depth 12, residue 3982. -/ +theorem bounds_12_3982 : exactInterval 12 3982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3982 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3982) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3982 : oddCount 3982 12 = 7 ∧ acceleratedOrbit 12 3982 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3982 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3982) = 3 ^ 7 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3982.1, data_12_3982.2] + +/-- Complete interval computation for depth 12, residue 3983. -/ +theorem bounds_12_3983 : exactInterval 12 3983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3983 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3983) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3983 : oddCount 3983 12 = 7 ∧ acceleratedOrbit 12 3983 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3983 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3983) = 3 ^ 7 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3983.1, data_12_3983.2] + +/-- Complete interval computation for depth 12, residue 3984. -/ +theorem bounds_12_3984 : exactInterval 12 3984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3984 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3984) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3984 : oddCount 3984 12 = 5 ∧ acceleratedOrbit 12 3984 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3984 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3984) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3984.1, data_12_3984.2] + +/-- Complete interval computation for depth 12, residue 3985. -/ +theorem bounds_12_3985 : exactInterval 12 3985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3985 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3985) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3985 : oddCount 3985 12 = 7 ∧ acceleratedOrbit 12 3985 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3985 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3985) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3985.1, data_12_3985.2] + +/-- Complete interval computation for depth 12, residue 3986. -/ +theorem bounds_12_3986 : exactInterval 12 3986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3986 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3986) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3986 : oddCount 3986 12 = 7 ∧ acceleratedOrbit 12 3986 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3986 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3986) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3986.1, data_12_3986.2] + +/-- Complete interval computation for depth 12, residue 3987. -/ +theorem bounds_12_3987 : exactInterval 12 3987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3987 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3987) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3987 : oddCount 3987 12 = 7 ∧ acceleratedOrbit 12 3987 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3987 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3987) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3987.1, data_12_3987.2] + +/-- Complete interval computation for depth 12, residue 3988. -/ +theorem bounds_12_3988 : exactInterval 12 3988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3988 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3988) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3988 : oddCount 3988 12 = 5 ∧ acceleratedOrbit 12 3988 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3988 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3988) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3988.1, data_12_3988.2] + +/-- Complete interval computation for depth 12, residue 3989. -/ +theorem bounds_12_3989 : exactInterval 12 3989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3989 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3989) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3989 : oddCount 3989 12 = 5 ∧ acceleratedOrbit 12 3989 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3989 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3989) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3989.1, data_12_3989.2] + +/-- Complete interval computation for depth 12, residue 3990. -/ +theorem bounds_12_3990 : exactInterval 12 3990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3990 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3990) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3990 : oddCount 3990 12 = 4 ∧ acceleratedOrbit 12 3990 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3990 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3990) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3990.1, data_12_3990.2] + +/-- Complete interval computation for depth 12, residue 3991. -/ +theorem bounds_12_3991 : exactInterval 12 3991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3991 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3991) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3991 : oddCount 3991 12 = 4 ∧ acceleratedOrbit 12 3991 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3991 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3991) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3991.1, data_12_3991.2] + +/-- Complete interval computation for depth 12, residue 3992. -/ +theorem bounds_12_3992 : exactInterval 12 3992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3992 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3992) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3992 : oddCount 3992 12 = 5 ∧ acceleratedOrbit 12 3992 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3992 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3992) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3992.1, data_12_3992.2] + +end Collatz.Research.StoppingAtlas.Batch0460 From d1f0640a5dc589f9393a7ececed3a970583aa93c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:27 +0530 Subject: [PATCH 0461/1001] proof: certify atlas Batch0461 (12:3993 to 12:4007) --- Collatz/Research/StoppingAtlas/Batch0461.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0461.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0461.lean b/Collatz/Research/StoppingAtlas/Batch0461.lean new file mode 100644 index 00000000..f925979e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0461.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0461 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 3993. -/ +theorem bounds_12_3993 : exactInterval 12 3993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3993 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3993) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3993 : oddCount 3993 12 = 4 ∧ acceleratedOrbit 12 3993 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3993 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3993) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3993.1, data_12_3993.2] + +/-- Complete interval computation for depth 12, residue 3994. -/ +theorem bounds_12_3994 : exactInterval 12 3994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3994 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3994) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3994 : oddCount 3994 12 = 5 ∧ acceleratedOrbit 12 3994 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3994 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3994) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3994.1, data_12_3994.2] + +/-- Complete interval computation for depth 12, residue 3995. -/ +theorem bounds_12_3995 : exactInterval 12 3995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3995 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3995) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3995 : oddCount 3995 12 = 7 ∧ acceleratedOrbit 12 3995 = 2134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3995 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3995) = 3 ^ 7 * m + 2134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3995.1, data_12_3995.2] + +/-- Complete interval computation for depth 12, residue 3996. -/ +theorem bounds_12_3996 : exactInterval 12 3996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3996 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3996) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3996 : oddCount 3996 12 = 6 ∧ acceleratedOrbit 12 3996 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3996 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3996) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3996.1, data_12_3996.2] + +/-- Complete interval computation for depth 12, residue 3997. -/ +theorem bounds_12_3997 : exactInterval 12 3997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3997 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3997) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3997 : oddCount 3997 12 = 6 ∧ acceleratedOrbit 12 3997 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3997 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3997) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3997.1, data_12_3997.2] + +/-- Complete interval computation for depth 12, residue 3998. -/ +theorem bounds_12_3998 : exactInterval 12 3998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3998 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3998) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3998 : oddCount 3998 12 = 6 ∧ acceleratedOrbit 12 3998 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3998 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3998) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3998.1, data_12_3998.2] + +/-- Complete interval computation for depth 12, residue 3999. -/ +theorem bounds_12_3999 : exactInterval 12 3999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_3999 (m : Nat) : + stoppingTime (2 ^ 12 * m + 3999) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_3999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_3999 : oddCount 3999 12 = 9 ∧ acceleratedOrbit 12 3999 = 19223 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_3999 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 3999) = 3 ^ 9 * m + 19223 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_3999.1, data_12_3999.2] + +/-- Complete interval computation for depth 12, residue 4000. -/ +theorem bounds_12_4000 : exactInterval 12 4000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4000 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4000) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4000 : oddCount 4000 12 = 5 ∧ acceleratedOrbit 12 4000 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4000 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4000) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4000.1, data_12_4000.2] + +/-- Complete interval computation for depth 12, residue 4001. -/ +theorem bounds_12_4001 : exactInterval 12 4001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4001 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4001) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4001 : oddCount 4001 12 = 6 ∧ acceleratedOrbit 12 4001 = 713 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4001 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4001) = 3 ^ 6 * m + 713 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4001.1, data_12_4001.2] + +/-- Complete interval computation for depth 12, residue 4002. -/ +theorem bounds_12_4002 : exactInterval 12 4002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4002 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4002) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4002 : oddCount 4002 12 = 5 ∧ acceleratedOrbit 12 4002 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4002 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4002) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4002.1, data_12_4002.2] + +/-- Complete interval computation for depth 12, residue 4003. -/ +theorem bounds_12_4003 : exactInterval 12 4003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4003 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4003) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4003 : oddCount 4003 12 = 5 ∧ acceleratedOrbit 12 4003 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4003 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4003) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4003.1, data_12_4003.2] + +/-- Complete interval computation for depth 12, residue 4004. -/ +theorem bounds_12_4004 : exactInterval 12 4004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4004 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4004) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4004 : oddCount 4004 12 = 8 ∧ acceleratedOrbit 12 4004 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4004 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4004) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4004.1, data_12_4004.2] + +/-- Complete interval computation for depth 12, residue 4005. -/ +theorem bounds_12_4005 : exactInterval 12 4005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4005 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4005) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4005 : oddCount 4005 12 = 8 ∧ acceleratedOrbit 12 4005 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4005 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4005) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4005.1, data_12_4005.2] + +/-- Complete interval computation for depth 12, residue 4006. -/ +theorem bounds_12_4006 : exactInterval 12 4006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4006 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4006) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4006 : oddCount 4006 12 = 8 ∧ acceleratedOrbit 12 4006 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4006 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4006) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4006.1, data_12_4006.2] + +/-- Complete interval computation for depth 12, residue 4007. -/ +theorem bounds_12_4007 : exactInterval 12 4007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4007 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4007) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4007 : oddCount 4007 12 = 8 ∧ acceleratedOrbit 12 4007 = 6421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4007 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4007) = 3 ^ 8 * m + 6421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4007.1, data_12_4007.2] + +end Collatz.Research.StoppingAtlas.Batch0461 From 917a09cd046f7b2c9ba26bb2a813da0993df07a2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:27 +0530 Subject: [PATCH 0462/1001] proof: certify atlas Batch0462 (12:4008 to 12:4023) --- Collatz/Research/StoppingAtlas/Batch0462.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0462.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0462.lean b/Collatz/Research/StoppingAtlas/Batch0462.lean new file mode 100644 index 00000000..70fc70ab --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0462.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0462 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 4008. -/ +theorem bounds_12_4008 : exactInterval 12 4008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4008 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4008) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4008 : oddCount 4008 12 = 5 ∧ acceleratedOrbit 12 4008 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4008 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4008) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4008.1, data_12_4008.2] + +/-- Complete interval computation for depth 12, residue 4009. -/ +theorem bounds_12_4009 : exactInterval 12 4009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4009 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4009) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4009 : oddCount 4009 12 = 9 ∧ acceleratedOrbit 12 4009 = 19273 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4009 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4009) = 3 ^ 9 * m + 19273 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4009.1, data_12_4009.2] + +/-- Complete interval computation for depth 12, residue 4010. -/ +theorem bounds_12_4010 : exactInterval 12 4010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4010 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4010) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4010 : oddCount 4010 12 = 5 ∧ acceleratedOrbit 12 4010 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4010 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4010) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4010.1, data_12_4010.2] + +/-- Complete interval computation for depth 12, residue 4011. -/ +theorem bounds_12_4011 : exactInterval 12 4011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4011 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4011) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4011 : oddCount 4011 12 = 7 ∧ acceleratedOrbit 12 4011 = 2143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4011 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4011) = 3 ^ 7 * m + 2143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4011.1, data_12_4011.2] + +/-- Complete interval computation for depth 12, residue 4012. -/ +theorem bounds_12_4012 : exactInterval 12 4012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4012 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4012) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4012 : oddCount 4012 12 = 7 ∧ acceleratedOrbit 12 4012 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4012 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4012) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4012.1, data_12_4012.2] + +/-- Complete interval computation for depth 12, residue 4013. -/ +theorem bounds_12_4013 : exactInterval 12 4013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4013 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4013) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4013 : oddCount 4013 12 = 7 ∧ acceleratedOrbit 12 4013 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4013 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4013) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4013.1, data_12_4013.2] + +/-- Complete interval computation for depth 12, residue 4014. -/ +theorem bounds_12_4014 : exactInterval 12 4014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4014 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4014) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4014 : oddCount 4014 12 = 7 ∧ acceleratedOrbit 12 4014 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4014 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4014) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4014.1, data_12_4014.2] + +/-- Complete interval computation for depth 12, residue 4015. -/ +theorem bounds_12_4015 : exactInterval 12 4015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4015 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4015) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4015 : oddCount 4015 12 = 6 ∧ acceleratedOrbit 12 4015 = 715 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4015 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4015) = 3 ^ 6 * m + 715 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4015.1, data_12_4015.2] + +/-- Complete interval computation for depth 12, residue 4016. -/ +theorem bounds_12_4016 : exactInterval 12 4016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4016 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4016) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4016 : oddCount 4016 12 = 6 ∧ acceleratedOrbit 12 4016 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4016 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4016) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4016.1, data_12_4016.2] + +/-- Complete interval computation for depth 12, residue 4017. -/ +theorem bounds_12_4017 : exactInterval 12 4017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4017 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4017) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4017 : oddCount 4017 12 = 4 ∧ acceleratedOrbit 12 4017 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4017 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4017) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4017.1, data_12_4017.2] + +/-- Complete interval computation for depth 12, residue 4018. -/ +theorem bounds_12_4018 : exactInterval 12 4018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4018 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4018) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4018 : oddCount 4018 12 = 4 ∧ acceleratedOrbit 12 4018 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4018 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4018) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4018.1, data_12_4018.2] + +/-- Complete interval computation for depth 12, residue 4019. -/ +theorem bounds_12_4019 : exactInterval 12 4019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4019 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4019) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4019 : oddCount 4019 12 = 4 ∧ acceleratedOrbit 12 4019 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4019 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4019) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4019.1, data_12_4019.2] + +/-- Complete interval computation for depth 12, residue 4020. -/ +theorem bounds_12_4020 : exactInterval 12 4020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4020 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4020) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4020 : oddCount 4020 12 = 6 ∧ acceleratedOrbit 12 4020 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4020 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4020) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4020.1, data_12_4020.2] + +/-- Complete interval computation for depth 12, residue 4021. -/ +theorem bounds_12_4021 : exactInterval 12 4021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4021 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4021) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4021 : oddCount 4021 12 = 6 ∧ acceleratedOrbit 12 4021 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4021 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4021) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4021.1, data_12_4021.2] + +/-- Complete interval computation for depth 12, residue 4022. -/ +theorem bounds_12_4022 : exactInterval 12 4022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4022 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4022) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4022 : oddCount 4022 12 = 7 ∧ acceleratedOrbit 12 4022 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4022 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4022) = 3 ^ 7 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4022.1, data_12_4022.2] + +/-- Complete interval computation for depth 12, residue 4023. -/ +theorem bounds_12_4023 : exactInterval 12 4023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4023 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4023) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4023 : oddCount 4023 12 = 7 ∧ acceleratedOrbit 12 4023 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4023 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4023) = 3 ^ 7 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4023.1, data_12_4023.2] + +end Collatz.Research.StoppingAtlas.Batch0462 From 79d177cabed92ea1ae76ecdbe560b2f5f3b896ac Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:28 +0530 Subject: [PATCH 0463/1001] proof: certify atlas Batch0463 (12:4024 to 12:4038) --- Collatz/Research/StoppingAtlas/Batch0463.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0463.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0463.lean b/Collatz/Research/StoppingAtlas/Batch0463.lean new file mode 100644 index 00000000..2c73142c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0463.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0463 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 4024. -/ +theorem bounds_12_4024 : exactInterval 12 4024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4024 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4024) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4024 : oddCount 4024 12 = 6 ∧ acceleratedOrbit 12 4024 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4024 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4024) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4024.1, data_12_4024.2] + +/-- Complete interval computation for depth 12, residue 4025. -/ +theorem bounds_12_4025 : exactInterval 12 4025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4025 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4025) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4025 : oddCount 4025 12 = 5 ∧ acceleratedOrbit 12 4025 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4025 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4025) = 3 ^ 5 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4025.1, data_12_4025.2] + +/-- Complete interval computation for depth 12, residue 4026. -/ +theorem bounds_12_4026 : exactInterval 12 4026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4026 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4026) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4026 : oddCount 4026 12 = 6 ∧ acceleratedOrbit 12 4026 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4026 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4026) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4026.1, data_12_4026.2] + +/-- Complete interval computation for depth 12, residue 4027. -/ +theorem bounds_12_4027 : exactInterval 12 4027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4027 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4027) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4027 : oddCount 4027 12 = 5 ∧ acceleratedOrbit 12 4027 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4027 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4027) = 3 ^ 5 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4027.1, data_12_4027.2] + +/-- Complete interval computation for depth 12, residue 4028. -/ +theorem bounds_12_4028 : exactInterval 12 4028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4028 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4028) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4028 : oddCount 4028 12 = 7 ∧ acceleratedOrbit 12 4028 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4028 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4028) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4028.1, data_12_4028.2] + +/-- Complete interval computation for depth 12, residue 4029. -/ +theorem bounds_12_4029 : exactInterval 12 4029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4029 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4029) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4029 : oddCount 4029 12 = 7 ∧ acceleratedOrbit 12 4029 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4029 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4029) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4029.1, data_12_4029.2] + +/-- Complete interval computation for depth 12, residue 4030. -/ +theorem bounds_12_4030 : exactInterval 12 4030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4030 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4030) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4030 : oddCount 4030 12 = 7 ∧ acceleratedOrbit 12 4030 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4030 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4030) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4030.1, data_12_4030.2] + +/-- Complete interval computation for depth 12, residue 4031. -/ +theorem bounds_12_4031 : exactInterval 12 4031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4031 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4031) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4031 : oddCount 4031 12 = 9 ∧ acceleratedOrbit 12 4031 = 19376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4031 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4031) = 3 ^ 9 * m + 19376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4031.1, data_12_4031.2] + +/-- Complete interval computation for depth 12, residue 4032. -/ +theorem bounds_12_4032 : exactInterval 12 4032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4032 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4032) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4032 : oddCount 4032 12 = 6 ∧ acceleratedOrbit 12 4032 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4032 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4032) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4032.1, data_12_4032.2] + +/-- Complete interval computation for depth 12, residue 4033. -/ +theorem bounds_12_4033 : exactInterval 12 4033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4033 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4033) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4033 : oddCount 4033 12 = 6 ∧ acceleratedOrbit 12 4033 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4033 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4033) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4033.1, data_12_4033.2] + +/-- Complete interval computation for depth 12, residue 4034. -/ +theorem bounds_12_4034 : exactInterval 12 4034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4034 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4034) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4034 : oddCount 4034 12 = 8 ∧ acceleratedOrbit 12 4034 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4034 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4034) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4034.1, data_12_4034.2] + +/-- Complete interval computation for depth 12, residue 4035. -/ +theorem bounds_12_4035 : exactInterval 12 4035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4035 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4035) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4035 : oddCount 4035 12 = 8 ∧ acceleratedOrbit 12 4035 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4035 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4035) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4035.1, data_12_4035.2] + +/-- Complete interval computation for depth 12, residue 4036. -/ +theorem bounds_12_4036 : exactInterval 12 4036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4036 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4036) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4036 : oddCount 4036 12 = 5 ∧ acceleratedOrbit 12 4036 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4036 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4036) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4036.1, data_12_4036.2] + +/-- Complete interval computation for depth 12, residue 4037. -/ +theorem bounds_12_4037 : exactInterval 12 4037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4037 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4037) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4037 : oddCount 4037 12 = 5 ∧ acceleratedOrbit 12 4037 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4037 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4037) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4037.1, data_12_4037.2] + +/-- Complete interval computation for depth 12, residue 4038. -/ +theorem bounds_12_4038 : exactInterval 12 4038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4038 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4038) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4038 : oddCount 4038 12 = 5 ∧ acceleratedOrbit 12 4038 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4038 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4038) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4038.1, data_12_4038.2] + +end Collatz.Research.StoppingAtlas.Batch0463 From 36414e369177dbffb5b11994792904cd6d993203 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:28 +0530 Subject: [PATCH 0464/1001] proof: certify atlas Batch0464 (12:4039 to 12:4054) --- Collatz/Research/StoppingAtlas/Batch0464.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0464.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0464.lean b/Collatz/Research/StoppingAtlas/Batch0464.lean new file mode 100644 index 00000000..204ba30b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0464.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0464 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 4039. -/ +theorem bounds_12_4039 : exactInterval 12 4039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4039 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4039) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4039 : oddCount 4039 12 = 8 ∧ acceleratedOrbit 12 4039 = 6473 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4039 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4039) = 3 ^ 8 * m + 6473 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4039.1, data_12_4039.2] + +/-- Complete interval computation for depth 12, residue 4040. -/ +theorem bounds_12_4040 : exactInterval 12 4040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4040 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4040) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4040 : oddCount 4040 12 = 6 ∧ acceleratedOrbit 12 4040 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4040 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4040) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4040.1, data_12_4040.2] + +/-- Complete interval computation for depth 12, residue 4041. -/ +theorem bounds_12_4041 : exactInterval 12 4041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4041 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4041) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4041 : oddCount 4041 12 = 8 ∧ acceleratedOrbit 12 4041 = 6479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4041 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4041) = 3 ^ 8 * m + 6479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4041.1, data_12_4041.2] + +/-- Complete interval computation for depth 12, residue 4042. -/ +theorem bounds_12_4042 : exactInterval 12 4042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4042 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4042) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4042 : oddCount 4042 12 = 6 ∧ acceleratedOrbit 12 4042 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4042 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4042) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4042.1, data_12_4042.2] + +/-- Complete interval computation for depth 12, residue 4043. -/ +theorem bounds_12_4043 : exactInterval 12 4043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4043 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4043) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4043 : oddCount 4043 12 = 4 ∧ acceleratedOrbit 12 4043 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4043 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4043) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4043.1, data_12_4043.2] + +/-- Complete interval computation for depth 12, residue 4044. -/ +theorem bounds_12_4044 : exactInterval 12 4044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4044 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4044) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4044 : oddCount 4044 12 = 6 ∧ acceleratedOrbit 12 4044 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4044 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4044) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4044.1, data_12_4044.2] + +/-- Complete interval computation for depth 12, residue 4045. -/ +theorem bounds_12_4045 : exactInterval 12 4045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4045 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4045) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4045 : oddCount 4045 12 = 6 ∧ acceleratedOrbit 12 4045 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4045 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4045) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4045.1, data_12_4045.2] + +/-- Complete interval computation for depth 12, residue 4046. -/ +theorem bounds_12_4046 : exactInterval 12 4046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4046 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4046) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4046 : oddCount 4046 12 = 7 ∧ acceleratedOrbit 12 4046 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4046 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4046) = 3 ^ 7 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4046.1, data_12_4046.2] + +/-- Complete interval computation for depth 12, residue 4047. -/ +theorem bounds_12_4047 : exactInterval 12 4047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4047 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4047) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4047 : oddCount 4047 12 = 7 ∧ acceleratedOrbit 12 4047 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4047 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4047) = 3 ^ 7 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4047.1, data_12_4047.2] + +/-- Complete interval computation for depth 12, residue 4048. -/ +theorem bounds_12_4048 : exactInterval 12 4048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4048 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4048) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4048 : oddCount 4048 12 = 6 ∧ acceleratedOrbit 12 4048 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4048 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4048) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4048.1, data_12_4048.2] + +/-- Complete interval computation for depth 12, residue 4049. -/ +theorem bounds_12_4049 : exactInterval 12 4049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4049 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4049) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4049 : oddCount 4049 12 = 6 ∧ acceleratedOrbit 12 4049 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4049 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4049) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4049.1, data_12_4049.2] + +/-- Complete interval computation for depth 12, residue 4050. -/ +theorem bounds_12_4050 : exactInterval 12 4050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4050 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4050) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4050 : oddCount 4050 12 = 8 ∧ acceleratedOrbit 12 4050 = 6493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4050 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4050) = 3 ^ 8 * m + 6493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4050.1, data_12_4050.2] + +/-- Complete interval computation for depth 12, residue 4051. -/ +theorem bounds_12_4051 : exactInterval 12 4051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4051 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4051) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4051 : oddCount 4051 12 = 8 ∧ acceleratedOrbit 12 4051 = 6493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4051 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4051) = 3 ^ 8 * m + 6493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4051.1, data_12_4051.2] + +/-- Complete interval computation for depth 12, residue 4052. -/ +theorem bounds_12_4052 : exactInterval 12 4052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4052 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4052) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4052 : oddCount 4052 12 = 6 ∧ acceleratedOrbit 12 4052 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4052 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4052) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4052.1, data_12_4052.2] + +/-- Complete interval computation for depth 12, residue 4053. -/ +theorem bounds_12_4053 : exactInterval 12 4053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4053 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4053) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4053 : oddCount 4053 12 = 6 ∧ acceleratedOrbit 12 4053 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4053 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4053) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4053.1, data_12_4053.2] + +/-- Complete interval computation for depth 12, residue 4054. -/ +theorem bounds_12_4054 : exactInterval 12 4054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4054 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4054) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4054 : oddCount 4054 12 = 8 ∧ acceleratedOrbit 12 4054 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4054 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4054) = 3 ^ 8 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4054.1, data_12_4054.2] + +end Collatz.Research.StoppingAtlas.Batch0464 From 71e02f8fac773e08747a0ca25c778dfa4ac44d8e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:29 +0530 Subject: [PATCH 0465/1001] proof: certify atlas Batch0465 (12:4055 to 12:4069) --- Collatz/Research/StoppingAtlas/Batch0465.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0465.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0465.lean b/Collatz/Research/StoppingAtlas/Batch0465.lean new file mode 100644 index 00000000..2004d1ca --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0465.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0465 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 4055. -/ +theorem bounds_12_4055 : exactInterval 12 4055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4055 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4055) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4055 : oddCount 4055 12 = 8 ∧ acceleratedOrbit 12 4055 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4055 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4055) = 3 ^ 8 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4055.1, data_12_4055.2] + +/-- Complete interval computation for depth 12, residue 4056. -/ +theorem bounds_12_4056 : exactInterval 12 4056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4056 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4056) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4056 : oddCount 4056 12 = 6 ∧ acceleratedOrbit 12 4056 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4056 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4056) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4056.1, data_12_4056.2] + +/-- Complete interval computation for depth 12, residue 4057. -/ +theorem bounds_12_4057 : exactInterval 12 4057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4057 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4057) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4057 : oddCount 4057 12 = 5 ∧ acceleratedOrbit 12 4057 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4057 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4057) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4057.1, data_12_4057.2] + +/-- Complete interval computation for depth 12, residue 4058. -/ +theorem bounds_12_4058 : exactInterval 12 4058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4058 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4058) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4058 : oddCount 4058 12 = 6 ∧ acceleratedOrbit 12 4058 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4058 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4058) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4058.1, data_12_4058.2] + +/-- Complete interval computation for depth 12, residue 4059. -/ +theorem bounds_12_4059 : exactInterval 12 4059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4059 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4059) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4059 : oddCount 4059 12 = 8 ∧ acceleratedOrbit 12 4059 = 6506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4059 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4059) = 3 ^ 8 * m + 6506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4059.1, data_12_4059.2] + +/-- Complete interval computation for depth 12, residue 4060. -/ +theorem bounds_12_4060 : exactInterval 12 4060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4060 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4060) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4060 : oddCount 4060 12 = 6 ∧ acceleratedOrbit 12 4060 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4060 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4060) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4060.1, data_12_4060.2] + +/-- Complete interval computation for depth 12, residue 4061. -/ +theorem bounds_12_4061 : exactInterval 12 4061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4061 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4061) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4061 : oddCount 4061 12 = 6 ∧ acceleratedOrbit 12 4061 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4061 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4061) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4061.1, data_12_4061.2] + +/-- Complete interval computation for depth 12, residue 4062. -/ +theorem bounds_12_4062 : exactInterval 12 4062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4062 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4062) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4062 : oddCount 4062 12 = 7 ∧ acceleratedOrbit 12 4062 = 2170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4062 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4062) = 3 ^ 7 * m + 2170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4062.1, data_12_4062.2] + +/-- Complete interval computation for depth 12, residue 4063. -/ +theorem bounds_12_4063 : exactInterval 12 4063 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4063 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4063) 12 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4063 : oddCount 4063 12 = 7 ∧ acceleratedOrbit 12 4063 = 2170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4063 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4063) = 3 ^ 7 * m + 2170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4063.1, data_12_4063.2] + +/-- Complete interval computation for depth 12, residue 4064. -/ +theorem bounds_12_4064 : exactInterval 12 4064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4064 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4064) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4064 : oddCount 4064 12 = 7 ∧ acceleratedOrbit 12 4064 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4064 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4064) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4064.1, data_12_4064.2] + +/-- Complete interval computation for depth 12, residue 4065. -/ +theorem bounds_12_4065 : exactInterval 12 4065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4065 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4065) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4065 : oddCount 4065 12 = 9 ∧ acceleratedOrbit 12 4065 = 19547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4065 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4065) = 3 ^ 9 * m + 19547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4065.1, data_12_4065.2] + +/-- Complete interval computation for depth 12, residue 4066. -/ +theorem bounds_12_4066 : exactInterval 12 4066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4066 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4066) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4066 : oddCount 4066 12 = 6 ∧ acceleratedOrbit 12 4066 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4066 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4066) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4066.1, data_12_4066.2] + +/-- Complete interval computation for depth 12, residue 4067. -/ +theorem bounds_12_4067 : exactInterval 12 4067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4067 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4067) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4067 : oddCount 4067 12 = 6 ∧ acceleratedOrbit 12 4067 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4067 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4067) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4067.1, data_12_4067.2] + +/-- Complete interval computation for depth 12, residue 4068. -/ +theorem bounds_12_4068 : exactInterval 12 4068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4068 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4068) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4068 : oddCount 4068 12 = 7 ∧ acceleratedOrbit 12 4068 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4068 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4068) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4068.1, data_12_4068.2] + +/-- Complete interval computation for depth 12, residue 4069. -/ +theorem bounds_12_4069 : exactInterval 12 4069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4069 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4069) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4069 : oddCount 4069 12 = 7 ∧ acceleratedOrbit 12 4069 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4069 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4069) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4069.1, data_12_4069.2] + +end Collatz.Research.StoppingAtlas.Batch0465 From 872970702bc0808740766d86a4911216ac919553 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:29 +0530 Subject: [PATCH 0466/1001] proof: certify atlas Batch0466 (12:4070 to 12:4084) --- Collatz/Research/StoppingAtlas/Batch0466.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0466.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0466.lean b/Collatz/Research/StoppingAtlas/Batch0466.lean new file mode 100644 index 00000000..d918cf09 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0466.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0466 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 4070. -/ +theorem bounds_12_4070 : exactInterval 12 4070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4070 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4070) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4070 : oddCount 4070 12 = 7 ∧ acceleratedOrbit 12 4070 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4070 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4070) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4070.1, data_12_4070.2] + +/-- Complete interval computation for depth 12, residue 4071. -/ +theorem bounds_12_4071 : exactInterval 12 4071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4071 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4071) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4071 : oddCount 4071 12 = 8 ∧ acceleratedOrbit 12 4071 = 6524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4071 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4071) = 3 ^ 8 * m + 6524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4071.1, data_12_4071.2] + +/-- Complete interval computation for depth 12, residue 4072. -/ +theorem bounds_12_4072 : exactInterval 12 4072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4072 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4072) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4072 : oddCount 4072 12 = 7 ∧ acceleratedOrbit 12 4072 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4072 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4072) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4072.1, data_12_4072.2] + +/-- Complete interval computation for depth 12, residue 4073. -/ +theorem bounds_12_4073 : exactInterval 12 4073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4073 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4073) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4073 : oddCount 4073 12 = 8 ∧ acceleratedOrbit 12 4073 = 6527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4073 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4073) = 3 ^ 8 * m + 6527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4073.1, data_12_4073.2] + +/-- Complete interval computation for depth 12, residue 4074. -/ +theorem bounds_12_4074 : exactInterval 12 4074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4074 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4074) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4074 : oddCount 4074 12 = 7 ∧ acceleratedOrbit 12 4074 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4074 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4074) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4074.1, data_12_4074.2] + +/-- Complete interval computation for depth 12, residue 4075. -/ +theorem bounds_12_4075 : exactInterval 12 4075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4075 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4075) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4075 : oddCount 4075 12 = 9 ∧ acceleratedOrbit 12 4075 = 19592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4075 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4075) = 3 ^ 9 * m + 19592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4075.1, data_12_4075.2] + +/-- Complete interval computation for depth 12, residue 4076. -/ +theorem bounds_12_4076 : exactInterval 12 4076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4076 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4076) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4076 : oddCount 4076 12 = 7 ∧ acceleratedOrbit 12 4076 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4076 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4076) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4076.1, data_12_4076.2] + +/-- Complete interval computation for depth 12, residue 4077. -/ +theorem bounds_12_4077 : exactInterval 12 4077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4077 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4077) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4077 : oddCount 4077 12 = 7 ∧ acceleratedOrbit 12 4077 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4077 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4077) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4077.1, data_12_4077.2] + +/-- Complete interval computation for depth 12, residue 4078. -/ +theorem bounds_12_4078 : exactInterval 12 4078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4078 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4078) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4078 : oddCount 4078 12 = 7 ∧ acceleratedOrbit 12 4078 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4078 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4078) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4078.1, data_12_4078.2] + +/-- Complete interval computation for depth 12, residue 4079. -/ +theorem bounds_12_4079 : exactInterval 12 4079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4079 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4079) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4079 : oddCount 4079 12 = 8 ∧ acceleratedOrbit 12 4079 = 6536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4079 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4079) = 3 ^ 8 * m + 6536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4079.1, data_12_4079.2] + +/-- Complete interval computation for depth 12, residue 4080. -/ +theorem bounds_12_4080 : exactInterval 12 4080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4080 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4080) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4080 : oddCount 4080 12 = 8 ∧ acceleratedOrbit 12 4080 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4080 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4080) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4080.1, data_12_4080.2] + +/-- Complete interval computation for depth 12, residue 4081. -/ +theorem bounds_12_4081 : exactInterval 12 4081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4081 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4081) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4081 : oddCount 4081 12 = 7 ∧ acceleratedOrbit 12 4081 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4081 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4081) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4081.1, data_12_4081.2] + +/-- Complete interval computation for depth 12, residue 4082. -/ +theorem bounds_12_4082 : exactInterval 12 4082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4082 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4082) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4082 : oddCount 4082 12 = 7 ∧ acceleratedOrbit 12 4082 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4082 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4082) = 3 ^ 7 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4082.1, data_12_4082.2] + +/-- Complete interval computation for depth 12, residue 4083. -/ +theorem bounds_12_4083 : exactInterval 12 4083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4083 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4083) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4083 : oddCount 4083 12 = 7 ∧ acceleratedOrbit 12 4083 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4083 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4083) = 3 ^ 7 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4083.1, data_12_4083.2] + +/-- Complete interval computation for depth 12, residue 4084. -/ +theorem bounds_12_4084 : exactInterval 12 4084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4084 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4084) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4084 : oddCount 4084 12 = 8 ∧ acceleratedOrbit 12 4084 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4084 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4084) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4084.1, data_12_4084.2] + +end Collatz.Research.StoppingAtlas.Batch0466 From c0ed49dd3f54bcadd3b03c1bef06ff3f9f81a53f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:29 +0530 Subject: [PATCH 0467/1001] proof: certify atlas Batch0467 (12:4085 to 13:4) --- Collatz/Research/StoppingAtlas/Batch0467.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0467.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0467.lean b/Collatz/Research/StoppingAtlas/Batch0467.lean new file mode 100644 index 00000000..57083657 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0467.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0467 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 12, residue 4085. -/ +theorem bounds_12_4085 : exactInterval 12 4085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4085 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4085) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4085 : oddCount 4085 12 = 8 ∧ acceleratedOrbit 12 4085 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4085 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4085) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4085.1, data_12_4085.2] + +/-- Complete interval computation for depth 12, residue 4086. -/ +theorem bounds_12_4086 : exactInterval 12 4086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4086 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4086) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4086 : oddCount 4086 12 = 8 ∧ acceleratedOrbit 12 4086 = 6551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4086 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4086) = 3 ^ 8 * m + 6551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4086.1, data_12_4086.2] + +/-- Complete interval computation for depth 12, residue 4087. -/ +theorem bounds_12_4087 : exactInterval 12 4087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4087 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4087) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4087 : oddCount 4087 12 = 8 ∧ acceleratedOrbit 12 4087 = 6551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4087 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4087) = 3 ^ 8 * m + 6551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4087.1, data_12_4087.2] + +/-- Complete interval computation for depth 12, residue 4088. -/ +theorem bounds_12_4088 : exactInterval 12 4088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4088 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4088) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4088 : oddCount 4088 12 = 9 ∧ acceleratedOrbit 12 4088 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4088 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4088) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4088.1, data_12_4088.2] + +/-- Complete interval computation for depth 12, residue 4089. -/ +theorem bounds_12_4089 : exactInterval 12 4089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4089 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4089) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4089 : oddCount 4089 12 = 8 ∧ acceleratedOrbit 12 4089 = 6554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4089 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4089) = 3 ^ 8 * m + 6554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4089.1, data_12_4089.2] + +/-- Complete interval computation for depth 12, residue 4090. -/ +theorem bounds_12_4090 : exactInterval 12 4090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4090 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4090) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4090 : oddCount 4090 12 = 9 ∧ acceleratedOrbit 12 4090 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4090 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4090) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4090.1, data_12_4090.2] + +/-- Complete interval computation for depth 12, residue 4091. -/ +theorem bounds_12_4091 : exactInterval 12 4091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4091 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4091) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4091 : oddCount 4091 12 = 8 ∧ acceleratedOrbit 12 4091 = 6556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4091 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4091) = 3 ^ 8 * m + 6556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4091.1, data_12_4091.2] + +/-- Complete interval computation for depth 12, residue 4092. -/ +theorem bounds_12_4092 : exactInterval 12 4092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4092 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4092) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4092 : oddCount 4092 12 = 10 ∧ acceleratedOrbit 12 4092 = 59048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4092 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4092) = 3 ^ 10 * m + 59048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4092.1, data_12_4092.2] + +/-- Complete interval computation for depth 12, residue 4093. -/ +theorem bounds_12_4093 : exactInterval 12 4093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4093 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4093) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4093 : oddCount 4093 12 = 10 ∧ acceleratedOrbit 12 4093 = 59048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4093 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4093) = 3 ^ 10 * m + 59048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4093.1, data_12_4093.2] + +/-- Complete interval computation for depth 12, residue 4094. -/ +theorem bounds_12_4094 : exactInterval 12 4094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4094 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4094) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4094 : oddCount 4094 12 = 11 ∧ acceleratedOrbit 12 4094 = 177146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4094 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4094) = 3 ^ 11 * m + 177146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4094.1, data_12_4094.2] + +/-- Complete interval computation for depth 12, residue 4095. -/ +theorem bounds_12_4095 : exactInterval 12 4095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_12_4095 (m : Nat) : + stoppingTime (2 ^ 12 * m + 4095) 12 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_12_4095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_12_4095 : oddCount 4095 12 = 12 ∧ acceleratedOrbit 12 4095 = 531440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_12_4095 (m : Nat) : + acceleratedOrbit 12 (2 ^ 12 * m + 4095) = 3 ^ 12 * m + 531440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_12_4095.1, data_12_4095.2] + +/-- Complete interval computation for depth 13, residue 0. -/ +theorem bounds_13_0 : exactInterval 13 0 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_0 (m : Nat) : + stoppingTime (2 ^ 13 * m + 0) 13 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_0 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_0 : oddCount 0 13 = 0 ∧ acceleratedOrbit 13 0 = 0 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_0 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 0) = 3 ^ 0 * m + 0 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_0.1, data_13_0.2] + +/-- Complete interval computation for depth 13, residue 1. -/ +theorem bounds_13_1 : exactInterval 13 1 = ⟨1, some 1⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1) 13 ↔ 1 ≤ m ∧ m < 1 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1 : oddCount 1 13 = 7 ∧ acceleratedOrbit 13 1 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1) = 3 ^ 7 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1.1, data_13_1.2] + +/-- Complete interval computation for depth 13, residue 2. -/ +theorem bounds_13_2 : exactInterval 13 2 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2 : oddCount 2 13 = 6 ∧ acceleratedOrbit 13 2 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2) = 3 ^ 6 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2.1, data_13_2.2] + +/-- Complete interval computation for depth 13, residue 3. -/ +theorem bounds_13_3 : exactInterval 13 3 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3 : oddCount 3 13 = 6 ∧ acceleratedOrbit 13 3 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3) = 3 ^ 6 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3.1, data_13_3.2] + +/-- Complete interval computation for depth 13, residue 4. -/ +theorem bounds_13_4 : exactInterval 13 4 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4 : oddCount 4 13 = 6 ∧ acceleratedOrbit 13 4 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4.1, data_13_4.2] + +end Collatz.Research.StoppingAtlas.Batch0467 From 71d514e0b84410c923b8aa29f03ad979e77986c4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:29 +0530 Subject: [PATCH 0468/1001] proof: certify atlas Batch0468 (13:5 to 13:19) --- Collatz/Research/StoppingAtlas/Batch0468.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0468.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0468.lean b/Collatz/Research/StoppingAtlas/Batch0468.lean new file mode 100644 index 00000000..72732c69 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0468.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0468 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5. -/ +theorem bounds_13_5 : exactInterval 13 5 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5 : oddCount 5 13 = 6 ∧ acceleratedOrbit 13 5 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5.1, data_13_5.2] + +/-- Complete interval computation for depth 13, residue 6. -/ +theorem bounds_13_6 : exactInterval 13 6 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6 : oddCount 6 13 = 6 ∧ acceleratedOrbit 13 6 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6.1, data_13_6.2] + +/-- Complete interval computation for depth 13, residue 7. -/ +theorem bounds_13_7 : exactInterval 13 7 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7 : oddCount 7 13 = 6 ∧ acceleratedOrbit 13 7 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7) = 3 ^ 6 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7.1, data_13_7.2] + +/-- Complete interval computation for depth 13, residue 8. -/ +theorem bounds_13_8 : exactInterval 13 8 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8 : oddCount 8 13 = 5 ∧ acceleratedOrbit 13 8 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8.1, data_13_8.2] + +/-- Complete interval computation for depth 13, residue 9. -/ +theorem bounds_13_9 : exactInterval 13 9 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_9 (m : Nat) : + stoppingTime (2 ^ 13 * m + 9) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_9 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_9 : oddCount 9 13 = 6 ∧ acceleratedOrbit 13 9 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_9 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 9) = 3 ^ 6 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_9.1, data_13_9.2] + +/-- Complete interval computation for depth 13, residue 10. -/ +theorem bounds_13_10 : exactInterval 13 10 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_10 (m : Nat) : + stoppingTime (2 ^ 13 * m + 10) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_10 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_10 : oddCount 10 13 = 5 ∧ acceleratedOrbit 13 10 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_10 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 10) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_10.1, data_13_10.2] + +/-- Complete interval computation for depth 13, residue 11. -/ +theorem bounds_13_11 : exactInterval 13 11 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_11 (m : Nat) : + stoppingTime (2 ^ 13 * m + 11) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_11 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_11 : oddCount 11 13 = 6 ∧ acceleratedOrbit 13 11 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_11 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 11) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_11.1, data_13_11.2] + +/-- Complete interval computation for depth 13, residue 12. -/ +theorem bounds_13_12 : exactInterval 13 12 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_12 (m : Nat) : + stoppingTime (2 ^ 13 * m + 12) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_12 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_12 : oddCount 12 13 = 5 ∧ acceleratedOrbit 13 12 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_12 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 12) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_12.1, data_13_12.2] + +/-- Complete interval computation for depth 13, residue 13. -/ +theorem bounds_13_13 : exactInterval 13 13 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_13 (m : Nat) : + stoppingTime (2 ^ 13 * m + 13) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_13 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_13 : oddCount 13 13 = 5 ∧ acceleratedOrbit 13 13 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_13 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 13) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_13.1, data_13_13.2] + +/-- Complete interval computation for depth 13, residue 14. -/ +theorem bounds_13_14 : exactInterval 13 14 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_14 (m : Nat) : + stoppingTime (2 ^ 13 * m + 14) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_14 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_14 : oddCount 14 13 = 6 ∧ acceleratedOrbit 13 14 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_14 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 14) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_14.1, data_13_14.2] + +/-- Complete interval computation for depth 13, residue 15. -/ +theorem bounds_13_15 : exactInterval 13 15 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_15 (m : Nat) : + stoppingTime (2 ^ 13 * m + 15) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_15 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_15 : oddCount 15 13 = 6 ∧ acceleratedOrbit 13 15 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_15 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 15) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_15.1, data_13_15.2] + +/-- Complete interval computation for depth 13, residue 16. -/ +theorem bounds_13_16 : exactInterval 13 16 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_16 (m : Nat) : + stoppingTime (2 ^ 13 * m + 16) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_16 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_16 : oddCount 16 13 = 5 ∧ acceleratedOrbit 13 16 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_16 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 16) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_16.1, data_13_16.2] + +/-- Complete interval computation for depth 13, residue 17. -/ +theorem bounds_13_17 : exactInterval 13 17 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_17 (m : Nat) : + stoppingTime (2 ^ 13 * m + 17) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_17 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_17 : oddCount 17 13 = 5 ∧ acceleratedOrbit 13 17 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_17 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 17) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_17.1, data_13_17.2] + +/-- Complete interval computation for depth 13, residue 18. -/ +theorem bounds_13_18 : exactInterval 13 18 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_18 (m : Nat) : + stoppingTime (2 ^ 13 * m + 18) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_18 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_18 : oddCount 18 13 = 6 ∧ acceleratedOrbit 13 18 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_18 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 18) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_18.1, data_13_18.2] + +/-- Complete interval computation for depth 13, residue 19. -/ +theorem bounds_13_19 : exactInterval 13 19 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_19 (m : Nat) : + stoppingTime (2 ^ 13 * m + 19) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_19 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_19 : oddCount 19 13 = 6 ∧ acceleratedOrbit 13 19 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_19 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 19) = 3 ^ 6 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_19.1, data_13_19.2] + +end Collatz.Research.StoppingAtlas.Batch0468 From 3f47cf157ecd3e7660be56b228ef10288cccbb40 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:30 +0530 Subject: [PATCH 0469/1001] proof: certify atlas Batch0469 (13:20 to 13:34) --- Collatz/Research/StoppingAtlas/Batch0469.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0469.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0469.lean b/Collatz/Research/StoppingAtlas/Batch0469.lean new file mode 100644 index 00000000..42d139a9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0469.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0469 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 20. -/ +theorem bounds_13_20 : exactInterval 13 20 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_20 (m : Nat) : + stoppingTime (2 ^ 13 * m + 20) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_20 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_20 : oddCount 20 13 = 5 ∧ acceleratedOrbit 13 20 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_20 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 20) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_20.1, data_13_20.2] + +/-- Complete interval computation for depth 13, residue 21. -/ +theorem bounds_13_21 : exactInterval 13 21 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_21 (m : Nat) : + stoppingTime (2 ^ 13 * m + 21) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_21 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_21 : oddCount 21 13 = 5 ∧ acceleratedOrbit 13 21 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_21 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 21) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_21.1, data_13_21.2] + +/-- Complete interval computation for depth 13, residue 22. -/ +theorem bounds_13_22 : exactInterval 13 22 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_22 (m : Nat) : + stoppingTime (2 ^ 13 * m + 22) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_22 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_22 : oddCount 22 13 = 5 ∧ acceleratedOrbit 13 22 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_22 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 22) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_22.1, data_13_22.2] + +/-- Complete interval computation for depth 13, residue 23. -/ +theorem bounds_13_23 : exactInterval 13 23 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_23 (m : Nat) : + stoppingTime (2 ^ 13 * m + 23) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_23 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_23 : oddCount 23 13 = 5 ∧ acceleratedOrbit 13 23 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_23 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 23) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_23.1, data_13_23.2] + +/-- Complete interval computation for depth 13, residue 24. -/ +theorem bounds_13_24 : exactInterval 13 24 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_24 (m : Nat) : + stoppingTime (2 ^ 13 * m + 24) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_24 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_24 : oddCount 24 13 = 5 ∧ acceleratedOrbit 13 24 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_24 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 24) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_24.1, data_13_24.2] + +/-- Complete interval computation for depth 13, residue 25. -/ +theorem bounds_13_25 : exactInterval 13 25 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_25 (m : Nat) : + stoppingTime (2 ^ 13 * m + 25) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_25 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_25 : oddCount 25 13 = 7 ∧ acceleratedOrbit 13 25 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_25 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 25) = 3 ^ 7 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_25.1, data_13_25.2] + +/-- Complete interval computation for depth 13, residue 26. -/ +theorem bounds_13_26 : exactInterval 13 26 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_26 (m : Nat) : + stoppingTime (2 ^ 13 * m + 26) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_26 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_26 : oddCount 26 13 = 5 ∧ acceleratedOrbit 13 26 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_26 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 26) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_26.1, data_13_26.2] + +/-- Complete interval computation for depth 13, residue 27. -/ +theorem bounds_13_27 : exactInterval 13 27 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_27 (m : Nat) : + stoppingTime (2 ^ 13 * m + 27) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_27 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_27 : oddCount 27 13 = 10 ∧ acceleratedOrbit 13 27 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_27 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 27) = 3 ^ 10 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_27.1, data_13_27.2] + +/-- Complete interval computation for depth 13, residue 28. -/ +theorem bounds_13_28 : exactInterval 13 28 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_28 (m : Nat) : + stoppingTime (2 ^ 13 * m + 28) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_28 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_28 : oddCount 28 13 = 5 ∧ acceleratedOrbit 13 28 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_28 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 28) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_28.1, data_13_28.2] + +/-- Complete interval computation for depth 13, residue 29. -/ +theorem bounds_13_29 : exactInterval 13 29 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_29 (m : Nat) : + stoppingTime (2 ^ 13 * m + 29) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_29 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_29 : oddCount 29 13 = 5 ∧ acceleratedOrbit 13 29 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_29 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 29) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_29.1, data_13_29.2] + +/-- Complete interval computation for depth 13, residue 30. -/ +theorem bounds_13_30 : exactInterval 13 30 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_30 (m : Nat) : + stoppingTime (2 ^ 13 * m + 30) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_30 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_30 : oddCount 30 13 = 5 ∧ acceleratedOrbit 13 30 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_30 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 30) = 3 ^ 5 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_30.1, data_13_30.2] + +/-- Complete interval computation for depth 13, residue 31. -/ +theorem bounds_13_31 : exactInterval 13 31 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_31 (m : Nat) : + stoppingTime (2 ^ 13 * m + 31) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_31 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_31 : oddCount 31 13 = 10 ∧ acceleratedOrbit 13 31 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_31 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 31) = 3 ^ 10 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_31.1, data_13_31.2] + +/-- Complete interval computation for depth 13, residue 32. -/ +theorem bounds_13_32 : exactInterval 13 32 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_32 (m : Nat) : + stoppingTime (2 ^ 13 * m + 32) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_32 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_32 : oddCount 32 13 = 4 ∧ acceleratedOrbit 13 32 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_32 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 32) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_32.1, data_13_32.2] + +/-- Complete interval computation for depth 13, residue 33. -/ +theorem bounds_13_33 : exactInterval 13 33 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_33 (m : Nat) : + stoppingTime (2 ^ 13 * m + 33) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_33 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_33 : oddCount 33 13 = 7 ∧ acceleratedOrbit 13 33 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_33 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 33) = 3 ^ 7 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_33.1, data_13_33.2] + +/-- Complete interval computation for depth 13, residue 34. -/ +theorem bounds_13_34 : exactInterval 13 34 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_34 (m : Nat) : + stoppingTime (2 ^ 13 * m + 34) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_34 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_34 : oddCount 34 13 = 5 ∧ acceleratedOrbit 13 34 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_34 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 34) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_34.1, data_13_34.2] + +end Collatz.Research.StoppingAtlas.Batch0469 From d52c9176d1436d451fa85ddcfb2165332effdc7f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:30 +0530 Subject: [PATCH 0470/1001] proof: certify atlas Batch0470 (13:35 to 13:50) --- Collatz/Research/StoppingAtlas/Batch0470.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0470.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0470.lean b/Collatz/Research/StoppingAtlas/Batch0470.lean new file mode 100644 index 00000000..350d256a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0470.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0470 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 35. -/ +theorem bounds_13_35 : exactInterval 13 35 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_35 (m : Nat) : + stoppingTime (2 ^ 13 * m + 35) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_35 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_35 : oddCount 35 13 = 5 ∧ acceleratedOrbit 13 35 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_35 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 35) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_35.1, data_13_35.2] + +/-- Complete interval computation for depth 13, residue 36. -/ +theorem bounds_13_36 : exactInterval 13 36 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_36 (m : Nat) : + stoppingTime (2 ^ 13 * m + 36) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_36 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_36 : oddCount 36 13 = 6 ∧ acceleratedOrbit 13 36 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_36 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 36) = 3 ^ 6 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_36.1, data_13_36.2] + +/-- Complete interval computation for depth 13, residue 37. -/ +theorem bounds_13_37 : exactInterval 13 37 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_37 (m : Nat) : + stoppingTime (2 ^ 13 * m + 37) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_37 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_37 : oddCount 37 13 = 6 ∧ acceleratedOrbit 13 37 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_37 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 37) = 3 ^ 6 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_37.1, data_13_37.2] + +/-- Complete interval computation for depth 13, residue 38. -/ +theorem bounds_13_38 : exactInterval 13 38 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_38 (m : Nat) : + stoppingTime (2 ^ 13 * m + 38) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_38 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_38 : oddCount 38 13 = 6 ∧ acceleratedOrbit 13 38 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_38 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 38) = 3 ^ 6 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_38.1, data_13_38.2] + +/-- Complete interval computation for depth 13, residue 39. -/ +theorem bounds_13_39 : exactInterval 13 39 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_39 (m : Nat) : + stoppingTime (2 ^ 13 * m + 39) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_39 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_39 : oddCount 39 13 = 7 ∧ acceleratedOrbit 13 39 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_39 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 39) = 3 ^ 7 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_39.1, data_13_39.2] + +/-- Complete interval computation for depth 13, residue 40. -/ +theorem bounds_13_40 : exactInterval 13 40 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_40 (m : Nat) : + stoppingTime (2 ^ 13 * m + 40) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_40 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_40 : oddCount 40 13 = 4 ∧ acceleratedOrbit 13 40 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_40 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 40) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_40.1, data_13_40.2] + +/-- Complete interval computation for depth 13, residue 41. -/ +theorem bounds_13_41 : exactInterval 13 41 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_41 (m : Nat) : + stoppingTime (2 ^ 13 * m + 41) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_41 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_41 : oddCount 41 13 = 9 ∧ acceleratedOrbit 13 41 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_41 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 41) = 3 ^ 9 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_41.1, data_13_41.2] + +/-- Complete interval computation for depth 13, residue 42. -/ +theorem bounds_13_42 : exactInterval 13 42 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_42 (m : Nat) : + stoppingTime (2 ^ 13 * m + 42) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_42 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_42 : oddCount 42 13 = 4 ∧ acceleratedOrbit 13 42 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_42 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 42) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_42.1, data_13_42.2] + +/-- Complete interval computation for depth 13, residue 43. -/ +theorem bounds_13_43 : exactInterval 13 43 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_43 (m : Nat) : + stoppingTime (2 ^ 13 * m + 43) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_43 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_43 : oddCount 43 13 = 7 ∧ acceleratedOrbit 13 43 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_43 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 43) = 3 ^ 7 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_43.1, data_13_43.2] + +/-- Complete interval computation for depth 13, residue 44. -/ +theorem bounds_13_44 : exactInterval 13 44 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_44 (m : Nat) : + stoppingTime (2 ^ 13 * m + 44) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_44 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_44 : oddCount 44 13 = 5 ∧ acceleratedOrbit 13 44 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_44 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 44) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_44.1, data_13_44.2] + +/-- Complete interval computation for depth 13, residue 45. -/ +theorem bounds_13_45 : exactInterval 13 45 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_45 (m : Nat) : + stoppingTime (2 ^ 13 * m + 45) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_45 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_45 : oddCount 45 13 = 5 ∧ acceleratedOrbit 13 45 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_45 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 45) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_45.1, data_13_45.2] + +/-- Complete interval computation for depth 13, residue 46. -/ +theorem bounds_13_46 : exactInterval 13 46 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_46 (m : Nat) : + stoppingTime (2 ^ 13 * m + 46) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_46 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_46 : oddCount 46 13 = 5 ∧ acceleratedOrbit 13 46 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_46 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 46) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_46.1, data_13_46.2] + +/-- Complete interval computation for depth 13, residue 47. -/ +theorem bounds_13_47 : exactInterval 13 47 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_47 (m : Nat) : + stoppingTime (2 ^ 13 * m + 47) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_47 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_47 : oddCount 47 13 = 10 ∧ acceleratedOrbit 13 47 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_47 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 47) = 3 ^ 10 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_47.1, data_13_47.2] + +/-- Complete interval computation for depth 13, residue 48. -/ +theorem bounds_13_48 : exactInterval 13 48 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_48 (m : Nat) : + stoppingTime (2 ^ 13 * m + 48) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_48 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_48 : oddCount 48 13 = 4 ∧ acceleratedOrbit 13 48 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_48 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 48) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_48.1, data_13_48.2] + +/-- Complete interval computation for depth 13, residue 49. -/ +theorem bounds_13_49 : exactInterval 13 49 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_49 (m : Nat) : + stoppingTime (2 ^ 13 * m + 49) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_49 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_49 : oddCount 49 13 = 6 ∧ acceleratedOrbit 13 49 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_49 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 49) = 3 ^ 6 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_49.1, data_13_49.2] + +/-- Complete interval computation for depth 13, residue 50. -/ +theorem bounds_13_50 : exactInterval 13 50 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_50 (m : Nat) : + stoppingTime (2 ^ 13 * m + 50) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_50 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_50 : oddCount 50 13 = 6 ∧ acceleratedOrbit 13 50 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_50 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 50) = 3 ^ 6 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_50.1, data_13_50.2] + +end Collatz.Research.StoppingAtlas.Batch0470 From 95a896d6f52049e51f7b88763dd24e98faccc222 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:31 +0530 Subject: [PATCH 0471/1001] proof: certify atlas Batch0471 (13:51 to 13:65) --- Collatz/Research/StoppingAtlas/Batch0471.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0471.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0471.lean b/Collatz/Research/StoppingAtlas/Batch0471.lean new file mode 100644 index 00000000..d9026521 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0471.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0471 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 51. -/ +theorem bounds_13_51 : exactInterval 13 51 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_51 (m : Nat) : + stoppingTime (2 ^ 13 * m + 51) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_51 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_51 : oddCount 51 13 = 6 ∧ acceleratedOrbit 13 51 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_51 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 51) = 3 ^ 6 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_51.1, data_13_51.2] + +/-- Complete interval computation for depth 13, residue 52. -/ +theorem bounds_13_52 : exactInterval 13 52 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_52 (m : Nat) : + stoppingTime (2 ^ 13 * m + 52) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_52 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_52 : oddCount 52 13 = 4 ∧ acceleratedOrbit 13 52 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_52 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 52) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_52.1, data_13_52.2] + +/-- Complete interval computation for depth 13, residue 53. -/ +theorem bounds_13_53 : exactInterval 13 53 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_53 (m : Nat) : + stoppingTime (2 ^ 13 * m + 53) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_53 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_53 : oddCount 53 13 = 4 ∧ acceleratedOrbit 13 53 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_53 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 53) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_53.1, data_13_53.2] + +/-- Complete interval computation for depth 13, residue 54. -/ +theorem bounds_13_54 : exactInterval 13 54 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_54 (m : Nat) : + stoppingTime (2 ^ 13 * m + 54) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_54 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_54 : oddCount 54 13 = 9 ∧ acceleratedOrbit 13 54 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_54 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 54) = 3 ^ 9 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_54.1, data_13_54.2] + +/-- Complete interval computation for depth 13, residue 55. -/ +theorem bounds_13_55 : exactInterval 13 55 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_55 (m : Nat) : + stoppingTime (2 ^ 13 * m + 55) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_55 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_55 : oddCount 55 13 = 9 ∧ acceleratedOrbit 13 55 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_55 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 55) = 3 ^ 9 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_55.1, data_13_55.2] + +/-- Complete interval computation for depth 13, residue 56. -/ +theorem bounds_13_56 : exactInterval 13 56 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_56 (m : Nat) : + stoppingTime (2 ^ 13 * m + 56) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_56 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_56 : oddCount 56 13 = 5 ∧ acceleratedOrbit 13 56 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_56 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 56) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_56.1, data_13_56.2] + +/-- Complete interval computation for depth 13, residue 57. -/ +theorem bounds_13_57 : exactInterval 13 57 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_57 (m : Nat) : + stoppingTime (2 ^ 13 * m + 57) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_57 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_57 : oddCount 57 13 = 7 ∧ acceleratedOrbit 13 57 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_57 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 57) = 3 ^ 7 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_57.1, data_13_57.2] + +/-- Complete interval computation for depth 13, residue 58. -/ +theorem bounds_13_58 : exactInterval 13 58 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_58 (m : Nat) : + stoppingTime (2 ^ 13 * m + 58) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_58 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_58 : oddCount 58 13 = 5 ∧ acceleratedOrbit 13 58 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_58 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 58) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_58.1, data_13_58.2] + +/-- Complete interval computation for depth 13, residue 59. -/ +theorem bounds_13_59 : exactInterval 13 59 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_59 (m : Nat) : + stoppingTime (2 ^ 13 * m + 59) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_59 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_59 : oddCount 59 13 = 7 ∧ acceleratedOrbit 13 59 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_59 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 59) = 3 ^ 7 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_59.1, data_13_59.2] + +/-- Complete interval computation for depth 13, residue 60. -/ +theorem bounds_13_60 : exactInterval 13 60 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_60 (m : Nat) : + stoppingTime (2 ^ 13 * m + 60) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_60 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_60 : oddCount 60 13 = 5 ∧ acceleratedOrbit 13 60 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_60 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 60) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_60.1, data_13_60.2] + +/-- Complete interval computation for depth 13, residue 61. -/ +theorem bounds_13_61 : exactInterval 13 61 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_61 (m : Nat) : + stoppingTime (2 ^ 13 * m + 61) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_61 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_61 : oddCount 61 13 = 5 ∧ acceleratedOrbit 13 61 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_61 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 61) = 3 ^ 5 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_61.1, data_13_61.2] + +/-- Complete interval computation for depth 13, residue 62. -/ +theorem bounds_13_62 : exactInterval 13 62 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_62 (m : Nat) : + stoppingTime (2 ^ 13 * m + 62) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_62 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_62 : oddCount 62 13 = 9 ∧ acceleratedOrbit 13 62 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_62 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 62) = 3 ^ 9 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_62.1, data_13_62.2] + +/-- Complete interval computation for depth 13, residue 63. -/ +theorem bounds_13_63 : exactInterval 13 63 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_63 (m : Nat) : + stoppingTime (2 ^ 13 * m + 63) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_63 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_63 : oddCount 63 13 = 9 ∧ acceleratedOrbit 13 63 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_63 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 63) = 3 ^ 9 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_63.1, data_13_63.2] + +/-- Complete interval computation for depth 13, residue 64. -/ +theorem bounds_13_64 : exactInterval 13 64 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_64 (m : Nat) : + stoppingTime (2 ^ 13 * m + 64) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_64 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_64 : oddCount 64 13 = 4 ∧ acceleratedOrbit 13 64 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_64 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 64) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_64.1, data_13_64.2] + +/-- Complete interval computation for depth 13, residue 65. -/ +theorem bounds_13_65 : exactInterval 13 65 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_65 (m : Nat) : + stoppingTime (2 ^ 13 * m + 65) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_65 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_65 : oddCount 65 13 = 7 ∧ acceleratedOrbit 13 65 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_65 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 65) = 3 ^ 7 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_65.1, data_13_65.2] + +end Collatz.Research.StoppingAtlas.Batch0471 From 67a43e1a82f260e3c9efade8c033b84c5eac4648 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:31 +0530 Subject: [PATCH 0472/1001] proof: certify atlas Batch0472 (13:66 to 13:80) --- Collatz/Research/StoppingAtlas/Batch0472.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0472.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0472.lean b/Collatz/Research/StoppingAtlas/Batch0472.lean new file mode 100644 index 00000000..0681d0a9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0472.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0472 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 66. -/ +theorem bounds_13_66 : exactInterval 13 66 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_66 (m : Nat) : + stoppingTime (2 ^ 13 * m + 66) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_66 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_66 : oddCount 66 13 = 7 ∧ acceleratedOrbit 13 66 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_66 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 66) = 3 ^ 7 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_66.1, data_13_66.2] + +/-- Complete interval computation for depth 13, residue 67. -/ +theorem bounds_13_67 : exactInterval 13 67 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_67 (m : Nat) : + stoppingTime (2 ^ 13 * m + 67) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_67 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_67 : oddCount 67 13 = 7 ∧ acceleratedOrbit 13 67 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_67 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 67) = 3 ^ 7 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_67.1, data_13_67.2] + +/-- Complete interval computation for depth 13, residue 68. -/ +theorem bounds_13_68 : exactInterval 13 68 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_68 (m : Nat) : + stoppingTime (2 ^ 13 * m + 68) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_68 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_68 : oddCount 68 13 = 4 ∧ acceleratedOrbit 13 68 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_68 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 68) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_68.1, data_13_68.2] + +/-- Complete interval computation for depth 13, residue 69. -/ +theorem bounds_13_69 : exactInterval 13 69 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_69 (m : Nat) : + stoppingTime (2 ^ 13 * m + 69) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_69 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_69 : oddCount 69 13 = 4 ∧ acceleratedOrbit 13 69 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_69 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 69) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_69.1, data_13_69.2] + +/-- Complete interval computation for depth 13, residue 70. -/ +theorem bounds_13_70 : exactInterval 13 70 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_70 (m : Nat) : + stoppingTime (2 ^ 13 * m + 70) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_70 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_70 : oddCount 70 13 = 4 ∧ acceleratedOrbit 13 70 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_70 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 70) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_70.1, data_13_70.2] + +/-- Complete interval computation for depth 13, residue 71. -/ +theorem bounds_13_71 : exactInterval 13 71 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_71 (m : Nat) : + stoppingTime (2 ^ 13 * m + 71) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_71 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_71 : oddCount 71 13 = 9 ∧ acceleratedOrbit 13 71 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_71 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 71) = 3 ^ 9 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_71.1, data_13_71.2] + +/-- Complete interval computation for depth 13, residue 72. -/ +theorem bounds_13_72 : exactInterval 13 72 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_72 (m : Nat) : + stoppingTime (2 ^ 13 * m + 72) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_72 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_72 : oddCount 72 13 = 6 ∧ acceleratedOrbit 13 72 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_72 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 72) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_72.1, data_13_72.2] + +/-- Complete interval computation for depth 13, residue 73. -/ +theorem bounds_13_73 : exactInterval 13 73 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_73 (m : Nat) : + stoppingTime (2 ^ 13 * m + 73) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_73 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_73 : oddCount 73 13 = 9 ∧ acceleratedOrbit 13 73 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_73 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 73) = 3 ^ 9 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_73.1, data_13_73.2] + +/-- Complete interval computation for depth 13, residue 74. -/ +theorem bounds_13_74 : exactInterval 13 74 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_74 (m : Nat) : + stoppingTime (2 ^ 13 * m + 74) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_74 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_74 : oddCount 74 13 = 6 ∧ acceleratedOrbit 13 74 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_74 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 74) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_74.1, data_13_74.2] + +/-- Complete interval computation for depth 13, residue 75. -/ +theorem bounds_13_75 : exactInterval 13 75 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_75 (m : Nat) : + stoppingTime (2 ^ 13 * m + 75) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_75 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_75 : oddCount 75 13 = 4 ∧ acceleratedOrbit 13 75 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_75 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 75) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_75.1, data_13_75.2] + +/-- Complete interval computation for depth 13, residue 76. -/ +theorem bounds_13_76 : exactInterval 13 76 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_76 (m : Nat) : + stoppingTime (2 ^ 13 * m + 76) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_76 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_76 : oddCount 76 13 = 6 ∧ acceleratedOrbit 13 76 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_76 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 76) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_76.1, data_13_76.2] + +/-- Complete interval computation for depth 13, residue 77. -/ +theorem bounds_13_77 : exactInterval 13 77 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_77 (m : Nat) : + stoppingTime (2 ^ 13 * m + 77) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_77 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_77 : oddCount 77 13 = 6 ∧ acceleratedOrbit 13 77 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_77 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 77) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_77.1, data_13_77.2] + +/-- Complete interval computation for depth 13, residue 78. -/ +theorem bounds_13_78 : exactInterval 13 78 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_78 (m : Nat) : + stoppingTime (2 ^ 13 * m + 78) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_78 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_78 : oddCount 78 13 = 7 ∧ acceleratedOrbit 13 78 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_78 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 78) = 3 ^ 7 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_78.1, data_13_78.2] + +/-- Complete interval computation for depth 13, residue 79. -/ +theorem bounds_13_79 : exactInterval 13 79 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_79 (m : Nat) : + stoppingTime (2 ^ 13 * m + 79) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_79 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_79 : oddCount 79 13 = 7 ∧ acceleratedOrbit 13 79 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_79 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 79) = 3 ^ 7 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_79.1, data_13_79.2] + +/-- Complete interval computation for depth 13, residue 80. -/ +theorem bounds_13_80 : exactInterval 13 80 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_80 (m : Nat) : + stoppingTime (2 ^ 13 * m + 80) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_80 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_80 : oddCount 80 13 = 4 ∧ acceleratedOrbit 13 80 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_80 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 80) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_80.1, data_13_80.2] + +end Collatz.Research.StoppingAtlas.Batch0472 From d743abec6fae73081375d00693c143832414dd7d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:31 +0530 Subject: [PATCH 0473/1001] proof: certify atlas Batch0473 (13:81 to 13:96) --- Collatz/Research/StoppingAtlas/Batch0473.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0473.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0473.lean b/Collatz/Research/StoppingAtlas/Batch0473.lean new file mode 100644 index 00000000..e18f1171 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0473.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0473 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 81. -/ +theorem bounds_13_81 : exactInterval 13 81 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_81 (m : Nat) : + stoppingTime (2 ^ 13 * m + 81) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_81 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_81 : oddCount 81 13 = 6 ∧ acceleratedOrbit 13 81 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_81 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 81) = 3 ^ 6 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_81.1, data_13_81.2] + +/-- Complete interval computation for depth 13, residue 82. -/ +theorem bounds_13_82 : exactInterval 13 82 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_82 (m : Nat) : + stoppingTime (2 ^ 13 * m + 82) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_82 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_82 : oddCount 82 13 = 9 ∧ acceleratedOrbit 13 82 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_82 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 82) = 3 ^ 9 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_82.1, data_13_82.2] + +/-- Complete interval computation for depth 13, residue 83. -/ +theorem bounds_13_83 : exactInterval 13 83 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_83 (m : Nat) : + stoppingTime (2 ^ 13 * m + 83) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_83 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_83 : oddCount 83 13 = 9 ∧ acceleratedOrbit 13 83 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_83 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 83) = 3 ^ 9 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_83.1, data_13_83.2] + +/-- Complete interval computation for depth 13, residue 84. -/ +theorem bounds_13_84 : exactInterval 13 84 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_84 (m : Nat) : + stoppingTime (2 ^ 13 * m + 84) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_84 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_84 : oddCount 84 13 = 4 ∧ acceleratedOrbit 13 84 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_84 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 84) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_84.1, data_13_84.2] + +/-- Complete interval computation for depth 13, residue 85. -/ +theorem bounds_13_85 : exactInterval 13 85 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_85 (m : Nat) : + stoppingTime (2 ^ 13 * m + 85) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_85 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_85 : oddCount 85 13 = 4 ∧ acceleratedOrbit 13 85 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_85 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 85) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_85.1, data_13_85.2] + +/-- Complete interval computation for depth 13, residue 86. -/ +theorem bounds_13_86 : exactInterval 13 86 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_86 (m : Nat) : + stoppingTime (2 ^ 13 * m + 86) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_86 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_86 : oddCount 86 13 = 7 ∧ acceleratedOrbit 13 86 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_86 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 86) = 3 ^ 7 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_86.1, data_13_86.2] + +/-- Complete interval computation for depth 13, residue 87. -/ +theorem bounds_13_87 : exactInterval 13 87 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_87 (m : Nat) : + stoppingTime (2 ^ 13 * m + 87) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_87 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_87 : oddCount 87 13 = 7 ∧ acceleratedOrbit 13 87 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_87 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 87) = 3 ^ 7 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_87.1, data_13_87.2] + +/-- Complete interval computation for depth 13, residue 88. -/ +theorem bounds_13_88 : exactInterval 13 88 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_88 (m : Nat) : + stoppingTime (2 ^ 13 * m + 88) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_88 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_88 : oddCount 88 13 = 4 ∧ acceleratedOrbit 13 88 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_88 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 88) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_88.1, data_13_88.2] + +/-- Complete interval computation for depth 13, residue 89. -/ +theorem bounds_13_89 : exactInterval 13 89 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_89 (m : Nat) : + stoppingTime (2 ^ 13 * m + 89) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_89 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_89 : oddCount 89 13 = 7 ∧ acceleratedOrbit 13 89 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_89 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 89) = 3 ^ 7 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_89.1, data_13_89.2] + +/-- Complete interval computation for depth 13, residue 90. -/ +theorem bounds_13_90 : exactInterval 13 90 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_90 (m : Nat) : + stoppingTime (2 ^ 13 * m + 90) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_90 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_90 : oddCount 90 13 = 4 ∧ acceleratedOrbit 13 90 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_90 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 90) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_90.1, data_13_90.2] + +/-- Complete interval computation for depth 13, residue 91. -/ +theorem bounds_13_91 : exactInterval 13 91 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_91 (m : Nat) : + stoppingTime (2 ^ 13 * m + 91) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_91 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_91 : oddCount 91 13 = 10 ∧ acceleratedOrbit 13 91 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_91 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 91) = 3 ^ 10 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_91.1, data_13_91.2] + +/-- Complete interval computation for depth 13, residue 92. -/ +theorem bounds_13_92 : exactInterval 13 92 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_92 (m : Nat) : + stoppingTime (2 ^ 13 * m + 92) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_92 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_92 : oddCount 92 13 = 4 ∧ acceleratedOrbit 13 92 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_92 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 92) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_92.1, data_13_92.2] + +/-- Complete interval computation for depth 13, residue 93. -/ +theorem bounds_13_93 : exactInterval 13 93 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_93 (m : Nat) : + stoppingTime (2 ^ 13 * m + 93) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_93 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_93 : oddCount 93 13 = 4 ∧ acceleratedOrbit 13 93 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_93 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 93) = 3 ^ 4 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_93.1, data_13_93.2] + +/-- Complete interval computation for depth 13, residue 94. -/ +theorem bounds_13_94 : exactInterval 13 94 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_94 (m : Nat) : + stoppingTime (2 ^ 13 * m + 94) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_94 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_94 : oddCount 94 13 = 9 ∧ acceleratedOrbit 13 94 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_94 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 94) = 3 ^ 9 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_94.1, data_13_94.2] + +/-- Complete interval computation for depth 13, residue 95. -/ +theorem bounds_13_95 : exactInterval 13 95 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_95 (m : Nat) : + stoppingTime (2 ^ 13 * m + 95) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_95 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_95 : oddCount 95 13 = 9 ∧ acceleratedOrbit 13 95 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_95 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 95) = 3 ^ 9 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_95.1, data_13_95.2] + +/-- Complete interval computation for depth 13, residue 96. -/ +theorem bounds_13_96 : exactInterval 13 96 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_96 (m : Nat) : + stoppingTime (2 ^ 13 * m + 96) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_96 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_96 : oddCount 96 13 = 4 ∧ acceleratedOrbit 13 96 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_96 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 96) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_96.1, data_13_96.2] + +end Collatz.Research.StoppingAtlas.Batch0473 From 2930c9edf8691679c52ecdf9402f066cd7391174 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:32 +0530 Subject: [PATCH 0474/1001] proof: certify atlas Batch0474 (13:97 to 13:111) --- Collatz/Research/StoppingAtlas/Batch0474.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0474.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0474.lean b/Collatz/Research/StoppingAtlas/Batch0474.lean new file mode 100644 index 00000000..26cb2b8d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0474.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0474 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 97. -/ +theorem bounds_13_97 : exactInterval 13 97 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_97 (m : Nat) : + stoppingTime (2 ^ 13 * m + 97) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_97 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_97 : oddCount 97 13 = 9 ∧ acceleratedOrbit 13 97 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_97 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 97) = 3 ^ 9 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_97.1, data_13_97.2] + +/-- Complete interval computation for depth 13, residue 98. -/ +theorem bounds_13_98 : exactInterval 13 98 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_98 (m : Nat) : + stoppingTime (2 ^ 13 * m + 98) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_98 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_98 : oddCount 98 13 = 6 ∧ acceleratedOrbit 13 98 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_98 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 98) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_98.1, data_13_98.2] + +/-- Complete interval computation for depth 13, residue 99. -/ +theorem bounds_13_99 : exactInterval 13 99 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_99 (m : Nat) : + stoppingTime (2 ^ 13 * m + 99) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_99 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_99 : oddCount 99 13 = 6 ∧ acceleratedOrbit 13 99 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_99 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 99) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_99.1, data_13_99.2] + +/-- Complete interval computation for depth 13, residue 100. -/ +theorem bounds_13_100 : exactInterval 13 100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_100 : oddCount 100 13 = 6 ∧ acceleratedOrbit 13 100 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 100) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_100.1, data_13_100.2] + +/-- Complete interval computation for depth 13, residue 101. -/ +theorem bounds_13_101 : exactInterval 13 101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_101 : oddCount 101 13 = 6 ∧ acceleratedOrbit 13 101 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 101) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_101.1, data_13_101.2] + +/-- Complete interval computation for depth 13, residue 102. -/ +theorem bounds_13_102 : exactInterval 13 102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_102 : oddCount 102 13 = 6 ∧ acceleratedOrbit 13 102 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 102) = 3 ^ 6 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_102.1, data_13_102.2] + +/-- Complete interval computation for depth 13, residue 103. -/ +theorem bounds_13_103 : exactInterval 13 103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_103 : oddCount 103 13 = 9 ∧ acceleratedOrbit 13 103 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 103) = 3 ^ 9 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_103.1, data_13_103.2] + +/-- Complete interval computation for depth 13, residue 104. -/ +theorem bounds_13_104 : exactInterval 13 104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_104 : oddCount 104 13 = 4 ∧ acceleratedOrbit 13 104 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 104) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_104.1, data_13_104.2] + +/-- Complete interval computation for depth 13, residue 105. -/ +theorem bounds_13_105 : exactInterval 13 105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_105 : oddCount 105 13 = 7 ∧ acceleratedOrbit 13 105 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 105) = 3 ^ 7 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_105.1, data_13_105.2] + +/-- Complete interval computation for depth 13, residue 106. -/ +theorem bounds_13_106 : exactInterval 13 106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_106 : oddCount 106 13 = 4 ∧ acceleratedOrbit 13 106 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 106) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_106.1, data_13_106.2] + +/-- Complete interval computation for depth 13, residue 107. -/ +theorem bounds_13_107 : exactInterval 13 107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_107 : oddCount 107 13 = 9 ∧ acceleratedOrbit 13 107 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 107) = 3 ^ 9 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_107.1, data_13_107.2] + +/-- Complete interval computation for depth 13, residue 108. -/ +theorem bounds_13_108 : exactInterval 13 108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_108 : oddCount 108 13 = 8 ∧ acceleratedOrbit 13 108 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 108) = 3 ^ 8 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_108.1, data_13_108.2] + +/-- Complete interval computation for depth 13, residue 109. -/ +theorem bounds_13_109 : exactInterval 13 109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_109 : oddCount 109 13 = 8 ∧ acceleratedOrbit 13 109 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 109) = 3 ^ 8 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_109.1, data_13_109.2] + +/-- Complete interval computation for depth 13, residue 110. -/ +theorem bounds_13_110 : exactInterval 13 110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_110 : oddCount 110 13 = 8 ∧ acceleratedOrbit 13 110 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 110) = 3 ^ 8 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_110.1, data_13_110.2] + +/-- Complete interval computation for depth 13, residue 111. -/ +theorem bounds_13_111 : exactInterval 13 111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_111 : oddCount 111 13 = 11 ∧ acceleratedOrbit 13 111 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 111) = 3 ^ 11 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_111.1, data_13_111.2] + +end Collatz.Research.StoppingAtlas.Batch0474 From 68251a9129b450065c163f60ac00d789413efb02 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:32 +0530 Subject: [PATCH 0475/1001] proof: certify atlas Batch0475 (13:112 to 13:127) --- Collatz/Research/StoppingAtlas/Batch0475.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0475.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0475.lean b/Collatz/Research/StoppingAtlas/Batch0475.lean new file mode 100644 index 00000000..a9b3df7d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0475.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0475 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 112. -/ +theorem bounds_13_112 : exactInterval 13 112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_112 : oddCount 112 13 = 5 ∧ acceleratedOrbit 13 112 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 112) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_112.1, data_13_112.2] + +/-- Complete interval computation for depth 13, residue 113. -/ +theorem bounds_13_113 : exactInterval 13 113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_113 : oddCount 113 13 = 4 ∧ acceleratedOrbit 13 113 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 113) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_113.1, data_13_113.2] + +/-- Complete interval computation for depth 13, residue 114. -/ +theorem bounds_13_114 : exactInterval 13 114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_114 : oddCount 114 13 = 6 ∧ acceleratedOrbit 13 114 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 114) = 3 ^ 6 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_114.1, data_13_114.2] + +/-- Complete interval computation for depth 13, residue 115. -/ +theorem bounds_13_115 : exactInterval 13 115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_115 : oddCount 115 13 = 6 ∧ acceleratedOrbit 13 115 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 115) = 3 ^ 6 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_115.1, data_13_115.2] + +/-- Complete interval computation for depth 13, residue 116. -/ +theorem bounds_13_116 : exactInterval 13 116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_116 : oddCount 116 13 = 5 ∧ acceleratedOrbit 13 116 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 116) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_116.1, data_13_116.2] + +/-- Complete interval computation for depth 13, residue 117. -/ +theorem bounds_13_117 : exactInterval 13 117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_117 : oddCount 117 13 = 5 ∧ acceleratedOrbit 13 117 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 117) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_117.1, data_13_117.2] + +/-- Complete interval computation for depth 13, residue 118. -/ +theorem bounds_13_118 : exactInterval 13 118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_118 : oddCount 118 13 = 6 ∧ acceleratedOrbit 13 118 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 118) = 3 ^ 6 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_118.1, data_13_118.2] + +/-- Complete interval computation for depth 13, residue 119. -/ +theorem bounds_13_119 : exactInterval 13 119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_119 : oddCount 119 13 = 6 ∧ acceleratedOrbit 13 119 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 119) = 3 ^ 6 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_119.1, data_13_119.2] + +/-- Complete interval computation for depth 13, residue 120. -/ +theorem bounds_13_120 : exactInterval 13 120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_120 : oddCount 120 13 = 5 ∧ acceleratedOrbit 13 120 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 120) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_120.1, data_13_120.2] + +/-- Complete interval computation for depth 13, residue 121. -/ +theorem bounds_13_121 : exactInterval 13 121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_121 : oddCount 121 13 = 10 ∧ acceleratedOrbit 13 121 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 121) = 3 ^ 10 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_121.1, data_13_121.2] + +/-- Complete interval computation for depth 13, residue 122. -/ +theorem bounds_13_122 : exactInterval 13 122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_122 : oddCount 122 13 = 5 ∧ acceleratedOrbit 13 122 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 122) = 3 ^ 5 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_122.1, data_13_122.2] + +/-- Complete interval computation for depth 13, residue 123. -/ +theorem bounds_13_123 : exactInterval 13 123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_123 : oddCount 123 13 = 8 ∧ acceleratedOrbit 13 123 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 123) = 3 ^ 8 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_123.1, data_13_123.2] + +/-- Complete interval computation for depth 13, residue 124. -/ +theorem bounds_13_124 : exactInterval 13 124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_124 : oddCount 124 13 = 8 ∧ acceleratedOrbit 13 124 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 124) = 3 ^ 8 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_124.1, data_13_124.2] + +/-- Complete interval computation for depth 13, residue 125. -/ +theorem bounds_13_125 : exactInterval 13 125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_125 : oddCount 125 13 = 8 ∧ acceleratedOrbit 13 125 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 125) = 3 ^ 8 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_125.1, data_13_125.2] + +/-- Complete interval computation for depth 13, residue 126. -/ +theorem bounds_13_126 : exactInterval 13 126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_126 : oddCount 126 13 = 8 ∧ acceleratedOrbit 13 126 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 126) = 3 ^ 8 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_126.1, data_13_126.2] + +/-- Complete interval computation for depth 13, residue 127. -/ +theorem bounds_13_127 : exactInterval 13 127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_127 : oddCount 127 13 = 9 ∧ acceleratedOrbit 13 127 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 127) = 3 ^ 9 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_127.1, data_13_127.2] + +end Collatz.Research.StoppingAtlas.Batch0475 From ff3a1987bbc159bbc7d6d9407b64d47129e7bd6a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:32 +0530 Subject: [PATCH 0476/1001] proof: certify atlas Batch0476 (13:128 to 13:142) --- Collatz/Research/StoppingAtlas/Batch0476.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0476.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0476.lean b/Collatz/Research/StoppingAtlas/Batch0476.lean new file mode 100644 index 00000000..685b8677 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0476.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0476 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 128. -/ +theorem bounds_13_128 : exactInterval 13 128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_128 : oddCount 128 13 = 3 ∧ acceleratedOrbit 13 128 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 128) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_128.1, data_13_128.2] + +/-- Complete interval computation for depth 13, residue 129. -/ +theorem bounds_13_129 : exactInterval 13 129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_129 : oddCount 129 13 = 8 ∧ acceleratedOrbit 13 129 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 129) = 3 ^ 8 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_129.1, data_13_129.2] + +/-- Complete interval computation for depth 13, residue 130. -/ +theorem bounds_13_130 : exactInterval 13 130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_130 : oddCount 130 13 = 6 ∧ acceleratedOrbit 13 130 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 130) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_130.1, data_13_130.2] + +/-- Complete interval computation for depth 13, residue 131. -/ +theorem bounds_13_131 : exactInterval 13 131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_131 : oddCount 131 13 = 6 ∧ acceleratedOrbit 13 131 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 131) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_131.1, data_13_131.2] + +/-- Complete interval computation for depth 13, residue 132. -/ +theorem bounds_13_132 : exactInterval 13 132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_132 : oddCount 132 13 = 6 ∧ acceleratedOrbit 13 132 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 132) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_132.1, data_13_132.2] + +/-- Complete interval computation for depth 13, residue 133. -/ +theorem bounds_13_133 : exactInterval 13 133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_133 : oddCount 133 13 = 6 ∧ acceleratedOrbit 13 133 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 133) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_133.1, data_13_133.2] + +/-- Complete interval computation for depth 13, residue 134. -/ +theorem bounds_13_134 : exactInterval 13 134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_134 : oddCount 134 13 = 6 ∧ acceleratedOrbit 13 134 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 134) = 3 ^ 6 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_134.1, data_13_134.2] + +/-- Complete interval computation for depth 13, residue 135. -/ +theorem bounds_13_135 : exactInterval 13 135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_135 : oddCount 135 13 = 7 ∧ acceleratedOrbit 13 135 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 135) = 3 ^ 7 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_135.1, data_13_135.2] + +/-- Complete interval computation for depth 13, residue 136. -/ +theorem bounds_13_136 : exactInterval 13 136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_136 : oddCount 136 13 = 4 ∧ acceleratedOrbit 13 136 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 136) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_136.1, data_13_136.2] + +/-- Complete interval computation for depth 13, residue 137. -/ +theorem bounds_13_137 : exactInterval 13 137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_137 : oddCount 137 13 = 9 ∧ acceleratedOrbit 13 137 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 137) = 3 ^ 9 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_137.1, data_13_137.2] + +/-- Complete interval computation for depth 13, residue 138. -/ +theorem bounds_13_138 : exactInterval 13 138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_138 : oddCount 138 13 = 4 ∧ acceleratedOrbit 13 138 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 138) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_138.1, data_13_138.2] + +/-- Complete interval computation for depth 13, residue 139. -/ +theorem bounds_13_139 : exactInterval 13 139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_139 : oddCount 139 13 = 7 ∧ acceleratedOrbit 13 139 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 139) = 3 ^ 7 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_139.1, data_13_139.2] + +/-- Complete interval computation for depth 13, residue 140. -/ +theorem bounds_13_140 : exactInterval 13 140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_140 : oddCount 140 13 = 4 ∧ acceleratedOrbit 13 140 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 140) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_140.1, data_13_140.2] + +/-- Complete interval computation for depth 13, residue 141. -/ +theorem bounds_13_141 : exactInterval 13 141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_141 : oddCount 141 13 = 4 ∧ acceleratedOrbit 13 141 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 141) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_141.1, data_13_141.2] + +/-- Complete interval computation for depth 13, residue 142. -/ +theorem bounds_13_142 : exactInterval 13 142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_142 : oddCount 142 13 = 9 ∧ acceleratedOrbit 13 142 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 142) = 3 ^ 9 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_142.1, data_13_142.2] + +end Collatz.Research.StoppingAtlas.Batch0476 From 1f63b284826eba1c3356c6013b5d697d8bfec37e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:33 +0530 Subject: [PATCH 0477/1001] proof: certify atlas Batch0477 (13:143 to 13:157) --- Collatz/Research/StoppingAtlas/Batch0477.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0477.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0477.lean b/Collatz/Research/StoppingAtlas/Batch0477.lean new file mode 100644 index 00000000..deaf7f2e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0477.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0477 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 143. -/ +theorem bounds_13_143 : exactInterval 13 143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_143 : oddCount 143 13 = 9 ∧ acceleratedOrbit 13 143 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 143) = 3 ^ 9 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_143.1, data_13_143.2] + +/-- Complete interval computation for depth 13, residue 144. -/ +theorem bounds_13_144 : exactInterval 13 144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_144 : oddCount 144 13 = 5 ∧ acceleratedOrbit 13 144 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 144) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_144.1, data_13_144.2] + +/-- Complete interval computation for depth 13, residue 145. -/ +theorem bounds_13_145 : exactInterval 13 145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_145 : oddCount 145 13 = 8 ∧ acceleratedOrbit 13 145 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 145) = 3 ^ 8 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_145.1, data_13_145.2] + +/-- Complete interval computation for depth 13, residue 146. -/ +theorem bounds_13_146 : exactInterval 13 146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_146 : oddCount 146 13 = 8 ∧ acceleratedOrbit 13 146 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 146) = 3 ^ 8 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_146.1, data_13_146.2] + +/-- Complete interval computation for depth 13, residue 147. -/ +theorem bounds_13_147 : exactInterval 13 147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_147 : oddCount 147 13 = 8 ∧ acceleratedOrbit 13 147 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 147) = 3 ^ 8 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_147.1, data_13_147.2] + +/-- Complete interval computation for depth 13, residue 148. -/ +theorem bounds_13_148 : exactInterval 13 148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_148 : oddCount 148 13 = 5 ∧ acceleratedOrbit 13 148 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 148) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_148.1, data_13_148.2] + +/-- Complete interval computation for depth 13, residue 149. -/ +theorem bounds_13_149 : exactInterval 13 149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_149 : oddCount 149 13 = 5 ∧ acceleratedOrbit 13 149 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 149) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_149.1, data_13_149.2] + +/-- Complete interval computation for depth 13, residue 150. -/ +theorem bounds_13_150 : exactInterval 13 150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_150 : oddCount 150 13 = 4 ∧ acceleratedOrbit 13 150 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 150) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_150.1, data_13_150.2] + +/-- Complete interval computation for depth 13, residue 151. -/ +theorem bounds_13_151 : exactInterval 13 151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_151 : oddCount 151 13 = 4 ∧ acceleratedOrbit 13 151 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 151) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_151.1, data_13_151.2] + +/-- Complete interval computation for depth 13, residue 152. -/ +theorem bounds_13_152 : exactInterval 13 152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_152 : oddCount 152 13 = 5 ∧ acceleratedOrbit 13 152 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 152) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_152.1, data_13_152.2] + +/-- Complete interval computation for depth 13, residue 153. -/ +theorem bounds_13_153 : exactInterval 13 153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_153 : oddCount 153 13 = 6 ∧ acceleratedOrbit 13 153 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 153) = 3 ^ 6 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_153.1, data_13_153.2] + +/-- Complete interval computation for depth 13, residue 154. -/ +theorem bounds_13_154 : exactInterval 13 154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_154 : oddCount 154 13 = 5 ∧ acceleratedOrbit 13 154 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 154) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_154.1, data_13_154.2] + +/-- Complete interval computation for depth 13, residue 155. -/ +theorem bounds_13_155 : exactInterval 13 155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_155 : oddCount 155 13 = 9 ∧ acceleratedOrbit 13 155 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 155) = 3 ^ 9 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_155.1, data_13_155.2] + +/-- Complete interval computation for depth 13, residue 156. -/ +theorem bounds_13_156 : exactInterval 13 156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_156 : oddCount 156 13 = 7 ∧ acceleratedOrbit 13 156 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 156) = 3 ^ 7 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_156.1, data_13_156.2] + +/-- Complete interval computation for depth 13, residue 157. -/ +theorem bounds_13_157 : exactInterval 13 157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_157 : oddCount 157 13 = 7 ∧ acceleratedOrbit 13 157 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 157) = 3 ^ 7 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_157.1, data_13_157.2] + +end Collatz.Research.StoppingAtlas.Batch0477 From cbcb132c96b88c00e695333e1645eca23939a8af Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:33 +0530 Subject: [PATCH 0478/1001] proof: certify atlas Batch0478 (13:158 to 13:173) --- Collatz/Research/StoppingAtlas/Batch0478.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0478.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0478.lean b/Collatz/Research/StoppingAtlas/Batch0478.lean new file mode 100644 index 00000000..8e67c90c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0478.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0478 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 158. -/ +theorem bounds_13_158 : exactInterval 13 158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_158 : oddCount 158 13 = 7 ∧ acceleratedOrbit 13 158 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 158) = 3 ^ 7 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_158.1, data_13_158.2] + +/-- Complete interval computation for depth 13, residue 159. -/ +theorem bounds_13_159 : exactInterval 13 159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_159 : oddCount 159 13 = 10 ∧ acceleratedOrbit 13 159 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 159) = 3 ^ 10 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_159.1, data_13_159.2] + +/-- Complete interval computation for depth 13, residue 160. -/ +theorem bounds_13_160 : exactInterval 13 160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_160 : oddCount 160 13 = 3 ∧ acceleratedOrbit 13 160 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 160) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_160.1, data_13_160.2] + +/-- Complete interval computation for depth 13, residue 161. -/ +theorem bounds_13_161 : exactInterval 13 161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_161 : oddCount 161 13 = 9 ∧ acceleratedOrbit 13 161 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 161) = 3 ^ 9 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_161.1, data_13_161.2] + +/-- Complete interval computation for depth 13, residue 162. -/ +theorem bounds_13_162 : exactInterval 13 162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_162 : oddCount 162 13 = 5 ∧ acceleratedOrbit 13 162 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 162) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_162.1, data_13_162.2] + +/-- Complete interval computation for depth 13, residue 163. -/ +theorem bounds_13_163 : exactInterval 13 163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_163 : oddCount 163 13 = 5 ∧ acceleratedOrbit 13 163 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 163) = 3 ^ 5 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_163.1, data_13_163.2] + +/-- Complete interval computation for depth 13, residue 164. -/ +theorem bounds_13_164 : exactInterval 13 164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_164 : oddCount 164 13 = 8 ∧ acceleratedOrbit 13 164 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 164) = 3 ^ 8 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_164.1, data_13_164.2] + +/-- Complete interval computation for depth 13, residue 165. -/ +theorem bounds_13_165 : exactInterval 13 165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_165 : oddCount 165 13 = 8 ∧ acceleratedOrbit 13 165 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 165) = 3 ^ 8 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_165.1, data_13_165.2] + +/-- Complete interval computation for depth 13, residue 166. -/ +theorem bounds_13_166 : exactInterval 13 166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_166 : oddCount 166 13 = 8 ∧ acceleratedOrbit 13 166 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 166) = 3 ^ 8 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_166.1, data_13_166.2] + +/-- Complete interval computation for depth 13, residue 167. -/ +theorem bounds_13_167 : exactInterval 13 167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_167 : oddCount 167 13 = 11 ∧ acceleratedOrbit 13 167 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 167) = 3 ^ 11 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_167.1, data_13_167.2] + +/-- Complete interval computation for depth 13, residue 168. -/ +theorem bounds_13_168 : exactInterval 13 168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_168 : oddCount 168 13 = 3 ∧ acceleratedOrbit 13 168 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 168) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_168.1, data_13_168.2] + +/-- Complete interval computation for depth 13, residue 169. -/ +theorem bounds_13_169 : exactInterval 13 169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_169 : oddCount 169 13 = 9 ∧ acceleratedOrbit 13 169 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 169) = 3 ^ 9 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_169.1, data_13_169.2] + +/-- Complete interval computation for depth 13, residue 170. -/ +theorem bounds_13_170 : exactInterval 13 170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_170 : oddCount 170 13 = 3 ∧ acceleratedOrbit 13 170 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 170) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_170.1, data_13_170.2] + +/-- Complete interval computation for depth 13, residue 171. -/ +theorem bounds_13_171 : exactInterval 13 171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_171 : oddCount 171 13 = 7 ∧ acceleratedOrbit 13 171 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 171) = 3 ^ 7 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_171.1, data_13_171.2] + +/-- Complete interval computation for depth 13, residue 172. -/ +theorem bounds_13_172 : exactInterval 13 172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_172 : oddCount 172 13 = 6 ∧ acceleratedOrbit 13 172 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 172) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_172.1, data_13_172.2] + +/-- Complete interval computation for depth 13, residue 173. -/ +theorem bounds_13_173 : exactInterval 13 173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_173 : oddCount 173 13 = 6 ∧ acceleratedOrbit 13 173 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 173) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_173.1, data_13_173.2] + +end Collatz.Research.StoppingAtlas.Batch0478 From 75aa3735697ac65623ef71296eb90d223a359b78 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:33 +0530 Subject: [PATCH 0479/1001] proof: certify atlas Batch0479 (13:174 to 13:188) --- Collatz/Research/StoppingAtlas/Batch0479.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0479.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0479.lean b/Collatz/Research/StoppingAtlas/Batch0479.lean new file mode 100644 index 00000000..e759f302 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0479.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0479 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 174. -/ +theorem bounds_13_174 : exactInterval 13 174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_174 : oddCount 174 13 = 6 ∧ acceleratedOrbit 13 174 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 174) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_174.1, data_13_174.2] + +/-- Complete interval computation for depth 13, residue 175. -/ +theorem bounds_13_175 : exactInterval 13 175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_175 : oddCount 175 13 = 9 ∧ acceleratedOrbit 13 175 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 175) = 3 ^ 9 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_175.1, data_13_175.2] + +/-- Complete interval computation for depth 13, residue 176. -/ +theorem bounds_13_176 : exactInterval 13 176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_176 : oddCount 176 13 = 4 ∧ acceleratedOrbit 13 176 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 176) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_176.1, data_13_176.2] + +/-- Complete interval computation for depth 13, residue 177. -/ +theorem bounds_13_177 : exactInterval 13 177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_177 : oddCount 177 13 = 6 ∧ acceleratedOrbit 13 177 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 177) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_177.1, data_13_177.2] + +/-- Complete interval computation for depth 13, residue 178. -/ +theorem bounds_13_178 : exactInterval 13 178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_178 : oddCount 178 13 = 6 ∧ acceleratedOrbit 13 178 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 178) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_178.1, data_13_178.2] + +/-- Complete interval computation for depth 13, residue 179. -/ +theorem bounds_13_179 : exactInterval 13 179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_179 : oddCount 179 13 = 6 ∧ acceleratedOrbit 13 179 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 179) = 3 ^ 6 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_179.1, data_13_179.2] + +/-- Complete interval computation for depth 13, residue 180. -/ +theorem bounds_13_180 : exactInterval 13 180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_180 : oddCount 180 13 = 4 ∧ acceleratedOrbit 13 180 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 180) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_180.1, data_13_180.2] + +/-- Complete interval computation for depth 13, residue 181. -/ +theorem bounds_13_181 : exactInterval 13 181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_181 : oddCount 181 13 = 4 ∧ acceleratedOrbit 13 181 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 181) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_181.1, data_13_181.2] + +/-- Complete interval computation for depth 13, residue 182. -/ +theorem bounds_13_182 : exactInterval 13 182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_182 : oddCount 182 13 = 9 ∧ acceleratedOrbit 13 182 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 182) = 3 ^ 9 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_182.1, data_13_182.2] + +/-- Complete interval computation for depth 13, residue 183. -/ +theorem bounds_13_183 : exactInterval 13 183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_183 : oddCount 183 13 = 9 ∧ acceleratedOrbit 13 183 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 183) = 3 ^ 9 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_183.1, data_13_183.2] + +/-- Complete interval computation for depth 13, residue 184. -/ +theorem bounds_13_184 : exactInterval 13 184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_184 : oddCount 184 13 = 4 ∧ acceleratedOrbit 13 184 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 184) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_184.1, data_13_184.2] + +/-- Complete interval computation for depth 13, residue 185. -/ +theorem bounds_13_185 : exactInterval 13 185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_185 : oddCount 185 13 = 8 ∧ acceleratedOrbit 13 185 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 185) = 3 ^ 8 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_185.1, data_13_185.2] + +/-- Complete interval computation for depth 13, residue 186. -/ +theorem bounds_13_186 : exactInterval 13 186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_186 : oddCount 186 13 = 4 ∧ acceleratedOrbit 13 186 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 186) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_186.1, data_13_186.2] + +/-- Complete interval computation for depth 13, residue 187. -/ +theorem bounds_13_187 : exactInterval 13 187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_187 : oddCount 187 13 = 8 ∧ acceleratedOrbit 13 187 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 187) = 3 ^ 8 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_187.1, data_13_187.2] + +/-- Complete interval computation for depth 13, residue 188. -/ +theorem bounds_13_188 : exactInterval 13 188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_188 : oddCount 188 13 = 8 ∧ acceleratedOrbit 13 188 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 188) = 3 ^ 8 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_188.1, data_13_188.2] + +end Collatz.Research.StoppingAtlas.Batch0479 From ca47cf47219a3196b5c8cc17f11b0f1d986e6fa7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:34 +0530 Subject: [PATCH 0480/1001] proof: certify atlas Batch0480 (13:189 to 13:203) --- Collatz/Research/StoppingAtlas/Batch0480.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0480.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0480.lean b/Collatz/Research/StoppingAtlas/Batch0480.lean new file mode 100644 index 00000000..3aef29a7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0480.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0480 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 189. -/ +theorem bounds_13_189 : exactInterval 13 189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_189 : oddCount 189 13 = 8 ∧ acceleratedOrbit 13 189 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 189) = 3 ^ 8 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_189.1, data_13_189.2] + +/-- Complete interval computation for depth 13, residue 190. -/ +theorem bounds_13_190 : exactInterval 13 190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_190 : oddCount 190 13 = 8 ∧ acceleratedOrbit 13 190 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 190) = 3 ^ 8 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_190.1, data_13_190.2] + +/-- Complete interval computation for depth 13, residue 191. -/ +theorem bounds_13_191 : exactInterval 13 191 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 191) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_191 : oddCount 191 13 = 8 ∧ acceleratedOrbit 13 191 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 191) = 3 ^ 8 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_191.1, data_13_191.2] + +/-- Complete interval computation for depth 13, residue 192. -/ +theorem bounds_13_192 : exactInterval 13 192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_192 : oddCount 192 13 = 3 ∧ acceleratedOrbit 13 192 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 192) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_192.1, data_13_192.2] + +/-- Complete interval computation for depth 13, residue 193. -/ +theorem bounds_13_193 : exactInterval 13 193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_193 : oddCount 193 13 = 8 ∧ acceleratedOrbit 13 193 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 193) = 3 ^ 8 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_193.1, data_13_193.2] + +/-- Complete interval computation for depth 13, residue 194. -/ +theorem bounds_13_194 : exactInterval 13 194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_194 : oddCount 194 13 = 8 ∧ acceleratedOrbit 13 194 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 194) = 3 ^ 8 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_194.1, data_13_194.2] + +/-- Complete interval computation for depth 13, residue 195. -/ +theorem bounds_13_195 : exactInterval 13 195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_195 : oddCount 195 13 = 8 ∧ acceleratedOrbit 13 195 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 195) = 3 ^ 8 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_195.1, data_13_195.2] + +/-- Complete interval computation for depth 13, residue 196. -/ +theorem bounds_13_196 : exactInterval 13 196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_196 : oddCount 196 13 = 6 ∧ acceleratedOrbit 13 196 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 196) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_196.1, data_13_196.2] + +/-- Complete interval computation for depth 13, residue 197. -/ +theorem bounds_13_197 : exactInterval 13 197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_197 : oddCount 197 13 = 6 ∧ acceleratedOrbit 13 197 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 197) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_197.1, data_13_197.2] + +/-- Complete interval computation for depth 13, residue 198. -/ +theorem bounds_13_198 : exactInterval 13 198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_198 : oddCount 198 13 = 6 ∧ acceleratedOrbit 13 198 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 198) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_198.1, data_13_198.2] + +/-- Complete interval computation for depth 13, residue 199. -/ +theorem bounds_13_199 : exactInterval 13 199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_199 : oddCount 199 13 = 9 ∧ acceleratedOrbit 13 199 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 199) = 3 ^ 9 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_199.1, data_13_199.2] + +/-- Complete interval computation for depth 13, residue 200. -/ +theorem bounds_13_200 : exactInterval 13 200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_200 : oddCount 200 13 = 6 ∧ acceleratedOrbit 13 200 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 200) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_200.1, data_13_200.2] + +/-- Complete interval computation for depth 13, residue 201. -/ +theorem bounds_13_201 : exactInterval 13 201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_201 : oddCount 201 13 = 4 ∧ acceleratedOrbit 13 201 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 201) = 3 ^ 4 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_201.1, data_13_201.2] + +/-- Complete interval computation for depth 13, residue 202. -/ +theorem bounds_13_202 : exactInterval 13 202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_202 : oddCount 202 13 = 6 ∧ acceleratedOrbit 13 202 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 202) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_202.1, data_13_202.2] + +/-- Complete interval computation for depth 13, residue 203. -/ +theorem bounds_13_203 : exactInterval 13 203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_203 : oddCount 203 13 = 7 ∧ acceleratedOrbit 13 203 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 203) = 3 ^ 7 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_203.1, data_13_203.2] + +end Collatz.Research.StoppingAtlas.Batch0480 From 541a88ed520c6e1e1c425a2516a6055ac244e97d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:34 +0530 Subject: [PATCH 0481/1001] proof: certify atlas Batch0481 (13:204 to 13:219) --- Collatz/Research/StoppingAtlas/Batch0481.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0481.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0481.lean b/Collatz/Research/StoppingAtlas/Batch0481.lean new file mode 100644 index 00000000..027b31c9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0481.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0481 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 204. -/ +theorem bounds_13_204 : exactInterval 13 204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_204 : oddCount 204 13 = 6 ∧ acceleratedOrbit 13 204 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 204) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_204.1, data_13_204.2] + +/-- Complete interval computation for depth 13, residue 205. -/ +theorem bounds_13_205 : exactInterval 13 205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_205 : oddCount 205 13 = 6 ∧ acceleratedOrbit 13 205 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 205) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_205.1, data_13_205.2] + +/-- Complete interval computation for depth 13, residue 206. -/ +theorem bounds_13_206 : exactInterval 13 206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_206 : oddCount 206 13 = 8 ∧ acceleratedOrbit 13 206 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 206) = 3 ^ 8 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_206.1, data_13_206.2] + +/-- Complete interval computation for depth 13, residue 207. -/ +theorem bounds_13_207 : exactInterval 13 207 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 207) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_207 : oddCount 207 13 = 8 ∧ acceleratedOrbit 13 207 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 207) = 3 ^ 8 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_207.1, data_13_207.2] + +/-- Complete interval computation for depth 13, residue 208. -/ +theorem bounds_13_208 : exactInterval 13 208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_208 : oddCount 208 13 = 3 ∧ acceleratedOrbit 13 208 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 208) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_208.1, data_13_208.2] + +/-- Complete interval computation for depth 13, residue 209. -/ +theorem bounds_13_209 : exactInterval 13 209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_209 : oddCount 209 13 = 6 ∧ acceleratedOrbit 13 209 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 209) = 3 ^ 6 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_209.1, data_13_209.2] + +/-- Complete interval computation for depth 13, residue 210. -/ +theorem bounds_13_210 : exactInterval 13 210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_210 : oddCount 210 13 = 6 ∧ acceleratedOrbit 13 210 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 210) = 3 ^ 6 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_210.1, data_13_210.2] + +/-- Complete interval computation for depth 13, residue 211. -/ +theorem bounds_13_211 : exactInterval 13 211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_211 : oddCount 211 13 = 6 ∧ acceleratedOrbit 13 211 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 211) = 3 ^ 6 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_211.1, data_13_211.2] + +/-- Complete interval computation for depth 13, residue 212. -/ +theorem bounds_13_212 : exactInterval 13 212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_212 : oddCount 212 13 = 3 ∧ acceleratedOrbit 13 212 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 212) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_212.1, data_13_212.2] + +/-- Complete interval computation for depth 13, residue 213. -/ +theorem bounds_13_213 : exactInterval 13 213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_213 : oddCount 213 13 = 3 ∧ acceleratedOrbit 13 213 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 213) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_213.1, data_13_213.2] + +/-- Complete interval computation for depth 13, residue 214. -/ +theorem bounds_13_214 : exactInterval 13 214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_214 : oddCount 214 13 = 8 ∧ acceleratedOrbit 13 214 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 214) = 3 ^ 8 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_214.1, data_13_214.2] + +/-- Complete interval computation for depth 13, residue 215. -/ +theorem bounds_13_215 : exactInterval 13 215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 215) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_215 : oddCount 215 13 = 8 ∧ acceleratedOrbit 13 215 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 215) = 3 ^ 8 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_215.1, data_13_215.2] + +/-- Complete interval computation for depth 13, residue 216. -/ +theorem bounds_13_216 : exactInterval 13 216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_216 : oddCount 216 13 = 8 ∧ acceleratedOrbit 13 216 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 216) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_216.1, data_13_216.2] + +/-- Complete interval computation for depth 13, residue 217. -/ +theorem bounds_13_217 : exactInterval 13 217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_217 : oddCount 217 13 = 6 ∧ acceleratedOrbit 13 217 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 217) = 3 ^ 6 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_217.1, data_13_217.2] + +/-- Complete interval computation for depth 13, residue 218. -/ +theorem bounds_13_218 : exactInterval 13 218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_218 : oddCount 218 13 = 8 ∧ acceleratedOrbit 13 218 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 218) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_218.1, data_13_218.2] + +/-- Complete interval computation for depth 13, residue 219. -/ +theorem bounds_13_219 : exactInterval 13 219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_219 : oddCount 219 13 = 7 ∧ acceleratedOrbit 13 219 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 219) = 3 ^ 7 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_219.1, data_13_219.2] + +end Collatz.Research.StoppingAtlas.Batch0481 From 7ea362a318f87aa61f93da7b389305e29a7af03b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:34 +0530 Subject: [PATCH 0482/1001] proof: certify atlas Batch0482 (13:220 to 13:234) --- Collatz/Research/StoppingAtlas/Batch0482.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0482.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0482.lean b/Collatz/Research/StoppingAtlas/Batch0482.lean new file mode 100644 index 00000000..a3c4cfed --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0482.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0482 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 220. -/ +theorem bounds_13_220 : exactInterval 13 220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_220 : oddCount 220 13 = 8 ∧ acceleratedOrbit 13 220 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 220) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_220.1, data_13_220.2] + +/-- Complete interval computation for depth 13, residue 221. -/ +theorem bounds_13_221 : exactInterval 13 221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_221 : oddCount 221 13 = 8 ∧ acceleratedOrbit 13 221 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 221) = 3 ^ 8 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_221.1, data_13_221.2] + +/-- Complete interval computation for depth 13, residue 222. -/ +theorem bounds_13_222 : exactInterval 13 222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_222 : oddCount 222 13 = 10 ∧ acceleratedOrbit 13 222 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 222) = 3 ^ 10 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_222.1, data_13_222.2] + +/-- Complete interval computation for depth 13, residue 223. -/ +theorem bounds_13_223 : exactInterval 13 223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_223 : oddCount 223 13 = 10 ∧ acceleratedOrbit 13 223 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 223) = 3 ^ 10 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_223.1, data_13_223.2] + +/-- Complete interval computation for depth 13, residue 224. -/ +theorem bounds_13_224 : exactInterval 13 224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_224 : oddCount 224 13 = 5 ∧ acceleratedOrbit 13 224 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 224) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_224.1, data_13_224.2] + +/-- Complete interval computation for depth 13, residue 225. -/ +theorem bounds_13_225 : exactInterval 13 225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_225 : oddCount 225 13 = 10 ∧ acceleratedOrbit 13 225 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 225) = 3 ^ 10 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_225.1, data_13_225.2] + +/-- Complete interval computation for depth 13, residue 226. -/ +theorem bounds_13_226 : exactInterval 13 226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_226 : oddCount 226 13 = 3 ∧ acceleratedOrbit 13 226 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 226) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_226.1, data_13_226.2] + +/-- Complete interval computation for depth 13, residue 227. -/ +theorem bounds_13_227 : exactInterval 13 227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_227 : oddCount 227 13 = 3 ∧ acceleratedOrbit 13 227 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 227) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_227.1, data_13_227.2] + +/-- Complete interval computation for depth 13, residue 228. -/ +theorem bounds_13_228 : exactInterval 13 228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_228 : oddCount 228 13 = 5 ∧ acceleratedOrbit 13 228 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 228) = 3 ^ 5 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_228.1, data_13_228.2] + +/-- Complete interval computation for depth 13, residue 229. -/ +theorem bounds_13_229 : exactInterval 13 229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_229 : oddCount 229 13 = 5 ∧ acceleratedOrbit 13 229 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 229) = 3 ^ 5 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_229.1, data_13_229.2] + +/-- Complete interval computation for depth 13, residue 230. -/ +theorem bounds_13_230 : exactInterval 13 230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_230 : oddCount 230 13 = 5 ∧ acceleratedOrbit 13 230 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 230) = 3 ^ 5 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_230.1, data_13_230.2] + +/-- Complete interval computation for depth 13, residue 231. -/ +theorem bounds_13_231 : exactInterval 13 231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_231 : oddCount 231 13 = 7 ∧ acceleratedOrbit 13 231 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 231) = 3 ^ 7 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_231.1, data_13_231.2] + +/-- Complete interval computation for depth 13, residue 232. -/ +theorem bounds_13_232 : exactInterval 13 232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_232 : oddCount 232 13 = 5 ∧ acceleratedOrbit 13 232 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 232) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_232.1, data_13_232.2] + +/-- Complete interval computation for depth 13, residue 233. -/ +theorem bounds_13_233 : exactInterval 13 233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_233 : oddCount 233 13 = 9 ∧ acceleratedOrbit 13 233 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 233) = 3 ^ 9 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_233.1, data_13_233.2] + +/-- Complete interval computation for depth 13, residue 234. -/ +theorem bounds_13_234 : exactInterval 13 234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_234 : oddCount 234 13 = 5 ∧ acceleratedOrbit 13 234 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 234) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_234.1, data_13_234.2] + +end Collatz.Research.StoppingAtlas.Batch0482 From fde64362574203515fce341669f926e88fa306d3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:35 +0530 Subject: [PATCH 0483/1001] proof: certify atlas Batch0483 (13:235 to 13:249) --- Collatz/Research/StoppingAtlas/Batch0483.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0483.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0483.lean b/Collatz/Research/StoppingAtlas/Batch0483.lean new file mode 100644 index 00000000..e7e06602 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0483.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0483 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 235. -/ +theorem bounds_13_235 : exactInterval 13 235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_235 : oddCount 235 13 = 8 ∧ acceleratedOrbit 13 235 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 235) = 3 ^ 8 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_235.1, data_13_235.2] + +/-- Complete interval computation for depth 13, residue 236. -/ +theorem bounds_13_236 : exactInterval 13 236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_236 : oddCount 236 13 = 6 ∧ acceleratedOrbit 13 236 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 236) = 3 ^ 6 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_236.1, data_13_236.2] + +/-- Complete interval computation for depth 13, residue 237. -/ +theorem bounds_13_237 : exactInterval 13 237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_237 : oddCount 237 13 = 6 ∧ acceleratedOrbit 13 237 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 237) = 3 ^ 6 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_237.1, data_13_237.2] + +/-- Complete interval computation for depth 13, residue 238. -/ +theorem bounds_13_238 : exactInterval 13 238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_238 : oddCount 238 13 = 6 ∧ acceleratedOrbit 13 238 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 238) = 3 ^ 6 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_238.1, data_13_238.2] + +/-- Complete interval computation for depth 13, residue 239. -/ +theorem bounds_13_239 : exactInterval 13 239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_239 : oddCount 239 13 = 9 ∧ acceleratedOrbit 13 239 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 239) = 3 ^ 9 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_239.1, data_13_239.2] + +/-- Complete interval computation for depth 13, residue 240. -/ +theorem bounds_13_240 : exactInterval 13 240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_240 : oddCount 240 13 = 5 ∧ acceleratedOrbit 13 240 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 240) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_240.1, data_13_240.2] + +/-- Complete interval computation for depth 13, residue 241. -/ +theorem bounds_13_241 : exactInterval 13 241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_241 : oddCount 241 13 = 5 ∧ acceleratedOrbit 13 241 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 241) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_241.1, data_13_241.2] + +/-- Complete interval computation for depth 13, residue 242. -/ +theorem bounds_13_242 : exactInterval 13 242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_242 : oddCount 242 13 = 9 ∧ acceleratedOrbit 13 242 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 242) = 3 ^ 9 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_242.1, data_13_242.2] + +/-- Complete interval computation for depth 13, residue 243. -/ +theorem bounds_13_243 : exactInterval 13 243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_243 : oddCount 243 13 = 9 ∧ acceleratedOrbit 13 243 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 243) = 3 ^ 9 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_243.1, data_13_243.2] + +/-- Complete interval computation for depth 13, residue 244. -/ +theorem bounds_13_244 : exactInterval 13 244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_244 : oddCount 244 13 = 5 ∧ acceleratedOrbit 13 244 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 244) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_244.1, data_13_244.2] + +/-- Complete interval computation for depth 13, residue 245. -/ +theorem bounds_13_245 : exactInterval 13 245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_245 : oddCount 245 13 = 5 ∧ acceleratedOrbit 13 245 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 245) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_245.1, data_13_245.2] + +/-- Complete interval computation for depth 13, residue 246. -/ +theorem bounds_13_246 : exactInterval 13 246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_246 : oddCount 246 13 = 7 ∧ acceleratedOrbit 13 246 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 246) = 3 ^ 7 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_246.1, data_13_246.2] + +/-- Complete interval computation for depth 13, residue 247. -/ +theorem bounds_13_247 : exactInterval 13 247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_247 : oddCount 247 13 = 7 ∧ acceleratedOrbit 13 247 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 247) = 3 ^ 7 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_247.1, data_13_247.2] + +/-- Complete interval computation for depth 13, residue 248. -/ +theorem bounds_13_248 : exactInterval 13 248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_248 : oddCount 248 13 = 8 ∧ acceleratedOrbit 13 248 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 248) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_248.1, data_13_248.2] + +/-- Complete interval computation for depth 13, residue 249. -/ +theorem bounds_13_249 : exactInterval 13 249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_249 : oddCount 249 13 = 8 ∧ acceleratedOrbit 13 249 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 249) = 3 ^ 8 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_249.1, data_13_249.2] + +end Collatz.Research.StoppingAtlas.Batch0483 From f60551559ac51029c710100600eec885256f538d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:35 +0530 Subject: [PATCH 0484/1001] proof: certify atlas Batch0484 (13:250 to 13:265) --- Collatz/Research/StoppingAtlas/Batch0484.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0484.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0484.lean b/Collatz/Research/StoppingAtlas/Batch0484.lean new file mode 100644 index 00000000..1046f896 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0484.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0484 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 250. -/ +theorem bounds_13_250 : exactInterval 13 250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_250 : oddCount 250 13 = 8 ∧ acceleratedOrbit 13 250 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 250) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_250.1, data_13_250.2] + +/-- Complete interval computation for depth 13, residue 251. -/ +theorem bounds_13_251 : exactInterval 13 251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_251 : oddCount 251 13 = 10 ∧ acceleratedOrbit 13 251 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 251) = 3 ^ 10 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_251.1, data_13_251.2] + +/-- Complete interval computation for depth 13, residue 252. -/ +theorem bounds_13_252 : exactInterval 13 252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_252 : oddCount 252 13 = 8 ∧ acceleratedOrbit 13 252 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 252) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_252.1, data_13_252.2] + +/-- Complete interval computation for depth 13, residue 253. -/ +theorem bounds_13_253 : exactInterval 13 253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_253 : oddCount 253 13 = 8 ∧ acceleratedOrbit 13 253 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 253) = 3 ^ 8 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_253.1, data_13_253.2] + +/-- Complete interval computation for depth 13, residue 254. -/ +theorem bounds_13_254 : exactInterval 13 254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_254 : oddCount 254 13 = 8 ∧ acceleratedOrbit 13 254 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 254) = 3 ^ 8 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_254.1, data_13_254.2] + +/-- Complete interval computation for depth 13, residue 255. -/ +theorem bounds_13_255 : exactInterval 13 255 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 255) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_255 : oddCount 255 13 = 8 ∧ acceleratedOrbit 13 255 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 255) = 3 ^ 8 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_255.1, data_13_255.2] + +/-- Complete interval computation for depth 13, residue 256. -/ +theorem bounds_13_256 : exactInterval 13 256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_256 : oddCount 256 13 = 3 ∧ acceleratedOrbit 13 256 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 256) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_256.1, data_13_256.2] + +/-- Complete interval computation for depth 13, residue 257. -/ +theorem bounds_13_257 : exactInterval 13 257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_257 : oddCount 257 13 = 7 ∧ acceleratedOrbit 13 257 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 257) = 3 ^ 7 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_257.1, data_13_257.2] + +/-- Complete interval computation for depth 13, residue 258. -/ +theorem bounds_13_258 : exactInterval 13 258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_258 : oddCount 258 13 = 7 ∧ acceleratedOrbit 13 258 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 258) = 3 ^ 7 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_258.1, data_13_258.2] + +/-- Complete interval computation for depth 13, residue 259. -/ +theorem bounds_13_259 : exactInterval 13 259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_259 : oddCount 259 13 = 7 ∧ acceleratedOrbit 13 259 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 259) = 3 ^ 7 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_259.1, data_13_259.2] + +/-- Complete interval computation for depth 13, residue 260. -/ +theorem bounds_13_260 : exactInterval 13 260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_260 : oddCount 260 13 = 6 ∧ acceleratedOrbit 13 260 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 260) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_260.1, data_13_260.2] + +/-- Complete interval computation for depth 13, residue 261. -/ +theorem bounds_13_261 : exactInterval 13 261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_261 : oddCount 261 13 = 6 ∧ acceleratedOrbit 13 261 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 261) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_261.1, data_13_261.2] + +/-- Complete interval computation for depth 13, residue 262. -/ +theorem bounds_13_262 : exactInterval 13 262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_262 : oddCount 262 13 = 6 ∧ acceleratedOrbit 13 262 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 262) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_262.1, data_13_262.2] + +/-- Complete interval computation for depth 13, residue 263. -/ +theorem bounds_13_263 : exactInterval 13 263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_263 : oddCount 263 13 = 9 ∧ acceleratedOrbit 13 263 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 263) = 3 ^ 9 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_263.1, data_13_263.2] + +/-- Complete interval computation for depth 13, residue 264. -/ +theorem bounds_13_264 : exactInterval 13 264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_264 : oddCount 264 13 = 6 ∧ acceleratedOrbit 13 264 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 264) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_264.1, data_13_264.2] + +/-- Complete interval computation for depth 13, residue 265. -/ +theorem bounds_13_265 : exactInterval 13 265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_265 : oddCount 265 13 = 8 ∧ acceleratedOrbit 13 265 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 265) = 3 ^ 8 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_265.1, data_13_265.2] + +end Collatz.Research.StoppingAtlas.Batch0484 From 8e0bb27ac0bdf2fb6772ab1025df882c8ae2c67b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:35 +0530 Subject: [PATCH 0485/1001] proof: certify atlas Batch0485 (13:266 to 13:280) --- Collatz/Research/StoppingAtlas/Batch0485.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0485.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0485.lean b/Collatz/Research/StoppingAtlas/Batch0485.lean new file mode 100644 index 00000000..52de6ba0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0485.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0485 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 266. -/ +theorem bounds_13_266 : exactInterval 13 266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_266 : oddCount 266 13 = 6 ∧ acceleratedOrbit 13 266 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 266) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_266.1, data_13_266.2] + +/-- Complete interval computation for depth 13, residue 267. -/ +theorem bounds_13_267 : exactInterval 13 267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_267 : oddCount 267 13 = 5 ∧ acceleratedOrbit 13 267 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 267) = 3 ^ 5 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_267.1, data_13_267.2] + +/-- Complete interval computation for depth 13, residue 268. -/ +theorem bounds_13_268 : exactInterval 13 268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_268 : oddCount 268 13 = 6 ∧ acceleratedOrbit 13 268 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 268) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_268.1, data_13_268.2] + +/-- Complete interval computation for depth 13, residue 269. -/ +theorem bounds_13_269 : exactInterval 13 269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_269 : oddCount 269 13 = 6 ∧ acceleratedOrbit 13 269 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 269) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_269.1, data_13_269.2] + +/-- Complete interval computation for depth 13, residue 270. -/ +theorem bounds_13_270 : exactInterval 13 270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_270 : oddCount 270 13 = 7 ∧ acceleratedOrbit 13 270 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 270) = 3 ^ 7 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_270.1, data_13_270.2] + +/-- Complete interval computation for depth 13, residue 271. -/ +theorem bounds_13_271 : exactInterval 13 271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_271 : oddCount 271 13 = 7 ∧ acceleratedOrbit 13 271 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 271) = 3 ^ 7 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_271.1, data_13_271.2] + +/-- Complete interval computation for depth 13, residue 272. -/ +theorem bounds_13_272 : exactInterval 13 272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_272 : oddCount 272 13 = 3 ∧ acceleratedOrbit 13 272 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 272) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_272.1, data_13_272.2] + +/-- Complete interval computation for depth 13, residue 273. -/ +theorem bounds_13_273 : exactInterval 13 273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_273 : oddCount 273 13 = 6 ∧ acceleratedOrbit 13 273 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 273) = 3 ^ 6 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_273.1, data_13_273.2] + +/-- Complete interval computation for depth 13, residue 274. -/ +theorem bounds_13_274 : exactInterval 13 274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_274 : oddCount 274 13 = 9 ∧ acceleratedOrbit 13 274 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 274) = 3 ^ 9 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_274.1, data_13_274.2] + +/-- Complete interval computation for depth 13, residue 275. -/ +theorem bounds_13_275 : exactInterval 13 275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_275 : oddCount 275 13 = 9 ∧ acceleratedOrbit 13 275 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 275) = 3 ^ 9 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_275.1, data_13_275.2] + +/-- Complete interval computation for depth 13, residue 276. -/ +theorem bounds_13_276 : exactInterval 13 276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_276 : oddCount 276 13 = 3 ∧ acceleratedOrbit 13 276 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 276) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_276.1, data_13_276.2] + +/-- Complete interval computation for depth 13, residue 277. -/ +theorem bounds_13_277 : exactInterval 13 277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_277 : oddCount 277 13 = 3 ∧ acceleratedOrbit 13 277 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 277) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_277.1, data_13_277.2] + +/-- Complete interval computation for depth 13, residue 278. -/ +theorem bounds_13_278 : exactInterval 13 278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_278 : oddCount 278 13 = 7 ∧ acceleratedOrbit 13 278 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 278) = 3 ^ 7 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_278.1, data_13_278.2] + +/-- Complete interval computation for depth 13, residue 279. -/ +theorem bounds_13_279 : exactInterval 13 279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_279 : oddCount 279 13 = 7 ∧ acceleratedOrbit 13 279 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 279) = 3 ^ 7 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_279.1, data_13_279.2] + +/-- Complete interval computation for depth 13, residue 280. -/ +theorem bounds_13_280 : exactInterval 13 280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_280 : oddCount 280 13 = 3 ∧ acceleratedOrbit 13 280 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 280) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_280.1, data_13_280.2] + +end Collatz.Research.StoppingAtlas.Batch0485 From cd46f523c4e73f13a6b9c0a73f524129dc1c55cf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:35 +0530 Subject: [PATCH 0486/1001] proof: certify atlas Batch0486 (13:281 to 13:295) --- Collatz/Research/StoppingAtlas/Batch0486.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0486.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0486.lean b/Collatz/Research/StoppingAtlas/Batch0486.lean new file mode 100644 index 00000000..a9eff3be --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0486.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0486 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 281. -/ +theorem bounds_13_281 : exactInterval 13 281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_281 : oddCount 281 13 = 7 ∧ acceleratedOrbit 13 281 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 281) = 3 ^ 7 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_281.1, data_13_281.2] + +/-- Complete interval computation for depth 13, residue 282. -/ +theorem bounds_13_282 : exactInterval 13 282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_282 : oddCount 282 13 = 3 ∧ acceleratedOrbit 13 282 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 282) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_282.1, data_13_282.2] + +/-- Complete interval computation for depth 13, residue 283. -/ +theorem bounds_13_283 : exactInterval 13 283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_283 : oddCount 283 13 = 10 ∧ acceleratedOrbit 13 283 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 283) = 3 ^ 10 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_283.1, data_13_283.2] + +/-- Complete interval computation for depth 13, residue 284. -/ +theorem bounds_13_284 : exactInterval 13 284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_284 : oddCount 284 13 = 8 ∧ acceleratedOrbit 13 284 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 284) = 3 ^ 8 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_284.1, data_13_284.2] + +/-- Complete interval computation for depth 13, residue 285. -/ +theorem bounds_13_285 : exactInterval 13 285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_285 : oddCount 285 13 = 8 ∧ acceleratedOrbit 13 285 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 285) = 3 ^ 8 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_285.1, data_13_285.2] + +/-- Complete interval computation for depth 13, residue 286. -/ +theorem bounds_13_286 : exactInterval 13 286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_286 : oddCount 286 13 = 8 ∧ acceleratedOrbit 13 286 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 286) = 3 ^ 8 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_286.1, data_13_286.2] + +/-- Complete interval computation for depth 13, residue 287. -/ +theorem bounds_13_287 : exactInterval 13 287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_287 : oddCount 287 13 = 7 ∧ acceleratedOrbit 13 287 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 287) = 3 ^ 7 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_287.1, data_13_287.2] + +/-- Complete interval computation for depth 13, residue 288. -/ +theorem bounds_13_288 : exactInterval 13 288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_288 : oddCount 288 13 = 5 ∧ acceleratedOrbit 13 288 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 288) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_288.1, data_13_288.2] + +/-- Complete interval computation for depth 13, residue 289. -/ +theorem bounds_13_289 : exactInterval 13 289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_289 : oddCount 289 13 = 7 ∧ acceleratedOrbit 13 289 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 289) = 3 ^ 7 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_289.1, data_13_289.2] + +/-- Complete interval computation for depth 13, residue 290. -/ +theorem bounds_13_290 : exactInterval 13 290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_290 : oddCount 290 13 = 8 ∧ acceleratedOrbit 13 290 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 290) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_290.1, data_13_290.2] + +/-- Complete interval computation for depth 13, residue 291. -/ +theorem bounds_13_291 : exactInterval 13 291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_291 : oddCount 291 13 = 8 ∧ acceleratedOrbit 13 291 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 291) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_291.1, data_13_291.2] + +/-- Complete interval computation for depth 13, residue 292. -/ +theorem bounds_13_292 : exactInterval 13 292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_292 : oddCount 292 13 = 8 ∧ acceleratedOrbit 13 292 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 292) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_292.1, data_13_292.2] + +/-- Complete interval computation for depth 13, residue 293. -/ +theorem bounds_13_293 : exactInterval 13 293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_293 : oddCount 293 13 = 8 ∧ acceleratedOrbit 13 293 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 293) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_293.1, data_13_293.2] + +/-- Complete interval computation for depth 13, residue 294. -/ +theorem bounds_13_294 : exactInterval 13 294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_294 : oddCount 294 13 = 8 ∧ acceleratedOrbit 13 294 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 294) = 3 ^ 8 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_294.1, data_13_294.2] + +/-- Complete interval computation for depth 13, residue 295. -/ +theorem bounds_13_295 : exactInterval 13 295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_295 : oddCount 295 13 = 8 ∧ acceleratedOrbit 13 295 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 295) = 3 ^ 8 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_295.1, data_13_295.2] + +end Collatz.Research.StoppingAtlas.Batch0486 From b2d14d7119d09596cc89f00f06bd8fae0fc0fd3d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:24:36 +0530 Subject: [PATCH 0487/1001] proof: certify atlas Batch0487 (13:296 to 13:311) --- Collatz/Research/StoppingAtlas/Batch0487.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0487.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0487.lean b/Collatz/Research/StoppingAtlas/Batch0487.lean new file mode 100644 index 00000000..dca1a0f0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0487.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0487 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 296. -/ +theorem bounds_13_296 : exactInterval 13 296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_296 : oddCount 296 13 = 5 ∧ acceleratedOrbit 13 296 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 296) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_296.1, data_13_296.2] + +/-- Complete interval computation for depth 13, residue 297. -/ +theorem bounds_13_297 : exactInterval 13 297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_297 : oddCount 297 13 = 9 ∧ acceleratedOrbit 13 297 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 297) = 3 ^ 9 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_297.1, data_13_297.2] + +/-- Complete interval computation for depth 13, residue 298. -/ +theorem bounds_13_298 : exactInterval 13 298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_298 : oddCount 298 13 = 5 ∧ acceleratedOrbit 13 298 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 298) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_298.1, data_13_298.2] + +/-- Complete interval computation for depth 13, residue 299. -/ +theorem bounds_13_299 : exactInterval 13 299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_299 : oddCount 299 13 = 9 ∧ acceleratedOrbit 13 299 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 299) = 3 ^ 9 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_299.1, data_13_299.2] + +/-- Complete interval computation for depth 13, residue 300. -/ +theorem bounds_13_300 : exactInterval 13 300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_300 : oddCount 300 13 = 3 ∧ acceleratedOrbit 13 300 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 300) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_300.1, data_13_300.2] + +/-- Complete interval computation for depth 13, residue 301. -/ +theorem bounds_13_301 : exactInterval 13 301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_301 : oddCount 301 13 = 3 ∧ acceleratedOrbit 13 301 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 301) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_301.1, data_13_301.2] + +/-- Complete interval computation for depth 13, residue 302. -/ +theorem bounds_13_302 : exactInterval 13 302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_302 : oddCount 302 13 = 3 ∧ acceleratedOrbit 13 302 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 302) = 3 ^ 3 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_302.1, data_13_302.2] + +/-- Complete interval computation for depth 13, residue 303. -/ +theorem bounds_13_303 : exactInterval 13 303 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 303) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_303 : oddCount 303 13 = 8 ∧ acceleratedOrbit 13 303 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 303) = 3 ^ 8 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_303.1, data_13_303.2] + +/-- Complete interval computation for depth 13, residue 304. -/ +theorem bounds_13_304 : exactInterval 13 304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_304 : oddCount 304 13 = 5 ∧ acceleratedOrbit 13 304 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 304) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_304.1, data_13_304.2] + +/-- Complete interval computation for depth 13, residue 305. -/ +theorem bounds_13_305 : exactInterval 13 305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_305 : oddCount 305 13 = 6 ∧ acceleratedOrbit 13 305 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 305) = 3 ^ 6 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_305.1, data_13_305.2] + +/-- Complete interval computation for depth 13, residue 306. -/ +theorem bounds_13_306 : exactInterval 13 306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_306 : oddCount 306 13 = 6 ∧ acceleratedOrbit 13 306 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 306) = 3 ^ 6 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_306.1, data_13_306.2] + +/-- Complete interval computation for depth 13, residue 307. -/ +theorem bounds_13_307 : exactInterval 13 307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_307 : oddCount 307 13 = 6 ∧ acceleratedOrbit 13 307 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 307) = 3 ^ 6 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_307.1, data_13_307.2] + +/-- Complete interval computation for depth 13, residue 308. -/ +theorem bounds_13_308 : exactInterval 13 308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_308 : oddCount 308 13 = 5 ∧ acceleratedOrbit 13 308 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 308) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_308.1, data_13_308.2] + +/-- Complete interval computation for depth 13, residue 309. -/ +theorem bounds_13_309 : exactInterval 13 309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_309 : oddCount 309 13 = 5 ∧ acceleratedOrbit 13 309 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 309) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_309.1, data_13_309.2] + +/-- Complete interval computation for depth 13, residue 310. -/ +theorem bounds_13_310 : exactInterval 13 310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_310 : oddCount 310 13 = 8 ∧ acceleratedOrbit 13 310 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 310) = 3 ^ 8 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_310.1, data_13_310.2] + +/-- Complete interval computation for depth 13, residue 311. -/ +theorem bounds_13_311 : exactInterval 13 311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_311 : oddCount 311 13 = 8 ∧ acceleratedOrbit 13 311 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 311) = 3 ^ 8 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_311.1, data_13_311.2] + +end Collatz.Research.StoppingAtlas.Batch0487 From a0e351b5d978331c7dfaf9746cfb760bb862e8bb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:30:57 +0530 Subject: [PATCH 0488/1001] proof: certify atlas Batch0488 (13:312 to 13:326) --- Collatz/Research/StoppingAtlas/Batch0488.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0488.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0488.lean b/Collatz/Research/StoppingAtlas/Batch0488.lean new file mode 100644 index 00000000..9535461b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0488.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0488 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 312. -/ +theorem bounds_13_312 : exactInterval 13 312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_312 : oddCount 312 13 = 6 ∧ acceleratedOrbit 13 312 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 312) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_312.1, data_13_312.2] + +/-- Complete interval computation for depth 13, residue 313. -/ +theorem bounds_13_313 : exactInterval 13 313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_313 : oddCount 313 13 = 8 ∧ acceleratedOrbit 13 313 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 313) = 3 ^ 8 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_313.1, data_13_313.2] + +/-- Complete interval computation for depth 13, residue 314. -/ +theorem bounds_13_314 : exactInterval 13 314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_314 : oddCount 314 13 = 6 ∧ acceleratedOrbit 13 314 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 314) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_314.1, data_13_314.2] + +/-- Complete interval computation for depth 13, residue 315. -/ +theorem bounds_13_315 : exactInterval 13 315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_315 : oddCount 315 13 = 6 ∧ acceleratedOrbit 13 315 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 315) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_315.1, data_13_315.2] + +/-- Complete interval computation for depth 13, residue 316. -/ +theorem bounds_13_316 : exactInterval 13 316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_316 : oddCount 316 13 = 6 ∧ acceleratedOrbit 13 316 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 316) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_316.1, data_13_316.2] + +/-- Complete interval computation for depth 13, residue 317. -/ +theorem bounds_13_317 : exactInterval 13 317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_317 : oddCount 317 13 = 6 ∧ acceleratedOrbit 13 317 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 317) = 3 ^ 6 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_317.1, data_13_317.2] + +/-- Complete interval computation for depth 13, residue 318. -/ +theorem bounds_13_318 : exactInterval 13 318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_318 : oddCount 318 13 = 10 ∧ acceleratedOrbit 13 318 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 318) = 3 ^ 10 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_318.1, data_13_318.2] + +/-- Complete interval computation for depth 13, residue 319. -/ +theorem bounds_13_319 : exactInterval 13 319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_319 : oddCount 319 13 = 10 ∧ acceleratedOrbit 13 319 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 319) = 3 ^ 10 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_319.1, data_13_319.2] + +/-- Complete interval computation for depth 13, residue 320. -/ +theorem bounds_13_320 : exactInterval 13 320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_320 : oddCount 320 13 = 3 ∧ acceleratedOrbit 13 320 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 320) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_320.1, data_13_320.2] + +/-- Complete interval computation for depth 13, residue 321. -/ +theorem bounds_13_321 : exactInterval 13 321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_321 : oddCount 321 13 = 5 ∧ acceleratedOrbit 13 321 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 321) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_321.1, data_13_321.2] + +/-- Complete interval computation for depth 13, residue 322. -/ +theorem bounds_13_322 : exactInterval 13 322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_322 : oddCount 322 13 = 8 ∧ acceleratedOrbit 13 322 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 322) = 3 ^ 8 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_322.1, data_13_322.2] + +/-- Complete interval computation for depth 13, residue 323. -/ +theorem bounds_13_323 : exactInterval 13 323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_323 : oddCount 323 13 = 8 ∧ acceleratedOrbit 13 323 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 323) = 3 ^ 8 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_323.1, data_13_323.2] + +/-- Complete interval computation for depth 13, residue 324. -/ +theorem bounds_13_324 : exactInterval 13 324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_324 : oddCount 324 13 = 5 ∧ acceleratedOrbit 13 324 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 324) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_324.1, data_13_324.2] + +/-- Complete interval computation for depth 13, residue 325. -/ +theorem bounds_13_325 : exactInterval 13 325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_325 : oddCount 325 13 = 5 ∧ acceleratedOrbit 13 325 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 325) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_325.1, data_13_325.2] + +/-- Complete interval computation for depth 13, residue 326. -/ +theorem bounds_13_326 : exactInterval 13 326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_326 : oddCount 326 13 = 5 ∧ acceleratedOrbit 13 326 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 326) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_326.1, data_13_326.2] + +end Collatz.Research.StoppingAtlas.Batch0488 From b8b779b53a3f15879f0d91dd75ae712fe6b72248 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:30:58 +0530 Subject: [PATCH 0489/1001] proof: certify atlas Batch0489 (13:327 to 13:342) --- Collatz/Research/StoppingAtlas/Batch0489.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0489.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0489.lean b/Collatz/Research/StoppingAtlas/Batch0489.lean new file mode 100644 index 00000000..0ae2dd96 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0489.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0489 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 327. -/ +theorem bounds_13_327 : exactInterval 13 327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_327 : oddCount 327 13 = 10 ∧ acceleratedOrbit 13 327 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 327) = 3 ^ 10 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_327.1, data_13_327.2] + +/-- Complete interval computation for depth 13, residue 328. -/ +theorem bounds_13_328 : exactInterval 13 328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_328 : oddCount 328 13 = 7 ∧ acceleratedOrbit 13 328 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 328) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_328.1, data_13_328.2] + +/-- Complete interval computation for depth 13, residue 329. -/ +theorem bounds_13_329 : exactInterval 13 329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_329 : oddCount 329 13 = 7 ∧ acceleratedOrbit 13 329 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 329) = 3 ^ 7 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_329.1, data_13_329.2] + +/-- Complete interval computation for depth 13, residue 330. -/ +theorem bounds_13_330 : exactInterval 13 330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_330 : oddCount 330 13 = 7 ∧ acceleratedOrbit 13 330 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 330) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_330.1, data_13_330.2] + +/-- Complete interval computation for depth 13, residue 331. -/ +theorem bounds_13_331 : exactInterval 13 331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_331 : oddCount 331 13 = 5 ∧ acceleratedOrbit 13 331 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 331) = 3 ^ 5 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_331.1, data_13_331.2] + +/-- Complete interval computation for depth 13, residue 332. -/ +theorem bounds_13_332 : exactInterval 13 332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_332 : oddCount 332 13 = 7 ∧ acceleratedOrbit 13 332 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 332) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_332.1, data_13_332.2] + +/-- Complete interval computation for depth 13, residue 333. -/ +theorem bounds_13_333 : exactInterval 13 333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_333 : oddCount 333 13 = 7 ∧ acceleratedOrbit 13 333 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 333) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_333.1, data_13_333.2] + +/-- Complete interval computation for depth 13, residue 334. -/ +theorem bounds_13_334 : exactInterval 13 334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_334 : oddCount 334 13 = 10 ∧ acceleratedOrbit 13 334 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 334) = 3 ^ 10 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_334.1, data_13_334.2] + +/-- Complete interval computation for depth 13, residue 335. -/ +theorem bounds_13_335 : exactInterval 13 335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_335 : oddCount 335 13 = 10 ∧ acceleratedOrbit 13 335 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 335) = 3 ^ 10 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_335.1, data_13_335.2] + +/-- Complete interval computation for depth 13, residue 336. -/ +theorem bounds_13_336 : exactInterval 13 336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_336 : oddCount 336 13 = 3 ∧ acceleratedOrbit 13 336 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 336) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_336.1, data_13_336.2] + +/-- Complete interval computation for depth 13, residue 337. -/ +theorem bounds_13_337 : exactInterval 13 337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_337 : oddCount 337 13 = 7 ∧ acceleratedOrbit 13 337 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 337) = 3 ^ 7 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_337.1, data_13_337.2] + +/-- Complete interval computation for depth 13, residue 338. -/ +theorem bounds_13_338 : exactInterval 13 338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_338 : oddCount 338 13 = 9 ∧ acceleratedOrbit 13 338 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 338) = 3 ^ 9 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_338.1, data_13_338.2] + +/-- Complete interval computation for depth 13, residue 339. -/ +theorem bounds_13_339 : exactInterval 13 339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_339 : oddCount 339 13 = 9 ∧ acceleratedOrbit 13 339 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 339) = 3 ^ 9 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_339.1, data_13_339.2] + +/-- Complete interval computation for depth 13, residue 340. -/ +theorem bounds_13_340 : exactInterval 13 340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_340 : oddCount 340 13 = 3 ∧ acceleratedOrbit 13 340 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 340) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_340.1, data_13_340.2] + +/-- Complete interval computation for depth 13, residue 341. -/ +theorem bounds_13_341 : exactInterval 13 341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_341 : oddCount 341 13 = 3 ∧ acceleratedOrbit 13 341 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 341) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_341.1, data_13_341.2] + +/-- Complete interval computation for depth 13, residue 342. -/ +theorem bounds_13_342 : exactInterval 13 342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_342 : oddCount 342 13 = 6 ∧ acceleratedOrbit 13 342 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 342) = 3 ^ 6 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_342.1, data_13_342.2] + +end Collatz.Research.StoppingAtlas.Batch0489 From 2ad83e23eed8c52fd987d6b98425638f84f02cab Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:30:58 +0530 Subject: [PATCH 0490/1001] proof: certify atlas Batch0490 (13:343 to 13:357) --- Collatz/Research/StoppingAtlas/Batch0490.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0490.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0490.lean b/Collatz/Research/StoppingAtlas/Batch0490.lean new file mode 100644 index 00000000..657689d8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0490.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0490 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 343. -/ +theorem bounds_13_343 : exactInterval 13 343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_343 : oddCount 343 13 = 6 ∧ acceleratedOrbit 13 343 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 343) = 3 ^ 6 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_343.1, data_13_343.2] + +/-- Complete interval computation for depth 13, residue 344. -/ +theorem bounds_13_344 : exactInterval 13 344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_344 : oddCount 344 13 = 5 ∧ acceleratedOrbit 13 344 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 344) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_344.1, data_13_344.2] + +/-- Complete interval computation for depth 13, residue 345. -/ +theorem bounds_13_345 : exactInterval 13 345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_345 : oddCount 345 13 = 7 ∧ acceleratedOrbit 13 345 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 345) = 3 ^ 7 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_345.1, data_13_345.2] + +/-- Complete interval computation for depth 13, residue 346. -/ +theorem bounds_13_346 : exactInterval 13 346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_346 : oddCount 346 13 = 5 ∧ acceleratedOrbit 13 346 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 346) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_346.1, data_13_346.2] + +/-- Complete interval computation for depth 13, residue 347. -/ +theorem bounds_13_347 : exactInterval 13 347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_347 : oddCount 347 13 = 6 ∧ acceleratedOrbit 13 347 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 347) = 3 ^ 6 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_347.1, data_13_347.2] + +/-- Complete interval computation for depth 13, residue 348. -/ +theorem bounds_13_348 : exactInterval 13 348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_348 : oddCount 348 13 = 5 ∧ acceleratedOrbit 13 348 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 348) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_348.1, data_13_348.2] + +/-- Complete interval computation for depth 13, residue 349. -/ +theorem bounds_13_349 : exactInterval 13 349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_349 : oddCount 349 13 = 5 ∧ acceleratedOrbit 13 349 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 349) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_349.1, data_13_349.2] + +/-- Complete interval computation for depth 13, residue 350. -/ +theorem bounds_13_350 : exactInterval 13 350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_350 : oddCount 350 13 = 8 ∧ acceleratedOrbit 13 350 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 350) = 3 ^ 8 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_350.1, data_13_350.2] + +/-- Complete interval computation for depth 13, residue 351. -/ +theorem bounds_13_351 : exactInterval 13 351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_351 : oddCount 351 13 = 8 ∧ acceleratedOrbit 13 351 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 351) = 3 ^ 8 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_351.1, data_13_351.2] + +/-- Complete interval computation for depth 13, residue 352. -/ +theorem bounds_13_352 : exactInterval 13 352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_352 : oddCount 352 13 = 4 ∧ acceleratedOrbit 13 352 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 352) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_352.1, data_13_352.2] + +/-- Complete interval computation for depth 13, residue 353. -/ +theorem bounds_13_353 : exactInterval 13 353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_353 : oddCount 353 13 = 7 ∧ acceleratedOrbit 13 353 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 353) = 3 ^ 7 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_353.1, data_13_353.2] + +/-- Complete interval computation for depth 13, residue 354. -/ +theorem bounds_13_354 : exactInterval 13 354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_354 : oddCount 354 13 = 5 ∧ acceleratedOrbit 13 354 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 354) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_354.1, data_13_354.2] + +/-- Complete interval computation for depth 13, residue 355. -/ +theorem bounds_13_355 : exactInterval 13 355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_355 : oddCount 355 13 = 5 ∧ acceleratedOrbit 13 355 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 355) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_355.1, data_13_355.2] + +/-- Complete interval computation for depth 13, residue 356. -/ +theorem bounds_13_356 : exactInterval 13 356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_356 : oddCount 356 13 = 5 ∧ acceleratedOrbit 13 356 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 356) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_356.1, data_13_356.2] + +/-- Complete interval computation for depth 13, residue 357. -/ +theorem bounds_13_357 : exactInterval 13 357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_357 : oddCount 357 13 = 5 ∧ acceleratedOrbit 13 357 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 357) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_357.1, data_13_357.2] + +end Collatz.Research.StoppingAtlas.Batch0490 From e403d945ffef4e75a78896a5d60181b81667615a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:30:59 +0530 Subject: [PATCH 0491/1001] proof: certify atlas Batch0491 (13:358 to 13:372) --- Collatz/Research/StoppingAtlas/Batch0491.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0491.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0491.lean b/Collatz/Research/StoppingAtlas/Batch0491.lean new file mode 100644 index 00000000..945eb26a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0491.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0491 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 358. -/ +theorem bounds_13_358 : exactInterval 13 358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_358 : oddCount 358 13 = 5 ∧ acceleratedOrbit 13 358 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 358) = 3 ^ 5 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_358.1, data_13_358.2] + +/-- Complete interval computation for depth 13, residue 359. -/ +theorem bounds_13_359 : exactInterval 13 359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_359 : oddCount 359 13 = 9 ∧ acceleratedOrbit 13 359 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 359) = 3 ^ 9 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_359.1, data_13_359.2] + +/-- Complete interval computation for depth 13, residue 360. -/ +theorem bounds_13_360 : exactInterval 13 360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_360 : oddCount 360 13 = 4 ∧ acceleratedOrbit 13 360 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 360) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_360.1, data_13_360.2] + +/-- Complete interval computation for depth 13, residue 361. -/ +theorem bounds_13_361 : exactInterval 13 361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_361 : oddCount 361 13 = 7 ∧ acceleratedOrbit 13 361 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 361) = 3 ^ 7 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_361.1, data_13_361.2] + +/-- Complete interval computation for depth 13, residue 362. -/ +theorem bounds_13_362 : exactInterval 13 362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_362 : oddCount 362 13 = 4 ∧ acceleratedOrbit 13 362 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 362) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_362.1, data_13_362.2] + +/-- Complete interval computation for depth 13, residue 363. -/ +theorem bounds_13_363 : exactInterval 13 363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_363 : oddCount 363 13 = 7 ∧ acceleratedOrbit 13 363 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 363) = 3 ^ 7 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_363.1, data_13_363.2] + +/-- Complete interval computation for depth 13, residue 364. -/ +theorem bounds_13_364 : exactInterval 13 364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_364 : oddCount 364 13 = 9 ∧ acceleratedOrbit 13 364 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 364) = 3 ^ 9 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_364.1, data_13_364.2] + +/-- Complete interval computation for depth 13, residue 365. -/ +theorem bounds_13_365 : exactInterval 13 365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_365 : oddCount 365 13 = 9 ∧ acceleratedOrbit 13 365 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 365) = 3 ^ 9 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_365.1, data_13_365.2] + +/-- Complete interval computation for depth 13, residue 366. -/ +theorem bounds_13_366 : exactInterval 13 366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_366 : oddCount 366 13 = 9 ∧ acceleratedOrbit 13 366 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 366) = 3 ^ 9 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_366.1, data_13_366.2] + +/-- Complete interval computation for depth 13, residue 367. -/ +theorem bounds_13_367 : exactInterval 13 367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_367 : oddCount 367 13 = 8 ∧ acceleratedOrbit 13 367 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 367) = 3 ^ 8 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_367.1, data_13_367.2] + +/-- Complete interval computation for depth 13, residue 368. -/ +theorem bounds_13_368 : exactInterval 13 368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_368 : oddCount 368 13 = 4 ∧ acceleratedOrbit 13 368 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 368) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_368.1, data_13_368.2] + +/-- Complete interval computation for depth 13, residue 369. -/ +theorem bounds_13_369 : exactInterval 13 369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_369 : oddCount 369 13 = 4 ∧ acceleratedOrbit 13 369 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 369) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_369.1, data_13_369.2] + +/-- Complete interval computation for depth 13, residue 370. -/ +theorem bounds_13_370 : exactInterval 13 370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_370 : oddCount 370 13 = 7 ∧ acceleratedOrbit 13 370 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 370) = 3 ^ 7 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_370.1, data_13_370.2] + +/-- Complete interval computation for depth 13, residue 371. -/ +theorem bounds_13_371 : exactInterval 13 371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_371 : oddCount 371 13 = 7 ∧ acceleratedOrbit 13 371 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 371) = 3 ^ 7 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_371.1, data_13_371.2] + +/-- Complete interval computation for depth 13, residue 372. -/ +theorem bounds_13_372 : exactInterval 13 372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_372 : oddCount 372 13 = 4 ∧ acceleratedOrbit 13 372 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 372) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_372.1, data_13_372.2] + +end Collatz.Research.StoppingAtlas.Batch0491 From e5e5d0f8c323ec0c7aeefe551a184c5b51348a0c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:30:59 +0530 Subject: [PATCH 0492/1001] proof: certify atlas Batch0492 (13:373 to 13:388) --- Collatz/Research/StoppingAtlas/Batch0492.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0492.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0492.lean b/Collatz/Research/StoppingAtlas/Batch0492.lean new file mode 100644 index 00000000..ecdd9167 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0492.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0492 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 373. -/ +theorem bounds_13_373 : exactInterval 13 373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_373 : oddCount 373 13 = 4 ∧ acceleratedOrbit 13 373 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 373) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_373.1, data_13_373.2] + +/-- Complete interval computation for depth 13, residue 374. -/ +theorem bounds_13_374 : exactInterval 13 374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_374 : oddCount 374 13 = 7 ∧ acceleratedOrbit 13 374 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 374) = 3 ^ 7 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_374.1, data_13_374.2] + +/-- Complete interval computation for depth 13, residue 375. -/ +theorem bounds_13_375 : exactInterval 13 375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 375) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_375 : oddCount 375 13 = 7 ∧ acceleratedOrbit 13 375 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 375) = 3 ^ 7 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_375.1, data_13_375.2] + +/-- Complete interval computation for depth 13, residue 376. -/ +theorem bounds_13_376 : exactInterval 13 376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_376 : oddCount 376 13 = 7 ∧ acceleratedOrbit 13 376 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 376) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_376.1, data_13_376.2] + +/-- Complete interval computation for depth 13, residue 377. -/ +theorem bounds_13_377 : exactInterval 13 377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_377 : oddCount 377 13 = 9 ∧ acceleratedOrbit 13 377 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 377) = 3 ^ 9 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_377.1, data_13_377.2] + +/-- Complete interval computation for depth 13, residue 378. -/ +theorem bounds_13_378 : exactInterval 13 378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_378 : oddCount 378 13 = 7 ∧ acceleratedOrbit 13 378 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 378) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_378.1, data_13_378.2] + +/-- Complete interval computation for depth 13, residue 379. -/ +theorem bounds_13_379 : exactInterval 13 379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_379 : oddCount 379 13 = 9 ∧ acceleratedOrbit 13 379 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 379) = 3 ^ 9 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_379.1, data_13_379.2] + +/-- Complete interval computation for depth 13, residue 380. -/ +theorem bounds_13_380 : exactInterval 13 380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_380 : oddCount 380 13 = 7 ∧ acceleratedOrbit 13 380 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 380) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_380.1, data_13_380.2] + +/-- Complete interval computation for depth 13, residue 381. -/ +theorem bounds_13_381 : exactInterval 13 381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_381 : oddCount 381 13 = 7 ∧ acceleratedOrbit 13 381 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 381) = 3 ^ 7 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_381.1, data_13_381.2] + +/-- Complete interval computation for depth 13, residue 382. -/ +theorem bounds_13_382 : exactInterval 13 382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_382 : oddCount 382 13 = 8 ∧ acceleratedOrbit 13 382 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 382) = 3 ^ 8 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_382.1, data_13_382.2] + +/-- Complete interval computation for depth 13, residue 383. -/ +theorem bounds_13_383 : exactInterval 13 383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_383 : oddCount 383 13 = 8 ∧ acceleratedOrbit 13 383 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 383) = 3 ^ 8 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_383.1, data_13_383.2] + +/-- Complete interval computation for depth 13, residue 384. -/ +theorem bounds_13_384 : exactInterval 13 384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_384 : oddCount 384 13 = 3 ∧ acceleratedOrbit 13 384 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 384) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_384.1, data_13_384.2] + +/-- Complete interval computation for depth 13, residue 385. -/ +theorem bounds_13_385 : exactInterval 13 385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_385 : oddCount 385 13 = 6 ∧ acceleratedOrbit 13 385 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 385) = 3 ^ 6 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_385.1, data_13_385.2] + +/-- Complete interval computation for depth 13, residue 386. -/ +theorem bounds_13_386 : exactInterval 13 386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_386 : oddCount 386 13 = 7 ∧ acceleratedOrbit 13 386 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 386) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_386.1, data_13_386.2] + +/-- Complete interval computation for depth 13, residue 387. -/ +theorem bounds_13_387 : exactInterval 13 387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_387 : oddCount 387 13 = 7 ∧ acceleratedOrbit 13 387 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 387) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_387.1, data_13_387.2] + +/-- Complete interval computation for depth 13, residue 388. -/ +theorem bounds_13_388 : exactInterval 13 388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_388 : oddCount 388 13 = 7 ∧ acceleratedOrbit 13 388 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 388) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_388.1, data_13_388.2] + +end Collatz.Research.StoppingAtlas.Batch0492 From 3c08c6b99c12fe42a4c2b92028647fd38f9de070 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:00 +0530 Subject: [PATCH 0493/1001] proof: certify atlas Batch0493 (13:389 to 13:403) --- Collatz/Research/StoppingAtlas/Batch0493.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0493.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0493.lean b/Collatz/Research/StoppingAtlas/Batch0493.lean new file mode 100644 index 00000000..d16839e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0493.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0493 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 389. -/ +theorem bounds_13_389 : exactInterval 13 389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_389 : oddCount 389 13 = 7 ∧ acceleratedOrbit 13 389 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 389) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_389.1, data_13_389.2] + +/-- Complete interval computation for depth 13, residue 390. -/ +theorem bounds_13_390 : exactInterval 13 390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_390 : oddCount 390 13 = 7 ∧ acceleratedOrbit 13 390 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 390) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_390.1, data_13_390.2] + +/-- Complete interval computation for depth 13, residue 391. -/ +theorem bounds_13_391 : exactInterval 13 391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_391 : oddCount 391 13 = 7 ∧ acceleratedOrbit 13 391 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 391) = 3 ^ 7 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_391.1, data_13_391.2] + +/-- Complete interval computation for depth 13, residue 392. -/ +theorem bounds_13_392 : exactInterval 13 392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_392 : oddCount 392 13 = 5 ∧ acceleratedOrbit 13 392 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 392) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_392.1, data_13_392.2] + +/-- Complete interval computation for depth 13, residue 393. -/ +theorem bounds_13_393 : exactInterval 13 393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_393 : oddCount 393 13 = 8 ∧ acceleratedOrbit 13 393 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 393) = 3 ^ 8 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_393.1, data_13_393.2] + +/-- Complete interval computation for depth 13, residue 394. -/ +theorem bounds_13_394 : exactInterval 13 394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_394 : oddCount 394 13 = 5 ∧ acceleratedOrbit 13 394 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 394) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_394.1, data_13_394.2] + +/-- Complete interval computation for depth 13, residue 395. -/ +theorem bounds_13_395 : exactInterval 13 395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_395 : oddCount 395 13 = 8 ∧ acceleratedOrbit 13 395 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 395) = 3 ^ 8 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_395.1, data_13_395.2] + +/-- Complete interval computation for depth 13, residue 396. -/ +theorem bounds_13_396 : exactInterval 13 396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_396 : oddCount 396 13 = 5 ∧ acceleratedOrbit 13 396 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 396) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_396.1, data_13_396.2] + +/-- Complete interval computation for depth 13, residue 397. -/ +theorem bounds_13_397 : exactInterval 13 397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_397 : oddCount 397 13 = 5 ∧ acceleratedOrbit 13 397 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 397) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_397.1, data_13_397.2] + +/-- Complete interval computation for depth 13, residue 398. -/ +theorem bounds_13_398 : exactInterval 13 398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_398 : oddCount 398 13 = 8 ∧ acceleratedOrbit 13 398 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 398) = 3 ^ 8 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_398.1, data_13_398.2] + +/-- Complete interval computation for depth 13, residue 399. -/ +theorem bounds_13_399 : exactInterval 13 399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_399 : oddCount 399 13 = 8 ∧ acceleratedOrbit 13 399 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 399) = 3 ^ 8 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_399.1, data_13_399.2] + +/-- Complete interval computation for depth 13, residue 400. -/ +theorem bounds_13_400 : exactInterval 13 400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_400 : oddCount 400 13 = 5 ∧ acceleratedOrbit 13 400 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 400) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_400.1, data_13_400.2] + +/-- Complete interval computation for depth 13, residue 401. -/ +theorem bounds_13_401 : exactInterval 13 401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_401 : oddCount 401 13 = 4 ∧ acceleratedOrbit 13 401 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 401) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_401.1, data_13_401.2] + +/-- Complete interval computation for depth 13, residue 402. -/ +theorem bounds_13_402 : exactInterval 13 402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_402 : oddCount 402 13 = 4 ∧ acceleratedOrbit 13 402 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 402) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_402.1, data_13_402.2] + +/-- Complete interval computation for depth 13, residue 403. -/ +theorem bounds_13_403 : exactInterval 13 403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_403 : oddCount 403 13 = 4 ∧ acceleratedOrbit 13 403 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 403) = 3 ^ 4 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_403.1, data_13_403.2] + +end Collatz.Research.StoppingAtlas.Batch0493 From aa2fcd4f820838cc66b031ca3530970c5e93b246 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:00 +0530 Subject: [PATCH 0494/1001] proof: certify atlas Batch0494 (13:404 to 13:418) --- Collatz/Research/StoppingAtlas/Batch0494.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0494.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0494.lean b/Collatz/Research/StoppingAtlas/Batch0494.lean new file mode 100644 index 00000000..be4919f4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0494.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0494 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 404. -/ +theorem bounds_13_404 : exactInterval 13 404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_404 : oddCount 404 13 = 5 ∧ acceleratedOrbit 13 404 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 404) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_404.1, data_13_404.2] + +/-- Complete interval computation for depth 13, residue 405. -/ +theorem bounds_13_405 : exactInterval 13 405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_405 : oddCount 405 13 = 5 ∧ acceleratedOrbit 13 405 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 405) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_405.1, data_13_405.2] + +/-- Complete interval computation for depth 13, residue 406. -/ +theorem bounds_13_406 : exactInterval 13 406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_406 : oddCount 406 13 = 6 ∧ acceleratedOrbit 13 406 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 406) = 3 ^ 6 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_406.1, data_13_406.2] + +/-- Complete interval computation for depth 13, residue 407. -/ +theorem bounds_13_407 : exactInterval 13 407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_407 : oddCount 407 13 = 6 ∧ acceleratedOrbit 13 407 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 407) = 3 ^ 6 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_407.1, data_13_407.2] + +/-- Complete interval computation for depth 13, residue 408. -/ +theorem bounds_13_408 : exactInterval 13 408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_408 : oddCount 408 13 = 5 ∧ acceleratedOrbit 13 408 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 408) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_408.1, data_13_408.2] + +/-- Complete interval computation for depth 13, residue 409. -/ +theorem bounds_13_409 : exactInterval 13 409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_409 : oddCount 409 13 = 6 ∧ acceleratedOrbit 13 409 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 409) = 3 ^ 6 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_409.1, data_13_409.2] + +/-- Complete interval computation for depth 13, residue 410. -/ +theorem bounds_13_410 : exactInterval 13 410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_410 : oddCount 410 13 = 5 ∧ acceleratedOrbit 13 410 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 410) = 3 ^ 5 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_410.1, data_13_410.2] + +/-- Complete interval computation for depth 13, residue 411. -/ +theorem bounds_13_411 : exactInterval 13 411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_411 : oddCount 411 13 = 9 ∧ acceleratedOrbit 13 411 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 411) = 3 ^ 9 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_411.1, data_13_411.2] + +/-- Complete interval computation for depth 13, residue 412. -/ +theorem bounds_13_412 : exactInterval 13 412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_412 : oddCount 412 13 = 8 ∧ acceleratedOrbit 13 412 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 412) = 3 ^ 8 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_412.1, data_13_412.2] + +/-- Complete interval computation for depth 13, residue 413. -/ +theorem bounds_13_413 : exactInterval 13 413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_413 : oddCount 413 13 = 8 ∧ acceleratedOrbit 13 413 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 413) = 3 ^ 8 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_413.1, data_13_413.2] + +/-- Complete interval computation for depth 13, residue 414. -/ +theorem bounds_13_414 : exactInterval 13 414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_414 : oddCount 414 13 = 8 ∧ acceleratedOrbit 13 414 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 414) = 3 ^ 8 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_414.1, data_13_414.2] + +/-- Complete interval computation for depth 13, residue 415. -/ +theorem bounds_13_415 : exactInterval 13 415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_415 : oddCount 415 13 = 9 ∧ acceleratedOrbit 13 415 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 415) = 3 ^ 9 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_415.1, data_13_415.2] + +/-- Complete interval computation for depth 13, residue 416. -/ +theorem bounds_13_416 : exactInterval 13 416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_416 : oddCount 416 13 = 3 ∧ acceleratedOrbit 13 416 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 416) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_416.1, data_13_416.2] + +/-- Complete interval computation for depth 13, residue 417. -/ +theorem bounds_13_417 : exactInterval 13 417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_417 : oddCount 417 13 = 8 ∧ acceleratedOrbit 13 417 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 417) = 3 ^ 8 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_417.1, data_13_417.2] + +/-- Complete interval computation for depth 13, residue 418. -/ +theorem bounds_13_418 : exactInterval 13 418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_418 : oddCount 418 13 = 6 ∧ acceleratedOrbit 13 418 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 418) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_418.1, data_13_418.2] + +end Collatz.Research.StoppingAtlas.Batch0494 From 635456e3a0a03d88f77c2a2c4013c2f12ce021bd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:00 +0530 Subject: [PATCH 0495/1001] proof: certify atlas Batch0495 (13:419 to 13:434) --- Collatz/Research/StoppingAtlas/Batch0495.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0495.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0495.lean b/Collatz/Research/StoppingAtlas/Batch0495.lean new file mode 100644 index 00000000..58e7a999 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0495.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0495 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 419. -/ +theorem bounds_13_419 : exactInterval 13 419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_419 : oddCount 419 13 = 6 ∧ acceleratedOrbit 13 419 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 419) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_419.1, data_13_419.2] + +/-- Complete interval computation for depth 13, residue 420. -/ +theorem bounds_13_420 : exactInterval 13 420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_420 : oddCount 420 13 = 6 ∧ acceleratedOrbit 13 420 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 420) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_420.1, data_13_420.2] + +/-- Complete interval computation for depth 13, residue 421. -/ +theorem bounds_13_421 : exactInterval 13 421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_421 : oddCount 421 13 = 6 ∧ acceleratedOrbit 13 421 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 421) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_421.1, data_13_421.2] + +/-- Complete interval computation for depth 13, residue 422. -/ +theorem bounds_13_422 : exactInterval 13 422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_422 : oddCount 422 13 = 6 ∧ acceleratedOrbit 13 422 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 422) = 3 ^ 6 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_422.1, data_13_422.2] + +/-- Complete interval computation for depth 13, residue 423. -/ +theorem bounds_13_423 : exactInterval 13 423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_423 : oddCount 423 13 = 8 ∧ acceleratedOrbit 13 423 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 423) = 3 ^ 8 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_423.1, data_13_423.2] + +/-- Complete interval computation for depth 13, residue 424. -/ +theorem bounds_13_424 : exactInterval 13 424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_424 : oddCount 424 13 = 3 ∧ acceleratedOrbit 13 424 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 424) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_424.1, data_13_424.2] + +/-- Complete interval computation for depth 13, residue 425. -/ +theorem bounds_13_425 : exactInterval 13 425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_425 : oddCount 425 13 = 10 ∧ acceleratedOrbit 13 425 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 425) = 3 ^ 10 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_425.1, data_13_425.2] + +/-- Complete interval computation for depth 13, residue 426. -/ +theorem bounds_13_426 : exactInterval 13 426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_426 : oddCount 426 13 = 3 ∧ acceleratedOrbit 13 426 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 426) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_426.1, data_13_426.2] + +/-- Complete interval computation for depth 13, residue 427. -/ +theorem bounds_13_427 : exactInterval 13 427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_427 : oddCount 427 13 = 8 ∧ acceleratedOrbit 13 427 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 427) = 3 ^ 8 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_427.1, data_13_427.2] + +/-- Complete interval computation for depth 13, residue 428. -/ +theorem bounds_13_428 : exactInterval 13 428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_428 : oddCount 428 13 = 8 ∧ acceleratedOrbit 13 428 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 428) = 3 ^ 8 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_428.1, data_13_428.2] + +/-- Complete interval computation for depth 13, residue 429. -/ +theorem bounds_13_429 : exactInterval 13 429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_429 : oddCount 429 13 = 8 ∧ acceleratedOrbit 13 429 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 429) = 3 ^ 8 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_429.1, data_13_429.2] + +/-- Complete interval computation for depth 13, residue 430. -/ +theorem bounds_13_430 : exactInterval 13 430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_430 : oddCount 430 13 = 8 ∧ acceleratedOrbit 13 430 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 430) = 3 ^ 8 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_430.1, data_13_430.2] + +/-- Complete interval computation for depth 13, residue 431. -/ +theorem bounds_13_431 : exactInterval 13 431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_431 : oddCount 431 13 = 7 ∧ acceleratedOrbit 13 431 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 431) = 3 ^ 7 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_431.1, data_13_431.2] + +/-- Complete interval computation for depth 13, residue 432. -/ +theorem bounds_13_432 : exactInterval 13 432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_432 : oddCount 432 13 = 7 ∧ acceleratedOrbit 13 432 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 432) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_432.1, data_13_432.2] + +/-- Complete interval computation for depth 13, residue 433. -/ +theorem bounds_13_433 : exactInterval 13 433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_433 : oddCount 433 13 = 6 ∧ acceleratedOrbit 13 433 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 433) = 3 ^ 6 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_433.1, data_13_433.2] + +/-- Complete interval computation for depth 13, residue 434. -/ +theorem bounds_13_434 : exactInterval 13 434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_434 : oddCount 434 13 = 6 ∧ acceleratedOrbit 13 434 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 434) = 3 ^ 6 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_434.1, data_13_434.2] + +end Collatz.Research.StoppingAtlas.Batch0495 From 68919d63e4d85513e32c7c8e5c83afe2b132129f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:00 +0530 Subject: [PATCH 0496/1001] proof: certify atlas Batch0496 (13:435 to 13:449) --- Collatz/Research/StoppingAtlas/Batch0496.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0496.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0496.lean b/Collatz/Research/StoppingAtlas/Batch0496.lean new file mode 100644 index 00000000..92081f21 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0496.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0496 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 435. -/ +theorem bounds_13_435 : exactInterval 13 435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_435 : oddCount 435 13 = 6 ∧ acceleratedOrbit 13 435 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 435) = 3 ^ 6 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_435.1, data_13_435.2] + +/-- Complete interval computation for depth 13, residue 436. -/ +theorem bounds_13_436 : exactInterval 13 436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_436 : oddCount 436 13 = 7 ∧ acceleratedOrbit 13 436 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 436) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_436.1, data_13_436.2] + +/-- Complete interval computation for depth 13, residue 437. -/ +theorem bounds_13_437 : exactInterval 13 437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_437 : oddCount 437 13 = 7 ∧ acceleratedOrbit 13 437 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 437) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_437.1, data_13_437.2] + +/-- Complete interval computation for depth 13, residue 438. -/ +theorem bounds_13_438 : exactInterval 13 438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_438 : oddCount 438 13 = 7 ∧ acceleratedOrbit 13 438 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 438) = 3 ^ 7 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_438.1, data_13_438.2] + +/-- Complete interval computation for depth 13, residue 439. -/ +theorem bounds_13_439 : exactInterval 13 439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_439 : oddCount 439 13 = 7 ∧ acceleratedOrbit 13 439 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 439) = 3 ^ 7 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_439.1, data_13_439.2] + +/-- Complete interval computation for depth 13, residue 440. -/ +theorem bounds_13_440 : exactInterval 13 440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_440 : oddCount 440 13 = 7 ∧ acceleratedOrbit 13 440 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 440) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_440.1, data_13_440.2] + +/-- Complete interval computation for depth 13, residue 441. -/ +theorem bounds_13_441 : exactInterval 13 441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_441 : oddCount 441 13 = 6 ∧ acceleratedOrbit 13 441 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 441) = 3 ^ 6 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_441.1, data_13_441.2] + +/-- Complete interval computation for depth 13, residue 442. -/ +theorem bounds_13_442 : exactInterval 13 442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_442 : oddCount 442 13 = 7 ∧ acceleratedOrbit 13 442 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 442) = 3 ^ 7 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_442.1, data_13_442.2] + +/-- Complete interval computation for depth 13, residue 443. -/ +theorem bounds_13_443 : exactInterval 13 443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_443 : oddCount 443 13 = 7 ∧ acceleratedOrbit 13 443 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 443) = 3 ^ 7 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_443.1, data_13_443.2] + +/-- Complete interval computation for depth 13, residue 444. -/ +theorem bounds_13_444 : exactInterval 13 444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_444 : oddCount 444 13 = 9 ∧ acceleratedOrbit 13 444 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 444) = 3 ^ 9 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_444.1, data_13_444.2] + +/-- Complete interval computation for depth 13, residue 445. -/ +theorem bounds_13_445 : exactInterval 13 445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_445 : oddCount 445 13 = 9 ∧ acceleratedOrbit 13 445 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 445) = 3 ^ 9 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_445.1, data_13_445.2] + +/-- Complete interval computation for depth 13, residue 446. -/ +theorem bounds_13_446 : exactInterval 13 446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_446 : oddCount 446 13 = 9 ∧ acceleratedOrbit 13 446 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 446) = 3 ^ 9 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_446.1, data_13_446.2] + +/-- Complete interval computation for depth 13, residue 447. -/ +theorem bounds_13_447 : exactInterval 13 447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_447 : oddCount 447 13 = 10 ∧ acceleratedOrbit 13 447 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 447) = 3 ^ 10 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_447.1, data_13_447.2] + +/-- Complete interval computation for depth 13, residue 448. -/ +theorem bounds_13_448 : exactInterval 13 448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_448 : oddCount 448 13 = 4 ∧ acceleratedOrbit 13 448 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 448) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_448.1, data_13_448.2] + +/-- Complete interval computation for depth 13, residue 449. -/ +theorem bounds_13_449 : exactInterval 13 449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_449 : oddCount 449 13 = 8 ∧ acceleratedOrbit 13 449 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 449) = 3 ^ 8 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_449.1, data_13_449.2] + +end Collatz.Research.StoppingAtlas.Batch0496 From 48f5510d563224607ce7956637271d427f79cbc9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:01 +0530 Subject: [PATCH 0497/1001] proof: certify atlas Batch0497 (13:450 to 13:464) --- Collatz/Research/StoppingAtlas/Batch0497.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0497.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0497.lean b/Collatz/Research/StoppingAtlas/Batch0497.lean new file mode 100644 index 00000000..0dade672 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0497.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0497 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 450. -/ +theorem bounds_13_450 : exactInterval 13 450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_450 : oddCount 450 13 = 9 ∧ acceleratedOrbit 13 450 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 450) = 3 ^ 9 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_450.1, data_13_450.2] + +/-- Complete interval computation for depth 13, residue 451. -/ +theorem bounds_13_451 : exactInterval 13 451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_451 : oddCount 451 13 = 9 ∧ acceleratedOrbit 13 451 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 451) = 3 ^ 9 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_451.1, data_13_451.2] + +/-- Complete interval computation for depth 13, residue 452. -/ +theorem bounds_13_452 : exactInterval 13 452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_452 : oddCount 452 13 = 3 ∧ acceleratedOrbit 13 452 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 452) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_452.1, data_13_452.2] + +/-- Complete interval computation for depth 13, residue 453. -/ +theorem bounds_13_453 : exactInterval 13 453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_453 : oddCount 453 13 = 3 ∧ acceleratedOrbit 13 453 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 453) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_453.1, data_13_453.2] + +/-- Complete interval computation for depth 13, residue 454. -/ +theorem bounds_13_454 : exactInterval 13 454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_454 : oddCount 454 13 = 3 ∧ acceleratedOrbit 13 454 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 454) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_454.1, data_13_454.2] + +/-- Complete interval computation for depth 13, residue 455. -/ +theorem bounds_13_455 : exactInterval 13 455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 455) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_455 : oddCount 455 13 = 7 ∧ acceleratedOrbit 13 455 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 455) = 3 ^ 7 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_455.1, data_13_455.2] + +/-- Complete interval computation for depth 13, residue 456. -/ +theorem bounds_13_456 : exactInterval 13 456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_456 : oddCount 456 13 = 5 ∧ acceleratedOrbit 13 456 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 456) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_456.1, data_13_456.2] + +/-- Complete interval computation for depth 13, residue 457. -/ +theorem bounds_13_457 : exactInterval 13 457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_457 : oddCount 457 13 = 6 ∧ acceleratedOrbit 13 457 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 457) = 3 ^ 6 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_457.1, data_13_457.2] + +/-- Complete interval computation for depth 13, residue 458. -/ +theorem bounds_13_458 : exactInterval 13 458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_458 : oddCount 458 13 = 5 ∧ acceleratedOrbit 13 458 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 458) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_458.1, data_13_458.2] + +/-- Complete interval computation for depth 13, residue 459. -/ +theorem bounds_13_459 : exactInterval 13 459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_459 : oddCount 459 13 = 7 ∧ acceleratedOrbit 13 459 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 459) = 3 ^ 7 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_459.1, data_13_459.2] + +/-- Complete interval computation for depth 13, residue 460. -/ +theorem bounds_13_460 : exactInterval 13 460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_460 : oddCount 460 13 = 5 ∧ acceleratedOrbit 13 460 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 460) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_460.1, data_13_460.2] + +/-- Complete interval computation for depth 13, residue 461. -/ +theorem bounds_13_461 : exactInterval 13 461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_461 : oddCount 461 13 = 5 ∧ acceleratedOrbit 13 461 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 461) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_461.1, data_13_461.2] + +/-- Complete interval computation for depth 13, residue 462. -/ +theorem bounds_13_462 : exactInterval 13 462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_462 : oddCount 462 13 = 7 ∧ acceleratedOrbit 13 462 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 462) = 3 ^ 7 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_462.1, data_13_462.2] + +/-- Complete interval computation for depth 13, residue 463. -/ +theorem bounds_13_463 : exactInterval 13 463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_463 : oddCount 463 13 = 7 ∧ acceleratedOrbit 13 463 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 463) = 3 ^ 7 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_463.1, data_13_463.2] + +/-- Complete interval computation for depth 13, residue 464. -/ +theorem bounds_13_464 : exactInterval 13 464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_464 : oddCount 464 13 = 4 ∧ acceleratedOrbit 13 464 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 464) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_464.1, data_13_464.2] + +end Collatz.Research.StoppingAtlas.Batch0497 From 2391c2fad5e915aad7c48beb9e916ba606a274d1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:01 +0530 Subject: [PATCH 0498/1001] proof: certify atlas Batch0498 (13:465 to 13:480) --- Collatz/Research/StoppingAtlas/Batch0498.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0498.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0498.lean b/Collatz/Research/StoppingAtlas/Batch0498.lean new file mode 100644 index 00000000..90818d0a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0498.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0498 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 465. -/ +theorem bounds_13_465 : exactInterval 13 465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_465 : oddCount 465 13 = 5 ∧ acceleratedOrbit 13 465 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 465) = 3 ^ 5 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_465.1, data_13_465.2] + +/-- Complete interval computation for depth 13, residue 466. -/ +theorem bounds_13_466 : exactInterval 13 466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_466 : oddCount 466 13 = 8 ∧ acceleratedOrbit 13 466 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 466) = 3 ^ 8 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_466.1, data_13_466.2] + +/-- Complete interval computation for depth 13, residue 467. -/ +theorem bounds_13_467 : exactInterval 13 467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_467 : oddCount 467 13 = 8 ∧ acceleratedOrbit 13 467 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 467) = 3 ^ 8 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_467.1, data_13_467.2] + +/-- Complete interval computation for depth 13, residue 468. -/ +theorem bounds_13_468 : exactInterval 13 468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_468 : oddCount 468 13 = 4 ∧ acceleratedOrbit 13 468 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 468) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_468.1, data_13_468.2] + +/-- Complete interval computation for depth 13, residue 469. -/ +theorem bounds_13_469 : exactInterval 13 469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_469 : oddCount 469 13 = 4 ∧ acceleratedOrbit 13 469 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 469) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_469.1, data_13_469.2] + +/-- Complete interval computation for depth 13, residue 470. -/ +theorem bounds_13_470 : exactInterval 13 470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_470 : oddCount 470 13 = 8 ∧ acceleratedOrbit 13 470 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 470) = 3 ^ 8 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_470.1, data_13_470.2] + +/-- Complete interval computation for depth 13, residue 471. -/ +theorem bounds_13_471 : exactInterval 13 471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_471 : oddCount 471 13 = 8 ∧ acceleratedOrbit 13 471 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 471) = 3 ^ 8 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_471.1, data_13_471.2] + +/-- Complete interval computation for depth 13, residue 472. -/ +theorem bounds_13_472 : exactInterval 13 472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_472 : oddCount 472 13 = 6 ∧ acceleratedOrbit 13 472 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 472) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_472.1, data_13_472.2] + +/-- Complete interval computation for depth 13, residue 473. -/ +theorem bounds_13_473 : exactInterval 13 473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_473 : oddCount 473 13 = 6 ∧ acceleratedOrbit 13 473 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 473) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_473.1, data_13_473.2] + +/-- Complete interval computation for depth 13, residue 474. -/ +theorem bounds_13_474 : exactInterval 13 474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_474 : oddCount 474 13 = 6 ∧ acceleratedOrbit 13 474 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 474) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_474.1, data_13_474.2] + +/-- Complete interval computation for depth 13, residue 475. -/ +theorem bounds_13_475 : exactInterval 13 475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_475 : oddCount 475 13 = 7 ∧ acceleratedOrbit 13 475 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 475) = 3 ^ 7 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_475.1, data_13_475.2] + +/-- Complete interval computation for depth 13, residue 476. -/ +theorem bounds_13_476 : exactInterval 13 476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_476 : oddCount 476 13 = 6 ∧ acceleratedOrbit 13 476 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 476) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_476.1, data_13_476.2] + +/-- Complete interval computation for depth 13, residue 477. -/ +theorem bounds_13_477 : exactInterval 13 477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_477 : oddCount 477 13 = 6 ∧ acceleratedOrbit 13 477 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 477) = 3 ^ 6 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_477.1, data_13_477.2] + +/-- Complete interval computation for depth 13, residue 478. -/ +theorem bounds_13_478 : exactInterval 13 478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_478 : oddCount 478 13 = 9 ∧ acceleratedOrbit 13 478 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 478) = 3 ^ 9 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_478.1, data_13_478.2] + +/-- Complete interval computation for depth 13, residue 479. -/ +theorem bounds_13_479 : exactInterval 13 479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_479 : oddCount 479 13 = 9 ∧ acceleratedOrbit 13 479 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 479) = 3 ^ 9 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_479.1, data_13_479.2] + +/-- Complete interval computation for depth 13, residue 480. -/ +theorem bounds_13_480 : exactInterval 13 480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_480 : oddCount 480 13 = 4 ∧ acceleratedOrbit 13 480 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 480) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_480.1, data_13_480.2] + +end Collatz.Research.StoppingAtlas.Batch0498 From 3246a3088fda057be37bbe85ab12bf8acc28c39d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:02 +0530 Subject: [PATCH 0499/1001] proof: certify atlas Batch0499 (13:481 to 13:495) --- Collatz/Research/StoppingAtlas/Batch0499.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0499.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0499.lean b/Collatz/Research/StoppingAtlas/Batch0499.lean new file mode 100644 index 00000000..cdd97788 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0499.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0499 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 481. -/ +theorem bounds_13_481 : exactInterval 13 481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_481 : oddCount 481 13 = 6 ∧ acceleratedOrbit 13 481 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 481) = 3 ^ 6 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_481.1, data_13_481.2] + +/-- Complete interval computation for depth 13, residue 482. -/ +theorem bounds_13_482 : exactInterval 13 482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_482 : oddCount 482 13 = 4 ∧ acceleratedOrbit 13 482 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 482) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_482.1, data_13_482.2] + +/-- Complete interval computation for depth 13, residue 483. -/ +theorem bounds_13_483 : exactInterval 13 483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_483 : oddCount 483 13 = 4 ∧ acceleratedOrbit 13 483 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 483) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_483.1, data_13_483.2] + +/-- Complete interval computation for depth 13, residue 484. -/ +theorem bounds_13_484 : exactInterval 13 484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_484 : oddCount 484 13 = 8 ∧ acceleratedOrbit 13 484 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 484) = 3 ^ 8 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_484.1, data_13_484.2] + +/-- Complete interval computation for depth 13, residue 485. -/ +theorem bounds_13_485 : exactInterval 13 485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_485 : oddCount 485 13 = 8 ∧ acceleratedOrbit 13 485 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 485) = 3 ^ 8 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_485.1, data_13_485.2] + +/-- Complete interval computation for depth 13, residue 486. -/ +theorem bounds_13_486 : exactInterval 13 486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_486 : oddCount 486 13 = 8 ∧ acceleratedOrbit 13 486 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 486) = 3 ^ 8 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_486.1, data_13_486.2] + +/-- Complete interval computation for depth 13, residue 487. -/ +theorem bounds_13_487 : exactInterval 13 487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_487 : oddCount 487 13 = 9 ∧ acceleratedOrbit 13 487 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 487) = 3 ^ 9 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_487.1, data_13_487.2] + +/-- Complete interval computation for depth 13, residue 488. -/ +theorem bounds_13_488 : exactInterval 13 488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_488 : oddCount 488 13 = 4 ∧ acceleratedOrbit 13 488 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 488) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_488.1, data_13_488.2] + +/-- Complete interval computation for depth 13, residue 489. -/ +theorem bounds_13_489 : exactInterval 13 489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_489 : oddCount 489 13 = 7 ∧ acceleratedOrbit 13 489 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 489) = 3 ^ 7 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_489.1, data_13_489.2] + +/-- Complete interval computation for depth 13, residue 490. -/ +theorem bounds_13_490 : exactInterval 13 490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_490 : oddCount 490 13 = 4 ∧ acceleratedOrbit 13 490 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 490) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_490.1, data_13_490.2] + +/-- Complete interval computation for depth 13, residue 491. -/ +theorem bounds_13_491 : exactInterval 13 491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_491 : oddCount 491 13 = 10 ∧ acceleratedOrbit 13 491 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 491) = 3 ^ 10 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_491.1, data_13_491.2] + +/-- Complete interval computation for depth 13, residue 492. -/ +theorem bounds_13_492 : exactInterval 13 492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_492 : oddCount 492 13 = 7 ∧ acceleratedOrbit 13 492 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 492) = 3 ^ 7 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_492.1, data_13_492.2] + +/-- Complete interval computation for depth 13, residue 493. -/ +theorem bounds_13_493 : exactInterval 13 493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_493 : oddCount 493 13 = 7 ∧ acceleratedOrbit 13 493 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 493) = 3 ^ 7 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_493.1, data_13_493.2] + +/-- Complete interval computation for depth 13, residue 494. -/ +theorem bounds_13_494 : exactInterval 13 494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_494 : oddCount 494 13 = 7 ∧ acceleratedOrbit 13 494 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 494) = 3 ^ 7 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_494.1, data_13_494.2] + +/-- Complete interval computation for depth 13, residue 495. -/ +theorem bounds_13_495 : exactInterval 13 495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_495 : oddCount 495 13 = 10 ∧ acceleratedOrbit 13 495 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 495) = 3 ^ 10 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_495.1, data_13_495.2] + +end Collatz.Research.StoppingAtlas.Batch0499 From 7b3cb6b2530e38973ae9f77c1b573a3e98a7cfce Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:02 +0530 Subject: [PATCH 0500/1001] proof: certify atlas Batch0500 (13:496 to 13:511) --- Collatz/Research/StoppingAtlas/Batch0500.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0500.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0500.lean b/Collatz/Research/StoppingAtlas/Batch0500.lean new file mode 100644 index 00000000..f50bc00b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0500.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0500 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 496. -/ +theorem bounds_13_496 : exactInterval 13 496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_496 : oddCount 496 13 = 7 ∧ acceleratedOrbit 13 496 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 496) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_496.1, data_13_496.2] + +/-- Complete interval computation for depth 13, residue 497. -/ +theorem bounds_13_497 : exactInterval 13 497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_497 : oddCount 497 13 = 4 ∧ acceleratedOrbit 13 497 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 497) = 3 ^ 4 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_497.1, data_13_497.2] + +/-- Complete interval computation for depth 13, residue 498. -/ +theorem bounds_13_498 : exactInterval 13 498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_498 : oddCount 498 13 = 8 ∧ acceleratedOrbit 13 498 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 498) = 3 ^ 8 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_498.1, data_13_498.2] + +/-- Complete interval computation for depth 13, residue 499. -/ +theorem bounds_13_499 : exactInterval 13 499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_499 : oddCount 499 13 = 8 ∧ acceleratedOrbit 13 499 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 499) = 3 ^ 8 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_499.1, data_13_499.2] + +/-- Complete interval computation for depth 13, residue 500. -/ +theorem bounds_13_500 : exactInterval 13 500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_500 : oddCount 500 13 = 7 ∧ acceleratedOrbit 13 500 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 500) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_500.1, data_13_500.2] + +/-- Complete interval computation for depth 13, residue 501. -/ +theorem bounds_13_501 : exactInterval 13 501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_501 : oddCount 501 13 = 7 ∧ acceleratedOrbit 13 501 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 501) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_501.1, data_13_501.2] + +/-- Complete interval computation for depth 13, residue 502. -/ +theorem bounds_13_502 : exactInterval 13 502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_502 : oddCount 502 13 = 10 ∧ acceleratedOrbit 13 502 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 502) = 3 ^ 10 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_502.1, data_13_502.2] + +/-- Complete interval computation for depth 13, residue 503. -/ +theorem bounds_13_503 : exactInterval 13 503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_503 : oddCount 503 13 = 10 ∧ acceleratedOrbit 13 503 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 503) = 3 ^ 10 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_503.1, data_13_503.2] + +/-- Complete interval computation for depth 13, residue 504. -/ +theorem bounds_13_504 : exactInterval 13 504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_504 : oddCount 504 13 = 7 ∧ acceleratedOrbit 13 504 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 504) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_504.1, data_13_504.2] + +/-- Complete interval computation for depth 13, residue 505. -/ +theorem bounds_13_505 : exactInterval 13 505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_505 : oddCount 505 13 = 8 ∧ acceleratedOrbit 13 505 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 505) = 3 ^ 8 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_505.1, data_13_505.2] + +/-- Complete interval computation for depth 13, residue 506. -/ +theorem bounds_13_506 : exactInterval 13 506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_506 : oddCount 506 13 = 7 ∧ acceleratedOrbit 13 506 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 506) = 3 ^ 7 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_506.1, data_13_506.2] + +/-- Complete interval computation for depth 13, residue 507. -/ +theorem bounds_13_507 : exactInterval 13 507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_507 : oddCount 507 13 = 7 ∧ acceleratedOrbit 13 507 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 507) = 3 ^ 7 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_507.1, data_13_507.2] + +/-- Complete interval computation for depth 13, residue 508. -/ +theorem bounds_13_508 : exactInterval 13 508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_508 : oddCount 508 13 = 8 ∧ acceleratedOrbit 13 508 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 508) = 3 ^ 8 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_508.1, data_13_508.2] + +/-- Complete interval computation for depth 13, residue 509. -/ +theorem bounds_13_509 : exactInterval 13 509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_509 : oddCount 509 13 = 8 ∧ acceleratedOrbit 13 509 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 509) = 3 ^ 8 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_509.1, data_13_509.2] + +/-- Complete interval computation for depth 13, residue 510. -/ +theorem bounds_13_510 : exactInterval 13 510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_510 : oddCount 510 13 = 8 ∧ acceleratedOrbit 13 510 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 510) = 3 ^ 8 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_510.1, data_13_510.2] + +/-- Complete interval computation for depth 13, residue 511. -/ +theorem bounds_13_511 : exactInterval 13 511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_511 : oddCount 511 13 = 11 ∧ acceleratedOrbit 13 511 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 511) = 3 ^ 11 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_511.1, data_13_511.2] + +end Collatz.Research.StoppingAtlas.Batch0500 From 0776534fad580c7eb3ef93c20f34c985f14257dc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:03 +0530 Subject: [PATCH 0501/1001] proof: certify atlas Batch0501 (13:512 to 13:526) --- Collatz/Research/StoppingAtlas/Batch0501.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0501.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0501.lean b/Collatz/Research/StoppingAtlas/Batch0501.lean new file mode 100644 index 00000000..0b9e730b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0501.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0501 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 512. -/ +theorem bounds_13_512 : exactInterval 13 512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_512 : oddCount 512 13 = 2 ∧ acceleratedOrbit 13 512 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 512) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_512.1, data_13_512.2] + +/-- Complete interval computation for depth 13, residue 513. -/ +theorem bounds_13_513 : exactInterval 13 513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_513 : oddCount 513 13 = 6 ∧ acceleratedOrbit 13 513 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 513) = 3 ^ 6 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_513.1, data_13_513.2] + +/-- Complete interval computation for depth 13, residue 514. -/ +theorem bounds_13_514 : exactInterval 13 514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_514 : oddCount 514 13 = 6 ∧ acceleratedOrbit 13 514 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 514) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_514.1, data_13_514.2] + +/-- Complete interval computation for depth 13, residue 515. -/ +theorem bounds_13_515 : exactInterval 13 515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_515 : oddCount 515 13 = 6 ∧ acceleratedOrbit 13 515 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 515) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_515.1, data_13_515.2] + +/-- Complete interval computation for depth 13, residue 516. -/ +theorem bounds_13_516 : exactInterval 13 516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_516 : oddCount 516 13 = 6 ∧ acceleratedOrbit 13 516 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 516) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_516.1, data_13_516.2] + +/-- Complete interval computation for depth 13, residue 517. -/ +theorem bounds_13_517 : exactInterval 13 517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_517 : oddCount 517 13 = 6 ∧ acceleratedOrbit 13 517 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 517) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_517.1, data_13_517.2] + +/-- Complete interval computation for depth 13, residue 518. -/ +theorem bounds_13_518 : exactInterval 13 518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_518 : oddCount 518 13 = 6 ∧ acceleratedOrbit 13 518 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 518) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_518.1, data_13_518.2] + +/-- Complete interval computation for depth 13, residue 519. -/ +theorem bounds_13_519 : exactInterval 13 519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_519 : oddCount 519 13 = 8 ∧ acceleratedOrbit 13 519 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 519) = 3 ^ 8 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_519.1, data_13_519.2] + +/-- Complete interval computation for depth 13, residue 520. -/ +theorem bounds_13_520 : exactInterval 13 520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_520 : oddCount 520 13 = 5 ∧ acceleratedOrbit 13 520 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 520) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_520.1, data_13_520.2] + +/-- Complete interval computation for depth 13, residue 521. -/ +theorem bounds_13_521 : exactInterval 13 521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_521 : oddCount 521 13 = 6 ∧ acceleratedOrbit 13 521 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 521) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_521.1, data_13_521.2] + +/-- Complete interval computation for depth 13, residue 522. -/ +theorem bounds_13_522 : exactInterval 13 522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_522 : oddCount 522 13 = 5 ∧ acceleratedOrbit 13 522 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 522) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_522.1, data_13_522.2] + +/-- Complete interval computation for depth 13, residue 523. -/ +theorem bounds_13_523 : exactInterval 13 523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_523 : oddCount 523 13 = 6 ∧ acceleratedOrbit 13 523 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 523) = 3 ^ 6 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_523.1, data_13_523.2] + +/-- Complete interval computation for depth 13, residue 524. -/ +theorem bounds_13_524 : exactInterval 13 524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_524 : oddCount 524 13 = 5 ∧ acceleratedOrbit 13 524 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 524) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_524.1, data_13_524.2] + +/-- Complete interval computation for depth 13, residue 525. -/ +theorem bounds_13_525 : exactInterval 13 525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_525 : oddCount 525 13 = 5 ∧ acceleratedOrbit 13 525 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 525) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_525.1, data_13_525.2] + +/-- Complete interval computation for depth 13, residue 526. -/ +theorem bounds_13_526 : exactInterval 13 526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_526 : oddCount 526 13 = 8 ∧ acceleratedOrbit 13 526 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 526) = 3 ^ 8 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_526.1, data_13_526.2] + +end Collatz.Research.StoppingAtlas.Batch0501 From 4e39da8d7abf92d92d632ad9fbf6d177d1cf7fa9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:03 +0530 Subject: [PATCH 0502/1001] proof: certify atlas Batch0502 (13:527 to 13:541) --- Collatz/Research/StoppingAtlas/Batch0502.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0502.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0502.lean b/Collatz/Research/StoppingAtlas/Batch0502.lean new file mode 100644 index 00000000..e9db36a7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0502.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0502 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 527. -/ +theorem bounds_13_527 : exactInterval 13 527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_527 : oddCount 527 13 = 8 ∧ acceleratedOrbit 13 527 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 527) = 3 ^ 8 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_527.1, data_13_527.2] + +/-- Complete interval computation for depth 13, residue 528. -/ +theorem bounds_13_528 : exactInterval 13 528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_528 : oddCount 528 13 = 5 ∧ acceleratedOrbit 13 528 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 528) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_528.1, data_13_528.2] + +/-- Complete interval computation for depth 13, residue 529. -/ +theorem bounds_13_529 : exactInterval 13 529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_529 : oddCount 529 13 = 5 ∧ acceleratedOrbit 13 529 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 529) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_529.1, data_13_529.2] + +/-- Complete interval computation for depth 13, residue 530. -/ +theorem bounds_13_530 : exactInterval 13 530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_530 : oddCount 530 13 = 7 ∧ acceleratedOrbit 13 530 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 530) = 3 ^ 7 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_530.1, data_13_530.2] + +/-- Complete interval computation for depth 13, residue 531. -/ +theorem bounds_13_531 : exactInterval 13 531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_531 : oddCount 531 13 = 7 ∧ acceleratedOrbit 13 531 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 531) = 3 ^ 7 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_531.1, data_13_531.2] + +/-- Complete interval computation for depth 13, residue 532. -/ +theorem bounds_13_532 : exactInterval 13 532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_532 : oddCount 532 13 = 5 ∧ acceleratedOrbit 13 532 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 532) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_532.1, data_13_532.2] + +/-- Complete interval computation for depth 13, residue 533. -/ +theorem bounds_13_533 : exactInterval 13 533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_533 : oddCount 533 13 = 5 ∧ acceleratedOrbit 13 533 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 533) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_533.1, data_13_533.2] + +/-- Complete interval computation for depth 13, residue 534. -/ +theorem bounds_13_534 : exactInterval 13 534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_534 : oddCount 534 13 = 5 ∧ acceleratedOrbit 13 534 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 534) = 3 ^ 5 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_534.1, data_13_534.2] + +/-- Complete interval computation for depth 13, residue 535. -/ +theorem bounds_13_535 : exactInterval 13 535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_535 : oddCount 535 13 = 5 ∧ acceleratedOrbit 13 535 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 535) = 3 ^ 5 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_535.1, data_13_535.2] + +/-- Complete interval computation for depth 13, residue 536. -/ +theorem bounds_13_536 : exactInterval 13 536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_536 : oddCount 536 13 = 5 ∧ acceleratedOrbit 13 536 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 536) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_536.1, data_13_536.2] + +/-- Complete interval computation for depth 13, residue 537. -/ +theorem bounds_13_537 : exactInterval 13 537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_537 : oddCount 537 13 = 5 ∧ acceleratedOrbit 13 537 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 537) = 3 ^ 5 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_537.1, data_13_537.2] + +/-- Complete interval computation for depth 13, residue 538. -/ +theorem bounds_13_538 : exactInterval 13 538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_538 : oddCount 538 13 = 5 ∧ acceleratedOrbit 13 538 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 538) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_538.1, data_13_538.2] + +/-- Complete interval computation for depth 13, residue 539. -/ +theorem bounds_13_539 : exactInterval 13 539 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 539) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_539 : oddCount 539 13 = 8 ∧ acceleratedOrbit 13 539 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 539) = 3 ^ 8 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_539.1, data_13_539.2] + +/-- Complete interval computation for depth 13, residue 540. -/ +theorem bounds_13_540 : exactInterval 13 540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_540 : oddCount 540 13 = 6 ∧ acceleratedOrbit 13 540 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 540) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_540.1, data_13_540.2] + +/-- Complete interval computation for depth 13, residue 541. -/ +theorem bounds_13_541 : exactInterval 13 541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_541 : oddCount 541 13 = 6 ∧ acceleratedOrbit 13 541 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 541) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_541.1, data_13_541.2] + +end Collatz.Research.StoppingAtlas.Batch0502 From c7a524d9f35fd0a6cfb840083e84f8f6b8730eb5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:03 +0530 Subject: [PATCH 0503/1001] proof: certify atlas Batch0503 (13:542 to 13:557) --- Collatz/Research/StoppingAtlas/Batch0503.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0503.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0503.lean b/Collatz/Research/StoppingAtlas/Batch0503.lean new file mode 100644 index 00000000..1a9d6780 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0503.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0503 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 542. -/ +theorem bounds_13_542 : exactInterval 13 542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_542 : oddCount 542 13 = 6 ∧ acceleratedOrbit 13 542 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 542) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_542.1, data_13_542.2] + +/-- Complete interval computation for depth 13, residue 543. -/ +theorem bounds_13_543 : exactInterval 13 543 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 543) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_543 : oddCount 543 13 = 8 ∧ acceleratedOrbit 13 543 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 543) = 3 ^ 8 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_543.1, data_13_543.2] + +/-- Complete interval computation for depth 13, residue 544. -/ +theorem bounds_13_544 : exactInterval 13 544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_544 : oddCount 544 13 = 3 ∧ acceleratedOrbit 13 544 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 544) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_544.1, data_13_544.2] + +/-- Complete interval computation for depth 13, residue 545. -/ +theorem bounds_13_545 : exactInterval 13 545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_545 : oddCount 545 13 = 6 ∧ acceleratedOrbit 13 545 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 545) = 3 ^ 6 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_545.1, data_13_545.2] + +/-- Complete interval computation for depth 13, residue 546. -/ +theorem bounds_13_546 : exactInterval 13 546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_546 : oddCount 546 13 = 5 ∧ acceleratedOrbit 13 546 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 546) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_546.1, data_13_546.2] + +/-- Complete interval computation for depth 13, residue 547. -/ +theorem bounds_13_547 : exactInterval 13 547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_547 : oddCount 547 13 = 5 ∧ acceleratedOrbit 13 547 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 547) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_547.1, data_13_547.2] + +/-- Complete interval computation for depth 13, residue 548. -/ +theorem bounds_13_548 : exactInterval 13 548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_548 : oddCount 548 13 = 8 ∧ acceleratedOrbit 13 548 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 548) = 3 ^ 8 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_548.1, data_13_548.2] + +/-- Complete interval computation for depth 13, residue 549. -/ +theorem bounds_13_549 : exactInterval 13 549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_549 : oddCount 549 13 = 8 ∧ acceleratedOrbit 13 549 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 549) = 3 ^ 8 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_549.1, data_13_549.2] + +/-- Complete interval computation for depth 13, residue 550. -/ +theorem bounds_13_550 : exactInterval 13 550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_550 : oddCount 550 13 = 8 ∧ acceleratedOrbit 13 550 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 550) = 3 ^ 8 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_550.1, data_13_550.2] + +/-- Complete interval computation for depth 13, residue 551. -/ +theorem bounds_13_551 : exactInterval 13 551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_551 : oddCount 551 13 = 7 ∧ acceleratedOrbit 13 551 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 551) = 3 ^ 7 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_551.1, data_13_551.2] + +/-- Complete interval computation for depth 13, residue 552. -/ +theorem bounds_13_552 : exactInterval 13 552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_552 : oddCount 552 13 = 3 ∧ acceleratedOrbit 13 552 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 552) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_552.1, data_13_552.2] + +/-- Complete interval computation for depth 13, residue 553. -/ +theorem bounds_13_553 : exactInterval 13 553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_553 : oddCount 553 13 = 9 ∧ acceleratedOrbit 13 553 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 553) = 3 ^ 9 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_553.1, data_13_553.2] + +/-- Complete interval computation for depth 13, residue 554. -/ +theorem bounds_13_554 : exactInterval 13 554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_554 : oddCount 554 13 = 3 ∧ acceleratedOrbit 13 554 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 554) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_554.1, data_13_554.2] + +/-- Complete interval computation for depth 13, residue 555. -/ +theorem bounds_13_555 : exactInterval 13 555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_555 : oddCount 555 13 = 5 ∧ acceleratedOrbit 13 555 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 555) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_555.1, data_13_555.2] + +/-- Complete interval computation for depth 13, residue 556. -/ +theorem bounds_13_556 : exactInterval 13 556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_556 : oddCount 556 13 = 7 ∧ acceleratedOrbit 13 556 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 556) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_556.1, data_13_556.2] + +/-- Complete interval computation for depth 13, residue 557. -/ +theorem bounds_13_557 : exactInterval 13 557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_557 : oddCount 557 13 = 7 ∧ acceleratedOrbit 13 557 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 557) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_557.1, data_13_557.2] + +end Collatz.Research.StoppingAtlas.Batch0503 From 8f9e4a28984cdc6f79abdb60092058b12e4b6360 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:03 +0530 Subject: [PATCH 0504/1001] proof: certify atlas Batch0504 (13:558 to 13:572) --- Collatz/Research/StoppingAtlas/Batch0504.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0504.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0504.lean b/Collatz/Research/StoppingAtlas/Batch0504.lean new file mode 100644 index 00000000..89d3a096 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0504.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0504 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 558. -/ +theorem bounds_13_558 : exactInterval 13 558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_558 : oddCount 558 13 = 7 ∧ acceleratedOrbit 13 558 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 558) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_558.1, data_13_558.2] + +/-- Complete interval computation for depth 13, residue 559. -/ +theorem bounds_13_559 : exactInterval 13 559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_559 : oddCount 559 13 = 10 ∧ acceleratedOrbit 13 559 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 559) = 3 ^ 10 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_559.1, data_13_559.2] + +/-- Complete interval computation for depth 13, residue 560. -/ +theorem bounds_13_560 : exactInterval 13 560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_560 : oddCount 560 13 = 3 ∧ acceleratedOrbit 13 560 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 560) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_560.1, data_13_560.2] + +/-- Complete interval computation for depth 13, residue 561. -/ +theorem bounds_13_561 : exactInterval 13 561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_561 : oddCount 561 13 = 7 ∧ acceleratedOrbit 13 561 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 561) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_561.1, data_13_561.2] + +/-- Complete interval computation for depth 13, residue 562. -/ +theorem bounds_13_562 : exactInterval 13 562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_562 : oddCount 562 13 = 7 ∧ acceleratedOrbit 13 562 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 562) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_562.1, data_13_562.2] + +/-- Complete interval computation for depth 13, residue 563. -/ +theorem bounds_13_563 : exactInterval 13 563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_563 : oddCount 563 13 = 7 ∧ acceleratedOrbit 13 563 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 563) = 3 ^ 7 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_563.1, data_13_563.2] + +/-- Complete interval computation for depth 13, residue 564. -/ +theorem bounds_13_564 : exactInterval 13 564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_564 : oddCount 564 13 = 3 ∧ acceleratedOrbit 13 564 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 564) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_564.1, data_13_564.2] + +/-- Complete interval computation for depth 13, residue 565. -/ +theorem bounds_13_565 : exactInterval 13 565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_565 : oddCount 565 13 = 3 ∧ acceleratedOrbit 13 565 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 565) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_565.1, data_13_565.2] + +/-- Complete interval computation for depth 13, residue 566. -/ +theorem bounds_13_566 : exactInterval 13 566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_566 : oddCount 566 13 = 9 ∧ acceleratedOrbit 13 566 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 566) = 3 ^ 9 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_566.1, data_13_566.2] + +/-- Complete interval computation for depth 13, residue 567. -/ +theorem bounds_13_567 : exactInterval 13 567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_567 : oddCount 567 13 = 9 ∧ acceleratedOrbit 13 567 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 567) = 3 ^ 9 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_567.1, data_13_567.2] + +/-- Complete interval computation for depth 13, residue 568. -/ +theorem bounds_13_568 : exactInterval 13 568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_568 : oddCount 568 13 = 7 ∧ acceleratedOrbit 13 568 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 568) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_568.1, data_13_568.2] + +/-- Complete interval computation for depth 13, residue 569. -/ +theorem bounds_13_569 : exactInterval 13 569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_569 : oddCount 569 13 = 9 ∧ acceleratedOrbit 13 569 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 569) = 3 ^ 9 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_569.1, data_13_569.2] + +/-- Complete interval computation for depth 13, residue 570. -/ +theorem bounds_13_570 : exactInterval 13 570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_570 : oddCount 570 13 = 7 ∧ acceleratedOrbit 13 570 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 570) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_570.1, data_13_570.2] + +/-- Complete interval computation for depth 13, residue 571. -/ +theorem bounds_13_571 : exactInterval 13 571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_571 : oddCount 571 13 = 5 ∧ acceleratedOrbit 13 571 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 571) = 3 ^ 5 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_571.1, data_13_571.2] + +/-- Complete interval computation for depth 13, residue 572. -/ +theorem bounds_13_572 : exactInterval 13 572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_572 : oddCount 572 13 = 7 ∧ acceleratedOrbit 13 572 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 572) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_572.1, data_13_572.2] + +end Collatz.Research.StoppingAtlas.Batch0504 From 0180d866332c35c872b090fa378f8ec2631ac309 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:04 +0530 Subject: [PATCH 0505/1001] proof: certify atlas Batch0505 (13:573 to 13:587) --- Collatz/Research/StoppingAtlas/Batch0505.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0505.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0505.lean b/Collatz/Research/StoppingAtlas/Batch0505.lean new file mode 100644 index 00000000..fe77c8be --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0505.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0505 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 573. -/ +theorem bounds_13_573 : exactInterval 13 573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_573 : oddCount 573 13 = 7 ∧ acceleratedOrbit 13 573 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 573) = 3 ^ 7 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_573.1, data_13_573.2] + +/-- Complete interval computation for depth 13, residue 574. -/ +theorem bounds_13_574 : exactInterval 13 574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_574 : oddCount 574 13 = 7 ∧ acceleratedOrbit 13 574 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 574) = 3 ^ 7 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_574.1, data_13_574.2] + +/-- Complete interval computation for depth 13, residue 575. -/ +theorem bounds_13_575 : exactInterval 13 575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_575 : oddCount 575 13 = 7 ∧ acceleratedOrbit 13 575 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 575) = 3 ^ 7 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_575.1, data_13_575.2] + +/-- Complete interval computation for depth 13, residue 576. -/ +theorem bounds_13_576 : exactInterval 13 576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_576 : oddCount 576 13 = 5 ∧ acceleratedOrbit 13 576 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 576) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_576.1, data_13_576.2] + +/-- Complete interval computation for depth 13, residue 577. -/ +theorem bounds_13_577 : exactInterval 13 577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_577 : oddCount 577 13 = 6 ∧ acceleratedOrbit 13 577 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 577) = 3 ^ 6 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_577.1, data_13_577.2] + +/-- Complete interval computation for depth 13, residue 578. -/ +theorem bounds_13_578 : exactInterval 13 578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_578 : oddCount 578 13 = 6 ∧ acceleratedOrbit 13 578 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 578) = 3 ^ 6 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_578.1, data_13_578.2] + +/-- Complete interval computation for depth 13, residue 579. -/ +theorem bounds_13_579 : exactInterval 13 579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_579 : oddCount 579 13 = 6 ∧ acceleratedOrbit 13 579 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 579) = 3 ^ 6 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_579.1, data_13_579.2] + +/-- Complete interval computation for depth 13, residue 580. -/ +theorem bounds_13_580 : exactInterval 13 580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_580 : oddCount 580 13 = 7 ∧ acceleratedOrbit 13 580 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 580) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_580.1, data_13_580.2] + +/-- Complete interval computation for depth 13, residue 581. -/ +theorem bounds_13_581 : exactInterval 13 581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_581 : oddCount 581 13 = 7 ∧ acceleratedOrbit 13 581 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 581) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_581.1, data_13_581.2] + +/-- Complete interval computation for depth 13, residue 582. -/ +theorem bounds_13_582 : exactInterval 13 582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_582 : oddCount 582 13 = 7 ∧ acceleratedOrbit 13 582 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 582) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_582.1, data_13_582.2] + +/-- Complete interval computation for depth 13, residue 583. -/ +theorem bounds_13_583 : exactInterval 13 583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_583 : oddCount 583 13 = 6 ∧ acceleratedOrbit 13 583 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 583) = 3 ^ 6 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_583.1, data_13_583.2] + +/-- Complete interval computation for depth 13, residue 584. -/ +theorem bounds_13_584 : exactInterval 13 584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_584 : oddCount 584 13 = 7 ∧ acceleratedOrbit 13 584 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 584) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_584.1, data_13_584.2] + +/-- Complete interval computation for depth 13, residue 585. -/ +theorem bounds_13_585 : exactInterval 13 585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_585 : oddCount 585 13 = 7 ∧ acceleratedOrbit 13 585 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 585) = 3 ^ 7 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_585.1, data_13_585.2] + +/-- Complete interval computation for depth 13, residue 586. -/ +theorem bounds_13_586 : exactInterval 13 586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_586 : oddCount 586 13 = 7 ∧ acceleratedOrbit 13 586 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 586) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_586.1, data_13_586.2] + +/-- Complete interval computation for depth 13, residue 587. -/ +theorem bounds_13_587 : exactInterval 13 587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_587 : oddCount 587 13 = 7 ∧ acceleratedOrbit 13 587 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 587) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_587.1, data_13_587.2] + +end Collatz.Research.StoppingAtlas.Batch0505 From 1656137169fc4b0fc56f38f18a983bcd1c90ff01 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:04 +0530 Subject: [PATCH 0506/1001] proof: certify atlas Batch0506 (13:588 to 13:603) --- Collatz/Research/StoppingAtlas/Batch0506.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0506.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0506.lean b/Collatz/Research/StoppingAtlas/Batch0506.lean new file mode 100644 index 00000000..f2681847 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0506.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0506 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 588. -/ +theorem bounds_13_588 : exactInterval 13 588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_588 : oddCount 588 13 = 7 ∧ acceleratedOrbit 13 588 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 588) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_588.1, data_13_588.2] + +/-- Complete interval computation for depth 13, residue 589. -/ +theorem bounds_13_589 : exactInterval 13 589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_589 : oddCount 589 13 = 7 ∧ acceleratedOrbit 13 589 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 589) = 3 ^ 7 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_589.1, data_13_589.2] + +/-- Complete interval computation for depth 13, residue 590. -/ +theorem bounds_13_590 : exactInterval 13 590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_590 : oddCount 590 13 = 8 ∧ acceleratedOrbit 13 590 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 590) = 3 ^ 8 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_590.1, data_13_590.2] + +/-- Complete interval computation for depth 13, residue 591. -/ +theorem bounds_13_591 : exactInterval 13 591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_591 : oddCount 591 13 = 8 ∧ acceleratedOrbit 13 591 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 591) = 3 ^ 8 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_591.1, data_13_591.2] + +/-- Complete interval computation for depth 13, residue 592. -/ +theorem bounds_13_592 : exactInterval 13 592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_592 : oddCount 592 13 = 5 ∧ acceleratedOrbit 13 592 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 592) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_592.1, data_13_592.2] + +/-- Complete interval computation for depth 13, residue 593. -/ +theorem bounds_13_593 : exactInterval 13 593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_593 : oddCount 593 13 = 8 ∧ acceleratedOrbit 13 593 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 593) = 3 ^ 8 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_593.1, data_13_593.2] + +/-- Complete interval computation for depth 13, residue 594. -/ +theorem bounds_13_594 : exactInterval 13 594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_594 : oddCount 594 13 = 8 ∧ acceleratedOrbit 13 594 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 594) = 3 ^ 8 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_594.1, data_13_594.2] + +/-- Complete interval computation for depth 13, residue 595. -/ +theorem bounds_13_595 : exactInterval 13 595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_595 : oddCount 595 13 = 8 ∧ acceleratedOrbit 13 595 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 595) = 3 ^ 8 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_595.1, data_13_595.2] + +/-- Complete interval computation for depth 13, residue 596. -/ +theorem bounds_13_596 : exactInterval 13 596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_596 : oddCount 596 13 = 5 ∧ acceleratedOrbit 13 596 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 596) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_596.1, data_13_596.2] + +/-- Complete interval computation for depth 13, residue 597. -/ +theorem bounds_13_597 : exactInterval 13 597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_597 : oddCount 597 13 = 5 ∧ acceleratedOrbit 13 597 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 597) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_597.1, data_13_597.2] + +/-- Complete interval computation for depth 13, residue 598. -/ +theorem bounds_13_598 : exactInterval 13 598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_598 : oddCount 598 13 = 8 ∧ acceleratedOrbit 13 598 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 598) = 3 ^ 8 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_598.1, data_13_598.2] + +/-- Complete interval computation for depth 13, residue 599. -/ +theorem bounds_13_599 : exactInterval 13 599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_599 : oddCount 599 13 = 8 ∧ acceleratedOrbit 13 599 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 599) = 3 ^ 8 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_599.1, data_13_599.2] + +/-- Complete interval computation for depth 13, residue 600. -/ +theorem bounds_13_600 : exactInterval 13 600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_600 : oddCount 600 13 = 3 ∧ acceleratedOrbit 13 600 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 600) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_600.1, data_13_600.2] + +/-- Complete interval computation for depth 13, residue 601. -/ +theorem bounds_13_601 : exactInterval 13 601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_601 : oddCount 601 13 = 9 ∧ acceleratedOrbit 13 601 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 601) = 3 ^ 9 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_601.1, data_13_601.2] + +/-- Complete interval computation for depth 13, residue 602. -/ +theorem bounds_13_602 : exactInterval 13 602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_602 : oddCount 602 13 = 3 ∧ acceleratedOrbit 13 602 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 602) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_602.1, data_13_602.2] + +/-- Complete interval computation for depth 13, residue 603. -/ +theorem bounds_13_603 : exactInterval 13 603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_603 : oddCount 603 13 = 9 ∧ acceleratedOrbit 13 603 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 603) = 3 ^ 9 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_603.1, data_13_603.2] + +end Collatz.Research.StoppingAtlas.Batch0506 From 75387f215eed54842f177742ae9fac6110e10f35 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:05 +0530 Subject: [PATCH 0507/1001] proof: certify atlas Batch0507 (13:604 to 13:618) --- Collatz/Research/StoppingAtlas/Batch0507.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0507.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0507.lean b/Collatz/Research/StoppingAtlas/Batch0507.lean new file mode 100644 index 00000000..db829208 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0507.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0507 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 604. -/ +theorem bounds_13_604 : exactInterval 13 604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_604 : oddCount 604 13 = 3 ∧ acceleratedOrbit 13 604 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 604) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_604.1, data_13_604.2] + +/-- Complete interval computation for depth 13, residue 605. -/ +theorem bounds_13_605 : exactInterval 13 605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_605 : oddCount 605 13 = 3 ∧ acceleratedOrbit 13 605 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 605) = 3 ^ 3 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_605.1, data_13_605.2] + +/-- Complete interval computation for depth 13, residue 606. -/ +theorem bounds_13_606 : exactInterval 13 606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_606 : oddCount 606 13 = 8 ∧ acceleratedOrbit 13 606 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 606) = 3 ^ 8 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_606.1, data_13_606.2] + +/-- Complete interval computation for depth 13, residue 607. -/ +theorem bounds_13_607 : exactInterval 13 607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 607) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_607 : oddCount 607 13 = 8 ∧ acceleratedOrbit 13 607 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 607) = 3 ^ 8 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_607.1, data_13_607.2] + +/-- Complete interval computation for depth 13, residue 608. -/ +theorem bounds_13_608 : exactInterval 13 608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_608 : oddCount 608 13 = 5 ∧ acceleratedOrbit 13 608 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 608) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_608.1, data_13_608.2] + +/-- Complete interval computation for depth 13, residue 609. -/ +theorem bounds_13_609 : exactInterval 13 609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_609 : oddCount 609 13 = 7 ∧ acceleratedOrbit 13 609 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 609) = 3 ^ 7 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_609.1, data_13_609.2] + +/-- Complete interval computation for depth 13, residue 610. -/ +theorem bounds_13_610 : exactInterval 13 610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_610 : oddCount 610 13 = 6 ∧ acceleratedOrbit 13 610 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 610) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_610.1, data_13_610.2] + +/-- Complete interval computation for depth 13, residue 611. -/ +theorem bounds_13_611 : exactInterval 13 611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_611 : oddCount 611 13 = 6 ∧ acceleratedOrbit 13 611 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 611) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_611.1, data_13_611.2] + +/-- Complete interval computation for depth 13, residue 612. -/ +theorem bounds_13_612 : exactInterval 13 612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_612 : oddCount 612 13 = 6 ∧ acceleratedOrbit 13 612 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 612) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_612.1, data_13_612.2] + +/-- Complete interval computation for depth 13, residue 613. -/ +theorem bounds_13_613 : exactInterval 13 613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_613 : oddCount 613 13 = 6 ∧ acceleratedOrbit 13 613 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 613) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_613.1, data_13_613.2] + +/-- Complete interval computation for depth 13, residue 614. -/ +theorem bounds_13_614 : exactInterval 13 614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_614 : oddCount 614 13 = 6 ∧ acceleratedOrbit 13 614 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 614) = 3 ^ 6 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_614.1, data_13_614.2] + +/-- Complete interval computation for depth 13, residue 615. -/ +theorem bounds_13_615 : exactInterval 13 615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_615 : oddCount 615 13 = 8 ∧ acceleratedOrbit 13 615 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 615) = 3 ^ 8 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_615.1, data_13_615.2] + +/-- Complete interval computation for depth 13, residue 616. -/ +theorem bounds_13_616 : exactInterval 13 616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_616 : oddCount 616 13 = 5 ∧ acceleratedOrbit 13 616 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 616) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_616.1, data_13_616.2] + +/-- Complete interval computation for depth 13, residue 617. -/ +theorem bounds_13_617 : exactInterval 13 617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_617 : oddCount 617 13 = 8 ∧ acceleratedOrbit 13 617 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 617) = 3 ^ 8 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_617.1, data_13_617.2] + +/-- Complete interval computation for depth 13, residue 618. -/ +theorem bounds_13_618 : exactInterval 13 618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_618 : oddCount 618 13 = 5 ∧ acceleratedOrbit 13 618 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 618) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_618.1, data_13_618.2] + +end Collatz.Research.StoppingAtlas.Batch0507 From 33f12f59d415122482b9ac42415621adefef35b8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:05 +0530 Subject: [PATCH 0508/1001] proof: certify atlas Batch0508 (13:619 to 13:633) --- Collatz/Research/StoppingAtlas/Batch0508.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0508.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0508.lean b/Collatz/Research/StoppingAtlas/Batch0508.lean new file mode 100644 index 00000000..e6ed218c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0508.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0508 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 619. -/ +theorem bounds_13_619 : exactInterval 13 619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_619 : oddCount 619 13 = 7 ∧ acceleratedOrbit 13 619 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 619) = 3 ^ 7 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_619.1, data_13_619.2] + +/-- Complete interval computation for depth 13, residue 620. -/ +theorem bounds_13_620 : exactInterval 13 620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_620 : oddCount 620 13 = 7 ∧ acceleratedOrbit 13 620 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 620) = 3 ^ 7 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_620.1, data_13_620.2] + +/-- Complete interval computation for depth 13, residue 621. -/ +theorem bounds_13_621 : exactInterval 13 621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_621 : oddCount 621 13 = 7 ∧ acceleratedOrbit 13 621 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 621) = 3 ^ 7 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_621.1, data_13_621.2] + +/-- Complete interval computation for depth 13, residue 622. -/ +theorem bounds_13_622 : exactInterval 13 622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_622 : oddCount 622 13 = 7 ∧ acceleratedOrbit 13 622 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 622) = 3 ^ 7 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_622.1, data_13_622.2] + +/-- Complete interval computation for depth 13, residue 623. -/ +theorem bounds_13_623 : exactInterval 13 623 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 623) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_623 : oddCount 623 13 = 8 ∧ acceleratedOrbit 13 623 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 623) = 3 ^ 8 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_623.1, data_13_623.2] + +/-- Complete interval computation for depth 13, residue 624. -/ +theorem bounds_13_624 : exactInterval 13 624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_624 : oddCount 624 13 = 5 ∧ acceleratedOrbit 13 624 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 624) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_624.1, data_13_624.2] + +/-- Complete interval computation for depth 13, residue 625. -/ +theorem bounds_13_625 : exactInterval 13 625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_625 : oddCount 625 13 = 5 ∧ acceleratedOrbit 13 625 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 625) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_625.1, data_13_625.2] + +/-- Complete interval computation for depth 13, residue 626. -/ +theorem bounds_13_626 : exactInterval 13 626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_626 : oddCount 626 13 = 8 ∧ acceleratedOrbit 13 626 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 626) = 3 ^ 8 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_626.1, data_13_626.2] + +/-- Complete interval computation for depth 13, residue 627. -/ +theorem bounds_13_627 : exactInterval 13 627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_627 : oddCount 627 13 = 8 ∧ acceleratedOrbit 13 627 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 627) = 3 ^ 8 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_627.1, data_13_627.2] + +/-- Complete interval computation for depth 13, residue 628. -/ +theorem bounds_13_628 : exactInterval 13 628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_628 : oddCount 628 13 = 5 ∧ acceleratedOrbit 13 628 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 628) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_628.1, data_13_628.2] + +/-- Complete interval computation for depth 13, residue 629. -/ +theorem bounds_13_629 : exactInterval 13 629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_629 : oddCount 629 13 = 5 ∧ acceleratedOrbit 13 629 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 629) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_629.1, data_13_629.2] + +/-- Complete interval computation for depth 13, residue 630. -/ +theorem bounds_13_630 : exactInterval 13 630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_630 : oddCount 630 13 = 5 ∧ acceleratedOrbit 13 630 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 630) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_630.1, data_13_630.2] + +/-- Complete interval computation for depth 13, residue 631. -/ +theorem bounds_13_631 : exactInterval 13 631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 631) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_631 : oddCount 631 13 = 5 ∧ acceleratedOrbit 13 631 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 631) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_631.1, data_13_631.2] + +/-- Complete interval computation for depth 13, residue 632. -/ +theorem bounds_13_632 : exactInterval 13 632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_632 : oddCount 632 13 = 5 ∧ acceleratedOrbit 13 632 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 632) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_632.1, data_13_632.2] + +/-- Complete interval computation for depth 13, residue 633. -/ +theorem bounds_13_633 : exactInterval 13 633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_633 : oddCount 633 13 = 7 ∧ acceleratedOrbit 13 633 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 633) = 3 ^ 7 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_633.1, data_13_633.2] + +end Collatz.Research.StoppingAtlas.Batch0508 From 8b4cedd4310978118e762c5e7201c94b650515e5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:06 +0530 Subject: [PATCH 0509/1001] proof: certify atlas Batch0509 (13:634 to 13:649) --- Collatz/Research/StoppingAtlas/Batch0509.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0509.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0509.lean b/Collatz/Research/StoppingAtlas/Batch0509.lean new file mode 100644 index 00000000..740ba1cf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0509.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0509 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 634. -/ +theorem bounds_13_634 : exactInterval 13 634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_634 : oddCount 634 13 = 5 ∧ acceleratedOrbit 13 634 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 634) = 3 ^ 5 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_634.1, data_13_634.2] + +/-- Complete interval computation for depth 13, residue 635. -/ +theorem bounds_13_635 : exactInterval 13 635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_635 : oddCount 635 13 = 8 ∧ acceleratedOrbit 13 635 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 635) = 3 ^ 8 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_635.1, data_13_635.2] + +/-- Complete interval computation for depth 13, residue 636. -/ +theorem bounds_13_636 : exactInterval 13 636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_636 : oddCount 636 13 = 10 ∧ acceleratedOrbit 13 636 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 636) = 3 ^ 10 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_636.1, data_13_636.2] + +/-- Complete interval computation for depth 13, residue 637. -/ +theorem bounds_13_637 : exactInterval 13 637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_637 : oddCount 637 13 = 10 ∧ acceleratedOrbit 13 637 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 637) = 3 ^ 10 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_637.1, data_13_637.2] + +/-- Complete interval computation for depth 13, residue 638. -/ +theorem bounds_13_638 : exactInterval 13 638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_638 : oddCount 638 13 = 10 ∧ acceleratedOrbit 13 638 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 638) = 3 ^ 10 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_638.1, data_13_638.2] + +/-- Complete interval computation for depth 13, residue 639. -/ +theorem bounds_13_639 : exactInterval 13 639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_639 : oddCount 639 13 = 11 ∧ acceleratedOrbit 13 639 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 639) = 3 ^ 11 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_639.1, data_13_639.2] + +/-- Complete interval computation for depth 13, residue 640. -/ +theorem bounds_13_640 : exactInterval 13 640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_640 : oddCount 640 13 = 2 ∧ acceleratedOrbit 13 640 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 640) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_640.1, data_13_640.2] + +/-- Complete interval computation for depth 13, residue 641. -/ +theorem bounds_13_641 : exactInterval 13 641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_641 : oddCount 641 13 = 7 ∧ acceleratedOrbit 13 641 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 641) = 3 ^ 7 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_641.1, data_13_641.2] + +/-- Complete interval computation for depth 13, residue 642. -/ +theorem bounds_13_642 : exactInterval 13 642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_642 : oddCount 642 13 = 5 ∧ acceleratedOrbit 13 642 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 642) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_642.1, data_13_642.2] + +/-- Complete interval computation for depth 13, residue 643. -/ +theorem bounds_13_643 : exactInterval 13 643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_643 : oddCount 643 13 = 5 ∧ acceleratedOrbit 13 643 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 643) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_643.1, data_13_643.2] + +/-- Complete interval computation for depth 13, residue 644. -/ +theorem bounds_13_644 : exactInterval 13 644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_644 : oddCount 644 13 = 7 ∧ acceleratedOrbit 13 644 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 644) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_644.1, data_13_644.2] + +/-- Complete interval computation for depth 13, residue 645. -/ +theorem bounds_13_645 : exactInterval 13 645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_645 : oddCount 645 13 = 7 ∧ acceleratedOrbit 13 645 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 645) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_645.1, data_13_645.2] + +/-- Complete interval computation for depth 13, residue 646. -/ +theorem bounds_13_646 : exactInterval 13 646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_646 : oddCount 646 13 = 7 ∧ acceleratedOrbit 13 646 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 646) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_646.1, data_13_646.2] + +/-- Complete interval computation for depth 13, residue 647. -/ +theorem bounds_13_647 : exactInterval 13 647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_647 : oddCount 647 13 = 6 ∧ acceleratedOrbit 13 647 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 647) = 3 ^ 6 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_647.1, data_13_647.2] + +/-- Complete interval computation for depth 13, residue 648. -/ +theorem bounds_13_648 : exactInterval 13 648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_648 : oddCount 648 13 = 5 ∧ acceleratedOrbit 13 648 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 648) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_648.1, data_13_648.2] + +/-- Complete interval computation for depth 13, residue 649. -/ +theorem bounds_13_649 : exactInterval 13 649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_649 : oddCount 649 13 = 9 ∧ acceleratedOrbit 13 649 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 649) = 3 ^ 9 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_649.1, data_13_649.2] + +end Collatz.Research.StoppingAtlas.Batch0509 From 0cc977e99f69ae9de9ed881cdefb2bf687a6d2c8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:06 +0530 Subject: [PATCH 0510/1001] proof: certify atlas Batch0510 (13:650 to 13:664) --- Collatz/Research/StoppingAtlas/Batch0510.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0510.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0510.lean b/Collatz/Research/StoppingAtlas/Batch0510.lean new file mode 100644 index 00000000..abe3124b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0510.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0510 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 650. -/ +theorem bounds_13_650 : exactInterval 13 650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_650 : oddCount 650 13 = 5 ∧ acceleratedOrbit 13 650 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 650) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_650.1, data_13_650.2] + +/-- Complete interval computation for depth 13, residue 651. -/ +theorem bounds_13_651 : exactInterval 13 651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_651 : oddCount 651 13 = 7 ∧ acceleratedOrbit 13 651 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 651) = 3 ^ 7 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_651.1, data_13_651.2] + +/-- Complete interval computation for depth 13, residue 652. -/ +theorem bounds_13_652 : exactInterval 13 652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_652 : oddCount 652 13 = 5 ∧ acceleratedOrbit 13 652 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 652) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_652.1, data_13_652.2] + +/-- Complete interval computation for depth 13, residue 653. -/ +theorem bounds_13_653 : exactInterval 13 653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_653 : oddCount 653 13 = 5 ∧ acceleratedOrbit 13 653 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 653) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_653.1, data_13_653.2] + +/-- Complete interval computation for depth 13, residue 654. -/ +theorem bounds_13_654 : exactInterval 13 654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_654 : oddCount 654 13 = 9 ∧ acceleratedOrbit 13 654 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 654) = 3 ^ 9 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_654.1, data_13_654.2] + +/-- Complete interval computation for depth 13, residue 655. -/ +theorem bounds_13_655 : exactInterval 13 655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_655 : oddCount 655 13 = 9 ∧ acceleratedOrbit 13 655 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 655) = 3 ^ 9 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_655.1, data_13_655.2] + +/-- Complete interval computation for depth 13, residue 656. -/ +theorem bounds_13_656 : exactInterval 13 656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_656 : oddCount 656 13 = 7 ∧ acceleratedOrbit 13 656 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 656) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_656.1, data_13_656.2] + +/-- Complete interval computation for depth 13, residue 657. -/ +theorem bounds_13_657 : exactInterval 13 657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_657 : oddCount 657 13 = 6 ∧ acceleratedOrbit 13 657 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 657) = 3 ^ 6 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_657.1, data_13_657.2] + +/-- Complete interval computation for depth 13, residue 658. -/ +theorem bounds_13_658 : exactInterval 13 658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_658 : oddCount 658 13 = 6 ∧ acceleratedOrbit 13 658 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 658) = 3 ^ 6 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_658.1, data_13_658.2] + +/-- Complete interval computation for depth 13, residue 659. -/ +theorem bounds_13_659 : exactInterval 13 659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_659 : oddCount 659 13 = 6 ∧ acceleratedOrbit 13 659 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 659) = 3 ^ 6 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_659.1, data_13_659.2] + +/-- Complete interval computation for depth 13, residue 660. -/ +theorem bounds_13_660 : exactInterval 13 660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_660 : oddCount 660 13 = 7 ∧ acceleratedOrbit 13 660 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 660) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_660.1, data_13_660.2] + +/-- Complete interval computation for depth 13, residue 661. -/ +theorem bounds_13_661 : exactInterval 13 661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_661 : oddCount 661 13 = 7 ∧ acceleratedOrbit 13 661 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 661) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_661.1, data_13_661.2] + +/-- Complete interval computation for depth 13, residue 662. -/ +theorem bounds_13_662 : exactInterval 13 662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_662 : oddCount 662 13 = 5 ∧ acceleratedOrbit 13 662 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 662) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_662.1, data_13_662.2] + +/-- Complete interval computation for depth 13, residue 663. -/ +theorem bounds_13_663 : exactInterval 13 663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_663 : oddCount 663 13 = 5 ∧ acceleratedOrbit 13 663 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 663) = 3 ^ 5 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_663.1, data_13_663.2] + +/-- Complete interval computation for depth 13, residue 664. -/ +theorem bounds_13_664 : exactInterval 13 664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_664 : oddCount 664 13 = 7 ∧ acceleratedOrbit 13 664 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 664) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_664.1, data_13_664.2] + +end Collatz.Research.StoppingAtlas.Batch0510 From e2c1d0c0f265181719f1ac75d3e7903279882ba1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:06 +0530 Subject: [PATCH 0511/1001] proof: certify atlas Batch0511 (13:665 to 13:679) --- Collatz/Research/StoppingAtlas/Batch0511.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0511.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0511.lean b/Collatz/Research/StoppingAtlas/Batch0511.lean new file mode 100644 index 00000000..c6e84bad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0511.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0511 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 665. -/ +theorem bounds_13_665 : exactInterval 13 665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_665 : oddCount 665 13 = 7 ∧ acceleratedOrbit 13 665 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 665) = 3 ^ 7 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_665.1, data_13_665.2] + +/-- Complete interval computation for depth 13, residue 666. -/ +theorem bounds_13_666 : exactInterval 13 666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_666 : oddCount 666 13 = 7 ∧ acceleratedOrbit 13 666 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 666) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_666.1, data_13_666.2] + +/-- Complete interval computation for depth 13, residue 667. -/ +theorem bounds_13_667 : exactInterval 13 667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_667 : oddCount 667 13 = 10 ∧ acceleratedOrbit 13 667 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 667) = 3 ^ 10 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_667.1, data_13_667.2] + +/-- Complete interval computation for depth 13, residue 668. -/ +theorem bounds_13_668 : exactInterval 13 668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_668 : oddCount 668 13 = 9 ∧ acceleratedOrbit 13 668 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 668) = 3 ^ 9 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_668.1, data_13_668.2] + +/-- Complete interval computation for depth 13, residue 669. -/ +theorem bounds_13_669 : exactInterval 13 669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_669 : oddCount 669 13 = 9 ∧ acceleratedOrbit 13 669 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 669) = 3 ^ 9 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_669.1, data_13_669.2] + +/-- Complete interval computation for depth 13, residue 670. -/ +theorem bounds_13_670 : exactInterval 13 670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_670 : oddCount 670 13 = 9 ∧ acceleratedOrbit 13 670 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 670) = 3 ^ 9 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_670.1, data_13_670.2] + +/-- Complete interval computation for depth 13, residue 671. -/ +theorem bounds_13_671 : exactInterval 13 671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_671 : oddCount 671 13 = 9 ∧ acceleratedOrbit 13 671 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 671) = 3 ^ 9 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_671.1, data_13_671.2] + +/-- Complete interval computation for depth 13, residue 672. -/ +theorem bounds_13_672 : exactInterval 13 672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_672 : oddCount 672 13 = 2 ∧ acceleratedOrbit 13 672 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 672) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_672.1, data_13_672.2] + +/-- Complete interval computation for depth 13, residue 673. -/ +theorem bounds_13_673 : exactInterval 13 673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_673 : oddCount 673 13 = 8 ∧ acceleratedOrbit 13 673 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 673) = 3 ^ 8 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_673.1, data_13_673.2] + +/-- Complete interval computation for depth 13, residue 674. -/ +theorem bounds_13_674 : exactInterval 13 674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_674 : oddCount 674 13 = 7 ∧ acceleratedOrbit 13 674 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 674) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_674.1, data_13_674.2] + +/-- Complete interval computation for depth 13, residue 675. -/ +theorem bounds_13_675 : exactInterval 13 675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_675 : oddCount 675 13 = 7 ∧ acceleratedOrbit 13 675 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 675) = 3 ^ 7 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_675.1, data_13_675.2] + +/-- Complete interval computation for depth 13, residue 676. -/ +theorem bounds_13_676 : exactInterval 13 676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_676 : oddCount 676 13 = 9 ∧ acceleratedOrbit 13 676 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 676) = 3 ^ 9 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_676.1, data_13_676.2] + +/-- Complete interval computation for depth 13, residue 677. -/ +theorem bounds_13_677 : exactInterval 13 677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_677 : oddCount 677 13 = 9 ∧ acceleratedOrbit 13 677 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 677) = 3 ^ 9 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_677.1, data_13_677.2] + +/-- Complete interval computation for depth 13, residue 678. -/ +theorem bounds_13_678 : exactInterval 13 678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_678 : oddCount 678 13 = 9 ∧ acceleratedOrbit 13 678 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 678) = 3 ^ 9 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_678.1, data_13_678.2] + +/-- Complete interval computation for depth 13, residue 679. -/ +theorem bounds_13_679 : exactInterval 13 679 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 679) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_679 : oddCount 679 13 = 8 ∧ acceleratedOrbit 13 679 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 679) = 3 ^ 8 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_679.1, data_13_679.2] + +end Collatz.Research.StoppingAtlas.Batch0511 From e519faae6d6537c1a847d953a1cfc12b6f5b56ba Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:07 +0530 Subject: [PATCH 0512/1001] proof: certify atlas Batch0512 (13:680 to 13:695) --- Collatz/Research/StoppingAtlas/Batch0512.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0512.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0512.lean b/Collatz/Research/StoppingAtlas/Batch0512.lean new file mode 100644 index 00000000..6f5e8025 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0512.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0512 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 680. -/ +theorem bounds_13_680 : exactInterval 13 680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_680 : oddCount 680 13 = 2 ∧ acceleratedOrbit 13 680 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 680) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_680.1, data_13_680.2] + +/-- Complete interval computation for depth 13, residue 681. -/ +theorem bounds_13_681 : exactInterval 13 681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_681 : oddCount 681 13 = 11 ∧ acceleratedOrbit 13 681 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 681) = 3 ^ 11 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_681.1, data_13_681.2] + +/-- Complete interval computation for depth 13, residue 682. -/ +theorem bounds_13_682 : exactInterval 13 682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_682 : oddCount 682 13 = 2 ∧ acceleratedOrbit 13 682 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 682) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_682.1, data_13_682.2] + +/-- Complete interval computation for depth 13, residue 683. -/ +theorem bounds_13_683 : exactInterval 13 683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_683 : oddCount 683 13 = 6 ∧ acceleratedOrbit 13 683 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 683) = 3 ^ 6 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_683.1, data_13_683.2] + +/-- Complete interval computation for depth 13, residue 684. -/ +theorem bounds_13_684 : exactInterval 13 684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_684 : oddCount 684 13 = 6 ∧ acceleratedOrbit 13 684 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 684) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_684.1, data_13_684.2] + +/-- Complete interval computation for depth 13, residue 685. -/ +theorem bounds_13_685 : exactInterval 13 685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_685 : oddCount 685 13 = 6 ∧ acceleratedOrbit 13 685 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 685) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_685.1, data_13_685.2] + +/-- Complete interval computation for depth 13, residue 686. -/ +theorem bounds_13_686 : exactInterval 13 686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_686 : oddCount 686 13 = 6 ∧ acceleratedOrbit 13 686 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 686) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_686.1, data_13_686.2] + +/-- Complete interval computation for depth 13, residue 687. -/ +theorem bounds_13_687 : exactInterval 13 687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_687 : oddCount 687 13 = 7 ∧ acceleratedOrbit 13 687 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 687) = 3 ^ 7 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_687.1, data_13_687.2] + +/-- Complete interval computation for depth 13, residue 688. -/ +theorem bounds_13_688 : exactInterval 13 688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_688 : oddCount 688 13 = 4 ∧ acceleratedOrbit 13 688 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 688) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_688.1, data_13_688.2] + +/-- Complete interval computation for depth 13, residue 689. -/ +theorem bounds_13_689 : exactInterval 13 689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_689 : oddCount 689 13 = 7 ∧ acceleratedOrbit 13 689 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 689) = 3 ^ 7 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_689.1, data_13_689.2] + +/-- Complete interval computation for depth 13, residue 690. -/ +theorem bounds_13_690 : exactInterval 13 690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_690 : oddCount 690 13 = 7 ∧ acceleratedOrbit 13 690 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 690) = 3 ^ 7 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_690.1, data_13_690.2] + +/-- Complete interval computation for depth 13, residue 691. -/ +theorem bounds_13_691 : exactInterval 13 691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_691 : oddCount 691 13 = 7 ∧ acceleratedOrbit 13 691 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 691) = 3 ^ 7 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_691.1, data_13_691.2] + +/-- Complete interval computation for depth 13, residue 692. -/ +theorem bounds_13_692 : exactInterval 13 692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_692 : oddCount 692 13 = 4 ∧ acceleratedOrbit 13 692 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 692) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_692.1, data_13_692.2] + +/-- Complete interval computation for depth 13, residue 693. -/ +theorem bounds_13_693 : exactInterval 13 693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_693 : oddCount 693 13 = 4 ∧ acceleratedOrbit 13 693 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 693) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_693.1, data_13_693.2] + +/-- Complete interval computation for depth 13, residue 694. -/ +theorem bounds_13_694 : exactInterval 13 694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_694 : oddCount 694 13 = 6 ∧ acceleratedOrbit 13 694 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 694) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_694.1, data_13_694.2] + +/-- Complete interval computation for depth 13, residue 695. -/ +theorem bounds_13_695 : exactInterval 13 695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_695 : oddCount 695 13 = 6 ∧ acceleratedOrbit 13 695 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 695) = 3 ^ 6 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_695.1, data_13_695.2] + +end Collatz.Research.StoppingAtlas.Batch0512 From 31f982ae2b44911fed232c79d83668cc4868a3a1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:07 +0530 Subject: [PATCH 0513/1001] proof: certify atlas Batch0513 (13:696 to 13:710) --- Collatz/Research/StoppingAtlas/Batch0513.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0513.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0513.lean b/Collatz/Research/StoppingAtlas/Batch0513.lean new file mode 100644 index 00000000..ed66027b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0513.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0513 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 696. -/ +theorem bounds_13_696 : exactInterval 13 696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_696 : oddCount 696 13 = 4 ∧ acceleratedOrbit 13 696 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 696) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_696.1, data_13_696.2] + +/-- Complete interval computation for depth 13, residue 697. -/ +theorem bounds_13_697 : exactInterval 13 697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_697 : oddCount 697 13 = 7 ∧ acceleratedOrbit 13 697 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 697) = 3 ^ 7 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_697.1, data_13_697.2] + +/-- Complete interval computation for depth 13, residue 698. -/ +theorem bounds_13_698 : exactInterval 13 698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_698 : oddCount 698 13 = 4 ∧ acceleratedOrbit 13 698 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 698) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_698.1, data_13_698.2] + +/-- Complete interval computation for depth 13, residue 699. -/ +theorem bounds_13_699 : exactInterval 13 699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_699 : oddCount 699 13 = 8 ∧ acceleratedOrbit 13 699 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 699) = 3 ^ 8 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_699.1, data_13_699.2] + +/-- Complete interval computation for depth 13, residue 700. -/ +theorem bounds_13_700 : exactInterval 13 700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_700 : oddCount 700 13 = 8 ∧ acceleratedOrbit 13 700 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 700) = 3 ^ 8 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_700.1, data_13_700.2] + +/-- Complete interval computation for depth 13, residue 701. -/ +theorem bounds_13_701 : exactInterval 13 701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_701 : oddCount 701 13 = 8 ∧ acceleratedOrbit 13 701 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 701) = 3 ^ 8 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_701.1, data_13_701.2] + +/-- Complete interval computation for depth 13, residue 702. -/ +theorem bounds_13_702 : exactInterval 13 702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_702 : oddCount 702 13 = 8 ∧ acceleratedOrbit 13 702 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 702) = 3 ^ 8 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_702.1, data_13_702.2] + +/-- Complete interval computation for depth 13, residue 703. -/ +theorem bounds_13_703 : exactInterval 13 703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_703 : oddCount 703 13 = 11 ∧ acceleratedOrbit 13 703 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 703) = 3 ^ 11 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_703.1, data_13_703.2] + +/-- Complete interval computation for depth 13, residue 704. -/ +theorem bounds_13_704 : exactInterval 13 704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_704 : oddCount 704 13 = 4 ∧ acceleratedOrbit 13 704 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 704) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_704.1, data_13_704.2] + +/-- Complete interval computation for depth 13, residue 705. -/ +theorem bounds_13_705 : exactInterval 13 705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_705 : oddCount 705 13 = 4 ∧ acceleratedOrbit 13 705 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 705) = 3 ^ 4 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_705.1, data_13_705.2] + +/-- Complete interval computation for depth 13, residue 706. -/ +theorem bounds_13_706 : exactInterval 13 706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_706 : oddCount 706 13 = 7 ∧ acceleratedOrbit 13 706 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 706) = 3 ^ 7 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_706.1, data_13_706.2] + +/-- Complete interval computation for depth 13, residue 707. -/ +theorem bounds_13_707 : exactInterval 13 707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_707 : oddCount 707 13 = 7 ∧ acceleratedOrbit 13 707 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 707) = 3 ^ 7 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_707.1, data_13_707.2] + +/-- Complete interval computation for depth 13, residue 708. -/ +theorem bounds_13_708 : exactInterval 13 708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_708 : oddCount 708 13 = 5 ∧ acceleratedOrbit 13 708 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 708) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_708.1, data_13_708.2] + +/-- Complete interval computation for depth 13, residue 709. -/ +theorem bounds_13_709 : exactInterval 13 709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_709 : oddCount 709 13 = 5 ∧ acceleratedOrbit 13 709 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 709) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_709.1, data_13_709.2] + +/-- Complete interval computation for depth 13, residue 710. -/ +theorem bounds_13_710 : exactInterval 13 710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_710 : oddCount 710 13 = 5 ∧ acceleratedOrbit 13 710 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 710) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_710.1, data_13_710.2] + +end Collatz.Research.StoppingAtlas.Batch0513 From def36be00935bf4c9cc604e113cd557b399e9ca3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:07 +0530 Subject: [PATCH 0514/1001] proof: certify atlas Batch0514 (13:711 to 13:726) --- Collatz/Research/StoppingAtlas/Batch0514.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0514.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0514.lean b/Collatz/Research/StoppingAtlas/Batch0514.lean new file mode 100644 index 00000000..b07d4c3c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0514.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0514 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 711. -/ +theorem bounds_13_711 : exactInterval 13 711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_711 : oddCount 711 13 = 7 ∧ acceleratedOrbit 13 711 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 711) = 3 ^ 7 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_711.1, data_13_711.2] + +/-- Complete interval computation for depth 13, residue 712. -/ +theorem bounds_13_712 : exactInterval 13 712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_712 : oddCount 712 13 = 5 ∧ acceleratedOrbit 13 712 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 712) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_712.1, data_13_712.2] + +/-- Complete interval computation for depth 13, residue 713. -/ +theorem bounds_13_713 : exactInterval 13 713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_713 : oddCount 713 13 = 6 ∧ acceleratedOrbit 13 713 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 713) = 3 ^ 6 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_713.1, data_13_713.2] + +/-- Complete interval computation for depth 13, residue 714. -/ +theorem bounds_13_714 : exactInterval 13 714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_714 : oddCount 714 13 = 5 ∧ acceleratedOrbit 13 714 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 714) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_714.1, data_13_714.2] + +/-- Complete interval computation for depth 13, residue 715. -/ +theorem bounds_13_715 : exactInterval 13 715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_715 : oddCount 715 13 = 6 ∧ acceleratedOrbit 13 715 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 715) = 3 ^ 6 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_715.1, data_13_715.2] + +/-- Complete interval computation for depth 13, residue 716. -/ +theorem bounds_13_716 : exactInterval 13 716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_716 : oddCount 716 13 = 5 ∧ acceleratedOrbit 13 716 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 716) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_716.1, data_13_716.2] + +/-- Complete interval computation for depth 13, residue 717. -/ +theorem bounds_13_717 : exactInterval 13 717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_717 : oddCount 717 13 = 5 ∧ acceleratedOrbit 13 717 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 717) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_717.1, data_13_717.2] + +/-- Complete interval computation for depth 13, residue 718. -/ +theorem bounds_13_718 : exactInterval 13 718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_718 : oddCount 718 13 = 8 ∧ acceleratedOrbit 13 718 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 718) = 3 ^ 8 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_718.1, data_13_718.2] + +/-- Complete interval computation for depth 13, residue 719. -/ +theorem bounds_13_719 : exactInterval 13 719 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 719) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_719 : oddCount 719 13 = 8 ∧ acceleratedOrbit 13 719 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 719) = 3 ^ 8 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_719.1, data_13_719.2] + +/-- Complete interval computation for depth 13, residue 720. -/ +theorem bounds_13_720 : exactInterval 13 720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_720 : oddCount 720 13 = 4 ∧ acceleratedOrbit 13 720 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 720) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_720.1, data_13_720.2] + +/-- Complete interval computation for depth 13, residue 721. -/ +theorem bounds_13_721 : exactInterval 13 721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_721 : oddCount 721 13 = 6 ∧ acceleratedOrbit 13 721 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 721) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_721.1, data_13_721.2] + +/-- Complete interval computation for depth 13, residue 722. -/ +theorem bounds_13_722 : exactInterval 13 722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_722 : oddCount 722 13 = 6 ∧ acceleratedOrbit 13 722 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 722) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_722.1, data_13_722.2] + +/-- Complete interval computation for depth 13, residue 723. -/ +theorem bounds_13_723 : exactInterval 13 723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_723 : oddCount 723 13 = 6 ∧ acceleratedOrbit 13 723 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 723) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_723.1, data_13_723.2] + +/-- Complete interval computation for depth 13, residue 724. -/ +theorem bounds_13_724 : exactInterval 13 724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_724 : oddCount 724 13 = 4 ∧ acceleratedOrbit 13 724 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 724) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_724.1, data_13_724.2] + +/-- Complete interval computation for depth 13, residue 725. -/ +theorem bounds_13_725 : exactInterval 13 725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_725 : oddCount 725 13 = 4 ∧ acceleratedOrbit 13 725 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 725) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_725.1, data_13_725.2] + +/-- Complete interval computation for depth 13, residue 726. -/ +theorem bounds_13_726 : exactInterval 13 726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_726 : oddCount 726 13 = 6 ∧ acceleratedOrbit 13 726 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 726) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_726.1, data_13_726.2] + +end Collatz.Research.StoppingAtlas.Batch0514 From 28d5b5240f1f0663c0d016da682297ca3c2477f5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:08 +0530 Subject: [PATCH 0515/1001] proof: certify atlas Batch0515 (13:727 to 13:741) --- Collatz/Research/StoppingAtlas/Batch0515.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0515.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0515.lean b/Collatz/Research/StoppingAtlas/Batch0515.lean new file mode 100644 index 00000000..e0faa710 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0515.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0515 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 727. -/ +theorem bounds_13_727 : exactInterval 13 727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_727 : oddCount 727 13 = 6 ∧ acceleratedOrbit 13 727 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 727) = 3 ^ 6 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_727.1, data_13_727.2] + +/-- Complete interval computation for depth 13, residue 728. -/ +theorem bounds_13_728 : exactInterval 13 728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_728 : oddCount 728 13 = 8 ∧ acceleratedOrbit 13 728 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 728) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_728.1, data_13_728.2] + +/-- Complete interval computation for depth 13, residue 729. -/ +theorem bounds_13_729 : exactInterval 13 729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_729 : oddCount 729 13 = 5 ∧ acceleratedOrbit 13 729 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 729) = 3 ^ 5 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_729.1, data_13_729.2] + +/-- Complete interval computation for depth 13, residue 730. -/ +theorem bounds_13_730 : exactInterval 13 730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_730 : oddCount 730 13 = 8 ∧ acceleratedOrbit 13 730 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 730) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_730.1, data_13_730.2] + +/-- Complete interval computation for depth 13, residue 731. -/ +theorem bounds_13_731 : exactInterval 13 731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_731 : oddCount 731 13 = 8 ∧ acceleratedOrbit 13 731 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 731) = 3 ^ 8 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_731.1, data_13_731.2] + +/-- Complete interval computation for depth 13, residue 732. -/ +theorem bounds_13_732 : exactInterval 13 732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_732 : oddCount 732 13 = 8 ∧ acceleratedOrbit 13 732 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 732) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_732.1, data_13_732.2] + +/-- Complete interval computation for depth 13, residue 733. -/ +theorem bounds_13_733 : exactInterval 13 733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_733 : oddCount 733 13 = 8 ∧ acceleratedOrbit 13 733 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 733) = 3 ^ 8 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_733.1, data_13_733.2] + +/-- Complete interval computation for depth 13, residue 734. -/ +theorem bounds_13_734 : exactInterval 13 734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_734 : oddCount 734 13 = 7 ∧ acceleratedOrbit 13 734 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 734) = 3 ^ 7 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_734.1, data_13_734.2] + +/-- Complete interval computation for depth 13, residue 735. -/ +theorem bounds_13_735 : exactInterval 13 735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_735 : oddCount 735 13 = 7 ∧ acceleratedOrbit 13 735 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 735) = 3 ^ 7 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_735.1, data_13_735.2] + +/-- Complete interval computation for depth 13, residue 736. -/ +theorem bounds_13_736 : exactInterval 13 736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_736 : oddCount 736 13 = 4 ∧ acceleratedOrbit 13 736 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 736) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_736.1, data_13_736.2] + +/-- Complete interval computation for depth 13, residue 737. -/ +theorem bounds_13_737 : exactInterval 13 737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_737 : oddCount 737 13 = 9 ∧ acceleratedOrbit 13 737 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 737) = 3 ^ 9 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_737.1, data_13_737.2] + +/-- Complete interval computation for depth 13, residue 738. -/ +theorem bounds_13_738 : exactInterval 13 738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_738 : oddCount 738 13 = 4 ∧ acceleratedOrbit 13 738 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 738) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_738.1, data_13_738.2] + +/-- Complete interval computation for depth 13, residue 739. -/ +theorem bounds_13_739 : exactInterval 13 739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_739 : oddCount 739 13 = 4 ∧ acceleratedOrbit 13 739 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 739) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_739.1, data_13_739.2] + +/-- Complete interval computation for depth 13, residue 740. -/ +theorem bounds_13_740 : exactInterval 13 740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_740 : oddCount 740 13 = 6 ∧ acceleratedOrbit 13 740 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 740) = 3 ^ 6 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_740.1, data_13_740.2] + +/-- Complete interval computation for depth 13, residue 741. -/ +theorem bounds_13_741 : exactInterval 13 741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_741 : oddCount 741 13 = 6 ∧ acceleratedOrbit 13 741 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 741) = 3 ^ 6 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_741.1, data_13_741.2] + +end Collatz.Research.StoppingAtlas.Batch0515 From 9acb00b88b6ddcfc4553bd371c0b58c3f6a34fce Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:08 +0530 Subject: [PATCH 0516/1001] proof: certify atlas Batch0516 (13:742 to 13:756) --- Collatz/Research/StoppingAtlas/Batch0516.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0516.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0516.lean b/Collatz/Research/StoppingAtlas/Batch0516.lean new file mode 100644 index 00000000..0419dba8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0516.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0516 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 742. -/ +theorem bounds_13_742 : exactInterval 13 742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_742 : oddCount 742 13 = 6 ∧ acceleratedOrbit 13 742 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 742) = 3 ^ 6 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_742.1, data_13_742.2] + +/-- Complete interval computation for depth 13, residue 743. -/ +theorem bounds_13_743 : exactInterval 13 743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_743 : oddCount 743 13 = 10 ∧ acceleratedOrbit 13 743 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 743) = 3 ^ 10 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_743.1, data_13_743.2] + +/-- Complete interval computation for depth 13, residue 744. -/ +theorem bounds_13_744 : exactInterval 13 744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_744 : oddCount 744 13 = 4 ∧ acceleratedOrbit 13 744 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 744) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_744.1, data_13_744.2] + +/-- Complete interval computation for depth 13, residue 745. -/ +theorem bounds_13_745 : exactInterval 13 745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_745 : oddCount 745 13 = 9 ∧ acceleratedOrbit 13 745 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 745) = 3 ^ 9 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_745.1, data_13_745.2] + +/-- Complete interval computation for depth 13, residue 746. -/ +theorem bounds_13_746 : exactInterval 13 746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_746 : oddCount 746 13 = 4 ∧ acceleratedOrbit 13 746 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 746) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_746.1, data_13_746.2] + +/-- Complete interval computation for depth 13, residue 747. -/ +theorem bounds_13_747 : exactInterval 13 747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_747 : oddCount 747 13 = 7 ∧ acceleratedOrbit 13 747 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 747) = 3 ^ 7 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_747.1, data_13_747.2] + +/-- Complete interval computation for depth 13, residue 748. -/ +theorem bounds_13_748 : exactInterval 13 748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_748 : oddCount 748 13 = 7 ∧ acceleratedOrbit 13 748 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 748) = 3 ^ 7 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_748.1, data_13_748.2] + +/-- Complete interval computation for depth 13, residue 749. -/ +theorem bounds_13_749 : exactInterval 13 749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_749 : oddCount 749 13 = 7 ∧ acceleratedOrbit 13 749 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 749) = 3 ^ 7 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_749.1, data_13_749.2] + +/-- Complete interval computation for depth 13, residue 750. -/ +theorem bounds_13_750 : exactInterval 13 750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_750 : oddCount 750 13 = 7 ∧ acceleratedOrbit 13 750 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 750) = 3 ^ 7 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_750.1, data_13_750.2] + +/-- Complete interval computation for depth 13, residue 751. -/ +theorem bounds_13_751 : exactInterval 13 751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_751 : oddCount 751 13 = 10 ∧ acceleratedOrbit 13 751 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 751) = 3 ^ 10 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_751.1, data_13_751.2] + +/-- Complete interval computation for depth 13, residue 752. -/ +theorem bounds_13_752 : exactInterval 13 752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_752 : oddCount 752 13 = 7 ∧ acceleratedOrbit 13 752 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 752) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_752.1, data_13_752.2] + +/-- Complete interval computation for depth 13, residue 753. -/ +theorem bounds_13_753 : exactInterval 13 753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_753 : oddCount 753 13 = 4 ∧ acceleratedOrbit 13 753 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 753) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_753.1, data_13_753.2] + +/-- Complete interval computation for depth 13, residue 754. -/ +theorem bounds_13_754 : exactInterval 13 754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_754 : oddCount 754 13 = 9 ∧ acceleratedOrbit 13 754 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 754) = 3 ^ 9 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_754.1, data_13_754.2] + +/-- Complete interval computation for depth 13, residue 755. -/ +theorem bounds_13_755 : exactInterval 13 755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_755 : oddCount 755 13 = 9 ∧ acceleratedOrbit 13 755 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 755) = 3 ^ 9 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_755.1, data_13_755.2] + +/-- Complete interval computation for depth 13, residue 756. -/ +theorem bounds_13_756 : exactInterval 13 756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_756 : oddCount 756 13 = 7 ∧ acceleratedOrbit 13 756 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 756) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_756.1, data_13_756.2] + +end Collatz.Research.StoppingAtlas.Batch0516 From 6233ae73d58ccefc8fce10f202cb355bc3276b56 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:09 +0530 Subject: [PATCH 0517/1001] proof: certify atlas Batch0517 (13:757 to 13:772) --- Collatz/Research/StoppingAtlas/Batch0517.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0517.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0517.lean b/Collatz/Research/StoppingAtlas/Batch0517.lean new file mode 100644 index 00000000..613405d7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0517.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0517 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 757. -/ +theorem bounds_13_757 : exactInterval 13 757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_757 : oddCount 757 13 = 7 ∧ acceleratedOrbit 13 757 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 757) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_757.1, data_13_757.2] + +/-- Complete interval computation for depth 13, residue 758. -/ +theorem bounds_13_758 : exactInterval 13 758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_758 : oddCount 758 13 = 8 ∧ acceleratedOrbit 13 758 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 758) = 3 ^ 8 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_758.1, data_13_758.2] + +/-- Complete interval computation for depth 13, residue 759. -/ +theorem bounds_13_759 : exactInterval 13 759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_759 : oddCount 759 13 = 8 ∧ acceleratedOrbit 13 759 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 759) = 3 ^ 8 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_759.1, data_13_759.2] + +/-- Complete interval computation for depth 13, residue 760. -/ +theorem bounds_13_760 : exactInterval 13 760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_760 : oddCount 760 13 = 7 ∧ acceleratedOrbit 13 760 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 760) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_760.1, data_13_760.2] + +/-- Complete interval computation for depth 13, residue 761. -/ +theorem bounds_13_761 : exactInterval 13 761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_761 : oddCount 761 13 = 6 ∧ acceleratedOrbit 13 761 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 761) = 3 ^ 6 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_761.1, data_13_761.2] + +/-- Complete interval computation for depth 13, residue 762. -/ +theorem bounds_13_762 : exactInterval 13 762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_762 : oddCount 762 13 = 7 ∧ acceleratedOrbit 13 762 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 762) = 3 ^ 7 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_762.1, data_13_762.2] + +/-- Complete interval computation for depth 13, residue 763. -/ +theorem bounds_13_763 : exactInterval 13 763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_763 : oddCount 763 13 = 9 ∧ acceleratedOrbit 13 763 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 763) = 3 ^ 9 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_763.1, data_13_763.2] + +/-- Complete interval computation for depth 13, residue 764. -/ +theorem bounds_13_764 : exactInterval 13 764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_764 : oddCount 764 13 = 7 ∧ acceleratedOrbit 13 764 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 764) = 3 ^ 7 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_764.1, data_13_764.2] + +/-- Complete interval computation for depth 13, residue 765. -/ +theorem bounds_13_765 : exactInterval 13 765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_765 : oddCount 765 13 = 7 ∧ acceleratedOrbit 13 765 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 765) = 3 ^ 7 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_765.1, data_13_765.2] + +/-- Complete interval computation for depth 13, residue 766. -/ +theorem bounds_13_766 : exactInterval 13 766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_766 : oddCount 766 13 = 7 ∧ acceleratedOrbit 13 766 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 766) = 3 ^ 7 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_766.1, data_13_766.2] + +/-- Complete interval computation for depth 13, residue 767. -/ +theorem bounds_13_767 : exactInterval 13 767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_767 : oddCount 767 13 = 10 ∧ acceleratedOrbit 13 767 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 767) = 3 ^ 10 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_767.1, data_13_767.2] + +/-- Complete interval computation for depth 13, residue 768. -/ +theorem bounds_13_768 : exactInterval 13 768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_768 : oddCount 768 13 = 2 ∧ acceleratedOrbit 13 768 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 768) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_768.1, data_13_768.2] + +/-- Complete interval computation for depth 13, residue 769. -/ +theorem bounds_13_769 : exactInterval 13 769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_769 : oddCount 769 13 = 5 ∧ acceleratedOrbit 13 769 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 769) = 3 ^ 5 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_769.1, data_13_769.2] + +/-- Complete interval computation for depth 13, residue 770. -/ +theorem bounds_13_770 : exactInterval 13 770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_770 : oddCount 770 13 = 5 ∧ acceleratedOrbit 13 770 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 770) = 3 ^ 5 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_770.1, data_13_770.2] + +/-- Complete interval computation for depth 13, residue 771. -/ +theorem bounds_13_771 : exactInterval 13 771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_771 : oddCount 771 13 = 5 ∧ acceleratedOrbit 13 771 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 771) = 3 ^ 5 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_771.1, data_13_771.2] + +/-- Complete interval computation for depth 13, residue 772. -/ +theorem bounds_13_772 : exactInterval 13 772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_772 : oddCount 772 13 = 6 ∧ acceleratedOrbit 13 772 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 772) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_772.1, data_13_772.2] + +end Collatz.Research.StoppingAtlas.Batch0517 From f896e3261458a6873e489509a82ed9b88526883c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:09 +0530 Subject: [PATCH 0518/1001] proof: certify atlas Batch0518 (13:773 to 13:787) --- Collatz/Research/StoppingAtlas/Batch0518.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0518.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0518.lean b/Collatz/Research/StoppingAtlas/Batch0518.lean new file mode 100644 index 00000000..ed7a0cef --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0518.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0518 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 773. -/ +theorem bounds_13_773 : exactInterval 13 773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_773 : oddCount 773 13 = 6 ∧ acceleratedOrbit 13 773 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 773) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_773.1, data_13_773.2] + +/-- Complete interval computation for depth 13, residue 774. -/ +theorem bounds_13_774 : exactInterval 13 774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_774 : oddCount 774 13 = 6 ∧ acceleratedOrbit 13 774 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 774) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_774.1, data_13_774.2] + +/-- Complete interval computation for depth 13, residue 775. -/ +theorem bounds_13_775 : exactInterval 13 775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_775 : oddCount 775 13 = 8 ∧ acceleratedOrbit 13 775 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 775) = 3 ^ 8 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_775.1, data_13_775.2] + +/-- Complete interval computation for depth 13, residue 776. -/ +theorem bounds_13_776 : exactInterval 13 776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_776 : oddCount 776 13 = 6 ∧ acceleratedOrbit 13 776 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 776) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_776.1, data_13_776.2] + +/-- Complete interval computation for depth 13, residue 777. -/ +theorem bounds_13_777 : exactInterval 13 777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_777 : oddCount 777 13 = 7 ∧ acceleratedOrbit 13 777 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 777) = 3 ^ 7 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_777.1, data_13_777.2] + +/-- Complete interval computation for depth 13, residue 778. -/ +theorem bounds_13_778 : exactInterval 13 778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_778 : oddCount 778 13 = 6 ∧ acceleratedOrbit 13 778 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 778) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_778.1, data_13_778.2] + +/-- Complete interval computation for depth 13, residue 779. -/ +theorem bounds_13_779 : exactInterval 13 779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_779 : oddCount 779 13 = 7 ∧ acceleratedOrbit 13 779 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 779) = 3 ^ 7 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_779.1, data_13_779.2] + +/-- Complete interval computation for depth 13, residue 780. -/ +theorem bounds_13_780 : exactInterval 13 780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_780 : oddCount 780 13 = 6 ∧ acceleratedOrbit 13 780 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 780) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_780.1, data_13_780.2] + +/-- Complete interval computation for depth 13, residue 781. -/ +theorem bounds_13_781 : exactInterval 13 781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_781 : oddCount 781 13 = 6 ∧ acceleratedOrbit 13 781 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 781) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_781.1, data_13_781.2] + +/-- Complete interval computation for depth 13, residue 782. -/ +theorem bounds_13_782 : exactInterval 13 782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_782 : oddCount 782 13 = 6 ∧ acceleratedOrbit 13 782 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 782) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_782.1, data_13_782.2] + +/-- Complete interval computation for depth 13, residue 783. -/ +theorem bounds_13_783 : exactInterval 13 783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_783 : oddCount 783 13 = 6 ∧ acceleratedOrbit 13 783 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 783) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_783.1, data_13_783.2] + +/-- Complete interval computation for depth 13, residue 784. -/ +theorem bounds_13_784 : exactInterval 13 784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_784 : oddCount 784 13 = 5 ∧ acceleratedOrbit 13 784 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 784) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_784.1, data_13_784.2] + +/-- Complete interval computation for depth 13, residue 785. -/ +theorem bounds_13_785 : exactInterval 13 785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_785 : oddCount 785 13 = 6 ∧ acceleratedOrbit 13 785 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 785) = 3 ^ 6 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_785.1, data_13_785.2] + +/-- Complete interval computation for depth 13, residue 786. -/ +theorem bounds_13_786 : exactInterval 13 786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_786 : oddCount 786 13 = 7 ∧ acceleratedOrbit 13 786 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 786) = 3 ^ 7 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_786.1, data_13_786.2] + +/-- Complete interval computation for depth 13, residue 787. -/ +theorem bounds_13_787 : exactInterval 13 787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_787 : oddCount 787 13 = 7 ∧ acceleratedOrbit 13 787 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 787) = 3 ^ 7 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_787.1, data_13_787.2] + +end Collatz.Research.StoppingAtlas.Batch0518 From d0632c6873083d25ab9b2e00fe5351207eea44bc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:10 +0530 Subject: [PATCH 0519/1001] proof: certify atlas Batch0519 (13:788 to 13:802) --- Collatz/Research/StoppingAtlas/Batch0519.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0519.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0519.lean b/Collatz/Research/StoppingAtlas/Batch0519.lean new file mode 100644 index 00000000..419fb0d6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0519.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0519 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 788. -/ +theorem bounds_13_788 : exactInterval 13 788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_788 : oddCount 788 13 = 5 ∧ acceleratedOrbit 13 788 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 788) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_788.1, data_13_788.2] + +/-- Complete interval computation for depth 13, residue 789. -/ +theorem bounds_13_789 : exactInterval 13 789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_789 : oddCount 789 13 = 5 ∧ acceleratedOrbit 13 789 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 789) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_789.1, data_13_789.2] + +/-- Complete interval computation for depth 13, residue 790. -/ +theorem bounds_13_790 : exactInterval 13 790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_790 : oddCount 790 13 = 8 ∧ acceleratedOrbit 13 790 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 790) = 3 ^ 8 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_790.1, data_13_790.2] + +/-- Complete interval computation for depth 13, residue 791. -/ +theorem bounds_13_791 : exactInterval 13 791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_791 : oddCount 791 13 = 8 ∧ acceleratedOrbit 13 791 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 791) = 3 ^ 8 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_791.1, data_13_791.2] + +/-- Complete interval computation for depth 13, residue 792. -/ +theorem bounds_13_792 : exactInterval 13 792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_792 : oddCount 792 13 = 5 ∧ acceleratedOrbit 13 792 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 792) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_792.1, data_13_792.2] + +/-- Complete interval computation for depth 13, residue 793. -/ +theorem bounds_13_793 : exactInterval 13 793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_793 : oddCount 793 13 = 8 ∧ acceleratedOrbit 13 793 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 793) = 3 ^ 8 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_793.1, data_13_793.2] + +/-- Complete interval computation for depth 13, residue 794. -/ +theorem bounds_13_794 : exactInterval 13 794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_794 : oddCount 794 13 = 5 ∧ acceleratedOrbit 13 794 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 794) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_794.1, data_13_794.2] + +/-- Complete interval computation for depth 13, residue 795. -/ +theorem bounds_13_795 : exactInterval 13 795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_795 : oddCount 795 13 = 10 ∧ acceleratedOrbit 13 795 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 795) = 3 ^ 10 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_795.1, data_13_795.2] + +/-- Complete interval computation for depth 13, residue 796. -/ +theorem bounds_13_796 : exactInterval 13 796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_796 : oddCount 796 13 = 7 ∧ acceleratedOrbit 13 796 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 796) = 3 ^ 7 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_796.1, data_13_796.2] + +/-- Complete interval computation for depth 13, residue 797. -/ +theorem bounds_13_797 : exactInterval 13 797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_797 : oddCount 797 13 = 7 ∧ acceleratedOrbit 13 797 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 797) = 3 ^ 7 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_797.1, data_13_797.2] + +/-- Complete interval computation for depth 13, residue 798. -/ +theorem bounds_13_798 : exactInterval 13 798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_798 : oddCount 798 13 = 7 ∧ acceleratedOrbit 13 798 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 798) = 3 ^ 7 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_798.1, data_13_798.2] + +/-- Complete interval computation for depth 13, residue 799. -/ +theorem bounds_13_799 : exactInterval 13 799 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 799) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_799 : oddCount 799 13 = 8 ∧ acceleratedOrbit 13 799 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 799) = 3 ^ 8 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_799.1, data_13_799.2] + +/-- Complete interval computation for depth 13, residue 800. -/ +theorem bounds_13_800 : exactInterval 13 800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_800 : oddCount 800 13 = 5 ∧ acceleratedOrbit 13 800 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 800) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_800.1, data_13_800.2] + +/-- Complete interval computation for depth 13, residue 801. -/ +theorem bounds_13_801 : exactInterval 13 801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_801 : oddCount 801 13 = 8 ∧ acceleratedOrbit 13 801 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 801) = 3 ^ 8 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_801.1, data_13_801.2] + +/-- Complete interval computation for depth 13, residue 802. -/ +theorem bounds_13_802 : exactInterval 13 802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_802 : oddCount 802 13 = 4 ∧ acceleratedOrbit 13 802 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 802) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_802.1, data_13_802.2] + +end Collatz.Research.StoppingAtlas.Batch0519 From 79a1c05fe7db6544efcfb55b376dfe59b87f9028 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:10 +0530 Subject: [PATCH 0520/1001] proof: certify atlas Batch0520 (13:803 to 13:818) --- Collatz/Research/StoppingAtlas/Batch0520.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0520.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0520.lean b/Collatz/Research/StoppingAtlas/Batch0520.lean new file mode 100644 index 00000000..094c449b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0520.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0520 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 803. -/ +theorem bounds_13_803 : exactInterval 13 803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_803 : oddCount 803 13 = 4 ∧ acceleratedOrbit 13 803 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 803) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_803.1, data_13_803.2] + +/-- Complete interval computation for depth 13, residue 804. -/ +theorem bounds_13_804 : exactInterval 13 804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_804 : oddCount 804 13 = 4 ∧ acceleratedOrbit 13 804 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 804) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_804.1, data_13_804.2] + +/-- Complete interval computation for depth 13, residue 805. -/ +theorem bounds_13_805 : exactInterval 13 805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_805 : oddCount 805 13 = 4 ∧ acceleratedOrbit 13 805 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 805) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_805.1, data_13_805.2] + +/-- Complete interval computation for depth 13, residue 806. -/ +theorem bounds_13_806 : exactInterval 13 806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_806 : oddCount 806 13 = 4 ∧ acceleratedOrbit 13 806 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 806) = 3 ^ 4 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_806.1, data_13_806.2] + +/-- Complete interval computation for depth 13, residue 807. -/ +theorem bounds_13_807 : exactInterval 13 807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_807 : oddCount 807 13 = 10 ∧ acceleratedOrbit 13 807 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 807) = 3 ^ 10 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_807.1, data_13_807.2] + +/-- Complete interval computation for depth 13, residue 808. -/ +theorem bounds_13_808 : exactInterval 13 808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_808 : oddCount 808 13 = 5 ∧ acceleratedOrbit 13 808 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 808) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_808.1, data_13_808.2] + +/-- Complete interval computation for depth 13, residue 809. -/ +theorem bounds_13_809 : exactInterval 13 809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_809 : oddCount 809 13 = 8 ∧ acceleratedOrbit 13 809 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 809) = 3 ^ 8 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_809.1, data_13_809.2] + +/-- Complete interval computation for depth 13, residue 810. -/ +theorem bounds_13_810 : exactInterval 13 810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_810 : oddCount 810 13 = 5 ∧ acceleratedOrbit 13 810 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 810) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_810.1, data_13_810.2] + +/-- Complete interval computation for depth 13, residue 811. -/ +theorem bounds_13_811 : exactInterval 13 811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_811 : oddCount 811 13 = 7 ∧ acceleratedOrbit 13 811 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 811) = 3 ^ 7 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_811.1, data_13_811.2] + +/-- Complete interval computation for depth 13, residue 812. -/ +theorem bounds_13_812 : exactInterval 13 812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_812 : oddCount 812 13 = 6 ∧ acceleratedOrbit 13 812 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 812) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_812.1, data_13_812.2] + +/-- Complete interval computation for depth 13, residue 813. -/ +theorem bounds_13_813 : exactInterval 13 813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_813 : oddCount 813 13 = 6 ∧ acceleratedOrbit 13 813 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 813) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_813.1, data_13_813.2] + +/-- Complete interval computation for depth 13, residue 814. -/ +theorem bounds_13_814 : exactInterval 13 814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_814 : oddCount 814 13 = 6 ∧ acceleratedOrbit 13 814 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 814) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_814.1, data_13_814.2] + +/-- Complete interval computation for depth 13, residue 815. -/ +theorem bounds_13_815 : exactInterval 13 815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_815 : oddCount 815 13 = 7 ∧ acceleratedOrbit 13 815 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 815) = 3 ^ 7 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_815.1, data_13_815.2] + +/-- Complete interval computation for depth 13, residue 816. -/ +theorem bounds_13_816 : exactInterval 13 816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_816 : oddCount 816 13 = 5 ∧ acceleratedOrbit 13 816 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 816) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_816.1, data_13_816.2] + +/-- Complete interval computation for depth 13, residue 817. -/ +theorem bounds_13_817 : exactInterval 13 817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_817 : oddCount 817 13 = 6 ∧ acceleratedOrbit 13 817 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 817) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_817.1, data_13_817.2] + +/-- Complete interval computation for depth 13, residue 818. -/ +theorem bounds_13_818 : exactInterval 13 818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_818 : oddCount 818 13 = 6 ∧ acceleratedOrbit 13 818 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 818) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_818.1, data_13_818.2] + +end Collatz.Research.StoppingAtlas.Batch0520 From f85c5584187020cd915b37b53fcfcd0173b950b7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:10 +0530 Subject: [PATCH 0521/1001] proof: certify atlas Batch0521 (13:819 to 13:833) --- Collatz/Research/StoppingAtlas/Batch0521.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0521.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0521.lean b/Collatz/Research/StoppingAtlas/Batch0521.lean new file mode 100644 index 00000000..abd5b479 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0521.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0521 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 819. -/ +theorem bounds_13_819 : exactInterval 13 819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_819 : oddCount 819 13 = 6 ∧ acceleratedOrbit 13 819 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 819) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_819.1, data_13_819.2] + +/-- Complete interval computation for depth 13, residue 820. -/ +theorem bounds_13_820 : exactInterval 13 820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_820 : oddCount 820 13 = 5 ∧ acceleratedOrbit 13 820 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 820) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_820.1, data_13_820.2] + +/-- Complete interval computation for depth 13, residue 821. -/ +theorem bounds_13_821 : exactInterval 13 821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_821 : oddCount 821 13 = 5 ∧ acceleratedOrbit 13 821 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 821) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_821.1, data_13_821.2] + +/-- Complete interval computation for depth 13, residue 822. -/ +theorem bounds_13_822 : exactInterval 13 822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_822 : oddCount 822 13 = 8 ∧ acceleratedOrbit 13 822 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 822) = 3 ^ 8 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_822.1, data_13_822.2] + +/-- Complete interval computation for depth 13, residue 823. -/ +theorem bounds_13_823 : exactInterval 13 823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_823 : oddCount 823 13 = 8 ∧ acceleratedOrbit 13 823 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 823) = 3 ^ 8 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_823.1, data_13_823.2] + +/-- Complete interval computation for depth 13, residue 824. -/ +theorem bounds_13_824 : exactInterval 13 824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_824 : oddCount 824 13 = 8 ∧ acceleratedOrbit 13 824 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 824) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_824.1, data_13_824.2] + +/-- Complete interval computation for depth 13, residue 825. -/ +theorem bounds_13_825 : exactInterval 13 825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_825 : oddCount 825 13 = 7 ∧ acceleratedOrbit 13 825 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 825) = 3 ^ 7 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_825.1, data_13_825.2] + +/-- Complete interval computation for depth 13, residue 826. -/ +theorem bounds_13_826 : exactInterval 13 826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_826 : oddCount 826 13 = 8 ∧ acceleratedOrbit 13 826 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 826) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_826.1, data_13_826.2] + +/-- Complete interval computation for depth 13, residue 827. -/ +theorem bounds_13_827 : exactInterval 13 827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_827 : oddCount 827 13 = 6 ∧ acceleratedOrbit 13 827 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 827) = 3 ^ 6 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_827.1, data_13_827.2] + +/-- Complete interval computation for depth 13, residue 828. -/ +theorem bounds_13_828 : exactInterval 13 828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_828 : oddCount 828 13 = 8 ∧ acceleratedOrbit 13 828 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 828) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_828.1, data_13_828.2] + +/-- Complete interval computation for depth 13, residue 829. -/ +theorem bounds_13_829 : exactInterval 13 829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_829 : oddCount 829 13 = 8 ∧ acceleratedOrbit 13 829 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 829) = 3 ^ 8 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_829.1, data_13_829.2] + +/-- Complete interval computation for depth 13, residue 830. -/ +theorem bounds_13_830 : exactInterval 13 830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_830 : oddCount 830 13 = 9 ∧ acceleratedOrbit 13 830 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 830) = 3 ^ 9 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_830.1, data_13_830.2] + +/-- Complete interval computation for depth 13, residue 831. -/ +theorem bounds_13_831 : exactInterval 13 831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_831 : oddCount 831 13 = 9 ∧ acceleratedOrbit 13 831 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 831) = 3 ^ 9 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_831.1, data_13_831.2] + +/-- Complete interval computation for depth 13, residue 832. -/ +theorem bounds_13_832 : exactInterval 13 832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_832 : oddCount 832 13 = 2 ∧ acceleratedOrbit 13 832 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 832) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_832.1, data_13_832.2] + +/-- Complete interval computation for depth 13, residue 833. -/ +theorem bounds_13_833 : exactInterval 13 833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_833 : oddCount 833 13 = 5 ∧ acceleratedOrbit 13 833 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 833) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_833.1, data_13_833.2] + +end Collatz.Research.StoppingAtlas.Batch0521 From e3624bf950d3b216048d8ad63ecf278fb8688d27 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:11 +0530 Subject: [PATCH 0522/1001] proof: certify atlas Batch0522 (13:834 to 13:848) --- Collatz/Research/StoppingAtlas/Batch0522.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0522.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0522.lean b/Collatz/Research/StoppingAtlas/Batch0522.lean new file mode 100644 index 00000000..d3c921fc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0522.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0522 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 834. -/ +theorem bounds_13_834 : exactInterval 13 834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_834 : oddCount 834 13 = 8 ∧ acceleratedOrbit 13 834 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 834) = 3 ^ 8 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_834.1, data_13_834.2] + +/-- Complete interval computation for depth 13, residue 835. -/ +theorem bounds_13_835 : exactInterval 13 835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_835 : oddCount 835 13 = 8 ∧ acceleratedOrbit 13 835 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 835) = 3 ^ 8 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_835.1, data_13_835.2] + +/-- Complete interval computation for depth 13, residue 836. -/ +theorem bounds_13_836 : exactInterval 13 836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_836 : oddCount 836 13 = 6 ∧ acceleratedOrbit 13 836 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 836) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_836.1, data_13_836.2] + +/-- Complete interval computation for depth 13, residue 837. -/ +theorem bounds_13_837 : exactInterval 13 837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_837 : oddCount 837 13 = 6 ∧ acceleratedOrbit 13 837 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 837) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_837.1, data_13_837.2] + +/-- Complete interval computation for depth 13, residue 838. -/ +theorem bounds_13_838 : exactInterval 13 838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_838 : oddCount 838 13 = 6 ∧ acceleratedOrbit 13 838 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 838) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_838.1, data_13_838.2] + +/-- Complete interval computation for depth 13, residue 839. -/ +theorem bounds_13_839 : exactInterval 13 839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_839 : oddCount 839 13 = 9 ∧ acceleratedOrbit 13 839 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 839) = 3 ^ 9 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_839.1, data_13_839.2] + +/-- Complete interval computation for depth 13, residue 840. -/ +theorem bounds_13_840 : exactInterval 13 840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_840 : oddCount 840 13 = 6 ∧ acceleratedOrbit 13 840 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 840) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_840.1, data_13_840.2] + +/-- Complete interval computation for depth 13, residue 841. -/ +theorem bounds_13_841 : exactInterval 13 841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_841 : oddCount 841 13 = 5 ∧ acceleratedOrbit 13 841 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 841) = 3 ^ 5 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_841.1, data_13_841.2] + +/-- Complete interval computation for depth 13, residue 842. -/ +theorem bounds_13_842 : exactInterval 13 842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_842 : oddCount 842 13 = 6 ∧ acceleratedOrbit 13 842 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 842) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_842.1, data_13_842.2] + +/-- Complete interval computation for depth 13, residue 843. -/ +theorem bounds_13_843 : exactInterval 13 843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_843 : oddCount 843 13 = 6 ∧ acceleratedOrbit 13 843 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 843) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_843.1, data_13_843.2] + +/-- Complete interval computation for depth 13, residue 844. -/ +theorem bounds_13_844 : exactInterval 13 844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_844 : oddCount 844 13 = 6 ∧ acceleratedOrbit 13 844 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 844) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_844.1, data_13_844.2] + +/-- Complete interval computation for depth 13, residue 845. -/ +theorem bounds_13_845 : exactInterval 13 845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_845 : oddCount 845 13 = 6 ∧ acceleratedOrbit 13 845 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 845) = 3 ^ 6 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_845.1, data_13_845.2] + +/-- Complete interval computation for depth 13, residue 846. -/ +theorem bounds_13_846 : exactInterval 13 846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_846 : oddCount 846 13 = 7 ∧ acceleratedOrbit 13 846 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 846) = 3 ^ 7 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_846.1, data_13_846.2] + +/-- Complete interval computation for depth 13, residue 847. -/ +theorem bounds_13_847 : exactInterval 13 847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_847 : oddCount 847 13 = 7 ∧ acceleratedOrbit 13 847 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 847) = 3 ^ 7 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_847.1, data_13_847.2] + +/-- Complete interval computation for depth 13, residue 848. -/ +theorem bounds_13_848 : exactInterval 13 848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_848 : oddCount 848 13 = 2 ∧ acceleratedOrbit 13 848 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 848) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_848.1, data_13_848.2] + +end Collatz.Research.StoppingAtlas.Batch0522 From b16903bfc8f1076f716e6e68cbdc928d711078a2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:12 +0530 Subject: [PATCH 0523/1001] proof: certify atlas Batch0523 (13:849 to 13:864) --- Collatz/Research/StoppingAtlas/Batch0523.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0523.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0523.lean b/Collatz/Research/StoppingAtlas/Batch0523.lean new file mode 100644 index 00000000..174b9622 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0523.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0523 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 849. -/ +theorem bounds_13_849 : exactInterval 13 849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_849 : oddCount 849 13 = 9 ∧ acceleratedOrbit 13 849 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 849) = 3 ^ 9 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_849.1, data_13_849.2] + +/-- Complete interval computation for depth 13, residue 850. -/ +theorem bounds_13_850 : exactInterval 13 850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_850 : oddCount 850 13 = 9 ∧ acceleratedOrbit 13 850 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 850) = 3 ^ 9 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_850.1, data_13_850.2] + +/-- Complete interval computation for depth 13, residue 851. -/ +theorem bounds_13_851 : exactInterval 13 851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_851 : oddCount 851 13 = 9 ∧ acceleratedOrbit 13 851 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 851) = 3 ^ 9 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_851.1, data_13_851.2] + +/-- Complete interval computation for depth 13, residue 852. -/ +theorem bounds_13_852 : exactInterval 13 852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_852 : oddCount 852 13 = 2 ∧ acceleratedOrbit 13 852 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 852) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_852.1, data_13_852.2] + +/-- Complete interval computation for depth 13, residue 853. -/ +theorem bounds_13_853 : exactInterval 13 853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_853 : oddCount 853 13 = 2 ∧ acceleratedOrbit 13 853 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 853) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_853.1, data_13_853.2] + +/-- Complete interval computation for depth 13, residue 854. -/ +theorem bounds_13_854 : exactInterval 13 854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_854 : oddCount 854 13 = 8 ∧ acceleratedOrbit 13 854 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 854) = 3 ^ 8 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_854.1, data_13_854.2] + +/-- Complete interval computation for depth 13, residue 855. -/ +theorem bounds_13_855 : exactInterval 13 855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_855 : oddCount 855 13 = 8 ∧ acceleratedOrbit 13 855 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 855) = 3 ^ 8 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_855.1, data_13_855.2] + +/-- Complete interval computation for depth 13, residue 856. -/ +theorem bounds_13_856 : exactInterval 13 856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_856 : oddCount 856 13 = 7 ∧ acceleratedOrbit 13 856 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 856) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_856.1, data_13_856.2] + +/-- Complete interval computation for depth 13, residue 857. -/ +theorem bounds_13_857 : exactInterval 13 857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_857 : oddCount 857 13 = 5 ∧ acceleratedOrbit 13 857 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 857) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_857.1, data_13_857.2] + +/-- Complete interval computation for depth 13, residue 858. -/ +theorem bounds_13_858 : exactInterval 13 858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_858 : oddCount 858 13 = 7 ∧ acceleratedOrbit 13 858 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 858) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_858.1, data_13_858.2] + +/-- Complete interval computation for depth 13, residue 859. -/ +theorem bounds_13_859 : exactInterval 13 859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_859 : oddCount 859 13 = 9 ∧ acceleratedOrbit 13 859 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 859) = 3 ^ 9 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_859.1, data_13_859.2] + +/-- Complete interval computation for depth 13, residue 860. -/ +theorem bounds_13_860 : exactInterval 13 860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_860 : oddCount 860 13 = 7 ∧ acceleratedOrbit 13 860 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 860) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_860.1, data_13_860.2] + +/-- Complete interval computation for depth 13, residue 861. -/ +theorem bounds_13_861 : exactInterval 13 861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_861 : oddCount 861 13 = 7 ∧ acceleratedOrbit 13 861 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 861) = 3 ^ 7 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_861.1, data_13_861.2] + +/-- Complete interval computation for depth 13, residue 862. -/ +theorem bounds_13_862 : exactInterval 13 862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_862 : oddCount 862 13 = 6 ∧ acceleratedOrbit 13 862 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 862) = 3 ^ 6 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_862.1, data_13_862.2] + +/-- Complete interval computation for depth 13, residue 863. -/ +theorem bounds_13_863 : exactInterval 13 863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_863 : oddCount 863 13 = 6 ∧ acceleratedOrbit 13 863 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 863) = 3 ^ 6 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_863.1, data_13_863.2] + +/-- Complete interval computation for depth 13, residue 864. -/ +theorem bounds_13_864 : exactInterval 13 864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_864 : oddCount 864 13 = 7 ∧ acceleratedOrbit 13 864 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 864) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_864.1, data_13_864.2] + +end Collatz.Research.StoppingAtlas.Batch0523 From c36bb0b58195d5cfde6edc40ec052a0c4159a60a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:12 +0530 Subject: [PATCH 0524/1001] proof: certify atlas Batch0524 (13:865 to 13:879) --- Collatz/Research/StoppingAtlas/Batch0524.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0524.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0524.lean b/Collatz/Research/StoppingAtlas/Batch0524.lean new file mode 100644 index 00000000..607eb5f6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0524.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0524 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 865. -/ +theorem bounds_13_865 : exactInterval 13 865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_865 : oddCount 865 13 = 8 ∧ acceleratedOrbit 13 865 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 865) = 3 ^ 8 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_865.1, data_13_865.2] + +/-- Complete interval computation for depth 13, residue 866. -/ +theorem bounds_13_866 : exactInterval 13 866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_866 : oddCount 866 13 = 6 ∧ acceleratedOrbit 13 866 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 866) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_866.1, data_13_866.2] + +/-- Complete interval computation for depth 13, residue 867. -/ +theorem bounds_13_867 : exactInterval 13 867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_867 : oddCount 867 13 = 6 ∧ acceleratedOrbit 13 867 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 867) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_867.1, data_13_867.2] + +/-- Complete interval computation for depth 13, residue 868. -/ +theorem bounds_13_868 : exactInterval 13 868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_868 : oddCount 868 13 = 6 ∧ acceleratedOrbit 13 868 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 868) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_868.1, data_13_868.2] + +/-- Complete interval computation for depth 13, residue 869. -/ +theorem bounds_13_869 : exactInterval 13 869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_869 : oddCount 869 13 = 6 ∧ acceleratedOrbit 13 869 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 869) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_869.1, data_13_869.2] + +/-- Complete interval computation for depth 13, residue 870. -/ +theorem bounds_13_870 : exactInterval 13 870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_870 : oddCount 870 13 = 6 ∧ acceleratedOrbit 13 870 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 870) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_870.1, data_13_870.2] + +/-- Complete interval computation for depth 13, residue 871. -/ +theorem bounds_13_871 : exactInterval 13 871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_871 : oddCount 871 13 = 11 ∧ acceleratedOrbit 13 871 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 871) = 3 ^ 11 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_871.1, data_13_871.2] + +/-- Complete interval computation for depth 13, residue 872. -/ +theorem bounds_13_872 : exactInterval 13 872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_872 : oddCount 872 13 = 7 ∧ acceleratedOrbit 13 872 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 872) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_872.1, data_13_872.2] + +/-- Complete interval computation for depth 13, residue 873. -/ +theorem bounds_13_873 : exactInterval 13 873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_873 : oddCount 873 13 = 9 ∧ acceleratedOrbit 13 873 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 873) = 3 ^ 9 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_873.1, data_13_873.2] + +/-- Complete interval computation for depth 13, residue 874. -/ +theorem bounds_13_874 : exactInterval 13 874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_874 : oddCount 874 13 = 7 ∧ acceleratedOrbit 13 874 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 874) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_874.1, data_13_874.2] + +/-- Complete interval computation for depth 13, residue 875. -/ +theorem bounds_13_875 : exactInterval 13 875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_875 : oddCount 875 13 = 5 ∧ acceleratedOrbit 13 875 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 875) = 3 ^ 5 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_875.1, data_13_875.2] + +/-- Complete interval computation for depth 13, residue 876. -/ +theorem bounds_13_876 : exactInterval 13 876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_876 : oddCount 876 13 = 7 ∧ acceleratedOrbit 13 876 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 876) = 3 ^ 7 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_876.1, data_13_876.2] + +/-- Complete interval computation for depth 13, residue 877. -/ +theorem bounds_13_877 : exactInterval 13 877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_877 : oddCount 877 13 = 7 ∧ acceleratedOrbit 13 877 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 877) = 3 ^ 7 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_877.1, data_13_877.2] + +/-- Complete interval computation for depth 13, residue 878. -/ +theorem bounds_13_878 : exactInterval 13 878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_878 : oddCount 878 13 = 7 ∧ acceleratedOrbit 13 878 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 878) = 3 ^ 7 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_878.1, data_13_878.2] + +/-- Complete interval computation for depth 13, residue 879. -/ +theorem bounds_13_879 : exactInterval 13 879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_879 : oddCount 879 13 = 7 ∧ acceleratedOrbit 13 879 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 879) = 3 ^ 7 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_879.1, data_13_879.2] + +end Collatz.Research.StoppingAtlas.Batch0524 From 1cd1deaf26d90ad22327bfe0f3a95370a2180d3f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:13 +0530 Subject: [PATCH 0525/1001] proof: certify atlas Batch0525 (13:880 to 13:895) --- Collatz/Research/StoppingAtlas/Batch0525.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0525.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0525.lean b/Collatz/Research/StoppingAtlas/Batch0525.lean new file mode 100644 index 00000000..a83af9b4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0525.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0525 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 880. -/ +theorem bounds_13_880 : exactInterval 13 880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_880 : oddCount 880 13 = 7 ∧ acceleratedOrbit 13 880 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 880) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_880.1, data_13_880.2] + +/-- Complete interval computation for depth 13, residue 881. -/ +theorem bounds_13_881 : exactInterval 13 881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_881 : oddCount 881 13 = 7 ∧ acceleratedOrbit 13 881 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 881) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_881.1, data_13_881.2] + +/-- Complete interval computation for depth 13, residue 882. -/ +theorem bounds_13_882 : exactInterval 13 882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_882 : oddCount 882 13 = 6 ∧ acceleratedOrbit 13 882 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 882) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_882.1, data_13_882.2] + +/-- Complete interval computation for depth 13, residue 883. -/ +theorem bounds_13_883 : exactInterval 13 883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_883 : oddCount 883 13 = 6 ∧ acceleratedOrbit 13 883 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 883) = 3 ^ 6 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_883.1, data_13_883.2] + +/-- Complete interval computation for depth 13, residue 884. -/ +theorem bounds_13_884 : exactInterval 13 884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_884 : oddCount 884 13 = 7 ∧ acceleratedOrbit 13 884 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 884) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_884.1, data_13_884.2] + +/-- Complete interval computation for depth 13, residue 885. -/ +theorem bounds_13_885 : exactInterval 13 885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_885 : oddCount 885 13 = 7 ∧ acceleratedOrbit 13 885 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 885) = 3 ^ 7 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_885.1, data_13_885.2] + +/-- Complete interval computation for depth 13, residue 886. -/ +theorem bounds_13_886 : exactInterval 13 886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_886 : oddCount 886 13 = 7 ∧ acceleratedOrbit 13 886 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 886) = 3 ^ 7 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_886.1, data_13_886.2] + +/-- Complete interval computation for depth 13, residue 887. -/ +theorem bounds_13_887 : exactInterval 13 887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_887 : oddCount 887 13 = 7 ∧ acceleratedOrbit 13 887 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 887) = 3 ^ 7 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_887.1, data_13_887.2] + +/-- Complete interval computation for depth 13, residue 888. -/ +theorem bounds_13_888 : exactInterval 13 888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_888 : oddCount 888 13 = 8 ∧ acceleratedOrbit 13 888 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 888) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_888.1, data_13_888.2] + +/-- Complete interval computation for depth 13, residue 889. -/ +theorem bounds_13_889 : exactInterval 13 889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_889 : oddCount 889 13 = 10 ∧ acceleratedOrbit 13 889 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 889) = 3 ^ 10 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_889.1, data_13_889.2] + +/-- Complete interval computation for depth 13, residue 890. -/ +theorem bounds_13_890 : exactInterval 13 890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_890 : oddCount 890 13 = 8 ∧ acceleratedOrbit 13 890 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 890) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_890.1, data_13_890.2] + +/-- Complete interval computation for depth 13, residue 891. -/ +theorem bounds_13_891 : exactInterval 13 891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_891 : oddCount 891 13 = 9 ∧ acceleratedOrbit 13 891 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 891) = 3 ^ 9 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_891.1, data_13_891.2] + +/-- Complete interval computation for depth 13, residue 892. -/ +theorem bounds_13_892 : exactInterval 13 892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_892 : oddCount 892 13 = 8 ∧ acceleratedOrbit 13 892 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 892) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_892.1, data_13_892.2] + +/-- Complete interval computation for depth 13, residue 893. -/ +theorem bounds_13_893 : exactInterval 13 893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_893 : oddCount 893 13 = 8 ∧ acceleratedOrbit 13 893 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 893) = 3 ^ 8 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_893.1, data_13_893.2] + +/-- Complete interval computation for depth 13, residue 894. -/ +theorem bounds_13_894 : exactInterval 13 894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_894 : oddCount 894 13 = 9 ∧ acceleratedOrbit 13 894 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 894) = 3 ^ 9 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_894.1, data_13_894.2] + +/-- Complete interval computation for depth 13, residue 895. -/ +theorem bounds_13_895 : exactInterval 13 895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_895 : oddCount 895 13 = 9 ∧ acceleratedOrbit 13 895 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 895) = 3 ^ 9 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_895.1, data_13_895.2] + +end Collatz.Research.StoppingAtlas.Batch0525 From cd616b9a8e69919d295d74152304368d6162d78d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:14 +0530 Subject: [PATCH 0526/1001] proof: certify atlas Batch0526 (13:896 to 13:910) --- Collatz/Research/StoppingAtlas/Batch0526.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0526.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0526.lean b/Collatz/Research/StoppingAtlas/Batch0526.lean new file mode 100644 index 00000000..52e7bb33 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0526.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0526 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 896. -/ +theorem bounds_13_896 : exactInterval 13 896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_896 : oddCount 896 13 = 4 ∧ acceleratedOrbit 13 896 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 896) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_896.1, data_13_896.2] + +/-- Complete interval computation for depth 13, residue 897. -/ +theorem bounds_13_897 : exactInterval 13 897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_897 : oddCount 897 13 = 8 ∧ acceleratedOrbit 13 897 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 897) = 3 ^ 8 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_897.1, data_13_897.2] + +/-- Complete interval computation for depth 13, residue 898. -/ +theorem bounds_13_898 : exactInterval 13 898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_898 : oddCount 898 13 = 8 ∧ acceleratedOrbit 13 898 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 898) = 3 ^ 8 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_898.1, data_13_898.2] + +/-- Complete interval computation for depth 13, residue 899. -/ +theorem bounds_13_899 : exactInterval 13 899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_899 : oddCount 899 13 = 8 ∧ acceleratedOrbit 13 899 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 899) = 3 ^ 8 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_899.1, data_13_899.2] + +/-- Complete interval computation for depth 13, residue 900. -/ +theorem bounds_13_900 : exactInterval 13 900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_900 : oddCount 900 13 = 9 ∧ acceleratedOrbit 13 900 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 900) = 3 ^ 9 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_900.1, data_13_900.2] + +/-- Complete interval computation for depth 13, residue 901. -/ +theorem bounds_13_901 : exactInterval 13 901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_901 : oddCount 901 13 = 9 ∧ acceleratedOrbit 13 901 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 901) = 3 ^ 9 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_901.1, data_13_901.2] + +/-- Complete interval computation for depth 13, residue 902. -/ +theorem bounds_13_902 : exactInterval 13 902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_902 : oddCount 902 13 = 9 ∧ acceleratedOrbit 13 902 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 902) = 3 ^ 9 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_902.1, data_13_902.2] + +/-- Complete interval computation for depth 13, residue 903. -/ +theorem bounds_13_903 : exactInterval 13 903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_903 : oddCount 903 13 = 8 ∧ acceleratedOrbit 13 903 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 903) = 3 ^ 8 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_903.1, data_13_903.2] + +/-- Complete interval computation for depth 13, residue 904. -/ +theorem bounds_13_904 : exactInterval 13 904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_904 : oddCount 904 13 = 2 ∧ acceleratedOrbit 13 904 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 904) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_904.1, data_13_904.2] + +/-- Complete interval computation for depth 13, residue 905. -/ +theorem bounds_13_905 : exactInterval 13 905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_905 : oddCount 905 13 = 9 ∧ acceleratedOrbit 13 905 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 905) = 3 ^ 9 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_905.1, data_13_905.2] + +/-- Complete interval computation for depth 13, residue 906. -/ +theorem bounds_13_906 : exactInterval 13 906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_906 : oddCount 906 13 = 2 ∧ acceleratedOrbit 13 906 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 906) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_906.1, data_13_906.2] + +/-- Complete interval computation for depth 13, residue 907. -/ +theorem bounds_13_907 : exactInterval 13 907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_907 : oddCount 907 13 = 10 ∧ acceleratedOrbit 13 907 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 907) = 3 ^ 10 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_907.1, data_13_907.2] + +/-- Complete interval computation for depth 13, residue 908. -/ +theorem bounds_13_908 : exactInterval 13 908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_908 : oddCount 908 13 = 2 ∧ acceleratedOrbit 13 908 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 908) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_908.1, data_13_908.2] + +/-- Complete interval computation for depth 13, residue 909. -/ +theorem bounds_13_909 : exactInterval 13 909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_909 : oddCount 909 13 = 2 ∧ acceleratedOrbit 13 909 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 909) = 3 ^ 2 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_909.1, data_13_909.2] + +/-- Complete interval computation for depth 13, residue 910. -/ +theorem bounds_13_910 : exactInterval 13 910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_910 : oddCount 910 13 = 7 ∧ acceleratedOrbit 13 910 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 910) = 3 ^ 7 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_910.1, data_13_910.2] + +end Collatz.Research.StoppingAtlas.Batch0526 From b51b9b02be8fb96a4dbfec957cd7106d89a9cfd2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:15 +0530 Subject: [PATCH 0527/1001] proof: certify atlas Batch0527 (13:911 to 13:925) --- Collatz/Research/StoppingAtlas/Batch0527.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0527.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0527.lean b/Collatz/Research/StoppingAtlas/Batch0527.lean new file mode 100644 index 00000000..c56738de --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0527.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0527 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 911. -/ +theorem bounds_13_911 : exactInterval 13 911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_911 : oddCount 911 13 = 7 ∧ acceleratedOrbit 13 911 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 911) = 3 ^ 7 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_911.1, data_13_911.2] + +/-- Complete interval computation for depth 13, residue 912. -/ +theorem bounds_13_912 : exactInterval 13 912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_912 : oddCount 912 13 = 5 ∧ acceleratedOrbit 13 912 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 912) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_912.1, data_13_912.2] + +/-- Complete interval computation for depth 13, residue 913. -/ +theorem bounds_13_913 : exactInterval 13 913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_913 : oddCount 913 13 = 6 ∧ acceleratedOrbit 13 913 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 913) = 3 ^ 6 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_913.1, data_13_913.2] + +/-- Complete interval computation for depth 13, residue 914. -/ +theorem bounds_13_914 : exactInterval 13 914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_914 : oddCount 914 13 = 6 ∧ acceleratedOrbit 13 914 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 914) = 3 ^ 6 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_914.1, data_13_914.2] + +/-- Complete interval computation for depth 13, residue 915. -/ +theorem bounds_13_915 : exactInterval 13 915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_915 : oddCount 915 13 = 6 ∧ acceleratedOrbit 13 915 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 915) = 3 ^ 6 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_915.1, data_13_915.2] + +/-- Complete interval computation for depth 13, residue 916. -/ +theorem bounds_13_916 : exactInterval 13 916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_916 : oddCount 916 13 = 5 ∧ acceleratedOrbit 13 916 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 916) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_916.1, data_13_916.2] + +/-- Complete interval computation for depth 13, residue 917. -/ +theorem bounds_13_917 : exactInterval 13 917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_917 : oddCount 917 13 = 5 ∧ acceleratedOrbit 13 917 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 917) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_917.1, data_13_917.2] + +/-- Complete interval computation for depth 13, residue 918. -/ +theorem bounds_13_918 : exactInterval 13 918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_918 : oddCount 918 13 = 6 ∧ acceleratedOrbit 13 918 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 918) = 3 ^ 6 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_918.1, data_13_918.2] + +/-- Complete interval computation for depth 13, residue 919. -/ +theorem bounds_13_919 : exactInterval 13 919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_919 : oddCount 919 13 = 6 ∧ acceleratedOrbit 13 919 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 919) = 3 ^ 6 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_919.1, data_13_919.2] + +/-- Complete interval computation for depth 13, residue 920. -/ +theorem bounds_13_920 : exactInterval 13 920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_920 : oddCount 920 13 = 5 ∧ acceleratedOrbit 13 920 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 920) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_920.1, data_13_920.2] + +/-- Complete interval computation for depth 13, residue 921. -/ +theorem bounds_13_921 : exactInterval 13 921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_921 : oddCount 921 13 = 6 ∧ acceleratedOrbit 13 921 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 921) = 3 ^ 6 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_921.1, data_13_921.2] + +/-- Complete interval computation for depth 13, residue 922. -/ +theorem bounds_13_922 : exactInterval 13 922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_922 : oddCount 922 13 = 5 ∧ acceleratedOrbit 13 922 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 922) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_922.1, data_13_922.2] + +/-- Complete interval computation for depth 13, residue 923. -/ +theorem bounds_13_923 : exactInterval 13 923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_923 : oddCount 923 13 = 7 ∧ acceleratedOrbit 13 923 = 247 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 923) = 3 ^ 7 * m + 247 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_923.1, data_13_923.2] + +/-- Complete interval computation for depth 13, residue 924. -/ +theorem bounds_13_924 : exactInterval 13 924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_924 : oddCount 924 13 = 7 ∧ acceleratedOrbit 13 924 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 924) = 3 ^ 7 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_924.1, data_13_924.2] + +/-- Complete interval computation for depth 13, residue 925. -/ +theorem bounds_13_925 : exactInterval 13 925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_925 : oddCount 925 13 = 7 ∧ acceleratedOrbit 13 925 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 925) = 3 ^ 7 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_925.1, data_13_925.2] + +end Collatz.Research.StoppingAtlas.Batch0527 From 93645f9d35b3b44c9a6ad406689854da2ef0679c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:15 +0530 Subject: [PATCH 0528/1001] proof: certify atlas Batch0528 (13:926 to 13:941) --- Collatz/Research/StoppingAtlas/Batch0528.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0528.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0528.lean b/Collatz/Research/StoppingAtlas/Batch0528.lean new file mode 100644 index 00000000..ef7bc51d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0528.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0528 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 926. -/ +theorem bounds_13_926 : exactInterval 13 926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_926 : oddCount 926 13 = 7 ∧ acceleratedOrbit 13 926 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 926) = 3 ^ 7 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_926.1, data_13_926.2] + +/-- Complete interval computation for depth 13, residue 927. -/ +theorem bounds_13_927 : exactInterval 13 927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_927 : oddCount 927 13 = 9 ∧ acceleratedOrbit 13 927 = 2231 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 927) = 3 ^ 9 * m + 2231 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_927.1, data_13_927.2] + +/-- Complete interval computation for depth 13, residue 928. -/ +theorem bounds_13_928 : exactInterval 13 928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_928 : oddCount 928 13 = 4 ∧ acceleratedOrbit 13 928 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 928) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_928.1, data_13_928.2] + +/-- Complete interval computation for depth 13, residue 929. -/ +theorem bounds_13_929 : exactInterval 13 929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_929 : oddCount 929 13 = 6 ∧ acceleratedOrbit 13 929 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 929) = 3 ^ 6 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_929.1, data_13_929.2] + +/-- Complete interval computation for depth 13, residue 930. -/ +theorem bounds_13_930 : exactInterval 13 930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_930 : oddCount 930 13 = 5 ∧ acceleratedOrbit 13 930 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 930) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_930.1, data_13_930.2] + +/-- Complete interval computation for depth 13, residue 931. -/ +theorem bounds_13_931 : exactInterval 13 931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_931 : oddCount 931 13 = 5 ∧ acceleratedOrbit 13 931 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 931) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_931.1, data_13_931.2] + +/-- Complete interval computation for depth 13, residue 932. -/ +theorem bounds_13_932 : exactInterval 13 932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_932 : oddCount 932 13 = 7 ∧ acceleratedOrbit 13 932 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 932) = 3 ^ 7 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_932.1, data_13_932.2] + +/-- Complete interval computation for depth 13, residue 933. -/ +theorem bounds_13_933 : exactInterval 13 933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_933 : oddCount 933 13 = 7 ∧ acceleratedOrbit 13 933 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 933) = 3 ^ 7 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_933.1, data_13_933.2] + +/-- Complete interval computation for depth 13, residue 934. -/ +theorem bounds_13_934 : exactInterval 13 934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_934 : oddCount 934 13 = 7 ∧ acceleratedOrbit 13 934 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 934) = 3 ^ 7 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_934.1, data_13_934.2] + +/-- Complete interval computation for depth 13, residue 935. -/ +theorem bounds_13_935 : exactInterval 13 935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_935 : oddCount 935 13 = 7 ∧ acceleratedOrbit 13 935 = 250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 935) = 3 ^ 7 * m + 250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_935.1, data_13_935.2] + +/-- Complete interval computation for depth 13, residue 936. -/ +theorem bounds_13_936 : exactInterval 13 936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_936 : oddCount 936 13 = 4 ∧ acceleratedOrbit 13 936 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 936) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_936.1, data_13_936.2] + +/-- Complete interval computation for depth 13, residue 937. -/ +theorem bounds_13_937 : exactInterval 13 937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_937 : oddCount 937 13 = 10 ∧ acceleratedOrbit 13 937 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 937) = 3 ^ 10 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_937.1, data_13_937.2] + +/-- Complete interval computation for depth 13, residue 938. -/ +theorem bounds_13_938 : exactInterval 13 938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_938 : oddCount 938 13 = 4 ∧ acceleratedOrbit 13 938 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 938) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_938.1, data_13_938.2] + +/-- Complete interval computation for depth 13, residue 939. -/ +theorem bounds_13_939 : exactInterval 13 939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_939 : oddCount 939 13 = 8 ∧ acceleratedOrbit 13 939 = 755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 939) = 3 ^ 8 * m + 755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_939.1, data_13_939.2] + +/-- Complete interval computation for depth 13, residue 940. -/ +theorem bounds_13_940 : exactInterval 13 940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_940 : oddCount 940 13 = 7 ∧ acceleratedOrbit 13 940 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 940) = 3 ^ 7 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_940.1, data_13_940.2] + +/-- Complete interval computation for depth 13, residue 941. -/ +theorem bounds_13_941 : exactInterval 13 941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_941 : oddCount 941 13 = 7 ∧ acceleratedOrbit 13 941 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 941) = 3 ^ 7 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_941.1, data_13_941.2] + +end Collatz.Research.StoppingAtlas.Batch0528 From 4f5a3289ea35945804d7af06c2e1882a06c7d5ce Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:16 +0530 Subject: [PATCH 0529/1001] proof: certify atlas Batch0529 (13:942 to 13:956) --- Collatz/Research/StoppingAtlas/Batch0529.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0529.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0529.lean b/Collatz/Research/StoppingAtlas/Batch0529.lean new file mode 100644 index 00000000..da968e75 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0529.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0529 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 942. -/ +theorem bounds_13_942 : exactInterval 13 942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_942 : oddCount 942 13 = 7 ∧ acceleratedOrbit 13 942 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 942) = 3 ^ 7 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_942.1, data_13_942.2] + +/-- Complete interval computation for depth 13, residue 943. -/ +theorem bounds_13_943 : exactInterval 13 943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_943 : oddCount 943 13 = 5 ∧ acceleratedOrbit 13 943 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 943) = 3 ^ 5 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_943.1, data_13_943.2] + +/-- Complete interval computation for depth 13, residue 944. -/ +theorem bounds_13_944 : exactInterval 13 944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_944 : oddCount 944 13 = 5 ∧ acceleratedOrbit 13 944 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 944) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_944.1, data_13_944.2] + +/-- Complete interval computation for depth 13, residue 945. -/ +theorem bounds_13_945 : exactInterval 13 945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_945 : oddCount 945 13 = 5 ∧ acceleratedOrbit 13 945 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 945) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_945.1, data_13_945.2] + +/-- Complete interval computation for depth 13, residue 946. -/ +theorem bounds_13_946 : exactInterval 13 946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_946 : oddCount 946 13 = 5 ∧ acceleratedOrbit 13 946 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 946) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_946.1, data_13_946.2] + +/-- Complete interval computation for depth 13, residue 947. -/ +theorem bounds_13_947 : exactInterval 13 947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_947 : oddCount 947 13 = 5 ∧ acceleratedOrbit 13 947 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 947) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_947.1, data_13_947.2] + +/-- Complete interval computation for depth 13, residue 948. -/ +theorem bounds_13_948 : exactInterval 13 948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_948 : oddCount 948 13 = 5 ∧ acceleratedOrbit 13 948 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 948) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_948.1, data_13_948.2] + +/-- Complete interval computation for depth 13, residue 949. -/ +theorem bounds_13_949 : exactInterval 13 949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_949 : oddCount 949 13 = 5 ∧ acceleratedOrbit 13 949 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 949) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_949.1, data_13_949.2] + +/-- Complete interval computation for depth 13, residue 950. -/ +theorem bounds_13_950 : exactInterval 13 950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_950 : oddCount 950 13 = 6 ∧ acceleratedOrbit 13 950 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 950) = 3 ^ 6 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_950.1, data_13_950.2] + +/-- Complete interval computation for depth 13, residue 951. -/ +theorem bounds_13_951 : exactInterval 13 951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_951 : oddCount 951 13 = 6 ∧ acceleratedOrbit 13 951 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 951) = 3 ^ 6 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_951.1, data_13_951.2] + +/-- Complete interval computation for depth 13, residue 952. -/ +theorem bounds_13_952 : exactInterval 13 952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_952 : oddCount 952 13 = 5 ∧ acceleratedOrbit 13 952 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 952) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_952.1, data_13_952.2] + +/-- Complete interval computation for depth 13, residue 953. -/ +theorem bounds_13_953 : exactInterval 13 953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_953 : oddCount 953 13 = 7 ∧ acceleratedOrbit 13 953 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 953) = 3 ^ 7 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_953.1, data_13_953.2] + +/-- Complete interval computation for depth 13, residue 954. -/ +theorem bounds_13_954 : exactInterval 13 954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_954 : oddCount 954 13 = 5 ∧ acceleratedOrbit 13 954 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 954) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_954.1, data_13_954.2] + +/-- Complete interval computation for depth 13, residue 955. -/ +theorem bounds_13_955 : exactInterval 13 955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_955 : oddCount 955 13 = 7 ∧ acceleratedOrbit 13 955 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 955) = 3 ^ 7 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_955.1, data_13_955.2] + +/-- Complete interval computation for depth 13, residue 956. -/ +theorem bounds_13_956 : exactInterval 13 956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_956 : oddCount 956 13 = 9 ∧ acceleratedOrbit 13 956 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 956) = 3 ^ 9 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_956.1, data_13_956.2] + +end Collatz.Research.StoppingAtlas.Batch0529 From 53ded4d3be6ec05c2d410bf863335a0e638bdd76 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:16 +0530 Subject: [PATCH 0530/1001] proof: certify atlas Batch0530 (13:957 to 13:971) --- Collatz/Research/StoppingAtlas/Batch0530.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0530.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0530.lean b/Collatz/Research/StoppingAtlas/Batch0530.lean new file mode 100644 index 00000000..bf2a3bfd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0530.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0530 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 957. -/ +theorem bounds_13_957 : exactInterval 13 957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_957 : oddCount 957 13 = 9 ∧ acceleratedOrbit 13 957 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 957) = 3 ^ 9 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_957.1, data_13_957.2] + +/-- Complete interval computation for depth 13, residue 958. -/ +theorem bounds_13_958 : exactInterval 13 958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_958 : oddCount 958 13 = 9 ∧ acceleratedOrbit 13 958 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 958) = 3 ^ 9 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_958.1, data_13_958.2] + +/-- Complete interval computation for depth 13, residue 959. -/ +theorem bounds_13_959 : exactInterval 13 959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_959 : oddCount 959 13 = 11 ∧ acceleratedOrbit 13 959 = 20762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 959) = 3 ^ 11 * m + 20762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_959.1, data_13_959.2] + +/-- Complete interval computation for depth 13, residue 960. -/ +theorem bounds_13_960 : exactInterval 13 960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_960 : oddCount 960 13 = 4 ∧ acceleratedOrbit 13 960 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 960) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_960.1, data_13_960.2] + +/-- Complete interval computation for depth 13, residue 961. -/ +theorem bounds_13_961 : exactInterval 13 961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_961 : oddCount 961 13 = 6 ∧ acceleratedOrbit 13 961 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 961) = 3 ^ 6 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_961.1, data_13_961.2] + +/-- Complete interval computation for depth 13, residue 962. -/ +theorem bounds_13_962 : exactInterval 13 962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_962 : oddCount 962 13 = 6 ∧ acceleratedOrbit 13 962 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 962) = 3 ^ 6 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_962.1, data_13_962.2] + +/-- Complete interval computation for depth 13, residue 963. -/ +theorem bounds_13_963 : exactInterval 13 963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_963 : oddCount 963 13 = 6 ∧ acceleratedOrbit 13 963 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 963) = 3 ^ 6 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_963.1, data_13_963.2] + +/-- Complete interval computation for depth 13, residue 964. -/ +theorem bounds_13_964 : exactInterval 13 964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_964 : oddCount 964 13 = 4 ∧ acceleratedOrbit 13 964 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 964) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_964.1, data_13_964.2] + +/-- Complete interval computation for depth 13, residue 965. -/ +theorem bounds_13_965 : exactInterval 13 965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_965 : oddCount 965 13 = 4 ∧ acceleratedOrbit 13 965 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 965) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_965.1, data_13_965.2] + +/-- Complete interval computation for depth 13, residue 966. -/ +theorem bounds_13_966 : exactInterval 13 966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_966 : oddCount 966 13 = 4 ∧ acceleratedOrbit 13 966 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 966) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_966.1, data_13_966.2] + +/-- Complete interval computation for depth 13, residue 967. -/ +theorem bounds_13_967 : exactInterval 13 967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 967) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_967 : oddCount 967 13 = 8 ∧ acceleratedOrbit 13 967 = 776 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 967) = 3 ^ 8 * m + 776 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_967.1, data_13_967.2] + +/-- Complete interval computation for depth 13, residue 968. -/ +theorem bounds_13_968 : exactInterval 13 968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_968 : oddCount 968 13 = 7 ∧ acceleratedOrbit 13 968 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 968) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_968.1, data_13_968.2] + +/-- Complete interval computation for depth 13, residue 969. -/ +theorem bounds_13_969 : exactInterval 13 969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_969 : oddCount 969 13 = 7 ∧ acceleratedOrbit 13 969 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 969) = 3 ^ 7 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_969.1, data_13_969.2] + +/-- Complete interval computation for depth 13, residue 970. -/ +theorem bounds_13_970 : exactInterval 13 970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_970 : oddCount 970 13 = 7 ∧ acceleratedOrbit 13 970 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 970) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_970.1, data_13_970.2] + +/-- Complete interval computation for depth 13, residue 971. -/ +theorem bounds_13_971 : exactInterval 13 971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_971 : oddCount 971 13 = 5 ∧ acceleratedOrbit 13 971 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 971) = 3 ^ 5 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_971.1, data_13_971.2] + +end Collatz.Research.StoppingAtlas.Batch0530 From 9ba0a11fcc44b0e93f9edd5524e708bd4b6a6659 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:17 +0530 Subject: [PATCH 0531/1001] proof: certify atlas Batch0531 (13:972 to 13:987) --- Collatz/Research/StoppingAtlas/Batch0531.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0531.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0531.lean b/Collatz/Research/StoppingAtlas/Batch0531.lean new file mode 100644 index 00000000..6bba14b7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0531.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0531 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 972. -/ +theorem bounds_13_972 : exactInterval 13 972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_972 : oddCount 972 13 = 7 ∧ acceleratedOrbit 13 972 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 972) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_972.1, data_13_972.2] + +/-- Complete interval computation for depth 13, residue 973. -/ +theorem bounds_13_973 : exactInterval 13 973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_973 : oddCount 973 13 = 7 ∧ acceleratedOrbit 13 973 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 973) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_973.1, data_13_973.2] + +/-- Complete interval computation for depth 13, residue 974. -/ +theorem bounds_13_974 : exactInterval 13 974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_974 : oddCount 974 13 = 9 ∧ acceleratedOrbit 13 974 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 974) = 3 ^ 9 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_974.1, data_13_974.2] + +/-- Complete interval computation for depth 13, residue 975. -/ +theorem bounds_13_975 : exactInterval 13 975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_975 : oddCount 975 13 = 9 ∧ acceleratedOrbit 13 975 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 975) = 3 ^ 9 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_975.1, data_13_975.2] + +/-- Complete interval computation for depth 13, residue 976. -/ +theorem bounds_13_976 : exactInterval 13 976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_976 : oddCount 976 13 = 4 ∧ acceleratedOrbit 13 976 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 976) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_976.1, data_13_976.2] + +/-- Complete interval computation for depth 13, residue 977. -/ +theorem bounds_13_977 : exactInterval 13 977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_977 : oddCount 977 13 = 7 ∧ acceleratedOrbit 13 977 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 977) = 3 ^ 7 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_977.1, data_13_977.2] + +/-- Complete interval computation for depth 13, residue 978. -/ +theorem bounds_13_978 : exactInterval 13 978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_978 : oddCount 978 13 = 7 ∧ acceleratedOrbit 13 978 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 978) = 3 ^ 7 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_978.1, data_13_978.2] + +/-- Complete interval computation for depth 13, residue 979. -/ +theorem bounds_13_979 : exactInterval 13 979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_979 : oddCount 979 13 = 7 ∧ acceleratedOrbit 13 979 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 979) = 3 ^ 7 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_979.1, data_13_979.2] + +/-- Complete interval computation for depth 13, residue 980. -/ +theorem bounds_13_980 : exactInterval 13 980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_980 : oddCount 980 13 = 4 ∧ acceleratedOrbit 13 980 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 980) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_980.1, data_13_980.2] + +/-- Complete interval computation for depth 13, residue 981. -/ +theorem bounds_13_981 : exactInterval 13 981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_981 : oddCount 981 13 = 4 ∧ acceleratedOrbit 13 981 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 981) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_981.1, data_13_981.2] + +/-- Complete interval computation for depth 13, residue 982. -/ +theorem bounds_13_982 : exactInterval 13 982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_982 : oddCount 982 13 = 9 ∧ acceleratedOrbit 13 982 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 982) = 3 ^ 9 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_982.1, data_13_982.2] + +/-- Complete interval computation for depth 13, residue 983. -/ +theorem bounds_13_983 : exactInterval 13 983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 983) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_983 : oddCount 983 13 = 9 ∧ acceleratedOrbit 13 983 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 983) = 3 ^ 9 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_983.1, data_13_983.2] + +/-- Complete interval computation for depth 13, residue 984. -/ +theorem bounds_13_984 : exactInterval 13 984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_984 : oddCount 984 13 = 6 ∧ acceleratedOrbit 13 984 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 984) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_984.1, data_13_984.2] + +/-- Complete interval computation for depth 13, residue 985. -/ +theorem bounds_13_985 : exactInterval 13 985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_985 : oddCount 985 13 = 4 ∧ acceleratedOrbit 13 985 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 985) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_985.1, data_13_985.2] + +/-- Complete interval computation for depth 13, residue 986. -/ +theorem bounds_13_986 : exactInterval 13 986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_986 : oddCount 986 13 = 6 ∧ acceleratedOrbit 13 986 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 986) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_986.1, data_13_986.2] + +/-- Complete interval computation for depth 13, residue 987. -/ +theorem bounds_13_987 : exactInterval 13 987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_987 : oddCount 987 13 = 6 ∧ acceleratedOrbit 13 987 = 88 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 987) = 3 ^ 6 * m + 88 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_987.1, data_13_987.2] + +end Collatz.Research.StoppingAtlas.Batch0531 From 408159749096c8c82c340720ed4e686cd0df2b33 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:17 +0530 Subject: [PATCH 0532/1001] proof: certify atlas Batch0532 (13:988 to 13:1002) --- Collatz/Research/StoppingAtlas/Batch0532.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0532.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0532.lean b/Collatz/Research/StoppingAtlas/Batch0532.lean new file mode 100644 index 00000000..f9337102 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0532.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0532 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 988. -/ +theorem bounds_13_988 : exactInterval 13 988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_988 : oddCount 988 13 = 6 ∧ acceleratedOrbit 13 988 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 988) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_988.1, data_13_988.2] + +/-- Complete interval computation for depth 13, residue 989. -/ +theorem bounds_13_989 : exactInterval 13 989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_989 : oddCount 989 13 = 6 ∧ acceleratedOrbit 13 989 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 989) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_989.1, data_13_989.2] + +/-- Complete interval computation for depth 13, residue 990. -/ +theorem bounds_13_990 : exactInterval 13 990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_990 : oddCount 990 13 = 10 ∧ acceleratedOrbit 13 990 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 990) = 3 ^ 10 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_990.1, data_13_990.2] + +/-- Complete interval computation for depth 13, residue 991. -/ +theorem bounds_13_991 : exactInterval 13 991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_991 : oddCount 991 13 = 10 ∧ acceleratedOrbit 13 991 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 991) = 3 ^ 10 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_991.1, data_13_991.2] + +/-- Complete interval computation for depth 13, residue 992. -/ +theorem bounds_13_992 : exactInterval 13 992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_992 : oddCount 992 13 = 6 ∧ acceleratedOrbit 13 992 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 992) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_992.1, data_13_992.2] + +/-- Complete interval computation for depth 13, residue 993. -/ +theorem bounds_13_993 : exactInterval 13 993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_993 : oddCount 993 13 = 9 ∧ acceleratedOrbit 13 993 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 993) = 3 ^ 9 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_993.1, data_13_993.2] + +/-- Complete interval computation for depth 13, residue 994. -/ +theorem bounds_13_994 : exactInterval 13 994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_994 : oddCount 994 13 = 4 ∧ acceleratedOrbit 13 994 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 994) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_994.1, data_13_994.2] + +/-- Complete interval computation for depth 13, residue 995. -/ +theorem bounds_13_995 : exactInterval 13 995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_995 : oddCount 995 13 = 4 ∧ acceleratedOrbit 13 995 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 995) = 3 ^ 4 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_995.1, data_13_995.2] + +/-- Complete interval computation for depth 13, residue 996. -/ +theorem bounds_13_996 : exactInterval 13 996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_996 : oddCount 996 13 = 7 ∧ acceleratedOrbit 13 996 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 996) = 3 ^ 7 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_996.1, data_13_996.2] + +/-- Complete interval computation for depth 13, residue 997. -/ +theorem bounds_13_997 : exactInterval 13 997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_997 : oddCount 997 13 = 7 ∧ acceleratedOrbit 13 997 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 997) = 3 ^ 7 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_997.1, data_13_997.2] + +/-- Complete interval computation for depth 13, residue 998. -/ +theorem bounds_13_998 : exactInterval 13 998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_998 : oddCount 998 13 = 7 ∧ acceleratedOrbit 13 998 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 998) = 3 ^ 7 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_998.1, data_13_998.2] + +/-- Complete interval computation for depth 13, residue 999. -/ +theorem bounds_13_999 : exactInterval 13 999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_999 : oddCount 999 13 = 6 ∧ acceleratedOrbit 13 999 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 999) = 3 ^ 6 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_999.1, data_13_999.2] + +/-- Complete interval computation for depth 13, residue 1000. -/ +theorem bounds_13_1000 : exactInterval 13 1000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1000 : oddCount 1000 13 = 6 ∧ acceleratedOrbit 13 1000 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1000) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1000.1, data_13_1000.2] + +/-- Complete interval computation for depth 13, residue 1001. -/ +theorem bounds_13_1001 : exactInterval 13 1001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1001 : oddCount 1001 13 = 10 ∧ acceleratedOrbit 13 1001 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1001) = 3 ^ 10 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1001.1, data_13_1001.2] + +/-- Complete interval computation for depth 13, residue 1002. -/ +theorem bounds_13_1002 : exactInterval 13 1002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1002 : oddCount 1002 13 = 6 ∧ acceleratedOrbit 13 1002 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1002) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1002.1, data_13_1002.2] + +end Collatz.Research.StoppingAtlas.Batch0532 From a266e0e546828968268488b81d1546a73867aa30 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:18 +0530 Subject: [PATCH 0533/1001] proof: certify atlas Batch0533 (13:1003 to 13:1017) --- Collatz/Research/StoppingAtlas/Batch0533.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0533.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0533.lean b/Collatz/Research/StoppingAtlas/Batch0533.lean new file mode 100644 index 00000000..7a3b51ed --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0533.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0533 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1003. -/ +theorem bounds_13_1003 : exactInterval 13 1003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1003 : oddCount 1003 13 = 8 ∧ acceleratedOrbit 13 1003 = 805 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1003) = 3 ^ 8 * m + 805 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1003.1, data_13_1003.2] + +/-- Complete interval computation for depth 13, residue 1004. -/ +theorem bounds_13_1004 : exactInterval 13 1004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1004 : oddCount 1004 13 = 9 ∧ acceleratedOrbit 13 1004 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1004) = 3 ^ 9 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1004.1, data_13_1004.2] + +/-- Complete interval computation for depth 13, residue 1005. -/ +theorem bounds_13_1005 : exactInterval 13 1005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1005 : oddCount 1005 13 = 9 ∧ acceleratedOrbit 13 1005 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1005) = 3 ^ 9 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1005.1, data_13_1005.2] + +/-- Complete interval computation for depth 13, residue 1006. -/ +theorem bounds_13_1006 : exactInterval 13 1006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1006 : oddCount 1006 13 = 9 ∧ acceleratedOrbit 13 1006 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1006) = 3 ^ 9 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1006.1, data_13_1006.2] + +/-- Complete interval computation for depth 13, residue 1007. -/ +theorem bounds_13_1007 : exactInterval 13 1007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1007 : oddCount 1007 13 = 9 ∧ acceleratedOrbit 13 1007 = 2423 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1007) = 3 ^ 9 * m + 2423 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1007.1, data_13_1007.2] + +/-- Complete interval computation for depth 13, residue 1008. -/ +theorem bounds_13_1008 : exactInterval 13 1008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1008 : oddCount 1008 13 = 6 ∧ acceleratedOrbit 13 1008 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1008) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1008.1, data_13_1008.2] + +/-- Complete interval computation for depth 13, residue 1009. -/ +theorem bounds_13_1009 : exactInterval 13 1009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1009 : oddCount 1009 13 = 6 ∧ acceleratedOrbit 13 1009 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1009) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1009.1, data_13_1009.2] + +/-- Complete interval computation for depth 13, residue 1010. -/ +theorem bounds_13_1010 : exactInterval 13 1010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1010 : oddCount 1010 13 = 7 ∧ acceleratedOrbit 13 1010 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1010) = 3 ^ 7 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1010.1, data_13_1010.2] + +/-- Complete interval computation for depth 13, residue 1011. -/ +theorem bounds_13_1011 : exactInterval 13 1011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1011 : oddCount 1011 13 = 7 ∧ acceleratedOrbit 13 1011 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1011) = 3 ^ 7 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1011.1, data_13_1011.2] + +/-- Complete interval computation for depth 13, residue 1012. -/ +theorem bounds_13_1012 : exactInterval 13 1012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1012 : oddCount 1012 13 = 6 ∧ acceleratedOrbit 13 1012 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1012) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1012.1, data_13_1012.2] + +/-- Complete interval computation for depth 13, residue 1013. -/ +theorem bounds_13_1013 : exactInterval 13 1013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1013 : oddCount 1013 13 = 6 ∧ acceleratedOrbit 13 1013 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1013) = 3 ^ 6 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1013.1, data_13_1013.2] + +/-- Complete interval computation for depth 13, residue 1014. -/ +theorem bounds_13_1014 : exactInterval 13 1014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1014 : oddCount 1014 13 = 7 ∧ acceleratedOrbit 13 1014 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1014) = 3 ^ 7 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1014.1, data_13_1014.2] + +/-- Complete interval computation for depth 13, residue 1015. -/ +theorem bounds_13_1015 : exactInterval 13 1015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1015 : oddCount 1015 13 = 7 ∧ acceleratedOrbit 13 1015 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1015) = 3 ^ 7 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1015.1, data_13_1015.2] + +/-- Complete interval computation for depth 13, residue 1016. -/ +theorem bounds_13_1016 : exactInterval 13 1016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1016 : oddCount 1016 13 = 8 ∧ acceleratedOrbit 13 1016 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1016) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1016.1, data_13_1016.2] + +/-- Complete interval computation for depth 13, residue 1017. -/ +theorem bounds_13_1017 : exactInterval 13 1017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1017 : oddCount 1017 13 = 9 ∧ acceleratedOrbit 13 1017 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1017) = 3 ^ 9 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1017.1, data_13_1017.2] + +end Collatz.Research.StoppingAtlas.Batch0533 From a08d465ba706077f0baa584f21130693df246eb2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:18 +0530 Subject: [PATCH 0534/1001] proof: certify atlas Batch0534 (13:1018 to 13:1033) --- Collatz/Research/StoppingAtlas/Batch0534.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0534.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0534.lean b/Collatz/Research/StoppingAtlas/Batch0534.lean new file mode 100644 index 00000000..9da488fe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0534.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0534 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1018. -/ +theorem bounds_13_1018 : exactInterval 13 1018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1018 : oddCount 1018 13 = 8 ∧ acceleratedOrbit 13 1018 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1018) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1018.1, data_13_1018.2] + +/-- Complete interval computation for depth 13, residue 1019. -/ +theorem bounds_13_1019 : exactInterval 13 1019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1019 : oddCount 1019 13 = 8 ∧ acceleratedOrbit 13 1019 = 818 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1019) = 3 ^ 8 * m + 818 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1019.1, data_13_1019.2] + +/-- Complete interval computation for depth 13, residue 1020. -/ +theorem bounds_13_1020 : exactInterval 13 1020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1020 : oddCount 1020 13 = 8 ∧ acceleratedOrbit 13 1020 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1020) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1020.1, data_13_1020.2] + +/-- Complete interval computation for depth 13, residue 1021. -/ +theorem bounds_13_1021 : exactInterval 13 1021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1021 : oddCount 1021 13 = 8 ∧ acceleratedOrbit 13 1021 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1021) = 3 ^ 8 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1021.1, data_13_1021.2] + +/-- Complete interval computation for depth 13, residue 1022. -/ +theorem bounds_13_1022 : exactInterval 13 1022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1022 : oddCount 1022 13 = 10 ∧ acceleratedOrbit 13 1022 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1022) = 3 ^ 10 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1022.1, data_13_1022.2] + +/-- Complete interval computation for depth 13, residue 1023. -/ +theorem bounds_13_1023 : exactInterval 13 1023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1023) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1023 : oddCount 1023 13 = 10 ∧ acceleratedOrbit 13 1023 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1023) = 3 ^ 10 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1023.1, data_13_1023.2] + +/-- Complete interval computation for depth 13, residue 1024. -/ +theorem bounds_13_1024 : exactInterval 13 1024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1024 : oddCount 1024 13 = 2 ∧ acceleratedOrbit 13 1024 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1024) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1024.1, data_13_1024.2] + +/-- Complete interval computation for depth 13, residue 1025. -/ +theorem bounds_13_1025 : exactInterval 13 1025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1025 : oddCount 1025 13 = 6 ∧ acceleratedOrbit 13 1025 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1025) = 3 ^ 6 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1025.1, data_13_1025.2] + +/-- Complete interval computation for depth 13, residue 1026. -/ +theorem bounds_13_1026 : exactInterval 13 1026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1026 : oddCount 1026 13 = 6 ∧ acceleratedOrbit 13 1026 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1026) = 3 ^ 6 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1026.1, data_13_1026.2] + +/-- Complete interval computation for depth 13, residue 1027. -/ +theorem bounds_13_1027 : exactInterval 13 1027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1027 : oddCount 1027 13 = 6 ∧ acceleratedOrbit 13 1027 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1027) = 3 ^ 6 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1027.1, data_13_1027.2] + +/-- Complete interval computation for depth 13, residue 1028. -/ +theorem bounds_13_1028 : exactInterval 13 1028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1028 : oddCount 1028 13 = 5 ∧ acceleratedOrbit 13 1028 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1028) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1028.1, data_13_1028.2] + +/-- Complete interval computation for depth 13, residue 1029. -/ +theorem bounds_13_1029 : exactInterval 13 1029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1029 : oddCount 1029 13 = 5 ∧ acceleratedOrbit 13 1029 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1029) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1029.1, data_13_1029.2] + +/-- Complete interval computation for depth 13, residue 1030. -/ +theorem bounds_13_1030 : exactInterval 13 1030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1030 : oddCount 1030 13 = 5 ∧ acceleratedOrbit 13 1030 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1030) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1030.1, data_13_1030.2] + +/-- Complete interval computation for depth 13, residue 1031. -/ +theorem bounds_13_1031 : exactInterval 13 1031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1031 : oddCount 1031 13 = 6 ∧ acceleratedOrbit 13 1031 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1031) = 3 ^ 6 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1031.1, data_13_1031.2] + +/-- Complete interval computation for depth 13, residue 1032. -/ +theorem bounds_13_1032 : exactInterval 13 1032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1032 : oddCount 1032 13 = 6 ∧ acceleratedOrbit 13 1032 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1032) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1032.1, data_13_1032.2] + +/-- Complete interval computation for depth 13, residue 1033. -/ +theorem bounds_13_1033 : exactInterval 13 1033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1033 : oddCount 1033 13 = 8 ∧ acceleratedOrbit 13 1033 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1033) = 3 ^ 8 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1033.1, data_13_1033.2] + +end Collatz.Research.StoppingAtlas.Batch0534 From e6cbad5a8371785e47caea1193318119b7fa0cbb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:18 +0530 Subject: [PATCH 0535/1001] proof: certify atlas Batch0535 (13:1034 to 13:1048) --- Collatz/Research/StoppingAtlas/Batch0535.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0535.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0535.lean b/Collatz/Research/StoppingAtlas/Batch0535.lean new file mode 100644 index 00000000..a98720e6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0535.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0535 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1034. -/ +theorem bounds_13_1034 : exactInterval 13 1034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1034 : oddCount 1034 13 = 6 ∧ acceleratedOrbit 13 1034 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1034) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1034.1, data_13_1034.2] + +/-- Complete interval computation for depth 13, residue 1035. -/ +theorem bounds_13_1035 : exactInterval 13 1035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1035 : oddCount 1035 13 = 5 ∧ acceleratedOrbit 13 1035 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1035) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1035.1, data_13_1035.2] + +/-- Complete interval computation for depth 13, residue 1036. -/ +theorem bounds_13_1036 : exactInterval 13 1036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1036 : oddCount 1036 13 = 6 ∧ acceleratedOrbit 13 1036 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1036) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1036.1, data_13_1036.2] + +/-- Complete interval computation for depth 13, residue 1037. -/ +theorem bounds_13_1037 : exactInterval 13 1037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1037 : oddCount 1037 13 = 6 ∧ acceleratedOrbit 13 1037 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1037) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1037.1, data_13_1037.2] + +/-- Complete interval computation for depth 13, residue 1038. -/ +theorem bounds_13_1038 : exactInterval 13 1038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1038 : oddCount 1038 13 = 8 ∧ acceleratedOrbit 13 1038 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1038) = 3 ^ 8 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1038.1, data_13_1038.2] + +/-- Complete interval computation for depth 13, residue 1039. -/ +theorem bounds_13_1039 : exactInterval 13 1039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1039 : oddCount 1039 13 = 8 ∧ acceleratedOrbit 13 1039 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1039) = 3 ^ 8 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1039.1, data_13_1039.2] + +/-- Complete interval computation for depth 13, residue 1040. -/ +theorem bounds_13_1040 : exactInterval 13 1040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1040 : oddCount 1040 13 = 4 ∧ acceleratedOrbit 13 1040 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1040) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1040.1, data_13_1040.2] + +/-- Complete interval computation for depth 13, residue 1041. -/ +theorem bounds_13_1041 : exactInterval 13 1041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1041 : oddCount 1041 13 = 6 ∧ acceleratedOrbit 13 1041 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1041) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1041.1, data_13_1041.2] + +/-- Complete interval computation for depth 13, residue 1042. -/ +theorem bounds_13_1042 : exactInterval 13 1042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1042 : oddCount 1042 13 = 5 ∧ acceleratedOrbit 13 1042 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1042) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1042.1, data_13_1042.2] + +/-- Complete interval computation for depth 13, residue 1043. -/ +theorem bounds_13_1043 : exactInterval 13 1043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1043 : oddCount 1043 13 = 5 ∧ acceleratedOrbit 13 1043 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1043) = 3 ^ 5 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1043.1, data_13_1043.2] + +/-- Complete interval computation for depth 13, residue 1044. -/ +theorem bounds_13_1044 : exactInterval 13 1044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1044 : oddCount 1044 13 = 4 ∧ acceleratedOrbit 13 1044 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1044) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1044.1, data_13_1044.2] + +/-- Complete interval computation for depth 13, residue 1045. -/ +theorem bounds_13_1045 : exactInterval 13 1045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1045 : oddCount 1045 13 = 4 ∧ acceleratedOrbit 13 1045 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1045) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1045.1, data_13_1045.2] + +/-- Complete interval computation for depth 13, residue 1046. -/ +theorem bounds_13_1046 : exactInterval 13 1046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1046 : oddCount 1046 13 = 6 ∧ acceleratedOrbit 13 1046 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1046) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1046.1, data_13_1046.2] + +/-- Complete interval computation for depth 13, residue 1047. -/ +theorem bounds_13_1047 : exactInterval 13 1047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1047) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1047 : oddCount 1047 13 = 6 ∧ acceleratedOrbit 13 1047 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1047) = 3 ^ 6 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1047.1, data_13_1047.2] + +/-- Complete interval computation for depth 13, residue 1048. -/ +theorem bounds_13_1048 : exactInterval 13 1048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1048 : oddCount 1048 13 = 4 ∧ acceleratedOrbit 13 1048 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1048) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1048.1, data_13_1048.2] + +end Collatz.Research.StoppingAtlas.Batch0535 From f351a869a0d0be22ff11e1bfa41e0938d8f4eb63 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:19 +0530 Subject: [PATCH 0536/1001] proof: certify atlas Batch0536 (13:1049 to 13:1063) --- Collatz/Research/StoppingAtlas/Batch0536.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0536.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0536.lean b/Collatz/Research/StoppingAtlas/Batch0536.lean new file mode 100644 index 00000000..175ad34e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0536.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0536 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1049. -/ +theorem bounds_13_1049 : exactInterval 13 1049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1049 : oddCount 1049 13 = 7 ∧ acceleratedOrbit 13 1049 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1049) = 3 ^ 7 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1049.1, data_13_1049.2] + +/-- Complete interval computation for depth 13, residue 1050. -/ +theorem bounds_13_1050 : exactInterval 13 1050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1050 : oddCount 1050 13 = 4 ∧ acceleratedOrbit 13 1050 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1050) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1050.1, data_13_1050.2] + +/-- Complete interval computation for depth 13, residue 1051. -/ +theorem bounds_13_1051 : exactInterval 13 1051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1051 : oddCount 1051 13 = 11 ∧ acceleratedOrbit 13 1051 = 22760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1051) = 3 ^ 11 * m + 22760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1051.1, data_13_1051.2] + +/-- Complete interval computation for depth 13, residue 1052. -/ +theorem bounds_13_1052 : exactInterval 13 1052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1052 : oddCount 1052 13 = 7 ∧ acceleratedOrbit 13 1052 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1052) = 3 ^ 7 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1052.1, data_13_1052.2] + +/-- Complete interval computation for depth 13, residue 1053. -/ +theorem bounds_13_1053 : exactInterval 13 1053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1053 : oddCount 1053 13 = 7 ∧ acceleratedOrbit 13 1053 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1053) = 3 ^ 7 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1053.1, data_13_1053.2] + +/-- Complete interval computation for depth 13, residue 1054. -/ +theorem bounds_13_1054 : exactInterval 13 1054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1054 : oddCount 1054 13 = 7 ∧ acceleratedOrbit 13 1054 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1054) = 3 ^ 7 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1054.1, data_13_1054.2] + +/-- Complete interval computation for depth 13, residue 1055. -/ +theorem bounds_13_1055 : exactInterval 13 1055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1055 : oddCount 1055 13 = 11 ∧ acceleratedOrbit 13 1055 = 22841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1055) = 3 ^ 11 * m + 22841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1055.1, data_13_1055.2] + +/-- Complete interval computation for depth 13, residue 1056. -/ +theorem bounds_13_1056 : exactInterval 13 1056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1056 : oddCount 1056 13 = 4 ∧ acceleratedOrbit 13 1056 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1056) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1056.1, data_13_1056.2] + +/-- Complete interval computation for depth 13, residue 1057. -/ +theorem bounds_13_1057 : exactInterval 13 1057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1057 : oddCount 1057 13 = 8 ∧ acceleratedOrbit 13 1057 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1057) = 3 ^ 8 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1057.1, data_13_1057.2] + +/-- Complete interval computation for depth 13, residue 1058. -/ +theorem bounds_13_1058 : exactInterval 13 1058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1058 : oddCount 1058 13 = 4 ∧ acceleratedOrbit 13 1058 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1058) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1058.1, data_13_1058.2] + +/-- Complete interval computation for depth 13, residue 1059. -/ +theorem bounds_13_1059 : exactInterval 13 1059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1059 : oddCount 1059 13 = 4 ∧ acceleratedOrbit 13 1059 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1059) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1059.1, data_13_1059.2] + +/-- Complete interval computation for depth 13, residue 1060. -/ +theorem bounds_13_1060 : exactInterval 13 1060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1060 : oddCount 1060 13 = 6 ∧ acceleratedOrbit 13 1060 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1060) = 3 ^ 6 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1060.1, data_13_1060.2] + +/-- Complete interval computation for depth 13, residue 1061. -/ +theorem bounds_13_1061 : exactInterval 13 1061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1061 : oddCount 1061 13 = 6 ∧ acceleratedOrbit 13 1061 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1061) = 3 ^ 6 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1061.1, data_13_1061.2] + +/-- Complete interval computation for depth 13, residue 1062. -/ +theorem bounds_13_1062 : exactInterval 13 1062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1062 : oddCount 1062 13 = 6 ∧ acceleratedOrbit 13 1062 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1062) = 3 ^ 6 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1062.1, data_13_1062.2] + +/-- Complete interval computation for depth 13, residue 1063. -/ +theorem bounds_13_1063 : exactInterval 13 1063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1063 : oddCount 1063 13 = 8 ∧ acceleratedOrbit 13 1063 = 854 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1063) = 3 ^ 8 * m + 854 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1063.1, data_13_1063.2] + +end Collatz.Research.StoppingAtlas.Batch0536 From e1410550524e8b58df41a61f7cac46749b9d8fc3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:19 +0530 Subject: [PATCH 0537/1001] proof: certify atlas Batch0537 (13:1064 to 13:1079) --- Collatz/Research/StoppingAtlas/Batch0537.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0537.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0537.lean b/Collatz/Research/StoppingAtlas/Batch0537.lean new file mode 100644 index 00000000..3611aa06 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0537.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0537 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1064. -/ +theorem bounds_13_1064 : exactInterval 13 1064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1064 : oddCount 1064 13 = 4 ∧ acceleratedOrbit 13 1064 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1064) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1064.1, data_13_1064.2] + +/-- Complete interval computation for depth 13, residue 1065. -/ +theorem bounds_13_1065 : exactInterval 13 1065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1065 : oddCount 1065 13 = 9 ∧ acceleratedOrbit 13 1065 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1065) = 3 ^ 9 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1065.1, data_13_1065.2] + +/-- Complete interval computation for depth 13, residue 1066. -/ +theorem bounds_13_1066 : exactInterval 13 1066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1066 : oddCount 1066 13 = 4 ∧ acceleratedOrbit 13 1066 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1066) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1066.1, data_13_1066.2] + +/-- Complete interval computation for depth 13, residue 1067. -/ +theorem bounds_13_1067 : exactInterval 13 1067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1067 : oddCount 1067 13 = 7 ∧ acceleratedOrbit 13 1067 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1067) = 3 ^ 7 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1067.1, data_13_1067.2] + +/-- Complete interval computation for depth 13, residue 1068. -/ +theorem bounds_13_1068 : exactInterval 13 1068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1068 : oddCount 1068 13 = 5 ∧ acceleratedOrbit 13 1068 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1068) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1068.1, data_13_1068.2] + +/-- Complete interval computation for depth 13, residue 1069. -/ +theorem bounds_13_1069 : exactInterval 13 1069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1069 : oddCount 1069 13 = 5 ∧ acceleratedOrbit 13 1069 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1069) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1069.1, data_13_1069.2] + +/-- Complete interval computation for depth 13, residue 1070. -/ +theorem bounds_13_1070 : exactInterval 13 1070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1070 : oddCount 1070 13 = 5 ∧ acceleratedOrbit 13 1070 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1070) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1070.1, data_13_1070.2] + +/-- Complete interval computation for depth 13, residue 1071. -/ +theorem bounds_13_1071 : exactInterval 13 1071 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1071) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1071 : oddCount 1071 13 = 8 ∧ acceleratedOrbit 13 1071 = 859 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1071) = 3 ^ 8 * m + 859 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1071.1, data_13_1071.2] + +/-- Complete interval computation for depth 13, residue 1072. -/ +theorem bounds_13_1072 : exactInterval 13 1072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1072 : oddCount 1072 13 = 4 ∧ acceleratedOrbit 13 1072 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1072) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1072.1, data_13_1072.2] + +/-- Complete interval computation for depth 13, residue 1073. -/ +theorem bounds_13_1073 : exactInterval 13 1073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1073 : oddCount 1073 13 = 5 ∧ acceleratedOrbit 13 1073 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1073) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1073.1, data_13_1073.2] + +/-- Complete interval computation for depth 13, residue 1074. -/ +theorem bounds_13_1074 : exactInterval 13 1074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1074 : oddCount 1074 13 = 5 ∧ acceleratedOrbit 13 1074 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1074) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1074.1, data_13_1074.2] + +/-- Complete interval computation for depth 13, residue 1075. -/ +theorem bounds_13_1075 : exactInterval 13 1075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1075 : oddCount 1075 13 = 5 ∧ acceleratedOrbit 13 1075 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1075) = 3 ^ 5 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1075.1, data_13_1075.2] + +/-- Complete interval computation for depth 13, residue 1076. -/ +theorem bounds_13_1076 : exactInterval 13 1076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1076 : oddCount 1076 13 = 4 ∧ acceleratedOrbit 13 1076 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1076) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1076.1, data_13_1076.2] + +/-- Complete interval computation for depth 13, residue 1077. -/ +theorem bounds_13_1077 : exactInterval 13 1077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1077 : oddCount 1077 13 = 4 ∧ acceleratedOrbit 13 1077 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1077) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1077.1, data_13_1077.2] + +/-- Complete interval computation for depth 13, residue 1078. -/ +theorem bounds_13_1078 : exactInterval 13 1078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1078 : oddCount 1078 13 = 8 ∧ acceleratedOrbit 13 1078 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1078) = 3 ^ 8 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1078.1, data_13_1078.2] + +/-- Complete interval computation for depth 13, residue 1079. -/ +theorem bounds_13_1079 : exactInterval 13 1079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1079) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1079 : oddCount 1079 13 = 8 ∧ acceleratedOrbit 13 1079 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1079) = 3 ^ 8 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1079.1, data_13_1079.2] + +end Collatz.Research.StoppingAtlas.Batch0537 From fc6f1bc92c74e9d3f5630fa0bf15e777fb8508b9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:20 +0530 Subject: [PATCH 0538/1001] proof: certify atlas Batch0538 (13:1080 to 13:1094) --- Collatz/Research/StoppingAtlas/Batch0538.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0538.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0538.lean b/Collatz/Research/StoppingAtlas/Batch0538.lean new file mode 100644 index 00000000..b806ec89 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0538.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0538 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1080. -/ +theorem bounds_13_1080 : exactInterval 13 1080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1080 : oddCount 1080 13 = 6 ∧ acceleratedOrbit 13 1080 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1080) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1080.1, data_13_1080.2] + +/-- Complete interval computation for depth 13, residue 1081. -/ +theorem bounds_13_1081 : exactInterval 13 1081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1081 : oddCount 1081 13 = 7 ∧ acceleratedOrbit 13 1081 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1081) = 3 ^ 7 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1081.1, data_13_1081.2] + +/-- Complete interval computation for depth 13, residue 1082. -/ +theorem bounds_13_1082 : exactInterval 13 1082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1082 : oddCount 1082 13 = 6 ∧ acceleratedOrbit 13 1082 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1082) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1082.1, data_13_1082.2] + +/-- Complete interval computation for depth 13, residue 1083. -/ +theorem bounds_13_1083 : exactInterval 13 1083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1083 : oddCount 1083 13 = 7 ∧ acceleratedOrbit 13 1083 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1083) = 3 ^ 7 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1083.1, data_13_1083.2] + +/-- Complete interval computation for depth 13, residue 1084. -/ +theorem bounds_13_1084 : exactInterval 13 1084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1084 : oddCount 1084 13 = 6 ∧ acceleratedOrbit 13 1084 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1084) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1084.1, data_13_1084.2] + +/-- Complete interval computation for depth 13, residue 1085. -/ +theorem bounds_13_1085 : exactInterval 13 1085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1085 : oddCount 1085 13 = 6 ∧ acceleratedOrbit 13 1085 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1085) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1085.1, data_13_1085.2] + +/-- Complete interval computation for depth 13, residue 1086. -/ +theorem bounds_13_1086 : exactInterval 13 1086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1086 : oddCount 1086 13 = 8 ∧ acceleratedOrbit 13 1086 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1086) = 3 ^ 8 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1086.1, data_13_1086.2] + +/-- Complete interval computation for depth 13, residue 1087. -/ +theorem bounds_13_1087 : exactInterval 13 1087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1087 : oddCount 1087 13 = 8 ∧ acceleratedOrbit 13 1087 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1087) = 3 ^ 8 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1087.1, data_13_1087.2] + +/-- Complete interval computation for depth 13, residue 1088. -/ +theorem bounds_13_1088 : exactInterval 13 1088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1088 : oddCount 1088 13 = 3 ∧ acceleratedOrbit 13 1088 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1088) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1088.1, data_13_1088.2] + +/-- Complete interval computation for depth 13, residue 1089. -/ +theorem bounds_13_1089 : exactInterval 13 1089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1089 : oddCount 1089 13 = 6 ∧ acceleratedOrbit 13 1089 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1089) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1089.1, data_13_1089.2] + +/-- Complete interval computation for depth 13, residue 1090. -/ +theorem bounds_13_1090 : exactInterval 13 1090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1090 : oddCount 1090 13 = 6 ∧ acceleratedOrbit 13 1090 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1090) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1090.1, data_13_1090.2] + +/-- Complete interval computation for depth 13, residue 1091. -/ +theorem bounds_13_1091 : exactInterval 13 1091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1091 : oddCount 1091 13 = 6 ∧ acceleratedOrbit 13 1091 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1091) = 3 ^ 6 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1091.1, data_13_1091.2] + +/-- Complete interval computation for depth 13, residue 1092. -/ +theorem bounds_13_1092 : exactInterval 13 1092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1092 : oddCount 1092 13 = 4 ∧ acceleratedOrbit 13 1092 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1092) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1092.1, data_13_1092.2] + +/-- Complete interval computation for depth 13, residue 1093. -/ +theorem bounds_13_1093 : exactInterval 13 1093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1093 : oddCount 1093 13 = 4 ∧ acceleratedOrbit 13 1093 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1093) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1093.1, data_13_1093.2] + +/-- Complete interval computation for depth 13, residue 1094. -/ +theorem bounds_13_1094 : exactInterval 13 1094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1094 : oddCount 1094 13 = 4 ∧ acceleratedOrbit 13 1094 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1094) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1094.1, data_13_1094.2] + +end Collatz.Research.StoppingAtlas.Batch0538 From e9c52a56401e7ef3f7b5357a474da7c3bf927d94 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:20 +0530 Subject: [PATCH 0539/1001] proof: certify atlas Batch0539 (13:1095 to 13:1110) --- Collatz/Research/StoppingAtlas/Batch0539.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0539.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0539.lean b/Collatz/Research/StoppingAtlas/Batch0539.lean new file mode 100644 index 00000000..3cfdb7ce --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0539.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0539 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1095. -/ +theorem bounds_13_1095 : exactInterval 13 1095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1095 : oddCount 1095 13 = 9 ∧ acceleratedOrbit 13 1095 = 2636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1095) = 3 ^ 9 * m + 2636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1095.1, data_13_1095.2] + +/-- Complete interval computation for depth 13, residue 1096. -/ +theorem bounds_13_1096 : exactInterval 13 1096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1096 : oddCount 1096 13 = 8 ∧ acceleratedOrbit 13 1096 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1096) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1096.1, data_13_1096.2] + +/-- Complete interval computation for depth 13, residue 1097. -/ +theorem bounds_13_1097 : exactInterval 13 1097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1097 : oddCount 1097 13 = 8 ∧ acceleratedOrbit 13 1097 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1097) = 3 ^ 8 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1097.1, data_13_1097.2] + +/-- Complete interval computation for depth 13, residue 1098. -/ +theorem bounds_13_1098 : exactInterval 13 1098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1098 : oddCount 1098 13 = 8 ∧ acceleratedOrbit 13 1098 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1098) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1098.1, data_13_1098.2] + +/-- Complete interval computation for depth 13, residue 1099. -/ +theorem bounds_13_1099 : exactInterval 13 1099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1099 : oddCount 1099 13 = 4 ∧ acceleratedOrbit 13 1099 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1099) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1099.1, data_13_1099.2] + +/-- Complete interval computation for depth 13, residue 1100. -/ +theorem bounds_13_1100 : exactInterval 13 1100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1100 : oddCount 1100 13 = 8 ∧ acceleratedOrbit 13 1100 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1100) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1100.1, data_13_1100.2] + +/-- Complete interval computation for depth 13, residue 1101. -/ +theorem bounds_13_1101 : exactInterval 13 1101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1101 : oddCount 1101 13 = 8 ∧ acceleratedOrbit 13 1101 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1101) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1101.1, data_13_1101.2] + +/-- Complete interval computation for depth 13, residue 1102. -/ +theorem bounds_13_1102 : exactInterval 13 1102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1102 : oddCount 1102 13 = 7 ∧ acceleratedOrbit 13 1102 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1102) = 3 ^ 7 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1102.1, data_13_1102.2] + +/-- Complete interval computation for depth 13, residue 1103. -/ +theorem bounds_13_1103 : exactInterval 13 1103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1103 : oddCount 1103 13 = 7 ∧ acceleratedOrbit 13 1103 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1103) = 3 ^ 7 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1103.1, data_13_1103.2] + +/-- Complete interval computation for depth 13, residue 1104. -/ +theorem bounds_13_1104 : exactInterval 13 1104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1104 : oddCount 1104 13 = 3 ∧ acceleratedOrbit 13 1104 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1104) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1104.1, data_13_1104.2] + +/-- Complete interval computation for depth 13, residue 1105. -/ +theorem bounds_13_1105 : exactInterval 13 1105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1105 : oddCount 1105 13 = 8 ∧ acceleratedOrbit 13 1105 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1105) = 3 ^ 8 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1105.1, data_13_1105.2] + +/-- Complete interval computation for depth 13, residue 1106. -/ +theorem bounds_13_1106 : exactInterval 13 1106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1106 : oddCount 1106 13 = 9 ∧ acceleratedOrbit 13 1106 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1106) = 3 ^ 9 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1106.1, data_13_1106.2] + +/-- Complete interval computation for depth 13, residue 1107. -/ +theorem bounds_13_1107 : exactInterval 13 1107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1107 : oddCount 1107 13 = 9 ∧ acceleratedOrbit 13 1107 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1107) = 3 ^ 9 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1107.1, data_13_1107.2] + +/-- Complete interval computation for depth 13, residue 1108. -/ +theorem bounds_13_1108 : exactInterval 13 1108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1108 : oddCount 1108 13 = 3 ∧ acceleratedOrbit 13 1108 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1108) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1108.1, data_13_1108.2] + +/-- Complete interval computation for depth 13, residue 1109. -/ +theorem bounds_13_1109 : exactInterval 13 1109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1109 : oddCount 1109 13 = 3 ∧ acceleratedOrbit 13 1109 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1109) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1109.1, data_13_1109.2] + +/-- Complete interval computation for depth 13, residue 1110. -/ +theorem bounds_13_1110 : exactInterval 13 1110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1110 : oddCount 1110 13 = 4 ∧ acceleratedOrbit 13 1110 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1110) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1110.1, data_13_1110.2] + +end Collatz.Research.StoppingAtlas.Batch0539 From 9a78bb25f8599b148950da650a0685045646736f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:20 +0530 Subject: [PATCH 0540/1001] proof: certify atlas Batch0540 (13:1111 to 13:1125) --- Collatz/Research/StoppingAtlas/Batch0540.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0540.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0540.lean b/Collatz/Research/StoppingAtlas/Batch0540.lean new file mode 100644 index 00000000..8f83d8d8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0540.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0540 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1111. -/ +theorem bounds_13_1111 : exactInterval 13 1111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1111 : oddCount 1111 13 = 4 ∧ acceleratedOrbit 13 1111 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1111) = 3 ^ 4 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1111.1, data_13_1111.2] + +/-- Complete interval computation for depth 13, residue 1112. -/ +theorem bounds_13_1112 : exactInterval 13 1112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1112 : oddCount 1112 13 = 6 ∧ acceleratedOrbit 13 1112 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1112) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1112.1, data_13_1112.2] + +/-- Complete interval computation for depth 13, residue 1113. -/ +theorem bounds_13_1113 : exactInterval 13 1113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1113 : oddCount 1113 13 = 7 ∧ acceleratedOrbit 13 1113 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1113) = 3 ^ 7 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1113.1, data_13_1113.2] + +/-- Complete interval computation for depth 13, residue 1114. -/ +theorem bounds_13_1114 : exactInterval 13 1114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1114 : oddCount 1114 13 = 6 ∧ acceleratedOrbit 13 1114 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1114) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1114.1, data_13_1114.2] + +/-- Complete interval computation for depth 13, residue 1115. -/ +theorem bounds_13_1115 : exactInterval 13 1115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1115 : oddCount 1115 13 = 9 ∧ acceleratedOrbit 13 1115 = 2683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1115) = 3 ^ 9 * m + 2683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1115.1, data_13_1115.2] + +/-- Complete interval computation for depth 13, residue 1116. -/ +theorem bounds_13_1116 : exactInterval 13 1116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1116 : oddCount 1116 13 = 6 ∧ acceleratedOrbit 13 1116 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1116) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1116.1, data_13_1116.2] + +/-- Complete interval computation for depth 13, residue 1117. -/ +theorem bounds_13_1117 : exactInterval 13 1117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1117 : oddCount 1117 13 = 6 ∧ acceleratedOrbit 13 1117 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1117) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1117.1, data_13_1117.2] + +/-- Complete interval computation for depth 13, residue 1118. -/ +theorem bounds_13_1118 : exactInterval 13 1118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1118 : oddCount 1118 13 = 9 ∧ acceleratedOrbit 13 1118 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1118) = 3 ^ 9 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1118.1, data_13_1118.2] + +/-- Complete interval computation for depth 13, residue 1119. -/ +theorem bounds_13_1119 : exactInterval 13 1119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1119 : oddCount 1119 13 = 9 ∧ acceleratedOrbit 13 1119 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1119) = 3 ^ 9 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1119.1, data_13_1119.2] + +/-- Complete interval computation for depth 13, residue 1120. -/ +theorem bounds_13_1120 : exactInterval 13 1120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1120 : oddCount 1120 13 = 3 ∧ acceleratedOrbit 13 1120 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1120) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1120.1, data_13_1120.2] + +/-- Complete interval computation for depth 13, residue 1121. -/ +theorem bounds_13_1121 : exactInterval 13 1121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1121 : oddCount 1121 13 = 6 ∧ acceleratedOrbit 13 1121 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1121) = 3 ^ 6 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1121.1, data_13_1121.2] + +/-- Complete interval computation for depth 13, residue 1122. -/ +theorem bounds_13_1122 : exactInterval 13 1122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1122 : oddCount 1122 13 = 6 ∧ acceleratedOrbit 13 1122 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1122) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1122.1, data_13_1122.2] + +/-- Complete interval computation for depth 13, residue 1123. -/ +theorem bounds_13_1123 : exactInterval 13 1123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1123 : oddCount 1123 13 = 6 ∧ acceleratedOrbit 13 1123 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1123) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1123.1, data_13_1123.2] + +/-- Complete interval computation for depth 13, residue 1124. -/ +theorem bounds_13_1124 : exactInterval 13 1124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1124 : oddCount 1124 13 = 6 ∧ acceleratedOrbit 13 1124 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1124) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1124.1, data_13_1124.2] + +/-- Complete interval computation for depth 13, residue 1125. -/ +theorem bounds_13_1125 : exactInterval 13 1125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1125 : oddCount 1125 13 = 6 ∧ acceleratedOrbit 13 1125 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1125) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1125.1, data_13_1125.2] + +end Collatz.Research.StoppingAtlas.Batch0540 From 206ce214d9a7349d37958684c6676cf77dd1d061 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:21 +0530 Subject: [PATCH 0541/1001] proof: certify atlas Batch0541 (13:1126 to 13:1140) --- Collatz/Research/StoppingAtlas/Batch0541.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0541.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0541.lean b/Collatz/Research/StoppingAtlas/Batch0541.lean new file mode 100644 index 00000000..5e291fc4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0541.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0541 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1126. -/ +theorem bounds_13_1126 : exactInterval 13 1126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1126 : oddCount 1126 13 = 6 ∧ acceleratedOrbit 13 1126 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1126) = 3 ^ 6 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1126.1, data_13_1126.2] + +/-- Complete interval computation for depth 13, residue 1127. -/ +theorem bounds_13_1127 : exactInterval 13 1127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1127 : oddCount 1127 13 = 9 ∧ acceleratedOrbit 13 1127 = 2711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1127) = 3 ^ 9 * m + 2711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1127.1, data_13_1127.2] + +/-- Complete interval computation for depth 13, residue 1128. -/ +theorem bounds_13_1128 : exactInterval 13 1128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1128 : oddCount 1128 13 = 3 ∧ acceleratedOrbit 13 1128 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1128) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1128.1, data_13_1128.2] + +/-- Complete interval computation for depth 13, residue 1129. -/ +theorem bounds_13_1129 : exactInterval 13 1129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1129 : oddCount 1129 13 = 7 ∧ acceleratedOrbit 13 1129 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1129) = 3 ^ 7 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1129.1, data_13_1129.2] + +/-- Complete interval computation for depth 13, residue 1130. -/ +theorem bounds_13_1130 : exactInterval 13 1130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1130 : oddCount 1130 13 = 3 ∧ acceleratedOrbit 13 1130 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1130) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1130.1, data_13_1130.2] + +/-- Complete interval computation for depth 13, residue 1131. -/ +theorem bounds_13_1131 : exactInterval 13 1131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1131 : oddCount 1131 13 = 8 ∧ acceleratedOrbit 13 1131 = 908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1131) = 3 ^ 8 * m + 908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1131.1, data_13_1131.2] + +/-- Complete interval computation for depth 13, residue 1132. -/ +theorem bounds_13_1132 : exactInterval 13 1132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1132 : oddCount 1132 13 = 8 ∧ acceleratedOrbit 13 1132 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1132) = 3 ^ 8 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1132.1, data_13_1132.2] + +/-- Complete interval computation for depth 13, residue 1133. -/ +theorem bounds_13_1133 : exactInterval 13 1133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1133 : oddCount 1133 13 = 8 ∧ acceleratedOrbit 13 1133 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1133) = 3 ^ 8 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1133.1, data_13_1133.2] + +/-- Complete interval computation for depth 13, residue 1134. -/ +theorem bounds_13_1134 : exactInterval 13 1134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1134 : oddCount 1134 13 = 8 ∧ acceleratedOrbit 13 1134 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1134) = 3 ^ 8 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1134.1, data_13_1134.2] + +/-- Complete interval computation for depth 13, residue 1135. -/ +theorem bounds_13_1135 : exactInterval 13 1135 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1135) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1135 : oddCount 1135 13 = 8 ∧ acceleratedOrbit 13 1135 = 910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1135) = 3 ^ 8 * m + 910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1135.1, data_13_1135.2] + +/-- Complete interval computation for depth 13, residue 1136. -/ +theorem bounds_13_1136 : exactInterval 13 1136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1136 : oddCount 1136 13 = 6 ∧ acceleratedOrbit 13 1136 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1136) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1136.1, data_13_1136.2] + +/-- Complete interval computation for depth 13, residue 1137. -/ +theorem bounds_13_1137 : exactInterval 13 1137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1137 : oddCount 1137 13 = 3 ∧ acceleratedOrbit 13 1137 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1137) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1137.1, data_13_1137.2] + +/-- Complete interval computation for depth 13, residue 1138. -/ +theorem bounds_13_1138 : exactInterval 13 1138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1138 : oddCount 1138 13 = 8 ∧ acceleratedOrbit 13 1138 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1138) = 3 ^ 8 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1138.1, data_13_1138.2] + +/-- Complete interval computation for depth 13, residue 1139. -/ +theorem bounds_13_1139 : exactInterval 13 1139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1139 : oddCount 1139 13 = 8 ∧ acceleratedOrbit 13 1139 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1139) = 3 ^ 8 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1139.1, data_13_1139.2] + +/-- Complete interval computation for depth 13, residue 1140. -/ +theorem bounds_13_1140 : exactInterval 13 1140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1140 : oddCount 1140 13 = 6 ∧ acceleratedOrbit 13 1140 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1140) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1140.1, data_13_1140.2] + +end Collatz.Research.StoppingAtlas.Batch0541 From ee85beb2307d29cdb5ef80a7a05ea8a245e8611f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:21 +0530 Subject: [PATCH 0542/1001] proof: certify atlas Batch0542 (13:1141 to 13:1156) --- Collatz/Research/StoppingAtlas/Batch0542.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0542.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0542.lean b/Collatz/Research/StoppingAtlas/Batch0542.lean new file mode 100644 index 00000000..829b5694 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0542.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0542 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1141. -/ +theorem bounds_13_1141 : exactInterval 13 1141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1141 : oddCount 1141 13 = 6 ∧ acceleratedOrbit 13 1141 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1141) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1141.1, data_13_1141.2] + +/-- Complete interval computation for depth 13, residue 1142. -/ +theorem bounds_13_1142 : exactInterval 13 1142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1142 : oddCount 1142 13 = 5 ∧ acceleratedOrbit 13 1142 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1142) = 3 ^ 5 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1142.1, data_13_1142.2] + +/-- Complete interval computation for depth 13, residue 1143. -/ +theorem bounds_13_1143 : exactInterval 13 1143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1143 : oddCount 1143 13 = 5 ∧ acceleratedOrbit 13 1143 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1143) = 3 ^ 5 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1143.1, data_13_1143.2] + +/-- Complete interval computation for depth 13, residue 1144. -/ +theorem bounds_13_1144 : exactInterval 13 1144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1144 : oddCount 1144 13 = 6 ∧ acceleratedOrbit 13 1144 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1144) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1144.1, data_13_1144.2] + +/-- Complete interval computation for depth 13, residue 1145. -/ +theorem bounds_13_1145 : exactInterval 13 1145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1145 : oddCount 1145 13 = 8 ∧ acceleratedOrbit 13 1145 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1145) = 3 ^ 8 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1145.1, data_13_1145.2] + +/-- Complete interval computation for depth 13, residue 1146. -/ +theorem bounds_13_1146 : exactInterval 13 1146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1146 : oddCount 1146 13 = 6 ∧ acceleratedOrbit 13 1146 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1146) = 3 ^ 6 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1146.1, data_13_1146.2] + +/-- Complete interval computation for depth 13, residue 1147. -/ +theorem bounds_13_1147 : exactInterval 13 1147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1147 : oddCount 1147 13 = 7 ∧ acceleratedOrbit 13 1147 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1147) = 3 ^ 7 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1147.1, data_13_1147.2] + +/-- Complete interval computation for depth 13, residue 1148. -/ +theorem bounds_13_1148 : exactInterval 13 1148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1148 : oddCount 1148 13 = 7 ∧ acceleratedOrbit 13 1148 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1148) = 3 ^ 7 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1148.1, data_13_1148.2] + +/-- Complete interval computation for depth 13, residue 1149. -/ +theorem bounds_13_1149 : exactInterval 13 1149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1149 : oddCount 1149 13 = 7 ∧ acceleratedOrbit 13 1149 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1149) = 3 ^ 7 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1149.1, data_13_1149.2] + +/-- Complete interval computation for depth 13, residue 1150. -/ +theorem bounds_13_1150 : exactInterval 13 1150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1150 : oddCount 1150 13 = 7 ∧ acceleratedOrbit 13 1150 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1150) = 3 ^ 7 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1150.1, data_13_1150.2] + +/-- Complete interval computation for depth 13, residue 1151. -/ +theorem bounds_13_1151 : exactInterval 13 1151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1151 : oddCount 1151 13 = 9 ∧ acceleratedOrbit 13 1151 = 2768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1151) = 3 ^ 9 * m + 2768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1151.1, data_13_1151.2] + +/-- Complete interval computation for depth 13, residue 1152. -/ +theorem bounds_13_1152 : exactInterval 13 1152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1152 : oddCount 1152 13 = 4 ∧ acceleratedOrbit 13 1152 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1152) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1152.1, data_13_1152.2] + +/-- Complete interval computation for depth 13, residue 1153. -/ +theorem bounds_13_1153 : exactInterval 13 1153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1153 : oddCount 1153 13 = 9 ∧ acceleratedOrbit 13 1153 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1153) = 3 ^ 9 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1153.1, data_13_1153.2] + +/-- Complete interval computation for depth 13, residue 1154. -/ +theorem bounds_13_1154 : exactInterval 13 1154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1154 : oddCount 1154 13 = 5 ∧ acceleratedOrbit 13 1154 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1154) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1154.1, data_13_1154.2] + +/-- Complete interval computation for depth 13, residue 1155. -/ +theorem bounds_13_1155 : exactInterval 13 1155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1155 : oddCount 1155 13 = 5 ∧ acceleratedOrbit 13 1155 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1155) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1155.1, data_13_1155.2] + +/-- Complete interval computation for depth 13, residue 1156. -/ +theorem bounds_13_1156 : exactInterval 13 1156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1156 : oddCount 1156 13 = 5 ∧ acceleratedOrbit 13 1156 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1156) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1156.1, data_13_1156.2] + +end Collatz.Research.StoppingAtlas.Batch0542 From d8484abe51d91b8eb99cd0331bdfbf64bbb0812c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:22 +0530 Subject: [PATCH 0543/1001] proof: certify atlas Batch0543 (13:1157 to 13:1171) --- Collatz/Research/StoppingAtlas/Batch0543.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0543.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0543.lean b/Collatz/Research/StoppingAtlas/Batch0543.lean new file mode 100644 index 00000000..f19298b3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0543.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0543 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1157. -/ +theorem bounds_13_1157 : exactInterval 13 1157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1157 : oddCount 1157 13 = 5 ∧ acceleratedOrbit 13 1157 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1157) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1157.1, data_13_1157.2] + +/-- Complete interval computation for depth 13, residue 1158. -/ +theorem bounds_13_1158 : exactInterval 13 1158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1158 : oddCount 1158 13 = 5 ∧ acceleratedOrbit 13 1158 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1158) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1158.1, data_13_1158.2] + +/-- Complete interval computation for depth 13, residue 1159. -/ +theorem bounds_13_1159 : exactInterval 13 1159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1159 : oddCount 1159 13 = 8 ∧ acceleratedOrbit 13 1159 = 931 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1159) = 3 ^ 8 * m + 931 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1159.1, data_13_1159.2] + +/-- Complete interval computation for depth 13, residue 1160. -/ +theorem bounds_13_1160 : exactInterval 13 1160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1160 : oddCount 1160 13 = 6 ∧ acceleratedOrbit 13 1160 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1160) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1160.1, data_13_1160.2] + +/-- Complete interval computation for depth 13, residue 1161. -/ +theorem bounds_13_1161 : exactInterval 13 1161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1161 : oddCount 1161 13 = 10 ∧ acceleratedOrbit 13 1161 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1161) = 3 ^ 10 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1161.1, data_13_1161.2] + +/-- Complete interval computation for depth 13, residue 1162. -/ +theorem bounds_13_1162 : exactInterval 13 1162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1162 : oddCount 1162 13 = 6 ∧ acceleratedOrbit 13 1162 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1162) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1162.1, data_13_1162.2] + +/-- Complete interval computation for depth 13, residue 1163. -/ +theorem bounds_13_1163 : exactInterval 13 1163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1163 : oddCount 1163 13 = 8 ∧ acceleratedOrbit 13 1163 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1163) = 3 ^ 8 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1163.1, data_13_1163.2] + +/-- Complete interval computation for depth 13, residue 1164. -/ +theorem bounds_13_1164 : exactInterval 13 1164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1164 : oddCount 1164 13 = 6 ∧ acceleratedOrbit 13 1164 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1164) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1164.1, data_13_1164.2] + +/-- Complete interval computation for depth 13, residue 1165. -/ +theorem bounds_13_1165 : exactInterval 13 1165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1165 : oddCount 1165 13 = 6 ∧ acceleratedOrbit 13 1165 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1165) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1165.1, data_13_1165.2] + +/-- Complete interval computation for depth 13, residue 1166. -/ +theorem bounds_13_1166 : exactInterval 13 1166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1166 : oddCount 1166 13 = 6 ∧ acceleratedOrbit 13 1166 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1166) = 3 ^ 6 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1166.1, data_13_1166.2] + +/-- Complete interval computation for depth 13, residue 1167. -/ +theorem bounds_13_1167 : exactInterval 13 1167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1167 : oddCount 1167 13 = 6 ∧ acceleratedOrbit 13 1167 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1167) = 3 ^ 6 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1167.1, data_13_1167.2] + +/-- Complete interval computation for depth 13, residue 1168. -/ +theorem bounds_13_1168 : exactInterval 13 1168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1168 : oddCount 1168 13 = 6 ∧ acceleratedOrbit 13 1168 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1168) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1168.1, data_13_1168.2] + +/-- Complete interval computation for depth 13, residue 1169. -/ +theorem bounds_13_1169 : exactInterval 13 1169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1169 : oddCount 1169 13 = 7 ∧ acceleratedOrbit 13 1169 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1169) = 3 ^ 7 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1169.1, data_13_1169.2] + +/-- Complete interval computation for depth 13, residue 1170. -/ +theorem bounds_13_1170 : exactInterval 13 1170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1170 : oddCount 1170 13 = 7 ∧ acceleratedOrbit 13 1170 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1170) = 3 ^ 7 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1170.1, data_13_1170.2] + +/-- Complete interval computation for depth 13, residue 1171. -/ +theorem bounds_13_1171 : exactInterval 13 1171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1171 : oddCount 1171 13 = 7 ∧ acceleratedOrbit 13 1171 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1171) = 3 ^ 7 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1171.1, data_13_1171.2] + +end Collatz.Research.StoppingAtlas.Batch0543 From a23a9100c040f3d7a24feea342b358e75d39d71f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:22 +0530 Subject: [PATCH 0544/1001] proof: certify atlas Batch0544 (13:1172 to 13:1186) --- Collatz/Research/StoppingAtlas/Batch0544.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0544.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0544.lean b/Collatz/Research/StoppingAtlas/Batch0544.lean new file mode 100644 index 00000000..84eb9e8f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0544.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0544 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1172. -/ +theorem bounds_13_1172 : exactInterval 13 1172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1172 : oddCount 1172 13 = 6 ∧ acceleratedOrbit 13 1172 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1172) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1172.1, data_13_1172.2] + +/-- Complete interval computation for depth 13, residue 1173. -/ +theorem bounds_13_1173 : exactInterval 13 1173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1173 : oddCount 1173 13 = 6 ∧ acceleratedOrbit 13 1173 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1173) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1173.1, data_13_1173.2] + +/-- Complete interval computation for depth 13, residue 1174. -/ +theorem bounds_13_1174 : exactInterval 13 1174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1174 : oddCount 1174 13 = 6 ∧ acceleratedOrbit 13 1174 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1174) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1174.1, data_13_1174.2] + +/-- Complete interval computation for depth 13, residue 1175. -/ +theorem bounds_13_1175 : exactInterval 13 1175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1175 : oddCount 1175 13 = 6 ∧ acceleratedOrbit 13 1175 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1175) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1175.1, data_13_1175.2] + +/-- Complete interval computation for depth 13, residue 1176. -/ +theorem bounds_13_1176 : exactInterval 13 1176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1176 : oddCount 1176 13 = 6 ∧ acceleratedOrbit 13 1176 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1176) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1176.1, data_13_1176.2] + +/-- Complete interval computation for depth 13, residue 1177. -/ +theorem bounds_13_1177 : exactInterval 13 1177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1177 : oddCount 1177 13 = 5 ∧ acceleratedOrbit 13 1177 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1177) = 3 ^ 5 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1177.1, data_13_1177.2] + +/-- Complete interval computation for depth 13, residue 1178. -/ +theorem bounds_13_1178 : exactInterval 13 1178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1178 : oddCount 1178 13 = 6 ∧ acceleratedOrbit 13 1178 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1178) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1178.1, data_13_1178.2] + +/-- Complete interval computation for depth 13, residue 1179. -/ +theorem bounds_13_1179 : exactInterval 13 1179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1179 : oddCount 1179 13 = 9 ∧ acceleratedOrbit 13 1179 = 2837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1179) = 3 ^ 9 * m + 2837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1179.1, data_13_1179.2] + +/-- Complete interval computation for depth 13, residue 1180. -/ +theorem bounds_13_1180 : exactInterval 13 1180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1180 : oddCount 1180 13 = 7 ∧ acceleratedOrbit 13 1180 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1180) = 3 ^ 7 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1180.1, data_13_1180.2] + +/-- Complete interval computation for depth 13, residue 1181. -/ +theorem bounds_13_1181 : exactInterval 13 1181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1181 : oddCount 1181 13 = 7 ∧ acceleratedOrbit 13 1181 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1181) = 3 ^ 7 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1181.1, data_13_1181.2] + +/-- Complete interval computation for depth 13, residue 1182. -/ +theorem bounds_13_1182 : exactInterval 13 1182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1182 : oddCount 1182 13 = 7 ∧ acceleratedOrbit 13 1182 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1182) = 3 ^ 7 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1182.1, data_13_1182.2] + +/-- Complete interval computation for depth 13, residue 1183. -/ +theorem bounds_13_1183 : exactInterval 13 1183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1183 : oddCount 1183 13 = 9 ∧ acceleratedOrbit 13 1183 = 2845 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1183) = 3 ^ 9 * m + 2845 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1183.1, data_13_1183.2] + +/-- Complete interval computation for depth 13, residue 1184. -/ +theorem bounds_13_1184 : exactInterval 13 1184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1184 : oddCount 1184 13 = 4 ∧ acceleratedOrbit 13 1184 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1184) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1184.1, data_13_1184.2] + +/-- Complete interval computation for depth 13, residue 1185. -/ +theorem bounds_13_1185 : exactInterval 13 1185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1185 : oddCount 1185 13 = 9 ∧ acceleratedOrbit 13 1185 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1185) = 3 ^ 9 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1185.1, data_13_1185.2] + +/-- Complete interval computation for depth 13, residue 1186. -/ +theorem bounds_13_1186 : exactInterval 13 1186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1186 : oddCount 1186 13 = 7 ∧ acceleratedOrbit 13 1186 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1186) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1186.1, data_13_1186.2] + +end Collatz.Research.StoppingAtlas.Batch0544 From 934ecb2bd79d48aca6697e72dcecb0faefdf4eb3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:23 +0530 Subject: [PATCH 0545/1001] proof: certify atlas Batch0545 (13:1187 to 13:1202) --- Collatz/Research/StoppingAtlas/Batch0545.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0545.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0545.lean b/Collatz/Research/StoppingAtlas/Batch0545.lean new file mode 100644 index 00000000..eba5ea93 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0545.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0545 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1187. -/ +theorem bounds_13_1187 : exactInterval 13 1187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1187 : oddCount 1187 13 = 7 ∧ acceleratedOrbit 13 1187 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1187) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1187.1, data_13_1187.2] + +/-- Complete interval computation for depth 13, residue 1188. -/ +theorem bounds_13_1188 : exactInterval 13 1188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1188 : oddCount 1188 13 = 7 ∧ acceleratedOrbit 13 1188 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1188) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1188.1, data_13_1188.2] + +/-- Complete interval computation for depth 13, residue 1189. -/ +theorem bounds_13_1189 : exactInterval 13 1189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1189 : oddCount 1189 13 = 7 ∧ acceleratedOrbit 13 1189 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1189) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1189.1, data_13_1189.2] + +/-- Complete interval computation for depth 13, residue 1190. -/ +theorem bounds_13_1190 : exactInterval 13 1190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1190 : oddCount 1190 13 = 7 ∧ acceleratedOrbit 13 1190 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1190) = 3 ^ 7 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1190.1, data_13_1190.2] + +/-- Complete interval computation for depth 13, residue 1191. -/ +theorem bounds_13_1191 : exactInterval 13 1191 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1191) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1191 : oddCount 1191 13 = 8 ∧ acceleratedOrbit 13 1191 = 955 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1191) = 3 ^ 8 * m + 955 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1191.1, data_13_1191.2] + +/-- Complete interval computation for depth 13, residue 1192. -/ +theorem bounds_13_1192 : exactInterval 13 1192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1192 : oddCount 1192 13 = 4 ∧ acceleratedOrbit 13 1192 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1192) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1192.1, data_13_1192.2] + +/-- Complete interval computation for depth 13, residue 1193. -/ +theorem bounds_13_1193 : exactInterval 13 1193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1193 : oddCount 1193 13 = 10 ∧ acceleratedOrbit 13 1193 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1193) = 3 ^ 10 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1193.1, data_13_1193.2] + +/-- Complete interval computation for depth 13, residue 1194. -/ +theorem bounds_13_1194 : exactInterval 13 1194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1194 : oddCount 1194 13 = 4 ∧ acceleratedOrbit 13 1194 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1194) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1194.1, data_13_1194.2] + +/-- Complete interval computation for depth 13, residue 1195. -/ +theorem bounds_13_1195 : exactInterval 13 1195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1195 : oddCount 1195 13 = 6 ∧ acceleratedOrbit 13 1195 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1195) = 3 ^ 6 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1195.1, data_13_1195.2] + +/-- Complete interval computation for depth 13, residue 1196. -/ +theorem bounds_13_1196 : exactInterval 13 1196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1196 : oddCount 1196 13 = 7 ∧ acceleratedOrbit 13 1196 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1196) = 3 ^ 7 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1196.1, data_13_1196.2] + +/-- Complete interval computation for depth 13, residue 1197. -/ +theorem bounds_13_1197 : exactInterval 13 1197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1197 : oddCount 1197 13 = 7 ∧ acceleratedOrbit 13 1197 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1197) = 3 ^ 7 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1197.1, data_13_1197.2] + +/-- Complete interval computation for depth 13, residue 1198. -/ +theorem bounds_13_1198 : exactInterval 13 1198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1198 : oddCount 1198 13 = 7 ∧ acceleratedOrbit 13 1198 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1198) = 3 ^ 7 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1198.1, data_13_1198.2] + +/-- Complete interval computation for depth 13, residue 1199. -/ +theorem bounds_13_1199 : exactInterval 13 1199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1199 : oddCount 1199 13 = 8 ∧ acceleratedOrbit 13 1199 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1199) = 3 ^ 8 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1199.1, data_13_1199.2] + +/-- Complete interval computation for depth 13, residue 1200. -/ +theorem bounds_13_1200 : exactInterval 13 1200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1200 : oddCount 1200 13 = 3 ∧ acceleratedOrbit 13 1200 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1200) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1200.1, data_13_1200.2] + +/-- Complete interval computation for depth 13, residue 1201. -/ +theorem bounds_13_1201 : exactInterval 13 1201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1201 : oddCount 1201 13 = 8 ∧ acceleratedOrbit 13 1201 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1201) = 3 ^ 8 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1201.1, data_13_1201.2] + +/-- Complete interval computation for depth 13, residue 1202. -/ +theorem bounds_13_1202 : exactInterval 13 1202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1202 : oddCount 1202 13 = 8 ∧ acceleratedOrbit 13 1202 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1202) = 3 ^ 8 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1202.1, data_13_1202.2] + +end Collatz.Research.StoppingAtlas.Batch0545 From 6996bc2fa7889ad59d93b9e47a3ea02928e340a6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:23 +0530 Subject: [PATCH 0546/1001] proof: certify atlas Batch0546 (13:1203 to 13:1217) --- Collatz/Research/StoppingAtlas/Batch0546.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0546.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0546.lean b/Collatz/Research/StoppingAtlas/Batch0546.lean new file mode 100644 index 00000000..16b93482 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0546.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0546 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1203. -/ +theorem bounds_13_1203 : exactInterval 13 1203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1203 : oddCount 1203 13 = 8 ∧ acceleratedOrbit 13 1203 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1203) = 3 ^ 8 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1203.1, data_13_1203.2] + +/-- Complete interval computation for depth 13, residue 1204. -/ +theorem bounds_13_1204 : exactInterval 13 1204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1204 : oddCount 1204 13 = 3 ∧ acceleratedOrbit 13 1204 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1204) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1204.1, data_13_1204.2] + +/-- Complete interval computation for depth 13, residue 1205. -/ +theorem bounds_13_1205 : exactInterval 13 1205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1205 : oddCount 1205 13 = 3 ∧ acceleratedOrbit 13 1205 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1205) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1205.1, data_13_1205.2] + +/-- Complete interval computation for depth 13, residue 1206. -/ +theorem bounds_13_1206 : exactInterval 13 1206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1206 : oddCount 1206 13 = 9 ∧ acceleratedOrbit 13 1206 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1206) = 3 ^ 9 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1206.1, data_13_1206.2] + +/-- Complete interval computation for depth 13, residue 1207. -/ +theorem bounds_13_1207 : exactInterval 13 1207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1207 : oddCount 1207 13 = 9 ∧ acceleratedOrbit 13 1207 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1207) = 3 ^ 9 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1207.1, data_13_1207.2] + +/-- Complete interval computation for depth 13, residue 1208. -/ +theorem bounds_13_1208 : exactInterval 13 1208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1208 : oddCount 1208 13 = 3 ∧ acceleratedOrbit 13 1208 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1208) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1208.1, data_13_1208.2] + +/-- Complete interval computation for depth 13, residue 1209. -/ +theorem bounds_13_1209 : exactInterval 13 1209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1209 : oddCount 1209 13 = 9 ∧ acceleratedOrbit 13 1209 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1209) = 3 ^ 9 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1209.1, data_13_1209.2] + +/-- Complete interval computation for depth 13, residue 1210. -/ +theorem bounds_13_1210 : exactInterval 13 1210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1210 : oddCount 1210 13 = 3 ∧ acceleratedOrbit 13 1210 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1210) = 3 ^ 3 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1210.1, data_13_1210.2] + +/-- Complete interval computation for depth 13, residue 1211. -/ +theorem bounds_13_1211 : exactInterval 13 1211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1211 : oddCount 1211 13 = 10 ∧ acceleratedOrbit 13 1211 = 8747 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1211) = 3 ^ 10 * m + 8747 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1211.1, data_13_1211.2] + +/-- Complete interval computation for depth 13, residue 1212. -/ +theorem bounds_13_1212 : exactInterval 13 1212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1212 : oddCount 1212 13 = 7 ∧ acceleratedOrbit 13 1212 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1212) = 3 ^ 7 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1212.1, data_13_1212.2] + +/-- Complete interval computation for depth 13, residue 1213. -/ +theorem bounds_13_1213 : exactInterval 13 1213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1213 : oddCount 1213 13 = 7 ∧ acceleratedOrbit 13 1213 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1213) = 3 ^ 7 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1213.1, data_13_1213.2] + +/-- Complete interval computation for depth 13, residue 1214. -/ +theorem bounds_13_1214 : exactInterval 13 1214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1214 : oddCount 1214 13 = 7 ∧ acceleratedOrbit 13 1214 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1214) = 3 ^ 7 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1214.1, data_13_1214.2] + +/-- Complete interval computation for depth 13, residue 1215. -/ +theorem bounds_13_1215 : exactInterval 13 1215 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1215) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1215 : oddCount 1215 13 = 8 ∧ acceleratedOrbit 13 1215 = 974 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1215) = 3 ^ 8 * m + 974 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1215.1, data_13_1215.2] + +/-- Complete interval computation for depth 13, residue 1216. -/ +theorem bounds_13_1216 : exactInterval 13 1216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1216 : oddCount 1216 13 = 4 ∧ acceleratedOrbit 13 1216 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1216) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1216.1, data_13_1216.2] + +/-- Complete interval computation for depth 13, residue 1217. -/ +theorem bounds_13_1217 : exactInterval 13 1217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1217 : oddCount 1217 13 = 6 ∧ acceleratedOrbit 13 1217 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1217) = 3 ^ 6 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1217.1, data_13_1217.2] + +end Collatz.Research.StoppingAtlas.Batch0546 From edd56f6fbaef2efa40bb80f6cd01d7ba3ed38152 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:24 +0530 Subject: [PATCH 0547/1001] proof: certify atlas Batch0547 (13:1218 to 13:1232) --- Collatz/Research/StoppingAtlas/Batch0547.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0547.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0547.lean b/Collatz/Research/StoppingAtlas/Batch0547.lean new file mode 100644 index 00000000..604a1d7f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0547.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0547 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1218. -/ +theorem bounds_13_1218 : exactInterval 13 1218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1218 : oddCount 1218 13 = 6 ∧ acceleratedOrbit 13 1218 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1218) = 3 ^ 6 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1218.1, data_13_1218.2] + +/-- Complete interval computation for depth 13, residue 1219. -/ +theorem bounds_13_1219 : exactInterval 13 1219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1219 : oddCount 1219 13 = 6 ∧ acceleratedOrbit 13 1219 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1219) = 3 ^ 6 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1219.1, data_13_1219.2] + +/-- Complete interval computation for depth 13, residue 1220. -/ +theorem bounds_13_1220 : exactInterval 13 1220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1220 : oddCount 1220 13 = 5 ∧ acceleratedOrbit 13 1220 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1220) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1220.1, data_13_1220.2] + +/-- Complete interval computation for depth 13, residue 1221. -/ +theorem bounds_13_1221 : exactInterval 13 1221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1221 : oddCount 1221 13 = 5 ∧ acceleratedOrbit 13 1221 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1221) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1221.1, data_13_1221.2] + +/-- Complete interval computation for depth 13, residue 1222. -/ +theorem bounds_13_1222 : exactInterval 13 1222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1222 : oddCount 1222 13 = 5 ∧ acceleratedOrbit 13 1222 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1222) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1222.1, data_13_1222.2] + +/-- Complete interval computation for depth 13, residue 1223. -/ +theorem bounds_13_1223 : exactInterval 13 1223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1223 : oddCount 1223 13 = 6 ∧ acceleratedOrbit 13 1223 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1223) = 3 ^ 6 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1223.1, data_13_1223.2] + +/-- Complete interval computation for depth 13, residue 1224. -/ +theorem bounds_13_1224 : exactInterval 13 1224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1224 : oddCount 1224 13 = 5 ∧ acceleratedOrbit 13 1224 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1224) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1224.1, data_13_1224.2] + +/-- Complete interval computation for depth 13, residue 1225. -/ +theorem bounds_13_1225 : exactInterval 13 1225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1225 : oddCount 1225 13 = 6 ∧ acceleratedOrbit 13 1225 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1225) = 3 ^ 6 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1225.1, data_13_1225.2] + +/-- Complete interval computation for depth 13, residue 1226. -/ +theorem bounds_13_1226 : exactInterval 13 1226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1226 : oddCount 1226 13 = 5 ∧ acceleratedOrbit 13 1226 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1226) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1226.1, data_13_1226.2] + +/-- Complete interval computation for depth 13, residue 1227. -/ +theorem bounds_13_1227 : exactInterval 13 1227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1227 : oddCount 1227 13 = 6 ∧ acceleratedOrbit 13 1227 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1227) = 3 ^ 6 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1227.1, data_13_1227.2] + +/-- Complete interval computation for depth 13, residue 1228. -/ +theorem bounds_13_1228 : exactInterval 13 1228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1228 : oddCount 1228 13 = 5 ∧ acceleratedOrbit 13 1228 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1228) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1228.1, data_13_1228.2] + +/-- Complete interval computation for depth 13, residue 1229. -/ +theorem bounds_13_1229 : exactInterval 13 1229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1229 : oddCount 1229 13 = 5 ∧ acceleratedOrbit 13 1229 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1229) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1229.1, data_13_1229.2] + +/-- Complete interval computation for depth 13, residue 1230. -/ +theorem bounds_13_1230 : exactInterval 13 1230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1230 : oddCount 1230 13 = 7 ∧ acceleratedOrbit 13 1230 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1230) = 3 ^ 7 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1230.1, data_13_1230.2] + +/-- Complete interval computation for depth 13, residue 1231. -/ +theorem bounds_13_1231 : exactInterval 13 1231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1231 : oddCount 1231 13 = 7 ∧ acceleratedOrbit 13 1231 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1231) = 3 ^ 7 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1231.1, data_13_1231.2] + +/-- Complete interval computation for depth 13, residue 1232. -/ +theorem bounds_13_1232 : exactInterval 13 1232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1232 : oddCount 1232 13 = 4 ∧ acceleratedOrbit 13 1232 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1232) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1232.1, data_13_1232.2] + +end Collatz.Research.StoppingAtlas.Batch0547 From c251b3e822d9829a43c99ff4eb8b2d7a6bc99702 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:24 +0530 Subject: [PATCH 0548/1001] proof: certify atlas Batch0548 (13:1233 to 13:1248) --- Collatz/Research/StoppingAtlas/Batch0548.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0548.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0548.lean b/Collatz/Research/StoppingAtlas/Batch0548.lean new file mode 100644 index 00000000..fc80c1c8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0548.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0548 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1233. -/ +theorem bounds_13_1233 : exactInterval 13 1233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1233 : oddCount 1233 13 = 8 ∧ acceleratedOrbit 13 1233 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1233) = 3 ^ 8 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1233.1, data_13_1233.2] + +/-- Complete interval computation for depth 13, residue 1234. -/ +theorem bounds_13_1234 : exactInterval 13 1234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1234 : oddCount 1234 13 = 8 ∧ acceleratedOrbit 13 1234 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1234) = 3 ^ 8 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1234.1, data_13_1234.2] + +/-- Complete interval computation for depth 13, residue 1235. -/ +theorem bounds_13_1235 : exactInterval 13 1235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1235 : oddCount 1235 13 = 8 ∧ acceleratedOrbit 13 1235 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1235) = 3 ^ 8 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1235.1, data_13_1235.2] + +/-- Complete interval computation for depth 13, residue 1236. -/ +theorem bounds_13_1236 : exactInterval 13 1236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1236 : oddCount 1236 13 = 4 ∧ acceleratedOrbit 13 1236 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1236) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1236.1, data_13_1236.2] + +/-- Complete interval computation for depth 13, residue 1237. -/ +theorem bounds_13_1237 : exactInterval 13 1237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1237 : oddCount 1237 13 = 4 ∧ acceleratedOrbit 13 1237 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1237) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1237.1, data_13_1237.2] + +/-- Complete interval computation for depth 13, residue 1238. -/ +theorem bounds_13_1238 : exactInterval 13 1238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1238 : oddCount 1238 13 = 7 ∧ acceleratedOrbit 13 1238 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1238) = 3 ^ 7 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1238.1, data_13_1238.2] + +/-- Complete interval computation for depth 13, residue 1239. -/ +theorem bounds_13_1239 : exactInterval 13 1239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1239 : oddCount 1239 13 = 7 ∧ acceleratedOrbit 13 1239 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1239) = 3 ^ 7 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1239.1, data_13_1239.2] + +/-- Complete interval computation for depth 13, residue 1240. -/ +theorem bounds_13_1240 : exactInterval 13 1240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1240 : oddCount 1240 13 = 7 ∧ acceleratedOrbit 13 1240 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1240) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1240.1, data_13_1240.2] + +/-- Complete interval computation for depth 13, residue 1241. -/ +theorem bounds_13_1241 : exactInterval 13 1241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1241 : oddCount 1241 13 = 5 ∧ acceleratedOrbit 13 1241 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1241) = 3 ^ 5 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1241.1, data_13_1241.2] + +/-- Complete interval computation for depth 13, residue 1242. -/ +theorem bounds_13_1242 : exactInterval 13 1242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1242 : oddCount 1242 13 = 7 ∧ acceleratedOrbit 13 1242 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1242) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1242.1, data_13_1242.2] + +/-- Complete interval computation for depth 13, residue 1243. -/ +theorem bounds_13_1243 : exactInterval 13 1243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1243 : oddCount 1243 13 = 8 ∧ acceleratedOrbit 13 1243 = 998 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1243) = 3 ^ 8 * m + 998 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1243.1, data_13_1243.2] + +/-- Complete interval computation for depth 13, residue 1244. -/ +theorem bounds_13_1244 : exactInterval 13 1244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1244 : oddCount 1244 13 = 7 ∧ acceleratedOrbit 13 1244 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1244) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1244.1, data_13_1244.2] + +/-- Complete interval computation for depth 13, residue 1245. -/ +theorem bounds_13_1245 : exactInterval 13 1245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1245 : oddCount 1245 13 = 7 ∧ acceleratedOrbit 13 1245 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1245) = 3 ^ 7 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1245.1, data_13_1245.2] + +/-- Complete interval computation for depth 13, residue 1246. -/ +theorem bounds_13_1246 : exactInterval 13 1246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1246 : oddCount 1246 13 = 8 ∧ acceleratedOrbit 13 1246 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1246) = 3 ^ 8 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1246.1, data_13_1246.2] + +/-- Complete interval computation for depth 13, residue 1247. -/ +theorem bounds_13_1247 : exactInterval 13 1247 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1247) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1247 : oddCount 1247 13 = 8 ∧ acceleratedOrbit 13 1247 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1247) = 3 ^ 8 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1247.1, data_13_1247.2] + +/-- Complete interval computation for depth 13, residue 1248. -/ +theorem bounds_13_1248 : exactInterval 13 1248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1248 : oddCount 1248 13 = 5 ∧ acceleratedOrbit 13 1248 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1248) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1248.1, data_13_1248.2] + +end Collatz.Research.StoppingAtlas.Batch0548 From a786f2b81847b0d2a0ad664afb7b49c0d3e48987 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:25 +0530 Subject: [PATCH 0549/1001] proof: certify atlas Batch0549 (13:1249 to 13:1263) --- Collatz/Research/StoppingAtlas/Batch0549.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0549.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0549.lean b/Collatz/Research/StoppingAtlas/Batch0549.lean new file mode 100644 index 00000000..6d5f55f9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0549.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0549 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1249. -/ +theorem bounds_13_1249 : exactInterval 13 1249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1249 : oddCount 1249 13 = 9 ∧ acceleratedOrbit 13 1249 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1249) = 3 ^ 9 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1249.1, data_13_1249.2] + +/-- Complete interval computation for depth 13, residue 1250. -/ +theorem bounds_13_1250 : exactInterval 13 1250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1250 : oddCount 1250 13 = 4 ∧ acceleratedOrbit 13 1250 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1250) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1250.1, data_13_1250.2] + +/-- Complete interval computation for depth 13, residue 1251. -/ +theorem bounds_13_1251 : exactInterval 13 1251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1251 : oddCount 1251 13 = 4 ∧ acceleratedOrbit 13 1251 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1251) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1251.1, data_13_1251.2] + +/-- Complete interval computation for depth 13, residue 1252. -/ +theorem bounds_13_1252 : exactInterval 13 1252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1252 : oddCount 1252 13 = 7 ∧ acceleratedOrbit 13 1252 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1252) = 3 ^ 7 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1252.1, data_13_1252.2] + +/-- Complete interval computation for depth 13, residue 1253. -/ +theorem bounds_13_1253 : exactInterval 13 1253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1253 : oddCount 1253 13 = 7 ∧ acceleratedOrbit 13 1253 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1253) = 3 ^ 7 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1253.1, data_13_1253.2] + +/-- Complete interval computation for depth 13, residue 1254. -/ +theorem bounds_13_1254 : exactInterval 13 1254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1254 : oddCount 1254 13 = 7 ∧ acceleratedOrbit 13 1254 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1254) = 3 ^ 7 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1254.1, data_13_1254.2] + +/-- Complete interval computation for depth 13, residue 1255. -/ +theorem bounds_13_1255 : exactInterval 13 1255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1255 : oddCount 1255 13 = 9 ∧ acceleratedOrbit 13 1255 = 3019 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1255) = 3 ^ 9 * m + 3019 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1255.1, data_13_1255.2] + +/-- Complete interval computation for depth 13, residue 1256. -/ +theorem bounds_13_1256 : exactInterval 13 1256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1256 : oddCount 1256 13 = 5 ∧ acceleratedOrbit 13 1256 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1256) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1256.1, data_13_1256.2] + +/-- Complete interval computation for depth 13, residue 1257. -/ +theorem bounds_13_1257 : exactInterval 13 1257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1257 : oddCount 1257 13 = 6 ∧ acceleratedOrbit 13 1257 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1257) = 3 ^ 6 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1257.1, data_13_1257.2] + +/-- Complete interval computation for depth 13, residue 1258. -/ +theorem bounds_13_1258 : exactInterval 13 1258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1258 : oddCount 1258 13 = 5 ∧ acceleratedOrbit 13 1258 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1258) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1258.1, data_13_1258.2] + +/-- Complete interval computation for depth 13, residue 1259. -/ +theorem bounds_13_1259 : exactInterval 13 1259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1259 : oddCount 1259 13 = 8 ∧ acceleratedOrbit 13 1259 = 1010 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1259) = 3 ^ 8 * m + 1010 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1259.1, data_13_1259.2] + +/-- Complete interval computation for depth 13, residue 1260. -/ +theorem bounds_13_1260 : exactInterval 13 1260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1260 : oddCount 1260 13 = 5 ∧ acceleratedOrbit 13 1260 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1260) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1260.1, data_13_1260.2] + +/-- Complete interval computation for depth 13, residue 1261. -/ +theorem bounds_13_1261 : exactInterval 13 1261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1261 : oddCount 1261 13 = 5 ∧ acceleratedOrbit 13 1261 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1261) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1261.1, data_13_1261.2] + +/-- Complete interval computation for depth 13, residue 1262. -/ +theorem bounds_13_1262 : exactInterval 13 1262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1262 : oddCount 1262 13 = 5 ∧ acceleratedOrbit 13 1262 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1262) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1262.1, data_13_1262.2] + +/-- Complete interval computation for depth 13, residue 1263. -/ +theorem bounds_13_1263 : exactInterval 13 1263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1263 : oddCount 1263 13 = 11 ∧ acceleratedOrbit 13 1263 = 27337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1263) = 3 ^ 11 * m + 27337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1263.1, data_13_1263.2] + +end Collatz.Research.StoppingAtlas.Batch0549 From 62bf7254dad9c3cb7622f0e80bf118734d317200 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:25 +0530 Subject: [PATCH 0550/1001] proof: certify atlas Batch0550 (13:1264 to 13:1279) --- Collatz/Research/StoppingAtlas/Batch0550.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0550.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0550.lean b/Collatz/Research/StoppingAtlas/Batch0550.lean new file mode 100644 index 00000000..1fbdc4e1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0550.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0550 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1264. -/ +theorem bounds_13_1264 : exactInterval 13 1264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1264 : oddCount 1264 13 = 5 ∧ acceleratedOrbit 13 1264 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1264) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1264.1, data_13_1264.2] + +/-- Complete interval computation for depth 13, residue 1265. -/ +theorem bounds_13_1265 : exactInterval 13 1265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1265 : oddCount 1265 13 = 5 ∧ acceleratedOrbit 13 1265 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1265) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1265.1, data_13_1265.2] + +/-- Complete interval computation for depth 13, residue 1266. -/ +theorem bounds_13_1266 : exactInterval 13 1266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1266 : oddCount 1266 13 = 6 ∧ acceleratedOrbit 13 1266 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1266) = 3 ^ 6 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1266.1, data_13_1266.2] + +/-- Complete interval computation for depth 13, residue 1267. -/ +theorem bounds_13_1267 : exactInterval 13 1267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1267 : oddCount 1267 13 = 6 ∧ acceleratedOrbit 13 1267 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1267) = 3 ^ 6 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1267.1, data_13_1267.2] + +/-- Complete interval computation for depth 13, residue 1268. -/ +theorem bounds_13_1268 : exactInterval 13 1268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1268 : oddCount 1268 13 = 5 ∧ acceleratedOrbit 13 1268 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1268) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1268.1, data_13_1268.2] + +/-- Complete interval computation for depth 13, residue 1269. -/ +theorem bounds_13_1269 : exactInterval 13 1269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1269 : oddCount 1269 13 = 5 ∧ acceleratedOrbit 13 1269 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1269) = 3 ^ 5 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1269.1, data_13_1269.2] + +/-- Complete interval computation for depth 13, residue 1270. -/ +theorem bounds_13_1270 : exactInterval 13 1270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1270 : oddCount 1270 13 = 7 ∧ acceleratedOrbit 13 1270 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1270) = 3 ^ 7 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1270.1, data_13_1270.2] + +/-- Complete interval computation for depth 13, residue 1271. -/ +theorem bounds_13_1271 : exactInterval 13 1271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1271 : oddCount 1271 13 = 7 ∧ acceleratedOrbit 13 1271 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1271) = 3 ^ 7 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1271.1, data_13_1271.2] + +/-- Complete interval computation for depth 13, residue 1272. -/ +theorem bounds_13_1272 : exactInterval 13 1272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1272 : oddCount 1272 13 = 9 ∧ acceleratedOrbit 13 1272 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1272) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1272.1, data_13_1272.2] + +/-- Complete interval computation for depth 13, residue 1273. -/ +theorem bounds_13_1273 : exactInterval 13 1273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1273 : oddCount 1273 13 = 7 ∧ acceleratedOrbit 13 1273 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1273) = 3 ^ 7 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1273.1, data_13_1273.2] + +/-- Complete interval computation for depth 13, residue 1274. -/ +theorem bounds_13_1274 : exactInterval 13 1274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1274 : oddCount 1274 13 = 9 ∧ acceleratedOrbit 13 1274 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1274) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1274.1, data_13_1274.2] + +/-- Complete interval computation for depth 13, residue 1275. -/ +theorem bounds_13_1275 : exactInterval 13 1275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1275 : oddCount 1275 13 = 9 ∧ acceleratedOrbit 13 1275 = 3068 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1275) = 3 ^ 9 * m + 3068 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1275.1, data_13_1275.2] + +/-- Complete interval computation for depth 13, residue 1276. -/ +theorem bounds_13_1276 : exactInterval 13 1276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1276 : oddCount 1276 13 = 9 ∧ acceleratedOrbit 13 1276 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1276) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1276.1, data_13_1276.2] + +/-- Complete interval computation for depth 13, residue 1277. -/ +theorem bounds_13_1277 : exactInterval 13 1277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1277 : oddCount 1277 13 = 9 ∧ acceleratedOrbit 13 1277 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1277) = 3 ^ 9 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1277.1, data_13_1277.2] + +/-- Complete interval computation for depth 13, residue 1278. -/ +theorem bounds_13_1278 : exactInterval 13 1278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1278 : oddCount 1278 13 = 10 ∧ acceleratedOrbit 13 1278 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1278) = 3 ^ 10 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1278.1, data_13_1278.2] + +/-- Complete interval computation for depth 13, residue 1279. -/ +theorem bounds_13_1279 : exactInterval 13 1279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1279 : oddCount 1279 13 = 10 ∧ acceleratedOrbit 13 1279 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1279) = 3 ^ 10 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1279.1, data_13_1279.2] + +end Collatz.Research.StoppingAtlas.Batch0550 From 8de6b915da2dd8968dcad199b8d70d9537026ad5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:26 +0530 Subject: [PATCH 0551/1001] proof: certify atlas Batch0551 (13:1280 to 13:1294) --- Collatz/Research/StoppingAtlas/Batch0551.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0551.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0551.lean b/Collatz/Research/StoppingAtlas/Batch0551.lean new file mode 100644 index 00000000..6f148577 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0551.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0551 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1280. -/ +theorem bounds_13_1280 : exactInterval 13 1280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1280 : oddCount 1280 13 = 2 ∧ acceleratedOrbit 13 1280 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1280) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1280.1, data_13_1280.2] + +/-- Complete interval computation for depth 13, residue 1281. -/ +theorem bounds_13_1281 : exactInterval 13 1281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1281 : oddCount 1281 13 = 7 ∧ acceleratedOrbit 13 1281 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1281) = 3 ^ 7 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1281.1, data_13_1281.2] + +/-- Complete interval computation for depth 13, residue 1282. -/ +theorem bounds_13_1282 : exactInterval 13 1282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1282 : oddCount 1282 13 = 7 ∧ acceleratedOrbit 13 1282 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1282) = 3 ^ 7 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1282.1, data_13_1282.2] + +/-- Complete interval computation for depth 13, residue 1283. -/ +theorem bounds_13_1283 : exactInterval 13 1283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1283 : oddCount 1283 13 = 7 ∧ acceleratedOrbit 13 1283 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1283) = 3 ^ 7 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1283.1, data_13_1283.2] + +/-- Complete interval computation for depth 13, residue 1284. -/ +theorem bounds_13_1284 : exactInterval 13 1284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1284 : oddCount 1284 13 = 4 ∧ acceleratedOrbit 13 1284 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1284) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1284.1, data_13_1284.2] + +/-- Complete interval computation for depth 13, residue 1285. -/ +theorem bounds_13_1285 : exactInterval 13 1285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1285 : oddCount 1285 13 = 4 ∧ acceleratedOrbit 13 1285 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1285) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1285.1, data_13_1285.2] + +/-- Complete interval computation for depth 13, residue 1286. -/ +theorem bounds_13_1286 : exactInterval 13 1286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1286 : oddCount 1286 13 = 4 ∧ acceleratedOrbit 13 1286 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1286) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1286.1, data_13_1286.2] + +/-- Complete interval computation for depth 13, residue 1287. -/ +theorem bounds_13_1287 : exactInterval 13 1287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1287 : oddCount 1287 13 = 9 ∧ acceleratedOrbit 13 1287 = 3098 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1287) = 3 ^ 9 * m + 3098 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1287.1, data_13_1287.2] + +/-- Complete interval computation for depth 13, residue 1288. -/ +theorem bounds_13_1288 : exactInterval 13 1288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1288 : oddCount 1288 13 = 7 ∧ acceleratedOrbit 13 1288 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1288) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1288.1, data_13_1288.2] + +/-- Complete interval computation for depth 13, residue 1289. -/ +theorem bounds_13_1289 : exactInterval 13 1289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1289 : oddCount 1289 13 = 9 ∧ acceleratedOrbit 13 1289 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1289) = 3 ^ 9 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1289.1, data_13_1289.2] + +/-- Complete interval computation for depth 13, residue 1290. -/ +theorem bounds_13_1290 : exactInterval 13 1290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1290 : oddCount 1290 13 = 7 ∧ acceleratedOrbit 13 1290 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1290) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1290.1, data_13_1290.2] + +/-- Complete interval computation for depth 13, residue 1291. -/ +theorem bounds_13_1291 : exactInterval 13 1291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1291 : oddCount 1291 13 = 7 ∧ acceleratedOrbit 13 1291 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1291) = 3 ^ 7 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1291.1, data_13_1291.2] + +/-- Complete interval computation for depth 13, residue 1292. -/ +theorem bounds_13_1292 : exactInterval 13 1292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1292 : oddCount 1292 13 = 7 ∧ acceleratedOrbit 13 1292 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1292) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1292.1, data_13_1292.2] + +/-- Complete interval computation for depth 13, residue 1293. -/ +theorem bounds_13_1293 : exactInterval 13 1293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1293 : oddCount 1293 13 = 7 ∧ acceleratedOrbit 13 1293 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1293) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1293.1, data_13_1293.2] + +/-- Complete interval computation for depth 13, residue 1294. -/ +theorem bounds_13_1294 : exactInterval 13 1294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1294 : oddCount 1294 13 = 6 ∧ acceleratedOrbit 13 1294 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1294) = 3 ^ 6 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1294.1, data_13_1294.2] + +end Collatz.Research.StoppingAtlas.Batch0551 From 19c644c4e4e477bb0ffa03a31632bc945f0f0b05 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:26 +0530 Subject: [PATCH 0552/1001] proof: certify atlas Batch0552 (13:1295 to 13:1309) --- Collatz/Research/StoppingAtlas/Batch0552.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0552.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0552.lean b/Collatz/Research/StoppingAtlas/Batch0552.lean new file mode 100644 index 00000000..c28c8010 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0552.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0552 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1295. -/ +theorem bounds_13_1295 : exactInterval 13 1295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1295 : oddCount 1295 13 = 6 ∧ acceleratedOrbit 13 1295 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1295) = 3 ^ 6 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1295.1, data_13_1295.2] + +/-- Complete interval computation for depth 13, residue 1296. -/ +theorem bounds_13_1296 : exactInterval 13 1296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1296 : oddCount 1296 13 = 5 ∧ acceleratedOrbit 13 1296 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1296) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1296.1, data_13_1296.2] + +/-- Complete interval computation for depth 13, residue 1297. -/ +theorem bounds_13_1297 : exactInterval 13 1297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1297 : oddCount 1297 13 = 7 ∧ acceleratedOrbit 13 1297 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1297) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1297.1, data_13_1297.2] + +/-- Complete interval computation for depth 13, residue 1298. -/ +theorem bounds_13_1298 : exactInterval 13 1298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1298 : oddCount 1298 13 = 8 ∧ acceleratedOrbit 13 1298 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1298) = 3 ^ 8 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1298.1, data_13_1298.2] + +/-- Complete interval computation for depth 13, residue 1299. -/ +theorem bounds_13_1299 : exactInterval 13 1299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1299 : oddCount 1299 13 = 8 ∧ acceleratedOrbit 13 1299 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1299) = 3 ^ 8 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1299.1, data_13_1299.2] + +/-- Complete interval computation for depth 13, residue 1300. -/ +theorem bounds_13_1300 : exactInterval 13 1300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1300 : oddCount 1300 13 = 5 ∧ acceleratedOrbit 13 1300 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1300) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1300.1, data_13_1300.2] + +/-- Complete interval computation for depth 13, residue 1301. -/ +theorem bounds_13_1301 : exactInterval 13 1301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1301 : oddCount 1301 13 = 5 ∧ acceleratedOrbit 13 1301 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1301) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1301.1, data_13_1301.2] + +/-- Complete interval computation for depth 13, residue 1302. -/ +theorem bounds_13_1302 : exactInterval 13 1302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1302 : oddCount 1302 13 = 7 ∧ acceleratedOrbit 13 1302 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1302) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1302.1, data_13_1302.2] + +/-- Complete interval computation for depth 13, residue 1303. -/ +theorem bounds_13_1303 : exactInterval 13 1303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1303 : oddCount 1303 13 = 7 ∧ acceleratedOrbit 13 1303 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1303) = 3 ^ 7 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1303.1, data_13_1303.2] + +/-- Complete interval computation for depth 13, residue 1304. -/ +theorem bounds_13_1304 : exactInterval 13 1304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1304 : oddCount 1304 13 = 5 ∧ acceleratedOrbit 13 1304 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1304) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1304.1, data_13_1304.2] + +/-- Complete interval computation for depth 13, residue 1305. -/ +theorem bounds_13_1305 : exactInterval 13 1305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1305 : oddCount 1305 13 = 8 ∧ acceleratedOrbit 13 1305 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1305) = 3 ^ 8 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1305.1, data_13_1305.2] + +/-- Complete interval computation for depth 13, residue 1306. -/ +theorem bounds_13_1306 : exactInterval 13 1306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1306 : oddCount 1306 13 = 5 ∧ acceleratedOrbit 13 1306 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1306) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1306.1, data_13_1306.2] + +/-- Complete interval computation for depth 13, residue 1307. -/ +theorem bounds_13_1307 : exactInterval 13 1307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1307 : oddCount 1307 13 = 11 ∧ acceleratedOrbit 13 1307 = 28295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1307) = 3 ^ 11 * m + 28295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1307.1, data_13_1307.2] + +/-- Complete interval computation for depth 13, residue 1308. -/ +theorem bounds_13_1308 : exactInterval 13 1308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1308 : oddCount 1308 13 = 9 ∧ acceleratedOrbit 13 1308 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1308) = 3 ^ 9 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1308.1, data_13_1308.2] + +/-- Complete interval computation for depth 13, residue 1309. -/ +theorem bounds_13_1309 : exactInterval 13 1309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1309 : oddCount 1309 13 = 9 ∧ acceleratedOrbit 13 1309 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1309) = 3 ^ 9 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1309.1, data_13_1309.2] + +end Collatz.Research.StoppingAtlas.Batch0552 From 2d27c83314100fb5585d70f2ade13aa5120f7ab4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:27 +0530 Subject: [PATCH 0553/1001] proof: certify atlas Batch0553 (13:1310 to 13:1325) --- Collatz/Research/StoppingAtlas/Batch0553.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0553.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0553.lean b/Collatz/Research/StoppingAtlas/Batch0553.lean new file mode 100644 index 00000000..d6895765 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0553.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0553 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1310. -/ +theorem bounds_13_1310 : exactInterval 13 1310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1310 : oddCount 1310 13 = 9 ∧ acceleratedOrbit 13 1310 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1310) = 3 ^ 9 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1310.1, data_13_1310.2] + +/-- Complete interval computation for depth 13, residue 1311. -/ +theorem bounds_13_1311 : exactInterval 13 1311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1311 : oddCount 1311 13 = 8 ∧ acceleratedOrbit 13 1311 = 1052 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1311) = 3 ^ 8 * m + 1052 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1311.1, data_13_1311.2] + +/-- Complete interval computation for depth 13, residue 1312. -/ +theorem bounds_13_1312 : exactInterval 13 1312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1312 : oddCount 1312 13 = 6 ∧ acceleratedOrbit 13 1312 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1312) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1312.1, data_13_1312.2] + +/-- Complete interval computation for depth 13, residue 1313. -/ +theorem bounds_13_1313 : exactInterval 13 1313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1313 : oddCount 1313 13 = 4 ∧ acceleratedOrbit 13 1313 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1313) = 3 ^ 4 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1313.1, data_13_1313.2] + +/-- Complete interval computation for depth 13, residue 1314. -/ +theorem bounds_13_1314 : exactInterval 13 1314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1314 : oddCount 1314 13 = 6 ∧ acceleratedOrbit 13 1314 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1314) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1314.1, data_13_1314.2] + +/-- Complete interval computation for depth 13, residue 1315. -/ +theorem bounds_13_1315 : exactInterval 13 1315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1315 : oddCount 1315 13 = 6 ∧ acceleratedOrbit 13 1315 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1315) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1315.1, data_13_1315.2] + +/-- Complete interval computation for depth 13, residue 1316. -/ +theorem bounds_13_1316 : exactInterval 13 1316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1316 : oddCount 1316 13 = 6 ∧ acceleratedOrbit 13 1316 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1316) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1316.1, data_13_1316.2] + +/-- Complete interval computation for depth 13, residue 1317. -/ +theorem bounds_13_1317 : exactInterval 13 1317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1317 : oddCount 1317 13 = 6 ∧ acceleratedOrbit 13 1317 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1317) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1317.1, data_13_1317.2] + +/-- Complete interval computation for depth 13, residue 1318. -/ +theorem bounds_13_1318 : exactInterval 13 1318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1318 : oddCount 1318 13 = 6 ∧ acceleratedOrbit 13 1318 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1318) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1318.1, data_13_1318.2] + +/-- Complete interval computation for depth 13, residue 1319. -/ +theorem bounds_13_1319 : exactInterval 13 1319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1319 : oddCount 1319 13 = 7 ∧ acceleratedOrbit 13 1319 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1319) = 3 ^ 7 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1319.1, data_13_1319.2] + +/-- Complete interval computation for depth 13, residue 1320. -/ +theorem bounds_13_1320 : exactInterval 13 1320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1320 : oddCount 1320 13 = 6 ∧ acceleratedOrbit 13 1320 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1320) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1320.1, data_13_1320.2] + +/-- Complete interval computation for depth 13, residue 1321. -/ +theorem bounds_13_1321 : exactInterval 13 1321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1321 : oddCount 1321 13 = 9 ∧ acceleratedOrbit 13 1321 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1321) = 3 ^ 9 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1321.1, data_13_1321.2] + +/-- Complete interval computation for depth 13, residue 1322. -/ +theorem bounds_13_1322 : exactInterval 13 1322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1322 : oddCount 1322 13 = 6 ∧ acceleratedOrbit 13 1322 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1322) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1322.1, data_13_1322.2] + +/-- Complete interval computation for depth 13, residue 1323. -/ +theorem bounds_13_1323 : exactInterval 13 1323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1323 : oddCount 1323 13 = 6 ∧ acceleratedOrbit 13 1323 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1323) = 3 ^ 6 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1323.1, data_13_1323.2] + +/-- Complete interval computation for depth 13, residue 1324. -/ +theorem bounds_13_1324 : exactInterval 13 1324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1324 : oddCount 1324 13 = 5 ∧ acceleratedOrbit 13 1324 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1324) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1324.1, data_13_1324.2] + +/-- Complete interval computation for depth 13, residue 1325. -/ +theorem bounds_13_1325 : exactInterval 13 1325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1325 : oddCount 1325 13 = 5 ∧ acceleratedOrbit 13 1325 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1325) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1325.1, data_13_1325.2] + +end Collatz.Research.StoppingAtlas.Batch0553 From 1b7422e647887cc1108bd1fc29d9acf4119008bf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:27 +0530 Subject: [PATCH 0554/1001] proof: certify atlas Batch0554 (13:1326 to 13:1340) --- Collatz/Research/StoppingAtlas/Batch0554.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0554.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0554.lean b/Collatz/Research/StoppingAtlas/Batch0554.lean new file mode 100644 index 00000000..344e5069 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0554.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0554 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1326. -/ +theorem bounds_13_1326 : exactInterval 13 1326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1326 : oddCount 1326 13 = 5 ∧ acceleratedOrbit 13 1326 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1326) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1326.1, data_13_1326.2] + +/-- Complete interval computation for depth 13, residue 1327. -/ +theorem bounds_13_1327 : exactInterval 13 1327 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1327) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1327 : oddCount 1327 13 = 8 ∧ acceleratedOrbit 13 1327 = 1064 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1327) = 3 ^ 8 * m + 1064 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1327.1, data_13_1327.2] + +/-- Complete interval computation for depth 13, residue 1328. -/ +theorem bounds_13_1328 : exactInterval 13 1328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1328 : oddCount 1328 13 = 6 ∧ acceleratedOrbit 13 1328 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1328) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1328.1, data_13_1328.2] + +/-- Complete interval computation for depth 13, residue 1329. -/ +theorem bounds_13_1329 : exactInterval 13 1329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1329 : oddCount 1329 13 = 6 ∧ acceleratedOrbit 13 1329 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1329) = 3 ^ 6 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1329.1, data_13_1329.2] + +/-- Complete interval computation for depth 13, residue 1330. -/ +theorem bounds_13_1330 : exactInterval 13 1330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1330 : oddCount 1330 13 = 6 ∧ acceleratedOrbit 13 1330 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1330) = 3 ^ 6 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1330.1, data_13_1330.2] + +/-- Complete interval computation for depth 13, residue 1331. -/ +theorem bounds_13_1331 : exactInterval 13 1331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1331 : oddCount 1331 13 = 6 ∧ acceleratedOrbit 13 1331 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1331) = 3 ^ 6 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1331.1, data_13_1331.2] + +/-- Complete interval computation for depth 13, residue 1332. -/ +theorem bounds_13_1332 : exactInterval 13 1332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1332 : oddCount 1332 13 = 6 ∧ acceleratedOrbit 13 1332 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1332) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1332.1, data_13_1332.2] + +/-- Complete interval computation for depth 13, residue 1333. -/ +theorem bounds_13_1333 : exactInterval 13 1333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1333 : oddCount 1333 13 = 6 ∧ acceleratedOrbit 13 1333 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1333) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1333.1, data_13_1333.2] + +/-- Complete interval computation for depth 13, residue 1334. -/ +theorem bounds_13_1334 : exactInterval 13 1334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1334 : oddCount 1334 13 = 10 ∧ acceleratedOrbit 13 1334 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1334) = 3 ^ 10 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1334.1, data_13_1334.2] + +/-- Complete interval computation for depth 13, residue 1335. -/ +theorem bounds_13_1335 : exactInterval 13 1335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1335 : oddCount 1335 13 = 10 ∧ acceleratedOrbit 13 1335 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1335) = 3 ^ 10 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1335.1, data_13_1335.2] + +/-- Complete interval computation for depth 13, residue 1336. -/ +theorem bounds_13_1336 : exactInterval 13 1336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1336 : oddCount 1336 13 = 8 ∧ acceleratedOrbit 13 1336 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1336) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1336.1, data_13_1336.2] + +/-- Complete interval computation for depth 13, residue 1337. -/ +theorem bounds_13_1337 : exactInterval 13 1337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1337 : oddCount 1337 13 = 8 ∧ acceleratedOrbit 13 1337 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1337) = 3 ^ 8 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1337.1, data_13_1337.2] + +/-- Complete interval computation for depth 13, residue 1338. -/ +theorem bounds_13_1338 : exactInterval 13 1338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1338 : oddCount 1338 13 = 8 ∧ acceleratedOrbit 13 1338 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1338) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1338.1, data_13_1338.2] + +/-- Complete interval computation for depth 13, residue 1339. -/ +theorem bounds_13_1339 : exactInterval 13 1339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1339 : oddCount 1339 13 = 5 ∧ acceleratedOrbit 13 1339 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1339) = 3 ^ 5 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1339.1, data_13_1339.2] + +/-- Complete interval computation for depth 13, residue 1340. -/ +theorem bounds_13_1340 : exactInterval 13 1340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1340 : oddCount 1340 13 = 8 ∧ acceleratedOrbit 13 1340 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1340) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1340.1, data_13_1340.2] + +end Collatz.Research.StoppingAtlas.Batch0554 From 1960d7f6e1a2bf6e68a6ae03941479e8e95a1543 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:28 +0530 Subject: [PATCH 0555/1001] proof: certify atlas Batch0555 (13:1341 to 13:1355) --- Collatz/Research/StoppingAtlas/Batch0555.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0555.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0555.lean b/Collatz/Research/StoppingAtlas/Batch0555.lean new file mode 100644 index 00000000..a95a84eb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0555.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0555 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1341. -/ +theorem bounds_13_1341 : exactInterval 13 1341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1341 : oddCount 1341 13 = 8 ∧ acceleratedOrbit 13 1341 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1341) = 3 ^ 8 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1341.1, data_13_1341.2] + +/-- Complete interval computation for depth 13, residue 1342. -/ +theorem bounds_13_1342 : exactInterval 13 1342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1342 : oddCount 1342 13 = 9 ∧ acceleratedOrbit 13 1342 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1342) = 3 ^ 9 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1342.1, data_13_1342.2] + +/-- Complete interval computation for depth 13, residue 1343. -/ +theorem bounds_13_1343 : exactInterval 13 1343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1343 : oddCount 1343 13 = 9 ∧ acceleratedOrbit 13 1343 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1343) = 3 ^ 9 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1343.1, data_13_1343.2] + +/-- Complete interval computation for depth 13, residue 1344. -/ +theorem bounds_13_1344 : exactInterval 13 1344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1344 : oddCount 1344 13 = 2 ∧ acceleratedOrbit 13 1344 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1344) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1344.1, data_13_1344.2] + +/-- Complete interval computation for depth 13, residue 1345. -/ +theorem bounds_13_1345 : exactInterval 13 1345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1345 : oddCount 1345 13 = 6 ∧ acceleratedOrbit 13 1345 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1345) = 3 ^ 6 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1345.1, data_13_1345.2] + +/-- Complete interval computation for depth 13, residue 1346. -/ +theorem bounds_13_1346 : exactInterval 13 1346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1346 : oddCount 1346 13 = 7 ∧ acceleratedOrbit 13 1346 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1346) = 3 ^ 7 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1346.1, data_13_1346.2] + +/-- Complete interval computation for depth 13, residue 1347. -/ +theorem bounds_13_1347 : exactInterval 13 1347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1347 : oddCount 1347 13 = 7 ∧ acceleratedOrbit 13 1347 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1347) = 3 ^ 7 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1347.1, data_13_1347.2] + +/-- Complete interval computation for depth 13, residue 1348. -/ +theorem bounds_13_1348 : exactInterval 13 1348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1348 : oddCount 1348 13 = 7 ∧ acceleratedOrbit 13 1348 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1348) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1348.1, data_13_1348.2] + +/-- Complete interval computation for depth 13, residue 1349. -/ +theorem bounds_13_1349 : exactInterval 13 1349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1349 : oddCount 1349 13 = 7 ∧ acceleratedOrbit 13 1349 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1349) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1349.1, data_13_1349.2] + +/-- Complete interval computation for depth 13, residue 1350. -/ +theorem bounds_13_1350 : exactInterval 13 1350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1350 : oddCount 1350 13 = 7 ∧ acceleratedOrbit 13 1350 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1350) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1350.1, data_13_1350.2] + +/-- Complete interval computation for depth 13, residue 1351. -/ +theorem bounds_13_1351 : exactInterval 13 1351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1351 : oddCount 1351 13 = 9 ∧ acceleratedOrbit 13 1351 = 3250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1351) = 3 ^ 9 * m + 3250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1351.1, data_13_1351.2] + +/-- Complete interval computation for depth 13, residue 1352. -/ +theorem bounds_13_1352 : exactInterval 13 1352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1352 : oddCount 1352 13 = 8 ∧ acceleratedOrbit 13 1352 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1352) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1352.1, data_13_1352.2] + +/-- Complete interval computation for depth 13, residue 1353. -/ +theorem bounds_13_1353 : exactInterval 13 1353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1353 : oddCount 1353 13 = 7 ∧ acceleratedOrbit 13 1353 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1353) = 3 ^ 7 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1353.1, data_13_1353.2] + +/-- Complete interval computation for depth 13, residue 1354. -/ +theorem bounds_13_1354 : exactInterval 13 1354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1354 : oddCount 1354 13 = 8 ∧ acceleratedOrbit 13 1354 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1354) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1354.1, data_13_1354.2] + +/-- Complete interval computation for depth 13, residue 1355. -/ +theorem bounds_13_1355 : exactInterval 13 1355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1355 : oddCount 1355 13 = 7 ∧ acceleratedOrbit 13 1355 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1355) = 3 ^ 7 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1355.1, data_13_1355.2] + +end Collatz.Research.StoppingAtlas.Batch0555 From e939071d7e279cd0f6f2fc78fb0203c7eb8ce84a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:28 +0530 Subject: [PATCH 0556/1001] proof: certify atlas Batch0556 (13:1356 to 13:1371) --- Collatz/Research/StoppingAtlas/Batch0556.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0556.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0556.lean b/Collatz/Research/StoppingAtlas/Batch0556.lean new file mode 100644 index 00000000..136d9d44 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0556.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0556 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1356. -/ +theorem bounds_13_1356 : exactInterval 13 1356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1356 : oddCount 1356 13 = 8 ∧ acceleratedOrbit 13 1356 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1356) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1356.1, data_13_1356.2] + +/-- Complete interval computation for depth 13, residue 1357. -/ +theorem bounds_13_1357 : exactInterval 13 1357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1357 : oddCount 1357 13 = 8 ∧ acceleratedOrbit 13 1357 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1357) = 3 ^ 8 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1357.1, data_13_1357.2] + +/-- Complete interval computation for depth 13, residue 1358. -/ +theorem bounds_13_1358 : exactInterval 13 1358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1358 : oddCount 1358 13 = 8 ∧ acceleratedOrbit 13 1358 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1358) = 3 ^ 8 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1358.1, data_13_1358.2] + +/-- Complete interval computation for depth 13, residue 1359. -/ +theorem bounds_13_1359 : exactInterval 13 1359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1359 : oddCount 1359 13 = 8 ∧ acceleratedOrbit 13 1359 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1359) = 3 ^ 8 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1359.1, data_13_1359.2] + +/-- Complete interval computation for depth 13, residue 1360. -/ +theorem bounds_13_1360 : exactInterval 13 1360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1360 : oddCount 1360 13 = 2 ∧ acceleratedOrbit 13 1360 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1360) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1360.1, data_13_1360.2] + +/-- Complete interval computation for depth 13, residue 1361. -/ +theorem bounds_13_1361 : exactInterval 13 1361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1361 : oddCount 1361 13 = 9 ∧ acceleratedOrbit 13 1361 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1361) = 3 ^ 9 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1361.1, data_13_1361.2] + +/-- Complete interval computation for depth 13, residue 1362. -/ +theorem bounds_13_1362 : exactInterval 13 1362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1362 : oddCount 1362 13 = 10 ∧ acceleratedOrbit 13 1362 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1362) = 3 ^ 10 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1362.1, data_13_1362.2] + +/-- Complete interval computation for depth 13, residue 1363. -/ +theorem bounds_13_1363 : exactInterval 13 1363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1363 : oddCount 1363 13 = 10 ∧ acceleratedOrbit 13 1363 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1363) = 3 ^ 10 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1363.1, data_13_1363.2] + +/-- Complete interval computation for depth 13, residue 1364. -/ +theorem bounds_13_1364 : exactInterval 13 1364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1364 : oddCount 1364 13 = 2 ∧ acceleratedOrbit 13 1364 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1364) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1364.1, data_13_1364.2] + +/-- Complete interval computation for depth 13, residue 1365. -/ +theorem bounds_13_1365 : exactInterval 13 1365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1365 : oddCount 1365 13 = 2 ∧ acceleratedOrbit 13 1365 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1365) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1365.1, data_13_1365.2] + +/-- Complete interval computation for depth 13, residue 1366. -/ +theorem bounds_13_1366 : exactInterval 13 1366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1366 : oddCount 1366 13 = 6 ∧ acceleratedOrbit 13 1366 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1366) = 3 ^ 6 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1366.1, data_13_1366.2] + +/-- Complete interval computation for depth 13, residue 1367. -/ +theorem bounds_13_1367 : exactInterval 13 1367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1367 : oddCount 1367 13 = 6 ∧ acceleratedOrbit 13 1367 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1367) = 3 ^ 6 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1367.1, data_13_1367.2] + +/-- Complete interval computation for depth 13, residue 1368. -/ +theorem bounds_13_1368 : exactInterval 13 1368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1368 : oddCount 1368 13 = 5 ∧ acceleratedOrbit 13 1368 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1368) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1368.1, data_13_1368.2] + +/-- Complete interval computation for depth 13, residue 1369. -/ +theorem bounds_13_1369 : exactInterval 13 1369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1369 : oddCount 1369 13 = 7 ∧ acceleratedOrbit 13 1369 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1369) = 3 ^ 7 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1369.1, data_13_1369.2] + +/-- Complete interval computation for depth 13, residue 1370. -/ +theorem bounds_13_1370 : exactInterval 13 1370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1370 : oddCount 1370 13 = 5 ∧ acceleratedOrbit 13 1370 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1370) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1370.1, data_13_1370.2] + +/-- Complete interval computation for depth 13, residue 1371. -/ +theorem bounds_13_1371 : exactInterval 13 1371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1371 : oddCount 1371 13 = 8 ∧ acceleratedOrbit 13 1371 = 1100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1371) = 3 ^ 8 * m + 1100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1371.1, data_13_1371.2] + +end Collatz.Research.StoppingAtlas.Batch0556 From aaeedc7807a4f7ffc7a241eba4dcfbab38461428 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:29 +0530 Subject: [PATCH 0557/1001] proof: certify atlas Batch0557 (13:1372 to 13:1386) --- Collatz/Research/StoppingAtlas/Batch0557.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0557.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0557.lean b/Collatz/Research/StoppingAtlas/Batch0557.lean new file mode 100644 index 00000000..8be78f3c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0557.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0557 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1372. -/ +theorem bounds_13_1372 : exactInterval 13 1372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1372 : oddCount 1372 13 = 5 ∧ acceleratedOrbit 13 1372 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1372) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1372.1, data_13_1372.2] + +/-- Complete interval computation for depth 13, residue 1373. -/ +theorem bounds_13_1373 : exactInterval 13 1373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1373 : oddCount 1373 13 = 5 ∧ acceleratedOrbit 13 1373 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1373) = 3 ^ 5 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1373.1, data_13_1373.2] + +/-- Complete interval computation for depth 13, residue 1374. -/ +theorem bounds_13_1374 : exactInterval 13 1374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1374 : oddCount 1374 13 = 7 ∧ acceleratedOrbit 13 1374 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1374) = 3 ^ 7 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1374.1, data_13_1374.2] + +/-- Complete interval computation for depth 13, residue 1375. -/ +theorem bounds_13_1375 : exactInterval 13 1375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1375) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1375 : oddCount 1375 13 = 7 ∧ acceleratedOrbit 13 1375 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1375) = 3 ^ 7 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1375.1, data_13_1375.2] + +/-- Complete interval computation for depth 13, residue 1376. -/ +theorem bounds_13_1376 : exactInterval 13 1376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1376 : oddCount 1376 13 = 4 ∧ acceleratedOrbit 13 1376 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1376) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1376.1, data_13_1376.2] + +/-- Complete interval computation for depth 13, residue 1377. -/ +theorem bounds_13_1377 : exactInterval 13 1377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1377 : oddCount 1377 13 = 8 ∧ acceleratedOrbit 13 1377 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1377) = 3 ^ 8 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1377.1, data_13_1377.2] + +/-- Complete interval computation for depth 13, residue 1378. -/ +theorem bounds_13_1378 : exactInterval 13 1378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1378 : oddCount 1378 13 = 6 ∧ acceleratedOrbit 13 1378 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1378) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1378.1, data_13_1378.2] + +/-- Complete interval computation for depth 13, residue 1379. -/ +theorem bounds_13_1379 : exactInterval 13 1379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1379 : oddCount 1379 13 = 6 ∧ acceleratedOrbit 13 1379 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1379) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1379.1, data_13_1379.2] + +/-- Complete interval computation for depth 13, residue 1380. -/ +theorem bounds_13_1380 : exactInterval 13 1380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1380 : oddCount 1380 13 = 6 ∧ acceleratedOrbit 13 1380 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1380) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1380.1, data_13_1380.2] + +/-- Complete interval computation for depth 13, residue 1381. -/ +theorem bounds_13_1381 : exactInterval 13 1381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1381 : oddCount 1381 13 = 6 ∧ acceleratedOrbit 13 1381 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1381) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1381.1, data_13_1381.2] + +/-- Complete interval computation for depth 13, residue 1382. -/ +theorem bounds_13_1382 : exactInterval 13 1382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1382 : oddCount 1382 13 = 6 ∧ acceleratedOrbit 13 1382 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1382) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1382.1, data_13_1382.2] + +/-- Complete interval computation for depth 13, residue 1383. -/ +theorem bounds_13_1383 : exactInterval 13 1383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1383 : oddCount 1383 13 = 9 ∧ acceleratedOrbit 13 1383 = 3326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1383) = 3 ^ 9 * m + 3326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1383.1, data_13_1383.2] + +/-- Complete interval computation for depth 13, residue 1384. -/ +theorem bounds_13_1384 : exactInterval 13 1384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1384 : oddCount 1384 13 = 4 ∧ acceleratedOrbit 13 1384 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1384) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1384.1, data_13_1384.2] + +/-- Complete interval computation for depth 13, residue 1385. -/ +theorem bounds_13_1385 : exactInterval 13 1385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1385 : oddCount 1385 13 = 7 ∧ acceleratedOrbit 13 1385 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1385) = 3 ^ 7 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1385.1, data_13_1385.2] + +/-- Complete interval computation for depth 13, residue 1386. -/ +theorem bounds_13_1386 : exactInterval 13 1386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1386 : oddCount 1386 13 = 4 ∧ acceleratedOrbit 13 1386 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1386) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1386.1, data_13_1386.2] + +end Collatz.Research.StoppingAtlas.Batch0557 From c6fdc94a05ec62ab48252e213d8fc1fab2e0978e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:29 +0530 Subject: [PATCH 0558/1001] proof: certify atlas Batch0558 (13:1387 to 13:1401) --- Collatz/Research/StoppingAtlas/Batch0558.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0558.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0558.lean b/Collatz/Research/StoppingAtlas/Batch0558.lean new file mode 100644 index 00000000..bc0ddc16 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0558.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0558 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1387. -/ +theorem bounds_13_1387 : exactInterval 13 1387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1387 : oddCount 1387 13 = 7 ∧ acceleratedOrbit 13 1387 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1387) = 3 ^ 7 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1387.1, data_13_1387.2] + +/-- Complete interval computation for depth 13, residue 1388. -/ +theorem bounds_13_1388 : exactInterval 13 1388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1388 : oddCount 1388 13 = 6 ∧ acceleratedOrbit 13 1388 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1388) = 3 ^ 6 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1388.1, data_13_1388.2] + +/-- Complete interval computation for depth 13, residue 1389. -/ +theorem bounds_13_1389 : exactInterval 13 1389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1389 : oddCount 1389 13 = 6 ∧ acceleratedOrbit 13 1389 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1389) = 3 ^ 6 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1389.1, data_13_1389.2] + +/-- Complete interval computation for depth 13, residue 1390. -/ +theorem bounds_13_1390 : exactInterval 13 1390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1390 : oddCount 1390 13 = 6 ∧ acceleratedOrbit 13 1390 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1390) = 3 ^ 6 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1390.1, data_13_1390.2] + +/-- Complete interval computation for depth 13, residue 1391. -/ +theorem bounds_13_1391 : exactInterval 13 1391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1391 : oddCount 1391 13 = 9 ∧ acceleratedOrbit 13 1391 = 3347 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1391) = 3 ^ 9 * m + 3347 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1391.1, data_13_1391.2] + +/-- Complete interval computation for depth 13, residue 1392. -/ +theorem bounds_13_1392 : exactInterval 13 1392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1392 : oddCount 1392 13 = 4 ∧ acceleratedOrbit 13 1392 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1392) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1392.1, data_13_1392.2] + +/-- Complete interval computation for depth 13, residue 1393. -/ +theorem bounds_13_1393 : exactInterval 13 1393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1393 : oddCount 1393 13 = 4 ∧ acceleratedOrbit 13 1393 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1393) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1393.1, data_13_1393.2] + +/-- Complete interval computation for depth 13, residue 1394. -/ +theorem bounds_13_1394 : exactInterval 13 1394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1394 : oddCount 1394 13 = 6 ∧ acceleratedOrbit 13 1394 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1394) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1394.1, data_13_1394.2] + +/-- Complete interval computation for depth 13, residue 1395. -/ +theorem bounds_13_1395 : exactInterval 13 1395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1395 : oddCount 1395 13 = 6 ∧ acceleratedOrbit 13 1395 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1395) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1395.1, data_13_1395.2] + +/-- Complete interval computation for depth 13, residue 1396. -/ +theorem bounds_13_1396 : exactInterval 13 1396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1396 : oddCount 1396 13 = 4 ∧ acceleratedOrbit 13 1396 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1396) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1396.1, data_13_1396.2] + +/-- Complete interval computation for depth 13, residue 1397. -/ +theorem bounds_13_1397 : exactInterval 13 1397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1397 : oddCount 1397 13 = 4 ∧ acceleratedOrbit 13 1397 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1397) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1397.1, data_13_1397.2] + +/-- Complete interval computation for depth 13, residue 1398. -/ +theorem bounds_13_1398 : exactInterval 13 1398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1398 : oddCount 1398 13 = 8 ∧ acceleratedOrbit 13 1398 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1398) = 3 ^ 8 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1398.1, data_13_1398.2] + +/-- Complete interval computation for depth 13, residue 1399. -/ +theorem bounds_13_1399 : exactInterval 13 1399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1399 : oddCount 1399 13 = 8 ∧ acceleratedOrbit 13 1399 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1399) = 3 ^ 8 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1399.1, data_13_1399.2] + +/-- Complete interval computation for depth 13, residue 1400. -/ +theorem bounds_13_1400 : exactInterval 13 1400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1400 : oddCount 1400 13 = 7 ∧ acceleratedOrbit 13 1400 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1400) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1400.1, data_13_1400.2] + +/-- Complete interval computation for depth 13, residue 1401. -/ +theorem bounds_13_1401 : exactInterval 13 1401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1401 : oddCount 1401 13 = 10 ∧ acceleratedOrbit 13 1401 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1401) = 3 ^ 10 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1401.1, data_13_1401.2] + +end Collatz.Research.StoppingAtlas.Batch0558 From 5d40b9e5a054e9355575eef57aa607293ffe1e06 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:29 +0530 Subject: [PATCH 0559/1001] proof: certify atlas Batch0559 (13:1402 to 13:1417) --- Collatz/Research/StoppingAtlas/Batch0559.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0559.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0559.lean b/Collatz/Research/StoppingAtlas/Batch0559.lean new file mode 100644 index 00000000..a9e0884f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0559.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0559 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1402. -/ +theorem bounds_13_1402 : exactInterval 13 1402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1402 : oddCount 1402 13 = 7 ∧ acceleratedOrbit 13 1402 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1402) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1402.1, data_13_1402.2] + +/-- Complete interval computation for depth 13, residue 1403. -/ +theorem bounds_13_1403 : exactInterval 13 1403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1403 : oddCount 1403 13 = 6 ∧ acceleratedOrbit 13 1403 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1403) = 3 ^ 6 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1403.1, data_13_1403.2] + +/-- Complete interval computation for depth 13, residue 1404. -/ +theorem bounds_13_1404 : exactInterval 13 1404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1404 : oddCount 1404 13 = 7 ∧ acceleratedOrbit 13 1404 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1404) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1404.1, data_13_1404.2] + +/-- Complete interval computation for depth 13, residue 1405. -/ +theorem bounds_13_1405 : exactInterval 13 1405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1405 : oddCount 1405 13 = 7 ∧ acceleratedOrbit 13 1405 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1405) = 3 ^ 7 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1405.1, data_13_1405.2] + +/-- Complete interval computation for depth 13, residue 1406. -/ +theorem bounds_13_1406 : exactInterval 13 1406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1406 : oddCount 1406 13 = 10 ∧ acceleratedOrbit 13 1406 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1406) = 3 ^ 10 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1406.1, data_13_1406.2] + +/-- Complete interval computation for depth 13, residue 1407. -/ +theorem bounds_13_1407 : exactInterval 13 1407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1407 : oddCount 1407 13 = 10 ∧ acceleratedOrbit 13 1407 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1407) = 3 ^ 10 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1407.1, data_13_1407.2] + +/-- Complete interval computation for depth 13, residue 1408. -/ +theorem bounds_13_1408 : exactInterval 13 1408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1408 : oddCount 1408 13 = 3 ∧ acceleratedOrbit 13 1408 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1408) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1408.1, data_13_1408.2] + +/-- Complete interval computation for depth 13, residue 1409. -/ +theorem bounds_13_1409 : exactInterval 13 1409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1409 : oddCount 1409 13 = 8 ∧ acceleratedOrbit 13 1409 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1409) = 3 ^ 8 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1409.1, data_13_1409.2] + +/-- Complete interval computation for depth 13, residue 1410. -/ +theorem bounds_13_1410 : exactInterval 13 1410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1410 : oddCount 1410 13 = 4 ∧ acceleratedOrbit 13 1410 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1410) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1410.1, data_13_1410.2] + +/-- Complete interval computation for depth 13, residue 1411. -/ +theorem bounds_13_1411 : exactInterval 13 1411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1411 : oddCount 1411 13 = 4 ∧ acceleratedOrbit 13 1411 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1411) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1411.1, data_13_1411.2] + +/-- Complete interval computation for depth 13, residue 1412. -/ +theorem bounds_13_1412 : exactInterval 13 1412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1412 : oddCount 1412 13 = 7 ∧ acceleratedOrbit 13 1412 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1412) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1412.1, data_13_1412.2] + +/-- Complete interval computation for depth 13, residue 1413. -/ +theorem bounds_13_1413 : exactInterval 13 1413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1413 : oddCount 1413 13 = 7 ∧ acceleratedOrbit 13 1413 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1413) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1413.1, data_13_1413.2] + +/-- Complete interval computation for depth 13, residue 1414. -/ +theorem bounds_13_1414 : exactInterval 13 1414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1414 : oddCount 1414 13 = 7 ∧ acceleratedOrbit 13 1414 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1414) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1414.1, data_13_1414.2] + +/-- Complete interval computation for depth 13, residue 1415. -/ +theorem bounds_13_1415 : exactInterval 13 1415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1415 : oddCount 1415 13 = 4 ∧ acceleratedOrbit 13 1415 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1415) = 3 ^ 4 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1415.1, data_13_1415.2] + +/-- Complete interval computation for depth 13, residue 1416. -/ +theorem bounds_13_1416 : exactInterval 13 1416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1416 : oddCount 1416 13 = 5 ∧ acceleratedOrbit 13 1416 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1416) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1416.1, data_13_1416.2] + +/-- Complete interval computation for depth 13, residue 1417. -/ +theorem bounds_13_1417 : exactInterval 13 1417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1417 : oddCount 1417 13 = 7 ∧ acceleratedOrbit 13 1417 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1417) = 3 ^ 7 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1417.1, data_13_1417.2] + +end Collatz.Research.StoppingAtlas.Batch0559 From db4be0d132ba6a2c106401b07574395749cf226a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:30 +0530 Subject: [PATCH 0560/1001] proof: certify atlas Batch0560 (13:1418 to 13:1432) --- Collatz/Research/StoppingAtlas/Batch0560.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0560.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0560.lean b/Collatz/Research/StoppingAtlas/Batch0560.lean new file mode 100644 index 00000000..272b0d33 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0560.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0560 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1418. -/ +theorem bounds_13_1418 : exactInterval 13 1418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1418 : oddCount 1418 13 = 5 ∧ acceleratedOrbit 13 1418 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1418) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1418.1, data_13_1418.2] + +/-- Complete interval computation for depth 13, residue 1419. -/ +theorem bounds_13_1419 : exactInterval 13 1419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1419 : oddCount 1419 13 = 7 ∧ acceleratedOrbit 13 1419 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1419) = 3 ^ 7 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1419.1, data_13_1419.2] + +/-- Complete interval computation for depth 13, residue 1420. -/ +theorem bounds_13_1420 : exactInterval 13 1420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1420 : oddCount 1420 13 = 5 ∧ acceleratedOrbit 13 1420 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1420) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1420.1, data_13_1420.2] + +/-- Complete interval computation for depth 13, residue 1421. -/ +theorem bounds_13_1421 : exactInterval 13 1421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1421 : oddCount 1421 13 = 5 ∧ acceleratedOrbit 13 1421 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1421) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1421.1, data_13_1421.2] + +/-- Complete interval computation for depth 13, residue 1422. -/ +theorem bounds_13_1422 : exactInterval 13 1422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1422 : oddCount 1422 13 = 6 ∧ acceleratedOrbit 13 1422 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1422) = 3 ^ 6 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1422.1, data_13_1422.2] + +/-- Complete interval computation for depth 13, residue 1423. -/ +theorem bounds_13_1423 : exactInterval 13 1423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1423 : oddCount 1423 13 = 6 ∧ acceleratedOrbit 13 1423 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1423) = 3 ^ 6 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1423.1, data_13_1423.2] + +/-- Complete interval computation for depth 13, residue 1424. -/ +theorem bounds_13_1424 : exactInterval 13 1424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1424 : oddCount 1424 13 = 5 ∧ acceleratedOrbit 13 1424 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1424) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1424.1, data_13_1424.2] + +/-- Complete interval computation for depth 13, residue 1425. -/ +theorem bounds_13_1425 : exactInterval 13 1425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1425 : oddCount 1425 13 = 6 ∧ acceleratedOrbit 13 1425 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1425) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1425.1, data_13_1425.2] + +/-- Complete interval computation for depth 13, residue 1426. -/ +theorem bounds_13_1426 : exactInterval 13 1426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1426 : oddCount 1426 13 = 6 ∧ acceleratedOrbit 13 1426 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1426) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1426.1, data_13_1426.2] + +/-- Complete interval computation for depth 13, residue 1427. -/ +theorem bounds_13_1427 : exactInterval 13 1427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1427 : oddCount 1427 13 = 6 ∧ acceleratedOrbit 13 1427 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1427) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1427.1, data_13_1427.2] + +/-- Complete interval computation for depth 13, residue 1428. -/ +theorem bounds_13_1428 : exactInterval 13 1428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1428 : oddCount 1428 13 = 5 ∧ acceleratedOrbit 13 1428 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1428) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1428.1, data_13_1428.2] + +/-- Complete interval computation for depth 13, residue 1429. -/ +theorem bounds_13_1429 : exactInterval 13 1429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1429 : oddCount 1429 13 = 5 ∧ acceleratedOrbit 13 1429 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1429) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1429.1, data_13_1429.2] + +/-- Complete interval computation for depth 13, residue 1430. -/ +theorem bounds_13_1430 : exactInterval 13 1430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1430 : oddCount 1430 13 = 6 ∧ acceleratedOrbit 13 1430 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1430) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1430.1, data_13_1430.2] + +/-- Complete interval computation for depth 13, residue 1431. -/ +theorem bounds_13_1431 : exactInterval 13 1431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1431 : oddCount 1431 13 = 6 ∧ acceleratedOrbit 13 1431 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1431) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1431.1, data_13_1431.2] + +/-- Complete interval computation for depth 13, residue 1432. -/ +theorem bounds_13_1432 : exactInterval 13 1432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1432 : oddCount 1432 13 = 5 ∧ acceleratedOrbit 13 1432 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1432) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1432.1, data_13_1432.2] + +end Collatz.Research.StoppingAtlas.Batch0560 From 463f426a28e8a6c1d25cc3df4c0e6b393b235122 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:30 +0530 Subject: [PATCH 0561/1001] proof: certify atlas Batch0561 (13:1433 to 13:1447) --- Collatz/Research/StoppingAtlas/Batch0561.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0561.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0561.lean b/Collatz/Research/StoppingAtlas/Batch0561.lean new file mode 100644 index 00000000..6a0a0df7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0561.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0561 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1433. -/ +theorem bounds_13_1433 : exactInterval 13 1433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1433 : oddCount 1433 13 = 6 ∧ acceleratedOrbit 13 1433 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1433) = 3 ^ 6 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1433.1, data_13_1433.2] + +/-- Complete interval computation for depth 13, residue 1434. -/ +theorem bounds_13_1434 : exactInterval 13 1434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1434 : oddCount 1434 13 = 5 ∧ acceleratedOrbit 13 1434 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1434) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1434.1, data_13_1434.2] + +/-- Complete interval computation for depth 13, residue 1435. -/ +theorem bounds_13_1435 : exactInterval 13 1435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1435 : oddCount 1435 13 = 8 ∧ acceleratedOrbit 13 1435 = 1151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1435) = 3 ^ 8 * m + 1151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1435.1, data_13_1435.2] + +/-- Complete interval computation for depth 13, residue 1436. -/ +theorem bounds_13_1436 : exactInterval 13 1436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1436 : oddCount 1436 13 = 8 ∧ acceleratedOrbit 13 1436 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1436) = 3 ^ 8 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1436.1, data_13_1436.2] + +/-- Complete interval computation for depth 13, residue 1437. -/ +theorem bounds_13_1437 : exactInterval 13 1437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1437 : oddCount 1437 13 = 8 ∧ acceleratedOrbit 13 1437 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1437) = 3 ^ 8 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1437.1, data_13_1437.2] + +/-- Complete interval computation for depth 13, residue 1438. -/ +theorem bounds_13_1438 : exactInterval 13 1438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1438 : oddCount 1438 13 = 8 ∧ acceleratedOrbit 13 1438 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1438) = 3 ^ 8 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1438.1, data_13_1438.2] + +/-- Complete interval computation for depth 13, residue 1439. -/ +theorem bounds_13_1439 : exactInterval 13 1439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1439 : oddCount 1439 13 = 10 ∧ acceleratedOrbit 13 1439 = 10381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1439) = 3 ^ 10 * m + 10381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1439.1, data_13_1439.2] + +/-- Complete interval computation for depth 13, residue 1440. -/ +theorem bounds_13_1440 : exactInterval 13 1440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1440 : oddCount 1440 13 = 3 ∧ acceleratedOrbit 13 1440 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1440) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1440.1, data_13_1440.2] + +/-- Complete interval computation for depth 13, residue 1441. -/ +theorem bounds_13_1441 : exactInterval 13 1441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1441 : oddCount 1441 13 = 7 ∧ acceleratedOrbit 13 1441 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1441) = 3 ^ 7 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1441.1, data_13_1441.2] + +/-- Complete interval computation for depth 13, residue 1442. -/ +theorem bounds_13_1442 : exactInterval 13 1442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1442 : oddCount 1442 13 = 5 ∧ acceleratedOrbit 13 1442 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1442) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1442.1, data_13_1442.2] + +/-- Complete interval computation for depth 13, residue 1443. -/ +theorem bounds_13_1443 : exactInterval 13 1443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1443 : oddCount 1443 13 = 5 ∧ acceleratedOrbit 13 1443 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1443) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1443.1, data_13_1443.2] + +/-- Complete interval computation for depth 13, residue 1444. -/ +theorem bounds_13_1444 : exactInterval 13 1444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1444 : oddCount 1444 13 = 5 ∧ acceleratedOrbit 13 1444 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1444) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1444.1, data_13_1444.2] + +/-- Complete interval computation for depth 13, residue 1445. -/ +theorem bounds_13_1445 : exactInterval 13 1445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1445 : oddCount 1445 13 = 5 ∧ acceleratedOrbit 13 1445 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1445) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1445.1, data_13_1445.2] + +/-- Complete interval computation for depth 13, residue 1446. -/ +theorem bounds_13_1446 : exactInterval 13 1446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1446 : oddCount 1446 13 = 5 ∧ acceleratedOrbit 13 1446 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1446) = 3 ^ 5 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1446.1, data_13_1446.2] + +/-- Complete interval computation for depth 13, residue 1447. -/ +theorem bounds_13_1447 : exactInterval 13 1447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1447 : oddCount 1447 13 = 9 ∧ acceleratedOrbit 13 1447 = 3482 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1447) = 3 ^ 9 * m + 3482 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1447.1, data_13_1447.2] + +end Collatz.Research.StoppingAtlas.Batch0561 From 25aee89eff505f6dec43cdf6ea38c735e41f8cbe Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:31 +0530 Subject: [PATCH 0562/1001] proof: certify atlas Batch0562 (13:1448 to 13:1463) --- Collatz/Research/StoppingAtlas/Batch0562.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0562.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0562.lean b/Collatz/Research/StoppingAtlas/Batch0562.lean new file mode 100644 index 00000000..2cad9352 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0562.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0562 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1448. -/ +theorem bounds_13_1448 : exactInterval 13 1448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1448 : oddCount 1448 13 = 3 ∧ acceleratedOrbit 13 1448 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1448) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1448.1, data_13_1448.2] + +/-- Complete interval computation for depth 13, residue 1449. -/ +theorem bounds_13_1449 : exactInterval 13 1449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1449 : oddCount 1449 13 = 8 ∧ acceleratedOrbit 13 1449 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1449) = 3 ^ 8 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1449.1, data_13_1449.2] + +/-- Complete interval computation for depth 13, residue 1450. -/ +theorem bounds_13_1450 : exactInterval 13 1450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1450 : oddCount 1450 13 = 3 ∧ acceleratedOrbit 13 1450 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1450) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1450.1, data_13_1450.2] + +/-- Complete interval computation for depth 13, residue 1451. -/ +theorem bounds_13_1451 : exactInterval 13 1451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1451 : oddCount 1451 13 = 7 ∧ acceleratedOrbit 13 1451 = 388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1451) = 3 ^ 7 * m + 388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1451.1, data_13_1451.2] + +/-- Complete interval computation for depth 13, residue 1452. -/ +theorem bounds_13_1452 : exactInterval 13 1452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1452 : oddCount 1452 13 = 6 ∧ acceleratedOrbit 13 1452 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1452) = 3 ^ 6 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1452.1, data_13_1452.2] + +/-- Complete interval computation for depth 13, residue 1453. -/ +theorem bounds_13_1453 : exactInterval 13 1453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1453 : oddCount 1453 13 = 6 ∧ acceleratedOrbit 13 1453 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1453) = 3 ^ 6 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1453.1, data_13_1453.2] + +/-- Complete interval computation for depth 13, residue 1454. -/ +theorem bounds_13_1454 : exactInterval 13 1454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1454 : oddCount 1454 13 = 6 ∧ acceleratedOrbit 13 1454 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1454) = 3 ^ 6 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1454.1, data_13_1454.2] + +/-- Complete interval computation for depth 13, residue 1455. -/ +theorem bounds_13_1455 : exactInterval 13 1455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1455) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1455 : oddCount 1455 13 = 7 ∧ acceleratedOrbit 13 1455 = 389 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1455) = 3 ^ 7 * m + 389 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1455.1, data_13_1455.2] + +/-- Complete interval computation for depth 13, residue 1456. -/ +theorem bounds_13_1456 : exactInterval 13 1456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1456 : oddCount 1456 13 = 7 ∧ acceleratedOrbit 13 1456 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1456) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1456.1, data_13_1456.2] + +/-- Complete interval computation for depth 13, residue 1457. -/ +theorem bounds_13_1457 : exactInterval 13 1457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1457 : oddCount 1457 13 = 5 ∧ acceleratedOrbit 13 1457 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1457) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1457.1, data_13_1457.2] + +/-- Complete interval computation for depth 13, residue 1458. -/ +theorem bounds_13_1458 : exactInterval 13 1458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1458 : oddCount 1458 13 = 5 ∧ acceleratedOrbit 13 1458 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1458) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1458.1, data_13_1458.2] + +/-- Complete interval computation for depth 13, residue 1459. -/ +theorem bounds_13_1459 : exactInterval 13 1459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1459 : oddCount 1459 13 = 5 ∧ acceleratedOrbit 13 1459 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1459) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1459.1, data_13_1459.2] + +/-- Complete interval computation for depth 13, residue 1460. -/ +theorem bounds_13_1460 : exactInterval 13 1460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1460 : oddCount 1460 13 = 7 ∧ acceleratedOrbit 13 1460 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1460) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1460.1, data_13_1460.2] + +/-- Complete interval computation for depth 13, residue 1461. -/ +theorem bounds_13_1461 : exactInterval 13 1461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1461 : oddCount 1461 13 = 7 ∧ acceleratedOrbit 13 1461 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1461) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1461.1, data_13_1461.2] + +/-- Complete interval computation for depth 13, residue 1462. -/ +theorem bounds_13_1462 : exactInterval 13 1462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1462 : oddCount 1462 13 = 8 ∧ acceleratedOrbit 13 1462 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1462) = 3 ^ 8 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1462.1, data_13_1462.2] + +/-- Complete interval computation for depth 13, residue 1463. -/ +theorem bounds_13_1463 : exactInterval 13 1463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1463 : oddCount 1463 13 = 8 ∧ acceleratedOrbit 13 1463 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1463) = 3 ^ 8 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1463.1, data_13_1463.2] + +end Collatz.Research.StoppingAtlas.Batch0562 From f4415e89560c7705bcdbf8adbcc20b425d1c02c0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:31 +0530 Subject: [PATCH 0563/1001] proof: certify atlas Batch0563 (13:1464 to 13:1478) --- Collatz/Research/StoppingAtlas/Batch0563.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0563.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0563.lean b/Collatz/Research/StoppingAtlas/Batch0563.lean new file mode 100644 index 00000000..5e057c21 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0563.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0563 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1464. -/ +theorem bounds_13_1464 : exactInterval 13 1464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1464 : oddCount 1464 13 = 7 ∧ acceleratedOrbit 13 1464 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1464) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1464.1, data_13_1464.2] + +/-- Complete interval computation for depth 13, residue 1465. -/ +theorem bounds_13_1465 : exactInterval 13 1465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1465 : oddCount 1465 13 = 5 ∧ acceleratedOrbit 13 1465 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1465) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1465.1, data_13_1465.2] + +/-- Complete interval computation for depth 13, residue 1466. -/ +theorem bounds_13_1466 : exactInterval 13 1466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1466 : oddCount 1466 13 = 7 ∧ acceleratedOrbit 13 1466 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1466) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1466.1, data_13_1466.2] + +/-- Complete interval computation for depth 13, residue 1467. -/ +theorem bounds_13_1467 : exactInterval 13 1467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1467 : oddCount 1467 13 = 8 ∧ acceleratedOrbit 13 1467 = 1178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1467) = 3 ^ 8 * m + 1178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1467.1, data_13_1467.2] + +/-- Complete interval computation for depth 13, residue 1468. -/ +theorem bounds_13_1468 : exactInterval 13 1468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1468 : oddCount 1468 13 = 6 ∧ acceleratedOrbit 13 1468 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1468) = 3 ^ 6 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1468.1, data_13_1468.2] + +/-- Complete interval computation for depth 13, residue 1469. -/ +theorem bounds_13_1469 : exactInterval 13 1469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1469 : oddCount 1469 13 = 6 ∧ acceleratedOrbit 13 1469 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1469) = 3 ^ 6 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1469.1, data_13_1469.2] + +/-- Complete interval computation for depth 13, residue 1470. -/ +theorem bounds_13_1470 : exactInterval 13 1470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1470 : oddCount 1470 13 = 6 ∧ acceleratedOrbit 13 1470 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1470) = 3 ^ 6 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1470.1, data_13_1470.2] + +/-- Complete interval computation for depth 13, residue 1471. -/ +theorem bounds_13_1471 : exactInterval 13 1471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1471 : oddCount 1471 13 = 12 ∧ acceleratedOrbit 13 1471 = 95498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1471) = 3 ^ 12 * m + 95498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1471.1, data_13_1471.2] + +/-- Complete interval computation for depth 13, residue 1472. -/ +theorem bounds_13_1472 : exactInterval 13 1472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1472 : oddCount 1472 13 = 3 ∧ acceleratedOrbit 13 1472 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1472) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1472.1, data_13_1472.2] + +/-- Complete interval computation for depth 13, residue 1473. -/ +theorem bounds_13_1473 : exactInterval 13 1473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1473 : oddCount 1473 13 = 7 ∧ acceleratedOrbit 13 1473 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1473) = 3 ^ 7 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1473.1, data_13_1473.2] + +/-- Complete interval computation for depth 13, residue 1474. -/ +theorem bounds_13_1474 : exactInterval 13 1474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1474 : oddCount 1474 13 = 9 ∧ acceleratedOrbit 13 1474 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1474) = 3 ^ 9 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1474.1, data_13_1474.2] + +/-- Complete interval computation for depth 13, residue 1475. -/ +theorem bounds_13_1475 : exactInterval 13 1475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1475 : oddCount 1475 13 = 9 ∧ acceleratedOrbit 13 1475 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1475) = 3 ^ 9 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1475.1, data_13_1475.2] + +/-- Complete interval computation for depth 13, residue 1476. -/ +theorem bounds_13_1476 : exactInterval 13 1476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1476 : oddCount 1476 13 = 3 ∧ acceleratedOrbit 13 1476 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1476) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1476.1, data_13_1476.2] + +/-- Complete interval computation for depth 13, residue 1477. -/ +theorem bounds_13_1477 : exactInterval 13 1477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1477 : oddCount 1477 13 = 3 ∧ acceleratedOrbit 13 1477 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1477) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1477.1, data_13_1477.2] + +/-- Complete interval computation for depth 13, residue 1478. -/ +theorem bounds_13_1478 : exactInterval 13 1478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1478 : oddCount 1478 13 = 3 ∧ acceleratedOrbit 13 1478 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1478) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1478.1, data_13_1478.2] + +end Collatz.Research.StoppingAtlas.Batch0563 From 5f0e3fd3b3cc9921c3d4d307bdfb2173f93fe1c8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:32 +0530 Subject: [PATCH 0564/1001] proof: certify atlas Batch0564 (13:1479 to 13:1494) --- Collatz/Research/StoppingAtlas/Batch0564.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0564.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0564.lean b/Collatz/Research/StoppingAtlas/Batch0564.lean new file mode 100644 index 00000000..75fe4979 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0564.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0564 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1479. -/ +theorem bounds_13_1479 : exactInterval 13 1479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1479 : oddCount 1479 13 = 8 ∧ acceleratedOrbit 13 1479 = 1187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1479) = 3 ^ 8 * m + 1187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1479.1, data_13_1479.2] + +/-- Complete interval computation for depth 13, residue 1480. -/ +theorem bounds_13_1480 : exactInterval 13 1480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1480 : oddCount 1480 13 = 6 ∧ acceleratedOrbit 13 1480 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1480) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1480.1, data_13_1480.2] + +/-- Complete interval computation for depth 13, residue 1481. -/ +theorem bounds_13_1481 : exactInterval 13 1481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1481 : oddCount 1481 13 = 5 ∧ acceleratedOrbit 13 1481 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1481) = 3 ^ 5 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1481.1, data_13_1481.2] + +/-- Complete interval computation for depth 13, residue 1482. -/ +theorem bounds_13_1482 : exactInterval 13 1482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1482 : oddCount 1482 13 = 6 ∧ acceleratedOrbit 13 1482 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1482) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1482.1, data_13_1482.2] + +/-- Complete interval computation for depth 13, residue 1483. -/ +theorem bounds_13_1483 : exactInterval 13 1483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1483 : oddCount 1483 13 = 7 ∧ acceleratedOrbit 13 1483 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1483) = 3 ^ 7 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1483.1, data_13_1483.2] + +/-- Complete interval computation for depth 13, residue 1484. -/ +theorem bounds_13_1484 : exactInterval 13 1484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1484 : oddCount 1484 13 = 6 ∧ acceleratedOrbit 13 1484 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1484) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1484.1, data_13_1484.2] + +/-- Complete interval computation for depth 13, residue 1485. -/ +theorem bounds_13_1485 : exactInterval 13 1485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1485 : oddCount 1485 13 = 6 ∧ acceleratedOrbit 13 1485 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1485) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1485.1, data_13_1485.2] + +/-- Complete interval computation for depth 13, residue 1486. -/ +theorem bounds_13_1486 : exactInterval 13 1486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1486 : oddCount 1486 13 = 9 ∧ acceleratedOrbit 13 1486 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1486) = 3 ^ 9 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1486.1, data_13_1486.2] + +/-- Complete interval computation for depth 13, residue 1487. -/ +theorem bounds_13_1487 : exactInterval 13 1487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1487 : oddCount 1487 13 = 9 ∧ acceleratedOrbit 13 1487 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1487) = 3 ^ 9 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1487.1, data_13_1487.2] + +/-- Complete interval computation for depth 13, residue 1488. -/ +theorem bounds_13_1488 : exactInterval 13 1488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1488 : oddCount 1488 13 = 3 ∧ acceleratedOrbit 13 1488 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1488) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1488.1, data_13_1488.2] + +/-- Complete interval computation for depth 13, residue 1489. -/ +theorem bounds_13_1489 : exactInterval 13 1489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1489 : oddCount 1489 13 = 6 ∧ acceleratedOrbit 13 1489 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1489) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1489.1, data_13_1489.2] + +/-- Complete interval computation for depth 13, residue 1490. -/ +theorem bounds_13_1490 : exactInterval 13 1490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1490 : oddCount 1490 13 = 9 ∧ acceleratedOrbit 13 1490 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1490) = 3 ^ 9 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1490.1, data_13_1490.2] + +/-- Complete interval computation for depth 13, residue 1491. -/ +theorem bounds_13_1491 : exactInterval 13 1491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1491 : oddCount 1491 13 = 9 ∧ acceleratedOrbit 13 1491 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1491) = 3 ^ 9 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1491.1, data_13_1491.2] + +/-- Complete interval computation for depth 13, residue 1492. -/ +theorem bounds_13_1492 : exactInterval 13 1492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1492 : oddCount 1492 13 = 3 ∧ acceleratedOrbit 13 1492 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1492) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1492.1, data_13_1492.2] + +/-- Complete interval computation for depth 13, residue 1493. -/ +theorem bounds_13_1493 : exactInterval 13 1493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1493 : oddCount 1493 13 = 3 ∧ acceleratedOrbit 13 1493 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1493) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1493.1, data_13_1493.2] + +/-- Complete interval computation for depth 13, residue 1494. -/ +theorem bounds_13_1494 : exactInterval 13 1494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1494 : oddCount 1494 13 = 7 ∧ acceleratedOrbit 13 1494 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1494) = 3 ^ 7 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1494.1, data_13_1494.2] + +end Collatz.Research.StoppingAtlas.Batch0564 From 6bf434f07245cffdb946aed5b6f8a591ffa03ab3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:32 +0530 Subject: [PATCH 0565/1001] proof: certify atlas Batch0565 (13:1495 to 13:1509) --- Collatz/Research/StoppingAtlas/Batch0565.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0565.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0565.lean b/Collatz/Research/StoppingAtlas/Batch0565.lean new file mode 100644 index 00000000..07d3779d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0565.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0565 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1495. -/ +theorem bounds_13_1495 : exactInterval 13 1495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1495 : oddCount 1495 13 = 7 ∧ acceleratedOrbit 13 1495 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1495) = 3 ^ 7 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1495.1, data_13_1495.2] + +/-- Complete interval computation for depth 13, residue 1496. -/ +theorem bounds_13_1496 : exactInterval 13 1496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1496 : oddCount 1496 13 = 7 ∧ acceleratedOrbit 13 1496 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1496) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1496.1, data_13_1496.2] + +/-- Complete interval computation for depth 13, residue 1497. -/ +theorem bounds_13_1497 : exactInterval 13 1497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1497 : oddCount 1497 13 = 7 ∧ acceleratedOrbit 13 1497 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1497) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1497.1, data_13_1497.2] + +/-- Complete interval computation for depth 13, residue 1498. -/ +theorem bounds_13_1498 : exactInterval 13 1498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1498 : oddCount 1498 13 = 7 ∧ acceleratedOrbit 13 1498 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1498) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1498.1, data_13_1498.2] + +/-- Complete interval computation for depth 13, residue 1499. -/ +theorem bounds_13_1499 : exactInterval 13 1499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1499 : oddCount 1499 13 = 6 ∧ acceleratedOrbit 13 1499 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1499) = 3 ^ 6 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1499.1, data_13_1499.2] + +/-- Complete interval computation for depth 13, residue 1500. -/ +theorem bounds_13_1500 : exactInterval 13 1500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1500 : oddCount 1500 13 = 7 ∧ acceleratedOrbit 13 1500 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1500) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1500.1, data_13_1500.2] + +/-- Complete interval computation for depth 13, residue 1501. -/ +theorem bounds_13_1501 : exactInterval 13 1501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1501 : oddCount 1501 13 = 7 ∧ acceleratedOrbit 13 1501 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1501) = 3 ^ 7 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1501.1, data_13_1501.2] + +/-- Complete interval computation for depth 13, residue 1502. -/ +theorem bounds_13_1502 : exactInterval 13 1502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1502 : oddCount 1502 13 = 10 ∧ acceleratedOrbit 13 1502 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1502) = 3 ^ 10 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1502.1, data_13_1502.2] + +/-- Complete interval computation for depth 13, residue 1503. -/ +theorem bounds_13_1503 : exactInterval 13 1503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1503 : oddCount 1503 13 = 10 ∧ acceleratedOrbit 13 1503 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1503) = 3 ^ 10 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1503.1, data_13_1503.2] + +/-- Complete interval computation for depth 13, residue 1504. -/ +theorem bounds_13_1504 : exactInterval 13 1504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1504 : oddCount 1504 13 = 6 ∧ acceleratedOrbit 13 1504 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1504) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1504.1, data_13_1504.2] + +/-- Complete interval computation for depth 13, residue 1505. -/ +theorem bounds_13_1505 : exactInterval 13 1505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1505 : oddCount 1505 13 = 8 ∧ acceleratedOrbit 13 1505 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1505) = 3 ^ 8 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1505.1, data_13_1505.2] + +/-- Complete interval computation for depth 13, residue 1506. -/ +theorem bounds_13_1506 : exactInterval 13 1506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1506 : oddCount 1506 13 = 3 ∧ acceleratedOrbit 13 1506 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1506) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1506.1, data_13_1506.2] + +/-- Complete interval computation for depth 13, residue 1507. -/ +theorem bounds_13_1507 : exactInterval 13 1507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1507 : oddCount 1507 13 = 3 ∧ acceleratedOrbit 13 1507 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1507) = 3 ^ 3 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1507.1, data_13_1507.2] + +/-- Complete interval computation for depth 13, residue 1508. -/ +theorem bounds_13_1508 : exactInterval 13 1508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1508 : oddCount 1508 13 = 9 ∧ acceleratedOrbit 13 1508 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1508) = 3 ^ 9 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1508.1, data_13_1508.2] + +/-- Complete interval computation for depth 13, residue 1509. -/ +theorem bounds_13_1509 : exactInterval 13 1509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1509 : oddCount 1509 13 = 9 ∧ acceleratedOrbit 13 1509 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1509) = 3 ^ 9 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1509.1, data_13_1509.2] + +end Collatz.Research.StoppingAtlas.Batch0565 From f5963dcba478b50be3d26157de5a0a8a14cd75a7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:33 +0530 Subject: [PATCH 0566/1001] proof: certify atlas Batch0566 (13:1510 to 13:1524) --- Collatz/Research/StoppingAtlas/Batch0566.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0566.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0566.lean b/Collatz/Research/StoppingAtlas/Batch0566.lean new file mode 100644 index 00000000..59b8d501 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0566.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0566 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1510. -/ +theorem bounds_13_1510 : exactInterval 13 1510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1510 : oddCount 1510 13 = 9 ∧ acceleratedOrbit 13 1510 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1510) = 3 ^ 9 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1510.1, data_13_1510.2] + +/-- Complete interval computation for depth 13, residue 1511. -/ +theorem bounds_13_1511 : exactInterval 13 1511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1511 : oddCount 1511 13 = 9 ∧ acceleratedOrbit 13 1511 = 3635 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1511) = 3 ^ 9 * m + 3635 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1511.1, data_13_1511.2] + +/-- Complete interval computation for depth 13, residue 1512. -/ +theorem bounds_13_1512 : exactInterval 13 1512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1512 : oddCount 1512 13 = 6 ∧ acceleratedOrbit 13 1512 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1512) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1512.1, data_13_1512.2] + +/-- Complete interval computation for depth 13, residue 1513. -/ +theorem bounds_13_1513 : exactInterval 13 1513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1513 : oddCount 1513 13 = 9 ∧ acceleratedOrbit 13 1513 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1513) = 3 ^ 9 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1513.1, data_13_1513.2] + +/-- Complete interval computation for depth 13, residue 1514. -/ +theorem bounds_13_1514 : exactInterval 13 1514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1514 : oddCount 1514 13 = 6 ∧ acceleratedOrbit 13 1514 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1514) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1514.1, data_13_1514.2] + +/-- Complete interval computation for depth 13, residue 1515. -/ +theorem bounds_13_1515 : exactInterval 13 1515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1515 : oddCount 1515 13 = 11 ∧ acceleratedOrbit 13 1515 = 32804 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1515) = 3 ^ 11 * m + 32804 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1515.1, data_13_1515.2] + +/-- Complete interval computation for depth 13, residue 1516. -/ +theorem bounds_13_1516 : exactInterval 13 1516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1516 : oddCount 1516 13 = 7 ∧ acceleratedOrbit 13 1516 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1516) = 3 ^ 7 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1516.1, data_13_1516.2] + +/-- Complete interval computation for depth 13, residue 1517. -/ +theorem bounds_13_1517 : exactInterval 13 1517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1517 : oddCount 1517 13 = 7 ∧ acceleratedOrbit 13 1517 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1517) = 3 ^ 7 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1517.1, data_13_1517.2] + +/-- Complete interval computation for depth 13, residue 1518. -/ +theorem bounds_13_1518 : exactInterval 13 1518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1518 : oddCount 1518 13 = 7 ∧ acceleratedOrbit 13 1518 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1518) = 3 ^ 7 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1518.1, data_13_1518.2] + +/-- Complete interval computation for depth 13, residue 1519. -/ +theorem bounds_13_1519 : exactInterval 13 1519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1519 : oddCount 1519 13 = 9 ∧ acceleratedOrbit 13 1519 = 3653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1519) = 3 ^ 9 * m + 3653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1519.1, data_13_1519.2] + +/-- Complete interval computation for depth 13, residue 1520. -/ +theorem bounds_13_1520 : exactInterval 13 1520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1520 : oddCount 1520 13 = 6 ∧ acceleratedOrbit 13 1520 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1520) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1520.1, data_13_1520.2] + +/-- Complete interval computation for depth 13, residue 1521. -/ +theorem bounds_13_1521 : exactInterval 13 1521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1521 : oddCount 1521 13 = 6 ∧ acceleratedOrbit 13 1521 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1521) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1521.1, data_13_1521.2] + +/-- Complete interval computation for depth 13, residue 1522. -/ +theorem bounds_13_1522 : exactInterval 13 1522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1522 : oddCount 1522 13 = 6 ∧ acceleratedOrbit 13 1522 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1522) = 3 ^ 6 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1522.1, data_13_1522.2] + +/-- Complete interval computation for depth 13, residue 1523. -/ +theorem bounds_13_1523 : exactInterval 13 1523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1523 : oddCount 1523 13 = 6 ∧ acceleratedOrbit 13 1523 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1523) = 3 ^ 6 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1523.1, data_13_1523.2] + +/-- Complete interval computation for depth 13, residue 1524. -/ +theorem bounds_13_1524 : exactInterval 13 1524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1524 : oddCount 1524 13 = 6 ∧ acceleratedOrbit 13 1524 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1524) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1524.1, data_13_1524.2] + +end Collatz.Research.StoppingAtlas.Batch0566 From 521d5bad3d5b2fd0874b1b8e036010d987010c2f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:33 +0530 Subject: [PATCH 0567/1001] proof: certify atlas Batch0567 (13:1525 to 13:1540) --- Collatz/Research/StoppingAtlas/Batch0567.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0567.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0567.lean b/Collatz/Research/StoppingAtlas/Batch0567.lean new file mode 100644 index 00000000..d9064461 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0567.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0567 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1525. -/ +theorem bounds_13_1525 : exactInterval 13 1525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1525 : oddCount 1525 13 = 6 ∧ acceleratedOrbit 13 1525 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1525) = 3 ^ 6 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1525.1, data_13_1525.2] + +/-- Complete interval computation for depth 13, residue 1526. -/ +theorem bounds_13_1526 : exactInterval 13 1526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1526 : oddCount 1526 13 = 8 ∧ acceleratedOrbit 13 1526 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1526) = 3 ^ 8 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1526.1, data_13_1526.2] + +/-- Complete interval computation for depth 13, residue 1527. -/ +theorem bounds_13_1527 : exactInterval 13 1527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1527 : oddCount 1527 13 = 8 ∧ acceleratedOrbit 13 1527 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1527) = 3 ^ 8 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1527.1, data_13_1527.2] + +/-- Complete interval computation for depth 13, residue 1528. -/ +theorem bounds_13_1528 : exactInterval 13 1528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1528 : oddCount 1528 13 = 7 ∧ acceleratedOrbit 13 1528 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1528) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1528.1, data_13_1528.2] + +/-- Complete interval computation for depth 13, residue 1529. -/ +theorem bounds_13_1529 : exactInterval 13 1529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1529 : oddCount 1529 13 = 7 ∧ acceleratedOrbit 13 1529 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1529) = 3 ^ 7 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1529.1, data_13_1529.2] + +/-- Complete interval computation for depth 13, residue 1530. -/ +theorem bounds_13_1530 : exactInterval 13 1530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1530 : oddCount 1530 13 = 7 ∧ acceleratedOrbit 13 1530 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1530) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1530.1, data_13_1530.2] + +/-- Complete interval computation for depth 13, residue 1531. -/ +theorem bounds_13_1531 : exactInterval 13 1531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1531 : oddCount 1531 13 = 8 ∧ acceleratedOrbit 13 1531 = 1228 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1531) = 3 ^ 8 * m + 1228 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1531.1, data_13_1531.2] + +/-- Complete interval computation for depth 13, residue 1532. -/ +theorem bounds_13_1532 : exactInterval 13 1532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1532 : oddCount 1532 13 = 7 ∧ acceleratedOrbit 13 1532 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1532) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1532.1, data_13_1532.2] + +/-- Complete interval computation for depth 13, residue 1533. -/ +theorem bounds_13_1533 : exactInterval 13 1533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1533 : oddCount 1533 13 = 7 ∧ acceleratedOrbit 13 1533 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1533) = 3 ^ 7 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1533.1, data_13_1533.2] + +/-- Complete interval computation for depth 13, residue 1534. -/ +theorem bounds_13_1534 : exactInterval 13 1534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1534 : oddCount 1534 13 = 10 ∧ acceleratedOrbit 13 1534 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1534) = 3 ^ 10 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1534.1, data_13_1534.2] + +/-- Complete interval computation for depth 13, residue 1535. -/ +theorem bounds_13_1535 : exactInterval 13 1535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1535 : oddCount 1535 13 = 10 ∧ acceleratedOrbit 13 1535 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1535) = 3 ^ 10 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1535.1, data_13_1535.2] + +/-- Complete interval computation for depth 13, residue 1536. -/ +theorem bounds_13_1536 : exactInterval 13 1536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1536 : oddCount 1536 13 = 2 ∧ acceleratedOrbit 13 1536 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1536) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1536.1, data_13_1536.2] + +/-- Complete interval computation for depth 13, residue 1537. -/ +theorem bounds_13_1537 : exactInterval 13 1537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1537 : oddCount 1537 13 = 8 ∧ acceleratedOrbit 13 1537 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1537) = 3 ^ 8 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1537.1, data_13_1537.2] + +/-- Complete interval computation for depth 13, residue 1538. -/ +theorem bounds_13_1538 : exactInterval 13 1538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1538 : oddCount 1538 13 = 5 ∧ acceleratedOrbit 13 1538 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1538) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1538.1, data_13_1538.2] + +/-- Complete interval computation for depth 13, residue 1539. -/ +theorem bounds_13_1539 : exactInterval 13 1539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1539 : oddCount 1539 13 = 5 ∧ acceleratedOrbit 13 1539 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1539) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1539.1, data_13_1539.2] + +/-- Complete interval computation for depth 13, residue 1540. -/ +theorem bounds_13_1540 : exactInterval 13 1540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1540 : oddCount 1540 13 = 5 ∧ acceleratedOrbit 13 1540 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1540) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1540.1, data_13_1540.2] + +end Collatz.Research.StoppingAtlas.Batch0567 From df8b8097422242121359a37ba2a7a941a91b610a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:34 +0530 Subject: [PATCH 0568/1001] proof: certify atlas Batch0568 (13:1541 to 13:1555) --- Collatz/Research/StoppingAtlas/Batch0568.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0568.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0568.lean b/Collatz/Research/StoppingAtlas/Batch0568.lean new file mode 100644 index 00000000..555d0b28 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0568.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0568 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1541. -/ +theorem bounds_13_1541 : exactInterval 13 1541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1541 : oddCount 1541 13 = 5 ∧ acceleratedOrbit 13 1541 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1541) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1541.1, data_13_1541.2] + +/-- Complete interval computation for depth 13, residue 1542. -/ +theorem bounds_13_1542 : exactInterval 13 1542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1542 : oddCount 1542 13 = 5 ∧ acceleratedOrbit 13 1542 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1542) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1542.1, data_13_1542.2] + +/-- Complete interval computation for depth 13, residue 1543. -/ +theorem bounds_13_1543 : exactInterval 13 1543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1543 : oddCount 1543 13 = 7 ∧ acceleratedOrbit 13 1543 = 413 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1543) = 3 ^ 7 * m + 413 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1543.1, data_13_1543.2] + +/-- Complete interval computation for depth 13, residue 1544. -/ +theorem bounds_13_1544 : exactInterval 13 1544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1544 : oddCount 1544 13 = 5 ∧ acceleratedOrbit 13 1544 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1544) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1544.1, data_13_1544.2] + +/-- Complete interval computation for depth 13, residue 1545. -/ +theorem bounds_13_1545 : exactInterval 13 1545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1545 : oddCount 1545 13 = 8 ∧ acceleratedOrbit 13 1545 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1545) = 3 ^ 8 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1545.1, data_13_1545.2] + +/-- Complete interval computation for depth 13, residue 1546. -/ +theorem bounds_13_1546 : exactInterval 13 1546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1546 : oddCount 1546 13 = 5 ∧ acceleratedOrbit 13 1546 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1546) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1546.1, data_13_1546.2] + +/-- Complete interval computation for depth 13, residue 1547. -/ +theorem bounds_13_1547 : exactInterval 13 1547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1547 : oddCount 1547 13 = 5 ∧ acceleratedOrbit 13 1547 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1547) = 3 ^ 5 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1547.1, data_13_1547.2] + +/-- Complete interval computation for depth 13, residue 1548. -/ +theorem bounds_13_1548 : exactInterval 13 1548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1548 : oddCount 1548 13 = 5 ∧ acceleratedOrbit 13 1548 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1548) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1548.1, data_13_1548.2] + +/-- Complete interval computation for depth 13, residue 1549. -/ +theorem bounds_13_1549 : exactInterval 13 1549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1549 : oddCount 1549 13 = 5 ∧ acceleratedOrbit 13 1549 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1549) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1549.1, data_13_1549.2] + +/-- Complete interval computation for depth 13, residue 1550. -/ +theorem bounds_13_1550 : exactInterval 13 1550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1550 : oddCount 1550 13 = 7 ∧ acceleratedOrbit 13 1550 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1550) = 3 ^ 7 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1550.1, data_13_1550.2] + +/-- Complete interval computation for depth 13, residue 1551. -/ +theorem bounds_13_1551 : exactInterval 13 1551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1551 : oddCount 1551 13 = 7 ∧ acceleratedOrbit 13 1551 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1551) = 3 ^ 7 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1551.1, data_13_1551.2] + +/-- Complete interval computation for depth 13, residue 1552. -/ +theorem bounds_13_1552 : exactInterval 13 1552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1552 : oddCount 1552 13 = 5 ∧ acceleratedOrbit 13 1552 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1552) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1552.1, data_13_1552.2] + +/-- Complete interval computation for depth 13, residue 1553. -/ +theorem bounds_13_1553 : exactInterval 13 1553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1553 : oddCount 1553 13 = 5 ∧ acceleratedOrbit 13 1553 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1553) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1553.1, data_13_1553.2] + +/-- Complete interval computation for depth 13, residue 1554. -/ +theorem bounds_13_1554 : exactInterval 13 1554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1554 : oddCount 1554 13 = 7 ∧ acceleratedOrbit 13 1554 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1554) = 3 ^ 7 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1554.1, data_13_1554.2] + +/-- Complete interval computation for depth 13, residue 1555. -/ +theorem bounds_13_1555 : exactInterval 13 1555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1555 : oddCount 1555 13 = 7 ∧ acceleratedOrbit 13 1555 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1555) = 3 ^ 7 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1555.1, data_13_1555.2] + +end Collatz.Research.StoppingAtlas.Batch0568 From ef1ba6d193e027308bd303a1f5f740fea7646ba9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:35 +0530 Subject: [PATCH 0569/1001] proof: certify atlas Batch0569 (13:1556 to 13:1570) --- Collatz/Research/StoppingAtlas/Batch0569.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0569.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0569.lean b/Collatz/Research/StoppingAtlas/Batch0569.lean new file mode 100644 index 00000000..c87579cc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0569.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0569 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1556. -/ +theorem bounds_13_1556 : exactInterval 13 1556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1556 : oddCount 1556 13 = 5 ∧ acceleratedOrbit 13 1556 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1556) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1556.1, data_13_1556.2] + +/-- Complete interval computation for depth 13, residue 1557. -/ +theorem bounds_13_1557 : exactInterval 13 1557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1557 : oddCount 1557 13 = 5 ∧ acceleratedOrbit 13 1557 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1557) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1557.1, data_13_1557.2] + +/-- Complete interval computation for depth 13, residue 1558. -/ +theorem bounds_13_1558 : exactInterval 13 1558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1558 : oddCount 1558 13 = 7 ∧ acceleratedOrbit 13 1558 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1558) = 3 ^ 7 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1558.1, data_13_1558.2] + +/-- Complete interval computation for depth 13, residue 1559. -/ +theorem bounds_13_1559 : exactInterval 13 1559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1559 : oddCount 1559 13 = 7 ∧ acceleratedOrbit 13 1559 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1559) = 3 ^ 7 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1559.1, data_13_1559.2] + +/-- Complete interval computation for depth 13, residue 1560. -/ +theorem bounds_13_1560 : exactInterval 13 1560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1560 : oddCount 1560 13 = 5 ∧ acceleratedOrbit 13 1560 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1560) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1560.1, data_13_1560.2] + +/-- Complete interval computation for depth 13, residue 1561. -/ +theorem bounds_13_1561 : exactInterval 13 1561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1561 : oddCount 1561 13 = 7 ∧ acceleratedOrbit 13 1561 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1561) = 3 ^ 7 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1561.1, data_13_1561.2] + +/-- Complete interval computation for depth 13, residue 1562. -/ +theorem bounds_13_1562 : exactInterval 13 1562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1562 : oddCount 1562 13 = 5 ∧ acceleratedOrbit 13 1562 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1562) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1562.1, data_13_1562.2] + +/-- Complete interval computation for depth 13, residue 1563. -/ +theorem bounds_13_1563 : exactInterval 13 1563 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1563) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1563 : oddCount 1563 13 = 8 ∧ acceleratedOrbit 13 1563 = 1253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1563) = 3 ^ 8 * m + 1253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1563.1, data_13_1563.2] + +/-- Complete interval computation for depth 13, residue 1564. -/ +theorem bounds_13_1564 : exactInterval 13 1564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1564 : oddCount 1564 13 = 5 ∧ acceleratedOrbit 13 1564 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1564) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1564.1, data_13_1564.2] + +/-- Complete interval computation for depth 13, residue 1565. -/ +theorem bounds_13_1565 : exactInterval 13 1565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1565 : oddCount 1565 13 = 5 ∧ acceleratedOrbit 13 1565 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1565) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1565.1, data_13_1565.2] + +/-- Complete interval computation for depth 13, residue 1566. -/ +theorem bounds_13_1566 : exactInterval 13 1566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1566 : oddCount 1566 13 = 5 ∧ acceleratedOrbit 13 1566 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1566) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1566.1, data_13_1566.2] + +/-- Complete interval computation for depth 13, residue 1567. -/ +theorem bounds_13_1567 : exactInterval 13 1567 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1567) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1567 : oddCount 1567 13 = 8 ∧ acceleratedOrbit 13 1567 = 1256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1567) = 3 ^ 8 * m + 1256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1567.1, data_13_1567.2] + +/-- Complete interval computation for depth 13, residue 1568. -/ +theorem bounds_13_1568 : exactInterval 13 1568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1568 : oddCount 1568 13 = 4 ∧ acceleratedOrbit 13 1568 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1568) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1568.1, data_13_1568.2] + +/-- Complete interval computation for depth 13, residue 1569. -/ +theorem bounds_13_1569 : exactInterval 13 1569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1569 : oddCount 1569 13 = 6 ∧ acceleratedOrbit 13 1569 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1569) = 3 ^ 6 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1569.1, data_13_1569.2] + +/-- Complete interval computation for depth 13, residue 1570. -/ +theorem bounds_13_1570 : exactInterval 13 1570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1570 : oddCount 1570 13 = 5 ∧ acceleratedOrbit 13 1570 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1570) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1570.1, data_13_1570.2] + +end Collatz.Research.StoppingAtlas.Batch0569 From 52beb90191a7e5239281b3b9515dfd4c8b08797c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:35 +0530 Subject: [PATCH 0570/1001] proof: certify atlas Batch0570 (13:1571 to 13:1586) --- Collatz/Research/StoppingAtlas/Batch0570.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0570.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0570.lean b/Collatz/Research/StoppingAtlas/Batch0570.lean new file mode 100644 index 00000000..7b96eaca --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0570.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0570 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1571. -/ +theorem bounds_13_1571 : exactInterval 13 1571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1571 : oddCount 1571 13 = 5 ∧ acceleratedOrbit 13 1571 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1571) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1571.1, data_13_1571.2] + +/-- Complete interval computation for depth 13, residue 1572. -/ +theorem bounds_13_1572 : exactInterval 13 1572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1572 : oddCount 1572 13 = 7 ∧ acceleratedOrbit 13 1572 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1572) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1572.1, data_13_1572.2] + +/-- Complete interval computation for depth 13, residue 1573. -/ +theorem bounds_13_1573 : exactInterval 13 1573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1573 : oddCount 1573 13 = 7 ∧ acceleratedOrbit 13 1573 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1573) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1573.1, data_13_1573.2] + +/-- Complete interval computation for depth 13, residue 1574. -/ +theorem bounds_13_1574 : exactInterval 13 1574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1574 : oddCount 1574 13 = 7 ∧ acceleratedOrbit 13 1574 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1574) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1574.1, data_13_1574.2] + +/-- Complete interval computation for depth 13, residue 1575. -/ +theorem bounds_13_1575 : exactInterval 13 1575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1575 : oddCount 1575 13 = 7 ∧ acceleratedOrbit 13 1575 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1575) = 3 ^ 7 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1575.1, data_13_1575.2] + +/-- Complete interval computation for depth 13, residue 1576. -/ +theorem bounds_13_1576 : exactInterval 13 1576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1576 : oddCount 1576 13 = 4 ∧ acceleratedOrbit 13 1576 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1576) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1576.1, data_13_1576.2] + +/-- Complete interval computation for depth 13, residue 1577. -/ +theorem bounds_13_1577 : exactInterval 13 1577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1577 : oddCount 1577 13 = 10 ∧ acceleratedOrbit 13 1577 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1577) = 3 ^ 10 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1577.1, data_13_1577.2] + +/-- Complete interval computation for depth 13, residue 1578. -/ +theorem bounds_13_1578 : exactInterval 13 1578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1578 : oddCount 1578 13 = 4 ∧ acceleratedOrbit 13 1578 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1578) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1578.1, data_13_1578.2] + +/-- Complete interval computation for depth 13, residue 1579. -/ +theorem bounds_13_1579 : exactInterval 13 1579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1579 : oddCount 1579 13 = 5 ∧ acceleratedOrbit 13 1579 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1579) = 3 ^ 5 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1579.1, data_13_1579.2] + +/-- Complete interval computation for depth 13, residue 1580. -/ +theorem bounds_13_1580 : exactInterval 13 1580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1580 : oddCount 1580 13 = 7 ∧ acceleratedOrbit 13 1580 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1580) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1580.1, data_13_1580.2] + +/-- Complete interval computation for depth 13, residue 1581. -/ +theorem bounds_13_1581 : exactInterval 13 1581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1581 : oddCount 1581 13 = 7 ∧ acceleratedOrbit 13 1581 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1581) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1581.1, data_13_1581.2] + +/-- Complete interval computation for depth 13, residue 1582. -/ +theorem bounds_13_1582 : exactInterval 13 1582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1582 : oddCount 1582 13 = 7 ∧ acceleratedOrbit 13 1582 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1582) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1582.1, data_13_1582.2] + +/-- Complete interval computation for depth 13, residue 1583. -/ +theorem bounds_13_1583 : exactInterval 13 1583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1583 : oddCount 1583 13 = 11 ∧ acceleratedOrbit 13 1583 = 34262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1583) = 3 ^ 11 * m + 34262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1583.1, data_13_1583.2] + +/-- Complete interval computation for depth 13, residue 1584. -/ +theorem bounds_13_1584 : exactInterval 13 1584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1584 : oddCount 1584 13 = 4 ∧ acceleratedOrbit 13 1584 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1584) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1584.1, data_13_1584.2] + +/-- Complete interval computation for depth 13, residue 1585. -/ +theorem bounds_13_1585 : exactInterval 13 1585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1585 : oddCount 1585 13 = 7 ∧ acceleratedOrbit 13 1585 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1585) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1585.1, data_13_1585.2] + +/-- Complete interval computation for depth 13, residue 1586. -/ +theorem bounds_13_1586 : exactInterval 13 1586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1586 : oddCount 1586 13 = 7 ∧ acceleratedOrbit 13 1586 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1586) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1586.1, data_13_1586.2] + +end Collatz.Research.StoppingAtlas.Batch0570 From e02442a6b7ddab1ea14b54144fc1be5b9902160c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:35 +0530 Subject: [PATCH 0571/1001] proof: certify atlas Batch0571 (13:1587 to 13:1601) --- Collatz/Research/StoppingAtlas/Batch0571.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0571.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0571.lean b/Collatz/Research/StoppingAtlas/Batch0571.lean new file mode 100644 index 00000000..569732b8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0571.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0571 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1587. -/ +theorem bounds_13_1587 : exactInterval 13 1587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1587 : oddCount 1587 13 = 7 ∧ acceleratedOrbit 13 1587 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1587) = 3 ^ 7 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1587.1, data_13_1587.2] + +/-- Complete interval computation for depth 13, residue 1588. -/ +theorem bounds_13_1588 : exactInterval 13 1588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1588 : oddCount 1588 13 = 4 ∧ acceleratedOrbit 13 1588 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1588) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1588.1, data_13_1588.2] + +/-- Complete interval computation for depth 13, residue 1589. -/ +theorem bounds_13_1589 : exactInterval 13 1589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1589 : oddCount 1589 13 = 4 ∧ acceleratedOrbit 13 1589 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1589) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1589.1, data_13_1589.2] + +/-- Complete interval computation for depth 13, residue 1590. -/ +theorem bounds_13_1590 : exactInterval 13 1590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1590 : oddCount 1590 13 = 9 ∧ acceleratedOrbit 13 1590 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1590) = 3 ^ 9 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1590.1, data_13_1590.2] + +/-- Complete interval computation for depth 13, residue 1591. -/ +theorem bounds_13_1591 : exactInterval 13 1591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1591 : oddCount 1591 13 = 9 ∧ acceleratedOrbit 13 1591 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1591) = 3 ^ 9 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1591.1, data_13_1591.2] + +/-- Complete interval computation for depth 13, residue 1592. -/ +theorem bounds_13_1592 : exactInterval 13 1592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1592 : oddCount 1592 13 = 6 ∧ acceleratedOrbit 13 1592 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1592) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1592.1, data_13_1592.2] + +/-- Complete interval computation for depth 13, residue 1593. -/ +theorem bounds_13_1593 : exactInterval 13 1593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1593 : oddCount 1593 13 = 6 ∧ acceleratedOrbit 13 1593 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1593) = 3 ^ 6 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1593.1, data_13_1593.2] + +/-- Complete interval computation for depth 13, residue 1594. -/ +theorem bounds_13_1594 : exactInterval 13 1594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1594 : oddCount 1594 13 = 6 ∧ acceleratedOrbit 13 1594 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1594) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1594.1, data_13_1594.2] + +/-- Complete interval computation for depth 13, residue 1595. -/ +theorem bounds_13_1595 : exactInterval 13 1595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1595 : oddCount 1595 13 = 7 ∧ acceleratedOrbit 13 1595 = 427 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1595) = 3 ^ 7 * m + 427 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1595.1, data_13_1595.2] + +/-- Complete interval computation for depth 13, residue 1596. -/ +theorem bounds_13_1596 : exactInterval 13 1596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1596 : oddCount 1596 13 = 6 ∧ acceleratedOrbit 13 1596 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1596) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1596.1, data_13_1596.2] + +/-- Complete interval computation for depth 13, residue 1597. -/ +theorem bounds_13_1597 : exactInterval 13 1597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1597 : oddCount 1597 13 = 6 ∧ acceleratedOrbit 13 1597 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1597) = 3 ^ 6 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1597.1, data_13_1597.2] + +/-- Complete interval computation for depth 13, residue 1598. -/ +theorem bounds_13_1598 : exactInterval 13 1598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1598 : oddCount 1598 13 = 8 ∧ acceleratedOrbit 13 1598 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1598) = 3 ^ 8 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1598.1, data_13_1598.2] + +/-- Complete interval computation for depth 13, residue 1599. -/ +theorem bounds_13_1599 : exactInterval 13 1599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1599 : oddCount 1599 13 = 8 ∧ acceleratedOrbit 13 1599 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1599) = 3 ^ 8 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1599.1, data_13_1599.2] + +/-- Complete interval computation for depth 13, residue 1600. -/ +theorem bounds_13_1600 : exactInterval 13 1600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1600 : oddCount 1600 13 = 4 ∧ acceleratedOrbit 13 1600 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1600) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1600.1, data_13_1600.2] + +/-- Complete interval computation for depth 13, residue 1601. -/ +theorem bounds_13_1601 : exactInterval 13 1601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1601 : oddCount 1601 13 = 7 ∧ acceleratedOrbit 13 1601 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1601) = 3 ^ 7 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1601.1, data_13_1601.2] + +end Collatz.Research.StoppingAtlas.Batch0571 From f9eb85c047c20f7eeda245614543b80489d0e9d2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:36 +0530 Subject: [PATCH 0572/1001] proof: certify atlas Batch0572 (13:1602 to 13:1616) --- Collatz/Research/StoppingAtlas/Batch0572.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0572.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0572.lean b/Collatz/Research/StoppingAtlas/Batch0572.lean new file mode 100644 index 00000000..cdb60926 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0572.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0572 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1602. -/ +theorem bounds_13_1602 : exactInterval 13 1602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1602 : oddCount 1602 13 = 7 ∧ acceleratedOrbit 13 1602 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1602) = 3 ^ 7 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1602.1, data_13_1602.2] + +/-- Complete interval computation for depth 13, residue 1603. -/ +theorem bounds_13_1603 : exactInterval 13 1603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1603 : oddCount 1603 13 = 7 ∧ acceleratedOrbit 13 1603 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1603) = 3 ^ 7 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1603.1, data_13_1603.2] + +/-- Complete interval computation for depth 13, residue 1604. -/ +theorem bounds_13_1604 : exactInterval 13 1604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1604 : oddCount 1604 13 = 4 ∧ acceleratedOrbit 13 1604 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1604) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1604.1, data_13_1604.2] + +/-- Complete interval computation for depth 13, residue 1605. -/ +theorem bounds_13_1605 : exactInterval 13 1605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1605 : oddCount 1605 13 = 4 ∧ acceleratedOrbit 13 1605 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1605) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1605.1, data_13_1605.2] + +/-- Complete interval computation for depth 13, residue 1606. -/ +theorem bounds_13_1606 : exactInterval 13 1606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1606 : oddCount 1606 13 = 4 ∧ acceleratedOrbit 13 1606 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1606) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1606.1, data_13_1606.2] + +/-- Complete interval computation for depth 13, residue 1607. -/ +theorem bounds_13_1607 : exactInterval 13 1607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1607) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1607 : oddCount 1607 13 = 8 ∧ acceleratedOrbit 13 1607 = 1289 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1607) = 3 ^ 8 * m + 1289 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1607.1, data_13_1607.2] + +/-- Complete interval computation for depth 13, residue 1608. -/ +theorem bounds_13_1608 : exactInterval 13 1608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1608 : oddCount 1608 13 = 4 ∧ acceleratedOrbit 13 1608 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1608) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1608.1, data_13_1608.2] + +/-- Complete interval computation for depth 13, residue 1609. -/ +theorem bounds_13_1609 : exactInterval 13 1609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1609 : oddCount 1609 13 = 8 ∧ acceleratedOrbit 13 1609 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1609) = 3 ^ 8 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1609.1, data_13_1609.2] + +/-- Complete interval computation for depth 13, residue 1610. -/ +theorem bounds_13_1610 : exactInterval 13 1610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1610 : oddCount 1610 13 = 4 ∧ acceleratedOrbit 13 1610 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1610) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1610.1, data_13_1610.2] + +/-- Complete interval computation for depth 13, residue 1611. -/ +theorem bounds_13_1611 : exactInterval 13 1611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1611 : oddCount 1611 13 = 4 ∧ acceleratedOrbit 13 1611 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1611) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1611.1, data_13_1611.2] + +/-- Complete interval computation for depth 13, residue 1612. -/ +theorem bounds_13_1612 : exactInterval 13 1612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1612 : oddCount 1612 13 = 4 ∧ acceleratedOrbit 13 1612 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1612) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1612.1, data_13_1612.2] + +/-- Complete interval computation for depth 13, residue 1613. -/ +theorem bounds_13_1613 : exactInterval 13 1613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1613 : oddCount 1613 13 = 4 ∧ acceleratedOrbit 13 1613 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1613) = 3 ^ 4 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1613.1, data_13_1613.2] + +/-- Complete interval computation for depth 13, residue 1614. -/ +theorem bounds_13_1614 : exactInterval 13 1614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1614 : oddCount 1614 13 = 9 ∧ acceleratedOrbit 13 1614 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1614) = 3 ^ 9 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1614.1, data_13_1614.2] + +/-- Complete interval computation for depth 13, residue 1615. -/ +theorem bounds_13_1615 : exactInterval 13 1615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1615 : oddCount 1615 13 = 9 ∧ acceleratedOrbit 13 1615 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1615) = 3 ^ 9 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1615.1, data_13_1615.2] + +/-- Complete interval computation for depth 13, residue 1616. -/ +theorem bounds_13_1616 : exactInterval 13 1616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1616 : oddCount 1616 13 = 4 ∧ acceleratedOrbit 13 1616 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1616) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1616.1, data_13_1616.2] + +end Collatz.Research.StoppingAtlas.Batch0572 From ce5205c726b059ac03819778cb57d01bce5354cf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:37 +0530 Subject: [PATCH 0573/1001] proof: certify atlas Batch0573 (13:1617 to 13:1632) --- Collatz/Research/StoppingAtlas/Batch0573.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0573.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0573.lean b/Collatz/Research/StoppingAtlas/Batch0573.lean new file mode 100644 index 00000000..517d5012 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0573.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0573 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1617. -/ +theorem bounds_13_1617 : exactInterval 13 1617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1617 : oddCount 1617 13 = 7 ∧ acceleratedOrbit 13 1617 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1617) = 3 ^ 7 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1617.1, data_13_1617.2] + +/-- Complete interval computation for depth 13, residue 1618. -/ +theorem bounds_13_1618 : exactInterval 13 1618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1618 : oddCount 1618 13 = 7 ∧ acceleratedOrbit 13 1618 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1618) = 3 ^ 7 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1618.1, data_13_1618.2] + +/-- Complete interval computation for depth 13, residue 1619. -/ +theorem bounds_13_1619 : exactInterval 13 1619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1619 : oddCount 1619 13 = 7 ∧ acceleratedOrbit 13 1619 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1619) = 3 ^ 7 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1619.1, data_13_1619.2] + +/-- Complete interval computation for depth 13, residue 1620. -/ +theorem bounds_13_1620 : exactInterval 13 1620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1620 : oddCount 1620 13 = 4 ∧ acceleratedOrbit 13 1620 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1620) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1620.1, data_13_1620.2] + +/-- Complete interval computation for depth 13, residue 1621. -/ +theorem bounds_13_1621 : exactInterval 13 1621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1621 : oddCount 1621 13 = 4 ∧ acceleratedOrbit 13 1621 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1621) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1621.1, data_13_1621.2] + +/-- Complete interval computation for depth 13, residue 1622. -/ +theorem bounds_13_1622 : exactInterval 13 1622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1622 : oddCount 1622 13 = 6 ∧ acceleratedOrbit 13 1622 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1622) = 3 ^ 6 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1622.1, data_13_1622.2] + +/-- Complete interval computation for depth 13, residue 1623. -/ +theorem bounds_13_1623 : exactInterval 13 1623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1623 : oddCount 1623 13 = 6 ∧ acceleratedOrbit 13 1623 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1623) = 3 ^ 6 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1623.1, data_13_1623.2] + +/-- Complete interval computation for depth 13, residue 1624. -/ +theorem bounds_13_1624 : exactInterval 13 1624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1624 : oddCount 1624 13 = 5 ∧ acceleratedOrbit 13 1624 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1624) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1624.1, data_13_1624.2] + +/-- Complete interval computation for depth 13, residue 1625. -/ +theorem bounds_13_1625 : exactInterval 13 1625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1625 : oddCount 1625 13 = 6 ∧ acceleratedOrbit 13 1625 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1625) = 3 ^ 6 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1625.1, data_13_1625.2] + +/-- Complete interval computation for depth 13, residue 1626. -/ +theorem bounds_13_1626 : exactInterval 13 1626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1626 : oddCount 1626 13 = 5 ∧ acceleratedOrbit 13 1626 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1626) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1626.1, data_13_1626.2] + +/-- Complete interval computation for depth 13, residue 1627. -/ +theorem bounds_13_1627 : exactInterval 13 1627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1627 : oddCount 1627 13 = 9 ∧ acceleratedOrbit 13 1627 = 3914 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1627) = 3 ^ 9 * m + 3914 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1627.1, data_13_1627.2] + +/-- Complete interval computation for depth 13, residue 1628. -/ +theorem bounds_13_1628 : exactInterval 13 1628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1628 : oddCount 1628 13 = 5 ∧ acceleratedOrbit 13 1628 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1628) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1628.1, data_13_1628.2] + +/-- Complete interval computation for depth 13, residue 1629. -/ +theorem bounds_13_1629 : exactInterval 13 1629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1629 : oddCount 1629 13 = 5 ∧ acceleratedOrbit 13 1629 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1629) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1629.1, data_13_1629.2] + +/-- Complete interval computation for depth 13, residue 1630. -/ +theorem bounds_13_1630 : exactInterval 13 1630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1630 : oddCount 1630 13 = 7 ∧ acceleratedOrbit 13 1630 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1630) = 3 ^ 7 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1630.1, data_13_1630.2] + +/-- Complete interval computation for depth 13, residue 1631. -/ +theorem bounds_13_1631 : exactInterval 13 1631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1631) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1631 : oddCount 1631 13 = 7 ∧ acceleratedOrbit 13 1631 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1631) = 3 ^ 7 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1631.1, data_13_1631.2] + +/-- Complete interval computation for depth 13, residue 1632. -/ +theorem bounds_13_1632 : exactInterval 13 1632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1632 : oddCount 1632 13 = 4 ∧ acceleratedOrbit 13 1632 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1632) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1632.1, data_13_1632.2] + +end Collatz.Research.StoppingAtlas.Batch0573 From e36cde598b709b97e87832f43b7b9a1f5631a530 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:37 +0530 Subject: [PATCH 0574/1001] proof: certify atlas Batch0574 (13:1633 to 13:1647) --- Collatz/Research/StoppingAtlas/Batch0574.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0574.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0574.lean b/Collatz/Research/StoppingAtlas/Batch0574.lean new file mode 100644 index 00000000..08f90d40 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0574.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0574 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1633. -/ +theorem bounds_13_1633 : exactInterval 13 1633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1633 : oddCount 1633 13 = 6 ∧ acceleratedOrbit 13 1633 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1633) = 3 ^ 6 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1633.1, data_13_1633.2] + +/-- Complete interval computation for depth 13, residue 1634. -/ +theorem bounds_13_1634 : exactInterval 13 1634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1634 : oddCount 1634 13 = 5 ∧ acceleratedOrbit 13 1634 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1634) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1634.1, data_13_1634.2] + +/-- Complete interval computation for depth 13, residue 1635. -/ +theorem bounds_13_1635 : exactInterval 13 1635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1635 : oddCount 1635 13 = 5 ∧ acceleratedOrbit 13 1635 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1635) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1635.1, data_13_1635.2] + +/-- Complete interval computation for depth 13, residue 1636. -/ +theorem bounds_13_1636 : exactInterval 13 1636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1636 : oddCount 1636 13 = 5 ∧ acceleratedOrbit 13 1636 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1636) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1636.1, data_13_1636.2] + +/-- Complete interval computation for depth 13, residue 1637. -/ +theorem bounds_13_1637 : exactInterval 13 1637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1637 : oddCount 1637 13 = 5 ∧ acceleratedOrbit 13 1637 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1637) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1637.1, data_13_1637.2] + +/-- Complete interval computation for depth 13, residue 1638. -/ +theorem bounds_13_1638 : exactInterval 13 1638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1638 : oddCount 1638 13 = 5 ∧ acceleratedOrbit 13 1638 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1638) = 3 ^ 5 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1638.1, data_13_1638.2] + +/-- Complete interval computation for depth 13, residue 1639. -/ +theorem bounds_13_1639 : exactInterval 13 1639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1639 : oddCount 1639 13 = 10 ∧ acceleratedOrbit 13 1639 = 11825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1639) = 3 ^ 10 * m + 11825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1639.1, data_13_1639.2] + +/-- Complete interval computation for depth 13, residue 1640. -/ +theorem bounds_13_1640 : exactInterval 13 1640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1640 : oddCount 1640 13 = 4 ∧ acceleratedOrbit 13 1640 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1640) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1640.1, data_13_1640.2] + +/-- Complete interval computation for depth 13, residue 1641. -/ +theorem bounds_13_1641 : exactInterval 13 1641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1641 : oddCount 1641 13 = 8 ∧ acceleratedOrbit 13 1641 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1641) = 3 ^ 8 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1641.1, data_13_1641.2] + +/-- Complete interval computation for depth 13, residue 1642. -/ +theorem bounds_13_1642 : exactInterval 13 1642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1642 : oddCount 1642 13 = 4 ∧ acceleratedOrbit 13 1642 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1642) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1642.1, data_13_1642.2] + +/-- Complete interval computation for depth 13, residue 1643. -/ +theorem bounds_13_1643 : exactInterval 13 1643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1643 : oddCount 1643 13 = 8 ∧ acceleratedOrbit 13 1643 = 1318 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1643) = 3 ^ 8 * m + 1318 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1643.1, data_13_1643.2] + +/-- Complete interval computation for depth 13, residue 1644. -/ +theorem bounds_13_1644 : exactInterval 13 1644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1644 : oddCount 1644 13 = 8 ∧ acceleratedOrbit 13 1644 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1644) = 3 ^ 8 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1644.1, data_13_1644.2] + +/-- Complete interval computation for depth 13, residue 1645. -/ +theorem bounds_13_1645 : exactInterval 13 1645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1645 : oddCount 1645 13 = 8 ∧ acceleratedOrbit 13 1645 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1645) = 3 ^ 8 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1645.1, data_13_1645.2] + +/-- Complete interval computation for depth 13, residue 1646. -/ +theorem bounds_13_1646 : exactInterval 13 1646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1646 : oddCount 1646 13 = 8 ∧ acceleratedOrbit 13 1646 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1646) = 3 ^ 8 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1646.1, data_13_1646.2] + +/-- Complete interval computation for depth 13, residue 1647. -/ +theorem bounds_13_1647 : exactInterval 13 1647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1647 : oddCount 1647 13 = 7 ∧ acceleratedOrbit 13 1647 = 440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1647) = 3 ^ 7 * m + 440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1647.1, data_13_1647.2] + +end Collatz.Research.StoppingAtlas.Batch0574 From be4811b06c2b1c4d706ab4fe8416cd658000be43 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:38 +0530 Subject: [PATCH 0575/1001] proof: certify atlas Batch0575 (13:1648 to 13:1663) --- Collatz/Research/StoppingAtlas/Batch0575.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0575.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0575.lean b/Collatz/Research/StoppingAtlas/Batch0575.lean new file mode 100644 index 00000000..5172f6c3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0575.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0575 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1648. -/ +theorem bounds_13_1648 : exactInterval 13 1648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1648 : oddCount 1648 13 = 7 ∧ acceleratedOrbit 13 1648 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1648) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1648.1, data_13_1648.2] + +/-- Complete interval computation for depth 13, residue 1649. -/ +theorem bounds_13_1649 : exactInterval 13 1649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1649 : oddCount 1649 13 = 4 ∧ acceleratedOrbit 13 1649 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1649) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1649.1, data_13_1649.2] + +/-- Complete interval computation for depth 13, residue 1650. -/ +theorem bounds_13_1650 : exactInterval 13 1650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1650 : oddCount 1650 13 = 7 ∧ acceleratedOrbit 13 1650 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1650) = 3 ^ 7 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1650.1, data_13_1650.2] + +/-- Complete interval computation for depth 13, residue 1651. -/ +theorem bounds_13_1651 : exactInterval 13 1651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1651 : oddCount 1651 13 = 7 ∧ acceleratedOrbit 13 1651 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1651) = 3 ^ 7 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1651.1, data_13_1651.2] + +/-- Complete interval computation for depth 13, residue 1652. -/ +theorem bounds_13_1652 : exactInterval 13 1652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1652 : oddCount 1652 13 = 7 ∧ acceleratedOrbit 13 1652 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1652) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1652.1, data_13_1652.2] + +/-- Complete interval computation for depth 13, residue 1653. -/ +theorem bounds_13_1653 : exactInterval 13 1653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1653 : oddCount 1653 13 = 7 ∧ acceleratedOrbit 13 1653 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1653) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1653.1, data_13_1653.2] + +/-- Complete interval computation for depth 13, residue 1654. -/ +theorem bounds_13_1654 : exactInterval 13 1654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1654 : oddCount 1654 13 = 6 ∧ acceleratedOrbit 13 1654 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1654) = 3 ^ 6 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1654.1, data_13_1654.2] + +/-- Complete interval computation for depth 13, residue 1655. -/ +theorem bounds_13_1655 : exactInterval 13 1655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1655 : oddCount 1655 13 = 6 ∧ acceleratedOrbit 13 1655 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1655) = 3 ^ 6 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1655.1, data_13_1655.2] + +/-- Complete interval computation for depth 13, residue 1656. -/ +theorem bounds_13_1656 : exactInterval 13 1656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1656 : oddCount 1656 13 = 7 ∧ acceleratedOrbit 13 1656 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1656) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1656.1, data_13_1656.2] + +/-- Complete interval computation for depth 13, residue 1657. -/ +theorem bounds_13_1657 : exactInterval 13 1657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1657 : oddCount 1657 13 = 7 ∧ acceleratedOrbit 13 1657 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1657) = 3 ^ 7 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1657.1, data_13_1657.2] + +/-- Complete interval computation for depth 13, residue 1658. -/ +theorem bounds_13_1658 : exactInterval 13 1658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1658 : oddCount 1658 13 = 7 ∧ acceleratedOrbit 13 1658 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1658) = 3 ^ 7 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1658.1, data_13_1658.2] + +/-- Complete interval computation for depth 13, residue 1659. -/ +theorem bounds_13_1659 : exactInterval 13 1659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1659 : oddCount 1659 13 = 6 ∧ acceleratedOrbit 13 1659 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1659) = 3 ^ 6 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1659.1, data_13_1659.2] + +/-- Complete interval computation for depth 13, residue 1660. -/ +theorem bounds_13_1660 : exactInterval 13 1660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1660 : oddCount 1660 13 = 8 ∧ acceleratedOrbit 13 1660 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1660) = 3 ^ 8 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1660.1, data_13_1660.2] + +/-- Complete interval computation for depth 13, residue 1661. -/ +theorem bounds_13_1661 : exactInterval 13 1661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1661 : oddCount 1661 13 = 8 ∧ acceleratedOrbit 13 1661 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1661) = 3 ^ 8 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1661.1, data_13_1661.2] + +/-- Complete interval computation for depth 13, residue 1662. -/ +theorem bounds_13_1662 : exactInterval 13 1662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1662 : oddCount 1662 13 = 8 ∧ acceleratedOrbit 13 1662 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1662) = 3 ^ 8 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1662.1, data_13_1662.2] + +/-- Complete interval computation for depth 13, residue 1663. -/ +theorem bounds_13_1663 : exactInterval 13 1663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1663 : oddCount 1663 13 = 11 ∧ acceleratedOrbit 13 1663 = 35984 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1663) = 3 ^ 11 * m + 35984 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1663.1, data_13_1663.2] + +end Collatz.Research.StoppingAtlas.Batch0575 From 8c389872755ddeef807fa19065972001e2c1451e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:39 +0530 Subject: [PATCH 0576/1001] proof: certify atlas Batch0576 (13:1664 to 13:1678) --- Collatz/Research/StoppingAtlas/Batch0576.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0576.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0576.lean b/Collatz/Research/StoppingAtlas/Batch0576.lean new file mode 100644 index 00000000..91bd9458 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0576.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0576 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1664. -/ +theorem bounds_13_1664 : exactInterval 13 1664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1664 : oddCount 1664 13 = 2 ∧ acceleratedOrbit 13 1664 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1664) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1664.1, data_13_1664.2] + +/-- Complete interval computation for depth 13, residue 1665. -/ +theorem bounds_13_1665 : exactInterval 13 1665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1665 : oddCount 1665 13 = 9 ∧ acceleratedOrbit 13 1665 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1665) = 3 ^ 9 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1665.1, data_13_1665.2] + +/-- Complete interval computation for depth 13, residue 1666. -/ +theorem bounds_13_1666 : exactInterval 13 1666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1666 : oddCount 1666 13 = 4 ∧ acceleratedOrbit 13 1666 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1666) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1666.1, data_13_1666.2] + +/-- Complete interval computation for depth 13, residue 1667. -/ +theorem bounds_13_1667 : exactInterval 13 1667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1667 : oddCount 1667 13 = 4 ∧ acceleratedOrbit 13 1667 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1667) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1667.1, data_13_1667.2] + +/-- Complete interval computation for depth 13, residue 1668. -/ +theorem bounds_13_1668 : exactInterval 13 1668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1668 : oddCount 1668 13 = 7 ∧ acceleratedOrbit 13 1668 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1668) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1668.1, data_13_1668.2] + +/-- Complete interval computation for depth 13, residue 1669. -/ +theorem bounds_13_1669 : exactInterval 13 1669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1669 : oddCount 1669 13 = 7 ∧ acceleratedOrbit 13 1669 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1669) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1669.1, data_13_1669.2] + +/-- Complete interval computation for depth 13, residue 1670. -/ +theorem bounds_13_1670 : exactInterval 13 1670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1670 : oddCount 1670 13 = 7 ∧ acceleratedOrbit 13 1670 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1670) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1670.1, data_13_1670.2] + +/-- Complete interval computation for depth 13, residue 1671. -/ +theorem bounds_13_1671 : exactInterval 13 1671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1671 : oddCount 1671 13 = 6 ∧ acceleratedOrbit 13 1671 = 149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1671) = 3 ^ 6 * m + 149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1671.1, data_13_1671.2] + +/-- Complete interval computation for depth 13, residue 1672. -/ +theorem bounds_13_1672 : exactInterval 13 1672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1672 : oddCount 1672 13 = 6 ∧ acceleratedOrbit 13 1672 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1672) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1672.1, data_13_1672.2] + +/-- Complete interval computation for depth 13, residue 1673. -/ +theorem bounds_13_1673 : exactInterval 13 1673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1673 : oddCount 1673 13 = 9 ∧ acceleratedOrbit 13 1673 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1673) = 3 ^ 9 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1673.1, data_13_1673.2] + +/-- Complete interval computation for depth 13, residue 1674. -/ +theorem bounds_13_1674 : exactInterval 13 1674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1674 : oddCount 1674 13 = 6 ∧ acceleratedOrbit 13 1674 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1674) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1674.1, data_13_1674.2] + +/-- Complete interval computation for depth 13, residue 1675. -/ +theorem bounds_13_1675 : exactInterval 13 1675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1675 : oddCount 1675 13 = 7 ∧ acceleratedOrbit 13 1675 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1675) = 3 ^ 7 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1675.1, data_13_1675.2] + +/-- Complete interval computation for depth 13, residue 1676. -/ +theorem bounds_13_1676 : exactInterval 13 1676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1676 : oddCount 1676 13 = 6 ∧ acceleratedOrbit 13 1676 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1676) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1676.1, data_13_1676.2] + +/-- Complete interval computation for depth 13, residue 1677. -/ +theorem bounds_13_1677 : exactInterval 13 1677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1677 : oddCount 1677 13 = 6 ∧ acceleratedOrbit 13 1677 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1677) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1677.1, data_13_1677.2] + +/-- Complete interval computation for depth 13, residue 1678. -/ +theorem bounds_13_1678 : exactInterval 13 1678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1678 : oddCount 1678 13 = 9 ∧ acceleratedOrbit 13 1678 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1678) = 3 ^ 9 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1678.1, data_13_1678.2] + +end Collatz.Research.StoppingAtlas.Batch0576 From 3240d8f17cd903d8767c55e8f84ebe3f16b7c6a8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:40 +0530 Subject: [PATCH 0577/1001] proof: certify atlas Batch0577 (13:1679 to 13:1693) --- Collatz/Research/StoppingAtlas/Batch0577.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0577.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0577.lean b/Collatz/Research/StoppingAtlas/Batch0577.lean new file mode 100644 index 00000000..7b4e27a6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0577.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0577 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1679. -/ +theorem bounds_13_1679 : exactInterval 13 1679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1679 : oddCount 1679 13 = 9 ∧ acceleratedOrbit 13 1679 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1679) = 3 ^ 9 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1679.1, data_13_1679.2] + +/-- Complete interval computation for depth 13, residue 1680. -/ +theorem bounds_13_1680 : exactInterval 13 1680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1680 : oddCount 1680 13 = 6 ∧ acceleratedOrbit 13 1680 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1680) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1680.1, data_13_1680.2] + +/-- Complete interval computation for depth 13, residue 1681. -/ +theorem bounds_13_1681 : exactInterval 13 1681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1681 : oddCount 1681 13 = 5 ∧ acceleratedOrbit 13 1681 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1681) = 3 ^ 5 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1681.1, data_13_1681.2] + +/-- Complete interval computation for depth 13, residue 1682. -/ +theorem bounds_13_1682 : exactInterval 13 1682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1682 : oddCount 1682 13 = 5 ∧ acceleratedOrbit 13 1682 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1682) = 3 ^ 5 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1682.1, data_13_1682.2] + +/-- Complete interval computation for depth 13, residue 1683. -/ +theorem bounds_13_1683 : exactInterval 13 1683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1683 : oddCount 1683 13 = 5 ∧ acceleratedOrbit 13 1683 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1683) = 3 ^ 5 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1683.1, data_13_1683.2] + +/-- Complete interval computation for depth 13, residue 1684. -/ +theorem bounds_13_1684 : exactInterval 13 1684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1684 : oddCount 1684 13 = 6 ∧ acceleratedOrbit 13 1684 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1684) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1684.1, data_13_1684.2] + +/-- Complete interval computation for depth 13, residue 1685. -/ +theorem bounds_13_1685 : exactInterval 13 1685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1685 : oddCount 1685 13 = 6 ∧ acceleratedOrbit 13 1685 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1685) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1685.1, data_13_1685.2] + +/-- Complete interval computation for depth 13, residue 1686. -/ +theorem bounds_13_1686 : exactInterval 13 1686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1686 : oddCount 1686 13 = 6 ∧ acceleratedOrbit 13 1686 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1686) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1686.1, data_13_1686.2] + +/-- Complete interval computation for depth 13, residue 1687. -/ +theorem bounds_13_1687 : exactInterval 13 1687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1687 : oddCount 1687 13 = 6 ∧ acceleratedOrbit 13 1687 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1687) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1687.1, data_13_1687.2] + +/-- Complete interval computation for depth 13, residue 1688. -/ +theorem bounds_13_1688 : exactInterval 13 1688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1688 : oddCount 1688 13 = 6 ∧ acceleratedOrbit 13 1688 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1688) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1688.1, data_13_1688.2] + +/-- Complete interval computation for depth 13, residue 1689. -/ +theorem bounds_13_1689 : exactInterval 13 1689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1689 : oddCount 1689 13 = 7 ∧ acceleratedOrbit 13 1689 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1689) = 3 ^ 7 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1689.1, data_13_1689.2] + +/-- Complete interval computation for depth 13, residue 1690. -/ +theorem bounds_13_1690 : exactInterval 13 1690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1690 : oddCount 1690 13 = 6 ∧ acceleratedOrbit 13 1690 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1690) = 3 ^ 6 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1690.1, data_13_1690.2] + +/-- Complete interval computation for depth 13, residue 1691. -/ +theorem bounds_13_1691 : exactInterval 13 1691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1691 : oddCount 1691 13 = 9 ∧ acceleratedOrbit 13 1691 = 4067 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1691) = 3 ^ 9 * m + 4067 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1691.1, data_13_1691.2] + +/-- Complete interval computation for depth 13, residue 1692. -/ +theorem bounds_13_1692 : exactInterval 13 1692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1692 : oddCount 1692 13 = 6 ∧ acceleratedOrbit 13 1692 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1692) = 3 ^ 6 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1692.1, data_13_1692.2] + +/-- Complete interval computation for depth 13, residue 1693. -/ +theorem bounds_13_1693 : exactInterval 13 1693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1693 : oddCount 1693 13 = 6 ∧ acceleratedOrbit 13 1693 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1693) = 3 ^ 6 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1693.1, data_13_1693.2] + +end Collatz.Research.StoppingAtlas.Batch0577 From 2c1737f73560f2808e3ba2882adfa9abf7e2408c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:40 +0530 Subject: [PATCH 0578/1001] proof: certify atlas Batch0578 (13:1694 to 13:1709) --- Collatz/Research/StoppingAtlas/Batch0578.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0578.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0578.lean b/Collatz/Research/StoppingAtlas/Batch0578.lean new file mode 100644 index 00000000..cdb9d994 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0578.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0578 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1694. -/ +theorem bounds_13_1694 : exactInterval 13 1694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1694 : oddCount 1694 13 = 6 ∧ acceleratedOrbit 13 1694 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1694) = 3 ^ 6 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1694.1, data_13_1694.2] + +/-- Complete interval computation for depth 13, residue 1695. -/ +theorem bounds_13_1695 : exactInterval 13 1695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1695 : oddCount 1695 13 = 10 ∧ acceleratedOrbit 13 1695 = 12226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1695) = 3 ^ 10 * m + 12226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1695.1, data_13_1695.2] + +/-- Complete interval computation for depth 13, residue 1696. -/ +theorem bounds_13_1696 : exactInterval 13 1696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1696 : oddCount 1696 13 = 2 ∧ acceleratedOrbit 13 1696 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1696) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1696.1, data_13_1696.2] + +/-- Complete interval computation for depth 13, residue 1697. -/ +theorem bounds_13_1697 : exactInterval 13 1697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1697 : oddCount 1697 13 = 7 ∧ acceleratedOrbit 13 1697 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1697) = 3 ^ 7 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1697.1, data_13_1697.2] + +/-- Complete interval computation for depth 13, residue 1698. -/ +theorem bounds_13_1698 : exactInterval 13 1698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1698 : oddCount 1698 13 = 8 ∧ acceleratedOrbit 13 1698 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1698) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1698.1, data_13_1698.2] + +/-- Complete interval computation for depth 13, residue 1699. -/ +theorem bounds_13_1699 : exactInterval 13 1699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1699 : oddCount 1699 13 = 8 ∧ acceleratedOrbit 13 1699 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1699) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1699.1, data_13_1699.2] + +/-- Complete interval computation for depth 13, residue 1700. -/ +theorem bounds_13_1700 : exactInterval 13 1700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1700 : oddCount 1700 13 = 8 ∧ acceleratedOrbit 13 1700 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1700) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1700.1, data_13_1700.2] + +/-- Complete interval computation for depth 13, residue 1701. -/ +theorem bounds_13_1701 : exactInterval 13 1701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1701 : oddCount 1701 13 = 8 ∧ acceleratedOrbit 13 1701 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1701) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1701.1, data_13_1701.2] + +/-- Complete interval computation for depth 13, residue 1702. -/ +theorem bounds_13_1702 : exactInterval 13 1702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1702 : oddCount 1702 13 = 8 ∧ acceleratedOrbit 13 1702 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1702) = 3 ^ 8 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1702.1, data_13_1702.2] + +/-- Complete interval computation for depth 13, residue 1703. -/ +theorem bounds_13_1703 : exactInterval 13 1703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1703 : oddCount 1703 13 = 7 ∧ acceleratedOrbit 13 1703 = 455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1703) = 3 ^ 7 * m + 455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1703.1, data_13_1703.2] + +/-- Complete interval computation for depth 13, residue 1704. -/ +theorem bounds_13_1704 : exactInterval 13 1704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1704 : oddCount 1704 13 = 2 ∧ acceleratedOrbit 13 1704 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1704) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1704.1, data_13_1704.2] + +/-- Complete interval computation for depth 13, residue 1705. -/ +theorem bounds_13_1705 : exactInterval 13 1705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1705 : oddCount 1705 13 = 10 ∧ acceleratedOrbit 13 1705 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1705) = 3 ^ 10 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1705.1, data_13_1705.2] + +/-- Complete interval computation for depth 13, residue 1706. -/ +theorem bounds_13_1706 : exactInterval 13 1706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1706 : oddCount 1706 13 = 2 ∧ acceleratedOrbit 13 1706 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1706) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1706.1, data_13_1706.2] + +/-- Complete interval computation for depth 13, residue 1707. -/ +theorem bounds_13_1707 : exactInterval 13 1707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1707 : oddCount 1707 13 = 8 ∧ acceleratedOrbit 13 1707 = 1370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1707) = 3 ^ 8 * m + 1370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1707.1, data_13_1707.2] + +/-- Complete interval computation for depth 13, residue 1708. -/ +theorem bounds_13_1708 : exactInterval 13 1708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1708 : oddCount 1708 13 = 8 ∧ acceleratedOrbit 13 1708 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1708) = 3 ^ 8 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1708.1, data_13_1708.2] + +/-- Complete interval computation for depth 13, residue 1709. -/ +theorem bounds_13_1709 : exactInterval 13 1709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1709 : oddCount 1709 13 = 8 ∧ acceleratedOrbit 13 1709 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1709) = 3 ^ 8 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1709.1, data_13_1709.2] + +end Collatz.Research.StoppingAtlas.Batch0578 From aa7ea2ca0e94322b4c9cc92734de9522ac156b2c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:40 +0530 Subject: [PATCH 0579/1001] proof: certify atlas Batch0579 (13:1710 to 13:1724) --- Collatz/Research/StoppingAtlas/Batch0579.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0579.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0579.lean b/Collatz/Research/StoppingAtlas/Batch0579.lean new file mode 100644 index 00000000..86824ef4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0579.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0579 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1710. -/ +theorem bounds_13_1710 : exactInterval 13 1710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1710 : oddCount 1710 13 = 8 ∧ acceleratedOrbit 13 1710 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1710) = 3 ^ 8 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1710.1, data_13_1710.2] + +/-- Complete interval computation for depth 13, residue 1711. -/ +theorem bounds_13_1711 : exactInterval 13 1711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1711 : oddCount 1711 13 = 8 ∧ acceleratedOrbit 13 1711 = 1372 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1711) = 3 ^ 8 * m + 1372 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1711.1, data_13_1711.2] + +/-- Complete interval computation for depth 13, residue 1712. -/ +theorem bounds_13_1712 : exactInterval 13 1712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1712 : oddCount 1712 13 = 6 ∧ acceleratedOrbit 13 1712 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1712) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1712.1, data_13_1712.2] + +/-- Complete interval computation for depth 13, residue 1713. -/ +theorem bounds_13_1713 : exactInterval 13 1713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1713 : oddCount 1713 13 = 4 ∧ acceleratedOrbit 13 1713 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1713) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1713.1, data_13_1713.2] + +/-- Complete interval computation for depth 13, residue 1714. -/ +theorem bounds_13_1714 : exactInterval 13 1714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1714 : oddCount 1714 13 = 4 ∧ acceleratedOrbit 13 1714 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1714) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1714.1, data_13_1714.2] + +/-- Complete interval computation for depth 13, residue 1715. -/ +theorem bounds_13_1715 : exactInterval 13 1715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1715 : oddCount 1715 13 = 4 ∧ acceleratedOrbit 13 1715 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1715) = 3 ^ 4 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1715.1, data_13_1715.2] + +/-- Complete interval computation for depth 13, residue 1716. -/ +theorem bounds_13_1716 : exactInterval 13 1716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1716 : oddCount 1716 13 = 6 ∧ acceleratedOrbit 13 1716 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1716) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1716.1, data_13_1716.2] + +/-- Complete interval computation for depth 13, residue 1717. -/ +theorem bounds_13_1717 : exactInterval 13 1717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1717 : oddCount 1717 13 = 6 ∧ acceleratedOrbit 13 1717 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1717) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1717.1, data_13_1717.2] + +/-- Complete interval computation for depth 13, residue 1718. -/ +theorem bounds_13_1718 : exactInterval 13 1718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1718 : oddCount 1718 13 = 8 ∧ acceleratedOrbit 13 1718 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1718) = 3 ^ 8 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1718.1, data_13_1718.2] + +/-- Complete interval computation for depth 13, residue 1719. -/ +theorem bounds_13_1719 : exactInterval 13 1719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1719 : oddCount 1719 13 = 8 ∧ acceleratedOrbit 13 1719 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1719) = 3 ^ 8 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1719.1, data_13_1719.2] + +/-- Complete interval computation for depth 13, residue 1720. -/ +theorem bounds_13_1720 : exactInterval 13 1720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1720 : oddCount 1720 13 = 6 ∧ acceleratedOrbit 13 1720 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1720) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1720.1, data_13_1720.2] + +/-- Complete interval computation for depth 13, residue 1721. -/ +theorem bounds_13_1721 : exactInterval 13 1721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1721 : oddCount 1721 13 = 7 ∧ acceleratedOrbit 13 1721 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1721) = 3 ^ 7 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1721.1, data_13_1721.2] + +/-- Complete interval computation for depth 13, residue 1722. -/ +theorem bounds_13_1722 : exactInterval 13 1722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1722 : oddCount 1722 13 = 6 ∧ acceleratedOrbit 13 1722 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1722) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1722.1, data_13_1722.2] + +/-- Complete interval computation for depth 13, residue 1723. -/ +theorem bounds_13_1723 : exactInterval 13 1723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1723 : oddCount 1723 13 = 7 ∧ acceleratedOrbit 13 1723 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1723) = 3 ^ 7 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1723.1, data_13_1723.2] + +/-- Complete interval computation for depth 13, residue 1724. -/ +theorem bounds_13_1724 : exactInterval 13 1724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1724 : oddCount 1724 13 = 6 ∧ acceleratedOrbit 13 1724 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1724) = 3 ^ 6 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1724.1, data_13_1724.2] + +end Collatz.Research.StoppingAtlas.Batch0579 From 6ac05201defd5189dac84b122975e442afef37a8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:41 +0530 Subject: [PATCH 0580/1001] proof: certify atlas Batch0580 (13:1725 to 13:1739) --- Collatz/Research/StoppingAtlas/Batch0580.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0580.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0580.lean b/Collatz/Research/StoppingAtlas/Batch0580.lean new file mode 100644 index 00000000..19b5ea21 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0580.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0580 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1725. -/ +theorem bounds_13_1725 : exactInterval 13 1725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1725 : oddCount 1725 13 = 6 ∧ acceleratedOrbit 13 1725 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1725) = 3 ^ 6 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1725.1, data_13_1725.2] + +/-- Complete interval computation for depth 13, residue 1726. -/ +theorem bounds_13_1726 : exactInterval 13 1726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1726 : oddCount 1726 13 = 6 ∧ acceleratedOrbit 13 1726 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1726) = 3 ^ 6 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1726.1, data_13_1726.2] + +/-- Complete interval computation for depth 13, residue 1727. -/ +theorem bounds_13_1727 : exactInterval 13 1727 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1727) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1727 : oddCount 1727 13 = 8 ∧ acceleratedOrbit 13 1727 = 1384 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1727) = 3 ^ 8 * m + 1384 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1727.1, data_13_1727.2] + +/-- Complete interval computation for depth 13, residue 1728. -/ +theorem bounds_13_1728 : exactInterval 13 1728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1728 : oddCount 1728 13 = 6 ∧ acceleratedOrbit 13 1728 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1728) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1728.1, data_13_1728.2] + +/-- Complete interval computation for depth 13, residue 1729. -/ +theorem bounds_13_1729 : exactInterval 13 1729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1729 : oddCount 1729 13 = 6 ∧ acceleratedOrbit 13 1729 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1729) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1729.1, data_13_1729.2] + +/-- Complete interval computation for depth 13, residue 1730. -/ +theorem bounds_13_1730 : exactInterval 13 1730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1730 : oddCount 1730 13 = 8 ∧ acceleratedOrbit 13 1730 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1730) = 3 ^ 8 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1730.1, data_13_1730.2] + +/-- Complete interval computation for depth 13, residue 1731. -/ +theorem bounds_13_1731 : exactInterval 13 1731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1731 : oddCount 1731 13 = 8 ∧ acceleratedOrbit 13 1731 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1731) = 3 ^ 8 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1731.1, data_13_1731.2] + +/-- Complete interval computation for depth 13, residue 1732. -/ +theorem bounds_13_1732 : exactInterval 13 1732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1732 : oddCount 1732 13 = 5 ∧ acceleratedOrbit 13 1732 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1732) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1732.1, data_13_1732.2] + +/-- Complete interval computation for depth 13, residue 1733. -/ +theorem bounds_13_1733 : exactInterval 13 1733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1733 : oddCount 1733 13 = 5 ∧ acceleratedOrbit 13 1733 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1733) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1733.1, data_13_1733.2] + +/-- Complete interval computation for depth 13, residue 1734. -/ +theorem bounds_13_1734 : exactInterval 13 1734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1734 : oddCount 1734 13 = 5 ∧ acceleratedOrbit 13 1734 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1734) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1734.1, data_13_1734.2] + +/-- Complete interval computation for depth 13, residue 1735. -/ +theorem bounds_13_1735 : exactInterval 13 1735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1735 : oddCount 1735 13 = 6 ∧ acceleratedOrbit 13 1735 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1735) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1735.1, data_13_1735.2] + +/-- Complete interval computation for depth 13, residue 1736. -/ +theorem bounds_13_1736 : exactInterval 13 1736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1736 : oddCount 1736 13 = 5 ∧ acceleratedOrbit 13 1736 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1736) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1736.1, data_13_1736.2] + +/-- Complete interval computation for depth 13, residue 1737. -/ +theorem bounds_13_1737 : exactInterval 13 1737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1737 : oddCount 1737 13 = 6 ∧ acceleratedOrbit 13 1737 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1737) = 3 ^ 6 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1737.1, data_13_1737.2] + +/-- Complete interval computation for depth 13, residue 1738. -/ +theorem bounds_13_1738 : exactInterval 13 1738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1738 : oddCount 1738 13 = 5 ∧ acceleratedOrbit 13 1738 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1738) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1738.1, data_13_1738.2] + +/-- Complete interval computation for depth 13, residue 1739. -/ +theorem bounds_13_1739 : exactInterval 13 1739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1739 : oddCount 1739 13 = 8 ∧ acceleratedOrbit 13 1739 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1739) = 3 ^ 8 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1739.1, data_13_1739.2] + +end Collatz.Research.StoppingAtlas.Batch0580 From 3e7a3532ef79f392a0281230506c8c401285ab84 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:42 +0530 Subject: [PATCH 0581/1001] proof: certify atlas Batch0581 (13:1740 to 13:1755) --- Collatz/Research/StoppingAtlas/Batch0581.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0581.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0581.lean b/Collatz/Research/StoppingAtlas/Batch0581.lean new file mode 100644 index 00000000..212de9b1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0581.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0581 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1740. -/ +theorem bounds_13_1740 : exactInterval 13 1740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1740 : oddCount 1740 13 = 5 ∧ acceleratedOrbit 13 1740 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1740) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1740.1, data_13_1740.2] + +/-- Complete interval computation for depth 13, residue 1741. -/ +theorem bounds_13_1741 : exactInterval 13 1741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1741 : oddCount 1741 13 = 5 ∧ acceleratedOrbit 13 1741 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1741) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1741.1, data_13_1741.2] + +/-- Complete interval computation for depth 13, residue 1742. -/ +theorem bounds_13_1742 : exactInterval 13 1742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1742 : oddCount 1742 13 = 10 ∧ acceleratedOrbit 13 1742 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1742) = 3 ^ 10 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1742.1, data_13_1742.2] + +/-- Complete interval computation for depth 13, residue 1743. -/ +theorem bounds_13_1743 : exactInterval 13 1743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1743 : oddCount 1743 13 = 10 ∧ acceleratedOrbit 13 1743 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1743) = 3 ^ 10 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1743.1, data_13_1743.2] + +/-- Complete interval computation for depth 13, residue 1744. -/ +theorem bounds_13_1744 : exactInterval 13 1744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1744 : oddCount 1744 13 = 6 ∧ acceleratedOrbit 13 1744 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1744) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1744.1, data_13_1744.2] + +/-- Complete interval computation for depth 13, residue 1745. -/ +theorem bounds_13_1745 : exactInterval 13 1745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1745 : oddCount 1745 13 = 8 ∧ acceleratedOrbit 13 1745 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1745) = 3 ^ 8 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1745.1, data_13_1745.2] + +/-- Complete interval computation for depth 13, residue 1746. -/ +theorem bounds_13_1746 : exactInterval 13 1746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1746 : oddCount 1746 13 = 8 ∧ acceleratedOrbit 13 1746 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1746) = 3 ^ 8 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1746.1, data_13_1746.2] + +/-- Complete interval computation for depth 13, residue 1747. -/ +theorem bounds_13_1747 : exactInterval 13 1747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1747 : oddCount 1747 13 = 8 ∧ acceleratedOrbit 13 1747 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1747) = 3 ^ 8 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1747.1, data_13_1747.2] + +/-- Complete interval computation for depth 13, residue 1748. -/ +theorem bounds_13_1748 : exactInterval 13 1748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1748 : oddCount 1748 13 = 6 ∧ acceleratedOrbit 13 1748 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1748) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1748.1, data_13_1748.2] + +/-- Complete interval computation for depth 13, residue 1749. -/ +theorem bounds_13_1749 : exactInterval 13 1749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1749 : oddCount 1749 13 = 6 ∧ acceleratedOrbit 13 1749 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1749) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1749.1, data_13_1749.2] + +/-- Complete interval computation for depth 13, residue 1750. -/ +theorem bounds_13_1750 : exactInterval 13 1750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1750 : oddCount 1750 13 = 5 ∧ acceleratedOrbit 13 1750 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1750) = 3 ^ 5 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1750.1, data_13_1750.2] + +/-- Complete interval computation for depth 13, residue 1751. -/ +theorem bounds_13_1751 : exactInterval 13 1751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1751 : oddCount 1751 13 = 5 ∧ acceleratedOrbit 13 1751 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1751) = 3 ^ 5 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1751.1, data_13_1751.2] + +/-- Complete interval computation for depth 13, residue 1752. -/ +theorem bounds_13_1752 : exactInterval 13 1752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1752 : oddCount 1752 13 = 6 ∧ acceleratedOrbit 13 1752 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1752) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1752.1, data_13_1752.2] + +/-- Complete interval computation for depth 13, residue 1753. -/ +theorem bounds_13_1753 : exactInterval 13 1753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1753 : oddCount 1753 13 = 6 ∧ acceleratedOrbit 13 1753 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1753) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1753.1, data_13_1753.2] + +/-- Complete interval computation for depth 13, residue 1754. -/ +theorem bounds_13_1754 : exactInterval 13 1754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1754 : oddCount 1754 13 = 6 ∧ acceleratedOrbit 13 1754 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1754) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1754.1, data_13_1754.2] + +/-- Complete interval computation for depth 13, residue 1755. -/ +theorem bounds_13_1755 : exactInterval 13 1755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1755 : oddCount 1755 13 = 7 ∧ acceleratedOrbit 13 1755 = 469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1755) = 3 ^ 7 * m + 469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1755.1, data_13_1755.2] + +end Collatz.Research.StoppingAtlas.Batch0581 From 29aa326697a0a9c4c9feabfe79582b608ed9453c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:42 +0530 Subject: [PATCH 0582/1001] proof: certify atlas Batch0582 (13:1756 to 13:1770) --- Collatz/Research/StoppingAtlas/Batch0582.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0582.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0582.lean b/Collatz/Research/StoppingAtlas/Batch0582.lean new file mode 100644 index 00000000..72708b9d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0582.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0582 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1756. -/ +theorem bounds_13_1756 : exactInterval 13 1756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1756 : oddCount 1756 13 = 6 ∧ acceleratedOrbit 13 1756 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1756) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1756.1, data_13_1756.2] + +/-- Complete interval computation for depth 13, residue 1757. -/ +theorem bounds_13_1757 : exactInterval 13 1757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1757 : oddCount 1757 13 = 6 ∧ acceleratedOrbit 13 1757 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1757) = 3 ^ 6 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1757.1, data_13_1757.2] + +/-- Complete interval computation for depth 13, residue 1758. -/ +theorem bounds_13_1758 : exactInterval 13 1758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1758 : oddCount 1758 13 = 7 ∧ acceleratedOrbit 13 1758 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1758) = 3 ^ 7 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1758.1, data_13_1758.2] + +/-- Complete interval computation for depth 13, residue 1759. -/ +theorem bounds_13_1759 : exactInterval 13 1759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1759 : oddCount 1759 13 = 7 ∧ acceleratedOrbit 13 1759 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1759) = 3 ^ 7 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1759.1, data_13_1759.2] + +/-- Complete interval computation for depth 13, residue 1760. -/ +theorem bounds_13_1760 : exactInterval 13 1760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1760 : oddCount 1760 13 = 6 ∧ acceleratedOrbit 13 1760 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1760) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1760.1, data_13_1760.2] + +/-- Complete interval computation for depth 13, residue 1761. -/ +theorem bounds_13_1761 : exactInterval 13 1761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1761 : oddCount 1761 13 = 9 ∧ acceleratedOrbit 13 1761 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1761) = 3 ^ 9 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1761.1, data_13_1761.2] + +/-- Complete interval computation for depth 13, residue 1762. -/ +theorem bounds_13_1762 : exactInterval 13 1762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1762 : oddCount 1762 13 = 6 ∧ acceleratedOrbit 13 1762 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1762) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1762.1, data_13_1762.2] + +/-- Complete interval computation for depth 13, residue 1763. -/ +theorem bounds_13_1763 : exactInterval 13 1763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1763 : oddCount 1763 13 = 6 ∧ acceleratedOrbit 13 1763 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1763) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1763.1, data_13_1763.2] + +/-- Complete interval computation for depth 13, residue 1764. -/ +theorem bounds_13_1764 : exactInterval 13 1764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1764 : oddCount 1764 13 = 5 ∧ acceleratedOrbit 13 1764 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1764) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1764.1, data_13_1764.2] + +/-- Complete interval computation for depth 13, residue 1765. -/ +theorem bounds_13_1765 : exactInterval 13 1765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1765 : oddCount 1765 13 = 5 ∧ acceleratedOrbit 13 1765 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1765) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1765.1, data_13_1765.2] + +/-- Complete interval computation for depth 13, residue 1766. -/ +theorem bounds_13_1766 : exactInterval 13 1766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1766 : oddCount 1766 13 = 5 ∧ acceleratedOrbit 13 1766 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1766) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1766.1, data_13_1766.2] + +/-- Complete interval computation for depth 13, residue 1767. -/ +theorem bounds_13_1767 : exactInterval 13 1767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1767 : oddCount 1767 13 = 9 ∧ acceleratedOrbit 13 1767 = 4249 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1767) = 3 ^ 9 * m + 4249 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1767.1, data_13_1767.2] + +/-- Complete interval computation for depth 13, residue 1768. -/ +theorem bounds_13_1768 : exactInterval 13 1768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1768 : oddCount 1768 13 = 6 ∧ acceleratedOrbit 13 1768 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1768) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1768.1, data_13_1768.2] + +/-- Complete interval computation for depth 13, residue 1769. -/ +theorem bounds_13_1769 : exactInterval 13 1769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1769 : oddCount 1769 13 = 9 ∧ acceleratedOrbit 13 1769 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1769) = 3 ^ 9 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1769.1, data_13_1769.2] + +/-- Complete interval computation for depth 13, residue 1770. -/ +theorem bounds_13_1770 : exactInterval 13 1770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1770 : oddCount 1770 13 = 6 ∧ acceleratedOrbit 13 1770 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1770) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1770.1, data_13_1770.2] + +end Collatz.Research.StoppingAtlas.Batch0582 From b6736a576d68e2c2d51fbe04d0211b03631c6524 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:43 +0530 Subject: [PATCH 0583/1001] proof: certify atlas Batch0583 (13:1771 to 13:1785) --- Collatz/Research/StoppingAtlas/Batch0583.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0583.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0583.lean b/Collatz/Research/StoppingAtlas/Batch0583.lean new file mode 100644 index 00000000..effbc2b4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0583.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0583 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1771. -/ +theorem bounds_13_1771 : exactInterval 13 1771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1771 : oddCount 1771 13 = 8 ∧ acceleratedOrbit 13 1771 = 1421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1771) = 3 ^ 8 * m + 1421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1771.1, data_13_1771.2] + +/-- Complete interval computation for depth 13, residue 1772. -/ +theorem bounds_13_1772 : exactInterval 13 1772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1772 : oddCount 1772 13 = 7 ∧ acceleratedOrbit 13 1772 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1772) = 3 ^ 7 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1772.1, data_13_1772.2] + +/-- Complete interval computation for depth 13, residue 1773. -/ +theorem bounds_13_1773 : exactInterval 13 1773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1773 : oddCount 1773 13 = 7 ∧ acceleratedOrbit 13 1773 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1773) = 3 ^ 7 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1773.1, data_13_1773.2] + +/-- Complete interval computation for depth 13, residue 1774. -/ +theorem bounds_13_1774 : exactInterval 13 1774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1774 : oddCount 1774 13 = 7 ∧ acceleratedOrbit 13 1774 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1774) = 3 ^ 7 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1774.1, data_13_1774.2] + +/-- Complete interval computation for depth 13, residue 1775. -/ +theorem bounds_13_1775 : exactInterval 13 1775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1775 : oddCount 1775 13 = 9 ∧ acceleratedOrbit 13 1775 = 4268 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1775) = 3 ^ 9 * m + 4268 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1775.1, data_13_1775.2] + +/-- Complete interval computation for depth 13, residue 1776. -/ +theorem bounds_13_1776 : exactInterval 13 1776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1776 : oddCount 1776 13 = 7 ∧ acceleratedOrbit 13 1776 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1776) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1776.1, data_13_1776.2] + +/-- Complete interval computation for depth 13, residue 1777. -/ +theorem bounds_13_1777 : exactInterval 13 1777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1777 : oddCount 1777 13 = 6 ∧ acceleratedOrbit 13 1777 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1777) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1777.1, data_13_1777.2] + +/-- Complete interval computation for depth 13, residue 1778. -/ +theorem bounds_13_1778 : exactInterval 13 1778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1778 : oddCount 1778 13 = 9 ∧ acceleratedOrbit 13 1778 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1778) = 3 ^ 9 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1778.1, data_13_1778.2] + +/-- Complete interval computation for depth 13, residue 1779. -/ +theorem bounds_13_1779 : exactInterval 13 1779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1779 : oddCount 1779 13 = 9 ∧ acceleratedOrbit 13 1779 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1779) = 3 ^ 9 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1779.1, data_13_1779.2] + +/-- Complete interval computation for depth 13, residue 1780. -/ +theorem bounds_13_1780 : exactInterval 13 1780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1780 : oddCount 1780 13 = 7 ∧ acceleratedOrbit 13 1780 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1780) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1780.1, data_13_1780.2] + +/-- Complete interval computation for depth 13, residue 1781. -/ +theorem bounds_13_1781 : exactInterval 13 1781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1781 : oddCount 1781 13 = 7 ∧ acceleratedOrbit 13 1781 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1781) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1781.1, data_13_1781.2] + +/-- Complete interval computation for depth 13, residue 1782. -/ +theorem bounds_13_1782 : exactInterval 13 1782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1782 : oddCount 1782 13 = 9 ∧ acceleratedOrbit 13 1782 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1782) = 3 ^ 9 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1782.1, data_13_1782.2] + +/-- Complete interval computation for depth 13, residue 1783. -/ +theorem bounds_13_1783 : exactInterval 13 1783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1783 : oddCount 1783 13 = 9 ∧ acceleratedOrbit 13 1783 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1783) = 3 ^ 9 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1783.1, data_13_1783.2] + +/-- Complete interval computation for depth 13, residue 1784. -/ +theorem bounds_13_1784 : exactInterval 13 1784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1784 : oddCount 1784 13 = 7 ∧ acceleratedOrbit 13 1784 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1784) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1784.1, data_13_1784.2] + +/-- Complete interval computation for depth 13, residue 1785. -/ +theorem bounds_13_1785 : exactInterval 13 1785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1785 : oddCount 1785 13 = 5 ∧ acceleratedOrbit 13 1785 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1785) = 3 ^ 5 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1785.1, data_13_1785.2] + +end Collatz.Research.StoppingAtlas.Batch0583 From ce16698b573180895090ce7f4b596b813e72d31b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:43 +0530 Subject: [PATCH 0584/1001] proof: certify atlas Batch0584 (13:1786 to 13:1801) --- Collatz/Research/StoppingAtlas/Batch0584.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0584.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0584.lean b/Collatz/Research/StoppingAtlas/Batch0584.lean new file mode 100644 index 00000000..a09ad0d5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0584.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0584 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1786. -/ +theorem bounds_13_1786 : exactInterval 13 1786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1786 : oddCount 1786 13 = 7 ∧ acceleratedOrbit 13 1786 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1786) = 3 ^ 7 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1786.1, data_13_1786.2] + +/-- Complete interval computation for depth 13, residue 1787. -/ +theorem bounds_13_1787 : exactInterval 13 1787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1787 : oddCount 1787 13 = 8 ∧ acceleratedOrbit 13 1787 = 1433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1787) = 3 ^ 8 * m + 1433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1787.1, data_13_1787.2] + +/-- Complete interval computation for depth 13, residue 1788. -/ +theorem bounds_13_1788 : exactInterval 13 1788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1788 : oddCount 1788 13 = 9 ∧ acceleratedOrbit 13 1788 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1788) = 3 ^ 9 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1788.1, data_13_1788.2] + +/-- Complete interval computation for depth 13, residue 1789. -/ +theorem bounds_13_1789 : exactInterval 13 1789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1789 : oddCount 1789 13 = 9 ∧ acceleratedOrbit 13 1789 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1789) = 3 ^ 9 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1789.1, data_13_1789.2] + +/-- Complete interval computation for depth 13, residue 1790. -/ +theorem bounds_13_1790 : exactInterval 13 1790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1790 : oddCount 1790 13 = 9 ∧ acceleratedOrbit 13 1790 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1790) = 3 ^ 9 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1790.1, data_13_1790.2] + +/-- Complete interval computation for depth 13, residue 1791. -/ +theorem bounds_13_1791 : exactInterval 13 1791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1791 : oddCount 1791 13 = 10 ∧ acceleratedOrbit 13 1791 = 12917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1791) = 3 ^ 10 * m + 12917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1791.1, data_13_1791.2] + +/-- Complete interval computation for depth 13, residue 1792. -/ +theorem bounds_13_1792 : exactInterval 13 1792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1792 : oddCount 1792 13 = 4 ∧ acceleratedOrbit 13 1792 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1792) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1792.1, data_13_1792.2] + +/-- Complete interval computation for depth 13, residue 1793. -/ +theorem bounds_13_1793 : exactInterval 13 1793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1793 : oddCount 1793 13 = 6 ∧ acceleratedOrbit 13 1793 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1793) = 3 ^ 6 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1793.1, data_13_1793.2] + +/-- Complete interval computation for depth 13, residue 1794. -/ +theorem bounds_13_1794 : exactInterval 13 1794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1794 : oddCount 1794 13 = 7 ∧ acceleratedOrbit 13 1794 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1794) = 3 ^ 7 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1794.1, data_13_1794.2] + +/-- Complete interval computation for depth 13, residue 1795. -/ +theorem bounds_13_1795 : exactInterval 13 1795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1795 : oddCount 1795 13 = 7 ∧ acceleratedOrbit 13 1795 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1795) = 3 ^ 7 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1795.1, data_13_1795.2] + +/-- Complete interval computation for depth 13, residue 1796. -/ +theorem bounds_13_1796 : exactInterval 13 1796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1796 : oddCount 1796 13 = 7 ∧ acceleratedOrbit 13 1796 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1796) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1796.1, data_13_1796.2] + +/-- Complete interval computation for depth 13, residue 1797. -/ +theorem bounds_13_1797 : exactInterval 13 1797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1797 : oddCount 1797 13 = 7 ∧ acceleratedOrbit 13 1797 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1797) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1797.1, data_13_1797.2] + +/-- Complete interval computation for depth 13, residue 1798. -/ +theorem bounds_13_1798 : exactInterval 13 1798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1798 : oddCount 1798 13 = 7 ∧ acceleratedOrbit 13 1798 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1798) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1798.1, data_13_1798.2] + +/-- Complete interval computation for depth 13, residue 1799. -/ +theorem bounds_13_1799 : exactInterval 13 1799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1799 : oddCount 1799 13 = 7 ∧ acceleratedOrbit 13 1799 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1799) = 3 ^ 7 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1799.1, data_13_1799.2] + +/-- Complete interval computation for depth 13, residue 1800. -/ +theorem bounds_13_1800 : exactInterval 13 1800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1800 : oddCount 1800 13 = 8 ∧ acceleratedOrbit 13 1800 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1800) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1800.1, data_13_1800.2] + +/-- Complete interval computation for depth 13, residue 1801. -/ +theorem bounds_13_1801 : exactInterval 13 1801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1801 : oddCount 1801 13 = 9 ∧ acceleratedOrbit 13 1801 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1801) = 3 ^ 9 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1801.1, data_13_1801.2] + +end Collatz.Research.StoppingAtlas.Batch0584 From 297cba0e2a71ec695cfcbd7be9b23e9eb5ccbc48 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:45 +0530 Subject: [PATCH 0585/1001] proof: certify atlas Batch0585 (13:1802 to 13:1816) --- Collatz/Research/StoppingAtlas/Batch0585.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0585.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0585.lean b/Collatz/Research/StoppingAtlas/Batch0585.lean new file mode 100644 index 00000000..9233dc27 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0585.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0585 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1802. -/ +theorem bounds_13_1802 : exactInterval 13 1802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1802 : oddCount 1802 13 = 8 ∧ acceleratedOrbit 13 1802 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1802) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1802.1, data_13_1802.2] + +/-- Complete interval computation for depth 13, residue 1803. -/ +theorem bounds_13_1803 : exactInterval 13 1803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1803 : oddCount 1803 13 = 8 ∧ acceleratedOrbit 13 1803 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1803) = 3 ^ 8 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1803.1, data_13_1803.2] + +/-- Complete interval computation for depth 13, residue 1804. -/ +theorem bounds_13_1804 : exactInterval 13 1804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1804 : oddCount 1804 13 = 8 ∧ acceleratedOrbit 13 1804 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1804) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1804.1, data_13_1804.2] + +/-- Complete interval computation for depth 13, residue 1805. -/ +theorem bounds_13_1805 : exactInterval 13 1805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1805 : oddCount 1805 13 = 8 ∧ acceleratedOrbit 13 1805 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1805) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1805.1, data_13_1805.2] + +/-- Complete interval computation for depth 13, residue 1806. -/ +theorem bounds_13_1806 : exactInterval 13 1806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1806 : oddCount 1806 13 = 7 ∧ acceleratedOrbit 13 1806 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1806) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1806.1, data_13_1806.2] + +/-- Complete interval computation for depth 13, residue 1807. -/ +theorem bounds_13_1807 : exactInterval 13 1807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1807 : oddCount 1807 13 = 7 ∧ acceleratedOrbit 13 1807 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1807) = 3 ^ 7 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1807.1, data_13_1807.2] + +/-- Complete interval computation for depth 13, residue 1808. -/ +theorem bounds_13_1808 : exactInterval 13 1808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1808 : oddCount 1808 13 = 2 ∧ acceleratedOrbit 13 1808 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1808) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1808.1, data_13_1808.2] + +/-- Complete interval computation for depth 13, residue 1809. -/ +theorem bounds_13_1809 : exactInterval 13 1809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1809 : oddCount 1809 13 = 8 ∧ acceleratedOrbit 13 1809 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1809) = 3 ^ 8 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1809.1, data_13_1809.2] + +/-- Complete interval computation for depth 13, residue 1810. -/ +theorem bounds_13_1810 : exactInterval 13 1810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1810 : oddCount 1810 13 = 8 ∧ acceleratedOrbit 13 1810 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1810) = 3 ^ 8 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1810.1, data_13_1810.2] + +/-- Complete interval computation for depth 13, residue 1811. -/ +theorem bounds_13_1811 : exactInterval 13 1811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1811 : oddCount 1811 13 = 8 ∧ acceleratedOrbit 13 1811 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1811) = 3 ^ 8 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1811.1, data_13_1811.2] + +/-- Complete interval computation for depth 13, residue 1812. -/ +theorem bounds_13_1812 : exactInterval 13 1812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1812 : oddCount 1812 13 = 2 ∧ acceleratedOrbit 13 1812 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1812) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1812.1, data_13_1812.2] + +/-- Complete interval computation for depth 13, residue 1813. -/ +theorem bounds_13_1813 : exactInterval 13 1813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1813 : oddCount 1813 13 = 2 ∧ acceleratedOrbit 13 1813 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1813) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1813.1, data_13_1813.2] + +/-- Complete interval computation for depth 13, residue 1814. -/ +theorem bounds_13_1814 : exactInterval 13 1814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1814 : oddCount 1814 13 = 9 ∧ acceleratedOrbit 13 1814 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1814) = 3 ^ 9 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1814.1, data_13_1814.2] + +/-- Complete interval computation for depth 13, residue 1815. -/ +theorem bounds_13_1815 : exactInterval 13 1815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1815 : oddCount 1815 13 = 9 ∧ acceleratedOrbit 13 1815 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1815) = 3 ^ 9 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1815.1, data_13_1815.2] + +/-- Complete interval computation for depth 13, residue 1816. -/ +theorem bounds_13_1816 : exactInterval 13 1816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1816 : oddCount 1816 13 = 2 ∧ acceleratedOrbit 13 1816 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1816) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1816.1, data_13_1816.2] + +end Collatz.Research.StoppingAtlas.Batch0585 From c48ce69bc0b13d32d968bc6b9843106d88f981ee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:45 +0530 Subject: [PATCH 0586/1001] proof: certify atlas Batch0586 (13:1817 to 13:1831) --- Collatz/Research/StoppingAtlas/Batch0586.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0586.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0586.lean b/Collatz/Research/StoppingAtlas/Batch0586.lean new file mode 100644 index 00000000..b2f3dc28 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0586.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0586 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1817. -/ +theorem bounds_13_1817 : exactInterval 13 1817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1817 : oddCount 1817 13 = 10 ∧ acceleratedOrbit 13 1817 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1817) = 3 ^ 10 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1817.1, data_13_1817.2] + +/-- Complete interval computation for depth 13, residue 1818. -/ +theorem bounds_13_1818 : exactInterval 13 1818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1818 : oddCount 1818 13 = 2 ∧ acceleratedOrbit 13 1818 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1818) = 3 ^ 2 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1818.1, data_13_1818.2] + +/-- Complete interval computation for depth 13, residue 1819. -/ +theorem bounds_13_1819 : exactInterval 13 1819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1819 : oddCount 1819 13 = 12 ∧ acceleratedOrbit 13 1819 = 118097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1819) = 3 ^ 12 * m + 118097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1819.1, data_13_1819.2] + +/-- Complete interval computation for depth 13, residue 1820. -/ +theorem bounds_13_1820 : exactInterval 13 1820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1820 : oddCount 1820 13 = 7 ∧ acceleratedOrbit 13 1820 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1820) = 3 ^ 7 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1820.1, data_13_1820.2] + +/-- Complete interval computation for depth 13, residue 1821. -/ +theorem bounds_13_1821 : exactInterval 13 1821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1821 : oddCount 1821 13 = 7 ∧ acceleratedOrbit 13 1821 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1821) = 3 ^ 7 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1821.1, data_13_1821.2] + +/-- Complete interval computation for depth 13, residue 1822. -/ +theorem bounds_13_1822 : exactInterval 13 1822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1822 : oddCount 1822 13 = 7 ∧ acceleratedOrbit 13 1822 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1822) = 3 ^ 7 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1822.1, data_13_1822.2] + +/-- Complete interval computation for depth 13, residue 1823. -/ +theorem bounds_13_1823 : exactInterval 13 1823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1823 : oddCount 1823 13 = 7 ∧ acceleratedOrbit 13 1823 = 487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1823) = 3 ^ 7 * m + 487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1823.1, data_13_1823.2] + +/-- Complete interval computation for depth 13, residue 1824. -/ +theorem bounds_13_1824 : exactInterval 13 1824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1824 : oddCount 1824 13 = 5 ∧ acceleratedOrbit 13 1824 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1824) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1824.1, data_13_1824.2] + +/-- Complete interval computation for depth 13, residue 1825. -/ +theorem bounds_13_1825 : exactInterval 13 1825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1825 : oddCount 1825 13 = 6 ∧ acceleratedOrbit 13 1825 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1825) = 3 ^ 6 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1825.1, data_13_1825.2] + +/-- Complete interval computation for depth 13, residue 1826. -/ +theorem bounds_13_1826 : exactInterval 13 1826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1826 : oddCount 1826 13 = 6 ∧ acceleratedOrbit 13 1826 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1826) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1826.1, data_13_1826.2] + +/-- Complete interval computation for depth 13, residue 1827. -/ +theorem bounds_13_1827 : exactInterval 13 1827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1827 : oddCount 1827 13 = 6 ∧ acceleratedOrbit 13 1827 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1827) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1827.1, data_13_1827.2] + +/-- Complete interval computation for depth 13, residue 1828. -/ +theorem bounds_13_1828 : exactInterval 13 1828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1828 : oddCount 1828 13 = 6 ∧ acceleratedOrbit 13 1828 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1828) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1828.1, data_13_1828.2] + +/-- Complete interval computation for depth 13, residue 1829. -/ +theorem bounds_13_1829 : exactInterval 13 1829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1829 : oddCount 1829 13 = 6 ∧ acceleratedOrbit 13 1829 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1829) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1829.1, data_13_1829.2] + +/-- Complete interval computation for depth 13, residue 1830. -/ +theorem bounds_13_1830 : exactInterval 13 1830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1830 : oddCount 1830 13 = 6 ∧ acceleratedOrbit 13 1830 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1830) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1830.1, data_13_1830.2] + +/-- Complete interval computation for depth 13, residue 1831. -/ +theorem bounds_13_1831 : exactInterval 13 1831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1831 : oddCount 1831 13 = 8 ∧ acceleratedOrbit 13 1831 = 1468 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1831) = 3 ^ 8 * m + 1468 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1831.1, data_13_1831.2] + +end Collatz.Research.StoppingAtlas.Batch0586 From 9b81671c2cb71e066339479c122c166e0d214a1c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:45 +0530 Subject: [PATCH 0587/1001] proof: certify atlas Batch0587 (13:1832 to 13:1847) --- Collatz/Research/StoppingAtlas/Batch0587.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0587.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0587.lean b/Collatz/Research/StoppingAtlas/Batch0587.lean new file mode 100644 index 00000000..585630e4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0587.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0587 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1832. -/ +theorem bounds_13_1832 : exactInterval 13 1832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1832 : oddCount 1832 13 = 5 ∧ acceleratedOrbit 13 1832 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1832) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1832.1, data_13_1832.2] + +/-- Complete interval computation for depth 13, residue 1833. -/ +theorem bounds_13_1833 : exactInterval 13 1833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1833 : oddCount 1833 13 = 7 ∧ acceleratedOrbit 13 1833 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1833) = 3 ^ 7 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1833.1, data_13_1833.2] + +/-- Complete interval computation for depth 13, residue 1834. -/ +theorem bounds_13_1834 : exactInterval 13 1834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1834 : oddCount 1834 13 = 5 ∧ acceleratedOrbit 13 1834 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1834) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1834.1, data_13_1834.2] + +/-- Complete interval computation for depth 13, residue 1835. -/ +theorem bounds_13_1835 : exactInterval 13 1835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1835 : oddCount 1835 13 = 6 ∧ acceleratedOrbit 13 1835 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1835) = 3 ^ 6 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1835.1, data_13_1835.2] + +/-- Complete interval computation for depth 13, residue 1836. -/ +theorem bounds_13_1836 : exactInterval 13 1836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1836 : oddCount 1836 13 = 5 ∧ acceleratedOrbit 13 1836 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1836) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1836.1, data_13_1836.2] + +/-- Complete interval computation for depth 13, residue 1837. -/ +theorem bounds_13_1837 : exactInterval 13 1837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1837 : oddCount 1837 13 = 5 ∧ acceleratedOrbit 13 1837 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1837) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1837.1, data_13_1837.2] + +/-- Complete interval computation for depth 13, residue 1838. -/ +theorem bounds_13_1838 : exactInterval 13 1838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1838 : oddCount 1838 13 = 5 ∧ acceleratedOrbit 13 1838 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1838) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1838.1, data_13_1838.2] + +/-- Complete interval computation for depth 13, residue 1839. -/ +theorem bounds_13_1839 : exactInterval 13 1839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1839 : oddCount 1839 13 = 8 ∧ acceleratedOrbit 13 1839 = 1475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1839) = 3 ^ 8 * m + 1475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1839.1, data_13_1839.2] + +/-- Complete interval computation for depth 13, residue 1840. -/ +theorem bounds_13_1840 : exactInterval 13 1840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1840 : oddCount 1840 13 = 5 ∧ acceleratedOrbit 13 1840 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1840) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1840.1, data_13_1840.2] + +/-- Complete interval computation for depth 13, residue 1841. -/ +theorem bounds_13_1841 : exactInterval 13 1841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1841 : oddCount 1841 13 = 5 ∧ acceleratedOrbit 13 1841 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1841) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1841.1, data_13_1841.2] + +/-- Complete interval computation for depth 13, residue 1842. -/ +theorem bounds_13_1842 : exactInterval 13 1842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1842 : oddCount 1842 13 = 5 ∧ acceleratedOrbit 13 1842 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1842) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1842.1, data_13_1842.2] + +/-- Complete interval computation for depth 13, residue 1843. -/ +theorem bounds_13_1843 : exactInterval 13 1843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1843 : oddCount 1843 13 = 5 ∧ acceleratedOrbit 13 1843 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1843) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1843.1, data_13_1843.2] + +/-- Complete interval computation for depth 13, residue 1844. -/ +theorem bounds_13_1844 : exactInterval 13 1844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1844 : oddCount 1844 13 = 5 ∧ acceleratedOrbit 13 1844 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1844) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1844.1, data_13_1844.2] + +/-- Complete interval computation for depth 13, residue 1845. -/ +theorem bounds_13_1845 : exactInterval 13 1845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1845 : oddCount 1845 13 = 5 ∧ acceleratedOrbit 13 1845 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1845) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1845.1, data_13_1845.2] + +/-- Complete interval computation for depth 13, residue 1846. -/ +theorem bounds_13_1846 : exactInterval 13 1846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1846 : oddCount 1846 13 = 7 ∧ acceleratedOrbit 13 1846 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1846) = 3 ^ 7 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1846.1, data_13_1846.2] + +/-- Complete interval computation for depth 13, residue 1847. -/ +theorem bounds_13_1847 : exactInterval 13 1847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1847 : oddCount 1847 13 = 7 ∧ acceleratedOrbit 13 1847 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1847) = 3 ^ 7 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1847.1, data_13_1847.2] + +end Collatz.Research.StoppingAtlas.Batch0587 From 72e96d05708bd2a45c6a099a6e71df2bacb6dc7f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:46 +0530 Subject: [PATCH 0588/1001] proof: certify atlas Batch0588 (13:1848 to 13:1862) --- Collatz/Research/StoppingAtlas/Batch0588.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0588.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0588.lean b/Collatz/Research/StoppingAtlas/Batch0588.lean new file mode 100644 index 00000000..a664bd61 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0588.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0588 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1848. -/ +theorem bounds_13_1848 : exactInterval 13 1848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1848 : oddCount 1848 13 = 7 ∧ acceleratedOrbit 13 1848 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1848) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1848.1, data_13_1848.2] + +/-- Complete interval computation for depth 13, residue 1849. -/ +theorem bounds_13_1849 : exactInterval 13 1849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1849 : oddCount 1849 13 = 8 ∧ acceleratedOrbit 13 1849 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1849) = 3 ^ 8 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1849.1, data_13_1849.2] + +/-- Complete interval computation for depth 13, residue 1850. -/ +theorem bounds_13_1850 : exactInterval 13 1850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1850 : oddCount 1850 13 = 7 ∧ acceleratedOrbit 13 1850 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1850) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1850.1, data_13_1850.2] + +/-- Complete interval computation for depth 13, residue 1851. -/ +theorem bounds_13_1851 : exactInterval 13 1851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1851 : oddCount 1851 13 = 5 ∧ acceleratedOrbit 13 1851 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1851) = 3 ^ 5 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1851.1, data_13_1851.2] + +/-- Complete interval computation for depth 13, residue 1852. -/ +theorem bounds_13_1852 : exactInterval 13 1852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1852 : oddCount 1852 13 = 7 ∧ acceleratedOrbit 13 1852 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1852) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1852.1, data_13_1852.2] + +/-- Complete interval computation for depth 13, residue 1853. -/ +theorem bounds_13_1853 : exactInterval 13 1853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1853 : oddCount 1853 13 = 7 ∧ acceleratedOrbit 13 1853 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1853) = 3 ^ 7 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1853.1, data_13_1853.2] + +/-- Complete interval computation for depth 13, residue 1854. -/ +theorem bounds_13_1854 : exactInterval 13 1854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1854 : oddCount 1854 13 = 8 ∧ acceleratedOrbit 13 1854 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1854) = 3 ^ 8 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1854.1, data_13_1854.2] + +/-- Complete interval computation for depth 13, residue 1855. -/ +theorem bounds_13_1855 : exactInterval 13 1855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1855 : oddCount 1855 13 = 8 ∧ acceleratedOrbit 13 1855 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1855) = 3 ^ 8 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1855.1, data_13_1855.2] + +/-- Complete interval computation for depth 13, residue 1856. -/ +theorem bounds_13_1856 : exactInterval 13 1856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1856 : oddCount 1856 13 = 4 ∧ acceleratedOrbit 13 1856 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1856) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1856.1, data_13_1856.2] + +/-- Complete interval computation for depth 13, residue 1857. -/ +theorem bounds_13_1857 : exactInterval 13 1857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1857 : oddCount 1857 13 = 5 ∧ acceleratedOrbit 13 1857 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1857) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1857.1, data_13_1857.2] + +/-- Complete interval computation for depth 13, residue 1858. -/ +theorem bounds_13_1858 : exactInterval 13 1858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1858 : oddCount 1858 13 = 6 ∧ acceleratedOrbit 13 1858 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1858) = 3 ^ 6 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1858.1, data_13_1858.2] + +/-- Complete interval computation for depth 13, residue 1859. -/ +theorem bounds_13_1859 : exactInterval 13 1859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1859 : oddCount 1859 13 = 6 ∧ acceleratedOrbit 13 1859 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1859) = 3 ^ 6 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1859.1, data_13_1859.2] + +/-- Complete interval computation for depth 13, residue 1860. -/ +theorem bounds_13_1860 : exactInterval 13 1860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1860 : oddCount 1860 13 = 5 ∧ acceleratedOrbit 13 1860 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1860) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1860.1, data_13_1860.2] + +/-- Complete interval computation for depth 13, residue 1861. -/ +theorem bounds_13_1861 : exactInterval 13 1861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1861 : oddCount 1861 13 = 5 ∧ acceleratedOrbit 13 1861 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1861) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1861.1, data_13_1861.2] + +/-- Complete interval computation for depth 13, residue 1862. -/ +theorem bounds_13_1862 : exactInterval 13 1862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1862 : oddCount 1862 13 = 5 ∧ acceleratedOrbit 13 1862 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1862) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1862.1, data_13_1862.2] + +end Collatz.Research.StoppingAtlas.Batch0588 From 7bec7f455ae62845784ddc974a7253362f5c0e73 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:47 +0530 Subject: [PATCH 0589/1001] proof: certify atlas Batch0589 (13:1863 to 13:1878) --- Collatz/Research/StoppingAtlas/Batch0589.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0589.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0589.lean b/Collatz/Research/StoppingAtlas/Batch0589.lean new file mode 100644 index 00000000..b044bcc2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0589.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0589 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1863. -/ +theorem bounds_13_1863 : exactInterval 13 1863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1863 : oddCount 1863 13 = 9 ∧ acceleratedOrbit 13 1863 = 4481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1863) = 3 ^ 9 * m + 4481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1863.1, data_13_1863.2] + +/-- Complete interval computation for depth 13, residue 1864. -/ +theorem bounds_13_1864 : exactInterval 13 1864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1864 : oddCount 1864 13 = 6 ∧ acceleratedOrbit 13 1864 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1864) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1864.1, data_13_1864.2] + +/-- Complete interval computation for depth 13, residue 1865. -/ +theorem bounds_13_1865 : exactInterval 13 1865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1865 : oddCount 1865 13 = 7 ∧ acceleratedOrbit 13 1865 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1865) = 3 ^ 7 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1865.1, data_13_1865.2] + +/-- Complete interval computation for depth 13, residue 1866. -/ +theorem bounds_13_1866 : exactInterval 13 1866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1866 : oddCount 1866 13 = 6 ∧ acceleratedOrbit 13 1866 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1866) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1866.1, data_13_1866.2] + +/-- Complete interval computation for depth 13, residue 1867. -/ +theorem bounds_13_1867 : exactInterval 13 1867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1867 : oddCount 1867 13 = 5 ∧ acceleratedOrbit 13 1867 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1867) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1867.1, data_13_1867.2] + +/-- Complete interval computation for depth 13, residue 1868. -/ +theorem bounds_13_1868 : exactInterval 13 1868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1868 : oddCount 1868 13 = 6 ∧ acceleratedOrbit 13 1868 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1868) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1868.1, data_13_1868.2] + +/-- Complete interval computation for depth 13, residue 1869. -/ +theorem bounds_13_1869 : exactInterval 13 1869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1869 : oddCount 1869 13 = 6 ∧ acceleratedOrbit 13 1869 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1869) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1869.1, data_13_1869.2] + +/-- Complete interval computation for depth 13, residue 1870. -/ +theorem bounds_13_1870 : exactInterval 13 1870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1870 : oddCount 1870 13 = 7 ∧ acceleratedOrbit 13 1870 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1870) = 3 ^ 7 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1870.1, data_13_1870.2] + +/-- Complete interval computation for depth 13, residue 1871. -/ +theorem bounds_13_1871 : exactInterval 13 1871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1871 : oddCount 1871 13 = 7 ∧ acceleratedOrbit 13 1871 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1871) = 3 ^ 7 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1871.1, data_13_1871.2] + +/-- Complete interval computation for depth 13, residue 1872. -/ +theorem bounds_13_1872 : exactInterval 13 1872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1872 : oddCount 1872 13 = 4 ∧ acceleratedOrbit 13 1872 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1872) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1872.1, data_13_1872.2] + +/-- Complete interval computation for depth 13, residue 1873. -/ +theorem bounds_13_1873 : exactInterval 13 1873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1873 : oddCount 1873 13 = 6 ∧ acceleratedOrbit 13 1873 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1873) = 3 ^ 6 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1873.1, data_13_1873.2] + +/-- Complete interval computation for depth 13, residue 1874. -/ +theorem bounds_13_1874 : exactInterval 13 1874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1874 : oddCount 1874 13 = 9 ∧ acceleratedOrbit 13 1874 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1874) = 3 ^ 9 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1874.1, data_13_1874.2] + +/-- Complete interval computation for depth 13, residue 1875. -/ +theorem bounds_13_1875 : exactInterval 13 1875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1875 : oddCount 1875 13 = 9 ∧ acceleratedOrbit 13 1875 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1875) = 3 ^ 9 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1875.1, data_13_1875.2] + +/-- Complete interval computation for depth 13, residue 1876. -/ +theorem bounds_13_1876 : exactInterval 13 1876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1876 : oddCount 1876 13 = 4 ∧ acceleratedOrbit 13 1876 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1876) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1876.1, data_13_1876.2] + +/-- Complete interval computation for depth 13, residue 1877. -/ +theorem bounds_13_1877 : exactInterval 13 1877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1877 : oddCount 1877 13 = 4 ∧ acceleratedOrbit 13 1877 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1877) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1877.1, data_13_1877.2] + +/-- Complete interval computation for depth 13, residue 1878. -/ +theorem bounds_13_1878 : exactInterval 13 1878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1878 : oddCount 1878 13 = 7 ∧ acceleratedOrbit 13 1878 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1878) = 3 ^ 7 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1878.1, data_13_1878.2] + +end Collatz.Research.StoppingAtlas.Batch0589 From 723c6f1391a66aa3d3ee819f83c8902852fde3a0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:48 +0530 Subject: [PATCH 0590/1001] proof: certify atlas Batch0590 (13:1879 to 13:1893) --- Collatz/Research/StoppingAtlas/Batch0590.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0590.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0590.lean b/Collatz/Research/StoppingAtlas/Batch0590.lean new file mode 100644 index 00000000..c7c7a1dc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0590.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0590 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1879. -/ +theorem bounds_13_1879 : exactInterval 13 1879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1879 : oddCount 1879 13 = 7 ∧ acceleratedOrbit 13 1879 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1879) = 3 ^ 7 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1879.1, data_13_1879.2] + +/-- Complete interval computation for depth 13, residue 1880. -/ +theorem bounds_13_1880 : exactInterval 13 1880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1880 : oddCount 1880 13 = 7 ∧ acceleratedOrbit 13 1880 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1880) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1880.1, data_13_1880.2] + +/-- Complete interval computation for depth 13, residue 1881. -/ +theorem bounds_13_1881 : exactInterval 13 1881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1881 : oddCount 1881 13 = 5 ∧ acceleratedOrbit 13 1881 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1881) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1881.1, data_13_1881.2] + +/-- Complete interval computation for depth 13, residue 1882. -/ +theorem bounds_13_1882 : exactInterval 13 1882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1882 : oddCount 1882 13 = 7 ∧ acceleratedOrbit 13 1882 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1882) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1882.1, data_13_1882.2] + +/-- Complete interval computation for depth 13, residue 1883. -/ +theorem bounds_13_1883 : exactInterval 13 1883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1883 : oddCount 1883 13 = 9 ∧ acceleratedOrbit 13 1883 = 4529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1883) = 3 ^ 9 * m + 4529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1883.1, data_13_1883.2] + +/-- Complete interval computation for depth 13, residue 1884. -/ +theorem bounds_13_1884 : exactInterval 13 1884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1884 : oddCount 1884 13 = 7 ∧ acceleratedOrbit 13 1884 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1884) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1884.1, data_13_1884.2] + +/-- Complete interval computation for depth 13, residue 1885. -/ +theorem bounds_13_1885 : exactInterval 13 1885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1885 : oddCount 1885 13 = 7 ∧ acceleratedOrbit 13 1885 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1885) = 3 ^ 7 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1885.1, data_13_1885.2] + +/-- Complete interval computation for depth 13, residue 1886. -/ +theorem bounds_13_1886 : exactInterval 13 1886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1886 : oddCount 1886 13 = 5 ∧ acceleratedOrbit 13 1886 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1886) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1886.1, data_13_1886.2] + +/-- Complete interval computation for depth 13, residue 1887. -/ +theorem bounds_13_1887 : exactInterval 13 1887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1887 : oddCount 1887 13 = 5 ∧ acceleratedOrbit 13 1887 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1887) = 3 ^ 5 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1887.1, data_13_1887.2] + +/-- Complete interval computation for depth 13, residue 1888. -/ +theorem bounds_13_1888 : exactInterval 13 1888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1888 : oddCount 1888 13 = 4 ∧ acceleratedOrbit 13 1888 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1888) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1888.1, data_13_1888.2] + +/-- Complete interval computation for depth 13, residue 1889. -/ +theorem bounds_13_1889 : exactInterval 13 1889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1889 : oddCount 1889 13 = 7 ∧ acceleratedOrbit 13 1889 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1889) = 3 ^ 7 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1889.1, data_13_1889.2] + +/-- Complete interval computation for depth 13, residue 1890. -/ +theorem bounds_13_1890 : exactInterval 13 1890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1890 : oddCount 1890 13 = 4 ∧ acceleratedOrbit 13 1890 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1890) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1890.1, data_13_1890.2] + +/-- Complete interval computation for depth 13, residue 1891. -/ +theorem bounds_13_1891 : exactInterval 13 1891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1891 : oddCount 1891 13 = 4 ∧ acceleratedOrbit 13 1891 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1891) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1891.1, data_13_1891.2] + +/-- Complete interval computation for depth 13, residue 1892. -/ +theorem bounds_13_1892 : exactInterval 13 1892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1892 : oddCount 1892 13 = 4 ∧ acceleratedOrbit 13 1892 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1892) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1892.1, data_13_1892.2] + +/-- Complete interval computation for depth 13, residue 1893. -/ +theorem bounds_13_1893 : exactInterval 13 1893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1893 : oddCount 1893 13 = 4 ∧ acceleratedOrbit 13 1893 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1893) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1893.1, data_13_1893.2] + +end Collatz.Research.StoppingAtlas.Batch0590 From ce9ae9998cbbeae0cad3cd1b148ff7ea845d4615 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:48 +0530 Subject: [PATCH 0591/1001] proof: certify atlas Batch0591 (13:1894 to 13:1908) --- Collatz/Research/StoppingAtlas/Batch0591.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0591.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0591.lean b/Collatz/Research/StoppingAtlas/Batch0591.lean new file mode 100644 index 00000000..6acc8986 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0591.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0591 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1894. -/ +theorem bounds_13_1894 : exactInterval 13 1894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1894 : oddCount 1894 13 = 4 ∧ acceleratedOrbit 13 1894 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1894) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1894.1, data_13_1894.2] + +/-- Complete interval computation for depth 13, residue 1895. -/ +theorem bounds_13_1895 : exactInterval 13 1895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1895 : oddCount 1895 13 = 11 ∧ acceleratedOrbit 13 1895 = 41006 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1895) = 3 ^ 11 * m + 41006 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1895.1, data_13_1895.2] + +/-- Complete interval computation for depth 13, residue 1896. -/ +theorem bounds_13_1896 : exactInterval 13 1896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1896 : oddCount 1896 13 = 4 ∧ acceleratedOrbit 13 1896 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1896) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1896.1, data_13_1896.2] + +/-- Complete interval computation for depth 13, residue 1897. -/ +theorem bounds_13_1897 : exactInterval 13 1897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1897 : oddCount 1897 13 = 6 ∧ acceleratedOrbit 13 1897 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1897) = 3 ^ 6 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1897.1, data_13_1897.2] + +/-- Complete interval computation for depth 13, residue 1898. -/ +theorem bounds_13_1898 : exactInterval 13 1898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1898 : oddCount 1898 13 = 4 ∧ acceleratedOrbit 13 1898 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1898) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1898.1, data_13_1898.2] + +/-- Complete interval computation for depth 13, residue 1899. -/ +theorem bounds_13_1899 : exactInterval 13 1899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1899 : oddCount 1899 13 = 7 ∧ acceleratedOrbit 13 1899 = 508 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1899) = 3 ^ 7 * m + 508 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1899.1, data_13_1899.2] + +/-- Complete interval computation for depth 13, residue 1900. -/ +theorem bounds_13_1900 : exactInterval 13 1900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1900 : oddCount 1900 13 = 6 ∧ acceleratedOrbit 13 1900 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1900) = 3 ^ 6 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1900.1, data_13_1900.2] + +/-- Complete interval computation for depth 13, residue 1901. -/ +theorem bounds_13_1901 : exactInterval 13 1901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1901 : oddCount 1901 13 = 6 ∧ acceleratedOrbit 13 1901 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1901) = 3 ^ 6 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1901.1, data_13_1901.2] + +/-- Complete interval computation for depth 13, residue 1902. -/ +theorem bounds_13_1902 : exactInterval 13 1902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1902 : oddCount 1902 13 = 6 ∧ acceleratedOrbit 13 1902 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1902) = 3 ^ 6 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1902.1, data_13_1902.2] + +/-- Complete interval computation for depth 13, residue 1903. -/ +theorem bounds_13_1903 : exactInterval 13 1903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1903 : oddCount 1903 13 = 9 ∧ acceleratedOrbit 13 1903 = 4576 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1903) = 3 ^ 9 * m + 4576 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1903.1, data_13_1903.2] + +/-- Complete interval computation for depth 13, residue 1904. -/ +theorem bounds_13_1904 : exactInterval 13 1904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1904 : oddCount 1904 13 = 4 ∧ acceleratedOrbit 13 1904 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1904) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1904.1, data_13_1904.2] + +/-- Complete interval computation for depth 13, residue 1905. -/ +theorem bounds_13_1905 : exactInterval 13 1905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1905 : oddCount 1905 13 = 4 ∧ acceleratedOrbit 13 1905 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1905) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1905.1, data_13_1905.2] + +/-- Complete interval computation for depth 13, residue 1906. -/ +theorem bounds_13_1906 : exactInterval 13 1906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1906 : oddCount 1906 13 = 7 ∧ acceleratedOrbit 13 1906 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1906) = 3 ^ 7 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1906.1, data_13_1906.2] + +/-- Complete interval computation for depth 13, residue 1907. -/ +theorem bounds_13_1907 : exactInterval 13 1907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1907 : oddCount 1907 13 = 7 ∧ acceleratedOrbit 13 1907 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1907) = 3 ^ 7 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1907.1, data_13_1907.2] + +/-- Complete interval computation for depth 13, residue 1908. -/ +theorem bounds_13_1908 : exactInterval 13 1908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1908 : oddCount 1908 13 = 4 ∧ acceleratedOrbit 13 1908 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1908) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1908.1, data_13_1908.2] + +end Collatz.Research.StoppingAtlas.Batch0591 From 46d5da1fae9f0afa87fccfa50cf91d42221896c6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:49 +0530 Subject: [PATCH 0592/1001] proof: certify atlas Batch0592 (13:1909 to 13:1924) --- Collatz/Research/StoppingAtlas/Batch0592.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0592.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0592.lean b/Collatz/Research/StoppingAtlas/Batch0592.lean new file mode 100644 index 00000000..51f0b7ee --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0592.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0592 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1909. -/ +theorem bounds_13_1909 : exactInterval 13 1909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1909 : oddCount 1909 13 = 4 ∧ acceleratedOrbit 13 1909 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1909) = 3 ^ 4 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1909.1, data_13_1909.2] + +/-- Complete interval computation for depth 13, residue 1910. -/ +theorem bounds_13_1910 : exactInterval 13 1910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1910 : oddCount 1910 13 = 7 ∧ acceleratedOrbit 13 1910 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1910) = 3 ^ 7 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1910.1, data_13_1910.2] + +/-- Complete interval computation for depth 13, residue 1911. -/ +theorem bounds_13_1911 : exactInterval 13 1911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1911 : oddCount 1911 13 = 7 ∧ acceleratedOrbit 13 1911 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1911) = 3 ^ 7 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1911.1, data_13_1911.2] + +/-- Complete interval computation for depth 13, residue 1912. -/ +theorem bounds_13_1912 : exactInterval 13 1912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1912 : oddCount 1912 13 = 9 ∧ acceleratedOrbit 13 1912 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1912) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1912.1, data_13_1912.2] + +/-- Complete interval computation for depth 13, residue 1913. -/ +theorem bounds_13_1913 : exactInterval 13 1913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1913 : oddCount 1913 13 = 8 ∧ acceleratedOrbit 13 1913 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1913) = 3 ^ 8 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1913.1, data_13_1913.2] + +/-- Complete interval computation for depth 13, residue 1914. -/ +theorem bounds_13_1914 : exactInterval 13 1914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1914 : oddCount 1914 13 = 9 ∧ acceleratedOrbit 13 1914 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1914) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1914.1, data_13_1914.2] + +/-- Complete interval computation for depth 13, residue 1915. -/ +theorem bounds_13_1915 : exactInterval 13 1915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1915 : oddCount 1915 13 = 9 ∧ acceleratedOrbit 13 1915 = 4607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1915) = 3 ^ 9 * m + 4607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1915.1, data_13_1915.2] + +/-- Complete interval computation for depth 13, residue 1916. -/ +theorem bounds_13_1916 : exactInterval 13 1916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1916 : oddCount 1916 13 = 9 ∧ acceleratedOrbit 13 1916 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1916) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1916.1, data_13_1916.2] + +/-- Complete interval computation for depth 13, residue 1917. -/ +theorem bounds_13_1917 : exactInterval 13 1917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1917 : oddCount 1917 13 = 9 ∧ acceleratedOrbit 13 1917 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1917) = 3 ^ 9 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1917.1, data_13_1917.2] + +/-- Complete interval computation for depth 13, residue 1918. -/ +theorem bounds_13_1918 : exactInterval 13 1918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1918 : oddCount 1918 13 = 10 ∧ acceleratedOrbit 13 1918 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1918) = 3 ^ 10 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1918.1, data_13_1918.2] + +/-- Complete interval computation for depth 13, residue 1919. -/ +theorem bounds_13_1919 : exactInterval 13 1919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1919 : oddCount 1919 13 = 10 ∧ acceleratedOrbit 13 1919 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1919) = 3 ^ 10 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1919.1, data_13_1919.2] + +/-- Complete interval computation for depth 13, residue 1920. -/ +theorem bounds_13_1920 : exactInterval 13 1920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1920 : oddCount 1920 13 = 4 ∧ acceleratedOrbit 13 1920 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1920) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1920.1, data_13_1920.2] + +/-- Complete interval computation for depth 13, residue 1921. -/ +theorem bounds_13_1921 : exactInterval 13 1921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1921 : oddCount 1921 13 = 7 ∧ acceleratedOrbit 13 1921 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1921) = 3 ^ 7 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1921.1, data_13_1921.2] + +/-- Complete interval computation for depth 13, residue 1922. -/ +theorem bounds_13_1922 : exactInterval 13 1922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1922 : oddCount 1922 13 = 6 ∧ acceleratedOrbit 13 1922 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1922) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1922.1, data_13_1922.2] + +/-- Complete interval computation for depth 13, residue 1923. -/ +theorem bounds_13_1923 : exactInterval 13 1923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1923 : oddCount 1923 13 = 6 ∧ acceleratedOrbit 13 1923 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1923) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1923.1, data_13_1923.2] + +/-- Complete interval computation for depth 13, residue 1924. -/ +theorem bounds_13_1924 : exactInterval 13 1924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1924 : oddCount 1924 13 = 6 ∧ acceleratedOrbit 13 1924 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1924) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1924.1, data_13_1924.2] + +end Collatz.Research.StoppingAtlas.Batch0592 From 860a1396d5e271705a0e0484c4634faa982e4a66 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:50 +0530 Subject: [PATCH 0593/1001] proof: certify atlas Batch0593 (13:1925 to 13:1939) --- Collatz/Research/StoppingAtlas/Batch0593.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0593.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0593.lean b/Collatz/Research/StoppingAtlas/Batch0593.lean new file mode 100644 index 00000000..cc0e9081 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0593.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0593 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1925. -/ +theorem bounds_13_1925 : exactInterval 13 1925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1925 : oddCount 1925 13 = 6 ∧ acceleratedOrbit 13 1925 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1925) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1925.1, data_13_1925.2] + +/-- Complete interval computation for depth 13, residue 1926. -/ +theorem bounds_13_1926 : exactInterval 13 1926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1926 : oddCount 1926 13 = 6 ∧ acceleratedOrbit 13 1926 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1926) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1926.1, data_13_1926.2] + +/-- Complete interval computation for depth 13, residue 1927. -/ +theorem bounds_13_1927 : exactInterval 13 1927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1927 : oddCount 1927 13 = 6 ∧ acceleratedOrbit 13 1927 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1927) = 3 ^ 6 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1927.1, data_13_1927.2] + +/-- Complete interval computation for depth 13, residue 1928. -/ +theorem bounds_13_1928 : exactInterval 13 1928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1928 : oddCount 1928 13 = 4 ∧ acceleratedOrbit 13 1928 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1928) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1928.1, data_13_1928.2] + +/-- Complete interval computation for depth 13, residue 1929. -/ +theorem bounds_13_1929 : exactInterval 13 1929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1929 : oddCount 1929 13 = 8 ∧ acceleratedOrbit 13 1929 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1929) = 3 ^ 8 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1929.1, data_13_1929.2] + +/-- Complete interval computation for depth 13, residue 1930. -/ +theorem bounds_13_1930 : exactInterval 13 1930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1930 : oddCount 1930 13 = 4 ∧ acceleratedOrbit 13 1930 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1930) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1930.1, data_13_1930.2] + +/-- Complete interval computation for depth 13, residue 1931. -/ +theorem bounds_13_1931 : exactInterval 13 1931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1931 : oddCount 1931 13 = 8 ∧ acceleratedOrbit 13 1931 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1931) = 3 ^ 8 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1931.1, data_13_1931.2] + +/-- Complete interval computation for depth 13, residue 1932. -/ +theorem bounds_13_1932 : exactInterval 13 1932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1932 : oddCount 1932 13 = 4 ∧ acceleratedOrbit 13 1932 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1932) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1932.1, data_13_1932.2] + +/-- Complete interval computation for depth 13, residue 1933. -/ +theorem bounds_13_1933 : exactInterval 13 1933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1933 : oddCount 1933 13 = 4 ∧ acceleratedOrbit 13 1933 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1933) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1933.1, data_13_1933.2] + +/-- Complete interval computation for depth 13, residue 1934. -/ +theorem bounds_13_1934 : exactInterval 13 1934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1934 : oddCount 1934 13 = 8 ∧ acceleratedOrbit 13 1934 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1934) = 3 ^ 8 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1934.1, data_13_1934.2] + +/-- Complete interval computation for depth 13, residue 1935. -/ +theorem bounds_13_1935 : exactInterval 13 1935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1935 : oddCount 1935 13 = 8 ∧ acceleratedOrbit 13 1935 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1935) = 3 ^ 8 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1935.1, data_13_1935.2] + +/-- Complete interval computation for depth 13, residue 1936. -/ +theorem bounds_13_1936 : exactInterval 13 1936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1936 : oddCount 1936 13 = 6 ∧ acceleratedOrbit 13 1936 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1936) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1936.1, data_13_1936.2] + +/-- Complete interval computation for depth 13, residue 1937. -/ +theorem bounds_13_1937 : exactInterval 13 1937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1937 : oddCount 1937 13 = 6 ∧ acceleratedOrbit 13 1937 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1937) = 3 ^ 6 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1937.1, data_13_1937.2] + +/-- Complete interval computation for depth 13, residue 1938. -/ +theorem bounds_13_1938 : exactInterval 13 1938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1938 : oddCount 1938 13 = 6 ∧ acceleratedOrbit 13 1938 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1938) = 3 ^ 6 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1938.1, data_13_1938.2] + +/-- Complete interval computation for depth 13, residue 1939. -/ +theorem bounds_13_1939 : exactInterval 13 1939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1939 : oddCount 1939 13 = 6 ∧ acceleratedOrbit 13 1939 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1939) = 3 ^ 6 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1939.1, data_13_1939.2] + +end Collatz.Research.StoppingAtlas.Batch0593 From d9a3ddbd5862a8d260908713766dfc2d59007046 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:50 +0530 Subject: [PATCH 0594/1001] proof: certify atlas Batch0594 (13:1940 to 13:1954) --- Collatz/Research/StoppingAtlas/Batch0594.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0594.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0594.lean b/Collatz/Research/StoppingAtlas/Batch0594.lean new file mode 100644 index 00000000..63da7ed7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0594.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0594 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1940. -/ +theorem bounds_13_1940 : exactInterval 13 1940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1940 : oddCount 1940 13 = 6 ∧ acceleratedOrbit 13 1940 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1940) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1940.1, data_13_1940.2] + +/-- Complete interval computation for depth 13, residue 1941. -/ +theorem bounds_13_1941 : exactInterval 13 1941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1941 : oddCount 1941 13 = 6 ∧ acceleratedOrbit 13 1941 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1941) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1941.1, data_13_1941.2] + +/-- Complete interval computation for depth 13, residue 1942. -/ +theorem bounds_13_1942 : exactInterval 13 1942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1942 : oddCount 1942 13 = 5 ∧ acceleratedOrbit 13 1942 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1942) = 3 ^ 5 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1942.1, data_13_1942.2] + +/-- Complete interval computation for depth 13, residue 1943. -/ +theorem bounds_13_1943 : exactInterval 13 1943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1943 : oddCount 1943 13 = 5 ∧ acceleratedOrbit 13 1943 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1943) = 3 ^ 5 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1943.1, data_13_1943.2] + +/-- Complete interval computation for depth 13, residue 1944. -/ +theorem bounds_13_1944 : exactInterval 13 1944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1944 : oddCount 1944 13 = 6 ∧ acceleratedOrbit 13 1944 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1944) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1944.1, data_13_1944.2] + +/-- Complete interval computation for depth 13, residue 1945. -/ +theorem bounds_13_1945 : exactInterval 13 1945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1945 : oddCount 1945 13 = 5 ∧ acceleratedOrbit 13 1945 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1945) = 3 ^ 5 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1945.1, data_13_1945.2] + +/-- Complete interval computation for depth 13, residue 1946. -/ +theorem bounds_13_1946 : exactInterval 13 1946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1946 : oddCount 1946 13 = 6 ∧ acceleratedOrbit 13 1946 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1946) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1946.1, data_13_1946.2] + +/-- Complete interval computation for depth 13, residue 1947. -/ +theorem bounds_13_1947 : exactInterval 13 1947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1947 : oddCount 1947 13 = 8 ∧ acceleratedOrbit 13 1947 = 1561 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1947) = 3 ^ 8 * m + 1561 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1947.1, data_13_1947.2] + +/-- Complete interval computation for depth 13, residue 1948. -/ +theorem bounds_13_1948 : exactInterval 13 1948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1948 : oddCount 1948 13 = 8 ∧ acceleratedOrbit 13 1948 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1948) = 3 ^ 8 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1948.1, data_13_1948.2] + +/-- Complete interval computation for depth 13, residue 1949. -/ +theorem bounds_13_1949 : exactInterval 13 1949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1949 : oddCount 1949 13 = 8 ∧ acceleratedOrbit 13 1949 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1949) = 3 ^ 8 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1949.1, data_13_1949.2] + +/-- Complete interval computation for depth 13, residue 1950. -/ +theorem bounds_13_1950 : exactInterval 13 1950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1950 : oddCount 1950 13 = 8 ∧ acceleratedOrbit 13 1950 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1950) = 3 ^ 8 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1950.1, data_13_1950.2] + +/-- Complete interval computation for depth 13, residue 1951. -/ +theorem bounds_13_1951 : exactInterval 13 1951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1951 : oddCount 1951 13 = 9 ∧ acceleratedOrbit 13 1951 = 4691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1951) = 3 ^ 9 * m + 4691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1951.1, data_13_1951.2] + +/-- Complete interval computation for depth 13, residue 1952. -/ +theorem bounds_13_1952 : exactInterval 13 1952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1952 : oddCount 1952 13 = 4 ∧ acceleratedOrbit 13 1952 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1952) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1952.1, data_13_1952.2] + +/-- Complete interval computation for depth 13, residue 1953. -/ +theorem bounds_13_1953 : exactInterval 13 1953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1953 : oddCount 1953 13 = 5 ∧ acceleratedOrbit 13 1953 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1953) = 3 ^ 5 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1953.1, data_13_1953.2] + +/-- Complete interval computation for depth 13, residue 1954. -/ +theorem bounds_13_1954 : exactInterval 13 1954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1954 : oddCount 1954 13 = 6 ∧ acceleratedOrbit 13 1954 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1954) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1954.1, data_13_1954.2] + +end Collatz.Research.StoppingAtlas.Batch0594 From 266780f7e7103ad7f74cf5fe586c0ca65d9f7193 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:51 +0530 Subject: [PATCH 0595/1001] proof: certify atlas Batch0595 (13:1955 to 13:1970) --- Collatz/Research/StoppingAtlas/Batch0595.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0595.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0595.lean b/Collatz/Research/StoppingAtlas/Batch0595.lean new file mode 100644 index 00000000..f39af85f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0595.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0595 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1955. -/ +theorem bounds_13_1955 : exactInterval 13 1955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1955 : oddCount 1955 13 = 6 ∧ acceleratedOrbit 13 1955 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1955) = 3 ^ 6 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1955.1, data_13_1955.2] + +/-- Complete interval computation for depth 13, residue 1956. -/ +theorem bounds_13_1956 : exactInterval 13 1956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1956 : oddCount 1956 13 = 7 ∧ acceleratedOrbit 13 1956 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1956) = 3 ^ 7 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1956.1, data_13_1956.2] + +/-- Complete interval computation for depth 13, residue 1957. -/ +theorem bounds_13_1957 : exactInterval 13 1957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1957 : oddCount 1957 13 = 7 ∧ acceleratedOrbit 13 1957 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1957) = 3 ^ 7 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1957.1, data_13_1957.2] + +/-- Complete interval computation for depth 13, residue 1958. -/ +theorem bounds_13_1958 : exactInterval 13 1958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1958 : oddCount 1958 13 = 7 ∧ acceleratedOrbit 13 1958 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1958) = 3 ^ 7 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1958.1, data_13_1958.2] + +/-- Complete interval computation for depth 13, residue 1959. -/ +theorem bounds_13_1959 : exactInterval 13 1959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1959 : oddCount 1959 13 = 9 ∧ acceleratedOrbit 13 1959 = 4711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1959) = 3 ^ 9 * m + 4711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1959.1, data_13_1959.2] + +/-- Complete interval computation for depth 13, residue 1960. -/ +theorem bounds_13_1960 : exactInterval 13 1960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1960 : oddCount 1960 13 = 4 ∧ acceleratedOrbit 13 1960 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1960) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1960.1, data_13_1960.2] + +/-- Complete interval computation for depth 13, residue 1961. -/ +theorem bounds_13_1961 : exactInterval 13 1961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1961 : oddCount 1961 13 = 11 ∧ acceleratedOrbit 13 1961 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1961) = 3 ^ 11 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1961.1, data_13_1961.2] + +/-- Complete interval computation for depth 13, residue 1962. -/ +theorem bounds_13_1962 : exactInterval 13 1962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1962 : oddCount 1962 13 = 4 ∧ acceleratedOrbit 13 1962 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1962) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1962.1, data_13_1962.2] + +/-- Complete interval computation for depth 13, residue 1963. -/ +theorem bounds_13_1963 : exactInterval 13 1963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1963 : oddCount 1963 13 = 9 ∧ acceleratedOrbit 13 1963 = 4724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1963) = 3 ^ 9 * m + 4724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1963.1, data_13_1963.2] + +/-- Complete interval computation for depth 13, residue 1964. -/ +theorem bounds_13_1964 : exactInterval 13 1964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1964 : oddCount 1964 13 = 8 ∧ acceleratedOrbit 13 1964 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1964) = 3 ^ 8 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1964.1, data_13_1964.2] + +/-- Complete interval computation for depth 13, residue 1965. -/ +theorem bounds_13_1965 : exactInterval 13 1965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1965 : oddCount 1965 13 = 8 ∧ acceleratedOrbit 13 1965 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1965) = 3 ^ 8 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1965.1, data_13_1965.2] + +/-- Complete interval computation for depth 13, residue 1966. -/ +theorem bounds_13_1966 : exactInterval 13 1966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1966 : oddCount 1966 13 = 8 ∧ acceleratedOrbit 13 1966 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1966) = 3 ^ 8 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1966.1, data_13_1966.2] + +/-- Complete interval computation for depth 13, residue 1967. -/ +theorem bounds_13_1967 : exactInterval 13 1967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1967) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1967 : oddCount 1967 13 = 7 ∧ acceleratedOrbit 13 1967 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1967) = 3 ^ 7 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1967.1, data_13_1967.2] + +/-- Complete interval computation for depth 13, residue 1968. -/ +theorem bounds_13_1968 : exactInterval 13 1968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1968 : oddCount 1968 13 = 5 ∧ acceleratedOrbit 13 1968 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1968) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1968.1, data_13_1968.2] + +/-- Complete interval computation for depth 13, residue 1969. -/ +theorem bounds_13_1969 : exactInterval 13 1969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1969 : oddCount 1969 13 = 4 ∧ acceleratedOrbit 13 1969 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1969) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1969.1, data_13_1969.2] + +/-- Complete interval computation for depth 13, residue 1970. -/ +theorem bounds_13_1970 : exactInterval 13 1970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1970 : oddCount 1970 13 = 4 ∧ acceleratedOrbit 13 1970 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1970) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1970.1, data_13_1970.2] + +end Collatz.Research.StoppingAtlas.Batch0595 From ae49a359193b554eba0e66d06af9b78a1e9a189d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:51 +0530 Subject: [PATCH 0596/1001] proof: certify atlas Batch0596 (13:1971 to 13:1985) --- Collatz/Research/StoppingAtlas/Batch0596.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0596.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0596.lean b/Collatz/Research/StoppingAtlas/Batch0596.lean new file mode 100644 index 00000000..4ababe26 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0596.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0596 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1971. -/ +theorem bounds_13_1971 : exactInterval 13 1971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1971 : oddCount 1971 13 = 4 ∧ acceleratedOrbit 13 1971 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1971) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1971.1, data_13_1971.2] + +/-- Complete interval computation for depth 13, residue 1972. -/ +theorem bounds_13_1972 : exactInterval 13 1972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1972 : oddCount 1972 13 = 5 ∧ acceleratedOrbit 13 1972 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1972) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1972.1, data_13_1972.2] + +/-- Complete interval computation for depth 13, residue 1973. -/ +theorem bounds_13_1973 : exactInterval 13 1973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1973 : oddCount 1973 13 = 5 ∧ acceleratedOrbit 13 1973 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1973) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1973.1, data_13_1973.2] + +/-- Complete interval computation for depth 13, residue 1974. -/ +theorem bounds_13_1974 : exactInterval 13 1974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1974 : oddCount 1974 13 = 6 ∧ acceleratedOrbit 13 1974 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1974) = 3 ^ 6 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1974.1, data_13_1974.2] + +/-- Complete interval computation for depth 13, residue 1975. -/ +theorem bounds_13_1975 : exactInterval 13 1975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1975 : oddCount 1975 13 = 6 ∧ acceleratedOrbit 13 1975 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1975) = 3 ^ 6 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1975.1, data_13_1975.2] + +/-- Complete interval computation for depth 13, residue 1976. -/ +theorem bounds_13_1976 : exactInterval 13 1976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1976 : oddCount 1976 13 = 5 ∧ acceleratedOrbit 13 1976 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1976) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1976.1, data_13_1976.2] + +/-- Complete interval computation for depth 13, residue 1977. -/ +theorem bounds_13_1977 : exactInterval 13 1977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1977 : oddCount 1977 13 = 7 ∧ acceleratedOrbit 13 1977 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1977) = 3 ^ 7 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1977.1, data_13_1977.2] + +/-- Complete interval computation for depth 13, residue 1978. -/ +theorem bounds_13_1978 : exactInterval 13 1978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1978 : oddCount 1978 13 = 5 ∧ acceleratedOrbit 13 1978 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1978) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1978.1, data_13_1978.2] + +/-- Complete interval computation for depth 13, residue 1979. -/ +theorem bounds_13_1979 : exactInterval 13 1979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1979 : oddCount 1979 13 = 7 ∧ acceleratedOrbit 13 1979 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1979) = 3 ^ 7 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1979.1, data_13_1979.2] + +/-- Complete interval computation for depth 13, residue 1980. -/ +theorem bounds_13_1980 : exactInterval 13 1980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1980 : oddCount 1980 13 = 9 ∧ acceleratedOrbit 13 1980 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1980) = 3 ^ 9 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1980.1, data_13_1980.2] + +/-- Complete interval computation for depth 13, residue 1981. -/ +theorem bounds_13_1981 : exactInterval 13 1981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1981 : oddCount 1981 13 = 9 ∧ acceleratedOrbit 13 1981 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1981) = 3 ^ 9 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1981.1, data_13_1981.2] + +/-- Complete interval computation for depth 13, residue 1982. -/ +theorem bounds_13_1982 : exactInterval 13 1982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1982 : oddCount 1982 13 = 9 ∧ acceleratedOrbit 13 1982 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1982) = 3 ^ 9 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1982.1, data_13_1982.2] + +/-- Complete interval computation for depth 13, residue 1983. -/ +theorem bounds_13_1983 : exactInterval 13 1983 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1983) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1983 : oddCount 1983 13 = 8 ∧ acceleratedOrbit 13 1983 = 1589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1983) = 3 ^ 8 * m + 1589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1983.1, data_13_1983.2] + +/-- Complete interval computation for depth 13, residue 1984. -/ +theorem bounds_13_1984 : exactInterval 13 1984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1984 : oddCount 1984 13 = 6 ∧ acceleratedOrbit 13 1984 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1984) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1984.1, data_13_1984.2] + +/-- Complete interval computation for depth 13, residue 1985. -/ +theorem bounds_13_1985 : exactInterval 13 1985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1985 : oddCount 1985 13 = 5 ∧ acceleratedOrbit 13 1985 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1985) = 3 ^ 5 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1985.1, data_13_1985.2] + +end Collatz.Research.StoppingAtlas.Batch0596 From 507b2bcb46ad3589aced1cd6d792601ab88973a6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:53 +0530 Subject: [PATCH 0597/1001] proof: certify atlas Batch0597 (13:1986 to 13:2000) --- Collatz/Research/StoppingAtlas/Batch0597.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0597.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0597.lean b/Collatz/Research/StoppingAtlas/Batch0597.lean new file mode 100644 index 00000000..5088a8c4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0597.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0597 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 1986. -/ +theorem bounds_13_1986 : exactInterval 13 1986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1986 : oddCount 1986 13 = 8 ∧ acceleratedOrbit 13 1986 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1986) = 3 ^ 8 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1986.1, data_13_1986.2] + +/-- Complete interval computation for depth 13, residue 1987. -/ +theorem bounds_13_1987 : exactInterval 13 1987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1987 : oddCount 1987 13 = 8 ∧ acceleratedOrbit 13 1987 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1987) = 3 ^ 8 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1987.1, data_13_1987.2] + +/-- Complete interval computation for depth 13, residue 1988. -/ +theorem bounds_13_1988 : exactInterval 13 1988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1988 : oddCount 1988 13 = 4 ∧ acceleratedOrbit 13 1988 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1988) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1988.1, data_13_1988.2] + +/-- Complete interval computation for depth 13, residue 1989. -/ +theorem bounds_13_1989 : exactInterval 13 1989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1989 : oddCount 1989 13 = 4 ∧ acceleratedOrbit 13 1989 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1989) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1989.1, data_13_1989.2] + +/-- Complete interval computation for depth 13, residue 1990. -/ +theorem bounds_13_1990 : exactInterval 13 1990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1990 : oddCount 1990 13 = 4 ∧ acceleratedOrbit 13 1990 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1990) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1990.1, data_13_1990.2] + +/-- Complete interval computation for depth 13, residue 1991. -/ +theorem bounds_13_1991 : exactInterval 13 1991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1991 : oddCount 1991 13 = 7 ∧ acceleratedOrbit 13 1991 = 532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1991) = 3 ^ 7 * m + 532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1991.1, data_13_1991.2] + +/-- Complete interval computation for depth 13, residue 1992. -/ +theorem bounds_13_1992 : exactInterval 13 1992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1992 : oddCount 1992 13 = 6 ∧ acceleratedOrbit 13 1992 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1992) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1992.1, data_13_1992.2] + +/-- Complete interval computation for depth 13, residue 1993. -/ +theorem bounds_13_1993 : exactInterval 13 1993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1993 : oddCount 1993 13 = 7 ∧ acceleratedOrbit 13 1993 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1993) = 3 ^ 7 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1993.1, data_13_1993.2] + +/-- Complete interval computation for depth 13, residue 1994. -/ +theorem bounds_13_1994 : exactInterval 13 1994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1994 : oddCount 1994 13 = 6 ∧ acceleratedOrbit 13 1994 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1994) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1994.1, data_13_1994.2] + +/-- Complete interval computation for depth 13, residue 1995. -/ +theorem bounds_13_1995 : exactInterval 13 1995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1995 : oddCount 1995 13 = 6 ∧ acceleratedOrbit 13 1995 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1995) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1995.1, data_13_1995.2] + +/-- Complete interval computation for depth 13, residue 1996. -/ +theorem bounds_13_1996 : exactInterval 13 1996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1996 : oddCount 1996 13 = 6 ∧ acceleratedOrbit 13 1996 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1996) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1996.1, data_13_1996.2] + +/-- Complete interval computation for depth 13, residue 1997. -/ +theorem bounds_13_1997 : exactInterval 13 1997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1997 : oddCount 1997 13 = 6 ∧ acceleratedOrbit 13 1997 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1997) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1997.1, data_13_1997.2] + +/-- Complete interval computation for depth 13, residue 1998. -/ +theorem bounds_13_1998 : exactInterval 13 1998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1998 : oddCount 1998 13 = 6 ∧ acceleratedOrbit 13 1998 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1998) = 3 ^ 6 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1998.1, data_13_1998.2] + +/-- Complete interval computation for depth 13, residue 1999. -/ +theorem bounds_13_1999 : exactInterval 13 1999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_1999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 1999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_1999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_1999 : oddCount 1999 13 = 6 ∧ acceleratedOrbit 13 1999 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_1999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 1999) = 3 ^ 6 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_1999.1, data_13_1999.2] + +/-- Complete interval computation for depth 13, residue 2000. -/ +theorem bounds_13_2000 : exactInterval 13 2000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2000 : oddCount 2000 13 = 6 ∧ acceleratedOrbit 13 2000 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2000) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2000.1, data_13_2000.2] + +end Collatz.Research.StoppingAtlas.Batch0597 From 755590c6080dbec8f17b3171ba555700788799a6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:53 +0530 Subject: [PATCH 0598/1001] proof: certify atlas Batch0598 (13:2001 to 13:2016) --- Collatz/Research/StoppingAtlas/Batch0598.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0598.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0598.lean b/Collatz/Research/StoppingAtlas/Batch0598.lean new file mode 100644 index 00000000..ab9fded0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0598.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0598 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2001. -/ +theorem bounds_13_2001 : exactInterval 13 2001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2001 : oddCount 2001 13 = 6 ∧ acceleratedOrbit 13 2001 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2001) = 3 ^ 6 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2001.1, data_13_2001.2] + +/-- Complete interval computation for depth 13, residue 2002. -/ +theorem bounds_13_2002 : exactInterval 13 2002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2002 : oddCount 2002 13 = 9 ∧ acceleratedOrbit 13 2002 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2002) = 3 ^ 9 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2002.1, data_13_2002.2] + +/-- Complete interval computation for depth 13, residue 2003. -/ +theorem bounds_13_2003 : exactInterval 13 2003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2003 : oddCount 2003 13 = 9 ∧ acceleratedOrbit 13 2003 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2003) = 3 ^ 9 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2003.1, data_13_2003.2] + +/-- Complete interval computation for depth 13, residue 2004. -/ +theorem bounds_13_2004 : exactInterval 13 2004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2004 : oddCount 2004 13 = 6 ∧ acceleratedOrbit 13 2004 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2004) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2004.1, data_13_2004.2] + +/-- Complete interval computation for depth 13, residue 2005. -/ +theorem bounds_13_2005 : exactInterval 13 2005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2005 : oddCount 2005 13 = 6 ∧ acceleratedOrbit 13 2005 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2005) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2005.1, data_13_2005.2] + +/-- Complete interval computation for depth 13, residue 2006. -/ +theorem bounds_13_2006 : exactInterval 13 2006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2006 : oddCount 2006 13 = 8 ∧ acceleratedOrbit 13 2006 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2006) = 3 ^ 8 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2006.1, data_13_2006.2] + +/-- Complete interval computation for depth 13, residue 2007. -/ +theorem bounds_13_2007 : exactInterval 13 2007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2007 : oddCount 2007 13 = 8 ∧ acceleratedOrbit 13 2007 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2007) = 3 ^ 8 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2007.1, data_13_2007.2] + +/-- Complete interval computation for depth 13, residue 2008. -/ +theorem bounds_13_2008 : exactInterval 13 2008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2008 : oddCount 2008 13 = 8 ∧ acceleratedOrbit 13 2008 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2008) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2008.1, data_13_2008.2] + +/-- Complete interval computation for depth 13, residue 2009. -/ +theorem bounds_13_2009 : exactInterval 13 2009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2009 : oddCount 2009 13 = 4 ∧ acceleratedOrbit 13 2009 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2009) = 3 ^ 4 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2009.1, data_13_2009.2] + +/-- Complete interval computation for depth 13, residue 2010. -/ +theorem bounds_13_2010 : exactInterval 13 2010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2010 : oddCount 2010 13 = 8 ∧ acceleratedOrbit 13 2010 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2010) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2010.1, data_13_2010.2] + +/-- Complete interval computation for depth 13, residue 2011. -/ +theorem bounds_13_2011 : exactInterval 13 2011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2011 : oddCount 2011 13 = 8 ∧ acceleratedOrbit 13 2011 = 1613 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2011) = 3 ^ 8 * m + 1613 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2011.1, data_13_2011.2] + +/-- Complete interval computation for depth 13, residue 2012. -/ +theorem bounds_13_2012 : exactInterval 13 2012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2012 : oddCount 2012 13 = 8 ∧ acceleratedOrbit 13 2012 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2012) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2012.1, data_13_2012.2] + +/-- Complete interval computation for depth 13, residue 2013. -/ +theorem bounds_13_2013 : exactInterval 13 2013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2013 : oddCount 2013 13 = 8 ∧ acceleratedOrbit 13 2013 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2013) = 3 ^ 8 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2013.1, data_13_2013.2] + +/-- Complete interval computation for depth 13, residue 2014. -/ +theorem bounds_13_2014 : exactInterval 13 2014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2014 : oddCount 2014 13 = 8 ∧ acceleratedOrbit 13 2014 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2014) = 3 ^ 8 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2014.1, data_13_2014.2] + +/-- Complete interval computation for depth 13, residue 2015. -/ +theorem bounds_13_2015 : exactInterval 13 2015 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2015) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2015 : oddCount 2015 13 = 8 ∧ acceleratedOrbit 13 2015 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2015) = 3 ^ 8 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2015.1, data_13_2015.2] + +/-- Complete interval computation for depth 13, residue 2016. -/ +theorem bounds_13_2016 : exactInterval 13 2016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2016 : oddCount 2016 13 = 6 ∧ acceleratedOrbit 13 2016 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2016) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2016.1, data_13_2016.2] + +end Collatz.Research.StoppingAtlas.Batch0598 From 9d9ec0ff5695e64fe04fce61c337d456aee17c23 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:54 +0530 Subject: [PATCH 0599/1001] proof: certify atlas Batch0599 (13:2017 to 13:2031) --- Collatz/Research/StoppingAtlas/Batch0599.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0599.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0599.lean b/Collatz/Research/StoppingAtlas/Batch0599.lean new file mode 100644 index 00000000..2a90144b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0599.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0599 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2017. -/ +theorem bounds_13_2017 : exactInterval 13 2017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2017 : oddCount 2017 13 = 9 ∧ acceleratedOrbit 13 2017 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2017) = 3 ^ 9 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2017.1, data_13_2017.2] + +/-- Complete interval computation for depth 13, residue 2018. -/ +theorem bounds_13_2018 : exactInterval 13 2018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2018 : oddCount 2018 13 = 6 ∧ acceleratedOrbit 13 2018 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2018) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2018.1, data_13_2018.2] + +/-- Complete interval computation for depth 13, residue 2019. -/ +theorem bounds_13_2019 : exactInterval 13 2019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2019 : oddCount 2019 13 = 6 ∧ acceleratedOrbit 13 2019 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2019) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2019.1, data_13_2019.2] + +/-- Complete interval computation for depth 13, residue 2020. -/ +theorem bounds_13_2020 : exactInterval 13 2020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2020 : oddCount 2020 13 = 7 ∧ acceleratedOrbit 13 2020 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2020) = 3 ^ 7 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2020.1, data_13_2020.2] + +/-- Complete interval computation for depth 13, residue 2021. -/ +theorem bounds_13_2021 : exactInterval 13 2021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2021 : oddCount 2021 13 = 7 ∧ acceleratedOrbit 13 2021 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2021) = 3 ^ 7 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2021.1, data_13_2021.2] + +/-- Complete interval computation for depth 13, residue 2022. -/ +theorem bounds_13_2022 : exactInterval 13 2022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2022 : oddCount 2022 13 = 7 ∧ acceleratedOrbit 13 2022 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2022) = 3 ^ 7 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2022.1, data_13_2022.2] + +/-- Complete interval computation for depth 13, residue 2023. -/ +theorem bounds_13_2023 : exactInterval 13 2023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2023) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2023 : oddCount 2023 13 = 8 ∧ acceleratedOrbit 13 2023 = 1622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2023) = 3 ^ 8 * m + 1622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2023.1, data_13_2023.2] + +/-- Complete interval computation for depth 13, residue 2024. -/ +theorem bounds_13_2024 : exactInterval 13 2024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2024 : oddCount 2024 13 = 6 ∧ acceleratedOrbit 13 2024 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2024) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2024.1, data_13_2024.2] + +/-- Complete interval computation for depth 13, residue 2025. -/ +theorem bounds_13_2025 : exactInterval 13 2025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2025 : oddCount 2025 13 = 9 ∧ acceleratedOrbit 13 2025 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2025) = 3 ^ 9 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2025.1, data_13_2025.2] + +/-- Complete interval computation for depth 13, residue 2026. -/ +theorem bounds_13_2026 : exactInterval 13 2026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2026 : oddCount 2026 13 = 6 ∧ acceleratedOrbit 13 2026 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2026) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2026.1, data_13_2026.2] + +/-- Complete interval computation for depth 13, residue 2027. -/ +theorem bounds_13_2027 : exactInterval 13 2027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2027 : oddCount 2027 13 = 8 ∧ acceleratedOrbit 13 2027 = 1625 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2027) = 3 ^ 8 * m + 1625 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2027.1, data_13_2027.2] + +/-- Complete interval computation for depth 13, residue 2028. -/ +theorem bounds_13_2028 : exactInterval 13 2028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2028 : oddCount 2028 13 = 6 ∧ acceleratedOrbit 13 2028 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2028) = 3 ^ 6 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2028.1, data_13_2028.2] + +/-- Complete interval computation for depth 13, residue 2029. -/ +theorem bounds_13_2029 : exactInterval 13 2029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2029 : oddCount 2029 13 = 6 ∧ acceleratedOrbit 13 2029 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2029) = 3 ^ 6 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2029.1, data_13_2029.2] + +/-- Complete interval computation for depth 13, residue 2030. -/ +theorem bounds_13_2030 : exactInterval 13 2030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2030 : oddCount 2030 13 = 6 ∧ acceleratedOrbit 13 2030 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2030) = 3 ^ 6 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2030.1, data_13_2030.2] + +/-- Complete interval computation for depth 13, residue 2031. -/ +theorem bounds_13_2031 : exactInterval 13 2031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2031 : oddCount 2031 13 = 8 ∧ acceleratedOrbit 13 2031 = 1628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2031) = 3 ^ 8 * m + 1628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2031.1, data_13_2031.2] + +end Collatz.Research.StoppingAtlas.Batch0599 From 0d8586faa2a378ed0c8bd7ed4c024ea6c36bfd16 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:55 +0530 Subject: [PATCH 0600/1001] proof: certify atlas Batch0600 (13:2032 to 13:2047) --- Collatz/Research/StoppingAtlas/Batch0600.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0600.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0600.lean b/Collatz/Research/StoppingAtlas/Batch0600.lean new file mode 100644 index 00000000..36f0323b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0600.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0600 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2032. -/ +theorem bounds_13_2032 : exactInterval 13 2032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2032 : oddCount 2032 13 = 8 ∧ acceleratedOrbit 13 2032 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2032) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2032.1, data_13_2032.2] + +/-- Complete interval computation for depth 13, residue 2033. -/ +theorem bounds_13_2033 : exactInterval 13 2033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2033 : oddCount 2033 13 = 6 ∧ acceleratedOrbit 13 2033 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2033) = 3 ^ 6 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2033.1, data_13_2033.2] + +/-- Complete interval computation for depth 13, residue 2034. -/ +theorem bounds_13_2034 : exactInterval 13 2034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2034 : oddCount 2034 13 = 8 ∧ acceleratedOrbit 13 2034 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2034) = 3 ^ 8 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2034.1, data_13_2034.2] + +/-- Complete interval computation for depth 13, residue 2035. -/ +theorem bounds_13_2035 : exactInterval 13 2035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2035 : oddCount 2035 13 = 8 ∧ acceleratedOrbit 13 2035 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2035) = 3 ^ 8 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2035.1, data_13_2035.2] + +/-- Complete interval computation for depth 13, residue 2036. -/ +theorem bounds_13_2036 : exactInterval 13 2036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2036 : oddCount 2036 13 = 8 ∧ acceleratedOrbit 13 2036 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2036) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2036.1, data_13_2036.2] + +/-- Complete interval computation for depth 13, residue 2037. -/ +theorem bounds_13_2037 : exactInterval 13 2037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2037 : oddCount 2037 13 = 8 ∧ acceleratedOrbit 13 2037 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2037) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2037.1, data_13_2037.2] + +/-- Complete interval computation for depth 13, residue 2038. -/ +theorem bounds_13_2038 : exactInterval 13 2038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2038 : oddCount 2038 13 = 7 ∧ acceleratedOrbit 13 2038 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2038) = 3 ^ 7 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2038.1, data_13_2038.2] + +/-- Complete interval computation for depth 13, residue 2039. -/ +theorem bounds_13_2039 : exactInterval 13 2039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2039 : oddCount 2039 13 = 7 ∧ acceleratedOrbit 13 2039 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2039) = 3 ^ 7 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2039.1, data_13_2039.2] + +/-- Complete interval computation for depth 13, residue 2040. -/ +theorem bounds_13_2040 : exactInterval 13 2040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2040 : oddCount 2040 13 = 8 ∧ acceleratedOrbit 13 2040 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2040) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2040.1, data_13_2040.2] + +/-- Complete interval computation for depth 13, residue 2041. -/ +theorem bounds_13_2041 : exactInterval 13 2041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2041 : oddCount 2041 13 = 8 ∧ acceleratedOrbit 13 2041 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2041) = 3 ^ 8 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2041.1, data_13_2041.2] + +/-- Complete interval computation for depth 13, residue 2042. -/ +theorem bounds_13_2042 : exactInterval 13 2042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2042 : oddCount 2042 13 = 8 ∧ acceleratedOrbit 13 2042 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2042) = 3 ^ 8 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2042.1, data_13_2042.2] + +/-- Complete interval computation for depth 13, residue 2043. -/ +theorem bounds_13_2043 : exactInterval 13 2043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2043 : oddCount 2043 13 = 10 ∧ acceleratedOrbit 13 2043 = 14741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2043) = 3 ^ 10 * m + 14741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2043.1, data_13_2043.2] + +/-- Complete interval computation for depth 13, residue 2044. -/ +theorem bounds_13_2044 : exactInterval 13 2044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2044 : oddCount 2044 13 = 10 ∧ acceleratedOrbit 13 2044 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2044) = 3 ^ 10 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2044.1, data_13_2044.2] + +/-- Complete interval computation for depth 13, residue 2045. -/ +theorem bounds_13_2045 : exactInterval 13 2045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2045 : oddCount 2045 13 = 10 ∧ acceleratedOrbit 13 2045 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2045) = 3 ^ 10 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2045.1, data_13_2045.2] + +/-- Complete interval computation for depth 13, residue 2046. -/ +theorem bounds_13_2046 : exactInterval 13 2046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2046 : oddCount 2046 13 = 10 ∧ acceleratedOrbit 13 2046 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2046) = 3 ^ 10 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2046.1, data_13_2046.2] + +/-- Complete interval computation for depth 13, residue 2047. -/ +theorem bounds_13_2047 : exactInterval 13 2047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2047) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2047 : oddCount 2047 13 = 12 ∧ acceleratedOrbit 13 2047 = 132860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2047) = 3 ^ 12 * m + 132860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2047.1, data_13_2047.2] + +end Collatz.Research.StoppingAtlas.Batch0600 From 12a017907458e0d2c2148b910a821da1cf9d6898 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:56 +0530 Subject: [PATCH 0601/1001] proof: certify atlas Batch0601 (13:2048 to 13:2062) --- Collatz/Research/StoppingAtlas/Batch0601.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0601.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0601.lean b/Collatz/Research/StoppingAtlas/Batch0601.lean new file mode 100644 index 00000000..a9db1a28 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0601.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0601 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2048. -/ +theorem bounds_13_2048 : exactInterval 13 2048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2048 : oddCount 2048 13 = 1 ∧ acceleratedOrbit 13 2048 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2048) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2048.1, data_13_2048.2] + +/-- Complete interval computation for depth 13, residue 2049. -/ +theorem bounds_13_2049 : exactInterval 13 2049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2049 : oddCount 2049 13 = 8 ∧ acceleratedOrbit 13 2049 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2049) = 3 ^ 8 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2049.1, data_13_2049.2] + +/-- Complete interval computation for depth 13, residue 2050. -/ +theorem bounds_13_2050 : exactInterval 13 2050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2050 : oddCount 2050 13 = 5 ∧ acceleratedOrbit 13 2050 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2050) = 3 ^ 5 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2050.1, data_13_2050.2] + +/-- Complete interval computation for depth 13, residue 2051. -/ +theorem bounds_13_2051 : exactInterval 13 2051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2051 : oddCount 2051 13 = 5 ∧ acceleratedOrbit 13 2051 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2051) = 3 ^ 5 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2051.1, data_13_2051.2] + +/-- Complete interval computation for depth 13, residue 2052. -/ +theorem bounds_13_2052 : exactInterval 13 2052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2052 : oddCount 2052 13 = 6 ∧ acceleratedOrbit 13 2052 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2052) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2052.1, data_13_2052.2] + +/-- Complete interval computation for depth 13, residue 2053. -/ +theorem bounds_13_2053 : exactInterval 13 2053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2053 : oddCount 2053 13 = 6 ∧ acceleratedOrbit 13 2053 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2053) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2053.1, data_13_2053.2] + +/-- Complete interval computation for depth 13, residue 2054. -/ +theorem bounds_13_2054 : exactInterval 13 2054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2054 : oddCount 2054 13 = 6 ∧ acceleratedOrbit 13 2054 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2054) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2054.1, data_13_2054.2] + +/-- Complete interval computation for depth 13, residue 2055. -/ +theorem bounds_13_2055 : exactInterval 13 2055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2055 : oddCount 2055 13 = 5 ∧ acceleratedOrbit 13 2055 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2055) = 3 ^ 5 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2055.1, data_13_2055.2] + +/-- Complete interval computation for depth 13, residue 2056. -/ +theorem bounds_13_2056 : exactInterval 13 2056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2056 : oddCount 2056 13 = 5 ∧ acceleratedOrbit 13 2056 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2056) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2056.1, data_13_2056.2] + +/-- Complete interval computation for depth 13, residue 2057. -/ +theorem bounds_13_2057 : exactInterval 13 2057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2057 : oddCount 2057 13 = 7 ∧ acceleratedOrbit 13 2057 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2057) = 3 ^ 7 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2057.1, data_13_2057.2] + +/-- Complete interval computation for depth 13, residue 2058. -/ +theorem bounds_13_2058 : exactInterval 13 2058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2058 : oddCount 2058 13 = 5 ∧ acceleratedOrbit 13 2058 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2058) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2058.1, data_13_2058.2] + +/-- Complete interval computation for depth 13, residue 2059. -/ +theorem bounds_13_2059 : exactInterval 13 2059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2059 : oddCount 2059 13 = 6 ∧ acceleratedOrbit 13 2059 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2059) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2059.1, data_13_2059.2] + +/-- Complete interval computation for depth 13, residue 2060. -/ +theorem bounds_13_2060 : exactInterval 13 2060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2060 : oddCount 2060 13 = 5 ∧ acceleratedOrbit 13 2060 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2060) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2060.1, data_13_2060.2] + +/-- Complete interval computation for depth 13, residue 2061. -/ +theorem bounds_13_2061 : exactInterval 13 2061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2061 : oddCount 2061 13 = 5 ∧ acceleratedOrbit 13 2061 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2061) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2061.1, data_13_2061.2] + +/-- Complete interval computation for depth 13, residue 2062. -/ +theorem bounds_13_2062 : exactInterval 13 2062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2062 : oddCount 2062 13 = 6 ∧ acceleratedOrbit 13 2062 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2062) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2062.1, data_13_2062.2] + +end Collatz.Research.StoppingAtlas.Batch0601 From fdc89bace563ab7550a1e23a7fd4edc298d3f47e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:56 +0530 Subject: [PATCH 0602/1001] proof: certify atlas Batch0602 (13:2063 to 13:2077) --- Collatz/Research/StoppingAtlas/Batch0602.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0602.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0602.lean b/Collatz/Research/StoppingAtlas/Batch0602.lean new file mode 100644 index 00000000..a57d806f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0602.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0602 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2063. -/ +theorem bounds_13_2063 : exactInterval 13 2063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2063 : oddCount 2063 13 = 6 ∧ acceleratedOrbit 13 2063 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2063) = 3 ^ 6 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2063.1, data_13_2063.2] + +/-- Complete interval computation for depth 13, residue 2064. -/ +theorem bounds_13_2064 : exactInterval 13 2064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2064 : oddCount 2064 13 = 6 ∧ acceleratedOrbit 13 2064 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2064) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2064.1, data_13_2064.2] + +/-- Complete interval computation for depth 13, residue 2065. -/ +theorem bounds_13_2065 : exactInterval 13 2065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2065 : oddCount 2065 13 = 5 ∧ acceleratedOrbit 13 2065 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2065) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2065.1, data_13_2065.2] + +/-- Complete interval computation for depth 13, residue 2066. -/ +theorem bounds_13_2066 : exactInterval 13 2066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2066 : oddCount 2066 13 = 7 ∧ acceleratedOrbit 13 2066 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2066) = 3 ^ 7 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2066.1, data_13_2066.2] + +/-- Complete interval computation for depth 13, residue 2067. -/ +theorem bounds_13_2067 : exactInterval 13 2067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2067 : oddCount 2067 13 = 7 ∧ acceleratedOrbit 13 2067 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2067) = 3 ^ 7 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2067.1, data_13_2067.2] + +/-- Complete interval computation for depth 13, residue 2068. -/ +theorem bounds_13_2068 : exactInterval 13 2068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2068 : oddCount 2068 13 = 6 ∧ acceleratedOrbit 13 2068 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2068) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2068.1, data_13_2068.2] + +/-- Complete interval computation for depth 13, residue 2069. -/ +theorem bounds_13_2069 : exactInterval 13 2069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2069 : oddCount 2069 13 = 6 ∧ acceleratedOrbit 13 2069 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2069) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2069.1, data_13_2069.2] + +/-- Complete interval computation for depth 13, residue 2070. -/ +theorem bounds_13_2070 : exactInterval 13 2070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2070 : oddCount 2070 13 = 5 ∧ acceleratedOrbit 13 2070 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2070) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2070.1, data_13_2070.2] + +/-- Complete interval computation for depth 13, residue 2071. -/ +theorem bounds_13_2071 : exactInterval 13 2071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2071 : oddCount 2071 13 = 5 ∧ acceleratedOrbit 13 2071 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2071) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2071.1, data_13_2071.2] + +/-- Complete interval computation for depth 13, residue 2072. -/ +theorem bounds_13_2072 : exactInterval 13 2072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2072 : oddCount 2072 13 = 6 ∧ acceleratedOrbit 13 2072 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2072) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2072.1, data_13_2072.2] + +/-- Complete interval computation for depth 13, residue 2073. -/ +theorem bounds_13_2073 : exactInterval 13 2073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2073 : oddCount 2073 13 = 8 ∧ acceleratedOrbit 13 2073 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2073) = 3 ^ 8 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2073.1, data_13_2073.2] + +/-- Complete interval computation for depth 13, residue 2074. -/ +theorem bounds_13_2074 : exactInterval 13 2074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2074 : oddCount 2074 13 = 6 ∧ acceleratedOrbit 13 2074 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2074) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2074.1, data_13_2074.2] + +/-- Complete interval computation for depth 13, residue 2075. -/ +theorem bounds_13_2075 : exactInterval 13 2075 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2075) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2075 : oddCount 2075 13 = 8 ∧ acceleratedOrbit 13 2075 = 1663 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2075) = 3 ^ 8 * m + 1663 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2075.1, data_13_2075.2] + +/-- Complete interval computation for depth 13, residue 2076. -/ +theorem bounds_13_2076 : exactInterval 13 2076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2076 : oddCount 2076 13 = 7 ∧ acceleratedOrbit 13 2076 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2076) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2076.1, data_13_2076.2] + +/-- Complete interval computation for depth 13, residue 2077. -/ +theorem bounds_13_2077 : exactInterval 13 2077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2077 : oddCount 2077 13 = 7 ∧ acceleratedOrbit 13 2077 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2077) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2077.1, data_13_2077.2] + +end Collatz.Research.StoppingAtlas.Batch0602 From 8c857a275f76a1bf6493184ac7e8febe7de41f16 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:56 +0530 Subject: [PATCH 0603/1001] proof: certify atlas Batch0603 (13:2078 to 13:2093) --- Collatz/Research/StoppingAtlas/Batch0603.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0603.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0603.lean b/Collatz/Research/StoppingAtlas/Batch0603.lean new file mode 100644 index 00000000..7bc0b1b7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0603.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0603 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2078. -/ +theorem bounds_13_2078 : exactInterval 13 2078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2078 : oddCount 2078 13 = 7 ∧ acceleratedOrbit 13 2078 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2078) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2078.1, data_13_2078.2] + +/-- Complete interval computation for depth 13, residue 2079. -/ +theorem bounds_13_2079 : exactInterval 13 2079 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2079) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2079 : oddCount 2079 13 = 8 ∧ acceleratedOrbit 13 2079 = 1666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2079) = 3 ^ 8 * m + 1666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2079.1, data_13_2079.2] + +/-- Complete interval computation for depth 13, residue 2080. -/ +theorem bounds_13_2080 : exactInterval 13 2080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2080 : oddCount 2080 13 = 3 ∧ acceleratedOrbit 13 2080 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2080) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2080.1, data_13_2080.2] + +/-- Complete interval computation for depth 13, residue 2081. -/ +theorem bounds_13_2081 : exactInterval 13 2081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2081 : oddCount 2081 13 = 7 ∧ acceleratedOrbit 13 2081 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2081) = 3 ^ 7 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2081.1, data_13_2081.2] + +/-- Complete interval computation for depth 13, residue 2082. -/ +theorem bounds_13_2082 : exactInterval 13 2082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2082 : oddCount 2082 13 = 6 ∧ acceleratedOrbit 13 2082 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2082) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2082.1, data_13_2082.2] + +/-- Complete interval computation for depth 13, residue 2083. -/ +theorem bounds_13_2083 : exactInterval 13 2083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2083 : oddCount 2083 13 = 6 ∧ acceleratedOrbit 13 2083 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2083) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2083.1, data_13_2083.2] + +/-- Complete interval computation for depth 13, residue 2084. -/ +theorem bounds_13_2084 : exactInterval 13 2084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2084 : oddCount 2084 13 = 5 ∧ acceleratedOrbit 13 2084 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2084) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2084.1, data_13_2084.2] + +/-- Complete interval computation for depth 13, residue 2085. -/ +theorem bounds_13_2085 : exactInterval 13 2085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2085 : oddCount 2085 13 = 5 ∧ acceleratedOrbit 13 2085 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2085) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2085.1, data_13_2085.2] + +/-- Complete interval computation for depth 13, residue 2086. -/ +theorem bounds_13_2086 : exactInterval 13 2086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2086 : oddCount 2086 13 = 5 ∧ acceleratedOrbit 13 2086 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2086) = 3 ^ 5 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2086.1, data_13_2086.2] + +/-- Complete interval computation for depth 13, residue 2087. -/ +theorem bounds_13_2087 : exactInterval 13 2087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2087 : oddCount 2087 13 = 9 ∧ acceleratedOrbit 13 2087 = 5021 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2087) = 3 ^ 9 * m + 5021 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2087.1, data_13_2087.2] + +/-- Complete interval computation for depth 13, residue 2088. -/ +theorem bounds_13_2088 : exactInterval 13 2088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2088 : oddCount 2088 13 = 3 ∧ acceleratedOrbit 13 2088 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2088) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2088.1, data_13_2088.2] + +/-- Complete interval computation for depth 13, residue 2089. -/ +theorem bounds_13_2089 : exactInterval 13 2089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2089 : oddCount 2089 13 = 9 ∧ acceleratedOrbit 13 2089 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2089) = 3 ^ 9 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2089.1, data_13_2089.2] + +/-- Complete interval computation for depth 13, residue 2090. -/ +theorem bounds_13_2090 : exactInterval 13 2090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2090 : oddCount 2090 13 = 3 ∧ acceleratedOrbit 13 2090 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2090) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2090.1, data_13_2090.2] + +/-- Complete interval computation for depth 13, residue 2091. -/ +theorem bounds_13_2091 : exactInterval 13 2091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2091 : oddCount 2091 13 = 7 ∧ acceleratedOrbit 13 2091 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2091) = 3 ^ 7 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2091.1, data_13_2091.2] + +/-- Complete interval computation for depth 13, residue 2092. -/ +theorem bounds_13_2092 : exactInterval 13 2092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2092 : oddCount 2092 13 = 6 ∧ acceleratedOrbit 13 2092 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2092) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2092.1, data_13_2092.2] + +/-- Complete interval computation for depth 13, residue 2093. -/ +theorem bounds_13_2093 : exactInterval 13 2093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2093 : oddCount 2093 13 = 6 ∧ acceleratedOrbit 13 2093 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2093) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2093.1, data_13_2093.2] + +end Collatz.Research.StoppingAtlas.Batch0603 From a8eebfecb2ee2ed397281615070a651304654c22 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:57 +0530 Subject: [PATCH 0604/1001] proof: certify atlas Batch0604 (13:2094 to 13:2108) --- Collatz/Research/StoppingAtlas/Batch0604.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0604.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0604.lean b/Collatz/Research/StoppingAtlas/Batch0604.lean new file mode 100644 index 00000000..408db4bb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0604.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0604 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2094. -/ +theorem bounds_13_2094 : exactInterval 13 2094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2094 : oddCount 2094 13 = 6 ∧ acceleratedOrbit 13 2094 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2094) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2094.1, data_13_2094.2] + +/-- Complete interval computation for depth 13, residue 2095. -/ +theorem bounds_13_2095 : exactInterval 13 2095 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2095) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2095 : oddCount 2095 13 = 8 ∧ acceleratedOrbit 13 2095 = 1679 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2095) = 3 ^ 8 * m + 1679 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2095.1, data_13_2095.2] + +/-- Complete interval computation for depth 13, residue 2096. -/ +theorem bounds_13_2096 : exactInterval 13 2096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2096 : oddCount 2096 13 = 3 ∧ acceleratedOrbit 13 2096 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2096) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2096.1, data_13_2096.2] + +/-- Complete interval computation for depth 13, residue 2097. -/ +theorem bounds_13_2097 : exactInterval 13 2097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2097 : oddCount 2097 13 = 7 ∧ acceleratedOrbit 13 2097 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2097) = 3 ^ 7 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2097.1, data_13_2097.2] + +/-- Complete interval computation for depth 13, residue 2098. -/ +theorem bounds_13_2098 : exactInterval 13 2098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2098 : oddCount 2098 13 = 7 ∧ acceleratedOrbit 13 2098 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2098) = 3 ^ 7 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2098.1, data_13_2098.2] + +/-- Complete interval computation for depth 13, residue 2099. -/ +theorem bounds_13_2099 : exactInterval 13 2099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2099 : oddCount 2099 13 = 7 ∧ acceleratedOrbit 13 2099 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2099) = 3 ^ 7 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2099.1, data_13_2099.2] + +/-- Complete interval computation for depth 13, residue 2100. -/ +theorem bounds_13_2100 : exactInterval 13 2100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2100 : oddCount 2100 13 = 3 ∧ acceleratedOrbit 13 2100 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2100) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2100.1, data_13_2100.2] + +/-- Complete interval computation for depth 13, residue 2101. -/ +theorem bounds_13_2101 : exactInterval 13 2101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2101 : oddCount 2101 13 = 3 ∧ acceleratedOrbit 13 2101 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2101) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2101.1, data_13_2101.2] + +/-- Complete interval computation for depth 13, residue 2102. -/ +theorem bounds_13_2102 : exactInterval 13 2102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2102 : oddCount 2102 13 = 10 ∧ acceleratedOrbit 13 2102 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2102) = 3 ^ 10 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2102.1, data_13_2102.2] + +/-- Complete interval computation for depth 13, residue 2103. -/ +theorem bounds_13_2103 : exactInterval 13 2103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2103 : oddCount 2103 13 = 10 ∧ acceleratedOrbit 13 2103 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2103) = 3 ^ 10 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2103.1, data_13_2103.2] + +/-- Complete interval computation for depth 13, residue 2104. -/ +theorem bounds_13_2104 : exactInterval 13 2104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2104 : oddCount 2104 13 = 7 ∧ acceleratedOrbit 13 2104 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2104) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2104.1, data_13_2104.2] + +/-- Complete interval computation for depth 13, residue 2105. -/ +theorem bounds_13_2105 : exactInterval 13 2105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2105 : oddCount 2105 13 = 6 ∧ acceleratedOrbit 13 2105 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2105) = 3 ^ 6 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2105.1, data_13_2105.2] + +/-- Complete interval computation for depth 13, residue 2106. -/ +theorem bounds_13_2106 : exactInterval 13 2106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2106 : oddCount 2106 13 = 7 ∧ acceleratedOrbit 13 2106 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2106) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2106.1, data_13_2106.2] + +/-- Complete interval computation for depth 13, residue 2107. -/ +theorem bounds_13_2107 : exactInterval 13 2107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2107 : oddCount 2107 13 = 8 ∧ acceleratedOrbit 13 2107 = 1691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2107) = 3 ^ 8 * m + 1691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2107.1, data_13_2107.2] + +/-- Complete interval computation for depth 13, residue 2108. -/ +theorem bounds_13_2108 : exactInterval 13 2108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2108 : oddCount 2108 13 = 7 ∧ acceleratedOrbit 13 2108 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2108) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2108.1, data_13_2108.2] + +end Collatz.Research.StoppingAtlas.Batch0604 From fb986360e3143d28440d7aee303adfed0e871002 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:58 +0530 Subject: [PATCH 0605/1001] proof: certify atlas Batch0605 (13:2109 to 13:2123) --- Collatz/Research/StoppingAtlas/Batch0605.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0605.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0605.lean b/Collatz/Research/StoppingAtlas/Batch0605.lean new file mode 100644 index 00000000..6d500e02 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0605.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0605 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2109. -/ +theorem bounds_13_2109 : exactInterval 13 2109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2109 : oddCount 2109 13 = 7 ∧ acceleratedOrbit 13 2109 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2109) = 3 ^ 7 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2109.1, data_13_2109.2] + +/-- Complete interval computation for depth 13, residue 2110. -/ +theorem bounds_13_2110 : exactInterval 13 2110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2110 : oddCount 2110 13 = 10 ∧ acceleratedOrbit 13 2110 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2110) = 3 ^ 10 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2110.1, data_13_2110.2] + +/-- Complete interval computation for depth 13, residue 2111. -/ +theorem bounds_13_2111 : exactInterval 13 2111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2111 : oddCount 2111 13 = 10 ∧ acceleratedOrbit 13 2111 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2111) = 3 ^ 10 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2111.1, data_13_2111.2] + +/-- Complete interval computation for depth 13, residue 2112. -/ +theorem bounds_13_2112 : exactInterval 13 2112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2112 : oddCount 2112 13 = 4 ∧ acceleratedOrbit 13 2112 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2112) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2112.1, data_13_2112.2] + +/-- Complete interval computation for depth 13, residue 2113. -/ +theorem bounds_13_2113 : exactInterval 13 2113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2113 : oddCount 2113 13 = 8 ∧ acceleratedOrbit 13 2113 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2113) = 3 ^ 8 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2113.1, data_13_2113.2] + +/-- Complete interval computation for depth 13, residue 2114. -/ +theorem bounds_13_2114 : exactInterval 13 2114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2114 : oddCount 2114 13 = 8 ∧ acceleratedOrbit 13 2114 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2114) = 3 ^ 8 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2114.1, data_13_2114.2] + +/-- Complete interval computation for depth 13, residue 2115. -/ +theorem bounds_13_2115 : exactInterval 13 2115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2115 : oddCount 2115 13 = 8 ∧ acceleratedOrbit 13 2115 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2115) = 3 ^ 8 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2115.1, data_13_2115.2] + +/-- Complete interval computation for depth 13, residue 2116. -/ +theorem bounds_13_2116 : exactInterval 13 2116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2116 : oddCount 2116 13 = 3 ∧ acceleratedOrbit 13 2116 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2116) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2116.1, data_13_2116.2] + +/-- Complete interval computation for depth 13, residue 2117. -/ +theorem bounds_13_2117 : exactInterval 13 2117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2117 : oddCount 2117 13 = 3 ∧ acceleratedOrbit 13 2117 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2117) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2117.1, data_13_2117.2] + +/-- Complete interval computation for depth 13, residue 2118. -/ +theorem bounds_13_2118 : exactInterval 13 2118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2118 : oddCount 2118 13 = 3 ∧ acceleratedOrbit 13 2118 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2118) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2118.1, data_13_2118.2] + +/-- Complete interval computation for depth 13, residue 2119. -/ +theorem bounds_13_2119 : exactInterval 13 2119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2119 : oddCount 2119 13 = 9 ∧ acceleratedOrbit 13 2119 = 5096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2119) = 3 ^ 9 * m + 5096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2119.1, data_13_2119.2] + +/-- Complete interval computation for depth 13, residue 2120. -/ +theorem bounds_13_2120 : exactInterval 13 2120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2120 : oddCount 2120 13 = 6 ∧ acceleratedOrbit 13 2120 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2120) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2120.1, data_13_2120.2] + +/-- Complete interval computation for depth 13, residue 2121. -/ +theorem bounds_13_2121 : exactInterval 13 2121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2121 : oddCount 2121 13 = 10 ∧ acceleratedOrbit 13 2121 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2121) = 3 ^ 10 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2121.1, data_13_2121.2] + +/-- Complete interval computation for depth 13, residue 2122. -/ +theorem bounds_13_2122 : exactInterval 13 2122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2122 : oddCount 2122 13 = 6 ∧ acceleratedOrbit 13 2122 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2122) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2122.1, data_13_2122.2] + +/-- Complete interval computation for depth 13, residue 2123. -/ +theorem bounds_13_2123 : exactInterval 13 2123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2123 : oddCount 2123 13 = 3 ∧ acceleratedOrbit 13 2123 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2123) = 3 ^ 3 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2123.1, data_13_2123.2] + +end Collatz.Research.StoppingAtlas.Batch0605 From 203b22e52f39d1475fa630438cb8c805fd667ddc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:31:59 +0530 Subject: [PATCH 0606/1001] proof: certify atlas Batch0606 (13:2124 to 13:2139) --- Collatz/Research/StoppingAtlas/Batch0606.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0606.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0606.lean b/Collatz/Research/StoppingAtlas/Batch0606.lean new file mode 100644 index 00000000..ac911afc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0606.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0606 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2124. -/ +theorem bounds_13_2124 : exactInterval 13 2124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2124 : oddCount 2124 13 = 6 ∧ acceleratedOrbit 13 2124 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2124) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2124.1, data_13_2124.2] + +/-- Complete interval computation for depth 13, residue 2125. -/ +theorem bounds_13_2125 : exactInterval 13 2125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2125 : oddCount 2125 13 = 6 ∧ acceleratedOrbit 13 2125 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2125) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2125.1, data_13_2125.2] + +/-- Complete interval computation for depth 13, residue 2126. -/ +theorem bounds_13_2126 : exactInterval 13 2126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2126 : oddCount 2126 13 = 7 ∧ acceleratedOrbit 13 2126 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2126) = 3 ^ 7 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2126.1, data_13_2126.2] + +/-- Complete interval computation for depth 13, residue 2127. -/ +theorem bounds_13_2127 : exactInterval 13 2127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2127 : oddCount 2127 13 = 7 ∧ acceleratedOrbit 13 2127 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2127) = 3 ^ 7 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2127.1, data_13_2127.2] + +/-- Complete interval computation for depth 13, residue 2128. -/ +theorem bounds_13_2128 : exactInterval 13 2128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2128 : oddCount 2128 13 = 4 ∧ acceleratedOrbit 13 2128 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2128) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2128.1, data_13_2128.2] + +/-- Complete interval computation for depth 13, residue 2129. -/ +theorem bounds_13_2129 : exactInterval 13 2129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2129 : oddCount 2129 13 = 6 ∧ acceleratedOrbit 13 2129 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2129) = 3 ^ 6 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2129.1, data_13_2129.2] + +/-- Complete interval computation for depth 13, residue 2130. -/ +theorem bounds_13_2130 : exactInterval 13 2130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2130 : oddCount 2130 13 = 8 ∧ acceleratedOrbit 13 2130 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2130) = 3 ^ 8 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2130.1, data_13_2130.2] + +/-- Complete interval computation for depth 13, residue 2131. -/ +theorem bounds_13_2131 : exactInterval 13 2131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2131 : oddCount 2131 13 = 8 ∧ acceleratedOrbit 13 2131 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2131) = 3 ^ 8 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2131.1, data_13_2131.2] + +/-- Complete interval computation for depth 13, residue 2132. -/ +theorem bounds_13_2132 : exactInterval 13 2132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2132 : oddCount 2132 13 = 4 ∧ acceleratedOrbit 13 2132 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2132) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2132.1, data_13_2132.2] + +/-- Complete interval computation for depth 13, residue 2133. -/ +theorem bounds_13_2133 : exactInterval 13 2133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2133 : oddCount 2133 13 = 4 ∧ acceleratedOrbit 13 2133 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2133) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2133.1, data_13_2133.2] + +/-- Complete interval computation for depth 13, residue 2134. -/ +theorem bounds_13_2134 : exactInterval 13 2134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2134 : oddCount 2134 13 = 6 ∧ acceleratedOrbit 13 2134 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2134) = 3 ^ 6 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2134.1, data_13_2134.2] + +/-- Complete interval computation for depth 13, residue 2135. -/ +theorem bounds_13_2135 : exactInterval 13 2135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2135 : oddCount 2135 13 = 6 ∧ acceleratedOrbit 13 2135 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2135) = 3 ^ 6 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2135.1, data_13_2135.2] + +/-- Complete interval computation for depth 13, residue 2136. -/ +theorem bounds_13_2136 : exactInterval 13 2136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2136 : oddCount 2136 13 = 5 ∧ acceleratedOrbit 13 2136 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2136) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2136.1, data_13_2136.2] + +/-- Complete interval computation for depth 13, residue 2137. -/ +theorem bounds_13_2137 : exactInterval 13 2137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2137 : oddCount 2137 13 = 6 ∧ acceleratedOrbit 13 2137 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2137) = 3 ^ 6 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2137.1, data_13_2137.2] + +/-- Complete interval computation for depth 13, residue 2138. -/ +theorem bounds_13_2138 : exactInterval 13 2138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2138 : oddCount 2138 13 = 5 ∧ acceleratedOrbit 13 2138 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2138) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2138.1, data_13_2138.2] + +/-- Complete interval computation for depth 13, residue 2139. -/ +theorem bounds_13_2139 : exactInterval 13 2139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2139 : oddCount 2139 13 = 10 ∧ acceleratedOrbit 13 2139 = 15430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2139) = 3 ^ 10 * m + 15430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2139.1, data_13_2139.2] + +end Collatz.Research.StoppingAtlas.Batch0606 From 13ee94a8d4b934efe25f73aef9bca36c126c336a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:00 +0530 Subject: [PATCH 0607/1001] proof: certify atlas Batch0607 (13:2140 to 13:2154) --- Collatz/Research/StoppingAtlas/Batch0607.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0607.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0607.lean b/Collatz/Research/StoppingAtlas/Batch0607.lean new file mode 100644 index 00000000..95d77d26 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0607.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0607 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2140. -/ +theorem bounds_13_2140 : exactInterval 13 2140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2140 : oddCount 2140 13 = 5 ∧ acceleratedOrbit 13 2140 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2140) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2140.1, data_13_2140.2] + +/-- Complete interval computation for depth 13, residue 2141. -/ +theorem bounds_13_2141 : exactInterval 13 2141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2141 : oddCount 2141 13 = 5 ∧ acceleratedOrbit 13 2141 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2141) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2141.1, data_13_2141.2] + +/-- Complete interval computation for depth 13, residue 2142. -/ +theorem bounds_13_2142 : exactInterval 13 2142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2142 : oddCount 2142 13 = 8 ∧ acceleratedOrbit 13 2142 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2142) = 3 ^ 8 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2142.1, data_13_2142.2] + +/-- Complete interval computation for depth 13, residue 2143. -/ +theorem bounds_13_2143 : exactInterval 13 2143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2143 : oddCount 2143 13 = 8 ∧ acceleratedOrbit 13 2143 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2143) = 3 ^ 8 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2143.1, data_13_2143.2] + +/-- Complete interval computation for depth 13, residue 2144. -/ +theorem bounds_13_2144 : exactInterval 13 2144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2144 : oddCount 2144 13 = 4 ∧ acceleratedOrbit 13 2144 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2144) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2144.1, data_13_2144.2] + +/-- Complete interval computation for depth 13, residue 2145. -/ +theorem bounds_13_2145 : exactInterval 13 2145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2145 : oddCount 2145 13 = 8 ∧ acceleratedOrbit 13 2145 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2145) = 3 ^ 8 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2145.1, data_13_2145.2] + +/-- Complete interval computation for depth 13, residue 2146. -/ +theorem bounds_13_2146 : exactInterval 13 2146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2146 : oddCount 2146 13 = 5 ∧ acceleratedOrbit 13 2146 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2146) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2146.1, data_13_2146.2] + +/-- Complete interval computation for depth 13, residue 2147. -/ +theorem bounds_13_2147 : exactInterval 13 2147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2147 : oddCount 2147 13 = 5 ∧ acceleratedOrbit 13 2147 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2147) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2147.1, data_13_2147.2] + +/-- Complete interval computation for depth 13, residue 2148. -/ +theorem bounds_13_2148 : exactInterval 13 2148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2148 : oddCount 2148 13 = 5 ∧ acceleratedOrbit 13 2148 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2148) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2148.1, data_13_2148.2] + +/-- Complete interval computation for depth 13, residue 2149. -/ +theorem bounds_13_2149 : exactInterval 13 2149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2149 : oddCount 2149 13 = 5 ∧ acceleratedOrbit 13 2149 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2149) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2149.1, data_13_2149.2] + +/-- Complete interval computation for depth 13, residue 2150. -/ +theorem bounds_13_2150 : exactInterval 13 2150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2150 : oddCount 2150 13 = 5 ∧ acceleratedOrbit 13 2150 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2150) = 3 ^ 5 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2150.1, data_13_2150.2] + +/-- Complete interval computation for depth 13, residue 2151. -/ +theorem bounds_13_2151 : exactInterval 13 2151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2151 : oddCount 2151 13 = 10 ∧ acceleratedOrbit 13 2151 = 15515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2151) = 3 ^ 10 * m + 15515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2151.1, data_13_2151.2] + +/-- Complete interval computation for depth 13, residue 2152. -/ +theorem bounds_13_2152 : exactInterval 13 2152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2152 : oddCount 2152 13 = 4 ∧ acceleratedOrbit 13 2152 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2152) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2152.1, data_13_2152.2] + +/-- Complete interval computation for depth 13, residue 2153. -/ +theorem bounds_13_2153 : exactInterval 13 2153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2153 : oddCount 2153 13 = 8 ∧ acceleratedOrbit 13 2153 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2153) = 3 ^ 8 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2153.1, data_13_2153.2] + +/-- Complete interval computation for depth 13, residue 2154. -/ +theorem bounds_13_2154 : exactInterval 13 2154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2154 : oddCount 2154 13 = 4 ∧ acceleratedOrbit 13 2154 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2154) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2154.1, data_13_2154.2] + +end Collatz.Research.StoppingAtlas.Batch0607 From 8790b169675ef90c0581805d315fa141f8eb0027 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:00 +0530 Subject: [PATCH 0608/1001] proof: certify atlas Batch0608 (13:2155 to 13:2169) --- Collatz/Research/StoppingAtlas/Batch0608.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0608.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0608.lean b/Collatz/Research/StoppingAtlas/Batch0608.lean new file mode 100644 index 00000000..a03df99b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0608.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0608 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2155. -/ +theorem bounds_13_2155 : exactInterval 13 2155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2155 : oddCount 2155 13 = 10 ∧ acceleratedOrbit 13 2155 = 15551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2155) = 3 ^ 10 * m + 15551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2155.1, data_13_2155.2] + +/-- Complete interval computation for depth 13, residue 2156. -/ +theorem bounds_13_2156 : exactInterval 13 2156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2156 : oddCount 2156 13 = 7 ∧ acceleratedOrbit 13 2156 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2156) = 3 ^ 7 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2156.1, data_13_2156.2] + +/-- Complete interval computation for depth 13, residue 2157. -/ +theorem bounds_13_2157 : exactInterval 13 2157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2157 : oddCount 2157 13 = 7 ∧ acceleratedOrbit 13 2157 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2157) = 3 ^ 7 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2157.1, data_13_2157.2] + +/-- Complete interval computation for depth 13, residue 2158. -/ +theorem bounds_13_2158 : exactInterval 13 2158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2158 : oddCount 2158 13 = 7 ∧ acceleratedOrbit 13 2158 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2158) = 3 ^ 7 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2158.1, data_13_2158.2] + +/-- Complete interval computation for depth 13, residue 2159. -/ +theorem bounds_13_2159 : exactInterval 13 2159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2159 : oddCount 2159 13 = 10 ∧ acceleratedOrbit 13 2159 = 15572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2159) = 3 ^ 10 * m + 15572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2159.1, data_13_2159.2] + +/-- Complete interval computation for depth 13, residue 2160. -/ +theorem bounds_13_2160 : exactInterval 13 2160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2160 : oddCount 2160 13 = 5 ∧ acceleratedOrbit 13 2160 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2160) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2160.1, data_13_2160.2] + +/-- Complete interval computation for depth 13, residue 2161. -/ +theorem bounds_13_2161 : exactInterval 13 2161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2161 : oddCount 2161 13 = 4 ∧ acceleratedOrbit 13 2161 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2161) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2161.1, data_13_2161.2] + +/-- Complete interval computation for depth 13, residue 2162. -/ +theorem bounds_13_2162 : exactInterval 13 2162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2162 : oddCount 2162 13 = 6 ∧ acceleratedOrbit 13 2162 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2162) = 3 ^ 6 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2162.1, data_13_2162.2] + +/-- Complete interval computation for depth 13, residue 2163. -/ +theorem bounds_13_2163 : exactInterval 13 2163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2163 : oddCount 2163 13 = 6 ∧ acceleratedOrbit 13 2163 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2163) = 3 ^ 6 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2163.1, data_13_2163.2] + +/-- Complete interval computation for depth 13, residue 2164. -/ +theorem bounds_13_2164 : exactInterval 13 2164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2164 : oddCount 2164 13 = 5 ∧ acceleratedOrbit 13 2164 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2164) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2164.1, data_13_2164.2] + +/-- Complete interval computation for depth 13, residue 2165. -/ +theorem bounds_13_2165 : exactInterval 13 2165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2165 : oddCount 2165 13 = 5 ∧ acceleratedOrbit 13 2165 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2165) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2165.1, data_13_2165.2] + +/-- Complete interval computation for depth 13, residue 2166. -/ +theorem bounds_13_2166 : exactInterval 13 2166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2166 : oddCount 2166 13 = 7 ∧ acceleratedOrbit 13 2166 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2166) = 3 ^ 7 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2166.1, data_13_2166.2] + +/-- Complete interval computation for depth 13, residue 2167. -/ +theorem bounds_13_2167 : exactInterval 13 2167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2167 : oddCount 2167 13 = 7 ∧ acceleratedOrbit 13 2167 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2167) = 3 ^ 7 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2167.1, data_13_2167.2] + +/-- Complete interval computation for depth 13, residue 2168. -/ +theorem bounds_13_2168 : exactInterval 13 2168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2168 : oddCount 2168 13 = 5 ∧ acceleratedOrbit 13 2168 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2168) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2168.1, data_13_2168.2] + +/-- Complete interval computation for depth 13, residue 2169. -/ +theorem bounds_13_2169 : exactInterval 13 2169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2169 : oddCount 2169 13 = 8 ∧ acceleratedOrbit 13 2169 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2169) = 3 ^ 8 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2169.1, data_13_2169.2] + +end Collatz.Research.StoppingAtlas.Batch0608 From ccdfd68889e987a308de611c6fa167cb76918e25 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:02 +0530 Subject: [PATCH 0609/1001] proof: certify atlas Batch0609 (13:2170 to 13:2185) --- Collatz/Research/StoppingAtlas/Batch0609.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0609.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0609.lean b/Collatz/Research/StoppingAtlas/Batch0609.lean new file mode 100644 index 00000000..c7432932 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0609.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0609 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2170. -/ +theorem bounds_13_2170 : exactInterval 13 2170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2170 : oddCount 2170 13 = 5 ∧ acceleratedOrbit 13 2170 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2170) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2170.1, data_13_2170.2] + +/-- Complete interval computation for depth 13, residue 2171. -/ +theorem bounds_13_2171 : exactInterval 13 2171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2171 : oddCount 2171 13 = 8 ∧ acceleratedOrbit 13 2171 = 1741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2171) = 3 ^ 8 * m + 1741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2171.1, data_13_2171.2] + +/-- Complete interval computation for depth 13, residue 2172. -/ +theorem bounds_13_2172 : exactInterval 13 2172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2172 : oddCount 2172 13 = 7 ∧ acceleratedOrbit 13 2172 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2172) = 3 ^ 7 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2172.1, data_13_2172.2] + +/-- Complete interval computation for depth 13, residue 2173. -/ +theorem bounds_13_2173 : exactInterval 13 2173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2173 : oddCount 2173 13 = 7 ∧ acceleratedOrbit 13 2173 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2173) = 3 ^ 7 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2173.1, data_13_2173.2] + +/-- Complete interval computation for depth 13, residue 2174. -/ +theorem bounds_13_2174 : exactInterval 13 2174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2174 : oddCount 2174 13 = 7 ∧ acceleratedOrbit 13 2174 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2174) = 3 ^ 7 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2174.1, data_13_2174.2] + +/-- Complete interval computation for depth 13, residue 2175. -/ +theorem bounds_13_2175 : exactInterval 13 2175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2175 : oddCount 2175 13 = 10 ∧ acceleratedOrbit 13 2175 = 15686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2175) = 3 ^ 10 * m + 15686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2175.1, data_13_2175.2] + +/-- Complete interval computation for depth 13, residue 2176. -/ +theorem bounds_13_2176 : exactInterval 13 2176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2176 : oddCount 2176 13 = 3 ∧ acceleratedOrbit 13 2176 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2176) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2176.1, data_13_2176.2] + +/-- Complete interval computation for depth 13, residue 2177. -/ +theorem bounds_13_2177 : exactInterval 13 2177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2177 : oddCount 2177 13 = 6 ∧ acceleratedOrbit 13 2177 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2177) = 3 ^ 6 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2177.1, data_13_2177.2] + +/-- Complete interval computation for depth 13, residue 2178. -/ +theorem bounds_13_2178 : exactInterval 13 2178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2178 : oddCount 2178 13 = 5 ∧ acceleratedOrbit 13 2178 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2178) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2178.1, data_13_2178.2] + +/-- Complete interval computation for depth 13, residue 2179. -/ +theorem bounds_13_2179 : exactInterval 13 2179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2179 : oddCount 2179 13 = 5 ∧ acceleratedOrbit 13 2179 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2179) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2179.1, data_13_2179.2] + +/-- Complete interval computation for depth 13, residue 2180. -/ +theorem bounds_13_2180 : exactInterval 13 2180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2180 : oddCount 2180 13 = 5 ∧ acceleratedOrbit 13 2180 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2180) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2180.1, data_13_2180.2] + +/-- Complete interval computation for depth 13, residue 2181. -/ +theorem bounds_13_2181 : exactInterval 13 2181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2181 : oddCount 2181 13 = 5 ∧ acceleratedOrbit 13 2181 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2181) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2181.1, data_13_2181.2] + +/-- Complete interval computation for depth 13, residue 2182. -/ +theorem bounds_13_2182 : exactInterval 13 2182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2182 : oddCount 2182 13 = 5 ∧ acceleratedOrbit 13 2182 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2182) = 3 ^ 5 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2182.1, data_13_2182.2] + +/-- Complete interval computation for depth 13, residue 2183. -/ +theorem bounds_13_2183 : exactInterval 13 2183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2183 : oddCount 2183 13 = 7 ∧ acceleratedOrbit 13 2183 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2183) = 3 ^ 7 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2183.1, data_13_2183.2] + +/-- Complete interval computation for depth 13, residue 2184. -/ +theorem bounds_13_2184 : exactInterval 13 2184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2184 : oddCount 2184 13 = 4 ∧ acceleratedOrbit 13 2184 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2184) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2184.1, data_13_2184.2] + +/-- Complete interval computation for depth 13, residue 2185. -/ +theorem bounds_13_2185 : exactInterval 13 2185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2185 : oddCount 2185 13 = 9 ∧ acceleratedOrbit 13 2185 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2185) = 3 ^ 9 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2185.1, data_13_2185.2] + +end Collatz.Research.StoppingAtlas.Batch0609 From fae8ef5a36a2f61278898d54d17194ba164e5010 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:03 +0530 Subject: [PATCH 0610/1001] proof: certify atlas Batch0610 (13:2186 to 13:2200) --- Collatz/Research/StoppingAtlas/Batch0610.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0610.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0610.lean b/Collatz/Research/StoppingAtlas/Batch0610.lean new file mode 100644 index 00000000..76a49d1b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0610.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0610 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2186. -/ +theorem bounds_13_2186 : exactInterval 13 2186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2186 : oddCount 2186 13 = 4 ∧ acceleratedOrbit 13 2186 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2186) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2186.1, data_13_2186.2] + +/-- Complete interval computation for depth 13, residue 2187. -/ +theorem bounds_13_2187 : exactInterval 13 2187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2187 : oddCount 2187 13 = 9 ∧ acceleratedOrbit 13 2187 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2187) = 3 ^ 9 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2187.1, data_13_2187.2] + +/-- Complete interval computation for depth 13, residue 2188. -/ +theorem bounds_13_2188 : exactInterval 13 2188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2188 : oddCount 2188 13 = 4 ∧ acceleratedOrbit 13 2188 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2188) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2188.1, data_13_2188.2] + +/-- Complete interval computation for depth 13, residue 2189. -/ +theorem bounds_13_2189 : exactInterval 13 2189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2189 : oddCount 2189 13 = 4 ∧ acceleratedOrbit 13 2189 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2189) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2189.1, data_13_2189.2] + +/-- Complete interval computation for depth 13, residue 2190. -/ +theorem bounds_13_2190 : exactInterval 13 2190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2190 : oddCount 2190 13 = 8 ∧ acceleratedOrbit 13 2190 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2190) = 3 ^ 8 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2190.1, data_13_2190.2] + +/-- Complete interval computation for depth 13, residue 2191. -/ +theorem bounds_13_2191 : exactInterval 13 2191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2191) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2191 : oddCount 2191 13 = 8 ∧ acceleratedOrbit 13 2191 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2191) = 3 ^ 8 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2191.1, data_13_2191.2] + +/-- Complete interval computation for depth 13, residue 2192. -/ +theorem bounds_13_2192 : exactInterval 13 2192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2192 : oddCount 2192 13 = 7 ∧ acceleratedOrbit 13 2192 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2192) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2192.1, data_13_2192.2] + +/-- Complete interval computation for depth 13, residue 2193. -/ +theorem bounds_13_2193 : exactInterval 13 2193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2193 : oddCount 2193 13 = 7 ∧ acceleratedOrbit 13 2193 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2193) = 3 ^ 7 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2193.1, data_13_2193.2] + +/-- Complete interval computation for depth 13, residue 2194. -/ +theorem bounds_13_2194 : exactInterval 13 2194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2194 : oddCount 2194 13 = 7 ∧ acceleratedOrbit 13 2194 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2194) = 3 ^ 7 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2194.1, data_13_2194.2] + +/-- Complete interval computation for depth 13, residue 2195. -/ +theorem bounds_13_2195 : exactInterval 13 2195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2195 : oddCount 2195 13 = 7 ∧ acceleratedOrbit 13 2195 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2195) = 3 ^ 7 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2195.1, data_13_2195.2] + +/-- Complete interval computation for depth 13, residue 2196. -/ +theorem bounds_13_2196 : exactInterval 13 2196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2196 : oddCount 2196 13 = 7 ∧ acceleratedOrbit 13 2196 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2196) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2196.1, data_13_2196.2] + +/-- Complete interval computation for depth 13, residue 2197. -/ +theorem bounds_13_2197 : exactInterval 13 2197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2197 : oddCount 2197 13 = 7 ∧ acceleratedOrbit 13 2197 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2197) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2197.1, data_13_2197.2] + +/-- Complete interval computation for depth 13, residue 2198. -/ +theorem bounds_13_2198 : exactInterval 13 2198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2198 : oddCount 2198 13 = 4 ∧ acceleratedOrbit 13 2198 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2198) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2198.1, data_13_2198.2] + +/-- Complete interval computation for depth 13, residue 2199. -/ +theorem bounds_13_2199 : exactInterval 13 2199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2199 : oddCount 2199 13 = 4 ∧ acceleratedOrbit 13 2199 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2199) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2199.1, data_13_2199.2] + +/-- Complete interval computation for depth 13, residue 2200. -/ +theorem bounds_13_2200 : exactInterval 13 2200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2200 : oddCount 2200 13 = 7 ∧ acceleratedOrbit 13 2200 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2200) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2200.1, data_13_2200.2] + +end Collatz.Research.StoppingAtlas.Batch0610 From 7741134d4e2ba8a9dd4824574923b1fd66e3797a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:04 +0530 Subject: [PATCH 0611/1001] proof: certify atlas Batch0611 (13:2201 to 13:2215) --- Collatz/Research/StoppingAtlas/Batch0611.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0611.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0611.lean b/Collatz/Research/StoppingAtlas/Batch0611.lean new file mode 100644 index 00000000..a4391cac --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0611.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0611 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2201. -/ +theorem bounds_13_2201 : exactInterval 13 2201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2201 : oddCount 2201 13 = 7 ∧ acceleratedOrbit 13 2201 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2201) = 3 ^ 7 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2201.1, data_13_2201.2] + +/-- Complete interval computation for depth 13, residue 2202. -/ +theorem bounds_13_2202 : exactInterval 13 2202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2202 : oddCount 2202 13 = 7 ∧ acceleratedOrbit 13 2202 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2202) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2202.1, data_13_2202.2] + +/-- Complete interval computation for depth 13, residue 2203. -/ +theorem bounds_13_2203 : exactInterval 13 2203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2203 : oddCount 2203 13 = 8 ∧ acceleratedOrbit 13 2203 = 1766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2203) = 3 ^ 8 * m + 1766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2203.1, data_13_2203.2] + +/-- Complete interval computation for depth 13, residue 2204. -/ +theorem bounds_13_2204 : exactInterval 13 2204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2204 : oddCount 2204 13 = 6 ∧ acceleratedOrbit 13 2204 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2204) = 3 ^ 6 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2204.1, data_13_2204.2] + +/-- Complete interval computation for depth 13, residue 2205. -/ +theorem bounds_13_2205 : exactInterval 13 2205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2205 : oddCount 2205 13 = 6 ∧ acceleratedOrbit 13 2205 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2205) = 3 ^ 6 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2205.1, data_13_2205.2] + +/-- Complete interval computation for depth 13, residue 2206. -/ +theorem bounds_13_2206 : exactInterval 13 2206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2206 : oddCount 2206 13 = 6 ∧ acceleratedOrbit 13 2206 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2206) = 3 ^ 6 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2206.1, data_13_2206.2] + +/-- Complete interval computation for depth 13, residue 2207. -/ +theorem bounds_13_2207 : exactInterval 13 2207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2207 : oddCount 2207 13 = 11 ∧ acceleratedOrbit 13 2207 = 47749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2207) = 3 ^ 11 * m + 47749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2207.1, data_13_2207.2] + +/-- Complete interval computation for depth 13, residue 2208. -/ +theorem bounds_13_2208 : exactInterval 13 2208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2208 : oddCount 2208 13 = 3 ∧ acceleratedOrbit 13 2208 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2208) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2208.1, data_13_2208.2] + +/-- Complete interval computation for depth 13, residue 2209. -/ +theorem bounds_13_2209 : exactInterval 13 2209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2209 : oddCount 2209 13 = 8 ∧ acceleratedOrbit 13 2209 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2209) = 3 ^ 8 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2209.1, data_13_2209.2] + +/-- Complete interval computation for depth 13, residue 2210. -/ +theorem bounds_13_2210 : exactInterval 13 2210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2210 : oddCount 2210 13 = 7 ∧ acceleratedOrbit 13 2210 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2210) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2210.1, data_13_2210.2] + +/-- Complete interval computation for depth 13, residue 2211. -/ +theorem bounds_13_2211 : exactInterval 13 2211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2211 : oddCount 2211 13 = 7 ∧ acceleratedOrbit 13 2211 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2211) = 3 ^ 7 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2211.1, data_13_2211.2] + +/-- Complete interval computation for depth 13, residue 2212. -/ +theorem bounds_13_2212 : exactInterval 13 2212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2212 : oddCount 2212 13 = 8 ∧ acceleratedOrbit 13 2212 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2212) = 3 ^ 8 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2212.1, data_13_2212.2] + +/-- Complete interval computation for depth 13, residue 2213. -/ +theorem bounds_13_2213 : exactInterval 13 2213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2213 : oddCount 2213 13 = 8 ∧ acceleratedOrbit 13 2213 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2213) = 3 ^ 8 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2213.1, data_13_2213.2] + +/-- Complete interval computation for depth 13, residue 2214. -/ +theorem bounds_13_2214 : exactInterval 13 2214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2214 : oddCount 2214 13 = 8 ∧ acceleratedOrbit 13 2214 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2214) = 3 ^ 8 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2214.1, data_13_2214.2] + +/-- Complete interval computation for depth 13, residue 2215. -/ +theorem bounds_13_2215 : exactInterval 13 2215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2215) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2215 : oddCount 2215 13 = 10 ∧ acceleratedOrbit 13 2215 = 15977 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2215) = 3 ^ 10 * m + 15977 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2215.1, data_13_2215.2] + +end Collatz.Research.StoppingAtlas.Batch0611 From 9c6e881775874a7112c8c4d99a38800d891efc8c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:04 +0530 Subject: [PATCH 0612/1001] proof: certify atlas Batch0612 (13:2216 to 13:2231) --- Collatz/Research/StoppingAtlas/Batch0612.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0612.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0612.lean b/Collatz/Research/StoppingAtlas/Batch0612.lean new file mode 100644 index 00000000..53f91d05 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0612.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0612 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2216. -/ +theorem bounds_13_2216 : exactInterval 13 2216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2216 : oddCount 2216 13 = 3 ∧ acceleratedOrbit 13 2216 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2216) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2216.1, data_13_2216.2] + +/-- Complete interval computation for depth 13, residue 2217. -/ +theorem bounds_13_2217 : exactInterval 13 2217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2217 : oddCount 2217 13 = 11 ∧ acceleratedOrbit 13 2217 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2217) = 3 ^ 11 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2217.1, data_13_2217.2] + +/-- Complete interval computation for depth 13, residue 2218. -/ +theorem bounds_13_2218 : exactInterval 13 2218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2218 : oddCount 2218 13 = 3 ∧ acceleratedOrbit 13 2218 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2218) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2218.1, data_13_2218.2] + +/-- Complete interval computation for depth 13, residue 2219. -/ +theorem bounds_13_2219 : exactInterval 13 2219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2219 : oddCount 2219 13 = 8 ∧ acceleratedOrbit 13 2219 = 1781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2219) = 3 ^ 8 * m + 1781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2219.1, data_13_2219.2] + +/-- Complete interval computation for depth 13, residue 2220. -/ +theorem bounds_13_2220 : exactInterval 13 2220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2220 : oddCount 2220 13 = 4 ∧ acceleratedOrbit 13 2220 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2220) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2220.1, data_13_2220.2] + +/-- Complete interval computation for depth 13, residue 2221. -/ +theorem bounds_13_2221 : exactInterval 13 2221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2221 : oddCount 2221 13 = 4 ∧ acceleratedOrbit 13 2221 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2221) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2221.1, data_13_2221.2] + +/-- Complete interval computation for depth 13, residue 2222. -/ +theorem bounds_13_2222 : exactInterval 13 2222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2222 : oddCount 2222 13 = 4 ∧ acceleratedOrbit 13 2222 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2222) = 3 ^ 4 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2222.1, data_13_2222.2] + +/-- Complete interval computation for depth 13, residue 2223. -/ +theorem bounds_13_2223 : exactInterval 13 2223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2223 : oddCount 2223 13 = 10 ∧ acceleratedOrbit 13 2223 = 16037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2223) = 3 ^ 10 * m + 16037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2223.1, data_13_2223.2] + +/-- Complete interval computation for depth 13, residue 2224. -/ +theorem bounds_13_2224 : exactInterval 13 2224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2224 : oddCount 2224 13 = 5 ∧ acceleratedOrbit 13 2224 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2224) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2224.1, data_13_2224.2] + +/-- Complete interval computation for depth 13, residue 2225. -/ +theorem bounds_13_2225 : exactInterval 13 2225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2225 : oddCount 2225 13 = 6 ∧ acceleratedOrbit 13 2225 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2225) = 3 ^ 6 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2225.1, data_13_2225.2] + +/-- Complete interval computation for depth 13, residue 2226. -/ +theorem bounds_13_2226 : exactInterval 13 2226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2226 : oddCount 2226 13 = 6 ∧ acceleratedOrbit 13 2226 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2226) = 3 ^ 6 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2226.1, data_13_2226.2] + +/-- Complete interval computation for depth 13, residue 2227. -/ +theorem bounds_13_2227 : exactInterval 13 2227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2227 : oddCount 2227 13 = 6 ∧ acceleratedOrbit 13 2227 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2227) = 3 ^ 6 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2227.1, data_13_2227.2] + +/-- Complete interval computation for depth 13, residue 2228. -/ +theorem bounds_13_2228 : exactInterval 13 2228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2228 : oddCount 2228 13 = 5 ∧ acceleratedOrbit 13 2228 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2228) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2228.1, data_13_2228.2] + +/-- Complete interval computation for depth 13, residue 2229. -/ +theorem bounds_13_2229 : exactInterval 13 2229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2229 : oddCount 2229 13 = 5 ∧ acceleratedOrbit 13 2229 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2229) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2229.1, data_13_2229.2] + +/-- Complete interval computation for depth 13, residue 2230. -/ +theorem bounds_13_2230 : exactInterval 13 2230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2230 : oddCount 2230 13 = 9 ∧ acceleratedOrbit 13 2230 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2230) = 3 ^ 9 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2230.1, data_13_2230.2] + +/-- Complete interval computation for depth 13, residue 2231. -/ +theorem bounds_13_2231 : exactInterval 13 2231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2231 : oddCount 2231 13 = 9 ∧ acceleratedOrbit 13 2231 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2231) = 3 ^ 9 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2231.1, data_13_2231.2] + +end Collatz.Research.StoppingAtlas.Batch0612 From 92773e20a113a7472d6f13b0712bca0ff7b2d825 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:07 +0530 Subject: [PATCH 0613/1001] proof: certify atlas Batch0613 (13:2232 to 13:2246) --- Collatz/Research/StoppingAtlas/Batch0613.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0613.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0613.lean b/Collatz/Research/StoppingAtlas/Batch0613.lean new file mode 100644 index 00000000..b075e5ad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0613.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0613 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2232. -/ +theorem bounds_13_2232 : exactInterval 13 2232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2232 : oddCount 2232 13 = 5 ∧ acceleratedOrbit 13 2232 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2232) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2232.1, data_13_2232.2] + +/-- Complete interval computation for depth 13, residue 2233. -/ +theorem bounds_13_2233 : exactInterval 13 2233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2233 : oddCount 2233 13 = 6 ∧ acceleratedOrbit 13 2233 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2233) = 3 ^ 6 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2233.1, data_13_2233.2] + +/-- Complete interval computation for depth 13, residue 2234. -/ +theorem bounds_13_2234 : exactInterval 13 2234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2234 : oddCount 2234 13 = 5 ∧ acceleratedOrbit 13 2234 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2234) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2234.1, data_13_2234.2] + +/-- Complete interval computation for depth 13, residue 2235. -/ +theorem bounds_13_2235 : exactInterval 13 2235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2235 : oddCount 2235 13 = 8 ∧ acceleratedOrbit 13 2235 = 1792 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2235) = 3 ^ 8 * m + 1792 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2235.1, data_13_2235.2] + +/-- Complete interval computation for depth 13, residue 2236. -/ +theorem bounds_13_2236 : exactInterval 13 2236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2236 : oddCount 2236 13 = 8 ∧ acceleratedOrbit 13 2236 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2236) = 3 ^ 8 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2236.1, data_13_2236.2] + +/-- Complete interval computation for depth 13, residue 2237. -/ +theorem bounds_13_2237 : exactInterval 13 2237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2237 : oddCount 2237 13 = 8 ∧ acceleratedOrbit 13 2237 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2237) = 3 ^ 8 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2237.1, data_13_2237.2] + +/-- Complete interval computation for depth 13, residue 2238. -/ +theorem bounds_13_2238 : exactInterval 13 2238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2238 : oddCount 2238 13 = 8 ∧ acceleratedOrbit 13 2238 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2238) = 3 ^ 8 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2238.1, data_13_2238.2] + +/-- Complete interval computation for depth 13, residue 2239. -/ +theorem bounds_13_2239 : exactInterval 13 2239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2239 : oddCount 2239 13 = 7 ∧ acceleratedOrbit 13 2239 = 598 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2239) = 3 ^ 7 * m + 598 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2239.1, data_13_2239.2] + +/-- Complete interval computation for depth 13, residue 2240. -/ +theorem bounds_13_2240 : exactInterval 13 2240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2240 : oddCount 2240 13 = 3 ∧ acceleratedOrbit 13 2240 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2240) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2240.1, data_13_2240.2] + +/-- Complete interval computation for depth 13, residue 2241. -/ +theorem bounds_13_2241 : exactInterval 13 2241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2241 : oddCount 2241 13 = 6 ∧ acceleratedOrbit 13 2241 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2241) = 3 ^ 6 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2241.1, data_13_2241.2] + +/-- Complete interval computation for depth 13, residue 2242. -/ +theorem bounds_13_2242 : exactInterval 13 2242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2242 : oddCount 2242 13 = 6 ∧ acceleratedOrbit 13 2242 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2242) = 3 ^ 6 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2242.1, data_13_2242.2] + +/-- Complete interval computation for depth 13, residue 2243. -/ +theorem bounds_13_2243 : exactInterval 13 2243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2243 : oddCount 2243 13 = 6 ∧ acceleratedOrbit 13 2243 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2243) = 3 ^ 6 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2243.1, data_13_2243.2] + +/-- Complete interval computation for depth 13, residue 2244. -/ +theorem bounds_13_2244 : exactInterval 13 2244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2244 : oddCount 2244 13 = 6 ∧ acceleratedOrbit 13 2244 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2244) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2244.1, data_13_2244.2] + +/-- Complete interval computation for depth 13, residue 2245. -/ +theorem bounds_13_2245 : exactInterval 13 2245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2245 : oddCount 2245 13 = 6 ∧ acceleratedOrbit 13 2245 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2245) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2245.1, data_13_2245.2] + +/-- Complete interval computation for depth 13, residue 2246. -/ +theorem bounds_13_2246 : exactInterval 13 2246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2246 : oddCount 2246 13 = 6 ∧ acceleratedOrbit 13 2246 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2246) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2246.1, data_13_2246.2] + +end Collatz.Research.StoppingAtlas.Batch0613 From f1b4a9a712592081f5931a50efadf2d09c265b7f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:07 +0530 Subject: [PATCH 0614/1001] proof: certify atlas Batch0614 (13:2247 to 13:2262) --- Collatz/Research/StoppingAtlas/Batch0614.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0614.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0614.lean b/Collatz/Research/StoppingAtlas/Batch0614.lean new file mode 100644 index 00000000..b790c338 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0614.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0614 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2247. -/ +theorem bounds_13_2247 : exactInterval 13 2247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2247 : oddCount 2247 13 = 8 ∧ acceleratedOrbit 13 2247 = 1802 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2247) = 3 ^ 8 * m + 1802 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2247.1, data_13_2247.2] + +/-- Complete interval computation for depth 13, residue 2248. -/ +theorem bounds_13_2248 : exactInterval 13 2248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2248 : oddCount 2248 13 = 6 ∧ acceleratedOrbit 13 2248 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2248) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2248.1, data_13_2248.2] + +/-- Complete interval computation for depth 13, residue 2249. -/ +theorem bounds_13_2249 : exactInterval 13 2249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2249 : oddCount 2249 13 = 5 ∧ acceleratedOrbit 13 2249 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2249) = 3 ^ 5 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2249.1, data_13_2249.2] + +/-- Complete interval computation for depth 13, residue 2250. -/ +theorem bounds_13_2250 : exactInterval 13 2250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2250 : oddCount 2250 13 = 6 ∧ acceleratedOrbit 13 2250 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2250) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2250.1, data_13_2250.2] + +/-- Complete interval computation for depth 13, residue 2251. -/ +theorem bounds_13_2251 : exactInterval 13 2251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2251 : oddCount 2251 13 = 8 ∧ acceleratedOrbit 13 2251 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2251) = 3 ^ 8 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2251.1, data_13_2251.2] + +/-- Complete interval computation for depth 13, residue 2252. -/ +theorem bounds_13_2252 : exactInterval 13 2252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2252 : oddCount 2252 13 = 6 ∧ acceleratedOrbit 13 2252 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2252) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2252.1, data_13_2252.2] + +/-- Complete interval computation for depth 13, residue 2253. -/ +theorem bounds_13_2253 : exactInterval 13 2253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2253 : oddCount 2253 13 = 6 ∧ acceleratedOrbit 13 2253 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2253) = 3 ^ 6 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2253.1, data_13_2253.2] + +/-- Complete interval computation for depth 13, residue 2254. -/ +theorem bounds_13_2254 : exactInterval 13 2254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2254 : oddCount 2254 13 = 9 ∧ acceleratedOrbit 13 2254 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2254) = 3 ^ 9 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2254.1, data_13_2254.2] + +/-- Complete interval computation for depth 13, residue 2255. -/ +theorem bounds_13_2255 : exactInterval 13 2255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2255 : oddCount 2255 13 = 9 ∧ acceleratedOrbit 13 2255 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2255) = 3 ^ 9 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2255.1, data_13_2255.2] + +/-- Complete interval computation for depth 13, residue 2256. -/ +theorem bounds_13_2256 : exactInterval 13 2256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2256 : oddCount 2256 13 = 3 ∧ acceleratedOrbit 13 2256 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2256) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2256.1, data_13_2256.2] + +/-- Complete interval computation for depth 13, residue 2257. -/ +theorem bounds_13_2257 : exactInterval 13 2257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2257 : oddCount 2257 13 = 7 ∧ acceleratedOrbit 13 2257 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2257) = 3 ^ 7 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2257.1, data_13_2257.2] + +/-- Complete interval computation for depth 13, residue 2258. -/ +theorem bounds_13_2258 : exactInterval 13 2258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2258 : oddCount 2258 13 = 7 ∧ acceleratedOrbit 13 2258 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2258) = 3 ^ 7 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2258.1, data_13_2258.2] + +/-- Complete interval computation for depth 13, residue 2259. -/ +theorem bounds_13_2259 : exactInterval 13 2259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2259 : oddCount 2259 13 = 7 ∧ acceleratedOrbit 13 2259 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2259) = 3 ^ 7 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2259.1, data_13_2259.2] + +/-- Complete interval computation for depth 13, residue 2260. -/ +theorem bounds_13_2260 : exactInterval 13 2260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2260 : oddCount 2260 13 = 3 ∧ acceleratedOrbit 13 2260 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2260) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2260.1, data_13_2260.2] + +/-- Complete interval computation for depth 13, residue 2261. -/ +theorem bounds_13_2261 : exactInterval 13 2261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2261 : oddCount 2261 13 = 3 ∧ acceleratedOrbit 13 2261 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2261) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2261.1, data_13_2261.2] + +/-- Complete interval computation for depth 13, residue 2262. -/ +theorem bounds_13_2262 : exactInterval 13 2262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2262 : oddCount 2262 13 = 7 ∧ acceleratedOrbit 13 2262 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2262) = 3 ^ 7 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2262.1, data_13_2262.2] + +end Collatz.Research.StoppingAtlas.Batch0614 From 26373f76b43f73779922df6e9735a9f5a98373eb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:08 +0530 Subject: [PATCH 0615/1001] proof: certify atlas Batch0615 (13:2263 to 13:2277) --- Collatz/Research/StoppingAtlas/Batch0615.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0615.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0615.lean b/Collatz/Research/StoppingAtlas/Batch0615.lean new file mode 100644 index 00000000..063ab8fc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0615.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0615 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2263. -/ +theorem bounds_13_2263 : exactInterval 13 2263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2263 : oddCount 2263 13 = 7 ∧ acceleratedOrbit 13 2263 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2263) = 3 ^ 7 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2263.1, data_13_2263.2] + +/-- Complete interval computation for depth 13, residue 2264. -/ +theorem bounds_13_2264 : exactInterval 13 2264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2264 : oddCount 2264 13 = 8 ∧ acceleratedOrbit 13 2264 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2264) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2264.1, data_13_2264.2] + +/-- Complete interval computation for depth 13, residue 2265. -/ +theorem bounds_13_2265 : exactInterval 13 2265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2265 : oddCount 2265 13 = 7 ∧ acceleratedOrbit 13 2265 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2265) = 3 ^ 7 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2265.1, data_13_2265.2] + +/-- Complete interval computation for depth 13, residue 2266. -/ +theorem bounds_13_2266 : exactInterval 13 2266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2266 : oddCount 2266 13 = 8 ∧ acceleratedOrbit 13 2266 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2266) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2266.1, data_13_2266.2] + +/-- Complete interval computation for depth 13, residue 2267. -/ +theorem bounds_13_2267 : exactInterval 13 2267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2267 : oddCount 2267 13 = 9 ∧ acceleratedOrbit 13 2267 = 5453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2267) = 3 ^ 9 * m + 5453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2267.1, data_13_2267.2] + +/-- Complete interval computation for depth 13, residue 2268. -/ +theorem bounds_13_2268 : exactInterval 13 2268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2268 : oddCount 2268 13 = 8 ∧ acceleratedOrbit 13 2268 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2268) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2268.1, data_13_2268.2] + +/-- Complete interval computation for depth 13, residue 2269. -/ +theorem bounds_13_2269 : exactInterval 13 2269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2269 : oddCount 2269 13 = 8 ∧ acceleratedOrbit 13 2269 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2269) = 3 ^ 8 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2269.1, data_13_2269.2] + +/-- Complete interval computation for depth 13, residue 2270. -/ +theorem bounds_13_2270 : exactInterval 13 2270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2270 : oddCount 2270 13 = 8 ∧ acceleratedOrbit 13 2270 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2270) = 3 ^ 8 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2270.1, data_13_2270.2] + +/-- Complete interval computation for depth 13, residue 2271. -/ +theorem bounds_13_2271 : exactInterval 13 2271 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2271) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2271 : oddCount 2271 13 = 8 ∧ acceleratedOrbit 13 2271 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2271) = 3 ^ 8 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2271.1, data_13_2271.2] + +/-- Complete interval computation for depth 13, residue 2272. -/ +theorem bounds_13_2272 : exactInterval 13 2272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2272 : oddCount 2272 13 = 6 ∧ acceleratedOrbit 13 2272 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2272) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2272.1, data_13_2272.2] + +/-- Complete interval computation for depth 13, residue 2273. -/ +theorem bounds_13_2273 : exactInterval 13 2273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2273 : oddCount 2273 13 = 10 ∧ acceleratedOrbit 13 2273 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2273) = 3 ^ 10 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2273.1, data_13_2273.2] + +/-- Complete interval computation for depth 13, residue 2274. -/ +theorem bounds_13_2274 : exactInterval 13 2274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2274 : oddCount 2274 13 = 3 ∧ acceleratedOrbit 13 2274 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2274) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2274.1, data_13_2274.2] + +/-- Complete interval computation for depth 13, residue 2275. -/ +theorem bounds_13_2275 : exactInterval 13 2275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2275 : oddCount 2275 13 = 3 ∧ acceleratedOrbit 13 2275 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2275) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2275.1, data_13_2275.2] + +/-- Complete interval computation for depth 13, residue 2276. -/ +theorem bounds_13_2276 : exactInterval 13 2276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2276 : oddCount 2276 13 = 7 ∧ acceleratedOrbit 13 2276 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2276) = 3 ^ 7 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2276.1, data_13_2276.2] + +/-- Complete interval computation for depth 13, residue 2277. -/ +theorem bounds_13_2277 : exactInterval 13 2277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2277 : oddCount 2277 13 = 7 ∧ acceleratedOrbit 13 2277 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2277) = 3 ^ 7 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2277.1, data_13_2277.2] + +end Collatz.Research.StoppingAtlas.Batch0615 From 2ae8a9a1a3196ad2964033cad034a01c5ae9e522 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:08 +0530 Subject: [PATCH 0616/1001] proof: certify atlas Batch0616 (13:2278 to 13:2292) --- Collatz/Research/StoppingAtlas/Batch0616.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0616.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0616.lean b/Collatz/Research/StoppingAtlas/Batch0616.lean new file mode 100644 index 00000000..6b298491 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0616.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0616 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2278. -/ +theorem bounds_13_2278 : exactInterval 13 2278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2278 : oddCount 2278 13 = 7 ∧ acceleratedOrbit 13 2278 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2278) = 3 ^ 7 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2278.1, data_13_2278.2] + +/-- Complete interval computation for depth 13, residue 2279. -/ +theorem bounds_13_2279 : exactInterval 13 2279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2279 : oddCount 2279 13 = 9 ∧ acceleratedOrbit 13 2279 = 5480 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2279) = 3 ^ 9 * m + 5480 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2279.1, data_13_2279.2] + +/-- Complete interval computation for depth 13, residue 2280. -/ +theorem bounds_13_2280 : exactInterval 13 2280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2280 : oddCount 2280 13 = 6 ∧ acceleratedOrbit 13 2280 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2280) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2280.1, data_13_2280.2] + +/-- Complete interval computation for depth 13, residue 2281. -/ +theorem bounds_13_2281 : exactInterval 13 2281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2281 : oddCount 2281 13 = 8 ∧ acceleratedOrbit 13 2281 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2281) = 3 ^ 8 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2281.1, data_13_2281.2] + +/-- Complete interval computation for depth 13, residue 2282. -/ +theorem bounds_13_2282 : exactInterval 13 2282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2282 : oddCount 2282 13 = 6 ∧ acceleratedOrbit 13 2282 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2282) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2282.1, data_13_2282.2] + +/-- Complete interval computation for depth 13, residue 2283. -/ +theorem bounds_13_2283 : exactInterval 13 2283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2283 : oddCount 2283 13 = 7 ∧ acceleratedOrbit 13 2283 = 610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2283) = 3 ^ 7 * m + 610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2283.1, data_13_2283.2] + +/-- Complete interval computation for depth 13, residue 2284. -/ +theorem bounds_13_2284 : exactInterval 13 2284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2284 : oddCount 2284 13 = 5 ∧ acceleratedOrbit 13 2284 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2284) = 3 ^ 5 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2284.1, data_13_2284.2] + +/-- Complete interval computation for depth 13, residue 2285. -/ +theorem bounds_13_2285 : exactInterval 13 2285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2285 : oddCount 2285 13 = 5 ∧ acceleratedOrbit 13 2285 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2285) = 3 ^ 5 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2285.1, data_13_2285.2] + +/-- Complete interval computation for depth 13, residue 2286. -/ +theorem bounds_13_2286 : exactInterval 13 2286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2286 : oddCount 2286 13 = 5 ∧ acceleratedOrbit 13 2286 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2286) = 3 ^ 5 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2286.1, data_13_2286.2] + +/-- Complete interval computation for depth 13, residue 2287. -/ +theorem bounds_13_2287 : exactInterval 13 2287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2287 : oddCount 2287 13 = 11 ∧ acceleratedOrbit 13 2287 = 49481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2287) = 3 ^ 11 * m + 49481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2287.1, data_13_2287.2] + +/-- Complete interval computation for depth 13, residue 2288. -/ +theorem bounds_13_2288 : exactInterval 13 2288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2288 : oddCount 2288 13 = 6 ∧ acceleratedOrbit 13 2288 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2288) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2288.1, data_13_2288.2] + +/-- Complete interval computation for depth 13, residue 2289. -/ +theorem bounds_13_2289 : exactInterval 13 2289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2289 : oddCount 2289 13 = 6 ∧ acceleratedOrbit 13 2289 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2289) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2289.1, data_13_2289.2] + +/-- Complete interval computation for depth 13, residue 2290. -/ +theorem bounds_13_2290 : exactInterval 13 2290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2290 : oddCount 2290 13 = 8 ∧ acceleratedOrbit 13 2290 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2290) = 3 ^ 8 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2290.1, data_13_2290.2] + +/-- Complete interval computation for depth 13, residue 2291. -/ +theorem bounds_13_2291 : exactInterval 13 2291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2291 : oddCount 2291 13 = 8 ∧ acceleratedOrbit 13 2291 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2291) = 3 ^ 8 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2291.1, data_13_2291.2] + +/-- Complete interval computation for depth 13, residue 2292. -/ +theorem bounds_13_2292 : exactInterval 13 2292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2292 : oddCount 2292 13 = 6 ∧ acceleratedOrbit 13 2292 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2292) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2292.1, data_13_2292.2] + +end Collatz.Research.StoppingAtlas.Batch0616 From df4b5be9b812498c5069ee8c7c0587b1b78f2552 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:11 +0530 Subject: [PATCH 0617/1001] proof: certify atlas Batch0617 (13:2293 to 13:2308) --- Collatz/Research/StoppingAtlas/Batch0617.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0617.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0617.lean b/Collatz/Research/StoppingAtlas/Batch0617.lean new file mode 100644 index 00000000..20d495dc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0617.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0617 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2293. -/ +theorem bounds_13_2293 : exactInterval 13 2293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2293 : oddCount 2293 13 = 6 ∧ acceleratedOrbit 13 2293 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2293) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2293.1, data_13_2293.2] + +/-- Complete interval computation for depth 13, residue 2294. -/ +theorem bounds_13_2294 : exactInterval 13 2294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2294 : oddCount 2294 13 = 7 ∧ acceleratedOrbit 13 2294 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2294) = 3 ^ 7 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2294.1, data_13_2294.2] + +/-- Complete interval computation for depth 13, residue 2295. -/ +theorem bounds_13_2295 : exactInterval 13 2295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2295 : oddCount 2295 13 = 7 ∧ acceleratedOrbit 13 2295 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2295) = 3 ^ 7 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2295.1, data_13_2295.2] + +/-- Complete interval computation for depth 13, residue 2296. -/ +theorem bounds_13_2296 : exactInterval 13 2296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2296 : oddCount 2296 13 = 6 ∧ acceleratedOrbit 13 2296 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2296) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2296.1, data_13_2296.2] + +/-- Complete interval computation for depth 13, residue 2297. -/ +theorem bounds_13_2297 : exactInterval 13 2297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2297 : oddCount 2297 13 = 7 ∧ acceleratedOrbit 13 2297 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2297) = 3 ^ 7 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2297.1, data_13_2297.2] + +/-- Complete interval computation for depth 13, residue 2298. -/ +theorem bounds_13_2298 : exactInterval 13 2298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2298 : oddCount 2298 13 = 6 ∧ acceleratedOrbit 13 2298 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2298) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2298.1, data_13_2298.2] + +/-- Complete interval computation for depth 13, residue 2299. -/ +theorem bounds_13_2299 : exactInterval 13 2299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2299 : oddCount 2299 13 = 9 ∧ acceleratedOrbit 13 2299 = 5528 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2299) = 3 ^ 9 * m + 5528 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2299.1, data_13_2299.2] + +/-- Complete interval computation for depth 13, residue 2300. -/ +theorem bounds_13_2300 : exactInterval 13 2300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2300 : oddCount 2300 13 = 6 ∧ acceleratedOrbit 13 2300 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2300) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2300.1, data_13_2300.2] + +/-- Complete interval computation for depth 13, residue 2301. -/ +theorem bounds_13_2301 : exactInterval 13 2301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2301 : oddCount 2301 13 = 6 ∧ acceleratedOrbit 13 2301 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2301) = 3 ^ 6 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2301.1, data_13_2301.2] + +/-- Complete interval computation for depth 13, residue 2302. -/ +theorem bounds_13_2302 : exactInterval 13 2302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2302 : oddCount 2302 13 = 9 ∧ acceleratedOrbit 13 2302 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2302) = 3 ^ 9 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2302.1, data_13_2302.2] + +/-- Complete interval computation for depth 13, residue 2303. -/ +theorem bounds_13_2303 : exactInterval 13 2303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2303 : oddCount 2303 13 = 9 ∧ acceleratedOrbit 13 2303 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2303) = 3 ^ 9 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2303.1, data_13_2303.2] + +/-- Complete interval computation for depth 13, residue 2304. -/ +theorem bounds_13_2304 : exactInterval 13 2304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2304 : oddCount 2304 13 = 4 ∧ acceleratedOrbit 13 2304 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2304) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2304.1, data_13_2304.2] + +/-- Complete interval computation for depth 13, residue 2305. -/ +theorem bounds_13_2305 : exactInterval 13 2305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2305 : oddCount 2305 13 = 6 ∧ acceleratedOrbit 13 2305 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2305) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2305.1, data_13_2305.2] + +/-- Complete interval computation for depth 13, residue 2306. -/ +theorem bounds_13_2306 : exactInterval 13 2306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2306 : oddCount 2306 13 = 8 ∧ acceleratedOrbit 13 2306 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2306) = 3 ^ 8 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2306.1, data_13_2306.2] + +/-- Complete interval computation for depth 13, residue 2307. -/ +theorem bounds_13_2307 : exactInterval 13 2307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2307 : oddCount 2307 13 = 8 ∧ acceleratedOrbit 13 2307 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2307) = 3 ^ 8 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2307.1, data_13_2307.2] + +/-- Complete interval computation for depth 13, residue 2308. -/ +theorem bounds_13_2308 : exactInterval 13 2308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2308 : oddCount 2308 13 = 4 ∧ acceleratedOrbit 13 2308 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2308) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2308.1, data_13_2308.2] + +end Collatz.Research.StoppingAtlas.Batch0617 From 94ecc773e16c966b6454347e55e3ba79abb8b726 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:11 +0530 Subject: [PATCH 0618/1001] proof: certify atlas Batch0618 (13:2309 to 13:2323) --- Collatz/Research/StoppingAtlas/Batch0618.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0618.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0618.lean b/Collatz/Research/StoppingAtlas/Batch0618.lean new file mode 100644 index 00000000..a52b5a1c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0618.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0618 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2309. -/ +theorem bounds_13_2309 : exactInterval 13 2309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2309 : oddCount 2309 13 = 4 ∧ acceleratedOrbit 13 2309 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2309) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2309.1, data_13_2309.2] + +/-- Complete interval computation for depth 13, residue 2310. -/ +theorem bounds_13_2310 : exactInterval 13 2310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2310 : oddCount 2310 13 = 4 ∧ acceleratedOrbit 13 2310 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2310) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2310.1, data_13_2310.2] + +/-- Complete interval computation for depth 13, residue 2311. -/ +theorem bounds_13_2311 : exactInterval 13 2311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2311 : oddCount 2311 13 = 8 ∧ acceleratedOrbit 13 2311 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2311) = 3 ^ 8 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2311.1, data_13_2311.2] + +/-- Complete interval computation for depth 13, residue 2312. -/ +theorem bounds_13_2312 : exactInterval 13 2312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2312 : oddCount 2312 13 = 4 ∧ acceleratedOrbit 13 2312 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2312) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2312.1, data_13_2312.2] + +/-- Complete interval computation for depth 13, residue 2313. -/ +theorem bounds_13_2313 : exactInterval 13 2313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2313 : oddCount 2313 13 = 6 ∧ acceleratedOrbit 13 2313 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2313) = 3 ^ 6 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2313.1, data_13_2313.2] + +/-- Complete interval computation for depth 13, residue 2314. -/ +theorem bounds_13_2314 : exactInterval 13 2314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2314 : oddCount 2314 13 = 4 ∧ acceleratedOrbit 13 2314 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2314) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2314.1, data_13_2314.2] + +/-- Complete interval computation for depth 13, residue 2315. -/ +theorem bounds_13_2315 : exactInterval 13 2315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2315 : oddCount 2315 13 = 7 ∧ acceleratedOrbit 13 2315 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2315) = 3 ^ 7 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2315.1, data_13_2315.2] + +/-- Complete interval computation for depth 13, residue 2316. -/ +theorem bounds_13_2316 : exactInterval 13 2316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2316 : oddCount 2316 13 = 4 ∧ acceleratedOrbit 13 2316 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2316) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2316.1, data_13_2316.2] + +/-- Complete interval computation for depth 13, residue 2317. -/ +theorem bounds_13_2317 : exactInterval 13 2317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2317 : oddCount 2317 13 = 4 ∧ acceleratedOrbit 13 2317 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2317) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2317.1, data_13_2317.2] + +/-- Complete interval computation for depth 13, residue 2318. -/ +theorem bounds_13_2318 : exactInterval 13 2318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2318 : oddCount 2318 13 = 8 ∧ acceleratedOrbit 13 2318 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2318) = 3 ^ 8 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2318.1, data_13_2318.2] + +/-- Complete interval computation for depth 13, residue 2319. -/ +theorem bounds_13_2319 : exactInterval 13 2319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2319 : oddCount 2319 13 = 8 ∧ acceleratedOrbit 13 2319 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2319) = 3 ^ 8 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2319.1, data_13_2319.2] + +/-- Complete interval computation for depth 13, residue 2320. -/ +theorem bounds_13_2320 : exactInterval 13 2320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2320 : oddCount 2320 13 = 5 ∧ acceleratedOrbit 13 2320 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2320) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2320.1, data_13_2320.2] + +/-- Complete interval computation for depth 13, residue 2321. -/ +theorem bounds_13_2321 : exactInterval 13 2321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2321 : oddCount 2321 13 = 4 ∧ acceleratedOrbit 13 2321 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2321) = 3 ^ 4 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2321.1, data_13_2321.2] + +/-- Complete interval computation for depth 13, residue 2322. -/ +theorem bounds_13_2322 : exactInterval 13 2322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2322 : oddCount 2322 13 = 10 ∧ acceleratedOrbit 13 2322 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2322) = 3 ^ 10 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2322.1, data_13_2322.2] + +/-- Complete interval computation for depth 13, residue 2323. -/ +theorem bounds_13_2323 : exactInterval 13 2323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2323 : oddCount 2323 13 = 10 ∧ acceleratedOrbit 13 2323 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2323) = 3 ^ 10 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2323.1, data_13_2323.2] + +end Collatz.Research.StoppingAtlas.Batch0618 From 2b9b2713bdc9d789e75ee6372d66425263d18ba2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:11 +0530 Subject: [PATCH 0619/1001] proof: certify atlas Batch0619 (13:2324 to 13:2338) --- Collatz/Research/StoppingAtlas/Batch0619.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0619.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0619.lean b/Collatz/Research/StoppingAtlas/Batch0619.lean new file mode 100644 index 00000000..debaf220 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0619.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0619 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2324. -/ +theorem bounds_13_2324 : exactInterval 13 2324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2324 : oddCount 2324 13 = 5 ∧ acceleratedOrbit 13 2324 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2324) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2324.1, data_13_2324.2] + +/-- Complete interval computation for depth 13, residue 2325. -/ +theorem bounds_13_2325 : exactInterval 13 2325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2325 : oddCount 2325 13 = 5 ∧ acceleratedOrbit 13 2325 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2325) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2325.1, data_13_2325.2] + +/-- Complete interval computation for depth 13, residue 2326. -/ +theorem bounds_13_2326 : exactInterval 13 2326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2326 : oddCount 2326 13 = 7 ∧ acceleratedOrbit 13 2326 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2326) = 3 ^ 7 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2326.1, data_13_2326.2] + +/-- Complete interval computation for depth 13, residue 2327. -/ +theorem bounds_13_2327 : exactInterval 13 2327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2327 : oddCount 2327 13 = 7 ∧ acceleratedOrbit 13 2327 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2327) = 3 ^ 7 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2327.1, data_13_2327.2] + +/-- Complete interval computation for depth 13, residue 2328. -/ +theorem bounds_13_2328 : exactInterval 13 2328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2328 : oddCount 2328 13 = 5 ∧ acceleratedOrbit 13 2328 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2328) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2328.1, data_13_2328.2] + +/-- Complete interval computation for depth 13, residue 2329. -/ +theorem bounds_13_2329 : exactInterval 13 2329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2329 : oddCount 2329 13 = 7 ∧ acceleratedOrbit 13 2329 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2329) = 3 ^ 7 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2329.1, data_13_2329.2] + +/-- Complete interval computation for depth 13, residue 2330. -/ +theorem bounds_13_2330 : exactInterval 13 2330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2330 : oddCount 2330 13 = 5 ∧ acceleratedOrbit 13 2330 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2330) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2330.1, data_13_2330.2] + +/-- Complete interval computation for depth 13, residue 2331. -/ +theorem bounds_13_2331 : exactInterval 13 2331 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2331) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2331 : oddCount 2331 13 = 8 ∧ acceleratedOrbit 13 2331 = 1868 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2331) = 3 ^ 8 * m + 1868 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2331.1, data_13_2331.2] + +/-- Complete interval computation for depth 13, residue 2332. -/ +theorem bounds_13_2332 : exactInterval 13 2332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2332 : oddCount 2332 13 = 6 ∧ acceleratedOrbit 13 2332 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2332) = 3 ^ 6 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2332.1, data_13_2332.2] + +/-- Complete interval computation for depth 13, residue 2333. -/ +theorem bounds_13_2333 : exactInterval 13 2333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2333 : oddCount 2333 13 = 6 ∧ acceleratedOrbit 13 2333 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2333) = 3 ^ 6 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2333.1, data_13_2333.2] + +/-- Complete interval computation for depth 13, residue 2334. -/ +theorem bounds_13_2334 : exactInterval 13 2334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2334 : oddCount 2334 13 = 6 ∧ acceleratedOrbit 13 2334 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2334) = 3 ^ 6 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2334.1, data_13_2334.2] + +/-- Complete interval computation for depth 13, residue 2335. -/ +theorem bounds_13_2335 : exactInterval 13 2335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2335 : oddCount 2335 13 = 9 ∧ acceleratedOrbit 13 2335 = 5615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2335) = 3 ^ 9 * m + 5615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2335.1, data_13_2335.2] + +/-- Complete interval computation for depth 13, residue 2336. -/ +theorem bounds_13_2336 : exactInterval 13 2336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2336 : oddCount 2336 13 = 5 ∧ acceleratedOrbit 13 2336 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2336) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2336.1, data_13_2336.2] + +/-- Complete interval computation for depth 13, residue 2337. -/ +theorem bounds_13_2337 : exactInterval 13 2337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2337 : oddCount 2337 13 = 6 ∧ acceleratedOrbit 13 2337 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2337) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2337.1, data_13_2337.2] + +/-- Complete interval computation for depth 13, residue 2338. -/ +theorem bounds_13_2338 : exactInterval 13 2338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2338 : oddCount 2338 13 = 6 ∧ acceleratedOrbit 13 2338 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2338) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2338.1, data_13_2338.2] + +end Collatz.Research.StoppingAtlas.Batch0619 From 69959fd1c54febb1d94209d9bb29acf3b5e38f27 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:12 +0530 Subject: [PATCH 0620/1001] proof: certify atlas Batch0620 (13:2339 to 13:2354) --- Collatz/Research/StoppingAtlas/Batch0620.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0620.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0620.lean b/Collatz/Research/StoppingAtlas/Batch0620.lean new file mode 100644 index 00000000..6f77b0a4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0620.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0620 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2339. -/ +theorem bounds_13_2339 : exactInterval 13 2339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2339 : oddCount 2339 13 = 6 ∧ acceleratedOrbit 13 2339 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2339) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2339.1, data_13_2339.2] + +/-- Complete interval computation for depth 13, residue 2340. -/ +theorem bounds_13_2340 : exactInterval 13 2340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2340 : oddCount 2340 13 = 6 ∧ acceleratedOrbit 13 2340 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2340) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2340.1, data_13_2340.2] + +/-- Complete interval computation for depth 13, residue 2341. -/ +theorem bounds_13_2341 : exactInterval 13 2341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2341 : oddCount 2341 13 = 6 ∧ acceleratedOrbit 13 2341 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2341) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2341.1, data_13_2341.2] + +/-- Complete interval computation for depth 13, residue 2342. -/ +theorem bounds_13_2342 : exactInterval 13 2342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2342 : oddCount 2342 13 = 6 ∧ acceleratedOrbit 13 2342 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2342) = 3 ^ 6 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2342.1, data_13_2342.2] + +/-- Complete interval computation for depth 13, residue 2343. -/ +theorem bounds_13_2343 : exactInterval 13 2343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2343 : oddCount 2343 13 = 7 ∧ acceleratedOrbit 13 2343 = 626 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2343) = 3 ^ 7 * m + 626 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2343.1, data_13_2343.2] + +/-- Complete interval computation for depth 13, residue 2344. -/ +theorem bounds_13_2344 : exactInterval 13 2344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2344 : oddCount 2344 13 = 5 ∧ acceleratedOrbit 13 2344 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2344) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2344.1, data_13_2344.2] + +/-- Complete interval computation for depth 13, residue 2345. -/ +theorem bounds_13_2345 : exactInterval 13 2345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2345 : oddCount 2345 13 = 8 ∧ acceleratedOrbit 13 2345 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2345) = 3 ^ 8 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2345.1, data_13_2345.2] + +/-- Complete interval computation for depth 13, residue 2346. -/ +theorem bounds_13_2346 : exactInterval 13 2346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2346 : oddCount 2346 13 = 5 ∧ acceleratedOrbit 13 2346 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2346) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2346.1, data_13_2346.2] + +/-- Complete interval computation for depth 13, residue 2347. -/ +theorem bounds_13_2347 : exactInterval 13 2347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2347 : oddCount 2347 13 = 8 ∧ acceleratedOrbit 13 2347 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2347) = 3 ^ 8 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2347.1, data_13_2347.2] + +/-- Complete interval computation for depth 13, residue 2348. -/ +theorem bounds_13_2348 : exactInterval 13 2348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2348 : oddCount 2348 13 = 5 ∧ acceleratedOrbit 13 2348 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2348) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2348.1, data_13_2348.2] + +/-- Complete interval computation for depth 13, residue 2349. -/ +theorem bounds_13_2349 : exactInterval 13 2349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2349 : oddCount 2349 13 = 5 ∧ acceleratedOrbit 13 2349 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2349) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2349.1, data_13_2349.2] + +/-- Complete interval computation for depth 13, residue 2350. -/ +theorem bounds_13_2350 : exactInterval 13 2350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2350 : oddCount 2350 13 = 5 ∧ acceleratedOrbit 13 2350 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2350) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2350.1, data_13_2350.2] + +/-- Complete interval computation for depth 13, residue 2351. -/ +theorem bounds_13_2351 : exactInterval 13 2351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2351 : oddCount 2351 13 = 7 ∧ acceleratedOrbit 13 2351 = 628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2351) = 3 ^ 7 * m + 628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2351.1, data_13_2351.2] + +/-- Complete interval computation for depth 13, residue 2352. -/ +theorem bounds_13_2352 : exactInterval 13 2352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2352 : oddCount 2352 13 = 5 ∧ acceleratedOrbit 13 2352 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2352) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2352.1, data_13_2352.2] + +/-- Complete interval computation for depth 13, residue 2353. -/ +theorem bounds_13_2353 : exactInterval 13 2353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2353 : oddCount 2353 13 = 5 ∧ acceleratedOrbit 13 2353 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2353) = 3 ^ 5 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2353.1, data_13_2353.2] + +/-- Complete interval computation for depth 13, residue 2354. -/ +theorem bounds_13_2354 : exactInterval 13 2354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2354 : oddCount 2354 13 = 5 ∧ acceleratedOrbit 13 2354 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2354) = 3 ^ 5 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2354.1, data_13_2354.2] + +end Collatz.Research.StoppingAtlas.Batch0620 From fbd9fd47d7f8145d5487e5fc8c6036c11d0bfd70 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:13 +0530 Subject: [PATCH 0621/1001] proof: certify atlas Batch0621 (13:2355 to 13:2369) --- Collatz/Research/StoppingAtlas/Batch0621.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0621.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0621.lean b/Collatz/Research/StoppingAtlas/Batch0621.lean new file mode 100644 index 00000000..41a63c7f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0621.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0621 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2355. -/ +theorem bounds_13_2355 : exactInterval 13 2355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2355 : oddCount 2355 13 = 5 ∧ acceleratedOrbit 13 2355 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2355) = 3 ^ 5 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2355.1, data_13_2355.2] + +/-- Complete interval computation for depth 13, residue 2356. -/ +theorem bounds_13_2356 : exactInterval 13 2356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2356 : oddCount 2356 13 = 5 ∧ acceleratedOrbit 13 2356 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2356) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2356.1, data_13_2356.2] + +/-- Complete interval computation for depth 13, residue 2357. -/ +theorem bounds_13_2357 : exactInterval 13 2357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2357 : oddCount 2357 13 = 5 ∧ acceleratedOrbit 13 2357 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2357) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2357.1, data_13_2357.2] + +/-- Complete interval computation for depth 13, residue 2358. -/ +theorem bounds_13_2358 : exactInterval 13 2358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2358 : oddCount 2358 13 = 8 ∧ acceleratedOrbit 13 2358 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2358) = 3 ^ 8 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2358.1, data_13_2358.2] + +/-- Complete interval computation for depth 13, residue 2359. -/ +theorem bounds_13_2359 : exactInterval 13 2359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2359 : oddCount 2359 13 = 8 ∧ acceleratedOrbit 13 2359 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2359) = 3 ^ 8 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2359.1, data_13_2359.2] + +/-- Complete interval computation for depth 13, residue 2360. -/ +theorem bounds_13_2360 : exactInterval 13 2360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2360 : oddCount 2360 13 = 6 ∧ acceleratedOrbit 13 2360 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2360) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2360.1, data_13_2360.2] + +/-- Complete interval computation for depth 13, residue 2361. -/ +theorem bounds_13_2361 : exactInterval 13 2361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2361 : oddCount 2361 13 = 7 ∧ acceleratedOrbit 13 2361 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2361) = 3 ^ 7 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2361.1, data_13_2361.2] + +/-- Complete interval computation for depth 13, residue 2362. -/ +theorem bounds_13_2362 : exactInterval 13 2362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2362 : oddCount 2362 13 = 6 ∧ acceleratedOrbit 13 2362 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2362) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2362.1, data_13_2362.2] + +/-- Complete interval computation for depth 13, residue 2363. -/ +theorem bounds_13_2363 : exactInterval 13 2363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2363 : oddCount 2363 13 = 6 ∧ acceleratedOrbit 13 2363 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2363) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2363.1, data_13_2363.2] + +/-- Complete interval computation for depth 13, residue 2364. -/ +theorem bounds_13_2364 : exactInterval 13 2364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2364 : oddCount 2364 13 = 6 ∧ acceleratedOrbit 13 2364 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2364) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2364.1, data_13_2364.2] + +/-- Complete interval computation for depth 13, residue 2365. -/ +theorem bounds_13_2365 : exactInterval 13 2365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2365 : oddCount 2365 13 = 6 ∧ acceleratedOrbit 13 2365 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2365) = 3 ^ 6 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2365.1, data_13_2365.2] + +/-- Complete interval computation for depth 13, residue 2366. -/ +theorem bounds_13_2366 : exactInterval 13 2366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2366 : oddCount 2366 13 = 9 ∧ acceleratedOrbit 13 2366 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2366) = 3 ^ 9 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2366.1, data_13_2366.2] + +/-- Complete interval computation for depth 13, residue 2367. -/ +theorem bounds_13_2367 : exactInterval 13 2367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2367 : oddCount 2367 13 = 9 ∧ acceleratedOrbit 13 2367 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2367) = 3 ^ 9 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2367.1, data_13_2367.2] + +/-- Complete interval computation for depth 13, residue 2368. -/ +theorem bounds_13_2368 : exactInterval 13 2368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2368 : oddCount 2368 13 = 4 ∧ acceleratedOrbit 13 2368 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2368) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2368.1, data_13_2368.2] + +/-- Complete interval computation for depth 13, residue 2369. -/ +theorem bounds_13_2369 : exactInterval 13 2369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2369 : oddCount 2369 13 = 5 ∧ acceleratedOrbit 13 2369 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2369) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2369.1, data_13_2369.2] + +end Collatz.Research.StoppingAtlas.Batch0621 From c5e44de55e504e06307b07643a68f887d3b11190 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:13 +0530 Subject: [PATCH 0622/1001] proof: certify atlas Batch0622 (13:2370 to 13:2384) --- Collatz/Research/StoppingAtlas/Batch0622.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0622.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0622.lean b/Collatz/Research/StoppingAtlas/Batch0622.lean new file mode 100644 index 00000000..efca7936 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0622.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0622 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2370. -/ +theorem bounds_13_2370 : exactInterval 13 2370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2370 : oddCount 2370 13 = 8 ∧ acceleratedOrbit 13 2370 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2370) = 3 ^ 8 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2370.1, data_13_2370.2] + +/-- Complete interval computation for depth 13, residue 2371. -/ +theorem bounds_13_2371 : exactInterval 13 2371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2371 : oddCount 2371 13 = 8 ∧ acceleratedOrbit 13 2371 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2371) = 3 ^ 8 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2371.1, data_13_2371.2] + +/-- Complete interval computation for depth 13, residue 2372. -/ +theorem bounds_13_2372 : exactInterval 13 2372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2372 : oddCount 2372 13 = 7 ∧ acceleratedOrbit 13 2372 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2372) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2372.1, data_13_2372.2] + +/-- Complete interval computation for depth 13, residue 2373. -/ +theorem bounds_13_2373 : exactInterval 13 2373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2373 : oddCount 2373 13 = 7 ∧ acceleratedOrbit 13 2373 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2373) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2373.1, data_13_2373.2] + +/-- Complete interval computation for depth 13, residue 2374. -/ +theorem bounds_13_2374 : exactInterval 13 2374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2374 : oddCount 2374 13 = 7 ∧ acceleratedOrbit 13 2374 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2374) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2374.1, data_13_2374.2] + +/-- Complete interval computation for depth 13, residue 2375. -/ +theorem bounds_13_2375 : exactInterval 13 2375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2375) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2375 : oddCount 2375 13 = 10 ∧ acceleratedOrbit 13 2375 = 17131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2375) = 3 ^ 10 * m + 17131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2375.1, data_13_2375.2] + +/-- Complete interval computation for depth 13, residue 2376. -/ +theorem bounds_13_2376 : exactInterval 13 2376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2376 : oddCount 2376 13 = 7 ∧ acceleratedOrbit 13 2376 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2376) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2376.1, data_13_2376.2] + +/-- Complete interval computation for depth 13, residue 2377. -/ +theorem bounds_13_2377 : exactInterval 13 2377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2377 : oddCount 2377 13 = 8 ∧ acceleratedOrbit 13 2377 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2377) = 3 ^ 8 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2377.1, data_13_2377.2] + +/-- Complete interval computation for depth 13, residue 2378. -/ +theorem bounds_13_2378 : exactInterval 13 2378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2378 : oddCount 2378 13 = 7 ∧ acceleratedOrbit 13 2378 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2378) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2378.1, data_13_2378.2] + +/-- Complete interval computation for depth 13, residue 2379. -/ +theorem bounds_13_2379 : exactInterval 13 2379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2379 : oddCount 2379 13 = 7 ∧ acceleratedOrbit 13 2379 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2379) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2379.1, data_13_2379.2] + +/-- Complete interval computation for depth 13, residue 2380. -/ +theorem bounds_13_2380 : exactInterval 13 2380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2380 : oddCount 2380 13 = 7 ∧ acceleratedOrbit 13 2380 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2380) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2380.1, data_13_2380.2] + +/-- Complete interval computation for depth 13, residue 2381. -/ +theorem bounds_13_2381 : exactInterval 13 2381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2381 : oddCount 2381 13 = 7 ∧ acceleratedOrbit 13 2381 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2381) = 3 ^ 7 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2381.1, data_13_2381.2] + +/-- Complete interval computation for depth 13, residue 2382. -/ +theorem bounds_13_2382 : exactInterval 13 2382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2382 : oddCount 2382 13 = 8 ∧ acceleratedOrbit 13 2382 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2382) = 3 ^ 8 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2382.1, data_13_2382.2] + +/-- Complete interval computation for depth 13, residue 2383. -/ +theorem bounds_13_2383 : exactInterval 13 2383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2383 : oddCount 2383 13 = 8 ∧ acceleratedOrbit 13 2383 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2383) = 3 ^ 8 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2383.1, data_13_2383.2] + +/-- Complete interval computation for depth 13, residue 2384. -/ +theorem bounds_13_2384 : exactInterval 13 2384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2384 : oddCount 2384 13 = 4 ∧ acceleratedOrbit 13 2384 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2384) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2384.1, data_13_2384.2] + +end Collatz.Research.StoppingAtlas.Batch0622 From b98f4ae1fd9c82c91ac77cfea623fc00f031b49f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:14 +0530 Subject: [PATCH 0623/1001] proof: certify atlas Batch0623 (13:2385 to 13:2400) --- Collatz/Research/StoppingAtlas/Batch0623.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0623.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0623.lean b/Collatz/Research/StoppingAtlas/Batch0623.lean new file mode 100644 index 00000000..90ffa028 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0623.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0623 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2385. -/ +theorem bounds_13_2385 : exactInterval 13 2385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2385 : oddCount 2385 13 = 9 ∧ acceleratedOrbit 13 2385 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2385) = 3 ^ 9 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2385.1, data_13_2385.2] + +/-- Complete interval computation for depth 13, residue 2386. -/ +theorem bounds_13_2386 : exactInterval 13 2386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2386 : oddCount 2386 13 = 9 ∧ acceleratedOrbit 13 2386 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2386) = 3 ^ 9 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2386.1, data_13_2386.2] + +/-- Complete interval computation for depth 13, residue 2387. -/ +theorem bounds_13_2387 : exactInterval 13 2387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2387 : oddCount 2387 13 = 9 ∧ acceleratedOrbit 13 2387 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2387) = 3 ^ 9 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2387.1, data_13_2387.2] + +/-- Complete interval computation for depth 13, residue 2388. -/ +theorem bounds_13_2388 : exactInterval 13 2388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2388 : oddCount 2388 13 = 4 ∧ acceleratedOrbit 13 2388 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2388) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2388.1, data_13_2388.2] + +/-- Complete interval computation for depth 13, residue 2389. -/ +theorem bounds_13_2389 : exactInterval 13 2389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2389 : oddCount 2389 13 = 4 ∧ acceleratedOrbit 13 2389 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2389) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2389.1, data_13_2389.2] + +/-- Complete interval computation for depth 13, residue 2390. -/ +theorem bounds_13_2390 : exactInterval 13 2390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2390 : oddCount 2390 13 = 5 ∧ acceleratedOrbit 13 2390 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2390) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2390.1, data_13_2390.2] + +/-- Complete interval computation for depth 13, residue 2391. -/ +theorem bounds_13_2391 : exactInterval 13 2391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2391 : oddCount 2391 13 = 5 ∧ acceleratedOrbit 13 2391 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2391) = 3 ^ 5 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2391.1, data_13_2391.2] + +/-- Complete interval computation for depth 13, residue 2392. -/ +theorem bounds_13_2392 : exactInterval 13 2392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2392 : oddCount 2392 13 = 6 ∧ acceleratedOrbit 13 2392 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2392) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2392.1, data_13_2392.2] + +/-- Complete interval computation for depth 13, residue 2393. -/ +theorem bounds_13_2393 : exactInterval 13 2393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2393 : oddCount 2393 13 = 7 ∧ acceleratedOrbit 13 2393 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2393) = 3 ^ 7 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2393.1, data_13_2393.2] + +/-- Complete interval computation for depth 13, residue 2394. -/ +theorem bounds_13_2394 : exactInterval 13 2394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2394 : oddCount 2394 13 = 6 ∧ acceleratedOrbit 13 2394 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2394) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2394.1, data_13_2394.2] + +/-- Complete interval computation for depth 13, residue 2395. -/ +theorem bounds_13_2395 : exactInterval 13 2395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2395 : oddCount 2395 13 = 7 ∧ acceleratedOrbit 13 2395 = 640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2395) = 3 ^ 7 * m + 640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2395.1, data_13_2395.2] + +/-- Complete interval computation for depth 13, residue 2396. -/ +theorem bounds_13_2396 : exactInterval 13 2396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2396 : oddCount 2396 13 = 6 ∧ acceleratedOrbit 13 2396 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2396) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2396.1, data_13_2396.2] + +/-- Complete interval computation for depth 13, residue 2397. -/ +theorem bounds_13_2397 : exactInterval 13 2397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2397 : oddCount 2397 13 = 6 ∧ acceleratedOrbit 13 2397 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2397) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2397.1, data_13_2397.2] + +/-- Complete interval computation for depth 13, residue 2398. -/ +theorem bounds_13_2398 : exactInterval 13 2398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2398 : oddCount 2398 13 = 7 ∧ acceleratedOrbit 13 2398 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2398) = 3 ^ 7 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2398.1, data_13_2398.2] + +/-- Complete interval computation for depth 13, residue 2399. -/ +theorem bounds_13_2399 : exactInterval 13 2399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2399 : oddCount 2399 13 = 7 ∧ acceleratedOrbit 13 2399 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2399) = 3 ^ 7 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2399.1, data_13_2399.2] + +/-- Complete interval computation for depth 13, residue 2400. -/ +theorem bounds_13_2400 : exactInterval 13 2400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2400 : oddCount 2400 13 = 3 ∧ acceleratedOrbit 13 2400 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2400) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2400.1, data_13_2400.2] + +end Collatz.Research.StoppingAtlas.Batch0623 From 376a6bafb8c83b39da031cdec5eed475931294f9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:14 +0530 Subject: [PATCH 0624/1001] proof: certify atlas Batch0624 (13:2401 to 13:2415) --- Collatz/Research/StoppingAtlas/Batch0624.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0624.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0624.lean b/Collatz/Research/StoppingAtlas/Batch0624.lean new file mode 100644 index 00000000..5e04ba8c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0624.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0624 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2401. -/ +theorem bounds_13_2401 : exactInterval 13 2401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2401 : oddCount 2401 13 = 9 ∧ acceleratedOrbit 13 2401 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2401) = 3 ^ 9 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2401.1, data_13_2401.2] + +/-- Complete interval computation for depth 13, residue 2402. -/ +theorem bounds_13_2402 : exactInterval 13 2402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2402 : oddCount 2402 13 = 7 ∧ acceleratedOrbit 13 2402 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2402) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2402.1, data_13_2402.2] + +/-- Complete interval computation for depth 13, residue 2403. -/ +theorem bounds_13_2403 : exactInterval 13 2403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2403 : oddCount 2403 13 = 7 ∧ acceleratedOrbit 13 2403 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2403) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2403.1, data_13_2403.2] + +/-- Complete interval computation for depth 13, residue 2404. -/ +theorem bounds_13_2404 : exactInterval 13 2404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2404 : oddCount 2404 13 = 7 ∧ acceleratedOrbit 13 2404 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2404) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2404.1, data_13_2404.2] + +/-- Complete interval computation for depth 13, residue 2405. -/ +theorem bounds_13_2405 : exactInterval 13 2405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2405 : oddCount 2405 13 = 7 ∧ acceleratedOrbit 13 2405 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2405) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2405.1, data_13_2405.2] + +/-- Complete interval computation for depth 13, residue 2406. -/ +theorem bounds_13_2406 : exactInterval 13 2406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2406 : oddCount 2406 13 = 7 ∧ acceleratedOrbit 13 2406 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2406) = 3 ^ 7 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2406.1, data_13_2406.2] + +/-- Complete interval computation for depth 13, residue 2407. -/ +theorem bounds_13_2407 : exactInterval 13 2407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2407 : oddCount 2407 13 = 10 ∧ acceleratedOrbit 13 2407 = 17360 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2407) = 3 ^ 10 * m + 17360 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2407.1, data_13_2407.2] + +/-- Complete interval computation for depth 13, residue 2408. -/ +theorem bounds_13_2408 : exactInterval 13 2408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2408 : oddCount 2408 13 = 3 ∧ acceleratedOrbit 13 2408 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2408) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2408.1, data_13_2408.2] + +/-- Complete interval computation for depth 13, residue 2409. -/ +theorem bounds_13_2409 : exactInterval 13 2409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2409 : oddCount 2409 13 = 6 ∧ acceleratedOrbit 13 2409 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2409) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2409.1, data_13_2409.2] + +/-- Complete interval computation for depth 13, residue 2410. -/ +theorem bounds_13_2410 : exactInterval 13 2410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2410 : oddCount 2410 13 = 3 ∧ acceleratedOrbit 13 2410 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2410) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2410.1, data_13_2410.2] + +/-- Complete interval computation for depth 13, residue 2411. -/ +theorem bounds_13_2411 : exactInterval 13 2411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2411 : oddCount 2411 13 = 8 ∧ acceleratedOrbit 13 2411 = 1934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2411) = 3 ^ 8 * m + 1934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2411.1, data_13_2411.2] + +/-- Complete interval computation for depth 13, residue 2412. -/ +theorem bounds_13_2412 : exactInterval 13 2412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2412 : oddCount 2412 13 = 8 ∧ acceleratedOrbit 13 2412 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2412) = 3 ^ 8 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2412.1, data_13_2412.2] + +/-- Complete interval computation for depth 13, residue 2413. -/ +theorem bounds_13_2413 : exactInterval 13 2413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2413 : oddCount 2413 13 = 8 ∧ acceleratedOrbit 13 2413 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2413) = 3 ^ 8 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2413.1, data_13_2413.2] + +/-- Complete interval computation for depth 13, residue 2414. -/ +theorem bounds_13_2414 : exactInterval 13 2414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2414 : oddCount 2414 13 = 8 ∧ acceleratedOrbit 13 2414 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2414) = 3 ^ 8 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2414.1, data_13_2414.2] + +/-- Complete interval computation for depth 13, residue 2415. -/ +theorem bounds_13_2415 : exactInterval 13 2415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2415 : oddCount 2415 13 = 6 ∧ acceleratedOrbit 13 2415 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2415) = 3 ^ 6 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2415.1, data_13_2415.2] + +end Collatz.Research.StoppingAtlas.Batch0624 From bcdadfd906440a31e51dc5177b79eeca9b07f57c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:16 +0530 Subject: [PATCH 0625/1001] proof: certify atlas Batch0625 (13:2416 to 13:2431) --- Collatz/Research/StoppingAtlas/Batch0625.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0625.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0625.lean b/Collatz/Research/StoppingAtlas/Batch0625.lean new file mode 100644 index 00000000..82defb26 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0625.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0625 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2416. -/ +theorem bounds_13_2416 : exactInterval 13 2416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2416 : oddCount 2416 13 = 3 ∧ acceleratedOrbit 13 2416 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2416) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2416.1, data_13_2416.2] + +/-- Complete interval computation for depth 13, residue 2417. -/ +theorem bounds_13_2417 : exactInterval 13 2417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2417 : oddCount 2417 13 = 3 ∧ acceleratedOrbit 13 2417 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2417) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2417.1, data_13_2417.2] + +/-- Complete interval computation for depth 13, residue 2418. -/ +theorem bounds_13_2418 : exactInterval 13 2418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2418 : oddCount 2418 13 = 8 ∧ acceleratedOrbit 13 2418 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2418) = 3 ^ 8 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2418.1, data_13_2418.2] + +/-- Complete interval computation for depth 13, residue 2419. -/ +theorem bounds_13_2419 : exactInterval 13 2419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2419 : oddCount 2419 13 = 8 ∧ acceleratedOrbit 13 2419 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2419) = 3 ^ 8 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2419.1, data_13_2419.2] + +/-- Complete interval computation for depth 13, residue 2420. -/ +theorem bounds_13_2420 : exactInterval 13 2420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2420 : oddCount 2420 13 = 3 ∧ acceleratedOrbit 13 2420 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2420) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2420.1, data_13_2420.2] + +/-- Complete interval computation for depth 13, residue 2421. -/ +theorem bounds_13_2421 : exactInterval 13 2421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2421 : oddCount 2421 13 = 3 ∧ acceleratedOrbit 13 2421 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2421) = 3 ^ 3 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2421.1, data_13_2421.2] + +/-- Complete interval computation for depth 13, residue 2422. -/ +theorem bounds_13_2422 : exactInterval 13 2422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2422 : oddCount 2422 13 = 9 ∧ acceleratedOrbit 13 2422 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2422) = 3 ^ 9 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2422.1, data_13_2422.2] + +/-- Complete interval computation for depth 13, residue 2423. -/ +theorem bounds_13_2423 : exactInterval 13 2423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2423 : oddCount 2423 13 = 9 ∧ acceleratedOrbit 13 2423 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2423) = 3 ^ 9 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2423.1, data_13_2423.2] + +/-- Complete interval computation for depth 13, residue 2424. -/ +theorem bounds_13_2424 : exactInterval 13 2424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2424 : oddCount 2424 13 = 7 ∧ acceleratedOrbit 13 2424 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2424) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2424.1, data_13_2424.2] + +/-- Complete interval computation for depth 13, residue 2425. -/ +theorem bounds_13_2425 : exactInterval 13 2425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2425 : oddCount 2425 13 = 11 ∧ acceleratedOrbit 13 2425 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2425) = 3 ^ 11 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2425.1, data_13_2425.2] + +/-- Complete interval computation for depth 13, residue 2426. -/ +theorem bounds_13_2426 : exactInterval 13 2426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2426 : oddCount 2426 13 = 7 ∧ acceleratedOrbit 13 2426 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2426) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2426.1, data_13_2426.2] + +/-- Complete interval computation for depth 13, residue 2427. -/ +theorem bounds_13_2427 : exactInterval 13 2427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2427 : oddCount 2427 13 = 8 ∧ acceleratedOrbit 13 2427 = 1946 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2427) = 3 ^ 8 * m + 1946 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2427.1, data_13_2427.2] + +/-- Complete interval computation for depth 13, residue 2428. -/ +theorem bounds_13_2428 : exactInterval 13 2428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2428 : oddCount 2428 13 = 7 ∧ acceleratedOrbit 13 2428 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2428) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2428.1, data_13_2428.2] + +/-- Complete interval computation for depth 13, residue 2429. -/ +theorem bounds_13_2429 : exactInterval 13 2429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2429 : oddCount 2429 13 = 7 ∧ acceleratedOrbit 13 2429 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2429) = 3 ^ 7 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2429.1, data_13_2429.2] + +/-- Complete interval computation for depth 13, residue 2430. -/ +theorem bounds_13_2430 : exactInterval 13 2430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2430 : oddCount 2430 13 = 8 ∧ acceleratedOrbit 13 2430 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2430) = 3 ^ 8 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2430.1, data_13_2430.2] + +/-- Complete interval computation for depth 13, residue 2431. -/ +theorem bounds_13_2431 : exactInterval 13 2431 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2431) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2431 : oddCount 2431 13 = 8 ∧ acceleratedOrbit 13 2431 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2431) = 3 ^ 8 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2431.1, data_13_2431.2] + +end Collatz.Research.StoppingAtlas.Batch0625 From eb293a84fe1b1681896f95b2bc56316b554593b1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:17 +0530 Subject: [PATCH 0626/1001] proof: certify atlas Batch0626 (13:2432 to 13:2446) --- Collatz/Research/StoppingAtlas/Batch0626.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0626.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0626.lean b/Collatz/Research/StoppingAtlas/Batch0626.lean new file mode 100644 index 00000000..8e3c9db1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0626.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0626 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2432. -/ +theorem bounds_13_2432 : exactInterval 13 2432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2432 : oddCount 2432 13 = 4 ∧ acceleratedOrbit 13 2432 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2432) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2432.1, data_13_2432.2] + +/-- Complete interval computation for depth 13, residue 2433. -/ +theorem bounds_13_2433 : exactInterval 13 2433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2433 : oddCount 2433 13 = 6 ∧ acceleratedOrbit 13 2433 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2433) = 3 ^ 6 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2433.1, data_13_2433.2] + +/-- Complete interval computation for depth 13, residue 2434. -/ +theorem bounds_13_2434 : exactInterval 13 2434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2434 : oddCount 2434 13 = 6 ∧ acceleratedOrbit 13 2434 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2434) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2434.1, data_13_2434.2] + +/-- Complete interval computation for depth 13, residue 2435. -/ +theorem bounds_13_2435 : exactInterval 13 2435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2435 : oddCount 2435 13 = 6 ∧ acceleratedOrbit 13 2435 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2435) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2435.1, data_13_2435.2] + +/-- Complete interval computation for depth 13, residue 2436. -/ +theorem bounds_13_2436 : exactInterval 13 2436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2436 : oddCount 2436 13 = 6 ∧ acceleratedOrbit 13 2436 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2436) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2436.1, data_13_2436.2] + +/-- Complete interval computation for depth 13, residue 2437. -/ +theorem bounds_13_2437 : exactInterval 13 2437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2437 : oddCount 2437 13 = 6 ∧ acceleratedOrbit 13 2437 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2437) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2437.1, data_13_2437.2] + +/-- Complete interval computation for depth 13, residue 2438. -/ +theorem bounds_13_2438 : exactInterval 13 2438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2438 : oddCount 2438 13 = 6 ∧ acceleratedOrbit 13 2438 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2438) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2438.1, data_13_2438.2] + +/-- Complete interval computation for depth 13, residue 2439. -/ +theorem bounds_13_2439 : exactInterval 13 2439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2439 : oddCount 2439 13 = 6 ∧ acceleratedOrbit 13 2439 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2439) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2439.1, data_13_2439.2] + +/-- Complete interval computation for depth 13, residue 2440. -/ +theorem bounds_13_2440 : exactInterval 13 2440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2440 : oddCount 2440 13 = 5 ∧ acceleratedOrbit 13 2440 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2440) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2440.1, data_13_2440.2] + +/-- Complete interval computation for depth 13, residue 2441. -/ +theorem bounds_13_2441 : exactInterval 13 2441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2441 : oddCount 2441 13 = 8 ∧ acceleratedOrbit 13 2441 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2441) = 3 ^ 8 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2441.1, data_13_2441.2] + +/-- Complete interval computation for depth 13, residue 2442. -/ +theorem bounds_13_2442 : exactInterval 13 2442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2442 : oddCount 2442 13 = 5 ∧ acceleratedOrbit 13 2442 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2442) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2442.1, data_13_2442.2] + +/-- Complete interval computation for depth 13, residue 2443. -/ +theorem bounds_13_2443 : exactInterval 13 2443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2443 : oddCount 2443 13 = 7 ∧ acceleratedOrbit 13 2443 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2443) = 3 ^ 7 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2443.1, data_13_2443.2] + +/-- Complete interval computation for depth 13, residue 2444. -/ +theorem bounds_13_2444 : exactInterval 13 2444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2444 : oddCount 2444 13 = 5 ∧ acceleratedOrbit 13 2444 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2444) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2444.1, data_13_2444.2] + +/-- Complete interval computation for depth 13, residue 2445. -/ +theorem bounds_13_2445 : exactInterval 13 2445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2445 : oddCount 2445 13 = 5 ∧ acceleratedOrbit 13 2445 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2445) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2445.1, data_13_2445.2] + +/-- Complete interval computation for depth 13, residue 2446. -/ +theorem bounds_13_2446 : exactInterval 13 2446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2446 : oddCount 2446 13 = 6 ∧ acceleratedOrbit 13 2446 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2446) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2446.1, data_13_2446.2] + +end Collatz.Research.StoppingAtlas.Batch0626 From 02112005ae84761889f9fe9559e06075dcee5ac8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:18 +0530 Subject: [PATCH 0627/1001] proof: certify atlas Batch0627 (13:2447 to 13:2461) --- Collatz/Research/StoppingAtlas/Batch0627.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0627.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0627.lean b/Collatz/Research/StoppingAtlas/Batch0627.lean new file mode 100644 index 00000000..7b7fce83 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0627.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0627 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2447. -/ +theorem bounds_13_2447 : exactInterval 13 2447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2447 : oddCount 2447 13 = 6 ∧ acceleratedOrbit 13 2447 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2447) = 3 ^ 6 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2447.1, data_13_2447.2] + +/-- Complete interval computation for depth 13, residue 2448. -/ +theorem bounds_13_2448 : exactInterval 13 2448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2448 : oddCount 2448 13 = 5 ∧ acceleratedOrbit 13 2448 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2448) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2448.1, data_13_2448.2] + +/-- Complete interval computation for depth 13, residue 2449. -/ +theorem bounds_13_2449 : exactInterval 13 2449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2449 : oddCount 2449 13 = 5 ∧ acceleratedOrbit 13 2449 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2449) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2449.1, data_13_2449.2] + +/-- Complete interval computation for depth 13, residue 2450. -/ +theorem bounds_13_2450 : exactInterval 13 2450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2450 : oddCount 2450 13 = 5 ∧ acceleratedOrbit 13 2450 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2450) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2450.1, data_13_2450.2] + +/-- Complete interval computation for depth 13, residue 2451. -/ +theorem bounds_13_2451 : exactInterval 13 2451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2451 : oddCount 2451 13 = 5 ∧ acceleratedOrbit 13 2451 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2451) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2451.1, data_13_2451.2] + +/-- Complete interval computation for depth 13, residue 2452. -/ +theorem bounds_13_2452 : exactInterval 13 2452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2452 : oddCount 2452 13 = 5 ∧ acceleratedOrbit 13 2452 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2452) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2452.1, data_13_2452.2] + +/-- Complete interval computation for depth 13, residue 2453. -/ +theorem bounds_13_2453 : exactInterval 13 2453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2453 : oddCount 2453 13 = 5 ∧ acceleratedOrbit 13 2453 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2453) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2453.1, data_13_2453.2] + +/-- Complete interval computation for depth 13, residue 2454. -/ +theorem bounds_13_2454 : exactInterval 13 2454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2454 : oddCount 2454 13 = 5 ∧ acceleratedOrbit 13 2454 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2454) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2454.1, data_13_2454.2] + +/-- Complete interval computation for depth 13, residue 2455. -/ +theorem bounds_13_2455 : exactInterval 13 2455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2455) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2455 : oddCount 2455 13 = 5 ∧ acceleratedOrbit 13 2455 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2455) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2455.1, data_13_2455.2] + +/-- Complete interval computation for depth 13, residue 2456. -/ +theorem bounds_13_2456 : exactInterval 13 2456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2456 : oddCount 2456 13 = 5 ∧ acceleratedOrbit 13 2456 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2456) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2456.1, data_13_2456.2] + +/-- Complete interval computation for depth 13, residue 2457. -/ +theorem bounds_13_2457 : exactInterval 13 2457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2457 : oddCount 2457 13 = 5 ∧ acceleratedOrbit 13 2457 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2457) = 3 ^ 5 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2457.1, data_13_2457.2] + +/-- Complete interval computation for depth 13, residue 2458. -/ +theorem bounds_13_2458 : exactInterval 13 2458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2458 : oddCount 2458 13 = 5 ∧ acceleratedOrbit 13 2458 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2458) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2458.1, data_13_2458.2] + +/-- Complete interval computation for depth 13, residue 2459. -/ +theorem bounds_13_2459 : exactInterval 13 2459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2459 : oddCount 2459 13 = 10 ∧ acceleratedOrbit 13 2459 = 17738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2459) = 3 ^ 10 * m + 17738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2459.1, data_13_2459.2] + +/-- Complete interval computation for depth 13, residue 2460. -/ +theorem bounds_13_2460 : exactInterval 13 2460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2460 : oddCount 2460 13 = 7 ∧ acceleratedOrbit 13 2460 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2460) = 3 ^ 7 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2460.1, data_13_2460.2] + +/-- Complete interval computation for depth 13, residue 2461. -/ +theorem bounds_13_2461 : exactInterval 13 2461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2461 : oddCount 2461 13 = 7 ∧ acceleratedOrbit 13 2461 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2461) = 3 ^ 7 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2461.1, data_13_2461.2] + +end Collatz.Research.StoppingAtlas.Batch0627 From 8365c33ba43996fcf8163384a3e01497f602cdeb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:18 +0530 Subject: [PATCH 0628/1001] proof: certify atlas Batch0628 (13:2462 to 13:2477) --- Collatz/Research/StoppingAtlas/Batch0628.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0628.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0628.lean b/Collatz/Research/StoppingAtlas/Batch0628.lean new file mode 100644 index 00000000..46b38dad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0628.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0628 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2462. -/ +theorem bounds_13_2462 : exactInterval 13 2462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2462 : oddCount 2462 13 = 7 ∧ acceleratedOrbit 13 2462 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2462) = 3 ^ 7 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2462.1, data_13_2462.2] + +/-- Complete interval computation for depth 13, residue 2463. -/ +theorem bounds_13_2463 : exactInterval 13 2463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2463 : oddCount 2463 13 = 9 ∧ acceleratedOrbit 13 2463 = 5921 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2463) = 3 ^ 9 * m + 5921 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2463.1, data_13_2463.2] + +/-- Complete interval computation for depth 13, residue 2464. -/ +theorem bounds_13_2464 : exactInterval 13 2464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2464 : oddCount 2464 13 = 4 ∧ acceleratedOrbit 13 2464 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2464) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2464.1, data_13_2464.2] + +/-- Complete interval computation for depth 13, residue 2465. -/ +theorem bounds_13_2465 : exactInterval 13 2465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2465 : oddCount 2465 13 = 7 ∧ acceleratedOrbit 13 2465 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2465) = 3 ^ 7 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2465.1, data_13_2465.2] + +/-- Complete interval computation for depth 13, residue 2466. -/ +theorem bounds_13_2466 : exactInterval 13 2466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2466 : oddCount 2466 13 = 7 ∧ acceleratedOrbit 13 2466 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2466) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2466.1, data_13_2466.2] + +/-- Complete interval computation for depth 13, residue 2467. -/ +theorem bounds_13_2467 : exactInterval 13 2467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2467 : oddCount 2467 13 = 7 ∧ acceleratedOrbit 13 2467 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2467) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2467.1, data_13_2467.2] + +/-- Complete interval computation for depth 13, residue 2468. -/ +theorem bounds_13_2468 : exactInterval 13 2468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2468 : oddCount 2468 13 = 7 ∧ acceleratedOrbit 13 2468 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2468) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2468.1, data_13_2468.2] + +/-- Complete interval computation for depth 13, residue 2469. -/ +theorem bounds_13_2469 : exactInterval 13 2469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2469 : oddCount 2469 13 = 7 ∧ acceleratedOrbit 13 2469 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2469) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2469.1, data_13_2469.2] + +/-- Complete interval computation for depth 13, residue 2470. -/ +theorem bounds_13_2470 : exactInterval 13 2470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2470 : oddCount 2470 13 = 7 ∧ acceleratedOrbit 13 2470 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2470) = 3 ^ 7 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2470.1, data_13_2470.2] + +/-- Complete interval computation for depth 13, residue 2471. -/ +theorem bounds_13_2471 : exactInterval 13 2471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2471 : oddCount 2471 13 = 6 ∧ acceleratedOrbit 13 2471 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2471) = 3 ^ 6 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2471.1, data_13_2471.2] + +/-- Complete interval computation for depth 13, residue 2472. -/ +theorem bounds_13_2472 : exactInterval 13 2472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2472 : oddCount 2472 13 = 4 ∧ acceleratedOrbit 13 2472 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2472) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2472.1, data_13_2472.2] + +/-- Complete interval computation for depth 13, residue 2473. -/ +theorem bounds_13_2473 : exactInterval 13 2473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2473 : oddCount 2473 13 = 8 ∧ acceleratedOrbit 13 2473 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2473) = 3 ^ 8 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2473.1, data_13_2473.2] + +/-- Complete interval computation for depth 13, residue 2474. -/ +theorem bounds_13_2474 : exactInterval 13 2474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2474 : oddCount 2474 13 = 4 ∧ acceleratedOrbit 13 2474 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2474) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2474.1, data_13_2474.2] + +/-- Complete interval computation for depth 13, residue 2475. -/ +theorem bounds_13_2475 : exactInterval 13 2475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2475 : oddCount 2475 13 = 9 ∧ acceleratedOrbit 13 2475 = 5953 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2475) = 3 ^ 9 * m + 5953 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2475.1, data_13_2475.2] + +/-- Complete interval computation for depth 13, residue 2476. -/ +theorem bounds_13_2476 : exactInterval 13 2476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2476 : oddCount 2476 13 = 6 ∧ acceleratedOrbit 13 2476 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2476) = 3 ^ 6 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2476.1, data_13_2476.2] + +/-- Complete interval computation for depth 13, residue 2477. -/ +theorem bounds_13_2477 : exactInterval 13 2477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2477 : oddCount 2477 13 = 6 ∧ acceleratedOrbit 13 2477 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2477) = 3 ^ 6 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2477.1, data_13_2477.2] + +end Collatz.Research.StoppingAtlas.Batch0628 From 1e1096bae6407084955df759072bec1096cca1e7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:22 +0530 Subject: [PATCH 0629/1001] proof: certify atlas Batch0629 (13:2478 to 13:2492) --- Collatz/Research/StoppingAtlas/Batch0629.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0629.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0629.lean b/Collatz/Research/StoppingAtlas/Batch0629.lean new file mode 100644 index 00000000..633903fd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0629.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0629 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2478. -/ +theorem bounds_13_2478 : exactInterval 13 2478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2478 : oddCount 2478 13 = 6 ∧ acceleratedOrbit 13 2478 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2478) = 3 ^ 6 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2478.1, data_13_2478.2] + +/-- Complete interval computation for depth 13, residue 2479. -/ +theorem bounds_13_2479 : exactInterval 13 2479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2479 : oddCount 2479 13 = 8 ∧ acceleratedOrbit 13 2479 = 1988 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2479) = 3 ^ 8 * m + 1988 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2479.1, data_13_2479.2] + +/-- Complete interval computation for depth 13, residue 2480. -/ +theorem bounds_13_2480 : exactInterval 13 2480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2480 : oddCount 2480 13 = 7 ∧ acceleratedOrbit 13 2480 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2480) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2480.1, data_13_2480.2] + +/-- Complete interval computation for depth 13, residue 2481. -/ +theorem bounds_13_2481 : exactInterval 13 2481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2481 : oddCount 2481 13 = 5 ∧ acceleratedOrbit 13 2481 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2481) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2481.1, data_13_2481.2] + +/-- Complete interval computation for depth 13, residue 2482. -/ +theorem bounds_13_2482 : exactInterval 13 2482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2482 : oddCount 2482 13 = 5 ∧ acceleratedOrbit 13 2482 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2482) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2482.1, data_13_2482.2] + +/-- Complete interval computation for depth 13, residue 2483. -/ +theorem bounds_13_2483 : exactInterval 13 2483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2483 : oddCount 2483 13 = 5 ∧ acceleratedOrbit 13 2483 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2483) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2483.1, data_13_2483.2] + +/-- Complete interval computation for depth 13, residue 2484. -/ +theorem bounds_13_2484 : exactInterval 13 2484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2484 : oddCount 2484 13 = 7 ∧ acceleratedOrbit 13 2484 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2484) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2484.1, data_13_2484.2] + +/-- Complete interval computation for depth 13, residue 2485. -/ +theorem bounds_13_2485 : exactInterval 13 2485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2485 : oddCount 2485 13 = 7 ∧ acceleratedOrbit 13 2485 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2485) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2485.1, data_13_2485.2] + +/-- Complete interval computation for depth 13, residue 2486. -/ +theorem bounds_13_2486 : exactInterval 13 2486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2486 : oddCount 2486 13 = 7 ∧ acceleratedOrbit 13 2486 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2486) = 3 ^ 7 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2486.1, data_13_2486.2] + +/-- Complete interval computation for depth 13, residue 2487. -/ +theorem bounds_13_2487 : exactInterval 13 2487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2487 : oddCount 2487 13 = 7 ∧ acceleratedOrbit 13 2487 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2487) = 3 ^ 7 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2487.1, data_13_2487.2] + +/-- Complete interval computation for depth 13, residue 2488. -/ +theorem bounds_13_2488 : exactInterval 13 2488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2488 : oddCount 2488 13 = 7 ∧ acceleratedOrbit 13 2488 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2488) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2488.1, data_13_2488.2] + +/-- Complete interval computation for depth 13, residue 2489. -/ +theorem bounds_13_2489 : exactInterval 13 2489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2489 : oddCount 2489 13 = 5 ∧ acceleratedOrbit 13 2489 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2489) = 3 ^ 5 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2489.1, data_13_2489.2] + +/-- Complete interval computation for depth 13, residue 2490. -/ +theorem bounds_13_2490 : exactInterval 13 2490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2490 : oddCount 2490 13 = 7 ∧ acceleratedOrbit 13 2490 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2490) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2490.1, data_13_2490.2] + +/-- Complete interval computation for depth 13, residue 2491. -/ +theorem bounds_13_2491 : exactInterval 13 2491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2491 : oddCount 2491 13 = 9 ∧ acceleratedOrbit 13 2491 = 5993 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2491) = 3 ^ 9 * m + 5993 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2491.1, data_13_2491.2] + +/-- Complete interval computation for depth 13, residue 2492. -/ +theorem bounds_13_2492 : exactInterval 13 2492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2492 : oddCount 2492 13 = 8 ∧ acceleratedOrbit 13 2492 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2492) = 3 ^ 8 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2492.1, data_13_2492.2] + +end Collatz.Research.StoppingAtlas.Batch0629 From e3645feca2155f7e91708132e814b852a36bcf77 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:22 +0530 Subject: [PATCH 0630/1001] proof: certify atlas Batch0630 (13:2493 to 13:2507) --- Collatz/Research/StoppingAtlas/Batch0630.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0630.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0630.lean b/Collatz/Research/StoppingAtlas/Batch0630.lean new file mode 100644 index 00000000..5d9160a8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0630.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0630 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2493. -/ +theorem bounds_13_2493 : exactInterval 13 2493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2493 : oddCount 2493 13 = 8 ∧ acceleratedOrbit 13 2493 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2493) = 3 ^ 8 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2493.1, data_13_2493.2] + +/-- Complete interval computation for depth 13, residue 2494. -/ +theorem bounds_13_2494 : exactInterval 13 2494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2494 : oddCount 2494 13 = 8 ∧ acceleratedOrbit 13 2494 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2494) = 3 ^ 8 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2494.1, data_13_2494.2] + +/-- Complete interval computation for depth 13, residue 2495. -/ +theorem bounds_13_2495 : exactInterval 13 2495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2495 : oddCount 2495 13 = 10 ∧ acceleratedOrbit 13 2495 = 17992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2495) = 3 ^ 10 * m + 17992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2495.1, data_13_2495.2] + +/-- Complete interval computation for depth 13, residue 2496. -/ +theorem bounds_13_2496 : exactInterval 13 2496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2496 : oddCount 2496 13 = 5 ∧ acceleratedOrbit 13 2496 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2496) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2496.1, data_13_2496.2] + +/-- Complete interval computation for depth 13, residue 2497. -/ +theorem bounds_13_2497 : exactInterval 13 2497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2497 : oddCount 2497 13 = 7 ∧ acceleratedOrbit 13 2497 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2497) = 3 ^ 7 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2497.1, data_13_2497.2] + +/-- Complete interval computation for depth 13, residue 2498. -/ +theorem bounds_13_2498 : exactInterval 13 2498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2498 : oddCount 2498 13 = 9 ∧ acceleratedOrbit 13 2498 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2498) = 3 ^ 9 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2498.1, data_13_2498.2] + +/-- Complete interval computation for depth 13, residue 2499. -/ +theorem bounds_13_2499 : exactInterval 13 2499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2499 : oddCount 2499 13 = 9 ∧ acceleratedOrbit 13 2499 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2499) = 3 ^ 9 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2499.1, data_13_2499.2] + +/-- Complete interval computation for depth 13, residue 2500. -/ +theorem bounds_13_2500 : exactInterval 13 2500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2500 : oddCount 2500 13 = 4 ∧ acceleratedOrbit 13 2500 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2500) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2500.1, data_13_2500.2] + +/-- Complete interval computation for depth 13, residue 2501. -/ +theorem bounds_13_2501 : exactInterval 13 2501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2501 : oddCount 2501 13 = 4 ∧ acceleratedOrbit 13 2501 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2501) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2501.1, data_13_2501.2] + +/-- Complete interval computation for depth 13, residue 2502. -/ +theorem bounds_13_2502 : exactInterval 13 2502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2502 : oddCount 2502 13 = 4 ∧ acceleratedOrbit 13 2502 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2502) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2502.1, data_13_2502.2] + +/-- Complete interval computation for depth 13, residue 2503. -/ +theorem bounds_13_2503 : exactInterval 13 2503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2503 : oddCount 2503 13 = 9 ∧ acceleratedOrbit 13 2503 = 6020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2503) = 3 ^ 9 * m + 6020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2503.1, data_13_2503.2] + +/-- Complete interval computation for depth 13, residue 2504. -/ +theorem bounds_13_2504 : exactInterval 13 2504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2504 : oddCount 2504 13 = 7 ∧ acceleratedOrbit 13 2504 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2504) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2504.1, data_13_2504.2] + +/-- Complete interval computation for depth 13, residue 2505. -/ +theorem bounds_13_2505 : exactInterval 13 2505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2505 : oddCount 2505 13 = 7 ∧ acceleratedOrbit 13 2505 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2505) = 3 ^ 7 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2505.1, data_13_2505.2] + +/-- Complete interval computation for depth 13, residue 2506. -/ +theorem bounds_13_2506 : exactInterval 13 2506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2506 : oddCount 2506 13 = 7 ∧ acceleratedOrbit 13 2506 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2506) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2506.1, data_13_2506.2] + +/-- Complete interval computation for depth 13, residue 2507. -/ +theorem bounds_13_2507 : exactInterval 13 2507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2507 : oddCount 2507 13 = 6 ∧ acceleratedOrbit 13 2507 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2507) = 3 ^ 6 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2507.1, data_13_2507.2] + +end Collatz.Research.StoppingAtlas.Batch0630 From 147bf1ffbdc176037447975f7e0d21c62f2e624c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:22 +0530 Subject: [PATCH 0631/1001] proof: certify atlas Batch0631 (13:2508 to 13:2523) --- Collatz/Research/StoppingAtlas/Batch0631.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0631.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0631.lean b/Collatz/Research/StoppingAtlas/Batch0631.lean new file mode 100644 index 00000000..14ad5fbd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0631.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0631 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2508. -/ +theorem bounds_13_2508 : exactInterval 13 2508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2508 : oddCount 2508 13 = 7 ∧ acceleratedOrbit 13 2508 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2508) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2508.1, data_13_2508.2] + +/-- Complete interval computation for depth 13, residue 2509. -/ +theorem bounds_13_2509 : exactInterval 13 2509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2509 : oddCount 2509 13 = 7 ∧ acceleratedOrbit 13 2509 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2509) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2509.1, data_13_2509.2] + +/-- Complete interval computation for depth 13, residue 2510. -/ +theorem bounds_13_2510 : exactInterval 13 2510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2510 : oddCount 2510 13 = 9 ∧ acceleratedOrbit 13 2510 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2510) = 3 ^ 9 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2510.1, data_13_2510.2] + +/-- Complete interval computation for depth 13, residue 2511. -/ +theorem bounds_13_2511 : exactInterval 13 2511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2511 : oddCount 2511 13 = 9 ∧ acceleratedOrbit 13 2511 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2511) = 3 ^ 9 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2511.1, data_13_2511.2] + +/-- Complete interval computation for depth 13, residue 2512. -/ +theorem bounds_13_2512 : exactInterval 13 2512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2512 : oddCount 2512 13 = 5 ∧ acceleratedOrbit 13 2512 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2512) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2512.1, data_13_2512.2] + +/-- Complete interval computation for depth 13, residue 2513. -/ +theorem bounds_13_2513 : exactInterval 13 2513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2513 : oddCount 2513 13 = 7 ∧ acceleratedOrbit 13 2513 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2513) = 3 ^ 7 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2513.1, data_13_2513.2] + +/-- Complete interval computation for depth 13, residue 2514. -/ +theorem bounds_13_2514 : exactInterval 13 2514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2514 : oddCount 2514 13 = 6 ∧ acceleratedOrbit 13 2514 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2514) = 3 ^ 6 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2514.1, data_13_2514.2] + +/-- Complete interval computation for depth 13, residue 2515. -/ +theorem bounds_13_2515 : exactInterval 13 2515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2515 : oddCount 2515 13 = 6 ∧ acceleratedOrbit 13 2515 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2515) = 3 ^ 6 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2515.1, data_13_2515.2] + +/-- Complete interval computation for depth 13, residue 2516. -/ +theorem bounds_13_2516 : exactInterval 13 2516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2516 : oddCount 2516 13 = 5 ∧ acceleratedOrbit 13 2516 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2516) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2516.1, data_13_2516.2] + +/-- Complete interval computation for depth 13, residue 2517. -/ +theorem bounds_13_2517 : exactInterval 13 2517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2517 : oddCount 2517 13 = 5 ∧ acceleratedOrbit 13 2517 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2517) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2517.1, data_13_2517.2] + +/-- Complete interval computation for depth 13, residue 2518. -/ +theorem bounds_13_2518 : exactInterval 13 2518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2518 : oddCount 2518 13 = 8 ∧ acceleratedOrbit 13 2518 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2518) = 3 ^ 8 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2518.1, data_13_2518.2] + +/-- Complete interval computation for depth 13, residue 2519. -/ +theorem bounds_13_2519 : exactInterval 13 2519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2519 : oddCount 2519 13 = 8 ∧ acceleratedOrbit 13 2519 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2519) = 3 ^ 8 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2519.1, data_13_2519.2] + +/-- Complete interval computation for depth 13, residue 2520. -/ +theorem bounds_13_2520 : exactInterval 13 2520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2520 : oddCount 2520 13 = 4 ∧ acceleratedOrbit 13 2520 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2520) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2520.1, data_13_2520.2] + +/-- Complete interval computation for depth 13, residue 2521. -/ +theorem bounds_13_2521 : exactInterval 13 2521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2521 : oddCount 2521 13 = 4 ∧ acceleratedOrbit 13 2521 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2521) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2521.1, data_13_2521.2] + +/-- Complete interval computation for depth 13, residue 2522. -/ +theorem bounds_13_2522 : exactInterval 13 2522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2522 : oddCount 2522 13 = 4 ∧ acceleratedOrbit 13 2522 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2522) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2522.1, data_13_2522.2] + +/-- Complete interval computation for depth 13, residue 2523. -/ +theorem bounds_13_2523 : exactInterval 13 2523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2523 : oddCount 2523 13 = 8 ∧ acceleratedOrbit 13 2523 = 2024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2523) = 3 ^ 8 * m + 2024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2523.1, data_13_2523.2] + +end Collatz.Research.StoppingAtlas.Batch0631 From 86af91010027ffc556e0bd42c69df5c84a925314 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:23 +0530 Subject: [PATCH 0632/1001] proof: certify atlas Batch0632 (13:2524 to 13:2538) --- Collatz/Research/StoppingAtlas/Batch0632.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0632.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0632.lean b/Collatz/Research/StoppingAtlas/Batch0632.lean new file mode 100644 index 00000000..288ef1cd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0632.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0632 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2524. -/ +theorem bounds_13_2524 : exactInterval 13 2524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2524 : oddCount 2524 13 = 4 ∧ acceleratedOrbit 13 2524 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2524) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2524.1, data_13_2524.2] + +/-- Complete interval computation for depth 13, residue 2525. -/ +theorem bounds_13_2525 : exactInterval 13 2525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2525 : oddCount 2525 13 = 4 ∧ acceleratedOrbit 13 2525 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2525) = 3 ^ 4 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2525.1, data_13_2525.2] + +/-- Complete interval computation for depth 13, residue 2526. -/ +theorem bounds_13_2526 : exactInterval 13 2526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2526 : oddCount 2526 13 = 11 ∧ acceleratedOrbit 13 2526 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2526) = 3 ^ 11 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2526.1, data_13_2526.2] + +/-- Complete interval computation for depth 13, residue 2527. -/ +theorem bounds_13_2527 : exactInterval 13 2527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2527 : oddCount 2527 13 = 11 ∧ acceleratedOrbit 13 2527 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2527) = 3 ^ 11 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2527.1, data_13_2527.2] + +/-- Complete interval computation for depth 13, residue 2528. -/ +theorem bounds_13_2528 : exactInterval 13 2528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2528 : oddCount 2528 13 = 5 ∧ acceleratedOrbit 13 2528 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2528) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2528.1, data_13_2528.2] + +/-- Complete interval computation for depth 13, residue 2529. -/ +theorem bounds_13_2529 : exactInterval 13 2529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2529 : oddCount 2529 13 = 7 ∧ acceleratedOrbit 13 2529 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2529) = 3 ^ 7 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2529.1, data_13_2529.2] + +/-- Complete interval computation for depth 13, residue 2530. -/ +theorem bounds_13_2530 : exactInterval 13 2530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2530 : oddCount 2530 13 = 5 ∧ acceleratedOrbit 13 2530 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2530) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2530.1, data_13_2530.2] + +/-- Complete interval computation for depth 13, residue 2531. -/ +theorem bounds_13_2531 : exactInterval 13 2531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2531 : oddCount 2531 13 = 5 ∧ acceleratedOrbit 13 2531 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2531) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2531.1, data_13_2531.2] + +/-- Complete interval computation for depth 13, residue 2532. -/ +theorem bounds_13_2532 : exactInterval 13 2532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2532 : oddCount 2532 13 = 6 ∧ acceleratedOrbit 13 2532 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2532) = 3 ^ 6 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2532.1, data_13_2532.2] + +/-- Complete interval computation for depth 13, residue 2533. -/ +theorem bounds_13_2533 : exactInterval 13 2533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2533 : oddCount 2533 13 = 6 ∧ acceleratedOrbit 13 2533 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2533) = 3 ^ 6 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2533.1, data_13_2533.2] + +/-- Complete interval computation for depth 13, residue 2534. -/ +theorem bounds_13_2534 : exactInterval 13 2534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2534 : oddCount 2534 13 = 6 ∧ acceleratedOrbit 13 2534 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2534) = 3 ^ 6 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2534.1, data_13_2534.2] + +/-- Complete interval computation for depth 13, residue 2535. -/ +theorem bounds_13_2535 : exactInterval 13 2535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2535 : oddCount 2535 13 = 9 ∧ acceleratedOrbit 13 2535 = 6095 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2535) = 3 ^ 9 * m + 6095 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2535.1, data_13_2535.2] + +/-- Complete interval computation for depth 13, residue 2536. -/ +theorem bounds_13_2536 : exactInterval 13 2536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2536 : oddCount 2536 13 = 5 ∧ acceleratedOrbit 13 2536 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2536) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2536.1, data_13_2536.2] + +/-- Complete interval computation for depth 13, residue 2537. -/ +theorem bounds_13_2537 : exactInterval 13 2537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2537 : oddCount 2537 13 = 9 ∧ acceleratedOrbit 13 2537 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2537) = 3 ^ 9 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2537.1, data_13_2537.2] + +/-- Complete interval computation for depth 13, residue 2538. -/ +theorem bounds_13_2538 : exactInterval 13 2538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2538 : oddCount 2538 13 = 5 ∧ acceleratedOrbit 13 2538 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2538) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2538.1, data_13_2538.2] + +end Collatz.Research.StoppingAtlas.Batch0632 From ef49135624c85f2e82a142085e83732ab15d515d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:27 +0530 Subject: [PATCH 0633/1001] proof: certify atlas Batch0633 (13:2539 to 13:2553) --- Collatz/Research/StoppingAtlas/Batch0633.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0633.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0633.lean b/Collatz/Research/StoppingAtlas/Batch0633.lean new file mode 100644 index 00000000..1f7cd8fb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0633.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0633 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2539. -/ +theorem bounds_13_2539 : exactInterval 13 2539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2539 : oddCount 2539 13 = 8 ∧ acceleratedOrbit 13 2539 = 2035 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2539) = 3 ^ 8 * m + 2035 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2539.1, data_13_2539.2] + +/-- Complete interval computation for depth 13, residue 2540. -/ +theorem bounds_13_2540 : exactInterval 13 2540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2540 : oddCount 2540 13 = 6 ∧ acceleratedOrbit 13 2540 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2540) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2540.1, data_13_2540.2] + +/-- Complete interval computation for depth 13, residue 2541. -/ +theorem bounds_13_2541 : exactInterval 13 2541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2541 : oddCount 2541 13 = 6 ∧ acceleratedOrbit 13 2541 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2541) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2541.1, data_13_2541.2] + +/-- Complete interval computation for depth 13, residue 2542. -/ +theorem bounds_13_2542 : exactInterval 13 2542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2542 : oddCount 2542 13 = 6 ∧ acceleratedOrbit 13 2542 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2542) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2542.1, data_13_2542.2] + +/-- Complete interval computation for depth 13, residue 2543. -/ +theorem bounds_13_2543 : exactInterval 13 2543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2543 : oddCount 2543 13 = 9 ∧ acceleratedOrbit 13 2543 = 6113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2543) = 3 ^ 9 * m + 6113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2543.1, data_13_2543.2] + +/-- Complete interval computation for depth 13, residue 2544. -/ +theorem bounds_13_2544 : exactInterval 13 2544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2544 : oddCount 2544 13 = 8 ∧ acceleratedOrbit 13 2544 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2544) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2544.1, data_13_2544.2] + +/-- Complete interval computation for depth 13, residue 2545. -/ +theorem bounds_13_2545 : exactInterval 13 2545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2545 : oddCount 2545 13 = 5 ∧ acceleratedOrbit 13 2545 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2545) = 3 ^ 5 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2545.1, data_13_2545.2] + +/-- Complete interval computation for depth 13, residue 2546. -/ +theorem bounds_13_2546 : exactInterval 13 2546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2546 : oddCount 2546 13 = 6 ∧ acceleratedOrbit 13 2546 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2546) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2546.1, data_13_2546.2] + +/-- Complete interval computation for depth 13, residue 2547. -/ +theorem bounds_13_2547 : exactInterval 13 2547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2547 : oddCount 2547 13 = 6 ∧ acceleratedOrbit 13 2547 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2547) = 3 ^ 6 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2547.1, data_13_2547.2] + +/-- Complete interval computation for depth 13, residue 2548. -/ +theorem bounds_13_2548 : exactInterval 13 2548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2548 : oddCount 2548 13 = 8 ∧ acceleratedOrbit 13 2548 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2548) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2548.1, data_13_2548.2] + +/-- Complete interval computation for depth 13, residue 2549. -/ +theorem bounds_13_2549 : exactInterval 13 2549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2549 : oddCount 2549 13 = 8 ∧ acceleratedOrbit 13 2549 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2549) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2549.1, data_13_2549.2] + +/-- Complete interval computation for depth 13, residue 2550. -/ +theorem bounds_13_2550 : exactInterval 13 2550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2550 : oddCount 2550 13 = 8 ∧ acceleratedOrbit 13 2550 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2550) = 3 ^ 8 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2550.1, data_13_2550.2] + +/-- Complete interval computation for depth 13, residue 2551. -/ +theorem bounds_13_2551 : exactInterval 13 2551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2551 : oddCount 2551 13 = 8 ∧ acceleratedOrbit 13 2551 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2551) = 3 ^ 8 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2551.1, data_13_2551.2] + +/-- Complete interval computation for depth 13, residue 2552. -/ +theorem bounds_13_2552 : exactInterval 13 2552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2552 : oddCount 2552 13 = 8 ∧ acceleratedOrbit 13 2552 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2552) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2552.1, data_13_2552.2] + +/-- Complete interval computation for depth 13, residue 2553. -/ +theorem bounds_13_2553 : exactInterval 13 2553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2553 : oddCount 2553 13 = 8 ∧ acceleratedOrbit 13 2553 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2553) = 3 ^ 8 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2553.1, data_13_2553.2] + +end Collatz.Research.StoppingAtlas.Batch0633 From ffed6ec42537bbe795b3f0d5fafb95cb232fa5e0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:27 +0530 Subject: [PATCH 0634/1001] proof: certify atlas Batch0634 (13:2554 to 13:2569) --- Collatz/Research/StoppingAtlas/Batch0634.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0634.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0634.lean b/Collatz/Research/StoppingAtlas/Batch0634.lean new file mode 100644 index 00000000..70103750 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0634.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0634 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2554. -/ +theorem bounds_13_2554 : exactInterval 13 2554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2554 : oddCount 2554 13 = 8 ∧ acceleratedOrbit 13 2554 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2554) = 3 ^ 8 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2554.1, data_13_2554.2] + +/-- Complete interval computation for depth 13, residue 2555. -/ +theorem bounds_13_2555 : exactInterval 13 2555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2555 : oddCount 2555 13 = 7 ∧ acceleratedOrbit 13 2555 = 683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2555) = 3 ^ 7 * m + 683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2555.1, data_13_2555.2] + +/-- Complete interval computation for depth 13, residue 2556. -/ +theorem bounds_13_2556 : exactInterval 13 2556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2556 : oddCount 2556 13 = 9 ∧ acceleratedOrbit 13 2556 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2556) = 3 ^ 9 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2556.1, data_13_2556.2] + +/-- Complete interval computation for depth 13, residue 2557. -/ +theorem bounds_13_2557 : exactInterval 13 2557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2557 : oddCount 2557 13 = 9 ∧ acceleratedOrbit 13 2557 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2557) = 3 ^ 9 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2557.1, data_13_2557.2] + +/-- Complete interval computation for depth 13, residue 2558. -/ +theorem bounds_13_2558 : exactInterval 13 2558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2558 : oddCount 2558 13 = 9 ∧ acceleratedOrbit 13 2558 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2558) = 3 ^ 9 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2558.1, data_13_2558.2] + +/-- Complete interval computation for depth 13, residue 2559. -/ +theorem bounds_13_2559 : exactInterval 13 2559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2559 : oddCount 2559 13 = 12 ∧ acceleratedOrbit 13 2559 = 166076 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2559) = 3 ^ 12 * m + 166076 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2559.1, data_13_2559.2] + +/-- Complete interval computation for depth 13, residue 2560. -/ +theorem bounds_13_2560 : exactInterval 13 2560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2560 : oddCount 2560 13 = 1 ∧ acceleratedOrbit 13 2560 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2560) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2560.1, data_13_2560.2] + +/-- Complete interval computation for depth 13, residue 2561. -/ +theorem bounds_13_2561 : exactInterval 13 2561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2561 : oddCount 2561 13 = 7 ∧ acceleratedOrbit 13 2561 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2561) = 3 ^ 7 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2561.1, data_13_2561.2] + +/-- Complete interval computation for depth 13, residue 2562. -/ +theorem bounds_13_2562 : exactInterval 13 2562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2562 : oddCount 2562 13 = 6 ∧ acceleratedOrbit 13 2562 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2562) = 3 ^ 6 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2562.1, data_13_2562.2] + +/-- Complete interval computation for depth 13, residue 2563. -/ +theorem bounds_13_2563 : exactInterval 13 2563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2563 : oddCount 2563 13 = 6 ∧ acceleratedOrbit 13 2563 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2563) = 3 ^ 6 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2563.1, data_13_2563.2] + +/-- Complete interval computation for depth 13, residue 2564. -/ +theorem bounds_13_2564 : exactInterval 13 2564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2564 : oddCount 2564 13 = 7 ∧ acceleratedOrbit 13 2564 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2564) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2564.1, data_13_2564.2] + +/-- Complete interval computation for depth 13, residue 2565. -/ +theorem bounds_13_2565 : exactInterval 13 2565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2565 : oddCount 2565 13 = 7 ∧ acceleratedOrbit 13 2565 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2565) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2565.1, data_13_2565.2] + +/-- Complete interval computation for depth 13, residue 2566. -/ +theorem bounds_13_2566 : exactInterval 13 2566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2566 : oddCount 2566 13 = 7 ∧ acceleratedOrbit 13 2566 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2566) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2566.1, data_13_2566.2] + +/-- Complete interval computation for depth 13, residue 2567. -/ +theorem bounds_13_2567 : exactInterval 13 2567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2567 : oddCount 2567 13 = 7 ∧ acceleratedOrbit 13 2567 = 686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2567) = 3 ^ 7 * m + 686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2567.1, data_13_2567.2] + +/-- Complete interval computation for depth 13, residue 2568. -/ +theorem bounds_13_2568 : exactInterval 13 2568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2568 : oddCount 2568 13 = 4 ∧ acceleratedOrbit 13 2568 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2568) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2568.1, data_13_2568.2] + +/-- Complete interval computation for depth 13, residue 2569. -/ +theorem bounds_13_2569 : exactInterval 13 2569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2569 : oddCount 2569 13 = 6 ∧ acceleratedOrbit 13 2569 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2569) = 3 ^ 6 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2569.1, data_13_2569.2] + +end Collatz.Research.StoppingAtlas.Batch0634 From b1ef21029c45d357483edcb01e331b247de424a9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:29 +0530 Subject: [PATCH 0635/1001] proof: certify atlas Batch0635 (13:2570 to 13:2584) --- Collatz/Research/StoppingAtlas/Batch0635.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0635.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0635.lean b/Collatz/Research/StoppingAtlas/Batch0635.lean new file mode 100644 index 00000000..5a011fc0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0635.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0635 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2570. -/ +theorem bounds_13_2570 : exactInterval 13 2570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2570 : oddCount 2570 13 = 4 ∧ acceleratedOrbit 13 2570 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2570) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2570.1, data_13_2570.2] + +/-- Complete interval computation for depth 13, residue 2571. -/ +theorem bounds_13_2571 : exactInterval 13 2571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2571 : oddCount 2571 13 = 7 ∧ acceleratedOrbit 13 2571 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2571) = 3 ^ 7 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2571.1, data_13_2571.2] + +/-- Complete interval computation for depth 13, residue 2572. -/ +theorem bounds_13_2572 : exactInterval 13 2572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2572 : oddCount 2572 13 = 4 ∧ acceleratedOrbit 13 2572 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2572) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2572.1, data_13_2572.2] + +/-- Complete interval computation for depth 13, residue 2573. -/ +theorem bounds_13_2573 : exactInterval 13 2573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2573 : oddCount 2573 13 = 4 ∧ acceleratedOrbit 13 2573 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2573) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2573.1, data_13_2573.2] + +/-- Complete interval computation for depth 13, residue 2574. -/ +theorem bounds_13_2574 : exactInterval 13 2574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2574 : oddCount 2574 13 = 8 ∧ acceleratedOrbit 13 2574 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2574) = 3 ^ 8 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2574.1, data_13_2574.2] + +/-- Complete interval computation for depth 13, residue 2575. -/ +theorem bounds_13_2575 : exactInterval 13 2575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2575 : oddCount 2575 13 = 8 ∧ acceleratedOrbit 13 2575 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2575) = 3 ^ 8 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2575.1, data_13_2575.2] + +/-- Complete interval computation for depth 13, residue 2576. -/ +theorem bounds_13_2576 : exactInterval 13 2576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2576 : oddCount 2576 13 = 6 ∧ acceleratedOrbit 13 2576 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2576) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2576.1, data_13_2576.2] + +/-- Complete interval computation for depth 13, residue 2577. -/ +theorem bounds_13_2577 : exactInterval 13 2577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2577 : oddCount 2577 13 = 4 ∧ acceleratedOrbit 13 2577 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2577) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2577.1, data_13_2577.2] + +/-- Complete interval computation for depth 13, residue 2578. -/ +theorem bounds_13_2578 : exactInterval 13 2578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2578 : oddCount 2578 13 = 8 ∧ acceleratedOrbit 13 2578 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2578) = 3 ^ 8 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2578.1, data_13_2578.2] + +/-- Complete interval computation for depth 13, residue 2579. -/ +theorem bounds_13_2579 : exactInterval 13 2579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2579 : oddCount 2579 13 = 8 ∧ acceleratedOrbit 13 2579 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2579) = 3 ^ 8 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2579.1, data_13_2579.2] + +/-- Complete interval computation for depth 13, residue 2580. -/ +theorem bounds_13_2580 : exactInterval 13 2580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2580 : oddCount 2580 13 = 6 ∧ acceleratedOrbit 13 2580 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2580) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2580.1, data_13_2580.2] + +/-- Complete interval computation for depth 13, residue 2581. -/ +theorem bounds_13_2581 : exactInterval 13 2581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2581 : oddCount 2581 13 = 6 ∧ acceleratedOrbit 13 2581 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2581) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2581.1, data_13_2581.2] + +/-- Complete interval computation for depth 13, residue 2582. -/ +theorem bounds_13_2582 : exactInterval 13 2582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2582 : oddCount 2582 13 = 7 ∧ acceleratedOrbit 13 2582 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2582) = 3 ^ 7 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2582.1, data_13_2582.2] + +/-- Complete interval computation for depth 13, residue 2583. -/ +theorem bounds_13_2583 : exactInterval 13 2583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2583 : oddCount 2583 13 = 7 ∧ acceleratedOrbit 13 2583 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2583) = 3 ^ 7 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2583.1, data_13_2583.2] + +/-- Complete interval computation for depth 13, residue 2584. -/ +theorem bounds_13_2584 : exactInterval 13 2584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2584 : oddCount 2584 13 = 6 ∧ acceleratedOrbit 13 2584 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2584) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2584.1, data_13_2584.2] + +end Collatz.Research.StoppingAtlas.Batch0635 From ef28dd165650c936a6d75c983dfa8edf0c6f577a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:29 +0530 Subject: [PATCH 0636/1001] proof: certify atlas Batch0636 (13:2585 to 13:2599) --- Collatz/Research/StoppingAtlas/Batch0636.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0636.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0636.lean b/Collatz/Research/StoppingAtlas/Batch0636.lean new file mode 100644 index 00000000..0b46d228 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0636.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0636 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2585. -/ +theorem bounds_13_2585 : exactInterval 13 2585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2585 : oddCount 2585 13 = 7 ∧ acceleratedOrbit 13 2585 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2585) = 3 ^ 7 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2585.1, data_13_2585.2] + +/-- Complete interval computation for depth 13, residue 2586. -/ +theorem bounds_13_2586 : exactInterval 13 2586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2586 : oddCount 2586 13 = 6 ∧ acceleratedOrbit 13 2586 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2586) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2586.1, data_13_2586.2] + +/-- Complete interval computation for depth 13, residue 2587. -/ +theorem bounds_13_2587 : exactInterval 13 2587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2587 : oddCount 2587 13 = 7 ∧ acceleratedOrbit 13 2587 = 691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2587) = 3 ^ 7 * m + 691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2587.1, data_13_2587.2] + +/-- Complete interval computation for depth 13, residue 2588. -/ +theorem bounds_13_2588 : exactInterval 13 2588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2588 : oddCount 2588 13 = 5 ∧ acceleratedOrbit 13 2588 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2588) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2588.1, data_13_2588.2] + +/-- Complete interval computation for depth 13, residue 2589. -/ +theorem bounds_13_2589 : exactInterval 13 2589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2589 : oddCount 2589 13 = 5 ∧ acceleratedOrbit 13 2589 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2589) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2589.1, data_13_2589.2] + +/-- Complete interval computation for depth 13, residue 2590. -/ +theorem bounds_13_2590 : exactInterval 13 2590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2590 : oddCount 2590 13 = 5 ∧ acceleratedOrbit 13 2590 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2590) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2590.1, data_13_2590.2] + +/-- Complete interval computation for depth 13, residue 2591. -/ +theorem bounds_13_2591 : exactInterval 13 2591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2591 : oddCount 2591 13 = 7 ∧ acceleratedOrbit 13 2591 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2591) = 3 ^ 7 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2591.1, data_13_2591.2] + +/-- Complete interval computation for depth 13, residue 2592. -/ +theorem bounds_13_2592 : exactInterval 13 2592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2592 : oddCount 2592 13 = 5 ∧ acceleratedOrbit 13 2592 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2592) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2592.1, data_13_2592.2] + +/-- Complete interval computation for depth 13, residue 2593. -/ +theorem bounds_13_2593 : exactInterval 13 2593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2593 : oddCount 2593 13 = 5 ∧ acceleratedOrbit 13 2593 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2593) = 3 ^ 5 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2593.1, data_13_2593.2] + +/-- Complete interval computation for depth 13, residue 2594. -/ +theorem bounds_13_2594 : exactInterval 13 2594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2594 : oddCount 2594 13 = 6 ∧ acceleratedOrbit 13 2594 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2594) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2594.1, data_13_2594.2] + +/-- Complete interval computation for depth 13, residue 2595. -/ +theorem bounds_13_2595 : exactInterval 13 2595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2595 : oddCount 2595 13 = 6 ∧ acceleratedOrbit 13 2595 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2595) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2595.1, data_13_2595.2] + +/-- Complete interval computation for depth 13, residue 2596. -/ +theorem bounds_13_2596 : exactInterval 13 2596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2596 : oddCount 2596 13 = 7 ∧ acceleratedOrbit 13 2596 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2596) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2596.1, data_13_2596.2] + +/-- Complete interval computation for depth 13, residue 2597. -/ +theorem bounds_13_2597 : exactInterval 13 2597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2597 : oddCount 2597 13 = 7 ∧ acceleratedOrbit 13 2597 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2597) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2597.1, data_13_2597.2] + +/-- Complete interval computation for depth 13, residue 2598. -/ +theorem bounds_13_2598 : exactInterval 13 2598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2598 : oddCount 2598 13 = 7 ∧ acceleratedOrbit 13 2598 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2598) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2598.1, data_13_2598.2] + +/-- Complete interval computation for depth 13, residue 2599. -/ +theorem bounds_13_2599 : exactInterval 13 2599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2599 : oddCount 2599 13 = 7 ∧ acceleratedOrbit 13 2599 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2599) = 3 ^ 7 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2599.1, data_13_2599.2] + +end Collatz.Research.StoppingAtlas.Batch0636 From 8d3b7e64f7426fa1a61cd5a0d0f8724f5a5fc528 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:32 +0530 Subject: [PATCH 0637/1001] proof: certify atlas Batch0637 (13:2600 to 13:2615) --- Collatz/Research/StoppingAtlas/Batch0637.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0637.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0637.lean b/Collatz/Research/StoppingAtlas/Batch0637.lean new file mode 100644 index 00000000..c7e89f57 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0637.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0637 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2600. -/ +theorem bounds_13_2600 : exactInterval 13 2600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2600 : oddCount 2600 13 = 5 ∧ acceleratedOrbit 13 2600 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2600) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2600.1, data_13_2600.2] + +/-- Complete interval computation for depth 13, residue 2601. -/ +theorem bounds_13_2601 : exactInterval 13 2601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2601 : oddCount 2601 13 = 9 ∧ acceleratedOrbit 13 2601 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2601) = 3 ^ 9 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2601.1, data_13_2601.2] + +/-- Complete interval computation for depth 13, residue 2602. -/ +theorem bounds_13_2602 : exactInterval 13 2602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2602 : oddCount 2602 13 = 5 ∧ acceleratedOrbit 13 2602 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2602) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2602.1, data_13_2602.2] + +/-- Complete interval computation for depth 13, residue 2603. -/ +theorem bounds_13_2603 : exactInterval 13 2603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2603 : oddCount 2603 13 = 6 ∧ acceleratedOrbit 13 2603 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2603) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2603.1, data_13_2603.2] + +/-- Complete interval computation for depth 13, residue 2604. -/ +theorem bounds_13_2604 : exactInterval 13 2604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2604 : oddCount 2604 13 = 6 ∧ acceleratedOrbit 13 2604 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2604) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2604.1, data_13_2604.2] + +/-- Complete interval computation for depth 13, residue 2605. -/ +theorem bounds_13_2605 : exactInterval 13 2605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2605 : oddCount 2605 13 = 6 ∧ acceleratedOrbit 13 2605 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2605) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2605.1, data_13_2605.2] + +/-- Complete interval computation for depth 13, residue 2606. -/ +theorem bounds_13_2606 : exactInterval 13 2606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2606 : oddCount 2606 13 = 6 ∧ acceleratedOrbit 13 2606 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2606) = 3 ^ 6 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2606.1, data_13_2606.2] + +/-- Complete interval computation for depth 13, residue 2607. -/ +theorem bounds_13_2607 : exactInterval 13 2607 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2607) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2607 : oddCount 2607 13 = 8 ∧ acceleratedOrbit 13 2607 = 2089 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2607) = 3 ^ 8 * m + 2089 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2607.1, data_13_2607.2] + +/-- Complete interval computation for depth 13, residue 2608. -/ +theorem bounds_13_2608 : exactInterval 13 2608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2608 : oddCount 2608 13 = 5 ∧ acceleratedOrbit 13 2608 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2608) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2608.1, data_13_2608.2] + +/-- Complete interval computation for depth 13, residue 2609. -/ +theorem bounds_13_2609 : exactInterval 13 2609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2609 : oddCount 2609 13 = 8 ∧ acceleratedOrbit 13 2609 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2609) = 3 ^ 8 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2609.1, data_13_2609.2] + +/-- Complete interval computation for depth 13, residue 2610. -/ +theorem bounds_13_2610 : exactInterval 13 2610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2610 : oddCount 2610 13 = 8 ∧ acceleratedOrbit 13 2610 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2610) = 3 ^ 8 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2610.1, data_13_2610.2] + +/-- Complete interval computation for depth 13, residue 2611. -/ +theorem bounds_13_2611 : exactInterval 13 2611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2611 : oddCount 2611 13 = 8 ∧ acceleratedOrbit 13 2611 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2611) = 3 ^ 8 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2611.1, data_13_2611.2] + +/-- Complete interval computation for depth 13, residue 2612. -/ +theorem bounds_13_2612 : exactInterval 13 2612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2612 : oddCount 2612 13 = 5 ∧ acceleratedOrbit 13 2612 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2612) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2612.1, data_13_2612.2] + +/-- Complete interval computation for depth 13, residue 2613. -/ +theorem bounds_13_2613 : exactInterval 13 2613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2613 : oddCount 2613 13 = 5 ∧ acceleratedOrbit 13 2613 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2613) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2613.1, data_13_2613.2] + +/-- Complete interval computation for depth 13, residue 2614. -/ +theorem bounds_13_2614 : exactInterval 13 2614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2614 : oddCount 2614 13 = 10 ∧ acceleratedOrbit 13 2614 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2614) = 3 ^ 10 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2614.1, data_13_2614.2] + +/-- Complete interval computation for depth 13, residue 2615. -/ +theorem bounds_13_2615 : exactInterval 13 2615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2615 : oddCount 2615 13 = 10 ∧ acceleratedOrbit 13 2615 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2615) = 3 ^ 10 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2615.1, data_13_2615.2] + +end Collatz.Research.StoppingAtlas.Batch0637 From 937fa34b79a0694fb7922f83835b51db71076153 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:33 +0530 Subject: [PATCH 0638/1001] proof: certify atlas Batch0638 (13:2616 to 13:2630) --- Collatz/Research/StoppingAtlas/Batch0638.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0638.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0638.lean b/Collatz/Research/StoppingAtlas/Batch0638.lean new file mode 100644 index 00000000..8b35acb3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0638.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0638 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2616. -/ +theorem bounds_13_2616 : exactInterval 13 2616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2616 : oddCount 2616 13 = 8 ∧ acceleratedOrbit 13 2616 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2616) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2616.1, data_13_2616.2] + +/-- Complete interval computation for depth 13, residue 2617. -/ +theorem bounds_13_2617 : exactInterval 13 2617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2617 : oddCount 2617 13 = 8 ∧ acceleratedOrbit 13 2617 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2617) = 3 ^ 8 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2617.1, data_13_2617.2] + +/-- Complete interval computation for depth 13, residue 2618. -/ +theorem bounds_13_2618 : exactInterval 13 2618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2618 : oddCount 2618 13 = 8 ∧ acceleratedOrbit 13 2618 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2618) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2618.1, data_13_2618.2] + +/-- Complete interval computation for depth 13, residue 2619. -/ +theorem bounds_13_2619 : exactInterval 13 2619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2619 : oddCount 2619 13 = 7 ∧ acceleratedOrbit 13 2619 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2619) = 3 ^ 7 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2619.1, data_13_2619.2] + +/-- Complete interval computation for depth 13, residue 2620. -/ +theorem bounds_13_2620 : exactInterval 13 2620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2620 : oddCount 2620 13 = 8 ∧ acceleratedOrbit 13 2620 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2620) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2620.1, data_13_2620.2] + +/-- Complete interval computation for depth 13, residue 2621. -/ +theorem bounds_13_2621 : exactInterval 13 2621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2621 : oddCount 2621 13 = 8 ∧ acceleratedOrbit 13 2621 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2621) = 3 ^ 8 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2621.1, data_13_2621.2] + +/-- Complete interval computation for depth 13, residue 2622. -/ +theorem bounds_13_2622 : exactInterval 13 2622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2622 : oddCount 2622 13 = 7 ∧ acceleratedOrbit 13 2622 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2622) = 3 ^ 7 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2622.1, data_13_2622.2] + +/-- Complete interval computation for depth 13, residue 2623. -/ +theorem bounds_13_2623 : exactInterval 13 2623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2623 : oddCount 2623 13 = 7 ∧ acceleratedOrbit 13 2623 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2623) = 3 ^ 7 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2623.1, data_13_2623.2] + +/-- Complete interval computation for depth 13, residue 2624. -/ +theorem bounds_13_2624 : exactInterval 13 2624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2624 : oddCount 2624 13 = 6 ∧ acceleratedOrbit 13 2624 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2624) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2624.1, data_13_2624.2] + +/-- Complete interval computation for depth 13, residue 2625. -/ +theorem bounds_13_2625 : exactInterval 13 2625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2625 : oddCount 2625 13 = 4 ∧ acceleratedOrbit 13 2625 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2625) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2625.1, data_13_2625.2] + +/-- Complete interval computation for depth 13, residue 2626. -/ +theorem bounds_13_2626 : exactInterval 13 2626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2626 : oddCount 2626 13 = 4 ∧ acceleratedOrbit 13 2626 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2626) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2626.1, data_13_2626.2] + +/-- Complete interval computation for depth 13, residue 2627. -/ +theorem bounds_13_2627 : exactInterval 13 2627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2627 : oddCount 2627 13 = 4 ∧ acceleratedOrbit 13 2627 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2627) = 3 ^ 4 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2627.1, data_13_2627.2] + +/-- Complete interval computation for depth 13, residue 2628. -/ +theorem bounds_13_2628 : exactInterval 13 2628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2628 : oddCount 2628 13 = 6 ∧ acceleratedOrbit 13 2628 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2628) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2628.1, data_13_2628.2] + +/-- Complete interval computation for depth 13, residue 2629. -/ +theorem bounds_13_2629 : exactInterval 13 2629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2629 : oddCount 2629 13 = 6 ∧ acceleratedOrbit 13 2629 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2629) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2629.1, data_13_2629.2] + +/-- Complete interval computation for depth 13, residue 2630. -/ +theorem bounds_13_2630 : exactInterval 13 2630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2630 : oddCount 2630 13 = 6 ∧ acceleratedOrbit 13 2630 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2630) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2630.1, data_13_2630.2] + +end Collatz.Research.StoppingAtlas.Batch0638 From f120f800818719ad6652d6b4a4ea99a7b58289ae Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:34 +0530 Subject: [PATCH 0639/1001] proof: certify atlas Batch0639 (13:2631 to 13:2646) --- Collatz/Research/StoppingAtlas/Batch0639.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0639.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0639.lean b/Collatz/Research/StoppingAtlas/Batch0639.lean new file mode 100644 index 00000000..39afd4ca --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0639.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0639 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2631. -/ +theorem bounds_13_2631 : exactInterval 13 2631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2631) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2631 : oddCount 2631 13 = 7 ∧ acceleratedOrbit 13 2631 = 703 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2631) = 3 ^ 7 * m + 703 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2631.1, data_13_2631.2] + +/-- Complete interval computation for depth 13, residue 2632. -/ +theorem bounds_13_2632 : exactInterval 13 2632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2632 : oddCount 2632 13 = 6 ∧ acceleratedOrbit 13 2632 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2632) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2632.1, data_13_2632.2] + +/-- Complete interval computation for depth 13, residue 2633. -/ +theorem bounds_13_2633 : exactInterval 13 2633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2633 : oddCount 2633 13 = 7 ∧ acceleratedOrbit 13 2633 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2633) = 3 ^ 7 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2633.1, data_13_2633.2] + +/-- Complete interval computation for depth 13, residue 2634. -/ +theorem bounds_13_2634 : exactInterval 13 2634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2634 : oddCount 2634 13 = 6 ∧ acceleratedOrbit 13 2634 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2634) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2634.1, data_13_2634.2] + +/-- Complete interval computation for depth 13, residue 2635. -/ +theorem bounds_13_2635 : exactInterval 13 2635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2635 : oddCount 2635 13 = 6 ∧ acceleratedOrbit 13 2635 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2635) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2635.1, data_13_2635.2] + +/-- Complete interval computation for depth 13, residue 2636. -/ +theorem bounds_13_2636 : exactInterval 13 2636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2636 : oddCount 2636 13 = 6 ∧ acceleratedOrbit 13 2636 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2636) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2636.1, data_13_2636.2] + +/-- Complete interval computation for depth 13, residue 2637. -/ +theorem bounds_13_2637 : exactInterval 13 2637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2637 : oddCount 2637 13 = 6 ∧ acceleratedOrbit 13 2637 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2637) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2637.1, data_13_2637.2] + +/-- Complete interval computation for depth 13, residue 2638. -/ +theorem bounds_13_2638 : exactInterval 13 2638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2638 : oddCount 2638 13 = 6 ∧ acceleratedOrbit 13 2638 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2638) = 3 ^ 6 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2638.1, data_13_2638.2] + +/-- Complete interval computation for depth 13, residue 2639. -/ +theorem bounds_13_2639 : exactInterval 13 2639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2639 : oddCount 2639 13 = 6 ∧ acceleratedOrbit 13 2639 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2639) = 3 ^ 6 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2639.1, data_13_2639.2] + +/-- Complete interval computation for depth 13, residue 2640. -/ +theorem bounds_13_2640 : exactInterval 13 2640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2640 : oddCount 2640 13 = 6 ∧ acceleratedOrbit 13 2640 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2640) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2640.1, data_13_2640.2] + +/-- Complete interval computation for depth 13, residue 2641. -/ +theorem bounds_13_2641 : exactInterval 13 2641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2641 : oddCount 2641 13 = 8 ∧ acceleratedOrbit 13 2641 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2641) = 3 ^ 8 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2641.1, data_13_2641.2] + +/-- Complete interval computation for depth 13, residue 2642. -/ +theorem bounds_13_2642 : exactInterval 13 2642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2642 : oddCount 2642 13 = 8 ∧ acceleratedOrbit 13 2642 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2642) = 3 ^ 8 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2642.1, data_13_2642.2] + +/-- Complete interval computation for depth 13, residue 2643. -/ +theorem bounds_13_2643 : exactInterval 13 2643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2643 : oddCount 2643 13 = 8 ∧ acceleratedOrbit 13 2643 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2643) = 3 ^ 8 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2643.1, data_13_2643.2] + +/-- Complete interval computation for depth 13, residue 2644. -/ +theorem bounds_13_2644 : exactInterval 13 2644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2644 : oddCount 2644 13 = 6 ∧ acceleratedOrbit 13 2644 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2644) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2644.1, data_13_2644.2] + +/-- Complete interval computation for depth 13, residue 2645. -/ +theorem bounds_13_2645 : exactInterval 13 2645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2645 : oddCount 2645 13 = 6 ∧ acceleratedOrbit 13 2645 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2645) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2645.1, data_13_2645.2] + +/-- Complete interval computation for depth 13, residue 2646. -/ +theorem bounds_13_2646 : exactInterval 13 2646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2646 : oddCount 2646 13 = 6 ∧ acceleratedOrbit 13 2646 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2646) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2646.1, data_13_2646.2] + +end Collatz.Research.StoppingAtlas.Batch0639 From daa33cb3dd1229d5e85ee74419f551b3d0f46aea Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:34 +0530 Subject: [PATCH 0640/1001] proof: certify atlas Batch0640 (13:2647 to 13:2661) --- Collatz/Research/StoppingAtlas/Batch0640.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0640.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0640.lean b/Collatz/Research/StoppingAtlas/Batch0640.lean new file mode 100644 index 00000000..83d7301b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0640.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0640 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2647. -/ +theorem bounds_13_2647 : exactInterval 13 2647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2647 : oddCount 2647 13 = 6 ∧ acceleratedOrbit 13 2647 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2647) = 3 ^ 6 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2647.1, data_13_2647.2] + +/-- Complete interval computation for depth 13, residue 2648. -/ +theorem bounds_13_2648 : exactInterval 13 2648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2648 : oddCount 2648 13 = 5 ∧ acceleratedOrbit 13 2648 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2648) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2648.1, data_13_2648.2] + +/-- Complete interval computation for depth 13, residue 2649. -/ +theorem bounds_13_2649 : exactInterval 13 2649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2649 : oddCount 2649 13 = 8 ∧ acceleratedOrbit 13 2649 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2649) = 3 ^ 8 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2649.1, data_13_2649.2] + +/-- Complete interval computation for depth 13, residue 2650. -/ +theorem bounds_13_2650 : exactInterval 13 2650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2650 : oddCount 2650 13 = 5 ∧ acceleratedOrbit 13 2650 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2650) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2650.1, data_13_2650.2] + +/-- Complete interval computation for depth 13, residue 2651. -/ +theorem bounds_13_2651 : exactInterval 13 2651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2651 : oddCount 2651 13 = 9 ∧ acceleratedOrbit 13 2651 = 6374 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2651) = 3 ^ 9 * m + 6374 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2651.1, data_13_2651.2] + +/-- Complete interval computation for depth 13, residue 2652. -/ +theorem bounds_13_2652 : exactInterval 13 2652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2652 : oddCount 2652 13 = 5 ∧ acceleratedOrbit 13 2652 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2652) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2652.1, data_13_2652.2] + +/-- Complete interval computation for depth 13, residue 2653. -/ +theorem bounds_13_2653 : exactInterval 13 2653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2653 : oddCount 2653 13 = 5 ∧ acceleratedOrbit 13 2653 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2653) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2653.1, data_13_2653.2] + +/-- Complete interval computation for depth 13, residue 2654. -/ +theorem bounds_13_2654 : exactInterval 13 2654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2654 : oddCount 2654 13 = 8 ∧ acceleratedOrbit 13 2654 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2654) = 3 ^ 8 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2654.1, data_13_2654.2] + +/-- Complete interval computation for depth 13, residue 2655. -/ +theorem bounds_13_2655 : exactInterval 13 2655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2655 : oddCount 2655 13 = 8 ∧ acceleratedOrbit 13 2655 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2655) = 3 ^ 8 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2655.1, data_13_2655.2] + +/-- Complete interval computation for depth 13, residue 2656. -/ +theorem bounds_13_2656 : exactInterval 13 2656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2656 : oddCount 2656 13 = 6 ∧ acceleratedOrbit 13 2656 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2656) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2656.1, data_13_2656.2] + +/-- Complete interval computation for depth 13, residue 2657. -/ +theorem bounds_13_2657 : exactInterval 13 2657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2657 : oddCount 2657 13 = 8 ∧ acceleratedOrbit 13 2657 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2657) = 3 ^ 8 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2657.1, data_13_2657.2] + +/-- Complete interval computation for depth 13, residue 2658. -/ +theorem bounds_13_2658 : exactInterval 13 2658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2658 : oddCount 2658 13 = 6 ∧ acceleratedOrbit 13 2658 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2658) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2658.1, data_13_2658.2] + +/-- Complete interval computation for depth 13, residue 2659. -/ +theorem bounds_13_2659 : exactInterval 13 2659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2659 : oddCount 2659 13 = 6 ∧ acceleratedOrbit 13 2659 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2659) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2659.1, data_13_2659.2] + +/-- Complete interval computation for depth 13, residue 2660. -/ +theorem bounds_13_2660 : exactInterval 13 2660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2660 : oddCount 2660 13 = 6 ∧ acceleratedOrbit 13 2660 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2660) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2660.1, data_13_2660.2] + +/-- Complete interval computation for depth 13, residue 2661. -/ +theorem bounds_13_2661 : exactInterval 13 2661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2661 : oddCount 2661 13 = 6 ∧ acceleratedOrbit 13 2661 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2661) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2661.1, data_13_2661.2] + +end Collatz.Research.StoppingAtlas.Batch0640 From 7e473eb4b1e012d88ba1eb1921bc5be68cbcd4ef Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:38 +0530 Subject: [PATCH 0641/1001] proof: certify atlas Batch0641 (13:2662 to 13:2676) --- Collatz/Research/StoppingAtlas/Batch0641.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0641.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0641.lean b/Collatz/Research/StoppingAtlas/Batch0641.lean new file mode 100644 index 00000000..46489de7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0641.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0641 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2662. -/ +theorem bounds_13_2662 : exactInterval 13 2662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2662 : oddCount 2662 13 = 6 ∧ acceleratedOrbit 13 2662 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2662) = 3 ^ 6 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2662.1, data_13_2662.2] + +/-- Complete interval computation for depth 13, residue 2663. -/ +theorem bounds_13_2663 : exactInterval 13 2663 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2663) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2663 : oddCount 2663 13 = 8 ∧ acceleratedOrbit 13 2663 = 2134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2663) = 3 ^ 8 * m + 2134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2663.1, data_13_2663.2] + +/-- Complete interval computation for depth 13, residue 2664. -/ +theorem bounds_13_2664 : exactInterval 13 2664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2664 : oddCount 2664 13 = 6 ∧ acceleratedOrbit 13 2664 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2664) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2664.1, data_13_2664.2] + +/-- Complete interval computation for depth 13, residue 2665. -/ +theorem bounds_13_2665 : exactInterval 13 2665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2665 : oddCount 2665 13 = 7 ∧ acceleratedOrbit 13 2665 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2665) = 3 ^ 7 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2665.1, data_13_2665.2] + +/-- Complete interval computation for depth 13, residue 2666. -/ +theorem bounds_13_2666 : exactInterval 13 2666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2666 : oddCount 2666 13 = 6 ∧ acceleratedOrbit 13 2666 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2666) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2666.1, data_13_2666.2] + +/-- Complete interval computation for depth 13, residue 2667. -/ +theorem bounds_13_2667 : exactInterval 13 2667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2667 : oddCount 2667 13 = 7 ∧ acceleratedOrbit 13 2667 = 713 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2667) = 3 ^ 7 * m + 713 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2667.1, data_13_2667.2] + +/-- Complete interval computation for depth 13, residue 2668. -/ +theorem bounds_13_2668 : exactInterval 13 2668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2668 : oddCount 2668 13 = 9 ∧ acceleratedOrbit 13 2668 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2668) = 3 ^ 9 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2668.1, data_13_2668.2] + +/-- Complete interval computation for depth 13, residue 2669. -/ +theorem bounds_13_2669 : exactInterval 13 2669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2669 : oddCount 2669 13 = 9 ∧ acceleratedOrbit 13 2669 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2669) = 3 ^ 9 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2669.1, data_13_2669.2] + +/-- Complete interval computation for depth 13, residue 2670. -/ +theorem bounds_13_2670 : exactInterval 13 2670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2670 : oddCount 2670 13 = 9 ∧ acceleratedOrbit 13 2670 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2670) = 3 ^ 9 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2670.1, data_13_2670.2] + +/-- Complete interval computation for depth 13, residue 2671. -/ +theorem bounds_13_2671 : exactInterval 13 2671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2671 : oddCount 2671 13 = 9 ∧ acceleratedOrbit 13 2671 = 6421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2671) = 3 ^ 9 * m + 6421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2671.1, data_13_2671.2] + +/-- Complete interval computation for depth 13, residue 2672. -/ +theorem bounds_13_2672 : exactInterval 13 2672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2672 : oddCount 2672 13 = 7 ∧ acceleratedOrbit 13 2672 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2672) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2672.1, data_13_2672.2] + +/-- Complete interval computation for depth 13, residue 2673. -/ +theorem bounds_13_2673 : exactInterval 13 2673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2673 : oddCount 2673 13 = 6 ∧ acceleratedOrbit 13 2673 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2673) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2673.1, data_13_2673.2] + +/-- Complete interval computation for depth 13, residue 2674. -/ +theorem bounds_13_2674 : exactInterval 13 2674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2674 : oddCount 2674 13 = 8 ∧ acceleratedOrbit 13 2674 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2674) = 3 ^ 8 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2674.1, data_13_2674.2] + +/-- Complete interval computation for depth 13, residue 2675. -/ +theorem bounds_13_2675 : exactInterval 13 2675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2675 : oddCount 2675 13 = 8 ∧ acceleratedOrbit 13 2675 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2675) = 3 ^ 8 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2675.1, data_13_2675.2] + +/-- Complete interval computation for depth 13, residue 2676. -/ +theorem bounds_13_2676 : exactInterval 13 2676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2676 : oddCount 2676 13 = 7 ∧ acceleratedOrbit 13 2676 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2676) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2676.1, data_13_2676.2] + +end Collatz.Research.StoppingAtlas.Batch0641 From 987dbf253e6a4c614061047373da04dcdc0cf892 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:38 +0530 Subject: [PATCH 0642/1001] proof: certify atlas Batch0642 (13:2677 to 13:2692) --- Collatz/Research/StoppingAtlas/Batch0642.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0642.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0642.lean b/Collatz/Research/StoppingAtlas/Batch0642.lean new file mode 100644 index 00000000..72ca409c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0642.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0642 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2677. -/ +theorem bounds_13_2677 : exactInterval 13 2677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2677 : oddCount 2677 13 = 7 ∧ acceleratedOrbit 13 2677 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2677) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2677.1, data_13_2677.2] + +/-- Complete interval computation for depth 13, residue 2678. -/ +theorem bounds_13_2678 : exactInterval 13 2678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2678 : oddCount 2678 13 = 5 ∧ acceleratedOrbit 13 2678 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2678) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2678.1, data_13_2678.2] + +/-- Complete interval computation for depth 13, residue 2679. -/ +theorem bounds_13_2679 : exactInterval 13 2679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2679 : oddCount 2679 13 = 5 ∧ acceleratedOrbit 13 2679 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2679) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2679.1, data_13_2679.2] + +/-- Complete interval computation for depth 13, residue 2680. -/ +theorem bounds_13_2680 : exactInterval 13 2680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2680 : oddCount 2680 13 = 7 ∧ acceleratedOrbit 13 2680 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2680) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2680.1, data_13_2680.2] + +/-- Complete interval computation for depth 13, residue 2681. -/ +theorem bounds_13_2681 : exactInterval 13 2681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2681 : oddCount 2681 13 = 8 ∧ acceleratedOrbit 13 2681 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2681) = 3 ^ 8 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2681.1, data_13_2681.2] + +/-- Complete interval computation for depth 13, residue 2682. -/ +theorem bounds_13_2682 : exactInterval 13 2682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2682 : oddCount 2682 13 = 7 ∧ acceleratedOrbit 13 2682 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2682) = 3 ^ 7 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2682.1, data_13_2682.2] + +/-- Complete interval computation for depth 13, residue 2683. -/ +theorem bounds_13_2683 : exactInterval 13 2683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2683 : oddCount 2683 13 = 6 ∧ acceleratedOrbit 13 2683 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2683) = 3 ^ 6 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2683.1, data_13_2683.2] + +/-- Complete interval computation for depth 13, residue 2684. -/ +theorem bounds_13_2684 : exactInterval 13 2684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2684 : oddCount 2684 13 = 8 ∧ acceleratedOrbit 13 2684 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2684) = 3 ^ 8 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2684.1, data_13_2684.2] + +/-- Complete interval computation for depth 13, residue 2685. -/ +theorem bounds_13_2685 : exactInterval 13 2685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2685 : oddCount 2685 13 = 8 ∧ acceleratedOrbit 13 2685 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2685) = 3 ^ 8 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2685.1, data_13_2685.2] + +/-- Complete interval computation for depth 13, residue 2686. -/ +theorem bounds_13_2686 : exactInterval 13 2686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2686 : oddCount 2686 13 = 8 ∧ acceleratedOrbit 13 2686 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2686) = 3 ^ 8 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2686.1, data_13_2686.2] + +/-- Complete interval computation for depth 13, residue 2687. -/ +theorem bounds_13_2687 : exactInterval 13 2687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2687 : oddCount 2687 13 = 10 ∧ acceleratedOrbit 13 2687 = 19376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2687) = 3 ^ 10 * m + 19376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2687.1, data_13_2687.2] + +/-- Complete interval computation for depth 13, residue 2688. -/ +theorem bounds_13_2688 : exactInterval 13 2688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2688 : oddCount 2688 13 = 1 ∧ acceleratedOrbit 13 2688 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2688) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2688.1, data_13_2688.2] + +/-- Complete interval computation for depth 13, residue 2689. -/ +theorem bounds_13_2689 : exactInterval 13 2689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2689 : oddCount 2689 13 = 9 ∧ acceleratedOrbit 13 2689 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2689) = 3 ^ 9 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2689.1, data_13_2689.2] + +/-- Complete interval computation for depth 13, residue 2690. -/ +theorem bounds_13_2690 : exactInterval 13 2690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2690 : oddCount 2690 13 = 6 ∧ acceleratedOrbit 13 2690 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2690) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2690.1, data_13_2690.2] + +/-- Complete interval computation for depth 13, residue 2691. -/ +theorem bounds_13_2691 : exactInterval 13 2691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2691 : oddCount 2691 13 = 6 ∧ acceleratedOrbit 13 2691 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2691) = 3 ^ 6 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2691.1, data_13_2691.2] + +/-- Complete interval computation for depth 13, residue 2692. -/ +theorem bounds_13_2692 : exactInterval 13 2692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2692 : oddCount 2692 13 = 7 ∧ acceleratedOrbit 13 2692 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2692) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2692.1, data_13_2692.2] + +end Collatz.Research.StoppingAtlas.Batch0642 From 6df51bb18285cee38fb3a4630053a4fe61274172 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:39 +0530 Subject: [PATCH 0643/1001] proof: certify atlas Batch0643 (13:2693 to 13:2707) --- Collatz/Research/StoppingAtlas/Batch0643.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0643.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0643.lean b/Collatz/Research/StoppingAtlas/Batch0643.lean new file mode 100644 index 00000000..f89cb1bc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0643.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0643 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2693. -/ +theorem bounds_13_2693 : exactInterval 13 2693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2693 : oddCount 2693 13 = 7 ∧ acceleratedOrbit 13 2693 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2693) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2693.1, data_13_2693.2] + +/-- Complete interval computation for depth 13, residue 2694. -/ +theorem bounds_13_2694 : exactInterval 13 2694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2694 : oddCount 2694 13 = 7 ∧ acceleratedOrbit 13 2694 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2694) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2694.1, data_13_2694.2] + +/-- Complete interval computation for depth 13, residue 2695. -/ +theorem bounds_13_2695 : exactInterval 13 2695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2695 : oddCount 2695 13 = 5 ∧ acceleratedOrbit 13 2695 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2695) = 3 ^ 5 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2695.1, data_13_2695.2] + +/-- Complete interval computation for depth 13, residue 2696. -/ +theorem bounds_13_2696 : exactInterval 13 2696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2696 : oddCount 2696 13 = 7 ∧ acceleratedOrbit 13 2696 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2696) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2696.1, data_13_2696.2] + +/-- Complete interval computation for depth 13, residue 2697. -/ +theorem bounds_13_2697 : exactInterval 13 2697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2697 : oddCount 2697 13 = 8 ∧ acceleratedOrbit 13 2697 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2697) = 3 ^ 8 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2697.1, data_13_2697.2] + +/-- Complete interval computation for depth 13, residue 2698. -/ +theorem bounds_13_2698 : exactInterval 13 2698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2698 : oddCount 2698 13 = 7 ∧ acceleratedOrbit 13 2698 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2698) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2698.1, data_13_2698.2] + +/-- Complete interval computation for depth 13, residue 2699. -/ +theorem bounds_13_2699 : exactInterval 13 2699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2699 : oddCount 2699 13 = 7 ∧ acceleratedOrbit 13 2699 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2699) = 3 ^ 7 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2699.1, data_13_2699.2] + +/-- Complete interval computation for depth 13, residue 2700. -/ +theorem bounds_13_2700 : exactInterval 13 2700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2700 : oddCount 2700 13 = 7 ∧ acceleratedOrbit 13 2700 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2700) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2700.1, data_13_2700.2] + +/-- Complete interval computation for depth 13, residue 2701. -/ +theorem bounds_13_2701 : exactInterval 13 2701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2701 : oddCount 2701 13 = 7 ∧ acceleratedOrbit 13 2701 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2701) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2701.1, data_13_2701.2] + +/-- Complete interval computation for depth 13, residue 2702. -/ +theorem bounds_13_2702 : exactInterval 13 2702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2702 : oddCount 2702 13 = 9 ∧ acceleratedOrbit 13 2702 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2702) = 3 ^ 9 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2702.1, data_13_2702.2] + +/-- Complete interval computation for depth 13, residue 2703. -/ +theorem bounds_13_2703 : exactInterval 13 2703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2703 : oddCount 2703 13 = 9 ∧ acceleratedOrbit 13 2703 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2703) = 3 ^ 9 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2703.1, data_13_2703.2] + +/-- Complete interval computation for depth 13, residue 2704. -/ +theorem bounds_13_2704 : exactInterval 13 2704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2704 : oddCount 2704 13 = 8 ∧ acceleratedOrbit 13 2704 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2704) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2704.1, data_13_2704.2] + +/-- Complete interval computation for depth 13, residue 2705. -/ +theorem bounds_13_2705 : exactInterval 13 2705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2705 : oddCount 2705 13 = 7 ∧ acceleratedOrbit 13 2705 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2705) = 3 ^ 7 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2705.1, data_13_2705.2] + +/-- Complete interval computation for depth 13, residue 2706. -/ +theorem bounds_13_2706 : exactInterval 13 2706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2706 : oddCount 2706 13 = 7 ∧ acceleratedOrbit 13 2706 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2706) = 3 ^ 7 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2706.1, data_13_2706.2] + +/-- Complete interval computation for depth 13, residue 2707. -/ +theorem bounds_13_2707 : exactInterval 13 2707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2707 : oddCount 2707 13 = 7 ∧ acceleratedOrbit 13 2707 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2707) = 3 ^ 7 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2707.1, data_13_2707.2] + +end Collatz.Research.StoppingAtlas.Batch0643 From c4c2a349833ca50d9adf339445bf594868e5bff0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:40 +0530 Subject: [PATCH 0644/1001] proof: certify atlas Batch0644 (13:2708 to 13:2722) --- Collatz/Research/StoppingAtlas/Batch0644.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0644.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0644.lean b/Collatz/Research/StoppingAtlas/Batch0644.lean new file mode 100644 index 00000000..4fa1cc6a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0644.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0644 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2708. -/ +theorem bounds_13_2708 : exactInterval 13 2708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2708 : oddCount 2708 13 = 8 ∧ acceleratedOrbit 13 2708 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2708) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2708.1, data_13_2708.2] + +/-- Complete interval computation for depth 13, residue 2709. -/ +theorem bounds_13_2709 : exactInterval 13 2709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2709 : oddCount 2709 13 = 8 ∧ acceleratedOrbit 13 2709 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2709) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2709.1, data_13_2709.2] + +/-- Complete interval computation for depth 13, residue 2710. -/ +theorem bounds_13_2710 : exactInterval 13 2710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2710 : oddCount 2710 13 = 7 ∧ acceleratedOrbit 13 2710 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2710) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2710.1, data_13_2710.2] + +/-- Complete interval computation for depth 13, residue 2711. -/ +theorem bounds_13_2711 : exactInterval 13 2711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2711 : oddCount 2711 13 = 7 ∧ acceleratedOrbit 13 2711 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2711) = 3 ^ 7 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2711.1, data_13_2711.2] + +/-- Complete interval computation for depth 13, residue 2712. -/ +theorem bounds_13_2712 : exactInterval 13 2712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2712 : oddCount 2712 13 = 8 ∧ acceleratedOrbit 13 2712 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2712) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2712.1, data_13_2712.2] + +/-- Complete interval computation for depth 13, residue 2713. -/ +theorem bounds_13_2713 : exactInterval 13 2713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2713 : oddCount 2713 13 = 8 ∧ acceleratedOrbit 13 2713 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2713) = 3 ^ 8 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2713.1, data_13_2713.2] + +/-- Complete interval computation for depth 13, residue 2714. -/ +theorem bounds_13_2714 : exactInterval 13 2714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2714 : oddCount 2714 13 = 8 ∧ acceleratedOrbit 13 2714 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2714) = 3 ^ 8 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2714.1, data_13_2714.2] + +/-- Complete interval computation for depth 13, residue 2715. -/ +theorem bounds_13_2715 : exactInterval 13 2715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2715 : oddCount 2715 13 = 9 ∧ acceleratedOrbit 13 2715 = 6527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2715) = 3 ^ 9 * m + 6527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2715.1, data_13_2715.2] + +/-- Complete interval computation for depth 13, residue 2716. -/ +theorem bounds_13_2716 : exactInterval 13 2716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2716 : oddCount 2716 13 = 8 ∧ acceleratedOrbit 13 2716 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2716) = 3 ^ 8 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2716.1, data_13_2716.2] + +/-- Complete interval computation for depth 13, residue 2717. -/ +theorem bounds_13_2717 : exactInterval 13 2717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2717 : oddCount 2717 13 = 8 ∧ acceleratedOrbit 13 2717 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2717) = 3 ^ 8 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2717.1, data_13_2717.2] + +/-- Complete interval computation for depth 13, residue 2718. -/ +theorem bounds_13_2718 : exactInterval 13 2718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2718 : oddCount 2718 13 = 8 ∧ acceleratedOrbit 13 2718 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2718) = 3 ^ 8 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2718.1, data_13_2718.2] + +/-- Complete interval computation for depth 13, residue 2719. -/ +theorem bounds_13_2719 : exactInterval 13 2719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2719 : oddCount 2719 13 = 9 ∧ acceleratedOrbit 13 2719 = 6536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2719) = 3 ^ 9 * m + 6536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2719.1, data_13_2719.2] + +/-- Complete interval computation for depth 13, residue 2720. -/ +theorem bounds_13_2720 : exactInterval 13 2720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2720 : oddCount 2720 13 = 1 ∧ acceleratedOrbit 13 2720 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2720) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2720.1, data_13_2720.2] + +/-- Complete interval computation for depth 13, residue 2721. -/ +theorem bounds_13_2721 : exactInterval 13 2721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2721 : oddCount 2721 13 = 8 ∧ acceleratedOrbit 13 2721 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2721) = 3 ^ 8 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2721.1, data_13_2721.2] + +/-- Complete interval computation for depth 13, residue 2722. -/ +theorem bounds_13_2722 : exactInterval 13 2722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2722 : oddCount 2722 13 = 9 ∧ acceleratedOrbit 13 2722 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2722) = 3 ^ 9 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2722.1, data_13_2722.2] + +end Collatz.Research.StoppingAtlas.Batch0644 From 9abc35b7ab3f191f15356940d7be13f04936bf39 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:41 +0530 Subject: [PATCH 0645/1001] proof: certify atlas Batch0645 (13:2723 to 13:2738) --- Collatz/Research/StoppingAtlas/Batch0645.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0645.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0645.lean b/Collatz/Research/StoppingAtlas/Batch0645.lean new file mode 100644 index 00000000..042502ef --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0645.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0645 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2723. -/ +theorem bounds_13_2723 : exactInterval 13 2723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2723 : oddCount 2723 13 = 9 ∧ acceleratedOrbit 13 2723 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2723) = 3 ^ 9 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2723.1, data_13_2723.2] + +/-- Complete interval computation for depth 13, residue 2724. -/ +theorem bounds_13_2724 : exactInterval 13 2724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2724 : oddCount 2724 13 = 10 ∧ acceleratedOrbit 13 2724 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2724) = 3 ^ 10 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2724.1, data_13_2724.2] + +/-- Complete interval computation for depth 13, residue 2725. -/ +theorem bounds_13_2725 : exactInterval 13 2725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2725 : oddCount 2725 13 = 10 ∧ acceleratedOrbit 13 2725 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2725) = 3 ^ 10 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2725.1, data_13_2725.2] + +/-- Complete interval computation for depth 13, residue 2726. -/ +theorem bounds_13_2726 : exactInterval 13 2726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2726 : oddCount 2726 13 = 10 ∧ acceleratedOrbit 13 2726 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2726) = 3 ^ 10 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2726.1, data_13_2726.2] + +/-- Complete interval computation for depth 13, residue 2727. -/ +theorem bounds_13_2727 : exactInterval 13 2727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2727 : oddCount 2727 13 = 9 ∧ acceleratedOrbit 13 2727 = 6556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2727) = 3 ^ 9 * m + 6556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2727.1, data_13_2727.2] + +/-- Complete interval computation for depth 13, residue 2728. -/ +theorem bounds_13_2728 : exactInterval 13 2728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2728 : oddCount 2728 13 = 1 ∧ acceleratedOrbit 13 2728 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2728) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2728.1, data_13_2728.2] + +/-- Complete interval computation for depth 13, residue 2729. -/ +theorem bounds_13_2729 : exactInterval 13 2729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2729 : oddCount 2729 13 = 12 ∧ acceleratedOrbit 13 2729 = 177146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2729) = 3 ^ 12 * m + 177146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2729.1, data_13_2729.2] + +/-- Complete interval computation for depth 13, residue 2730. -/ +theorem bounds_13_2730 : exactInterval 13 2730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2730 : oddCount 2730 13 = 1 ∧ acceleratedOrbit 13 2730 = 1 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2730) = 3 ^ 1 * m + 1 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2730.1, data_13_2730.2] + +/-- Complete interval computation for depth 13, residue 2731. -/ +theorem bounds_13_2731 : exactInterval 13 2731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2731 : oddCount 2731 13 = 7 ∧ acceleratedOrbit 13 2731 = 730 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2731) = 3 ^ 7 * m + 730 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2731.1, data_13_2731.2] + +/-- Complete interval computation for depth 13, residue 2732. -/ +theorem bounds_13_2732 : exactInterval 13 2732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2732 : oddCount 2732 13 = 6 ∧ acceleratedOrbit 13 2732 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2732) = 3 ^ 6 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2732.1, data_13_2732.2] + +/-- Complete interval computation for depth 13, residue 2733. -/ +theorem bounds_13_2733 : exactInterval 13 2733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2733 : oddCount 2733 13 = 6 ∧ acceleratedOrbit 13 2733 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2733) = 3 ^ 6 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2733.1, data_13_2733.2] + +/-- Complete interval computation for depth 13, residue 2734. -/ +theorem bounds_13_2734 : exactInterval 13 2734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2734 : oddCount 2734 13 = 6 ∧ acceleratedOrbit 13 2734 = 244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2734) = 3 ^ 6 * m + 244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2734.1, data_13_2734.2] + +/-- Complete interval computation for depth 13, residue 2735. -/ +theorem bounds_13_2735 : exactInterval 13 2735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2735 : oddCount 2735 13 = 7 ∧ acceleratedOrbit 13 2735 = 731 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2735) = 3 ^ 7 * m + 731 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2735.1, data_13_2735.2] + +/-- Complete interval computation for depth 13, residue 2736. -/ +theorem bounds_13_2736 : exactInterval 13 2736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2736 : oddCount 2736 13 = 5 ∧ acceleratedOrbit 13 2736 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2736) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2736.1, data_13_2736.2] + +/-- Complete interval computation for depth 13, residue 2737. -/ +theorem bounds_13_2737 : exactInterval 13 2737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2737 : oddCount 2737 13 = 6 ∧ acceleratedOrbit 13 2737 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2737) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2737.1, data_13_2737.2] + +/-- Complete interval computation for depth 13, residue 2738. -/ +theorem bounds_13_2738 : exactInterval 13 2738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2738 : oddCount 2738 13 = 6 ∧ acceleratedOrbit 13 2738 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2738) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2738.1, data_13_2738.2] + +end Collatz.Research.StoppingAtlas.Batch0645 From 804b704d85773306ce9dae51746358d92c5279e0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:42 +0530 Subject: [PATCH 0646/1001] proof: certify atlas Batch0646 (13:2739 to 13:2753) --- Collatz/Research/StoppingAtlas/Batch0646.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0646.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0646.lean b/Collatz/Research/StoppingAtlas/Batch0646.lean new file mode 100644 index 00000000..2d01ff10 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0646.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0646 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2739. -/ +theorem bounds_13_2739 : exactInterval 13 2739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2739 : oddCount 2739 13 = 6 ∧ acceleratedOrbit 13 2739 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2739) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2739.1, data_13_2739.2] + +/-- Complete interval computation for depth 13, residue 2740. -/ +theorem bounds_13_2740 : exactInterval 13 2740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2740 : oddCount 2740 13 = 5 ∧ acceleratedOrbit 13 2740 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2740) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2740.1, data_13_2740.2] + +/-- Complete interval computation for depth 13, residue 2741. -/ +theorem bounds_13_2741 : exactInterval 13 2741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2741 : oddCount 2741 13 = 5 ∧ acceleratedOrbit 13 2741 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2741) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2741.1, data_13_2741.2] + +/-- Complete interval computation for depth 13, residue 2742. -/ +theorem bounds_13_2742 : exactInterval 13 2742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2742 : oddCount 2742 13 = 7 ∧ acceleratedOrbit 13 2742 = 733 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2742) = 3 ^ 7 * m + 733 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2742.1, data_13_2742.2] + +/-- Complete interval computation for depth 13, residue 2743. -/ +theorem bounds_13_2743 : exactInterval 13 2743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2743 : oddCount 2743 13 = 7 ∧ acceleratedOrbit 13 2743 = 733 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2743) = 3 ^ 7 * m + 733 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2743.1, data_13_2743.2] + +/-- Complete interval computation for depth 13, residue 2744. -/ +theorem bounds_13_2744 : exactInterval 13 2744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2744 : oddCount 2744 13 = 5 ∧ acceleratedOrbit 13 2744 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2744) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2744.1, data_13_2744.2] + +/-- Complete interval computation for depth 13, residue 2745. -/ +theorem bounds_13_2745 : exactInterval 13 2745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2745 : oddCount 2745 13 = 6 ∧ acceleratedOrbit 13 2745 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2745) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2745.1, data_13_2745.2] + +/-- Complete interval computation for depth 13, residue 2746. -/ +theorem bounds_13_2746 : exactInterval 13 2746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2746 : oddCount 2746 13 = 5 ∧ acceleratedOrbit 13 2746 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2746) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2746.1, data_13_2746.2] + +/-- Complete interval computation for depth 13, residue 2747. -/ +theorem bounds_13_2747 : exactInterval 13 2747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2747 : oddCount 2747 13 = 7 ∧ acceleratedOrbit 13 2747 = 734 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2747) = 3 ^ 7 * m + 734 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2747.1, data_13_2747.2] + +/-- Complete interval computation for depth 13, residue 2748. -/ +theorem bounds_13_2748 : exactInterval 13 2748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2748 : oddCount 2748 13 = 6 ∧ acceleratedOrbit 13 2748 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2748) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2748.1, data_13_2748.2] + +/-- Complete interval computation for depth 13, residue 2749. -/ +theorem bounds_13_2749 : exactInterval 13 2749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2749 : oddCount 2749 13 = 6 ∧ acceleratedOrbit 13 2749 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2749) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2749.1, data_13_2749.2] + +/-- Complete interval computation for depth 13, residue 2750. -/ +theorem bounds_13_2750 : exactInterval 13 2750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2750 : oddCount 2750 13 = 6 ∧ acceleratedOrbit 13 2750 = 245 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2750) = 3 ^ 6 * m + 245 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2750.1, data_13_2750.2] + +/-- Complete interval computation for depth 13, residue 2751. -/ +theorem bounds_13_2751 : exactInterval 13 2751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2751 : oddCount 2751 13 = 10 ∧ acceleratedOrbit 13 2751 = 19838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2751) = 3 ^ 10 * m + 19838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2751.1, data_13_2751.2] + +/-- Complete interval computation for depth 13, residue 2752. -/ +theorem bounds_13_2752 : exactInterval 13 2752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2752 : oddCount 2752 13 = 4 ∧ acceleratedOrbit 13 2752 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2752) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2752.1, data_13_2752.2] + +/-- Complete interval computation for depth 13, residue 2753. -/ +theorem bounds_13_2753 : exactInterval 13 2753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2753 : oddCount 2753 13 = 5 ∧ acceleratedOrbit 13 2753 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2753) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2753.1, data_13_2753.2] + +end Collatz.Research.StoppingAtlas.Batch0646 From f1bffb14bf03c2a695564bb787ea68be34041b4f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:42 +0530 Subject: [PATCH 0647/1001] proof: certify atlas Batch0647 (13:2754 to 13:2768) --- Collatz/Research/StoppingAtlas/Batch0647.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0647.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0647.lean b/Collatz/Research/StoppingAtlas/Batch0647.lean new file mode 100644 index 00000000..d7498319 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0647.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0647 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2754. -/ +theorem bounds_13_2754 : exactInterval 13 2754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2754 : oddCount 2754 13 = 7 ∧ acceleratedOrbit 13 2754 = 737 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2754) = 3 ^ 7 * m + 737 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2754.1, data_13_2754.2] + +/-- Complete interval computation for depth 13, residue 2755. -/ +theorem bounds_13_2755 : exactInterval 13 2755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2755 : oddCount 2755 13 = 7 ∧ acceleratedOrbit 13 2755 = 737 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2755) = 3 ^ 7 * m + 737 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2755.1, data_13_2755.2] + +/-- Complete interval computation for depth 13, residue 2756. -/ +theorem bounds_13_2756 : exactInterval 13 2756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2756 : oddCount 2756 13 = 5 ∧ acceleratedOrbit 13 2756 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2756) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2756.1, data_13_2756.2] + +/-- Complete interval computation for depth 13, residue 2757. -/ +theorem bounds_13_2757 : exactInterval 13 2757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2757 : oddCount 2757 13 = 5 ∧ acceleratedOrbit 13 2757 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2757) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2757.1, data_13_2757.2] + +/-- Complete interval computation for depth 13, residue 2758. -/ +theorem bounds_13_2758 : exactInterval 13 2758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2758 : oddCount 2758 13 = 5 ∧ acceleratedOrbit 13 2758 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2758) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2758.1, data_13_2758.2] + +/-- Complete interval computation for depth 13, residue 2759. -/ +theorem bounds_13_2759 : exactInterval 13 2759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2759 : oddCount 2759 13 = 8 ∧ acceleratedOrbit 13 2759 = 2213 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2759) = 3 ^ 8 * m + 2213 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2759.1, data_13_2759.2] + +/-- Complete interval computation for depth 13, residue 2760. -/ +theorem bounds_13_2760 : exactInterval 13 2760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2760 : oddCount 2760 13 = 5 ∧ acceleratedOrbit 13 2760 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2760) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2760.1, data_13_2760.2] + +/-- Complete interval computation for depth 13, residue 2761. -/ +theorem bounds_13_2761 : exactInterval 13 2761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2761 : oddCount 2761 13 = 5 ∧ acceleratedOrbit 13 2761 = 82 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2761) = 3 ^ 5 * m + 82 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2761.1, data_13_2761.2] + +/-- Complete interval computation for depth 13, residue 2762. -/ +theorem bounds_13_2762 : exactInterval 13 2762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2762 : oddCount 2762 13 = 5 ∧ acceleratedOrbit 13 2762 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2762) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2762.1, data_13_2762.2] + +/-- Complete interval computation for depth 13, residue 2763. -/ +theorem bounds_13_2763 : exactInterval 13 2763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2763 : oddCount 2763 13 = 7 ∧ acceleratedOrbit 13 2763 = 739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2763) = 3 ^ 7 * m + 739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2763.1, data_13_2763.2] + +/-- Complete interval computation for depth 13, residue 2764. -/ +theorem bounds_13_2764 : exactInterval 13 2764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2764 : oddCount 2764 13 = 5 ∧ acceleratedOrbit 13 2764 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2764) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2764.1, data_13_2764.2] + +/-- Complete interval computation for depth 13, residue 2765. -/ +theorem bounds_13_2765 : exactInterval 13 2765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2765 : oddCount 2765 13 = 5 ∧ acceleratedOrbit 13 2765 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2765) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2765.1, data_13_2765.2] + +/-- Complete interval computation for depth 13, residue 2766. -/ +theorem bounds_13_2766 : exactInterval 13 2766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2766 : oddCount 2766 13 = 9 ∧ acceleratedOrbit 13 2766 = 6652 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2766) = 3 ^ 9 * m + 6652 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2766.1, data_13_2766.2] + +/-- Complete interval computation for depth 13, residue 2767. -/ +theorem bounds_13_2767 : exactInterval 13 2767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2767 : oddCount 2767 13 = 9 ∧ acceleratedOrbit 13 2767 = 6652 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2767) = 3 ^ 9 * m + 6652 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2767.1, data_13_2767.2] + +/-- Complete interval computation for depth 13, residue 2768. -/ +theorem bounds_13_2768 : exactInterval 13 2768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2768 : oddCount 2768 13 = 4 ∧ acceleratedOrbit 13 2768 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2768) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2768.1, data_13_2768.2] + +end Collatz.Research.StoppingAtlas.Batch0647 From 8120f765b30173425da6c6aa417c186c23e7c7fb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:47 +0530 Subject: [PATCH 0648/1001] proof: certify atlas Batch0648 (13:2769 to 13:2784) --- Collatz/Research/StoppingAtlas/Batch0648.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0648.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0648.lean b/Collatz/Research/StoppingAtlas/Batch0648.lean new file mode 100644 index 00000000..5417e311 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0648.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0648 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2769. -/ +theorem bounds_13_2769 : exactInterval 13 2769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2769 : oddCount 2769 13 = 6 ∧ acceleratedOrbit 13 2769 = 247 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2769) = 3 ^ 6 * m + 247 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2769.1, data_13_2769.2] + +/-- Complete interval computation for depth 13, residue 2770. -/ +theorem bounds_13_2770 : exactInterval 13 2770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2770 : oddCount 2770 13 = 6 ∧ acceleratedOrbit 13 2770 = 247 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2770) = 3 ^ 6 * m + 247 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2770.1, data_13_2770.2] + +/-- Complete interval computation for depth 13, residue 2771. -/ +theorem bounds_13_2771 : exactInterval 13 2771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2771 : oddCount 2771 13 = 6 ∧ acceleratedOrbit 13 2771 = 247 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2771) = 3 ^ 6 * m + 247 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2771.1, data_13_2771.2] + +/-- Complete interval computation for depth 13, residue 2772. -/ +theorem bounds_13_2772 : exactInterval 13 2772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2772 : oddCount 2772 13 = 4 ∧ acceleratedOrbit 13 2772 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2772) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2772.1, data_13_2772.2] + +/-- Complete interval computation for depth 13, residue 2773. -/ +theorem bounds_13_2773 : exactInterval 13 2773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2773 : oddCount 2773 13 = 4 ∧ acceleratedOrbit 13 2773 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2773) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2773.1, data_13_2773.2] + +/-- Complete interval computation for depth 13, residue 2774. -/ +theorem bounds_13_2774 : exactInterval 13 2774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2774 : oddCount 2774 13 = 7 ∧ acceleratedOrbit 13 2774 = 742 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2774) = 3 ^ 7 * m + 742 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2774.1, data_13_2774.2] + +/-- Complete interval computation for depth 13, residue 2775. -/ +theorem bounds_13_2775 : exactInterval 13 2775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2775 : oddCount 2775 13 = 7 ∧ acceleratedOrbit 13 2775 = 742 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2775) = 3 ^ 7 * m + 742 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2775.1, data_13_2775.2] + +/-- Complete interval computation for depth 13, residue 2776. -/ +theorem bounds_13_2776 : exactInterval 13 2776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2776 : oddCount 2776 13 = 6 ∧ acceleratedOrbit 13 2776 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2776) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2776.1, data_13_2776.2] + +/-- Complete interval computation for depth 13, residue 2777. -/ +theorem bounds_13_2777 : exactInterval 13 2777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2777 : oddCount 2777 13 = 5 ∧ acceleratedOrbit 13 2777 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2777) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2777.1, data_13_2777.2] + +/-- Complete interval computation for depth 13, residue 2778. -/ +theorem bounds_13_2778 : exactInterval 13 2778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2778 : oddCount 2778 13 = 6 ∧ acceleratedOrbit 13 2778 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2778) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2778.1, data_13_2778.2] + +/-- Complete interval computation for depth 13, residue 2779. -/ +theorem bounds_13_2779 : exactInterval 13 2779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2779 : oddCount 2779 13 = 9 ∧ acceleratedOrbit 13 2779 = 6682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2779) = 3 ^ 9 * m + 6682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2779.1, data_13_2779.2] + +/-- Complete interval computation for depth 13, residue 2780. -/ +theorem bounds_13_2780 : exactInterval 13 2780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2780 : oddCount 2780 13 = 6 ∧ acceleratedOrbit 13 2780 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2780) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2780.1, data_13_2780.2] + +/-- Complete interval computation for depth 13, residue 2781. -/ +theorem bounds_13_2781 : exactInterval 13 2781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2781 : oddCount 2781 13 = 6 ∧ acceleratedOrbit 13 2781 = 248 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2781) = 3 ^ 6 * m + 248 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2781.1, data_13_2781.2] + +/-- Complete interval computation for depth 13, residue 2782. -/ +theorem bounds_13_2782 : exactInterval 13 2782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2782 : oddCount 2782 13 = 8 ∧ acceleratedOrbit 13 2782 = 2231 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2782) = 3 ^ 8 * m + 2231 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2782.1, data_13_2782.2] + +/-- Complete interval computation for depth 13, residue 2783. -/ +theorem bounds_13_2783 : exactInterval 13 2783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2783 : oddCount 2783 13 = 8 ∧ acceleratedOrbit 13 2783 = 2231 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2783) = 3 ^ 8 * m + 2231 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2783.1, data_13_2783.2] + +/-- Complete interval computation for depth 13, residue 2784. -/ +theorem bounds_13_2784 : exactInterval 13 2784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2784 : oddCount 2784 13 = 4 ∧ acceleratedOrbit 13 2784 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2784) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2784.1, data_13_2784.2] + +end Collatz.Research.StoppingAtlas.Batch0648 From aaf040ceb044c5e6f97ae7df9a4185578157c5dd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:48 +0530 Subject: [PATCH 0649/1001] proof: certify atlas Batch0649 (13:2785 to 13:2799) --- Collatz/Research/StoppingAtlas/Batch0649.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0649.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0649.lean b/Collatz/Research/StoppingAtlas/Batch0649.lean new file mode 100644 index 00000000..c678ec67 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0649.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0649 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2785. -/ +theorem bounds_13_2785 : exactInterval 13 2785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2785 : oddCount 2785 13 = 9 ∧ acceleratedOrbit 13 2785 = 6698 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2785) = 3 ^ 9 * m + 6698 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2785.1, data_13_2785.2] + +/-- Complete interval computation for depth 13, residue 2786. -/ +theorem bounds_13_2786 : exactInterval 13 2786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2786 : oddCount 2786 13 = 4 ∧ acceleratedOrbit 13 2786 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2786) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2786.1, data_13_2786.2] + +/-- Complete interval computation for depth 13, residue 2787. -/ +theorem bounds_13_2787 : exactInterval 13 2787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2787 : oddCount 2787 13 = 4 ∧ acceleratedOrbit 13 2787 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2787) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2787.1, data_13_2787.2] + +/-- Complete interval computation for depth 13, residue 2788. -/ +theorem bounds_13_2788 : exactInterval 13 2788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2788 : oddCount 2788 13 = 5 ∧ acceleratedOrbit 13 2788 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2788) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2788.1, data_13_2788.2] + +/-- Complete interval computation for depth 13, residue 2789. -/ +theorem bounds_13_2789 : exactInterval 13 2789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2789 : oddCount 2789 13 = 5 ∧ acceleratedOrbit 13 2789 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2789) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2789.1, data_13_2789.2] + +/-- Complete interval computation for depth 13, residue 2790. -/ +theorem bounds_13_2790 : exactInterval 13 2790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2790 : oddCount 2790 13 = 5 ∧ acceleratedOrbit 13 2790 = 83 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2790) = 3 ^ 5 * m + 83 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2790.1, data_13_2790.2] + +/-- Complete interval computation for depth 13, residue 2791. -/ +theorem bounds_13_2791 : exactInterval 13 2791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2791 : oddCount 2791 13 = 10 ∧ acceleratedOrbit 13 2791 = 20128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2791) = 3 ^ 10 * m + 20128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2791.1, data_13_2791.2] + +/-- Complete interval computation for depth 13, residue 2792. -/ +theorem bounds_13_2792 : exactInterval 13 2792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2792 : oddCount 2792 13 = 4 ∧ acceleratedOrbit 13 2792 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2792) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2792.1, data_13_2792.2] + +/-- Complete interval computation for depth 13, residue 2793. -/ +theorem bounds_13_2793 : exactInterval 13 2793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2793 : oddCount 2793 13 = 9 ∧ acceleratedOrbit 13 2793 = 6716 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2793) = 3 ^ 9 * m + 6716 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2793.1, data_13_2793.2] + +/-- Complete interval computation for depth 13, residue 2794. -/ +theorem bounds_13_2794 : exactInterval 13 2794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2794 : oddCount 2794 13 = 4 ∧ acceleratedOrbit 13 2794 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2794) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2794.1, data_13_2794.2] + +/-- Complete interval computation for depth 13, residue 2795. -/ +theorem bounds_13_2795 : exactInterval 13 2795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2795 : oddCount 2795 13 = 9 ∧ acceleratedOrbit 13 2795 = 6722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2795) = 3 ^ 9 * m + 6722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2795.1, data_13_2795.2] + +/-- Complete interval computation for depth 13, residue 2796. -/ +theorem bounds_13_2796 : exactInterval 13 2796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2796 : oddCount 2796 13 = 7 ∧ acceleratedOrbit 13 2796 = 749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2796) = 3 ^ 7 * m + 749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2796.1, data_13_2796.2] + +/-- Complete interval computation for depth 13, residue 2797. -/ +theorem bounds_13_2797 : exactInterval 13 2797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2797 : oddCount 2797 13 = 7 ∧ acceleratedOrbit 13 2797 = 749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2797) = 3 ^ 7 * m + 749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2797.1, data_13_2797.2] + +/-- Complete interval computation for depth 13, residue 2798. -/ +theorem bounds_13_2798 : exactInterval 13 2798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2798 : oddCount 2798 13 = 7 ∧ acceleratedOrbit 13 2798 = 749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2798) = 3 ^ 7 * m + 749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2798.1, data_13_2798.2] + +/-- Complete interval computation for depth 13, residue 2799. -/ +theorem bounds_13_2799 : exactInterval 13 2799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2799 : oddCount 2799 13 = 9 ∧ acceleratedOrbit 13 2799 = 6728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2799) = 3 ^ 9 * m + 6728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2799.1, data_13_2799.2] + +end Collatz.Research.StoppingAtlas.Batch0649 From 7e4d705276e79720925f2c45d09e8ec9ff941b5b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:48 +0530 Subject: [PATCH 0650/1001] proof: certify atlas Batch0650 (13:2800 to 13:2815) --- Collatz/Research/StoppingAtlas/Batch0650.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0650.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0650.lean b/Collatz/Research/StoppingAtlas/Batch0650.lean new file mode 100644 index 00000000..3f767aee --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0650.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0650 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2800. -/ +theorem bounds_13_2800 : exactInterval 13 2800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2800 : oddCount 2800 13 = 6 ∧ acceleratedOrbit 13 2800 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2800) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2800.1, data_13_2800.2] + +/-- Complete interval computation for depth 13, residue 2801. -/ +theorem bounds_13_2801 : exactInterval 13 2801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2801 : oddCount 2801 13 = 4 ∧ acceleratedOrbit 13 2801 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2801) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2801.1, data_13_2801.2] + +/-- Complete interval computation for depth 13, residue 2802. -/ +theorem bounds_13_2802 : exactInterval 13 2802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2802 : oddCount 2802 13 = 9 ∧ acceleratedOrbit 13 2802 = 6743 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2802) = 3 ^ 9 * m + 6743 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2802.1, data_13_2802.2] + +/-- Complete interval computation for depth 13, residue 2803. -/ +theorem bounds_13_2803 : exactInterval 13 2803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2803 : oddCount 2803 13 = 9 ∧ acceleratedOrbit 13 2803 = 6743 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2803) = 3 ^ 9 * m + 6743 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2803.1, data_13_2803.2] + +/-- Complete interval computation for depth 13, residue 2804. -/ +theorem bounds_13_2804 : exactInterval 13 2804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2804 : oddCount 2804 13 = 6 ∧ acceleratedOrbit 13 2804 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2804) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2804.1, data_13_2804.2] + +/-- Complete interval computation for depth 13, residue 2805. -/ +theorem bounds_13_2805 : exactInterval 13 2805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2805 : oddCount 2805 13 = 6 ∧ acceleratedOrbit 13 2805 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2805) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2805.1, data_13_2805.2] + +/-- Complete interval computation for depth 13, residue 2806. -/ +theorem bounds_13_2806 : exactInterval 13 2806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2806 : oddCount 2806 13 = 6 ∧ acceleratedOrbit 13 2806 = 250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2806) = 3 ^ 6 * m + 250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2806.1, data_13_2806.2] + +/-- Complete interval computation for depth 13, residue 2807. -/ +theorem bounds_13_2807 : exactInterval 13 2807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2807 : oddCount 2807 13 = 6 ∧ acceleratedOrbit 13 2807 = 250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2807) = 3 ^ 6 * m + 250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2807.1, data_13_2807.2] + +/-- Complete interval computation for depth 13, residue 2808. -/ +theorem bounds_13_2808 : exactInterval 13 2808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2808 : oddCount 2808 13 = 6 ∧ acceleratedOrbit 13 2808 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2808) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2808.1, data_13_2808.2] + +/-- Complete interval computation for depth 13, residue 2809. -/ +theorem bounds_13_2809 : exactInterval 13 2809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2809 : oddCount 2809 13 = 7 ∧ acceleratedOrbit 13 2809 = 751 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2809) = 3 ^ 7 * m + 751 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2809.1, data_13_2809.2] + +/-- Complete interval computation for depth 13, residue 2810. -/ +theorem bounds_13_2810 : exactInterval 13 2810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2810 : oddCount 2810 13 = 6 ∧ acceleratedOrbit 13 2810 = 251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2810) = 3 ^ 6 * m + 251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2810.1, data_13_2810.2] + +/-- Complete interval computation for depth 13, residue 2811. -/ +theorem bounds_13_2811 : exactInterval 13 2811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2811 : oddCount 2811 13 = 10 ∧ acceleratedOrbit 13 2811 = 20276 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2811) = 3 ^ 10 * m + 20276 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2811.1, data_13_2811.2] + +/-- Complete interval computation for depth 13, residue 2812. -/ +theorem bounds_13_2812 : exactInterval 13 2812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2812 : oddCount 2812 13 = 9 ∧ acceleratedOrbit 13 2812 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2812) = 3 ^ 9 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2812.1, data_13_2812.2] + +/-- Complete interval computation for depth 13, residue 2813. -/ +theorem bounds_13_2813 : exactInterval 13 2813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2813 : oddCount 2813 13 = 9 ∧ acceleratedOrbit 13 2813 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2813) = 3 ^ 9 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2813.1, data_13_2813.2] + +/-- Complete interval computation for depth 13, residue 2814. -/ +theorem bounds_13_2814 : exactInterval 13 2814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2814 : oddCount 2814 13 = 9 ∧ acceleratedOrbit 13 2814 = 6767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2814) = 3 ^ 9 * m + 6767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2814.1, data_13_2814.2] + +/-- Complete interval computation for depth 13, residue 2815. -/ +theorem bounds_13_2815 : exactInterval 13 2815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2815 : oddCount 2815 13 = 9 ∧ acceleratedOrbit 13 2815 = 6766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2815) = 3 ^ 9 * m + 6766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2815.1, data_13_2815.2] + +end Collatz.Research.StoppingAtlas.Batch0650 From b77a3a124d7859ce521047dbe1b086ae56745e23 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:49 +0530 Subject: [PATCH 0651/1001] proof: certify atlas Batch0651 (13:2816 to 13:2830) --- Collatz/Research/StoppingAtlas/Batch0651.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0651.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0651.lean b/Collatz/Research/StoppingAtlas/Batch0651.lean new file mode 100644 index 00000000..5406fb84 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0651.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0651 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2816. -/ +theorem bounds_13_2816 : exactInterval 13 2816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2816 : oddCount 2816 13 = 3 ∧ acceleratedOrbit 13 2816 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2816) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2816.1, data_13_2816.2] + +/-- Complete interval computation for depth 13, residue 2817. -/ +theorem bounds_13_2817 : exactInterval 13 2817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2817 : oddCount 2817 13 = 7 ∧ acceleratedOrbit 13 2817 = 755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2817) = 3 ^ 7 * m + 755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2817.1, data_13_2817.2] + +/-- Complete interval computation for depth 13, residue 2818. -/ +theorem bounds_13_2818 : exactInterval 13 2818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2818 : oddCount 2818 13 = 7 ∧ acceleratedOrbit 13 2818 = 755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2818) = 3 ^ 7 * m + 755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2818.1, data_13_2818.2] + +/-- Complete interval computation for depth 13, residue 2819. -/ +theorem bounds_13_2819 : exactInterval 13 2819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2819 : oddCount 2819 13 = 7 ∧ acceleratedOrbit 13 2819 = 755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2819) = 3 ^ 7 * m + 755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2819.1, data_13_2819.2] + +/-- Complete interval computation for depth 13, residue 2820. -/ +theorem bounds_13_2820 : exactInterval 13 2820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2820 : oddCount 2820 13 = 4 ∧ acceleratedOrbit 13 2820 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2820) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2820.1, data_13_2820.2] + +/-- Complete interval computation for depth 13, residue 2821. -/ +theorem bounds_13_2821 : exactInterval 13 2821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2821 : oddCount 2821 13 = 4 ∧ acceleratedOrbit 13 2821 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2821) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2821.1, data_13_2821.2] + +/-- Complete interval computation for depth 13, residue 2822. -/ +theorem bounds_13_2822 : exactInterval 13 2822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2822 : oddCount 2822 13 = 4 ∧ acceleratedOrbit 13 2822 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2822) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2822.1, data_13_2822.2] + +/-- Complete interval computation for depth 13, residue 2823. -/ +theorem bounds_13_2823 : exactInterval 13 2823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2823 : oddCount 2823 13 = 8 ∧ acceleratedOrbit 13 2823 = 2263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2823) = 3 ^ 8 * m + 2263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2823.1, data_13_2823.2] + +/-- Complete interval computation for depth 13, residue 2824. -/ +theorem bounds_13_2824 : exactInterval 13 2824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2824 : oddCount 2824 13 = 6 ∧ acceleratedOrbit 13 2824 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2824) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2824.1, data_13_2824.2] + +/-- Complete interval computation for depth 13, residue 2825. -/ +theorem bounds_13_2825 : exactInterval 13 2825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2825 : oddCount 2825 13 = 9 ∧ acceleratedOrbit 13 2825 = 6794 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2825) = 3 ^ 9 * m + 6794 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2825.1, data_13_2825.2] + +/-- Complete interval computation for depth 13, residue 2826. -/ +theorem bounds_13_2826 : exactInterval 13 2826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2826 : oddCount 2826 13 = 6 ∧ acceleratedOrbit 13 2826 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2826) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2826.1, data_13_2826.2] + +/-- Complete interval computation for depth 13, residue 2827. -/ +theorem bounds_13_2827 : exactInterval 13 2827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2827 : oddCount 2827 13 = 9 ∧ acceleratedOrbit 13 2827 = 6803 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2827) = 3 ^ 9 * m + 6803 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2827.1, data_13_2827.2] + +/-- Complete interval computation for depth 13, residue 2828. -/ +theorem bounds_13_2828 : exactInterval 13 2828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2828 : oddCount 2828 13 = 6 ∧ acceleratedOrbit 13 2828 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2828) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2828.1, data_13_2828.2] + +/-- Complete interval computation for depth 13, residue 2829. -/ +theorem bounds_13_2829 : exactInterval 13 2829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2829 : oddCount 2829 13 = 6 ∧ acceleratedOrbit 13 2829 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2829) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2829.1, data_13_2829.2] + +/-- Complete interval computation for depth 13, residue 2830. -/ +theorem bounds_13_2830 : exactInterval 13 2830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2830 : oddCount 2830 13 = 4 ∧ acceleratedOrbit 13 2830 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2830) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2830.1, data_13_2830.2] + +end Collatz.Research.StoppingAtlas.Batch0651 From 989f42ab92d4d2a004ae0baf18173d9c984cc0c0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:49 +0530 Subject: [PATCH 0652/1001] proof: certify atlas Batch0652 (13:2831 to 13:2845) --- Collatz/Research/StoppingAtlas/Batch0652.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0652.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0652.lean b/Collatz/Research/StoppingAtlas/Batch0652.lean new file mode 100644 index 00000000..cad50544 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0652.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0652 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2831. -/ +theorem bounds_13_2831 : exactInterval 13 2831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2831 : oddCount 2831 13 = 4 ∧ acceleratedOrbit 13 2831 = 28 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2831) = 3 ^ 4 * m + 28 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2831.1, data_13_2831.2] + +/-- Complete interval computation for depth 13, residue 2832. -/ +theorem bounds_13_2832 : exactInterval 13 2832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2832 : oddCount 2832 13 = 4 ∧ acceleratedOrbit 13 2832 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2832) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2832.1, data_13_2832.2] + +/-- Complete interval computation for depth 13, residue 2833. -/ +theorem bounds_13_2833 : exactInterval 13 2833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2833 : oddCount 2833 13 = 6 ∧ acceleratedOrbit 13 2833 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2833) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2833.1, data_13_2833.2] + +/-- Complete interval computation for depth 13, residue 2834. -/ +theorem bounds_13_2834 : exactInterval 13 2834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2834 : oddCount 2834 13 = 7 ∧ acceleratedOrbit 13 2834 = 758 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2834) = 3 ^ 7 * m + 758 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2834.1, data_13_2834.2] + +/-- Complete interval computation for depth 13, residue 2835. -/ +theorem bounds_13_2835 : exactInterval 13 2835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2835 : oddCount 2835 13 = 7 ∧ acceleratedOrbit 13 2835 = 758 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2835) = 3 ^ 7 * m + 758 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2835.1, data_13_2835.2] + +/-- Complete interval computation for depth 13, residue 2836. -/ +theorem bounds_13_2836 : exactInterval 13 2836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2836 : oddCount 2836 13 = 4 ∧ acceleratedOrbit 13 2836 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2836) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2836.1, data_13_2836.2] + +/-- Complete interval computation for depth 13, residue 2837. -/ +theorem bounds_13_2837 : exactInterval 13 2837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2837 : oddCount 2837 13 = 4 ∧ acceleratedOrbit 13 2837 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2837) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2837.1, data_13_2837.2] + +/-- Complete interval computation for depth 13, residue 2838. -/ +theorem bounds_13_2838 : exactInterval 13 2838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2838 : oddCount 2838 13 = 6 ∧ acceleratedOrbit 13 2838 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2838) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2838.1, data_13_2838.2] + +/-- Complete interval computation for depth 13, residue 2839. -/ +theorem bounds_13_2839 : exactInterval 13 2839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2839 : oddCount 2839 13 = 6 ∧ acceleratedOrbit 13 2839 = 253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2839) = 3 ^ 6 * m + 253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2839.1, data_13_2839.2] + +/-- Complete interval computation for depth 13, residue 2840. -/ +theorem bounds_13_2840 : exactInterval 13 2840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2840 : oddCount 2840 13 = 4 ∧ acceleratedOrbit 13 2840 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2840) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2840.1, data_13_2840.2] + +/-- Complete interval computation for depth 13, residue 2841. -/ +theorem bounds_13_2841 : exactInterval 13 2841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2841 : oddCount 2841 13 = 8 ∧ acceleratedOrbit 13 2841 = 2278 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2841) = 3 ^ 8 * m + 2278 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2841.1, data_13_2841.2] + +/-- Complete interval computation for depth 13, residue 2842. -/ +theorem bounds_13_2842 : exactInterval 13 2842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2842 : oddCount 2842 13 = 4 ∧ acceleratedOrbit 13 2842 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2842) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2842.1, data_13_2842.2] + +/-- Complete interval computation for depth 13, residue 2843. -/ +theorem bounds_13_2843 : exactInterval 13 2843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2843 : oddCount 2843 13 = 10 ∧ acceleratedOrbit 13 2843 = 20503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2843) = 3 ^ 10 * m + 20503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2843.1, data_13_2843.2] + +/-- Complete interval computation for depth 13, residue 2844. -/ +theorem bounds_13_2844 : exactInterval 13 2844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2844 : oddCount 2844 13 = 6 ∧ acceleratedOrbit 13 2844 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2844) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2844.1, data_13_2844.2] + +/-- Complete interval computation for depth 13, residue 2845. -/ +theorem bounds_13_2845 : exactInterval 13 2845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2845 : oddCount 2845 13 = 6 ∧ acceleratedOrbit 13 2845 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2845) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2845.1, data_13_2845.2] + +end Collatz.Research.StoppingAtlas.Batch0652 From 0260b735484ba4c3dee90b868f768f10584ec1b3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:49 +0530 Subject: [PATCH 0653/1001] proof: certify atlas Batch0653 (13:2846 to 13:2861) --- Collatz/Research/StoppingAtlas/Batch0653.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0653.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0653.lean b/Collatz/Research/StoppingAtlas/Batch0653.lean new file mode 100644 index 00000000..4cf9236b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0653.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0653 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2846. -/ +theorem bounds_13_2846 : exactInterval 13 2846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2846 : oddCount 2846 13 = 6 ∧ acceleratedOrbit 13 2846 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2846) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2846.1, data_13_2846.2] + +/-- Complete interval computation for depth 13, residue 2847. -/ +theorem bounds_13_2847 : exactInterval 13 2847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2847 : oddCount 2847 13 = 9 ∧ acceleratedOrbit 13 2847 = 6844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2847) = 3 ^ 9 * m + 6844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2847.1, data_13_2847.2] + +/-- Complete interval computation for depth 13, residue 2848. -/ +theorem bounds_13_2848 : exactInterval 13 2848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2848 : oddCount 2848 13 = 4 ∧ acceleratedOrbit 13 2848 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2848) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2848.1, data_13_2848.2] + +/-- Complete interval computation for depth 13, residue 2849. -/ +theorem bounds_13_2849 : exactInterval 13 2849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2849 : oddCount 2849 13 = 6 ∧ acceleratedOrbit 13 2849 = 254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2849) = 3 ^ 6 * m + 254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2849.1, data_13_2849.2] + +/-- Complete interval computation for depth 13, residue 2850. -/ +theorem bounds_13_2850 : exactInterval 13 2850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2850 : oddCount 2850 13 = 5 ∧ acceleratedOrbit 13 2850 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2850) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2850.1, data_13_2850.2] + +/-- Complete interval computation for depth 13, residue 2851. -/ +theorem bounds_13_2851 : exactInterval 13 2851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2851 : oddCount 2851 13 = 5 ∧ acceleratedOrbit 13 2851 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2851) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2851.1, data_13_2851.2] + +/-- Complete interval computation for depth 13, residue 2852. -/ +theorem bounds_13_2852 : exactInterval 13 2852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2852 : oddCount 2852 13 = 5 ∧ acceleratedOrbit 13 2852 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2852) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2852.1, data_13_2852.2] + +/-- Complete interval computation for depth 13, residue 2853. -/ +theorem bounds_13_2853 : exactInterval 13 2853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2853 : oddCount 2853 13 = 5 ∧ acceleratedOrbit 13 2853 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2853) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2853.1, data_13_2853.2] + +/-- Complete interval computation for depth 13, residue 2854. -/ +theorem bounds_13_2854 : exactInterval 13 2854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2854 : oddCount 2854 13 = 5 ∧ acceleratedOrbit 13 2854 = 85 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2854) = 3 ^ 5 * m + 85 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2854.1, data_13_2854.2] + +/-- Complete interval computation for depth 13, residue 2855. -/ +theorem bounds_13_2855 : exactInterval 13 2855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2855 : oddCount 2855 13 = 8 ∧ acceleratedOrbit 13 2855 = 2288 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2855) = 3 ^ 8 * m + 2288 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2855.1, data_13_2855.2] + +/-- Complete interval computation for depth 13, residue 2856. -/ +theorem bounds_13_2856 : exactInterval 13 2856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2856 : oddCount 2856 13 = 4 ∧ acceleratedOrbit 13 2856 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2856) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2856.1, data_13_2856.2] + +/-- Complete interval computation for depth 13, residue 2857. -/ +theorem bounds_13_2857 : exactInterval 13 2857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2857 : oddCount 2857 13 = 8 ∧ acceleratedOrbit 13 2857 = 2290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2857) = 3 ^ 8 * m + 2290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2857.1, data_13_2857.2] + +/-- Complete interval computation for depth 13, residue 2858. -/ +theorem bounds_13_2858 : exactInterval 13 2858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2858 : oddCount 2858 13 = 4 ∧ acceleratedOrbit 13 2858 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2858) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2858.1, data_13_2858.2] + +/-- Complete interval computation for depth 13, residue 2859. -/ +theorem bounds_13_2859 : exactInterval 13 2859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2859 : oddCount 2859 13 = 8 ∧ acceleratedOrbit 13 2859 = 2294 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2859) = 3 ^ 8 * m + 2294 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2859.1, data_13_2859.2] + +/-- Complete interval computation for depth 13, residue 2860. -/ +theorem bounds_13_2860 : exactInterval 13 2860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2860 : oddCount 2860 13 = 6 ∧ acceleratedOrbit 13 2860 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2860) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2860.1, data_13_2860.2] + +/-- Complete interval computation for depth 13, residue 2861. -/ +theorem bounds_13_2861 : exactInterval 13 2861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2861 : oddCount 2861 13 = 6 ∧ acceleratedOrbit 13 2861 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2861) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2861.1, data_13_2861.2] + +end Collatz.Research.StoppingAtlas.Batch0653 From a171ff217ee14b20c838cf48fef60f135221cd3d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:49 +0530 Subject: [PATCH 0654/1001] proof: certify atlas Batch0654 (13:2862 to 13:2876) --- Collatz/Research/StoppingAtlas/Batch0654.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0654.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0654.lean b/Collatz/Research/StoppingAtlas/Batch0654.lean new file mode 100644 index 00000000..7d935ffe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0654.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0654 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2862. -/ +theorem bounds_13_2862 : exactInterval 13 2862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2862 : oddCount 2862 13 = 6 ∧ acceleratedOrbit 13 2862 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2862) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2862.1, data_13_2862.2] + +/-- Complete interval computation for depth 13, residue 2863. -/ +theorem bounds_13_2863 : exactInterval 13 2863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2863 : oddCount 2863 13 = 9 ∧ acceleratedOrbit 13 2863 = 6884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2863) = 3 ^ 9 * m + 6884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2863.1, data_13_2863.2] + +/-- Complete interval computation for depth 13, residue 2864. -/ +theorem bounds_13_2864 : exactInterval 13 2864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2864 : oddCount 2864 13 = 4 ∧ acceleratedOrbit 13 2864 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2864) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2864.1, data_13_2864.2] + +/-- Complete interval computation for depth 13, residue 2865. -/ +theorem bounds_13_2865 : exactInterval 13 2865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2865 : oddCount 2865 13 = 6 ∧ acceleratedOrbit 13 2865 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2865) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2865.1, data_13_2865.2] + +/-- Complete interval computation for depth 13, residue 2866. -/ +theorem bounds_13_2866 : exactInterval 13 2866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2866 : oddCount 2866 13 = 6 ∧ acceleratedOrbit 13 2866 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2866) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2866.1, data_13_2866.2] + +/-- Complete interval computation for depth 13, residue 2867. -/ +theorem bounds_13_2867 : exactInterval 13 2867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2867 : oddCount 2867 13 = 6 ∧ acceleratedOrbit 13 2867 = 256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2867) = 3 ^ 6 * m + 256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2867.1, data_13_2867.2] + +/-- Complete interval computation for depth 13, residue 2868. -/ +theorem bounds_13_2868 : exactInterval 13 2868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2868 : oddCount 2868 13 = 4 ∧ acceleratedOrbit 13 2868 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2868) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2868.1, data_13_2868.2] + +/-- Complete interval computation for depth 13, residue 2869. -/ +theorem bounds_13_2869 : exactInterval 13 2869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2869 : oddCount 2869 13 = 4 ∧ acceleratedOrbit 13 2869 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2869) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2869.1, data_13_2869.2] + +/-- Complete interval computation for depth 13, residue 2870. -/ +theorem bounds_13_2870 : exactInterval 13 2870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2870 : oddCount 2870 13 = 7 ∧ acceleratedOrbit 13 2870 = 767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2870) = 3 ^ 7 * m + 767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2870.1, data_13_2870.2] + +/-- Complete interval computation for depth 13, residue 2871. -/ +theorem bounds_13_2871 : exactInterval 13 2871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2871 : oddCount 2871 13 = 7 ∧ acceleratedOrbit 13 2871 = 767 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2871) = 3 ^ 7 * m + 767 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2871.1, data_13_2871.2] + +/-- Complete interval computation for depth 13, residue 2872. -/ +theorem bounds_13_2872 : exactInterval 13 2872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2872 : oddCount 2872 13 = 8 ∧ acceleratedOrbit 13 2872 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2872) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2872.1, data_13_2872.2] + +/-- Complete interval computation for depth 13, residue 2873. -/ +theorem bounds_13_2873 : exactInterval 13 2873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2873 : oddCount 2873 13 = 9 ∧ acceleratedOrbit 13 2873 = 6911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2873) = 3 ^ 9 * m + 6911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2873.1, data_13_2873.2] + +/-- Complete interval computation for depth 13, residue 2874. -/ +theorem bounds_13_2874 : exactInterval 13 2874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2874 : oddCount 2874 13 = 8 ∧ acceleratedOrbit 13 2874 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2874) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2874.1, data_13_2874.2] + +/-- Complete interval computation for depth 13, residue 2875. -/ +theorem bounds_13_2875 : exactInterval 13 2875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2875 : oddCount 2875 13 = 7 ∧ acceleratedOrbit 13 2875 = 769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2875) = 3 ^ 7 * m + 769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2875.1, data_13_2875.2] + +/-- Complete interval computation for depth 13, residue 2876. -/ +theorem bounds_13_2876 : exactInterval 13 2876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2876 : oddCount 2876 13 = 8 ∧ acceleratedOrbit 13 2876 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2876) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2876.1, data_13_2876.2] + +end Collatz.Research.StoppingAtlas.Batch0654 From 139b280a2e87cfeb688e035a199799f147133067 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:50 +0530 Subject: [PATCH 0655/1001] proof: certify atlas Batch0655 (13:2877 to 13:2891) --- Collatz/Research/StoppingAtlas/Batch0655.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0655.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0655.lean b/Collatz/Research/StoppingAtlas/Batch0655.lean new file mode 100644 index 00000000..8bc6c3ea --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0655.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0655 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2877. -/ +theorem bounds_13_2877 : exactInterval 13 2877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2877 : oddCount 2877 13 = 8 ∧ acceleratedOrbit 13 2877 = 2308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2877) = 3 ^ 8 * m + 2308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2877.1, data_13_2877.2] + +/-- Complete interval computation for depth 13, residue 2878. -/ +theorem bounds_13_2878 : exactInterval 13 2878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2878 : oddCount 2878 13 = 10 ∧ acceleratedOrbit 13 2878 = 20762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2878) = 3 ^ 10 * m + 20762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2878.1, data_13_2878.2] + +/-- Complete interval computation for depth 13, residue 2879. -/ +theorem bounds_13_2879 : exactInterval 13 2879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2879 : oddCount 2879 13 = 10 ∧ acceleratedOrbit 13 2879 = 20762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2879) = 3 ^ 10 * m + 20762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2879.1, data_13_2879.2] + +/-- Complete interval computation for depth 13, residue 2880. -/ +theorem bounds_13_2880 : exactInterval 13 2880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2880 : oddCount 2880 13 = 3 ∧ acceleratedOrbit 13 2880 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2880) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2880.1, data_13_2880.2] + +/-- Complete interval computation for depth 13, residue 2881. -/ +theorem bounds_13_2881 : exactInterval 13 2881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2881 : oddCount 2881 13 = 4 ∧ acceleratedOrbit 13 2881 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2881) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2881.1, data_13_2881.2] + +/-- Complete interval computation for depth 13, residue 2882. -/ +theorem bounds_13_2882 : exactInterval 13 2882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2882 : oddCount 2882 13 = 6 ∧ acceleratedOrbit 13 2882 = 257 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2882) = 3 ^ 6 * m + 257 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2882.1, data_13_2882.2] + +/-- Complete interval computation for depth 13, residue 2883. -/ +theorem bounds_13_2883 : exactInterval 13 2883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2883 : oddCount 2883 13 = 6 ∧ acceleratedOrbit 13 2883 = 257 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2883) = 3 ^ 6 * m + 257 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2883.1, data_13_2883.2] + +/-- Complete interval computation for depth 13, residue 2884. -/ +theorem bounds_13_2884 : exactInterval 13 2884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2884 : oddCount 2884 13 = 5 ∧ acceleratedOrbit 13 2884 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2884) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2884.1, data_13_2884.2] + +/-- Complete interval computation for depth 13, residue 2885. -/ +theorem bounds_13_2885 : exactInterval 13 2885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2885 : oddCount 2885 13 = 5 ∧ acceleratedOrbit 13 2885 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2885) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2885.1, data_13_2885.2] + +/-- Complete interval computation for depth 13, residue 2886. -/ +theorem bounds_13_2886 : exactInterval 13 2886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2886 : oddCount 2886 13 = 5 ∧ acceleratedOrbit 13 2886 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2886) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2886.1, data_13_2886.2] + +/-- Complete interval computation for depth 13, residue 2887. -/ +theorem bounds_13_2887 : exactInterval 13 2887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2887 : oddCount 2887 13 = 9 ∧ acceleratedOrbit 13 2887 = 6941 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2887) = 3 ^ 9 * m + 6941 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2887.1, data_13_2887.2] + +/-- Complete interval computation for depth 13, residue 2888. -/ +theorem bounds_13_2888 : exactInterval 13 2888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2888 : oddCount 2888 13 = 5 ∧ acceleratedOrbit 13 2888 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2888) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2888.1, data_13_2888.2] + +/-- Complete interval computation for depth 13, residue 2889. -/ +theorem bounds_13_2889 : exactInterval 13 2889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2889 : oddCount 2889 13 = 7 ∧ acceleratedOrbit 13 2889 = 773 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2889) = 3 ^ 7 * m + 773 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2889.1, data_13_2889.2] + +/-- Complete interval computation for depth 13, residue 2890. -/ +theorem bounds_13_2890 : exactInterval 13 2890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2890 : oddCount 2890 13 = 5 ∧ acceleratedOrbit 13 2890 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2890) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2890.1, data_13_2890.2] + +/-- Complete interval computation for depth 13, residue 2891. -/ +theorem bounds_13_2891 : exactInterval 13 2891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2891 : oddCount 2891 13 = 5 ∧ acceleratedOrbit 13 2891 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2891) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2891.1, data_13_2891.2] + +end Collatz.Research.StoppingAtlas.Batch0655 From 3ffe424963a3b79a3f75e47511bba5334bf5f065 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:50 +0530 Subject: [PATCH 0656/1001] proof: certify atlas Batch0656 (13:2892 to 13:2907) --- Collatz/Research/StoppingAtlas/Batch0656.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0656.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0656.lean b/Collatz/Research/StoppingAtlas/Batch0656.lean new file mode 100644 index 00000000..96693fb0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0656.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0656 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2892. -/ +theorem bounds_13_2892 : exactInterval 13 2892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2892 : oddCount 2892 13 = 5 ∧ acceleratedOrbit 13 2892 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2892) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2892.1, data_13_2892.2] + +/-- Complete interval computation for depth 13, residue 2893. -/ +theorem bounds_13_2893 : exactInterval 13 2893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2893 : oddCount 2893 13 = 5 ∧ acceleratedOrbit 13 2893 = 86 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2893) = 3 ^ 5 * m + 86 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2893.1, data_13_2893.2] + +/-- Complete interval computation for depth 13, residue 2894. -/ +theorem bounds_13_2894 : exactInterval 13 2894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2894 : oddCount 2894 13 = 8 ∧ acceleratedOrbit 13 2894 = 2321 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2894) = 3 ^ 8 * m + 2321 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2894.1, data_13_2894.2] + +/-- Complete interval computation for depth 13, residue 2895. -/ +theorem bounds_13_2895 : exactInterval 13 2895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2895 : oddCount 2895 13 = 8 ∧ acceleratedOrbit 13 2895 = 2321 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2895) = 3 ^ 8 * m + 2321 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2895.1, data_13_2895.2] + +/-- Complete interval computation for depth 13, residue 2896. -/ +theorem bounds_13_2896 : exactInterval 13 2896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2896 : oddCount 2896 13 = 3 ∧ acceleratedOrbit 13 2896 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2896) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2896.1, data_13_2896.2] + +/-- Complete interval computation for depth 13, residue 2897. -/ +theorem bounds_13_2897 : exactInterval 13 2897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2897 : oddCount 2897 13 = 8 ∧ acceleratedOrbit 13 2897 = 2324 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2897) = 3 ^ 8 * m + 2324 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2897.1, data_13_2897.2] + +/-- Complete interval computation for depth 13, residue 2898. -/ +theorem bounds_13_2898 : exactInterval 13 2898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2898 : oddCount 2898 13 = 8 ∧ acceleratedOrbit 13 2898 = 2324 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2898) = 3 ^ 8 * m + 2324 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2898.1, data_13_2898.2] + +/-- Complete interval computation for depth 13, residue 2899. -/ +theorem bounds_13_2899 : exactInterval 13 2899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2899 : oddCount 2899 13 = 8 ∧ acceleratedOrbit 13 2899 = 2324 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2899) = 3 ^ 8 * m + 2324 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2899.1, data_13_2899.2] + +/-- Complete interval computation for depth 13, residue 2900. -/ +theorem bounds_13_2900 : exactInterval 13 2900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2900 : oddCount 2900 13 = 3 ∧ acceleratedOrbit 13 2900 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2900) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2900.1, data_13_2900.2] + +/-- Complete interval computation for depth 13, residue 2901. -/ +theorem bounds_13_2901 : exactInterval 13 2901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2901 : oddCount 2901 13 = 3 ∧ acceleratedOrbit 13 2901 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2901) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2901.1, data_13_2901.2] + +/-- Complete interval computation for depth 13, residue 2902. -/ +theorem bounds_13_2902 : exactInterval 13 2902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2902 : oddCount 2902 13 = 7 ∧ acceleratedOrbit 13 2902 = 776 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2902) = 3 ^ 7 * m + 776 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2902.1, data_13_2902.2] + +/-- Complete interval computation for depth 13, residue 2903. -/ +theorem bounds_13_2903 : exactInterval 13 2903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2903 : oddCount 2903 13 = 7 ∧ acceleratedOrbit 13 2903 = 776 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2903) = 3 ^ 7 * m + 776 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2903.1, data_13_2903.2] + +/-- Complete interval computation for depth 13, residue 2904. -/ +theorem bounds_13_2904 : exactInterval 13 2904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2904 : oddCount 2904 13 = 6 ∧ acceleratedOrbit 13 2904 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2904) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2904.1, data_13_2904.2] + +/-- Complete interval computation for depth 13, residue 2905. -/ +theorem bounds_13_2905 : exactInterval 13 2905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2905 : oddCount 2905 13 = 6 ∧ acceleratedOrbit 13 2905 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2905) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2905.1, data_13_2905.2] + +/-- Complete interval computation for depth 13, residue 2906. -/ +theorem bounds_13_2906 : exactInterval 13 2906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2906 : oddCount 2906 13 = 6 ∧ acceleratedOrbit 13 2906 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2906) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2906.1, data_13_2906.2] + +/-- Complete interval computation for depth 13, residue 2907. -/ +theorem bounds_13_2907 : exactInterval 13 2907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2907 : oddCount 2907 13 = 8 ∧ acceleratedOrbit 13 2907 = 2330 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2907) = 3 ^ 8 * m + 2330 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2907.1, data_13_2907.2] + +end Collatz.Research.StoppingAtlas.Batch0656 From 3cf4ab4f71e55a9c420fd6a671c081db5ebfe2f1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:52 +0530 Subject: [PATCH 0657/1001] proof: certify atlas Batch0657 (13:2908 to 13:2922) --- Collatz/Research/StoppingAtlas/Batch0657.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0657.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0657.lean b/Collatz/Research/StoppingAtlas/Batch0657.lean new file mode 100644 index 00000000..81cfb72b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0657.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0657 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2908. -/ +theorem bounds_13_2908 : exactInterval 13 2908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2908 : oddCount 2908 13 = 6 ∧ acceleratedOrbit 13 2908 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2908) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2908.1, data_13_2908.2] + +/-- Complete interval computation for depth 13, residue 2909. -/ +theorem bounds_13_2909 : exactInterval 13 2909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2909 : oddCount 2909 13 = 6 ∧ acceleratedOrbit 13 2909 = 260 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2909) = 3 ^ 6 * m + 260 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2909.1, data_13_2909.2] + +/-- Complete interval computation for depth 13, residue 2910. -/ +theorem bounds_13_2910 : exactInterval 13 2910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2910 : oddCount 2910 13 = 7 ∧ acceleratedOrbit 13 2910 = 778 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2910) = 3 ^ 7 * m + 778 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2910.1, data_13_2910.2] + +/-- Complete interval computation for depth 13, residue 2911. -/ +theorem bounds_13_2911 : exactInterval 13 2911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2911 : oddCount 2911 13 = 7 ∧ acceleratedOrbit 13 2911 = 778 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2911) = 3 ^ 7 * m + 778 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2911.1, data_13_2911.2] + +/-- Complete interval computation for depth 13, residue 2912. -/ +theorem bounds_13_2912 : exactInterval 13 2912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2912 : oddCount 2912 13 = 6 ∧ acceleratedOrbit 13 2912 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2912) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2912.1, data_13_2912.2] + +/-- Complete interval computation for depth 13, residue 2913. -/ +theorem bounds_13_2913 : exactInterval 13 2913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2913 : oddCount 2913 13 = 9 ∧ acceleratedOrbit 13 2913 = 7006 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2913) = 3 ^ 9 * m + 7006 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2913.1, data_13_2913.2] + +/-- Complete interval computation for depth 13, residue 2914. -/ +theorem bounds_13_2914 : exactInterval 13 2914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2914 : oddCount 2914 13 = 4 ∧ acceleratedOrbit 13 2914 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2914) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2914.1, data_13_2914.2] + +/-- Complete interval computation for depth 13, residue 2915. -/ +theorem bounds_13_2915 : exactInterval 13 2915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2915 : oddCount 2915 13 = 4 ∧ acceleratedOrbit 13 2915 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2915) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2915.1, data_13_2915.2] + +/-- Complete interval computation for depth 13, residue 2916. -/ +theorem bounds_13_2916 : exactInterval 13 2916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2916 : oddCount 2916 13 = 4 ∧ acceleratedOrbit 13 2916 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2916) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2916.1, data_13_2916.2] + +/-- Complete interval computation for depth 13, residue 2917. -/ +theorem bounds_13_2917 : exactInterval 13 2917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2917 : oddCount 2917 13 = 4 ∧ acceleratedOrbit 13 2917 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2917) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2917.1, data_13_2917.2] + +/-- Complete interval computation for depth 13, residue 2918. -/ +theorem bounds_13_2918 : exactInterval 13 2918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2918 : oddCount 2918 13 = 4 ∧ acceleratedOrbit 13 2918 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2918) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2918.1, data_13_2918.2] + +/-- Complete interval computation for depth 13, residue 2919. -/ +theorem bounds_13_2919 : exactInterval 13 2919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2919 : oddCount 2919 13 = 10 ∧ acceleratedOrbit 13 2919 = 21050 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2919) = 3 ^ 10 * m + 21050 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2919.1, data_13_2919.2] + +/-- Complete interval computation for depth 13, residue 2920. -/ +theorem bounds_13_2920 : exactInterval 13 2920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2920 : oddCount 2920 13 = 6 ∧ acceleratedOrbit 13 2920 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2920) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2920.1, data_13_2920.2] + +/-- Complete interval computation for depth 13, residue 2921. -/ +theorem bounds_13_2921 : exactInterval 13 2921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2921 : oddCount 2921 13 = 8 ∧ acceleratedOrbit 13 2921 = 2342 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2921) = 3 ^ 8 * m + 2342 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2921.1, data_13_2921.2] + +/-- Complete interval computation for depth 13, residue 2922. -/ +theorem bounds_13_2922 : exactInterval 13 2922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2922 : oddCount 2922 13 = 6 ∧ acceleratedOrbit 13 2922 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2922) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2922.1, data_13_2922.2] + +end Collatz.Research.StoppingAtlas.Batch0657 From 3737d44880d7e0396fb9af9fcaa5f4770cf44d13 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:52 +0530 Subject: [PATCH 0658/1001] proof: certify atlas Batch0658 (13:2923 to 13:2937) --- Collatz/Research/StoppingAtlas/Batch0658.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0658.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0658.lean b/Collatz/Research/StoppingAtlas/Batch0658.lean new file mode 100644 index 00000000..e4aeec09 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0658.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0658 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2923. -/ +theorem bounds_13_2923 : exactInterval 13 2923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2923 : oddCount 2923 13 = 7 ∧ acceleratedOrbit 13 2923 = 782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2923) = 3 ^ 7 * m + 782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2923.1, data_13_2923.2] + +/-- Complete interval computation for depth 13, residue 2924. -/ +theorem bounds_13_2924 : exactInterval 13 2924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2924 : oddCount 2924 13 = 8 ∧ acceleratedOrbit 13 2924 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2924) = 3 ^ 8 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2924.1, data_13_2924.2] + +/-- Complete interval computation for depth 13, residue 2925. -/ +theorem bounds_13_2925 : exactInterval 13 2925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2925 : oddCount 2925 13 = 8 ∧ acceleratedOrbit 13 2925 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2925) = 3 ^ 8 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2925.1, data_13_2925.2] + +/-- Complete interval computation for depth 13, residue 2926. -/ +theorem bounds_13_2926 : exactInterval 13 2926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2926 : oddCount 2926 13 = 8 ∧ acceleratedOrbit 13 2926 = 2348 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2926) = 3 ^ 8 * m + 2348 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2926.1, data_13_2926.2] + +/-- Complete interval computation for depth 13, residue 2927. -/ +theorem bounds_13_2927 : exactInterval 13 2927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2927 : oddCount 2927 13 = 9 ∧ acceleratedOrbit 13 2927 = 7037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2927) = 3 ^ 9 * m + 7037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2927.1, data_13_2927.2] + +/-- Complete interval computation for depth 13, residue 2928. -/ +theorem bounds_13_2928 : exactInterval 13 2928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2928 : oddCount 2928 13 = 6 ∧ acceleratedOrbit 13 2928 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2928) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2928.1, data_13_2928.2] + +/-- Complete interval computation for depth 13, residue 2929. -/ +theorem bounds_13_2929 : exactInterval 13 2929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2929 : oddCount 2929 13 = 6 ∧ acceleratedOrbit 13 2929 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2929) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2929.1, data_13_2929.2] + +/-- Complete interval computation for depth 13, residue 2930. -/ +theorem bounds_13_2930 : exactInterval 13 2930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2930 : oddCount 2930 13 = 4 ∧ acceleratedOrbit 13 2930 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2930) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2930.1, data_13_2930.2] + +/-- Complete interval computation for depth 13, residue 2931. -/ +theorem bounds_13_2931 : exactInterval 13 2931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2931 : oddCount 2931 13 = 4 ∧ acceleratedOrbit 13 2931 = 29 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2931) = 3 ^ 4 * m + 29 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2931.1, data_13_2931.2] + +/-- Complete interval computation for depth 13, residue 2932. -/ +theorem bounds_13_2932 : exactInterval 13 2932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2932 : oddCount 2932 13 = 6 ∧ acceleratedOrbit 13 2932 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2932) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2932.1, data_13_2932.2] + +/-- Complete interval computation for depth 13, residue 2933. -/ +theorem bounds_13_2933 : exactInterval 13 2933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2933 : oddCount 2933 13 = 6 ∧ acceleratedOrbit 13 2933 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2933) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2933.1, data_13_2933.2] + +/-- Complete interval computation for depth 13, residue 2934. -/ +theorem bounds_13_2934 : exactInterval 13 2934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2934 : oddCount 2934 13 = 7 ∧ acceleratedOrbit 13 2934 = 785 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2934) = 3 ^ 7 * m + 785 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2934.1, data_13_2934.2] + +/-- Complete interval computation for depth 13, residue 2935. -/ +theorem bounds_13_2935 : exactInterval 13 2935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2935 : oddCount 2935 13 = 7 ∧ acceleratedOrbit 13 2935 = 785 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2935) = 3 ^ 7 * m + 785 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2935.1, data_13_2935.2] + +/-- Complete interval computation for depth 13, residue 2936. -/ +theorem bounds_13_2936 : exactInterval 13 2936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2936 : oddCount 2936 13 = 6 ∧ acceleratedOrbit 13 2936 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2936) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2936.1, data_13_2936.2] + +/-- Complete interval computation for depth 13, residue 2937. -/ +theorem bounds_13_2937 : exactInterval 13 2937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2937 : oddCount 2937 13 = 8 ∧ acceleratedOrbit 13 2937 = 2354 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2937) = 3 ^ 8 * m + 2354 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2937.1, data_13_2937.2] + +end Collatz.Research.StoppingAtlas.Batch0658 From a513ad525df4f0a7078475f38326876831d1df20 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:53 +0530 Subject: [PATCH 0659/1001] proof: certify atlas Batch0659 (13:2938 to 13:2953) --- Collatz/Research/StoppingAtlas/Batch0659.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0659.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0659.lean b/Collatz/Research/StoppingAtlas/Batch0659.lean new file mode 100644 index 00000000..1bd99f19 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0659.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0659 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2938. -/ +theorem bounds_13_2938 : exactInterval 13 2938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2938 : oddCount 2938 13 = 6 ∧ acceleratedOrbit 13 2938 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2938) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2938.1, data_13_2938.2] + +/-- Complete interval computation for depth 13, residue 2939. -/ +theorem bounds_13_2939 : exactInterval 13 2939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2939 : oddCount 2939 13 = 9 ∧ acceleratedOrbit 13 2939 = 7067 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2939) = 3 ^ 9 * m + 7067 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2939.1, data_13_2939.2] + +/-- Complete interval computation for depth 13, residue 2940. -/ +theorem bounds_13_2940 : exactInterval 13 2940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2940 : oddCount 2940 13 = 6 ∧ acceleratedOrbit 13 2940 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2940) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2940.1, data_13_2940.2] + +/-- Complete interval computation for depth 13, residue 2941. -/ +theorem bounds_13_2941 : exactInterval 13 2941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2941 : oddCount 2941 13 = 6 ∧ acceleratedOrbit 13 2941 = 262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2941) = 3 ^ 6 * m + 262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2941.1, data_13_2941.2] + +/-- Complete interval computation for depth 13, residue 2942. -/ +theorem bounds_13_2942 : exactInterval 13 2942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2942 : oddCount 2942 13 = 11 ∧ acceleratedOrbit 13 2942 = 63665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2942) = 3 ^ 11 * m + 63665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2942.1, data_13_2942.2] + +/-- Complete interval computation for depth 13, residue 2943. -/ +theorem bounds_13_2943 : exactInterval 13 2943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2943 : oddCount 2943 13 = 11 ∧ acceleratedOrbit 13 2943 = 63665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2943) = 3 ^ 11 * m + 63665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2943.1, data_13_2943.2] + +/-- Complete interval computation for depth 13, residue 2944. -/ +theorem bounds_13_2944 : exactInterval 13 2944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2944 : oddCount 2944 13 = 3 ∧ acceleratedOrbit 13 2944 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2944) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2944.1, data_13_2944.2] + +/-- Complete interval computation for depth 13, residue 2945. -/ +theorem bounds_13_2945 : exactInterval 13 2945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2945 : oddCount 2945 13 = 8 ∧ acceleratedOrbit 13 2945 = 2362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2945) = 3 ^ 8 * m + 2362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2945.1, data_13_2945.2] + +/-- Complete interval computation for depth 13, residue 2946. -/ +theorem bounds_13_2946 : exactInterval 13 2946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2946 : oddCount 2946 13 = 6 ∧ acceleratedOrbit 13 2946 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2946) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2946.1, data_13_2946.2] + +/-- Complete interval computation for depth 13, residue 2947. -/ +theorem bounds_13_2947 : exactInterval 13 2947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2947 : oddCount 2947 13 = 6 ∧ acceleratedOrbit 13 2947 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2947) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2947.1, data_13_2947.2] + +/-- Complete interval computation for depth 13, residue 2948. -/ +theorem bounds_13_2948 : exactInterval 13 2948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2948 : oddCount 2948 13 = 8 ∧ acceleratedOrbit 13 2948 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2948) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2948.1, data_13_2948.2] + +/-- Complete interval computation for depth 13, residue 2949. -/ +theorem bounds_13_2949 : exactInterval 13 2949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2949 : oddCount 2949 13 = 8 ∧ acceleratedOrbit 13 2949 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2949) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2949.1, data_13_2949.2] + +/-- Complete interval computation for depth 13, residue 2950. -/ +theorem bounds_13_2950 : exactInterval 13 2950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2950 : oddCount 2950 13 = 8 ∧ acceleratedOrbit 13 2950 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2950) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2950.1, data_13_2950.2] + +/-- Complete interval computation for depth 13, residue 2951. -/ +theorem bounds_13_2951 : exactInterval 13 2951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2951 : oddCount 2951 13 = 6 ∧ acceleratedOrbit 13 2951 = 263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2951) = 3 ^ 6 * m + 263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2951.1, data_13_2951.2] + +/-- Complete interval computation for depth 13, residue 2952. -/ +theorem bounds_13_2952 : exactInterval 13 2952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2952 : oddCount 2952 13 = 3 ∧ acceleratedOrbit 13 2952 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2952) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2952.1, data_13_2952.2] + +/-- Complete interval computation for depth 13, residue 2953. -/ +theorem bounds_13_2953 : exactInterval 13 2953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2953 : oddCount 2953 13 = 10 ∧ acceleratedOrbit 13 2953 = 21302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2953) = 3 ^ 10 * m + 21302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2953.1, data_13_2953.2] + +end Collatz.Research.StoppingAtlas.Batch0659 From db4de2c2a8d55d7c2d09819e29c1ab3ef2b68691 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:54 +0530 Subject: [PATCH 0660/1001] proof: certify atlas Batch0660 (13:2954 to 13:2968) --- Collatz/Research/StoppingAtlas/Batch0660.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0660.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0660.lean b/Collatz/Research/StoppingAtlas/Batch0660.lean new file mode 100644 index 00000000..e818cd85 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0660.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0660 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2954. -/ +theorem bounds_13_2954 : exactInterval 13 2954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2954 : oddCount 2954 13 = 3 ∧ acceleratedOrbit 13 2954 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2954) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2954.1, data_13_2954.2] + +/-- Complete interval computation for depth 13, residue 2955. -/ +theorem bounds_13_2955 : exactInterval 13 2955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2955 : oddCount 2955 13 = 8 ∧ acceleratedOrbit 13 2955 = 2369 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2955) = 3 ^ 8 * m + 2369 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2955.1, data_13_2955.2] + +/-- Complete interval computation for depth 13, residue 2956. -/ +theorem bounds_13_2956 : exactInterval 13 2956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2956 : oddCount 2956 13 = 3 ∧ acceleratedOrbit 13 2956 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2956) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2956.1, data_13_2956.2] + +/-- Complete interval computation for depth 13, residue 2957. -/ +theorem bounds_13_2957 : exactInterval 13 2957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2957 : oddCount 2957 13 = 3 ∧ acceleratedOrbit 13 2957 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2957) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2957.1, data_13_2957.2] + +/-- Complete interval computation for depth 13, residue 2958. -/ +theorem bounds_13_2958 : exactInterval 13 2958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2958 : oddCount 2958 13 = 7 ∧ acceleratedOrbit 13 2958 = 791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2958) = 3 ^ 7 * m + 791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2958.1, data_13_2958.2] + +/-- Complete interval computation for depth 13, residue 2959. -/ +theorem bounds_13_2959 : exactInterval 13 2959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2959 : oddCount 2959 13 = 7 ∧ acceleratedOrbit 13 2959 = 791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2959) = 3 ^ 7 * m + 791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2959.1, data_13_2959.2] + +/-- Complete interval computation for depth 13, residue 2960. -/ +theorem bounds_13_2960 : exactInterval 13 2960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2960 : oddCount 2960 13 = 5 ∧ acceleratedOrbit 13 2960 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2960) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2960.1, data_13_2960.2] + +/-- Complete interval computation for depth 13, residue 2961. -/ +theorem bounds_13_2961 : exactInterval 13 2961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2961 : oddCount 2961 13 = 5 ∧ acceleratedOrbit 13 2961 = 88 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2961) = 3 ^ 5 * m + 88 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2961.1, data_13_2961.2] + +/-- Complete interval computation for depth 13, residue 2962. -/ +theorem bounds_13_2962 : exactInterval 13 2962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2962 : oddCount 2962 13 = 5 ∧ acceleratedOrbit 13 2962 = 88 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2962) = 3 ^ 5 * m + 88 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2962.1, data_13_2962.2] + +/-- Complete interval computation for depth 13, residue 2963. -/ +theorem bounds_13_2963 : exactInterval 13 2963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2963 : oddCount 2963 13 = 5 ∧ acceleratedOrbit 13 2963 = 88 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2963) = 3 ^ 5 * m + 88 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2963.1, data_13_2963.2] + +/-- Complete interval computation for depth 13, residue 2964. -/ +theorem bounds_13_2964 : exactInterval 13 2964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2964 : oddCount 2964 13 = 5 ∧ acceleratedOrbit 13 2964 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2964) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2964.1, data_13_2964.2] + +/-- Complete interval computation for depth 13, residue 2965. -/ +theorem bounds_13_2965 : exactInterval 13 2965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2965 : oddCount 2965 13 = 5 ∧ acceleratedOrbit 13 2965 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2965) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2965.1, data_13_2965.2] + +/-- Complete interval computation for depth 13, residue 2966. -/ +theorem bounds_13_2966 : exactInterval 13 2966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2966 : oddCount 2966 13 = 6 ∧ acceleratedOrbit 13 2966 = 265 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2966) = 3 ^ 6 * m + 265 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2966.1, data_13_2966.2] + +/-- Complete interval computation for depth 13, residue 2967. -/ +theorem bounds_13_2967 : exactInterval 13 2967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2967) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2967 : oddCount 2967 13 = 6 ∧ acceleratedOrbit 13 2967 = 265 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2967) = 3 ^ 6 * m + 265 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2967.1, data_13_2967.2] + +/-- Complete interval computation for depth 13, residue 2968. -/ +theorem bounds_13_2968 : exactInterval 13 2968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2968 : oddCount 2968 13 = 5 ∧ acceleratedOrbit 13 2968 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2968) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2968.1, data_13_2968.2] + +end Collatz.Research.StoppingAtlas.Batch0660 From 08c2253c28b48b89ec8110f25e6971195ca6ac4b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:58 +0530 Subject: [PATCH 0661/1001] proof: certify atlas Batch0661 (13:2969 to 13:2983) --- Collatz/Research/StoppingAtlas/Batch0661.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0661.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0661.lean b/Collatz/Research/StoppingAtlas/Batch0661.lean new file mode 100644 index 00000000..fe3caef9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0661.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0661 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2969. -/ +theorem bounds_13_2969 : exactInterval 13 2969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2969 : oddCount 2969 13 = 6 ∧ acceleratedOrbit 13 2969 = 265 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2969) = 3 ^ 6 * m + 265 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2969.1, data_13_2969.2] + +/-- Complete interval computation for depth 13, residue 2970. -/ +theorem bounds_13_2970 : exactInterval 13 2970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2970 : oddCount 2970 13 = 5 ∧ acceleratedOrbit 13 2970 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2970) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2970.1, data_13_2970.2] + +/-- Complete interval computation for depth 13, residue 2971. -/ +theorem bounds_13_2971 : exactInterval 13 2971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2971 : oddCount 2971 13 = 7 ∧ acceleratedOrbit 13 2971 = 794 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2971) = 3 ^ 7 * m + 794 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2971.1, data_13_2971.2] + +/-- Complete interval computation for depth 13, residue 2972. -/ +theorem bounds_13_2972 : exactInterval 13 2972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2972 : oddCount 2972 13 = 9 ∧ acceleratedOrbit 13 2972 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2972) = 3 ^ 9 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2972.1, data_13_2972.2] + +/-- Complete interval computation for depth 13, residue 2973. -/ +theorem bounds_13_2973 : exactInterval 13 2973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2973 : oddCount 2973 13 = 9 ∧ acceleratedOrbit 13 2973 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2973) = 3 ^ 9 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2973.1, data_13_2973.2] + +/-- Complete interval computation for depth 13, residue 2974. -/ +theorem bounds_13_2974 : exactInterval 13 2974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2974 : oddCount 2974 13 = 9 ∧ acceleratedOrbit 13 2974 = 7154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2974) = 3 ^ 9 * m + 7154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2974.1, data_13_2974.2] + +/-- Complete interval computation for depth 13, residue 2975. -/ +theorem bounds_13_2975 : exactInterval 13 2975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2975 : oddCount 2975 13 = 8 ∧ acceleratedOrbit 13 2975 = 2384 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2975) = 3 ^ 8 * m + 2384 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2975.1, data_13_2975.2] + +/-- Complete interval computation for depth 13, residue 2976. -/ +theorem bounds_13_2976 : exactInterval 13 2976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2976 : oddCount 2976 13 = 3 ∧ acceleratedOrbit 13 2976 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2976) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2976.1, data_13_2976.2] + +/-- Complete interval computation for depth 13, residue 2977. -/ +theorem bounds_13_2977 : exactInterval 13 2977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2977 : oddCount 2977 13 = 7 ∧ acceleratedOrbit 13 2977 = 796 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2977) = 3 ^ 7 * m + 796 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2977.1, data_13_2977.2] + +/-- Complete interval computation for depth 13, residue 2978. -/ +theorem bounds_13_2978 : exactInterval 13 2978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2978 : oddCount 2978 13 = 5 ∧ acceleratedOrbit 13 2978 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2978) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2978.1, data_13_2978.2] + +/-- Complete interval computation for depth 13, residue 2979. -/ +theorem bounds_13_2979 : exactInterval 13 2979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2979 : oddCount 2979 13 = 5 ∧ acceleratedOrbit 13 2979 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2979) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2979.1, data_13_2979.2] + +/-- Complete interval computation for depth 13, residue 2980. -/ +theorem bounds_13_2980 : exactInterval 13 2980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2980 : oddCount 2980 13 = 8 ∧ acceleratedOrbit 13 2980 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2980) = 3 ^ 8 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2980.1, data_13_2980.2] + +/-- Complete interval computation for depth 13, residue 2981. -/ +theorem bounds_13_2981 : exactInterval 13 2981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2981 : oddCount 2981 13 = 8 ∧ acceleratedOrbit 13 2981 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2981) = 3 ^ 8 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2981.1, data_13_2981.2] + +/-- Complete interval computation for depth 13, residue 2982. -/ +theorem bounds_13_2982 : exactInterval 13 2982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2982 : oddCount 2982 13 = 8 ∧ acceleratedOrbit 13 2982 = 2393 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2982) = 3 ^ 8 * m + 2393 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2982.1, data_13_2982.2] + +/-- Complete interval computation for depth 13, residue 2983. -/ +theorem bounds_13_2983 : exactInterval 13 2983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2983) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2983 : oddCount 2983 13 = 9 ∧ acceleratedOrbit 13 2983 = 7172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2983) = 3 ^ 9 * m + 7172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2983.1, data_13_2983.2] + +end Collatz.Research.StoppingAtlas.Batch0661 From 096841f5c2f46f025657e0dec292f59877397d31 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:58 +0530 Subject: [PATCH 0662/1001] proof: certify atlas Batch0662 (13:2984 to 13:2999) --- Collatz/Research/StoppingAtlas/Batch0662.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0662.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0662.lean b/Collatz/Research/StoppingAtlas/Batch0662.lean new file mode 100644 index 00000000..5c0a5b59 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0662.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0662 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 2984. -/ +theorem bounds_13_2984 : exactInterval 13 2984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2984 : oddCount 2984 13 = 3 ∧ acceleratedOrbit 13 2984 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2984) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2984.1, data_13_2984.2] + +/-- Complete interval computation for depth 13, residue 2985. -/ +theorem bounds_13_2985 : exactInterval 13 2985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2985 : oddCount 2985 13 = 8 ∧ acceleratedOrbit 13 2985 = 2392 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2985) = 3 ^ 8 * m + 2392 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2985.1, data_13_2985.2] + +/-- Complete interval computation for depth 13, residue 2986. -/ +theorem bounds_13_2986 : exactInterval 13 2986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2986 : oddCount 2986 13 = 3 ∧ acceleratedOrbit 13 2986 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2986) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2986.1, data_13_2986.2] + +/-- Complete interval computation for depth 13, residue 2987. -/ +theorem bounds_13_2987 : exactInterval 13 2987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2987 : oddCount 2987 13 = 6 ∧ acceleratedOrbit 13 2987 = 266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2987) = 3 ^ 6 * m + 266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2987.1, data_13_2987.2] + +/-- Complete interval computation for depth 13, residue 2988. -/ +theorem bounds_13_2988 : exactInterval 13 2988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2988 : oddCount 2988 13 = 7 ∧ acceleratedOrbit 13 2988 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2988) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2988.1, data_13_2988.2] + +/-- Complete interval computation for depth 13, residue 2989. -/ +theorem bounds_13_2989 : exactInterval 13 2989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2989 : oddCount 2989 13 = 7 ∧ acceleratedOrbit 13 2989 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2989) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2989.1, data_13_2989.2] + +/-- Complete interval computation for depth 13, residue 2990. -/ +theorem bounds_13_2990 : exactInterval 13 2990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2990 : oddCount 2990 13 = 7 ∧ acceleratedOrbit 13 2990 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2990) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2990.1, data_13_2990.2] + +/-- Complete interval computation for depth 13, residue 2991. -/ +theorem bounds_13_2991 : exactInterval 13 2991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2991 : oddCount 2991 13 = 7 ∧ acceleratedOrbit 13 2991 = 800 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2991) = 3 ^ 7 * m + 800 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2991.1, data_13_2991.2] + +/-- Complete interval computation for depth 13, residue 2992. -/ +theorem bounds_13_2992 : exactInterval 13 2992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2992 : oddCount 2992 13 = 6 ∧ acceleratedOrbit 13 2992 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2992) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2992.1, data_13_2992.2] + +/-- Complete interval computation for depth 13, residue 2993. -/ +theorem bounds_13_2993 : exactInterval 13 2993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2993 : oddCount 2993 13 = 6 ∧ acceleratedOrbit 13 2993 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2993) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2993.1, data_13_2993.2] + +/-- Complete interval computation for depth 13, residue 2994. -/ +theorem bounds_13_2994 : exactInterval 13 2994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2994 : oddCount 2994 13 = 6 ∧ acceleratedOrbit 13 2994 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2994) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2994.1, data_13_2994.2] + +/-- Complete interval computation for depth 13, residue 2995. -/ +theorem bounds_13_2995 : exactInterval 13 2995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2995 : oddCount 2995 13 = 6 ∧ acceleratedOrbit 13 2995 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2995) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2995.1, data_13_2995.2] + +/-- Complete interval computation for depth 13, residue 2996. -/ +theorem bounds_13_2996 : exactInterval 13 2996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2996 : oddCount 2996 13 = 6 ∧ acceleratedOrbit 13 2996 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2996) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2996.1, data_13_2996.2] + +/-- Complete interval computation for depth 13, residue 2997. -/ +theorem bounds_13_2997 : exactInterval 13 2997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2997 : oddCount 2997 13 = 6 ∧ acceleratedOrbit 13 2997 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2997) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2997.1, data_13_2997.2] + +/-- Complete interval computation for depth 13, residue 2998. -/ +theorem bounds_13_2998 : exactInterval 13 2998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2998 : oddCount 2998 13 = 5 ∧ acceleratedOrbit 13 2998 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2998) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2998.1, data_13_2998.2] + +/-- Complete interval computation for depth 13, residue 2999. -/ +theorem bounds_13_2999 : exactInterval 13 2999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_2999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 2999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_2999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_2999 : oddCount 2999 13 = 5 ∧ acceleratedOrbit 13 2999 = 89 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_2999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 2999) = 3 ^ 5 * m + 89 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_2999.1, data_13_2999.2] + +end Collatz.Research.StoppingAtlas.Batch0662 From 103efae4ae919c972458f49df1ca98ad0698919b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:58 +0530 Subject: [PATCH 0663/1001] proof: certify atlas Batch0663 (13:3000 to 13:3014) --- Collatz/Research/StoppingAtlas/Batch0663.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0663.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0663.lean b/Collatz/Research/StoppingAtlas/Batch0663.lean new file mode 100644 index 00000000..5db07be9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0663.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0663 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3000. -/ +theorem bounds_13_3000 : exactInterval 13 3000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3000 : oddCount 3000 13 = 6 ∧ acceleratedOrbit 13 3000 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3000) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3000.1, data_13_3000.2] + +/-- Complete interval computation for depth 13, residue 3001. -/ +theorem bounds_13_3001 : exactInterval 13 3001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3001 : oddCount 3001 13 = 7 ∧ acceleratedOrbit 13 3001 = 803 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3001) = 3 ^ 7 * m + 803 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3001.1, data_13_3001.2] + +/-- Complete interval computation for depth 13, residue 3002. -/ +theorem bounds_13_3002 : exactInterval 13 3002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3002 : oddCount 3002 13 = 6 ∧ acceleratedOrbit 13 3002 = 269 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3002) = 3 ^ 6 * m + 269 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3002.1, data_13_3002.2] + +/-- Complete interval computation for depth 13, residue 3003. -/ +theorem bounds_13_3003 : exactInterval 13 3003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3003 : oddCount 3003 13 = 7 ∧ acceleratedOrbit 13 3003 = 803 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3003) = 3 ^ 7 * m + 803 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3003.1, data_13_3003.2] + +/-- Complete interval computation for depth 13, residue 3004. -/ +theorem bounds_13_3004 : exactInterval 13 3004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3004 : oddCount 3004 13 = 9 ∧ acceleratedOrbit 13 3004 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3004) = 3 ^ 9 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3004.1, data_13_3004.2] + +/-- Complete interval computation for depth 13, residue 3005. -/ +theorem bounds_13_3005 : exactInterval 13 3005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3005 : oddCount 3005 13 = 9 ∧ acceleratedOrbit 13 3005 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3005) = 3 ^ 9 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3005.1, data_13_3005.2] + +/-- Complete interval computation for depth 13, residue 3006. -/ +theorem bounds_13_3006 : exactInterval 13 3006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3006 : oddCount 3006 13 = 9 ∧ acceleratedOrbit 13 3006 = 7229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3006) = 3 ^ 9 * m + 7229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3006.1, data_13_3006.2] + +/-- Complete interval computation for depth 13, residue 3007. -/ +theorem bounds_13_3007 : exactInterval 13 3007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3007 : oddCount 3007 13 = 10 ∧ acceleratedOrbit 13 3007 = 21683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3007) = 3 ^ 10 * m + 21683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3007.1, data_13_3007.2] + +/-- Complete interval computation for depth 13, residue 3008. -/ +theorem bounds_13_3008 : exactInterval 13 3008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3008 : oddCount 3008 13 = 5 ∧ acceleratedOrbit 13 3008 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3008) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3008.1, data_13_3008.2] + +/-- Complete interval computation for depth 13, residue 3009. -/ +theorem bounds_13_3009 : exactInterval 13 3009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3009 : oddCount 3009 13 = 7 ∧ acceleratedOrbit 13 3009 = 805 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3009) = 3 ^ 7 * m + 805 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3009.1, data_13_3009.2] + +/-- Complete interval computation for depth 13, residue 3010. -/ +theorem bounds_13_3010 : exactInterval 13 3010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3010 : oddCount 3010 13 = 7 ∧ acceleratedOrbit 13 3010 = 805 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3010) = 3 ^ 7 * m + 805 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3010.1, data_13_3010.2] + +/-- Complete interval computation for depth 13, residue 3011. -/ +theorem bounds_13_3011 : exactInterval 13 3011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3011 : oddCount 3011 13 = 7 ∧ acceleratedOrbit 13 3011 = 805 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3011) = 3 ^ 7 * m + 805 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3011.1, data_13_3011.2] + +/-- Complete interval computation for depth 13, residue 3012. -/ +theorem bounds_13_3012 : exactInterval 13 3012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3012 : oddCount 3012 13 = 3 ∧ acceleratedOrbit 13 3012 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3012) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3012.1, data_13_3012.2] + +/-- Complete interval computation for depth 13, residue 3013. -/ +theorem bounds_13_3013 : exactInterval 13 3013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3013 : oddCount 3013 13 = 3 ∧ acceleratedOrbit 13 3013 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3013) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3013.1, data_13_3013.2] + +/-- Complete interval computation for depth 13, residue 3014. -/ +theorem bounds_13_3014 : exactInterval 13 3014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3014 : oddCount 3014 13 = 3 ∧ acceleratedOrbit 13 3014 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3014) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3014.1, data_13_3014.2] + +end Collatz.Research.StoppingAtlas.Batch0663 From c3541bef4e9e413a2b2b9748c934e1f467ef6a6b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:32:59 +0530 Subject: [PATCH 0664/1001] proof: certify atlas Batch0664 (13:3015 to 13:3030) --- Collatz/Research/StoppingAtlas/Batch0664.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0664.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0664.lean b/Collatz/Research/StoppingAtlas/Batch0664.lean new file mode 100644 index 00000000..a5785af4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0664.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0664 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3015. -/ +theorem bounds_13_3015 : exactInterval 13 3015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3015 : oddCount 3015 13 = 9 ∧ acceleratedOrbit 13 3015 = 7249 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3015) = 3 ^ 9 * m + 7249 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3015.1, data_13_3015.2] + +/-- Complete interval computation for depth 13, residue 3016. -/ +theorem bounds_13_3016 : exactInterval 13 3016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3016 : oddCount 3016 13 = 8 ∧ acceleratedOrbit 13 3016 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3016) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3016.1, data_13_3016.2] + +/-- Complete interval computation for depth 13, residue 3017. -/ +theorem bounds_13_3017 : exactInterval 13 3017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3017 : oddCount 3017 13 = 8 ∧ acceleratedOrbit 13 3017 = 2420 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3017) = 3 ^ 8 * m + 2420 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3017.1, data_13_3017.2] + +/-- Complete interval computation for depth 13, residue 3018. -/ +theorem bounds_13_3018 : exactInterval 13 3018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3018 : oddCount 3018 13 = 8 ∧ acceleratedOrbit 13 3018 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3018) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3018.1, data_13_3018.2] + +/-- Complete interval computation for depth 13, residue 3019. -/ +theorem bounds_13_3019 : exactInterval 13 3019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3019 : oddCount 3019 13 = 7 ∧ acceleratedOrbit 13 3019 = 809 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3019) = 3 ^ 7 * m + 809 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3019.1, data_13_3019.2] + +/-- Complete interval computation for depth 13, residue 3020. -/ +theorem bounds_13_3020 : exactInterval 13 3020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3020 : oddCount 3020 13 = 8 ∧ acceleratedOrbit 13 3020 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3020) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3020.1, data_13_3020.2] + +/-- Complete interval computation for depth 13, residue 3021. -/ +theorem bounds_13_3021 : exactInterval 13 3021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3021 : oddCount 3021 13 = 8 ∧ acceleratedOrbit 13 3021 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3021) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3021.1, data_13_3021.2] + +/-- Complete interval computation for depth 13, residue 3022. -/ +theorem bounds_13_3022 : exactInterval 13 3022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3022 : oddCount 3022 13 = 8 ∧ acceleratedOrbit 13 3022 = 2423 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3022) = 3 ^ 8 * m + 2423 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3022.1, data_13_3022.2] + +/-- Complete interval computation for depth 13, residue 3023. -/ +theorem bounds_13_3023 : exactInterval 13 3023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3023) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3023 : oddCount 3023 13 = 8 ∧ acceleratedOrbit 13 3023 = 2423 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3023) = 3 ^ 8 * m + 2423 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3023.1, data_13_3023.2] + +/-- Complete interval computation for depth 13, residue 3024. -/ +theorem bounds_13_3024 : exactInterval 13 3024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3024 : oddCount 3024 13 = 5 ∧ acceleratedOrbit 13 3024 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3024) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3024.1, data_13_3024.2] + +/-- Complete interval computation for depth 13, residue 3025. -/ +theorem bounds_13_3025 : exactInterval 13 3025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3025 : oddCount 3025 13 = 8 ∧ acceleratedOrbit 13 3025 = 2429 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3025) = 3 ^ 8 * m + 2429 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3025.1, data_13_3025.2] + +/-- Complete interval computation for depth 13, residue 3026. -/ +theorem bounds_13_3026 : exactInterval 13 3026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3026 : oddCount 3026 13 = 9 ∧ acceleratedOrbit 13 3026 = 7280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3026) = 3 ^ 9 * m + 7280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3026.1, data_13_3026.2] + +/-- Complete interval computation for depth 13, residue 3027. -/ +theorem bounds_13_3027 : exactInterval 13 3027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3027 : oddCount 3027 13 = 9 ∧ acceleratedOrbit 13 3027 = 7280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3027) = 3 ^ 9 * m + 7280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3027.1, data_13_3027.2] + +/-- Complete interval computation for depth 13, residue 3028. -/ +theorem bounds_13_3028 : exactInterval 13 3028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3028 : oddCount 3028 13 = 5 ∧ acceleratedOrbit 13 3028 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3028) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3028.1, data_13_3028.2] + +/-- Complete interval computation for depth 13, residue 3029. -/ +theorem bounds_13_3029 : exactInterval 13 3029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3029 : oddCount 3029 13 = 5 ∧ acceleratedOrbit 13 3029 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3029) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3029.1, data_13_3029.2] + +/-- Complete interval computation for depth 13, residue 3030. -/ +theorem bounds_13_3030 : exactInterval 13 3030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3030 : oddCount 3030 13 = 10 ∧ acceleratedOrbit 13 3030 = 21869 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3030) = 3 ^ 10 * m + 21869 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3030.1, data_13_3030.2] + +end Collatz.Research.StoppingAtlas.Batch0664 From 8ff8e064a3f61ecb5dea59b3d6703ba9a4f39326 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:00 +0530 Subject: [PATCH 0665/1001] proof: certify atlas Batch0665 (13:3031 to 13:3045) --- Collatz/Research/StoppingAtlas/Batch0665.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0665.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0665.lean b/Collatz/Research/StoppingAtlas/Batch0665.lean new file mode 100644 index 00000000..0709143a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0665.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0665 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3031. -/ +theorem bounds_13_3031 : exactInterval 13 3031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3031 : oddCount 3031 13 = 10 ∧ acceleratedOrbit 13 3031 = 21869 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3031) = 3 ^ 10 * m + 21869 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3031.1, data_13_3031.2] + +/-- Complete interval computation for depth 13, residue 3032. -/ +theorem bounds_13_3032 : exactInterval 13 3032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3032 : oddCount 3032 13 = 6 ∧ acceleratedOrbit 13 3032 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3032) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3032.1, data_13_3032.2] + +/-- Complete interval computation for depth 13, residue 3033. -/ +theorem bounds_13_3033 : exactInterval 13 3033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3033 : oddCount 3033 13 = 3 ∧ acceleratedOrbit 13 3033 = 10 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3033) = 3 ^ 3 * m + 10 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3033.1, data_13_3033.2] + +/-- Complete interval computation for depth 13, residue 3034. -/ +theorem bounds_13_3034 : exactInterval 13 3034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3034 : oddCount 3034 13 = 6 ∧ acceleratedOrbit 13 3034 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3034) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3034.1, data_13_3034.2] + +/-- Complete interval computation for depth 13, residue 3035. -/ +theorem bounds_13_3035 : exactInterval 13 3035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3035 : oddCount 3035 13 = 7 ∧ acceleratedOrbit 13 3035 = 811 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3035) = 3 ^ 7 * m + 811 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3035.1, data_13_3035.2] + +/-- Complete interval computation for depth 13, residue 3036. -/ +theorem bounds_13_3036 : exactInterval 13 3036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3036 : oddCount 3036 13 = 6 ∧ acceleratedOrbit 13 3036 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3036) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3036.1, data_13_3036.2] + +/-- Complete interval computation for depth 13, residue 3037. -/ +theorem bounds_13_3037 : exactInterval 13 3037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3037 : oddCount 3037 13 = 6 ∧ acceleratedOrbit 13 3037 = 271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3037) = 3 ^ 6 * m + 271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3037.1, data_13_3037.2] + +/-- Complete interval computation for depth 13, residue 3038. -/ +theorem bounds_13_3038 : exactInterval 13 3038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3038 : oddCount 3038 13 = 8 ∧ acceleratedOrbit 13 3038 = 2435 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3038) = 3 ^ 8 * m + 2435 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3038.1, data_13_3038.2] + +/-- Complete interval computation for depth 13, residue 3039. -/ +theorem bounds_13_3039 : exactInterval 13 3039 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3039) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3039 : oddCount 3039 13 = 8 ∧ acceleratedOrbit 13 3039 = 2435 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3039) = 3 ^ 8 * m + 2435 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3039.1, data_13_3039.2] + +/-- Complete interval computation for depth 13, residue 3040. -/ +theorem bounds_13_3040 : exactInterval 13 3040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3040 : oddCount 3040 13 = 5 ∧ acceleratedOrbit 13 3040 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3040) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3040.1, data_13_3040.2] + +/-- Complete interval computation for depth 13, residue 3041. -/ +theorem bounds_13_3041 : exactInterval 13 3041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3041 : oddCount 3041 13 = 8 ∧ acceleratedOrbit 13 3041 = 2438 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3041) = 3 ^ 8 * m + 2438 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3041.1, data_13_3041.2] + +/-- Complete interval computation for depth 13, residue 3042. -/ +theorem bounds_13_3042 : exactInterval 13 3042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3042 : oddCount 3042 13 = 5 ∧ acceleratedOrbit 13 3042 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3042) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3042.1, data_13_3042.2] + +/-- Complete interval computation for depth 13, residue 3043. -/ +theorem bounds_13_3043 : exactInterval 13 3043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3043 : oddCount 3043 13 = 5 ∧ acceleratedOrbit 13 3043 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3043) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3043.1, data_13_3043.2] + +/-- Complete interval computation for depth 13, residue 3044. -/ +theorem bounds_13_3044 : exactInterval 13 3044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3044 : oddCount 3044 13 = 6 ∧ acceleratedOrbit 13 3044 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3044) = 3 ^ 6 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3044.1, data_13_3044.2] + +/-- Complete interval computation for depth 13, residue 3045. -/ +theorem bounds_13_3045 : exactInterval 13 3045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3045 : oddCount 3045 13 = 6 ∧ acceleratedOrbit 13 3045 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3045) = 3 ^ 6 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3045.1, data_13_3045.2] + +end Collatz.Research.StoppingAtlas.Batch0665 From f336008e9330fe1a6a9f37774679205e672101c5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:03 +0530 Subject: [PATCH 0666/1001] proof: certify atlas Batch0666 (13:3046 to 13:3060) --- Collatz/Research/StoppingAtlas/Batch0666.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0666.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0666.lean b/Collatz/Research/StoppingAtlas/Batch0666.lean new file mode 100644 index 00000000..139715c9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0666.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0666 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3046. -/ +theorem bounds_13_3046 : exactInterval 13 3046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3046 : oddCount 3046 13 = 6 ∧ acceleratedOrbit 13 3046 = 272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3046) = 3 ^ 6 * m + 272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3046.1, data_13_3046.2] + +/-- Complete interval computation for depth 13, residue 3047. -/ +theorem bounds_13_3047 : exactInterval 13 3047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3047) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3047 : oddCount 3047 13 = 7 ∧ acceleratedOrbit 13 3047 = 814 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3047) = 3 ^ 7 * m + 814 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3047.1, data_13_3047.2] + +/-- Complete interval computation for depth 13, residue 3048. -/ +theorem bounds_13_3048 : exactInterval 13 3048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3048 : oddCount 3048 13 = 5 ∧ acceleratedOrbit 13 3048 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3048) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3048.1, data_13_3048.2] + +/-- Complete interval computation for depth 13, residue 3049. -/ +theorem bounds_13_3049 : exactInterval 13 3049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3049 : oddCount 3049 13 = 10 ∧ acceleratedOrbit 13 3049 = 21991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3049) = 3 ^ 10 * m + 21991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3049.1, data_13_3049.2] + +/-- Complete interval computation for depth 13, residue 3050. -/ +theorem bounds_13_3050 : exactInterval 13 3050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3050 : oddCount 3050 13 = 5 ∧ acceleratedOrbit 13 3050 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3050) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3050.1, data_13_3050.2] + +/-- Complete interval computation for depth 13, residue 3051. -/ +theorem bounds_13_3051 : exactInterval 13 3051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3051 : oddCount 3051 13 = 7 ∧ acceleratedOrbit 13 3051 = 815 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3051) = 3 ^ 7 * m + 815 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3051.1, data_13_3051.2] + +/-- Complete interval computation for depth 13, residue 3052. -/ +theorem bounds_13_3052 : exactInterval 13 3052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3052 : oddCount 3052 13 = 8 ∧ acceleratedOrbit 13 3052 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3052) = 3 ^ 8 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3052.1, data_13_3052.2] + +/-- Complete interval computation for depth 13, residue 3053. -/ +theorem bounds_13_3053 : exactInterval 13 3053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3053 : oddCount 3053 13 = 8 ∧ acceleratedOrbit 13 3053 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3053) = 3 ^ 8 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3053.1, data_13_3053.2] + +/-- Complete interval computation for depth 13, residue 3054. -/ +theorem bounds_13_3054 : exactInterval 13 3054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3054 : oddCount 3054 13 = 8 ∧ acceleratedOrbit 13 3054 = 2450 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3054) = 3 ^ 8 * m + 2450 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3054.1, data_13_3054.2] + +/-- Complete interval computation for depth 13, residue 3055. -/ +theorem bounds_13_3055 : exactInterval 13 3055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3055 : oddCount 3055 13 = 10 ∧ acceleratedOrbit 13 3055 = 22031 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3055) = 3 ^ 10 * m + 22031 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3055.1, data_13_3055.2] + +/-- Complete interval computation for depth 13, residue 3056. -/ +theorem bounds_13_3056 : exactInterval 13 3056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3056 : oddCount 3056 13 = 7 ∧ acceleratedOrbit 13 3056 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3056) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3056.1, data_13_3056.2] + +/-- Complete interval computation for depth 13, residue 3057. -/ +theorem bounds_13_3057 : exactInterval 13 3057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3057 : oddCount 3057 13 = 5 ∧ acceleratedOrbit 13 3057 = 91 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3057) = 3 ^ 5 * m + 91 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3057.1, data_13_3057.2] + +/-- Complete interval computation for depth 13, residue 3058. -/ +theorem bounds_13_3058 : exactInterval 13 3058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3058 : oddCount 3058 13 = 7 ∧ acceleratedOrbit 13 3058 = 818 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3058) = 3 ^ 7 * m + 818 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3058.1, data_13_3058.2] + +/-- Complete interval computation for depth 13, residue 3059. -/ +theorem bounds_13_3059 : exactInterval 13 3059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3059 : oddCount 3059 13 = 7 ∧ acceleratedOrbit 13 3059 = 818 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3059) = 3 ^ 7 * m + 818 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3059.1, data_13_3059.2] + +/-- Complete interval computation for depth 13, residue 3060. -/ +theorem bounds_13_3060 : exactInterval 13 3060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3060 : oddCount 3060 13 = 7 ∧ acceleratedOrbit 13 3060 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3060) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3060.1, data_13_3060.2] + +end Collatz.Research.StoppingAtlas.Batch0666 From 4ee6ee0788f64d33a6d1bdc927ca3003be38d39a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:03 +0530 Subject: [PATCH 0667/1001] proof: certify atlas Batch0667 (13:3061 to 13:3076) --- Collatz/Research/StoppingAtlas/Batch0667.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0667.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0667.lean b/Collatz/Research/StoppingAtlas/Batch0667.lean new file mode 100644 index 00000000..1c10825a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0667.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0667 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3061. -/ +theorem bounds_13_3061 : exactInterval 13 3061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3061 : oddCount 3061 13 = 7 ∧ acceleratedOrbit 13 3061 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3061) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3061.1, data_13_3061.2] + +/-- Complete interval computation for depth 13, residue 3062. -/ +theorem bounds_13_3062 : exactInterval 13 3062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3062 : oddCount 3062 13 = 8 ∧ acceleratedOrbit 13 3062 = 2456 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3062) = 3 ^ 8 * m + 2456 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3062.1, data_13_3062.2] + +/-- Complete interval computation for depth 13, residue 3063. -/ +theorem bounds_13_3063 : exactInterval 13 3063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3063 : oddCount 3063 13 = 8 ∧ acceleratedOrbit 13 3063 = 2456 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3063) = 3 ^ 8 * m + 2456 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3063.1, data_13_3063.2] + +/-- Complete interval computation for depth 13, residue 3064. -/ +theorem bounds_13_3064 : exactInterval 13 3064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3064 : oddCount 3064 13 = 7 ∧ acceleratedOrbit 13 3064 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3064) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3064.1, data_13_3064.2] + +/-- Complete interval computation for depth 13, residue 3065. -/ +theorem bounds_13_3065 : exactInterval 13 3065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3065 : oddCount 3065 13 = 10 ∧ acceleratedOrbit 13 3065 = 22112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3065) = 3 ^ 10 * m + 22112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3065.1, data_13_3065.2] + +/-- Complete interval computation for depth 13, residue 3066. -/ +theorem bounds_13_3066 : exactInterval 13 3066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3066 : oddCount 3066 13 = 7 ∧ acceleratedOrbit 13 3066 = 820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3066) = 3 ^ 7 * m + 820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3066.1, data_13_3066.2] + +/-- Complete interval computation for depth 13, residue 3067. -/ +theorem bounds_13_3067 : exactInterval 13 3067 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3067) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3067 : oddCount 3067 13 = 8 ∧ acceleratedOrbit 13 3067 = 2458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3067) = 3 ^ 8 * m + 2458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3067.1, data_13_3067.2] + +/-- Complete interval computation for depth 13, residue 3068. -/ +theorem bounds_13_3068 : exactInterval 13 3068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3068 : oddCount 3068 13 = 9 ∧ acceleratedOrbit 13 3068 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3068) = 3 ^ 9 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3068.1, data_13_3068.2] + +/-- Complete interval computation for depth 13, residue 3069. -/ +theorem bounds_13_3069 : exactInterval 13 3069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3069 : oddCount 3069 13 = 9 ∧ acceleratedOrbit 13 3069 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3069) = 3 ^ 9 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3069.1, data_13_3069.2] + +/-- Complete interval computation for depth 13, residue 3070. -/ +theorem bounds_13_3070 : exactInterval 13 3070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3070 : oddCount 3070 13 = 9 ∧ acceleratedOrbit 13 3070 = 7381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3070) = 3 ^ 9 * m + 7381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3070.1, data_13_3070.2] + +/-- Complete interval computation for depth 13, residue 3071. -/ +theorem bounds_13_3071 : exactInterval 13 3071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3071 : oddCount 3071 13 = 11 ∧ acceleratedOrbit 13 3071 = 66430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3071) = 3 ^ 11 * m + 66430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3071.1, data_13_3071.2] + +/-- Complete interval computation for depth 13, residue 3072. -/ +theorem bounds_13_3072 : exactInterval 13 3072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3072 : oddCount 3072 13 = 2 ∧ acceleratedOrbit 13 3072 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3072) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3072.1, data_13_3072.2] + +/-- Complete interval computation for depth 13, residue 3073. -/ +theorem bounds_13_3073 : exactInterval 13 3073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3073 : oddCount 3073 13 = 6 ∧ acceleratedOrbit 13 3073 = 274 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3073) = 3 ^ 6 * m + 274 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3073.1, data_13_3073.2] + +/-- Complete interval computation for depth 13, residue 3074. -/ +theorem bounds_13_3074 : exactInterval 13 3074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3074 : oddCount 3074 13 = 7 ∧ acceleratedOrbit 13 3074 = 823 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3074) = 3 ^ 7 * m + 823 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3074.1, data_13_3074.2] + +/-- Complete interval computation for depth 13, residue 3075. -/ +theorem bounds_13_3075 : exactInterval 13 3075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3075 : oddCount 3075 13 = 7 ∧ acceleratedOrbit 13 3075 = 823 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3075) = 3 ^ 7 * m + 823 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3075.1, data_13_3075.2] + +/-- Complete interval computation for depth 13, residue 3076. -/ +theorem bounds_13_3076 : exactInterval 13 3076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3076 : oddCount 3076 13 = 5 ∧ acceleratedOrbit 13 3076 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3076) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3076.1, data_13_3076.2] + +end Collatz.Research.StoppingAtlas.Batch0667 From 8401a1aea08bbfeceeddc2e93499f045165a44f5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:04 +0530 Subject: [PATCH 0668/1001] proof: certify atlas Batch0668 (13:3077 to 13:3091) --- Collatz/Research/StoppingAtlas/Batch0668.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0668.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0668.lean b/Collatz/Research/StoppingAtlas/Batch0668.lean new file mode 100644 index 00000000..33c11ec0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0668.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0668 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3077. -/ +theorem bounds_13_3077 : exactInterval 13 3077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3077 : oddCount 3077 13 = 5 ∧ acceleratedOrbit 13 3077 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3077) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3077.1, data_13_3077.2] + +/-- Complete interval computation for depth 13, residue 3078. -/ +theorem bounds_13_3078 : exactInterval 13 3078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3078 : oddCount 3078 13 = 5 ∧ acceleratedOrbit 13 3078 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3078) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3078.1, data_13_3078.2] + +/-- Complete interval computation for depth 13, residue 3079. -/ +theorem bounds_13_3079 : exactInterval 13 3079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3079) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3079 : oddCount 3079 13 = 7 ∧ acceleratedOrbit 13 3079 = 823 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3079) = 3 ^ 7 * m + 823 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3079.1, data_13_3079.2] + +/-- Complete interval computation for depth 13, residue 3080. -/ +theorem bounds_13_3080 : exactInterval 13 3080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3080 : oddCount 3080 13 = 5 ∧ acceleratedOrbit 13 3080 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3080) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3080.1, data_13_3080.2] + +/-- Complete interval computation for depth 13, residue 3081. -/ +theorem bounds_13_3081 : exactInterval 13 3081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3081 : oddCount 3081 13 = 8 ∧ acceleratedOrbit 13 3081 = 2470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3081) = 3 ^ 8 * m + 2470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3081.1, data_13_3081.2] + +/-- Complete interval computation for depth 13, residue 3082. -/ +theorem bounds_13_3082 : exactInterval 13 3082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3082 : oddCount 3082 13 = 5 ∧ acceleratedOrbit 13 3082 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3082) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3082.1, data_13_3082.2] + +/-- Complete interval computation for depth 13, residue 3083. -/ +theorem bounds_13_3083 : exactInterval 13 3083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3083 : oddCount 3083 13 = 5 ∧ acceleratedOrbit 13 3083 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3083) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3083.1, data_13_3083.2] + +/-- Complete interval computation for depth 13, residue 3084. -/ +theorem bounds_13_3084 : exactInterval 13 3084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3084 : oddCount 3084 13 = 5 ∧ acceleratedOrbit 13 3084 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3084) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3084.1, data_13_3084.2] + +/-- Complete interval computation for depth 13, residue 3085. -/ +theorem bounds_13_3085 : exactInterval 13 3085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3085 : oddCount 3085 13 = 5 ∧ acceleratedOrbit 13 3085 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3085) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3085.1, data_13_3085.2] + +/-- Complete interval computation for depth 13, residue 3086. -/ +theorem bounds_13_3086 : exactInterval 13 3086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3086 : oddCount 3086 13 = 6 ∧ acceleratedOrbit 13 3086 = 275 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3086) = 3 ^ 6 * m + 275 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3086.1, data_13_3086.2] + +/-- Complete interval computation for depth 13, residue 3087. -/ +theorem bounds_13_3087 : exactInterval 13 3087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3087 : oddCount 3087 13 = 6 ∧ acceleratedOrbit 13 3087 = 275 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3087) = 3 ^ 6 * m + 275 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3087.1, data_13_3087.2] + +/-- Complete interval computation for depth 13, residue 3088. -/ +theorem bounds_13_3088 : exactInterval 13 3088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3088 : oddCount 3088 13 = 4 ∧ acceleratedOrbit 13 3088 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3088) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3088.1, data_13_3088.2] + +/-- Complete interval computation for depth 13, residue 3089. -/ +theorem bounds_13_3089 : exactInterval 13 3089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3089 : oddCount 3089 13 = 5 ∧ acceleratedOrbit 13 3089 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3089) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3089.1, data_13_3089.2] + +/-- Complete interval computation for depth 13, residue 3090. -/ +theorem bounds_13_3090 : exactInterval 13 3090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3090 : oddCount 3090 13 = 7 ∧ acceleratedOrbit 13 3090 = 827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3090) = 3 ^ 7 * m + 827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3090.1, data_13_3090.2] + +/-- Complete interval computation for depth 13, residue 3091. -/ +theorem bounds_13_3091 : exactInterval 13 3091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3091 : oddCount 3091 13 = 7 ∧ acceleratedOrbit 13 3091 = 827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3091) = 3 ^ 7 * m + 827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3091.1, data_13_3091.2] + +end Collatz.Research.StoppingAtlas.Batch0668 From 3847601d341b12e7a8d0d2faf7c2e9cc704ed972 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:05 +0530 Subject: [PATCH 0669/1001] proof: certify atlas Batch0669 (13:3092 to 13:3106) --- Collatz/Research/StoppingAtlas/Batch0669.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0669.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0669.lean b/Collatz/Research/StoppingAtlas/Batch0669.lean new file mode 100644 index 00000000..9d53139d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0669.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0669 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3092. -/ +theorem bounds_13_3092 : exactInterval 13 3092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3092 : oddCount 3092 13 = 4 ∧ acceleratedOrbit 13 3092 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3092) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3092.1, data_13_3092.2] + +/-- Complete interval computation for depth 13, residue 3093. -/ +theorem bounds_13_3093 : exactInterval 13 3093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3093 : oddCount 3093 13 = 4 ∧ acceleratedOrbit 13 3093 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3093) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3093.1, data_13_3093.2] + +/-- Complete interval computation for depth 13, residue 3094. -/ +theorem bounds_13_3094 : exactInterval 13 3094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3094 : oddCount 3094 13 = 5 ∧ acceleratedOrbit 13 3094 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3094) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3094.1, data_13_3094.2] + +/-- Complete interval computation for depth 13, residue 3095. -/ +theorem bounds_13_3095 : exactInterval 13 3095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3095 : oddCount 3095 13 = 5 ∧ acceleratedOrbit 13 3095 = 92 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3095) = 3 ^ 5 * m + 92 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3095.1, data_13_3095.2] + +/-- Complete interval computation for depth 13, residue 3096. -/ +theorem bounds_13_3096 : exactInterval 13 3096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3096 : oddCount 3096 13 = 4 ∧ acceleratedOrbit 13 3096 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3096) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3096.1, data_13_3096.2] + +/-- Complete interval computation for depth 13, residue 3097. -/ +theorem bounds_13_3097 : exactInterval 13 3097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3097 : oddCount 3097 13 = 9 ∧ acceleratedOrbit 13 3097 = 7451 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3097) = 3 ^ 9 * m + 7451 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3097.1, data_13_3097.2] + +/-- Complete interval computation for depth 13, residue 3098. -/ +theorem bounds_13_3098 : exactInterval 13 3098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3098 : oddCount 3098 13 = 4 ∧ acceleratedOrbit 13 3098 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3098) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3098.1, data_13_3098.2] + +/-- Complete interval computation for depth 13, residue 3099. -/ +theorem bounds_13_3099 : exactInterval 13 3099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3099 : oddCount 3099 13 = 10 ∧ acceleratedOrbit 13 3099 = 22349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3099) = 3 ^ 10 * m + 22349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3099.1, data_13_3099.2] + +/-- Complete interval computation for depth 13, residue 3100. -/ +theorem bounds_13_3100 : exactInterval 13 3100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3100 : oddCount 3100 13 = 7 ∧ acceleratedOrbit 13 3100 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3100) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3100.1, data_13_3100.2] + +/-- Complete interval computation for depth 13, residue 3101. -/ +theorem bounds_13_3101 : exactInterval 13 3101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3101 : oddCount 3101 13 = 7 ∧ acceleratedOrbit 13 3101 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3101) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3101.1, data_13_3101.2] + +/-- Complete interval computation for depth 13, residue 3102. -/ +theorem bounds_13_3102 : exactInterval 13 3102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3102 : oddCount 3102 13 = 7 ∧ acceleratedOrbit 13 3102 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3102) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3102.1, data_13_3102.2] + +/-- Complete interval computation for depth 13, residue 3103. -/ +theorem bounds_13_3103 : exactInterval 13 3103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3103 : oddCount 3103 13 = 10 ∧ acceleratedOrbit 13 3103 = 22376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3103) = 3 ^ 10 * m + 22376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3103.1, data_13_3103.2] + +/-- Complete interval computation for depth 13, residue 3104. -/ +theorem bounds_13_3104 : exactInterval 13 3104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3104 : oddCount 3104 13 = 5 ∧ acceleratedOrbit 13 3104 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3104) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3104.1, data_13_3104.2] + +/-- Complete interval computation for depth 13, residue 3105. -/ +theorem bounds_13_3105 : exactInterval 13 3105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3105 : oddCount 3105 13 = 7 ∧ acceleratedOrbit 13 3105 = 830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3105) = 3 ^ 7 * m + 830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3105.1, data_13_3105.2] + +/-- Complete interval computation for depth 13, residue 3106. -/ +theorem bounds_13_3106 : exactInterval 13 3106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3106 : oddCount 3106 13 = 4 ∧ acceleratedOrbit 13 3106 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3106) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3106.1, data_13_3106.2] + +end Collatz.Research.StoppingAtlas.Batch0669 From 930b38aa29cdb9e5ab0279924eb4ded5a7e1c812 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:08 +0530 Subject: [PATCH 0670/1001] proof: certify atlas Batch0670 (13:3107 to 13:3122) --- Collatz/Research/StoppingAtlas/Batch0670.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0670.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0670.lean b/Collatz/Research/StoppingAtlas/Batch0670.lean new file mode 100644 index 00000000..33dcaed5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0670.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0670 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3107. -/ +theorem bounds_13_3107 : exactInterval 13 3107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3107 : oddCount 3107 13 = 4 ∧ acceleratedOrbit 13 3107 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3107) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3107.1, data_13_3107.2] + +/-- Complete interval computation for depth 13, residue 3108. -/ +theorem bounds_13_3108 : exactInterval 13 3108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3108 : oddCount 3108 13 = 7 ∧ acceleratedOrbit 13 3108 = 832 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3108) = 3 ^ 7 * m + 832 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3108.1, data_13_3108.2] + +/-- Complete interval computation for depth 13, residue 3109. -/ +theorem bounds_13_3109 : exactInterval 13 3109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3109 : oddCount 3109 13 = 7 ∧ acceleratedOrbit 13 3109 = 832 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3109) = 3 ^ 7 * m + 832 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3109.1, data_13_3109.2] + +/-- Complete interval computation for depth 13, residue 3110. -/ +theorem bounds_13_3110 : exactInterval 13 3110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3110 : oddCount 3110 13 = 7 ∧ acceleratedOrbit 13 3110 = 832 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3110) = 3 ^ 7 * m + 832 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3110.1, data_13_3110.2] + +/-- Complete interval computation for depth 13, residue 3111. -/ +theorem bounds_13_3111 : exactInterval 13 3111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3111 : oddCount 3111 13 = 6 ∧ acceleratedOrbit 13 3111 = 277 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3111) = 3 ^ 6 * m + 277 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3111.1, data_13_3111.2] + +/-- Complete interval computation for depth 13, residue 3112. -/ +theorem bounds_13_3112 : exactInterval 13 3112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3112 : oddCount 3112 13 = 5 ∧ acceleratedOrbit 13 3112 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3112) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3112.1, data_13_3112.2] + +/-- Complete interval computation for depth 13, residue 3113. -/ +theorem bounds_13_3113 : exactInterval 13 3113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3113 : oddCount 3113 13 = 8 ∧ acceleratedOrbit 13 3113 = 2495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3113) = 3 ^ 8 * m + 2495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3113.1, data_13_3113.2] + +/-- Complete interval computation for depth 13, residue 3114. -/ +theorem bounds_13_3114 : exactInterval 13 3114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3114 : oddCount 3114 13 = 5 ∧ acceleratedOrbit 13 3114 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3114) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3114.1, data_13_3114.2] + +/-- Complete interval computation for depth 13, residue 3115. -/ +theorem bounds_13_3115 : exactInterval 13 3115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3115 : oddCount 3115 13 = 6 ∧ acceleratedOrbit 13 3115 = 278 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3115) = 3 ^ 6 * m + 278 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3115.1, data_13_3115.2] + +/-- Complete interval computation for depth 13, residue 3116. -/ +theorem bounds_13_3116 : exactInterval 13 3116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3116 : oddCount 3116 13 = 7 ∧ acceleratedOrbit 13 3116 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3116) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3116.1, data_13_3116.2] + +/-- Complete interval computation for depth 13, residue 3117. -/ +theorem bounds_13_3117 : exactInterval 13 3117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3117 : oddCount 3117 13 = 7 ∧ acceleratedOrbit 13 3117 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3117) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3117.1, data_13_3117.2] + +/-- Complete interval computation for depth 13, residue 3118. -/ +theorem bounds_13_3118 : exactInterval 13 3118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3118 : oddCount 3118 13 = 7 ∧ acceleratedOrbit 13 3118 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3118) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3118.1, data_13_3118.2] + +/-- Complete interval computation for depth 13, residue 3119. -/ +theorem bounds_13_3119 : exactInterval 13 3119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3119 : oddCount 3119 13 = 7 ∧ acceleratedOrbit 13 3119 = 833 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3119) = 3 ^ 7 * m + 833 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3119.1, data_13_3119.2] + +/-- Complete interval computation for depth 13, residue 3120. -/ +theorem bounds_13_3120 : exactInterval 13 3120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3120 : oddCount 3120 13 = 5 ∧ acceleratedOrbit 13 3120 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3120) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3120.1, data_13_3120.2] + +/-- Complete interval computation for depth 13, residue 3121. -/ +theorem bounds_13_3121 : exactInterval 13 3121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3121 : oddCount 3121 13 = 7 ∧ acceleratedOrbit 13 3121 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3121) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3121.1, data_13_3121.2] + +/-- Complete interval computation for depth 13, residue 3122. -/ +theorem bounds_13_3122 : exactInterval 13 3122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3122 : oddCount 3122 13 = 7 ∧ acceleratedOrbit 13 3122 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3122) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3122.1, data_13_3122.2] + +end Collatz.Research.StoppingAtlas.Batch0670 From 59a21c0b1fe4070653fff47ff71e58124c2c7e1e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:09 +0530 Subject: [PATCH 0671/1001] proof: certify atlas Batch0671 (13:3123 to 13:3137) --- Collatz/Research/StoppingAtlas/Batch0671.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0671.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0671.lean b/Collatz/Research/StoppingAtlas/Batch0671.lean new file mode 100644 index 00000000..d4346bab --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0671.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0671 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3123. -/ +theorem bounds_13_3123 : exactInterval 13 3123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3123 : oddCount 3123 13 = 7 ∧ acceleratedOrbit 13 3123 = 836 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3123) = 3 ^ 7 * m + 836 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3123.1, data_13_3123.2] + +/-- Complete interval computation for depth 13, residue 3124. -/ +theorem bounds_13_3124 : exactInterval 13 3124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3124 : oddCount 3124 13 = 5 ∧ acceleratedOrbit 13 3124 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3124) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3124.1, data_13_3124.2] + +/-- Complete interval computation for depth 13, residue 3125. -/ +theorem bounds_13_3125 : exactInterval 13 3125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3125 : oddCount 3125 13 = 5 ∧ acceleratedOrbit 13 3125 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3125) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3125.1, data_13_3125.2] + +/-- Complete interval computation for depth 13, residue 3126. -/ +theorem bounds_13_3126 : exactInterval 13 3126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3126 : oddCount 3126 13 = 8 ∧ acceleratedOrbit 13 3126 = 2506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3126) = 3 ^ 8 * m + 2506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3126.1, data_13_3126.2] + +/-- Complete interval computation for depth 13, residue 3127. -/ +theorem bounds_13_3127 : exactInterval 13 3127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3127 : oddCount 3127 13 = 8 ∧ acceleratedOrbit 13 3127 = 2506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3127) = 3 ^ 8 * m + 2506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3127.1, data_13_3127.2] + +/-- Complete interval computation for depth 13, residue 3128. -/ +theorem bounds_13_3128 : exactInterval 13 3128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3128 : oddCount 3128 13 = 4 ∧ acceleratedOrbit 13 3128 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3128) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3128.1, data_13_3128.2] + +/-- Complete interval computation for depth 13, residue 3129. -/ +theorem bounds_13_3129 : exactInterval 13 3129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3129 : oddCount 3129 13 = 8 ∧ acceleratedOrbit 13 3129 = 2510 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3129) = 3 ^ 8 * m + 2510 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3129.1, data_13_3129.2] + +/-- Complete interval computation for depth 13, residue 3130. -/ +theorem bounds_13_3130 : exactInterval 13 3130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3130 : oddCount 3130 13 = 4 ∧ acceleratedOrbit 13 3130 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3130) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3130.1, data_13_3130.2] + +/-- Complete interval computation for depth 13, residue 3131. -/ +theorem bounds_13_3131 : exactInterval 13 3131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3131 : oddCount 3131 13 = 9 ∧ acceleratedOrbit 13 3131 = 7532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3131) = 3 ^ 9 * m + 7532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3131.1, data_13_3131.2] + +/-- Complete interval computation for depth 13, residue 3132. -/ +theorem bounds_13_3132 : exactInterval 13 3132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3132 : oddCount 3132 13 = 4 ∧ acceleratedOrbit 13 3132 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3132) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3132.1, data_13_3132.2] + +/-- Complete interval computation for depth 13, residue 3133. -/ +theorem bounds_13_3133 : exactInterval 13 3133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3133 : oddCount 3133 13 = 4 ∧ acceleratedOrbit 13 3133 = 31 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3133) = 3 ^ 4 * m + 31 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3133.1, data_13_3133.2] + +/-- Complete interval computation for depth 13, residue 3134. -/ +theorem bounds_13_3134 : exactInterval 13 3134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3134 : oddCount 3134 13 = 8 ∧ acceleratedOrbit 13 3134 = 2512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3134) = 3 ^ 8 * m + 2512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3134.1, data_13_3134.2] + +/-- Complete interval computation for depth 13, residue 3135. -/ +theorem bounds_13_3135 : exactInterval 13 3135 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3135) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3135 : oddCount 3135 13 = 8 ∧ acceleratedOrbit 13 3135 = 2512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3135) = 3 ^ 8 * m + 2512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3135.1, data_13_3135.2] + +/-- Complete interval computation for depth 13, residue 3136. -/ +theorem bounds_13_3136 : exactInterval 13 3136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3136 : oddCount 3136 13 = 3 ∧ acceleratedOrbit 13 3136 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3136) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3136.1, data_13_3136.2] + +/-- Complete interval computation for depth 13, residue 3137. -/ +theorem bounds_13_3137 : exactInterval 13 3137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3137 : oddCount 3137 13 = 6 ∧ acceleratedOrbit 13 3137 = 280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3137) = 3 ^ 6 * m + 280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3137.1, data_13_3137.2] + +end Collatz.Research.StoppingAtlas.Batch0671 From 6d0a06e42f0d88197adbcec3f064c90946eaa061 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:09 +0530 Subject: [PATCH 0672/1001] proof: certify atlas Batch0672 (13:3138 to 13:3152) --- Collatz/Research/StoppingAtlas/Batch0672.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0672.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0672.lean b/Collatz/Research/StoppingAtlas/Batch0672.lean new file mode 100644 index 00000000..726559e9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0672.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0672 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3138. -/ +theorem bounds_13_3138 : exactInterval 13 3138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3138 : oddCount 3138 13 = 6 ∧ acceleratedOrbit 13 3138 = 280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3138) = 3 ^ 6 * m + 280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3138.1, data_13_3138.2] + +/-- Complete interval computation for depth 13, residue 3139. -/ +theorem bounds_13_3139 : exactInterval 13 3139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3139 : oddCount 3139 13 = 6 ∧ acceleratedOrbit 13 3139 = 280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3139) = 3 ^ 6 * m + 280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3139.1, data_13_3139.2] + +/-- Complete interval computation for depth 13, residue 3140. -/ +theorem bounds_13_3140 : exactInterval 13 3140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3140 : oddCount 3140 13 = 5 ∧ acceleratedOrbit 13 3140 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3140) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3140.1, data_13_3140.2] + +/-- Complete interval computation for depth 13, residue 3141. -/ +theorem bounds_13_3141 : exactInterval 13 3141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3141 : oddCount 3141 13 = 5 ∧ acceleratedOrbit 13 3141 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3141) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3141.1, data_13_3141.2] + +/-- Complete interval computation for depth 13, residue 3142. -/ +theorem bounds_13_3142 : exactInterval 13 3142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3142 : oddCount 3142 13 = 5 ∧ acceleratedOrbit 13 3142 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3142) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3142.1, data_13_3142.2] + +/-- Complete interval computation for depth 13, residue 3143. -/ +theorem bounds_13_3143 : exactInterval 13 3143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3143 : oddCount 3143 13 = 8 ∧ acceleratedOrbit 13 3143 = 2519 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3143) = 3 ^ 8 * m + 2519 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3143.1, data_13_3143.2] + +/-- Complete interval computation for depth 13, residue 3144. -/ +theorem bounds_13_3144 : exactInterval 13 3144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3144 : oddCount 3144 13 = 6 ∧ acceleratedOrbit 13 3144 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3144) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3144.1, data_13_3144.2] + +/-- Complete interval computation for depth 13, residue 3145. -/ +theorem bounds_13_3145 : exactInterval 13 3145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3145 : oddCount 3145 13 = 8 ∧ acceleratedOrbit 13 3145 = 2521 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3145) = 3 ^ 8 * m + 2521 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3145.1, data_13_3145.2] + +/-- Complete interval computation for depth 13, residue 3146. -/ +theorem bounds_13_3146 : exactInterval 13 3146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3146 : oddCount 3146 13 = 6 ∧ acceleratedOrbit 13 3146 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3146) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3146.1, data_13_3146.2] + +/-- Complete interval computation for depth 13, residue 3147. -/ +theorem bounds_13_3147 : exactInterval 13 3147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3147 : oddCount 3147 13 = 5 ∧ acceleratedOrbit 13 3147 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3147) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3147.1, data_13_3147.2] + +/-- Complete interval computation for depth 13, residue 3148. -/ +theorem bounds_13_3148 : exactInterval 13 3148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3148 : oddCount 3148 13 = 6 ∧ acceleratedOrbit 13 3148 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3148) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3148.1, data_13_3148.2] + +/-- Complete interval computation for depth 13, residue 3149. -/ +theorem bounds_13_3149 : exactInterval 13 3149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3149 : oddCount 3149 13 = 6 ∧ acceleratedOrbit 13 3149 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3149) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3149.1, data_13_3149.2] + +/-- Complete interval computation for depth 13, residue 3150. -/ +theorem bounds_13_3150 : exactInterval 13 3150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3150 : oddCount 3150 13 = 6 ∧ acceleratedOrbit 13 3150 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3150) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3150.1, data_13_3150.2] + +/-- Complete interval computation for depth 13, residue 3151. -/ +theorem bounds_13_3151 : exactInterval 13 3151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3151 : oddCount 3151 13 = 6 ∧ acceleratedOrbit 13 3151 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3151) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3151.1, data_13_3151.2] + +/-- Complete interval computation for depth 13, residue 3152. -/ +theorem bounds_13_3152 : exactInterval 13 3152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3152 : oddCount 3152 13 = 3 ∧ acceleratedOrbit 13 3152 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3152) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3152.1, data_13_3152.2] + +end Collatz.Research.StoppingAtlas.Batch0672 From a11304097d170cbcf1de1fba3c650e815bcfcb43 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:11 +0530 Subject: [PATCH 0673/1001] proof: certify atlas Batch0673 (13:3153 to 13:3168) --- Collatz/Research/StoppingAtlas/Batch0673.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0673.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0673.lean b/Collatz/Research/StoppingAtlas/Batch0673.lean new file mode 100644 index 00000000..e06ac97d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0673.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0673 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3153. -/ +theorem bounds_13_3153 : exactInterval 13 3153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3153 : oddCount 3153 13 = 6 ∧ acceleratedOrbit 13 3153 = 281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3153) = 3 ^ 6 * m + 281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3153.1, data_13_3153.2] + +/-- Complete interval computation for depth 13, residue 3154. -/ +theorem bounds_13_3154 : exactInterval 13 3154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3154 : oddCount 3154 13 = 10 ∧ acceleratedOrbit 13 3154 = 22760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3154) = 3 ^ 10 * m + 22760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3154.1, data_13_3154.2] + +/-- Complete interval computation for depth 13, residue 3155. -/ +theorem bounds_13_3155 : exactInterval 13 3155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3155 : oddCount 3155 13 = 10 ∧ acceleratedOrbit 13 3155 = 22760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3155) = 3 ^ 10 * m + 22760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3155.1, data_13_3155.2] + +/-- Complete interval computation for depth 13, residue 3156. -/ +theorem bounds_13_3156 : exactInterval 13 3156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3156 : oddCount 3156 13 = 3 ∧ acceleratedOrbit 13 3156 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3156) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3156.1, data_13_3156.2] + +/-- Complete interval computation for depth 13, residue 3157. -/ +theorem bounds_13_3157 : exactInterval 13 3157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3157 : oddCount 3157 13 = 3 ∧ acceleratedOrbit 13 3157 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3157) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3157.1, data_13_3157.2] + +/-- Complete interval computation for depth 13, residue 3158. -/ +theorem bounds_13_3158 : exactInterval 13 3158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3158 : oddCount 3158 13 = 5 ∧ acceleratedOrbit 13 3158 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3158) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3158.1, data_13_3158.2] + +/-- Complete interval computation for depth 13, residue 3159. -/ +theorem bounds_13_3159 : exactInterval 13 3159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3159 : oddCount 3159 13 = 5 ∧ acceleratedOrbit 13 3159 = 94 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3159) = 3 ^ 5 * m + 94 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3159.1, data_13_3159.2] + +/-- Complete interval computation for depth 13, residue 3160. -/ +theorem bounds_13_3160 : exactInterval 13 3160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3160 : oddCount 3160 13 = 6 ∧ acceleratedOrbit 13 3160 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3160) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3160.1, data_13_3160.2] + +/-- Complete interval computation for depth 13, residue 3161. -/ +theorem bounds_13_3161 : exactInterval 13 3161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3161 : oddCount 3161 13 = 8 ∧ acceleratedOrbit 13 3161 = 2537 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3161) = 3 ^ 8 * m + 2537 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3161.1, data_13_3161.2] + +/-- Complete interval computation for depth 13, residue 3162. -/ +theorem bounds_13_3162 : exactInterval 13 3162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3162 : oddCount 3162 13 = 6 ∧ acceleratedOrbit 13 3162 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3162) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3162.1, data_13_3162.2] + +/-- Complete interval computation for depth 13, residue 3163. -/ +theorem bounds_13_3163 : exactInterval 13 3163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3163 : oddCount 3163 13 = 9 ∧ acceleratedOrbit 13 3163 = 7604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3163) = 3 ^ 9 * m + 7604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3163.1, data_13_3163.2] + +/-- Complete interval computation for depth 13, residue 3164. -/ +theorem bounds_13_3164 : exactInterval 13 3164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3164 : oddCount 3164 13 = 6 ∧ acceleratedOrbit 13 3164 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3164) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3164.1, data_13_3164.2] + +/-- Complete interval computation for depth 13, residue 3165. -/ +theorem bounds_13_3165 : exactInterval 13 3165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3165 : oddCount 3165 13 = 6 ∧ acceleratedOrbit 13 3165 = 283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3165) = 3 ^ 6 * m + 283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3165.1, data_13_3165.2] + +/-- Complete interval computation for depth 13, residue 3166. -/ +theorem bounds_13_3166 : exactInterval 13 3166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3166 : oddCount 3166 13 = 10 ∧ acceleratedOrbit 13 3166 = 22841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3166) = 3 ^ 10 * m + 22841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3166.1, data_13_3166.2] + +/-- Complete interval computation for depth 13, residue 3167. -/ +theorem bounds_13_3167 : exactInterval 13 3167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3167 : oddCount 3167 13 = 10 ∧ acceleratedOrbit 13 3167 = 22841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3167) = 3 ^ 10 * m + 22841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3167.1, data_13_3167.2] + +/-- Complete interval computation for depth 13, residue 3168. -/ +theorem bounds_13_3168 : exactInterval 13 3168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3168 : oddCount 3168 13 = 3 ∧ acceleratedOrbit 13 3168 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3168) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3168.1, data_13_3168.2] + +end Collatz.Research.StoppingAtlas.Batch0673 From 214fcfcff77c42ef200aef175f18eca8635a9478 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:13 +0530 Subject: [PATCH 0674/1001] proof: certify atlas Batch0674 (13:3169 to 13:3183) --- Collatz/Research/StoppingAtlas/Batch0674.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0674.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0674.lean b/Collatz/Research/StoppingAtlas/Batch0674.lean new file mode 100644 index 00000000..366f00e0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0674.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0674 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3169. -/ +theorem bounds_13_3169 : exactInterval 13 3169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3169 : oddCount 3169 13 = 7 ∧ acceleratedOrbit 13 3169 = 847 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3169) = 3 ^ 7 * m + 847 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3169.1, data_13_3169.2] + +/-- Complete interval computation for depth 13, residue 3170. -/ +theorem bounds_13_3170 : exactInterval 13 3170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3170 : oddCount 3170 13 = 7 ∧ acceleratedOrbit 13 3170 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3170) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3170.1, data_13_3170.2] + +/-- Complete interval computation for depth 13, residue 3171. -/ +theorem bounds_13_3171 : exactInterval 13 3171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3171 : oddCount 3171 13 = 7 ∧ acceleratedOrbit 13 3171 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3171) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3171.1, data_13_3171.2] + +/-- Complete interval computation for depth 13, residue 3172. -/ +theorem bounds_13_3172 : exactInterval 13 3172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3172 : oddCount 3172 13 = 7 ∧ acceleratedOrbit 13 3172 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3172) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3172.1, data_13_3172.2] + +/-- Complete interval computation for depth 13, residue 3173. -/ +theorem bounds_13_3173 : exactInterval 13 3173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3173 : oddCount 3173 13 = 7 ∧ acceleratedOrbit 13 3173 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3173) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3173.1, data_13_3173.2] + +/-- Complete interval computation for depth 13, residue 3174. -/ +theorem bounds_13_3174 : exactInterval 13 3174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3174 : oddCount 3174 13 = 7 ∧ acceleratedOrbit 13 3174 = 850 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3174) = 3 ^ 7 * m + 850 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3174.1, data_13_3174.2] + +/-- Complete interval computation for depth 13, residue 3175. -/ +theorem bounds_13_3175 : exactInterval 13 3175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3175 : oddCount 3175 13 = 11 ∧ acceleratedOrbit 13 3175 = 68687 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3175) = 3 ^ 11 * m + 68687 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3175.1, data_13_3175.2] + +/-- Complete interval computation for depth 13, residue 3176. -/ +theorem bounds_13_3176 : exactInterval 13 3176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3176 : oddCount 3176 13 = 3 ∧ acceleratedOrbit 13 3176 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3176) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3176.1, data_13_3176.2] + +/-- Complete interval computation for depth 13, residue 3177. -/ +theorem bounds_13_3177 : exactInterval 13 3177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3177 : oddCount 3177 13 = 9 ∧ acceleratedOrbit 13 3177 = 7640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3177) = 3 ^ 9 * m + 7640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3177.1, data_13_3177.2] + +/-- Complete interval computation for depth 13, residue 3178. -/ +theorem bounds_13_3178 : exactInterval 13 3178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3178 : oddCount 3178 13 = 3 ∧ acceleratedOrbit 13 3178 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3178) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3178.1, data_13_3178.2] + +/-- Complete interval computation for depth 13, residue 3179. -/ +theorem bounds_13_3179 : exactInterval 13 3179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3179 : oddCount 3179 13 = 8 ∧ acceleratedOrbit 13 3179 = 2548 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3179) = 3 ^ 8 * m + 2548 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3179.1, data_13_3179.2] + +/-- Complete interval computation for depth 13, residue 3180. -/ +theorem bounds_13_3180 : exactInterval 13 3180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3180 : oddCount 3180 13 = 9 ∧ acceleratedOrbit 13 3180 = 7654 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3180) = 3 ^ 9 * m + 7654 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3180.1, data_13_3180.2] + +/-- Complete interval computation for depth 13, residue 3181. -/ +theorem bounds_13_3181 : exactInterval 13 3181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3181 : oddCount 3181 13 = 9 ∧ acceleratedOrbit 13 3181 = 7654 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3181) = 3 ^ 9 * m + 7654 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3181.1, data_13_3181.2] + +/-- Complete interval computation for depth 13, residue 3182. -/ +theorem bounds_13_3182 : exactInterval 13 3182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3182 : oddCount 3182 13 = 9 ∧ acceleratedOrbit 13 3182 = 7654 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3182) = 3 ^ 9 * m + 7654 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3182.1, data_13_3182.2] + +/-- Complete interval computation for depth 13, residue 3183. -/ +theorem bounds_13_3183 : exactInterval 13 3183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3183 : oddCount 3183 13 = 9 ∧ acceleratedOrbit 13 3183 = 7651 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3183) = 3 ^ 9 * m + 7651 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3183.1, data_13_3183.2] + +end Collatz.Research.StoppingAtlas.Batch0674 From af543aa762630797129636ab1aa8324d2f417b9e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:13 +0530 Subject: [PATCH 0675/1001] proof: certify atlas Batch0675 (13:3184 to 13:3199) --- Collatz/Research/StoppingAtlas/Batch0675.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0675.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0675.lean b/Collatz/Research/StoppingAtlas/Batch0675.lean new file mode 100644 index 00000000..55944422 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0675.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0675 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3184. -/ +theorem bounds_13_3184 : exactInterval 13 3184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3184 : oddCount 3184 13 = 5 ∧ acceleratedOrbit 13 3184 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3184) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3184.1, data_13_3184.2] + +/-- Complete interval computation for depth 13, residue 3185. -/ +theorem bounds_13_3185 : exactInterval 13 3185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3185 : oddCount 3185 13 = 3 ∧ acceleratedOrbit 13 3185 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3185) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3185.1, data_13_3185.2] + +/-- Complete interval computation for depth 13, residue 3186. -/ +theorem bounds_13_3186 : exactInterval 13 3186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3186 : oddCount 3186 13 = 6 ∧ acceleratedOrbit 13 3186 = 284 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3186) = 3 ^ 6 * m + 284 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3186.1, data_13_3186.2] + +/-- Complete interval computation for depth 13, residue 3187. -/ +theorem bounds_13_3187 : exactInterval 13 3187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3187 : oddCount 3187 13 = 6 ∧ acceleratedOrbit 13 3187 = 284 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3187) = 3 ^ 6 * m + 284 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3187.1, data_13_3187.2] + +/-- Complete interval computation for depth 13, residue 3188. -/ +theorem bounds_13_3188 : exactInterval 13 3188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3188 : oddCount 3188 13 = 5 ∧ acceleratedOrbit 13 3188 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3188) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3188.1, data_13_3188.2] + +/-- Complete interval computation for depth 13, residue 3189. -/ +theorem bounds_13_3189 : exactInterval 13 3189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3189 : oddCount 3189 13 = 5 ∧ acceleratedOrbit 13 3189 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3189) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3189.1, data_13_3189.2] + +/-- Complete interval computation for depth 13, residue 3190. -/ +theorem bounds_13_3190 : exactInterval 13 3190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3190 : oddCount 3190 13 = 7 ∧ acceleratedOrbit 13 3190 = 854 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3190) = 3 ^ 7 * m + 854 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3190.1, data_13_3190.2] + +/-- Complete interval computation for depth 13, residue 3191. -/ +theorem bounds_13_3191 : exactInterval 13 3191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3191) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3191 : oddCount 3191 13 = 7 ∧ acceleratedOrbit 13 3191 = 854 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3191) = 3 ^ 7 * m + 854 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3191.1, data_13_3191.2] + +/-- Complete interval computation for depth 13, residue 3192. -/ +theorem bounds_13_3192 : exactInterval 13 3192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3192 : oddCount 3192 13 = 5 ∧ acceleratedOrbit 13 3192 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3192) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3192.1, data_13_3192.2] + +/-- Complete interval computation for depth 13, residue 3193. -/ +theorem bounds_13_3193 : exactInterval 13 3193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3193 : oddCount 3193 13 = 7 ∧ acceleratedOrbit 13 3193 = 853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3193) = 3 ^ 7 * m + 853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3193.1, data_13_3193.2] + +/-- Complete interval computation for depth 13, residue 3194. -/ +theorem bounds_13_3194 : exactInterval 13 3194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3194 : oddCount 3194 13 = 5 ∧ acceleratedOrbit 13 3194 = 95 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3194) = 3 ^ 5 * m + 95 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3194.1, data_13_3194.2] + +/-- Complete interval computation for depth 13, residue 3195. -/ +theorem bounds_13_3195 : exactInterval 13 3195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3195 : oddCount 3195 13 = 7 ∧ acceleratedOrbit 13 3195 = 854 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3195) = 3 ^ 7 * m + 854 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3195.1, data_13_3195.2] + +/-- Complete interval computation for depth 13, residue 3196. -/ +theorem bounds_13_3196 : exactInterval 13 3196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3196 : oddCount 3196 13 = 8 ∧ acceleratedOrbit 13 3196 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3196) = 3 ^ 8 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3196.1, data_13_3196.2] + +/-- Complete interval computation for depth 13, residue 3197. -/ +theorem bounds_13_3197 : exactInterval 13 3197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3197 : oddCount 3197 13 = 8 ∧ acceleratedOrbit 13 3197 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3197) = 3 ^ 8 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3197.1, data_13_3197.2] + +/-- Complete interval computation for depth 13, residue 3198. -/ +theorem bounds_13_3198 : exactInterval 13 3198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3198 : oddCount 3198 13 = 8 ∧ acceleratedOrbit 13 3198 = 2564 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3198) = 3 ^ 8 * m + 2564 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3198.1, data_13_3198.2] + +/-- Complete interval computation for depth 13, residue 3199. -/ +theorem bounds_13_3199 : exactInterval 13 3199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3199 : oddCount 3199 13 = 11 ∧ acceleratedOrbit 13 3199 = 69200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3199) = 3 ^ 11 * m + 69200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3199.1, data_13_3199.2] + +end Collatz.Research.StoppingAtlas.Batch0675 From 744849bf291306342215b85e8f17ac4361d46402 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:14 +0530 Subject: [PATCH 0676/1001] proof: certify atlas Batch0676 (13:3200 to 13:3214) --- Collatz/Research/StoppingAtlas/Batch0676.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0676.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0676.lean b/Collatz/Research/StoppingAtlas/Batch0676.lean new file mode 100644 index 00000000..d4985dde --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0676.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0676 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3200. -/ +theorem bounds_13_3200 : exactInterval 13 3200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3200 : oddCount 3200 13 = 3 ∧ acceleratedOrbit 13 3200 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3200) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3200.1, data_13_3200.2] + +/-- Complete interval computation for depth 13, residue 3201. -/ +theorem bounds_13_3201 : exactInterval 13 3201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3201 : oddCount 3201 13 = 8 ∧ acceleratedOrbit 13 3201 = 2567 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3201) = 3 ^ 8 * m + 2567 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3201.1, data_13_3201.2] + +/-- Complete interval computation for depth 13, residue 3202. -/ +theorem bounds_13_3202 : exactInterval 13 3202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3202 : oddCount 3202 13 = 6 ∧ acceleratedOrbit 13 3202 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3202) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3202.1, data_13_3202.2] + +/-- Complete interval computation for depth 13, residue 3203. -/ +theorem bounds_13_3203 : exactInterval 13 3203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3203 : oddCount 3203 13 = 6 ∧ acceleratedOrbit 13 3203 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3203) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3203.1, data_13_3203.2] + +/-- Complete interval computation for depth 13, residue 3204. -/ +theorem bounds_13_3204 : exactInterval 13 3204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3204 : oddCount 3204 13 = 6 ∧ acceleratedOrbit 13 3204 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3204) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3204.1, data_13_3204.2] + +/-- Complete interval computation for depth 13, residue 3205. -/ +theorem bounds_13_3205 : exactInterval 13 3205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3205 : oddCount 3205 13 = 6 ∧ acceleratedOrbit 13 3205 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3205) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3205.1, data_13_3205.2] + +/-- Complete interval computation for depth 13, residue 3206. -/ +theorem bounds_13_3206 : exactInterval 13 3206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3206 : oddCount 3206 13 = 6 ∧ acceleratedOrbit 13 3206 = 287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3206) = 3 ^ 6 * m + 287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3206.1, data_13_3206.2] + +/-- Complete interval computation for depth 13, residue 3207. -/ +theorem bounds_13_3207 : exactInterval 13 3207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3207 : oddCount 3207 13 = 7 ∧ acceleratedOrbit 13 3207 = 857 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3207) = 3 ^ 7 * m + 857 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3207.1, data_13_3207.2] + +/-- Complete interval computation for depth 13, residue 3208. -/ +theorem bounds_13_3208 : exactInterval 13 3208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3208 : oddCount 3208 13 = 4 ∧ acceleratedOrbit 13 3208 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3208) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3208.1, data_13_3208.2] + +/-- Complete interval computation for depth 13, residue 3209. -/ +theorem bounds_13_3209 : exactInterval 13 3209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3209 : oddCount 3209 13 = 9 ∧ acceleratedOrbit 13 3209 = 7715 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3209) = 3 ^ 9 * m + 7715 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3209.1, data_13_3209.2] + +/-- Complete interval computation for depth 13, residue 3210. -/ +theorem bounds_13_3210 : exactInterval 13 3210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3210 : oddCount 3210 13 = 4 ∧ acceleratedOrbit 13 3210 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3210) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3210.1, data_13_3210.2] + +/-- Complete interval computation for depth 13, residue 3211. -/ +theorem bounds_13_3211 : exactInterval 13 3211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3211 : oddCount 3211 13 = 6 ∧ acceleratedOrbit 13 3211 = 286 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3211) = 3 ^ 6 * m + 286 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3211.1, data_13_3211.2] + +/-- Complete interval computation for depth 13, residue 3212. -/ +theorem bounds_13_3212 : exactInterval 13 3212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3212 : oddCount 3212 13 = 4 ∧ acceleratedOrbit 13 3212 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3212) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3212.1, data_13_3212.2] + +/-- Complete interval computation for depth 13, residue 3213. -/ +theorem bounds_13_3213 : exactInterval 13 3213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3213 : oddCount 3213 13 = 4 ∧ acceleratedOrbit 13 3213 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3213) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3213.1, data_13_3213.2] + +/-- Complete interval computation for depth 13, residue 3214. -/ +theorem bounds_13_3214 : exactInterval 13 3214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3214 : oddCount 3214 13 = 7 ∧ acceleratedOrbit 13 3214 = 859 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3214) = 3 ^ 7 * m + 859 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3214.1, data_13_3214.2] + +end Collatz.Research.StoppingAtlas.Batch0676 From 555ebbd9647e263a937a67c01d168bc5e0883298 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:15 +0530 Subject: [PATCH 0677/1001] proof: certify atlas Batch0677 (13:3215 to 13:3229) --- Collatz/Research/StoppingAtlas/Batch0677.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0677.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0677.lean b/Collatz/Research/StoppingAtlas/Batch0677.lean new file mode 100644 index 00000000..d942bb84 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0677.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0677 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3215. -/ +theorem bounds_13_3215 : exactInterval 13 3215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3215) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3215 : oddCount 3215 13 = 7 ∧ acceleratedOrbit 13 3215 = 859 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3215) = 3 ^ 7 * m + 859 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3215.1, data_13_3215.2] + +/-- Complete interval computation for depth 13, residue 3216. -/ +theorem bounds_13_3216 : exactInterval 13 3216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3216 : oddCount 3216 13 = 4 ∧ acceleratedOrbit 13 3216 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3216) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3216.1, data_13_3216.2] + +/-- Complete interval computation for depth 13, residue 3217. -/ +theorem bounds_13_3217 : exactInterval 13 3217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3217 : oddCount 3217 13 = 8 ∧ acceleratedOrbit 13 3217 = 2582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3217) = 3 ^ 8 * m + 2582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3217.1, data_13_3217.2] + +/-- Complete interval computation for depth 13, residue 3218. -/ +theorem bounds_13_3218 : exactInterval 13 3218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3218 : oddCount 3218 13 = 8 ∧ acceleratedOrbit 13 3218 = 2582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3218) = 3 ^ 8 * m + 2582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3218.1, data_13_3218.2] + +/-- Complete interval computation for depth 13, residue 3219. -/ +theorem bounds_13_3219 : exactInterval 13 3219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3219 : oddCount 3219 13 = 8 ∧ acceleratedOrbit 13 3219 = 2582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3219) = 3 ^ 8 * m + 2582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3219.1, data_13_3219.2] + +/-- Complete interval computation for depth 13, residue 3220. -/ +theorem bounds_13_3220 : exactInterval 13 3220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3220 : oddCount 3220 13 = 4 ∧ acceleratedOrbit 13 3220 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3220) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3220.1, data_13_3220.2] + +/-- Complete interval computation for depth 13, residue 3221. -/ +theorem bounds_13_3221 : exactInterval 13 3221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3221 : oddCount 3221 13 = 4 ∧ acceleratedOrbit 13 3221 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3221) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3221.1, data_13_3221.2] + +/-- Complete interval computation for depth 13, residue 3222. -/ +theorem bounds_13_3222 : exactInterval 13 3222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3222 : oddCount 3222 13 = 4 ∧ acceleratedOrbit 13 3222 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3222) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3222.1, data_13_3222.2] + +/-- Complete interval computation for depth 13, residue 3223. -/ +theorem bounds_13_3223 : exactInterval 13 3223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3223 : oddCount 3223 13 = 4 ∧ acceleratedOrbit 13 3223 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3223) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3223.1, data_13_3223.2] + +/-- Complete interval computation for depth 13, residue 3224. -/ +theorem bounds_13_3224 : exactInterval 13 3224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3224 : oddCount 3224 13 = 4 ∧ acceleratedOrbit 13 3224 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3224) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3224.1, data_13_3224.2] + +/-- Complete interval computation for depth 13, residue 3225. -/ +theorem bounds_13_3225 : exactInterval 13 3225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3225 : oddCount 3225 13 = 7 ∧ acceleratedOrbit 13 3225 = 863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3225) = 3 ^ 7 * m + 863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3225.1, data_13_3225.2] + +/-- Complete interval computation for depth 13, residue 3226. -/ +theorem bounds_13_3226 : exactInterval 13 3226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3226 : oddCount 3226 13 = 4 ∧ acceleratedOrbit 13 3226 = 32 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3226) = 3 ^ 4 * m + 32 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3226.1, data_13_3226.2] + +/-- Complete interval computation for depth 13, residue 3227. -/ +theorem bounds_13_3227 : exactInterval 13 3227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3227 : oddCount 3227 13 = 10 ∧ acceleratedOrbit 13 3227 = 23273 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3227) = 3 ^ 10 * m + 23273 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3227.1, data_13_3227.2] + +/-- Complete interval computation for depth 13, residue 3228. -/ +theorem bounds_13_3228 : exactInterval 13 3228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3228 : oddCount 3228 13 = 8 ∧ acceleratedOrbit 13 3228 = 2591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3228) = 3 ^ 8 * m + 2591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3228.1, data_13_3228.2] + +/-- Complete interval computation for depth 13, residue 3229. -/ +theorem bounds_13_3229 : exactInterval 13 3229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3229 : oddCount 3229 13 = 8 ∧ acceleratedOrbit 13 3229 = 2591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3229) = 3 ^ 8 * m + 2591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3229.1, data_13_3229.2] + +end Collatz.Research.StoppingAtlas.Batch0677 From 53de9675c13803d177ca37e8800b4c58df92a669 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:18 +0530 Subject: [PATCH 0678/1001] proof: certify atlas Batch0678 (13:3230 to 13:3245) --- Collatz/Research/StoppingAtlas/Batch0678.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0678.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0678.lean b/Collatz/Research/StoppingAtlas/Batch0678.lean new file mode 100644 index 00000000..d2c25732 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0678.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0678 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3230. -/ +theorem bounds_13_3230 : exactInterval 13 3230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3230 : oddCount 3230 13 = 8 ∧ acceleratedOrbit 13 3230 = 2591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3230) = 3 ^ 8 * m + 2591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3230.1, data_13_3230.2] + +/-- Complete interval computation for depth 13, residue 3231. -/ +theorem bounds_13_3231 : exactInterval 13 3231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3231 : oddCount 3231 13 = 11 ∧ acceleratedOrbit 13 3231 = 69893 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3231) = 3 ^ 11 * m + 69893 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3231.1, data_13_3231.2] + +/-- Complete interval computation for depth 13, residue 3232. -/ +theorem bounds_13_3232 : exactInterval 13 3232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3232 : oddCount 3232 13 = 3 ∧ acceleratedOrbit 13 3232 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3232) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3232.1, data_13_3232.2] + +/-- Complete interval computation for depth 13, residue 3233. -/ +theorem bounds_13_3233 : exactInterval 13 3233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3233 : oddCount 3233 13 = 10 ∧ acceleratedOrbit 13 3233 = 23327 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3233) = 3 ^ 10 * m + 23327 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3233.1, data_13_3233.2] + +/-- Complete interval computation for depth 13, residue 3234. -/ +theorem bounds_13_3234 : exactInterval 13 3234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3234 : oddCount 3234 13 = 7 ∧ acceleratedOrbit 13 3234 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3234) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3234.1, data_13_3234.2] + +/-- Complete interval computation for depth 13, residue 3235. -/ +theorem bounds_13_3235 : exactInterval 13 3235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3235 : oddCount 3235 13 = 7 ∧ acceleratedOrbit 13 3235 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3235) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3235.1, data_13_3235.2] + +/-- Complete interval computation for depth 13, residue 3236. -/ +theorem bounds_13_3236 : exactInterval 13 3236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3236 : oddCount 3236 13 = 7 ∧ acceleratedOrbit 13 3236 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3236) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3236.1, data_13_3236.2] + +/-- Complete interval computation for depth 13, residue 3237. -/ +theorem bounds_13_3237 : exactInterval 13 3237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3237 : oddCount 3237 13 = 7 ∧ acceleratedOrbit 13 3237 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3237) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3237.1, data_13_3237.2] + +/-- Complete interval computation for depth 13, residue 3238. -/ +theorem bounds_13_3238 : exactInterval 13 3238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3238 : oddCount 3238 13 = 7 ∧ acceleratedOrbit 13 3238 = 866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3238) = 3 ^ 7 * m + 866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3238.1, data_13_3238.2] + +/-- Complete interval computation for depth 13, residue 3239. -/ +theorem bounds_13_3239 : exactInterval 13 3239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3239 : oddCount 3239 13 = 9 ∧ acceleratedOrbit 13 3239 = 7786 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3239) = 3 ^ 9 * m + 7786 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3239.1, data_13_3239.2] + +/-- Complete interval computation for depth 13, residue 3240. -/ +theorem bounds_13_3240 : exactInterval 13 3240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3240 : oddCount 3240 13 = 3 ∧ acceleratedOrbit 13 3240 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3240) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3240.1, data_13_3240.2] + +/-- Complete interval computation for depth 13, residue 3241. -/ +theorem bounds_13_3241 : exactInterval 13 3241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3241 : oddCount 3241 13 = 8 ∧ acceleratedOrbit 13 3241 = 2597 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3241) = 3 ^ 8 * m + 2597 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3241.1, data_13_3241.2] + +/-- Complete interval computation for depth 13, residue 3242. -/ +theorem bounds_13_3242 : exactInterval 13 3242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3242 : oddCount 3242 13 = 3 ∧ acceleratedOrbit 13 3242 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3242) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3242.1, data_13_3242.2] + +/-- Complete interval computation for depth 13, residue 3243. -/ +theorem bounds_13_3243 : exactInterval 13 3243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3243 : oddCount 3243 13 = 6 ∧ acceleratedOrbit 13 3243 = 289 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3243) = 3 ^ 6 * m + 289 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3243.1, data_13_3243.2] + +/-- Complete interval computation for depth 13, residue 3244. -/ +theorem bounds_13_3244 : exactInterval 13 3244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3244 : oddCount 3244 13 = 6 ∧ acceleratedOrbit 13 3244 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3244) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3244.1, data_13_3244.2] + +/-- Complete interval computation for depth 13, residue 3245. -/ +theorem bounds_13_3245 : exactInterval 13 3245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3245 : oddCount 3245 13 = 6 ∧ acceleratedOrbit 13 3245 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3245) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3245.1, data_13_3245.2] + +end Collatz.Research.StoppingAtlas.Batch0678 From f8391f6be6472796290abfd9b87844de6c2e7a21 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:18 +0530 Subject: [PATCH 0679/1001] proof: certify atlas Batch0679 (13:3246 to 13:3260) --- Collatz/Research/StoppingAtlas/Batch0679.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0679.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0679.lean b/Collatz/Research/StoppingAtlas/Batch0679.lean new file mode 100644 index 00000000..cf0483f8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0679.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0679 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3246. -/ +theorem bounds_13_3246 : exactInterval 13 3246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3246 : oddCount 3246 13 = 6 ∧ acceleratedOrbit 13 3246 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3246) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3246.1, data_13_3246.2] + +/-- Complete interval computation for depth 13, residue 3247. -/ +theorem bounds_13_3247 : exactInterval 13 3247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3247 : oddCount 3247 13 = 8 ∧ acceleratedOrbit 13 3247 = 2602 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3247) = 3 ^ 8 * m + 2602 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3247.1, data_13_3247.2] + +/-- Complete interval computation for depth 13, residue 3248. -/ +theorem bounds_13_3248 : exactInterval 13 3248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3248 : oddCount 3248 13 = 5 ∧ acceleratedOrbit 13 3248 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3248) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3248.1, data_13_3248.2] + +/-- Complete interval computation for depth 13, residue 3249. -/ +theorem bounds_13_3249 : exactInterval 13 3249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3249 : oddCount 3249 13 = 6 ∧ acceleratedOrbit 13 3249 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3249) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3249.1, data_13_3249.2] + +/-- Complete interval computation for depth 13, residue 3250. -/ +theorem bounds_13_3250 : exactInterval 13 3250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3250 : oddCount 3250 13 = 6 ∧ acceleratedOrbit 13 3250 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3250) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3250.1, data_13_3250.2] + +/-- Complete interval computation for depth 13, residue 3251. -/ +theorem bounds_13_3251 : exactInterval 13 3251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3251 : oddCount 3251 13 = 6 ∧ acceleratedOrbit 13 3251 = 290 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3251) = 3 ^ 6 * m + 290 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3251.1, data_13_3251.2] + +/-- Complete interval computation for depth 13, residue 3252. -/ +theorem bounds_13_3252 : exactInterval 13 3252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3252 : oddCount 3252 13 = 5 ∧ acceleratedOrbit 13 3252 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3252) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3252.1, data_13_3252.2] + +/-- Complete interval computation for depth 13, residue 3253. -/ +theorem bounds_13_3253 : exactInterval 13 3253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3253 : oddCount 3253 13 = 5 ∧ acceleratedOrbit 13 3253 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3253) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3253.1, data_13_3253.2] + +/-- Complete interval computation for depth 13, residue 3254. -/ +theorem bounds_13_3254 : exactInterval 13 3254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3254 : oddCount 3254 13 = 8 ∧ acceleratedOrbit 13 3254 = 2609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3254) = 3 ^ 8 * m + 2609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3254.1, data_13_3254.2] + +/-- Complete interval computation for depth 13, residue 3255. -/ +theorem bounds_13_3255 : exactInterval 13 3255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3255 : oddCount 3255 13 = 8 ∧ acceleratedOrbit 13 3255 = 2609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3255) = 3 ^ 8 * m + 2609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3255.1, data_13_3255.2] + +/-- Complete interval computation for depth 13, residue 3256. -/ +theorem bounds_13_3256 : exactInterval 13 3256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3256 : oddCount 3256 13 = 5 ∧ acceleratedOrbit 13 3256 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3256) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3256.1, data_13_3256.2] + +/-- Complete interval computation for depth 13, residue 3257. -/ +theorem bounds_13_3257 : exactInterval 13 3257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3257 : oddCount 3257 13 = 8 ∧ acceleratedOrbit 13 3257 = 2612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3257) = 3 ^ 8 * m + 2612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3257.1, data_13_3257.2] + +/-- Complete interval computation for depth 13, residue 3258. -/ +theorem bounds_13_3258 : exactInterval 13 3258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3258 : oddCount 3258 13 = 5 ∧ acceleratedOrbit 13 3258 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3258) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3258.1, data_13_3258.2] + +/-- Complete interval computation for depth 13, residue 3259. -/ +theorem bounds_13_3259 : exactInterval 13 3259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3259 : oddCount 3259 13 = 8 ∧ acceleratedOrbit 13 3259 = 2612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3259) = 3 ^ 8 * m + 2612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3259.1, data_13_3259.2] + +/-- Complete interval computation for depth 13, residue 3260. -/ +theorem bounds_13_3260 : exactInterval 13 3260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3260 : oddCount 3260 13 = 7 ∧ acceleratedOrbit 13 3260 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3260) = 3 ^ 7 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3260.1, data_13_3260.2] + +end Collatz.Research.StoppingAtlas.Batch0679 From 9b4fa9e308537c78c6e563e8797c5c8712f863cf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:19 +0530 Subject: [PATCH 0680/1001] proof: certify atlas Batch0680 (13:3261 to 13:3275) --- Collatz/Research/StoppingAtlas/Batch0680.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0680.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0680.lean b/Collatz/Research/StoppingAtlas/Batch0680.lean new file mode 100644 index 00000000..ac71a118 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0680.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0680 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3261. -/ +theorem bounds_13_3261 : exactInterval 13 3261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3261 : oddCount 3261 13 = 7 ∧ acceleratedOrbit 13 3261 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3261) = 3 ^ 7 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3261.1, data_13_3261.2] + +/-- Complete interval computation for depth 13, residue 3262. -/ +theorem bounds_13_3262 : exactInterval 13 3262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3262 : oddCount 3262 13 = 7 ∧ acceleratedOrbit 13 3262 = 872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3262) = 3 ^ 7 * m + 872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3262.1, data_13_3262.2] + +/-- Complete interval computation for depth 13, residue 3263. -/ +theorem bounds_13_3263 : exactInterval 13 3263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3263 : oddCount 3263 13 = 9 ∧ acceleratedOrbit 13 3263 = 7843 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3263) = 3 ^ 9 * m + 7843 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3263.1, data_13_3263.2] + +/-- Complete interval computation for depth 13, residue 3264. -/ +theorem bounds_13_3264 : exactInterval 13 3264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3264 : oddCount 3264 13 = 3 ∧ acceleratedOrbit 13 3264 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3264) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3264.1, data_13_3264.2] + +/-- Complete interval computation for depth 13, residue 3265. -/ +theorem bounds_13_3265 : exactInterval 13 3265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3265 : oddCount 3265 13 = 5 ∧ acceleratedOrbit 13 3265 = 97 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3265) = 3 ^ 5 * m + 97 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3265.1, data_13_3265.2] + +/-- Complete interval computation for depth 13, residue 3266. -/ +theorem bounds_13_3266 : exactInterval 13 3266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3266 : oddCount 3266 13 = 5 ∧ acceleratedOrbit 13 3266 = 97 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3266) = 3 ^ 5 * m + 97 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3266.1, data_13_3266.2] + +/-- Complete interval computation for depth 13, residue 3267. -/ +theorem bounds_13_3267 : exactInterval 13 3267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3267 : oddCount 3267 13 = 5 ∧ acceleratedOrbit 13 3267 = 97 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3267) = 3 ^ 5 * m + 97 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3267.1, data_13_3267.2] + +/-- Complete interval computation for depth 13, residue 3268. -/ +theorem bounds_13_3268 : exactInterval 13 3268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3268 : oddCount 3268 13 = 5 ∧ acceleratedOrbit 13 3268 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3268) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3268.1, data_13_3268.2] + +/-- Complete interval computation for depth 13, residue 3269. -/ +theorem bounds_13_3269 : exactInterval 13 3269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3269 : oddCount 3269 13 = 5 ∧ acceleratedOrbit 13 3269 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3269) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3269.1, data_13_3269.2] + +/-- Complete interval computation for depth 13, residue 3270. -/ +theorem bounds_13_3270 : exactInterval 13 3270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3270 : oddCount 3270 13 = 5 ∧ acceleratedOrbit 13 3270 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3270) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3270.1, data_13_3270.2] + +/-- Complete interval computation for depth 13, residue 3271. -/ +theorem bounds_13_3271 : exactInterval 13 3271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3271 : oddCount 3271 13 = 7 ∧ acceleratedOrbit 13 3271 = 874 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3271) = 3 ^ 7 * m + 874 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3271.1, data_13_3271.2] + +/-- Complete interval computation for depth 13, residue 3272. -/ +theorem bounds_13_3272 : exactInterval 13 3272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3272 : oddCount 3272 13 = 5 ∧ acceleratedOrbit 13 3272 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3272) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3272.1, data_13_3272.2] + +/-- Complete interval computation for depth 13, residue 3273. -/ +theorem bounds_13_3273 : exactInterval 13 3273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3273 : oddCount 3273 13 = 6 ∧ acceleratedOrbit 13 3273 = 292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3273) = 3 ^ 6 * m + 292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3273.1, data_13_3273.2] + +/-- Complete interval computation for depth 13, residue 3274. -/ +theorem bounds_13_3274 : exactInterval 13 3274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3274 : oddCount 3274 13 = 5 ∧ acceleratedOrbit 13 3274 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3274) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3274.1, data_13_3274.2] + +/-- Complete interval computation for depth 13, residue 3275. -/ +theorem bounds_13_3275 : exactInterval 13 3275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3275 : oddCount 3275 13 = 6 ∧ acceleratedOrbit 13 3275 = 292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3275) = 3 ^ 6 * m + 292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3275.1, data_13_3275.2] + +end Collatz.Research.StoppingAtlas.Batch0680 From 00ffbdc9456c8e5576d84557a6d8d82f77156f21 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:21 +0530 Subject: [PATCH 0681/1001] proof: certify atlas Batch0681 (13:3276 to 13:3291) --- Collatz/Research/StoppingAtlas/Batch0681.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0681.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0681.lean b/Collatz/Research/StoppingAtlas/Batch0681.lean new file mode 100644 index 00000000..5199704a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0681.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0681 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3276. -/ +theorem bounds_13_3276 : exactInterval 13 3276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3276 : oddCount 3276 13 = 5 ∧ acceleratedOrbit 13 3276 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3276) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3276.1, data_13_3276.2] + +/-- Complete interval computation for depth 13, residue 3277. -/ +theorem bounds_13_3277 : exactInterval 13 3277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3277 : oddCount 3277 13 = 5 ∧ acceleratedOrbit 13 3277 = 98 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3277) = 3 ^ 5 * m + 98 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3277.1, data_13_3277.2] + +/-- Complete interval computation for depth 13, residue 3278. -/ +theorem bounds_13_3278 : exactInterval 13 3278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3278 : oddCount 3278 13 = 9 ∧ acceleratedOrbit 13 3278 = 7883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3278) = 3 ^ 9 * m + 7883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3278.1, data_13_3278.2] + +/-- Complete interval computation for depth 13, residue 3279. -/ +theorem bounds_13_3279 : exactInterval 13 3279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3279 : oddCount 3279 13 = 9 ∧ acceleratedOrbit 13 3279 = 7883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3279) = 3 ^ 9 * m + 7883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3279.1, data_13_3279.2] + +/-- Complete interval computation for depth 13, residue 3280. -/ +theorem bounds_13_3280 : exactInterval 13 3280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3280 : oddCount 3280 13 = 3 ∧ acceleratedOrbit 13 3280 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3280) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3280.1, data_13_3280.2] + +/-- Complete interval computation for depth 13, residue 3281. -/ +theorem bounds_13_3281 : exactInterval 13 3281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3281 : oddCount 3281 13 = 8 ∧ acceleratedOrbit 13 3281 = 2632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3281) = 3 ^ 8 * m + 2632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3281.1, data_13_3281.2] + +/-- Complete interval computation for depth 13, residue 3282. -/ +theorem bounds_13_3282 : exactInterval 13 3282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3282 : oddCount 3282 13 = 8 ∧ acceleratedOrbit 13 3282 = 2632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3282) = 3 ^ 8 * m + 2632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3282.1, data_13_3282.2] + +/-- Complete interval computation for depth 13, residue 3283. -/ +theorem bounds_13_3283 : exactInterval 13 3283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3283 : oddCount 3283 13 = 8 ∧ acceleratedOrbit 13 3283 = 2632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3283) = 3 ^ 8 * m + 2632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3283.1, data_13_3283.2] + +/-- Complete interval computation for depth 13, residue 3284. -/ +theorem bounds_13_3284 : exactInterval 13 3284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3284 : oddCount 3284 13 = 3 ∧ acceleratedOrbit 13 3284 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3284) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3284.1, data_13_3284.2] + +/-- Complete interval computation for depth 13, residue 3285. -/ +theorem bounds_13_3285 : exactInterval 13 3285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3285 : oddCount 3285 13 = 3 ∧ acceleratedOrbit 13 3285 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3285) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3285.1, data_13_3285.2] + +/-- Complete interval computation for depth 13, residue 3286. -/ +theorem bounds_13_3286 : exactInterval 13 3286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3286 : oddCount 3286 13 = 8 ∧ acceleratedOrbit 13 3286 = 2636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3286) = 3 ^ 8 * m + 2636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3286.1, data_13_3286.2] + +/-- Complete interval computation for depth 13, residue 3287. -/ +theorem bounds_13_3287 : exactInterval 13 3287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3287 : oddCount 3287 13 = 8 ∧ acceleratedOrbit 13 3287 = 2636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3287) = 3 ^ 8 * m + 2636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3287.1, data_13_3287.2] + +/-- Complete interval computation for depth 13, residue 3288. -/ +theorem bounds_13_3288 : exactInterval 13 3288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3288 : oddCount 3288 13 = 7 ∧ acceleratedOrbit 13 3288 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3288) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3288.1, data_13_3288.2] + +/-- Complete interval computation for depth 13, residue 3289. -/ +theorem bounds_13_3289 : exactInterval 13 3289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3289 : oddCount 3289 13 = 7 ∧ acceleratedOrbit 13 3289 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3289) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3289.1, data_13_3289.2] + +/-- Complete interval computation for depth 13, residue 3290. -/ +theorem bounds_13_3290 : exactInterval 13 3290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3290 : oddCount 3290 13 = 7 ∧ acceleratedOrbit 13 3290 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3290) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3290.1, data_13_3290.2] + +/-- Complete interval computation for depth 13, residue 3291. -/ +theorem bounds_13_3291 : exactInterval 13 3291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3291 : oddCount 3291 13 = 6 ∧ acceleratedOrbit 13 3291 = 293 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3291) = 3 ^ 6 * m + 293 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3291.1, data_13_3291.2] + +end Collatz.Research.StoppingAtlas.Batch0681 From e4f9a986aadb63a590b3c73f2984fa9102b77d5d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:24 +0530 Subject: [PATCH 0682/1001] proof: certify atlas Batch0682 (13:3292 to 13:3306) --- Collatz/Research/StoppingAtlas/Batch0682.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0682.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0682.lean b/Collatz/Research/StoppingAtlas/Batch0682.lean new file mode 100644 index 00000000..eef621cd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0682.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0682 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3292. -/ +theorem bounds_13_3292 : exactInterval 13 3292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3292 : oddCount 3292 13 = 7 ∧ acceleratedOrbit 13 3292 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3292) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3292.1, data_13_3292.2] + +/-- Complete interval computation for depth 13, residue 3293. -/ +theorem bounds_13_3293 : exactInterval 13 3293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3293 : oddCount 3293 13 = 7 ∧ acceleratedOrbit 13 3293 = 881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3293) = 3 ^ 7 * m + 881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3293.1, data_13_3293.2] + +/-- Complete interval computation for depth 13, residue 3294. -/ +theorem bounds_13_3294 : exactInterval 13 3294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3294 : oddCount 3294 13 = 7 ∧ acceleratedOrbit 13 3294 = 880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3294) = 3 ^ 7 * m + 880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3294.1, data_13_3294.2] + +/-- Complete interval computation for depth 13, residue 3295. -/ +theorem bounds_13_3295 : exactInterval 13 3295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3295 : oddCount 3295 13 = 7 ∧ acceleratedOrbit 13 3295 = 880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3295) = 3 ^ 7 * m + 880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3295.1, data_13_3295.2] + +/-- Complete interval computation for depth 13, residue 3296. -/ +theorem bounds_13_3296 : exactInterval 13 3296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3296 : oddCount 3296 13 = 7 ∧ acceleratedOrbit 13 3296 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3296) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3296.1, data_13_3296.2] + +/-- Complete interval computation for depth 13, residue 3297. -/ +theorem bounds_13_3297 : exactInterval 13 3297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3297 : oddCount 3297 13 = 9 ∧ acceleratedOrbit 13 3297 = 7928 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3297) = 3 ^ 9 * m + 7928 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3297.1, data_13_3297.2] + +/-- Complete interval computation for depth 13, residue 3298. -/ +theorem bounds_13_3298 : exactInterval 13 3298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3298 : oddCount 3298 13 = 3 ∧ acceleratedOrbit 13 3298 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3298) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3298.1, data_13_3298.2] + +/-- Complete interval computation for depth 13, residue 3299. -/ +theorem bounds_13_3299 : exactInterval 13 3299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3299 : oddCount 3299 13 = 3 ∧ acceleratedOrbit 13 3299 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3299) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3299.1, data_13_3299.2] + +/-- Complete interval computation for depth 13, residue 3300. -/ +theorem bounds_13_3300 : exactInterval 13 3300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3300 : oddCount 3300 13 = 7 ∧ acceleratedOrbit 13 3300 = 884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3300) = 3 ^ 7 * m + 884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3300.1, data_13_3300.2] + +/-- Complete interval computation for depth 13, residue 3301. -/ +theorem bounds_13_3301 : exactInterval 13 3301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3301 : oddCount 3301 13 = 7 ∧ acceleratedOrbit 13 3301 = 884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3301) = 3 ^ 7 * m + 884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3301.1, data_13_3301.2] + +/-- Complete interval computation for depth 13, residue 3302. -/ +theorem bounds_13_3302 : exactInterval 13 3302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3302 : oddCount 3302 13 = 7 ∧ acceleratedOrbit 13 3302 = 884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3302) = 3 ^ 7 * m + 884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3302.1, data_13_3302.2] + +/-- Complete interval computation for depth 13, residue 3303. -/ +theorem bounds_13_3303 : exactInterval 13 3303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3303 : oddCount 3303 13 = 9 ∧ acceleratedOrbit 13 3303 = 7940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3303) = 3 ^ 9 * m + 7940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3303.1, data_13_3303.2] + +/-- Complete interval computation for depth 13, residue 3304. -/ +theorem bounds_13_3304 : exactInterval 13 3304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3304 : oddCount 3304 13 = 7 ∧ acceleratedOrbit 13 3304 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3304) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3304.1, data_13_3304.2] + +/-- Complete interval computation for depth 13, residue 3305. -/ +theorem bounds_13_3305 : exactInterval 13 3305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3305 : oddCount 3305 13 = 7 ∧ acceleratedOrbit 13 3305 = 883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3305) = 3 ^ 7 * m + 883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3305.1, data_13_3305.2] + +/-- Complete interval computation for depth 13, residue 3306. -/ +theorem bounds_13_3306 : exactInterval 13 3306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3306 : oddCount 3306 13 = 7 ∧ acceleratedOrbit 13 3306 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3306) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3306.1, data_13_3306.2] + +end Collatz.Research.StoppingAtlas.Batch0682 From 4147de137cfcb5b74daa3e574b31f7c877325331 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:24 +0530 Subject: [PATCH 0683/1001] proof: certify atlas Batch0683 (13:3307 to 13:3321) --- Collatz/Research/StoppingAtlas/Batch0683.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0683.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0683.lean b/Collatz/Research/StoppingAtlas/Batch0683.lean new file mode 100644 index 00000000..7450e435 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0683.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0683 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3307. -/ +theorem bounds_13_3307 : exactInterval 13 3307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3307 : oddCount 3307 13 = 9 ∧ acceleratedOrbit 13 3307 = 7951 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3307) = 3 ^ 9 * m + 7951 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3307.1, data_13_3307.2] + +/-- Complete interval computation for depth 13, residue 3308. -/ +theorem bounds_13_3308 : exactInterval 13 3308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3308 : oddCount 3308 13 = 6 ∧ acceleratedOrbit 13 3308 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3308) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3308.1, data_13_3308.2] + +/-- Complete interval computation for depth 13, residue 3309. -/ +theorem bounds_13_3309 : exactInterval 13 3309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3309 : oddCount 3309 13 = 6 ∧ acceleratedOrbit 13 3309 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3309) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3309.1, data_13_3309.2] + +/-- Complete interval computation for depth 13, residue 3310. -/ +theorem bounds_13_3310 : exactInterval 13 3310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3310 : oddCount 3310 13 = 6 ∧ acceleratedOrbit 13 3310 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3310) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3310.1, data_13_3310.2] + +/-- Complete interval computation for depth 13, residue 3311. -/ +theorem bounds_13_3311 : exactInterval 13 3311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3311 : oddCount 3311 13 = 11 ∧ acceleratedOrbit 13 3311 = 71624 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3311) = 3 ^ 11 * m + 71624 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3311.1, data_13_3311.2] + +/-- Complete interval computation for depth 13, residue 3312. -/ +theorem bounds_13_3312 : exactInterval 13 3312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3312 : oddCount 3312 13 = 7 ∧ acceleratedOrbit 13 3312 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3312) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3312.1, data_13_3312.2] + +/-- Complete interval computation for depth 13, residue 3313. -/ +theorem bounds_13_3313 : exactInterval 13 3313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3313 : oddCount 3313 13 = 7 ∧ acceleratedOrbit 13 3313 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3313) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3313.1, data_13_3313.2] + +/-- Complete interval computation for depth 13, residue 3314. -/ +theorem bounds_13_3314 : exactInterval 13 3314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3314 : oddCount 3314 13 = 7 ∧ acceleratedOrbit 13 3314 = 886 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3314) = 3 ^ 7 * m + 886 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3314.1, data_13_3314.2] + +/-- Complete interval computation for depth 13, residue 3315. -/ +theorem bounds_13_3315 : exactInterval 13 3315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3315 : oddCount 3315 13 = 7 ∧ acceleratedOrbit 13 3315 = 886 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3315) = 3 ^ 7 * m + 886 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3315.1, data_13_3315.2] + +/-- Complete interval computation for depth 13, residue 3316. -/ +theorem bounds_13_3316 : exactInterval 13 3316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3316 : oddCount 3316 13 = 7 ∧ acceleratedOrbit 13 3316 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3316) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3316.1, data_13_3316.2] + +/-- Complete interval computation for depth 13, residue 3317. -/ +theorem bounds_13_3317 : exactInterval 13 3317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3317 : oddCount 3317 13 = 7 ∧ acceleratedOrbit 13 3317 = 890 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3317) = 3 ^ 7 * m + 890 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3317.1, data_13_3317.2] + +/-- Complete interval computation for depth 13, residue 3318. -/ +theorem bounds_13_3318 : exactInterval 13 3318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3318 : oddCount 3318 13 = 6 ∧ acceleratedOrbit 13 3318 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3318) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3318.1, data_13_3318.2] + +/-- Complete interval computation for depth 13, residue 3319. -/ +theorem bounds_13_3319 : exactInterval 13 3319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3319 : oddCount 3319 13 = 6 ∧ acceleratedOrbit 13 3319 = 296 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3319) = 3 ^ 6 * m + 296 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3319.1, data_13_3319.2] + +/-- Complete interval computation for depth 13, residue 3320. -/ +theorem bounds_13_3320 : exactInterval 13 3320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3320 : oddCount 3320 13 = 8 ∧ acceleratedOrbit 13 3320 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3320) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3320.1, data_13_3320.2] + +/-- Complete interval computation for depth 13, residue 3321. -/ +theorem bounds_13_3321 : exactInterval 13 3321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3321 : oddCount 3321 13 = 8 ∧ acceleratedOrbit 13 3321 = 2663 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3321) = 3 ^ 8 * m + 2663 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3321.1, data_13_3321.2] + +end Collatz.Research.StoppingAtlas.Batch0683 From 24256d0519984578434d992a2ceb1b9ea64f48f0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:25 +0530 Subject: [PATCH 0684/1001] proof: certify atlas Batch0684 (13:3322 to 13:3337) --- Collatz/Research/StoppingAtlas/Batch0684.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0684.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0684.lean b/Collatz/Research/StoppingAtlas/Batch0684.lean new file mode 100644 index 00000000..414fb218 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0684.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0684 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3322. -/ +theorem bounds_13_3322 : exactInterval 13 3322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3322 : oddCount 3322 13 = 8 ∧ acceleratedOrbit 13 3322 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3322) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3322.1, data_13_3322.2] + +/-- Complete interval computation for depth 13, residue 3323. -/ +theorem bounds_13_3323 : exactInterval 13 3323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3323 : oddCount 3323 13 = 10 ∧ acceleratedOrbit 13 3323 = 23966 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3323) = 3 ^ 10 * m + 23966 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3323.1, data_13_3323.2] + +/-- Complete interval computation for depth 13, residue 3324. -/ +theorem bounds_13_3324 : exactInterval 13 3324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3324 : oddCount 3324 13 = 8 ∧ acceleratedOrbit 13 3324 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3324) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3324.1, data_13_3324.2] + +/-- Complete interval computation for depth 13, residue 3325. -/ +theorem bounds_13_3325 : exactInterval 13 3325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3325 : oddCount 3325 13 = 8 ∧ acceleratedOrbit 13 3325 = 2666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3325) = 3 ^ 8 * m + 2666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3325.1, data_13_3325.2] + +/-- Complete interval computation for depth 13, residue 3326. -/ +theorem bounds_13_3326 : exactInterval 13 3326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3326 : oddCount 3326 13 = 10 ∧ acceleratedOrbit 13 3326 = 23989 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3326) = 3 ^ 10 * m + 23989 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3326.1, data_13_3326.2] + +/-- Complete interval computation for depth 13, residue 3327. -/ +theorem bounds_13_3327 : exactInterval 13 3327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3327 : oddCount 3327 13 = 10 ∧ acceleratedOrbit 13 3327 = 23989 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3327) = 3 ^ 10 * m + 23989 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3327.1, data_13_3327.2] + +/-- Complete interval computation for depth 13, residue 3328. -/ +theorem bounds_13_3328 : exactInterval 13 3328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3328 : oddCount 3328 13 = 2 ∧ acceleratedOrbit 13 3328 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3328) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3328.1, data_13_3328.2] + +/-- Complete interval computation for depth 13, residue 3329. -/ +theorem bounds_13_3329 : exactInterval 13 3329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3329 : oddCount 3329 13 = 8 ∧ acceleratedOrbit 13 3329 = 2672 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3329) = 3 ^ 8 * m + 2672 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3329.1, data_13_3329.2] + +/-- Complete interval computation for depth 13, residue 3330. -/ +theorem bounds_13_3330 : exactInterval 13 3330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3330 : oddCount 3330 13 = 9 ∧ acceleratedOrbit 13 3330 = 8018 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3330) = 3 ^ 9 * m + 8018 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3330.1, data_13_3330.2] + +/-- Complete interval computation for depth 13, residue 3331. -/ +theorem bounds_13_3331 : exactInterval 13 3331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3331 : oddCount 3331 13 = 9 ∧ acceleratedOrbit 13 3331 = 8018 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3331) = 3 ^ 9 * m + 8018 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3331.1, data_13_3331.2] + +/-- Complete interval computation for depth 13, residue 3332. -/ +theorem bounds_13_3332 : exactInterval 13 3332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3332 : oddCount 3332 13 = 3 ∧ acceleratedOrbit 13 3332 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3332) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3332.1, data_13_3332.2] + +/-- Complete interval computation for depth 13, residue 3333. -/ +theorem bounds_13_3333 : exactInterval 13 3333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3333 : oddCount 3333 13 = 3 ∧ acceleratedOrbit 13 3333 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3333) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3333.1, data_13_3333.2] + +/-- Complete interval computation for depth 13, residue 3334. -/ +theorem bounds_13_3334 : exactInterval 13 3334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3334 : oddCount 3334 13 = 3 ∧ acceleratedOrbit 13 3334 = 11 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3334) = 3 ^ 3 * m + 11 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3334.1, data_13_3334.2] + +/-- Complete interval computation for depth 13, residue 3335. -/ +theorem bounds_13_3335 : exactInterval 13 3335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3335 : oddCount 3335 13 = 10 ∧ acceleratedOrbit 13 3335 = 24056 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3335) = 3 ^ 10 * m + 24056 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3335.1, data_13_3335.2] + +/-- Complete interval computation for depth 13, residue 3336. -/ +theorem bounds_13_3336 : exactInterval 13 3336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3336 : oddCount 3336 13 = 6 ∧ acceleratedOrbit 13 3336 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3336) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3336.1, data_13_3336.2] + +/-- Complete interval computation for depth 13, residue 3337. -/ +theorem bounds_13_3337 : exactInterval 13 3337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3337 : oddCount 3337 13 = 8 ∧ acceleratedOrbit 13 3337 = 2675 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3337) = 3 ^ 8 * m + 2675 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3337.1, data_13_3337.2] + +end Collatz.Research.StoppingAtlas.Batch0684 From ba5d5b6aef57d7640f74fd03361093dd2e1226d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:27 +0530 Subject: [PATCH 0685/1001] proof: certify atlas Batch0685 (13:3338 to 13:3352) --- Collatz/Research/StoppingAtlas/Batch0685.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0685.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0685.lean b/Collatz/Research/StoppingAtlas/Batch0685.lean new file mode 100644 index 00000000..e4c518ad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0685.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0685 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3338. -/ +theorem bounds_13_3338 : exactInterval 13 3338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3338 : oddCount 3338 13 = 6 ∧ acceleratedOrbit 13 3338 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3338) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3338.1, data_13_3338.2] + +/-- Complete interval computation for depth 13, residue 3339. -/ +theorem bounds_13_3339 : exactInterval 13 3339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3339 : oddCount 3339 13 = 7 ∧ acceleratedOrbit 13 3339 = 893 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3339) = 3 ^ 7 * m + 893 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3339.1, data_13_3339.2] + +/-- Complete interval computation for depth 13, residue 3340. -/ +theorem bounds_13_3340 : exactInterval 13 3340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3340 : oddCount 3340 13 = 6 ∧ acceleratedOrbit 13 3340 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3340) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3340.1, data_13_3340.2] + +/-- Complete interval computation for depth 13, residue 3341. -/ +theorem bounds_13_3341 : exactInterval 13 3341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3341 : oddCount 3341 13 = 6 ∧ acceleratedOrbit 13 3341 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3341) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3341.1, data_13_3341.2] + +/-- Complete interval computation for depth 13, residue 3342. -/ +theorem bounds_13_3342 : exactInterval 13 3342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3342 : oddCount 3342 13 = 6 ∧ acceleratedOrbit 13 3342 = 298 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3342) = 3 ^ 6 * m + 298 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3342.1, data_13_3342.2] + +/-- Complete interval computation for depth 13, residue 3343. -/ +theorem bounds_13_3343 : exactInterval 13 3343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3343 : oddCount 3343 13 = 6 ∧ acceleratedOrbit 13 3343 = 298 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3343) = 3 ^ 6 * m + 298 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3343.1, data_13_3343.2] + +/-- Complete interval computation for depth 13, residue 3344. -/ +theorem bounds_13_3344 : exactInterval 13 3344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3344 : oddCount 3344 13 = 5 ∧ acceleratedOrbit 13 3344 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3344) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3344.1, data_13_3344.2] + +/-- Complete interval computation for depth 13, residue 3345. -/ +theorem bounds_13_3345 : exactInterval 13 3345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3345 : oddCount 3345 13 = 6 ∧ acceleratedOrbit 13 3345 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3345) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3345.1, data_13_3345.2] + +/-- Complete interval computation for depth 13, residue 3346. -/ +theorem bounds_13_3346 : exactInterval 13 3346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3346 : oddCount 3346 13 = 8 ∧ acceleratedOrbit 13 3346 = 2683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3346) = 3 ^ 8 * m + 2683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3346.1, data_13_3346.2] + +/-- Complete interval computation for depth 13, residue 3347. -/ +theorem bounds_13_3347 : exactInterval 13 3347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3347 : oddCount 3347 13 = 8 ∧ acceleratedOrbit 13 3347 = 2683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3347) = 3 ^ 8 * m + 2683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3347.1, data_13_3347.2] + +/-- Complete interval computation for depth 13, residue 3348. -/ +theorem bounds_13_3348 : exactInterval 13 3348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3348 : oddCount 3348 13 = 5 ∧ acceleratedOrbit 13 3348 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3348) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3348.1, data_13_3348.2] + +/-- Complete interval computation for depth 13, residue 3349. -/ +theorem bounds_13_3349 : exactInterval 13 3349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3349 : oddCount 3349 13 = 5 ∧ acceleratedOrbit 13 3349 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3349) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3349.1, data_13_3349.2] + +/-- Complete interval computation for depth 13, residue 3350. -/ +theorem bounds_13_3350 : exactInterval 13 3350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3350 : oddCount 3350 13 = 6 ∧ acceleratedOrbit 13 3350 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3350) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3350.1, data_13_3350.2] + +/-- Complete interval computation for depth 13, residue 3351. -/ +theorem bounds_13_3351 : exactInterval 13 3351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3351 : oddCount 3351 13 = 6 ∧ acceleratedOrbit 13 3351 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3351) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3351.1, data_13_3351.2] + +/-- Complete interval computation for depth 13, residue 3352. -/ +theorem bounds_13_3352 : exactInterval 13 3352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3352 : oddCount 3352 13 = 5 ∧ acceleratedOrbit 13 3352 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3352) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3352.1, data_13_3352.2] + +end Collatz.Research.StoppingAtlas.Batch0685 From edb2176c81877ff2d982091aefb061ba27471078 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:29 +0530 Subject: [PATCH 0686/1001] proof: certify atlas Batch0686 (13:3353 to 13:3367) --- Collatz/Research/StoppingAtlas/Batch0686.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0686.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0686.lean b/Collatz/Research/StoppingAtlas/Batch0686.lean new file mode 100644 index 00000000..7949e4a3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0686.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0686 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3353. -/ +theorem bounds_13_3353 : exactInterval 13 3353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3353 : oddCount 3353 13 = 7 ∧ acceleratedOrbit 13 3353 = 896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3353) = 3 ^ 7 * m + 896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3353.1, data_13_3353.2] + +/-- Complete interval computation for depth 13, residue 3354. -/ +theorem bounds_13_3354 : exactInterval 13 3354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3354 : oddCount 3354 13 = 5 ∧ acceleratedOrbit 13 3354 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3354) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3354.1, data_13_3354.2] + +/-- Complete interval computation for depth 13, residue 3355. -/ +theorem bounds_13_3355 : exactInterval 13 3355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3355 : oddCount 3355 13 = 10 ∧ acceleratedOrbit 13 3355 = 24194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3355) = 3 ^ 10 * m + 24194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3355.1, data_13_3355.2] + +/-- Complete interval computation for depth 13, residue 3356. -/ +theorem bounds_13_3356 : exactInterval 13 3356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3356 : oddCount 3356 13 = 8 ∧ acceleratedOrbit 13 3356 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3356) = 3 ^ 8 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3356.1, data_13_3356.2] + +/-- Complete interval computation for depth 13, residue 3357. -/ +theorem bounds_13_3357 : exactInterval 13 3357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3357 : oddCount 3357 13 = 8 ∧ acceleratedOrbit 13 3357 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3357) = 3 ^ 8 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3357.1, data_13_3357.2] + +/-- Complete interval computation for depth 13, residue 3358. -/ +theorem bounds_13_3358 : exactInterval 13 3358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3358 : oddCount 3358 13 = 8 ∧ acceleratedOrbit 13 3358 = 2693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3358) = 3 ^ 8 * m + 2693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3358.1, data_13_3358.2] + +/-- Complete interval computation for depth 13, residue 3359. -/ +theorem bounds_13_3359 : exactInterval 13 3359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3359 : oddCount 3359 13 = 6 ∧ acceleratedOrbit 13 3359 = 299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3359) = 3 ^ 6 * m + 299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3359.1, data_13_3359.2] + +/-- Complete interval computation for depth 13, residue 3360. -/ +theorem bounds_13_3360 : exactInterval 13 3360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3360 : oddCount 3360 13 = 5 ∧ acceleratedOrbit 13 3360 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3360) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3360.1, data_13_3360.2] + +/-- Complete interval computation for depth 13, residue 3361. -/ +theorem bounds_13_3361 : exactInterval 13 3361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3361 : oddCount 3361 13 = 5 ∧ acceleratedOrbit 13 3361 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3361) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3361.1, data_13_3361.2] + +/-- Complete interval computation for depth 13, residue 3362. -/ +theorem bounds_13_3362 : exactInterval 13 3362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3362 : oddCount 3362 13 = 5 ∧ acceleratedOrbit 13 3362 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3362) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3362.1, data_13_3362.2] + +/-- Complete interval computation for depth 13, residue 3363. -/ +theorem bounds_13_3363 : exactInterval 13 3363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3363 : oddCount 3363 13 = 5 ∧ acceleratedOrbit 13 3363 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3363) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3363.1, data_13_3363.2] + +/-- Complete interval computation for depth 13, residue 3364. -/ +theorem bounds_13_3364 : exactInterval 13 3364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3364 : oddCount 3364 13 = 5 ∧ acceleratedOrbit 13 3364 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3364) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3364.1, data_13_3364.2] + +/-- Complete interval computation for depth 13, residue 3365. -/ +theorem bounds_13_3365 : exactInterval 13 3365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3365 : oddCount 3365 13 = 5 ∧ acceleratedOrbit 13 3365 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3365) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3365.1, data_13_3365.2] + +/-- Complete interval computation for depth 13, residue 3366. -/ +theorem bounds_13_3366 : exactInterval 13 3366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3366 : oddCount 3366 13 = 5 ∧ acceleratedOrbit 13 3366 = 100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3366) = 3 ^ 5 * m + 100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3366.1, data_13_3366.2] + +/-- Complete interval computation for depth 13, residue 3367. -/ +theorem bounds_13_3367 : exactInterval 13 3367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3367 : oddCount 3367 13 = 8 ∧ acceleratedOrbit 13 3367 = 2699 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3367) = 3 ^ 8 * m + 2699 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3367.1, data_13_3367.2] + +end Collatz.Research.StoppingAtlas.Batch0686 From 2c80f4247ea1c0b5b59e1ad50b71e42d16f8255d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:30 +0530 Subject: [PATCH 0687/1001] proof: certify atlas Batch0687 (13:3368 to 13:3383) --- Collatz/Research/StoppingAtlas/Batch0687.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0687.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0687.lean b/Collatz/Research/StoppingAtlas/Batch0687.lean new file mode 100644 index 00000000..3a7c6618 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0687.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0687 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3368. -/ +theorem bounds_13_3368 : exactInterval 13 3368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3368 : oddCount 3368 13 = 5 ∧ acceleratedOrbit 13 3368 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3368) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3368.1, data_13_3368.2] + +/-- Complete interval computation for depth 13, residue 3369. -/ +theorem bounds_13_3369 : exactInterval 13 3369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3369 : oddCount 3369 13 = 10 ∧ acceleratedOrbit 13 3369 = 24299 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3369) = 3 ^ 10 * m + 24299 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3369.1, data_13_3369.2] + +/-- Complete interval computation for depth 13, residue 3370. -/ +theorem bounds_13_3370 : exactInterval 13 3370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3370 : oddCount 3370 13 = 5 ∧ acceleratedOrbit 13 3370 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3370) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3370.1, data_13_3370.2] + +/-- Complete interval computation for depth 13, residue 3371. -/ +theorem bounds_13_3371 : exactInterval 13 3371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3371 : oddCount 3371 13 = 7 ∧ acceleratedOrbit 13 3371 = 901 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3371) = 3 ^ 7 * m + 901 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3371.1, data_13_3371.2] + +/-- Complete interval computation for depth 13, residue 3372. -/ +theorem bounds_13_3372 : exactInterval 13 3372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3372 : oddCount 3372 13 = 5 ∧ acceleratedOrbit 13 3372 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3372) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3372.1, data_13_3372.2] + +/-- Complete interval computation for depth 13, residue 3373. -/ +theorem bounds_13_3373 : exactInterval 13 3373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3373 : oddCount 3373 13 = 5 ∧ acceleratedOrbit 13 3373 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3373) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3373.1, data_13_3373.2] + +/-- Complete interval computation for depth 13, residue 3374. -/ +theorem bounds_13_3374 : exactInterval 13 3374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3374 : oddCount 3374 13 = 5 ∧ acceleratedOrbit 13 3374 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3374) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3374.1, data_13_3374.2] + +/-- Complete interval computation for depth 13, residue 3375. -/ +theorem bounds_13_3375 : exactInterval 13 3375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3375) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3375 : oddCount 3375 13 = 9 ∧ acceleratedOrbit 13 3375 = 8113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3375) = 3 ^ 9 * m + 8113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3375.1, data_13_3375.2] + +/-- Complete interval computation for depth 13, residue 3376. -/ +theorem bounds_13_3376 : exactInterval 13 3376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3376 : oddCount 3376 13 = 5 ∧ acceleratedOrbit 13 3376 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3376) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3376.1, data_13_3376.2] + +/-- Complete interval computation for depth 13, residue 3377. -/ +theorem bounds_13_3377 : exactInterval 13 3377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3377 : oddCount 3377 13 = 7 ∧ acceleratedOrbit 13 3377 = 904 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3377) = 3 ^ 7 * m + 904 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3377.1, data_13_3377.2] + +/-- Complete interval computation for depth 13, residue 3378. -/ +theorem bounds_13_3378 : exactInterval 13 3378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3378 : oddCount 3378 13 = 7 ∧ acceleratedOrbit 13 3378 = 904 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3378) = 3 ^ 7 * m + 904 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3378.1, data_13_3378.2] + +/-- Complete interval computation for depth 13, residue 3379. -/ +theorem bounds_13_3379 : exactInterval 13 3379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3379 : oddCount 3379 13 = 7 ∧ acceleratedOrbit 13 3379 = 904 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3379) = 3 ^ 7 * m + 904 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3379.1, data_13_3379.2] + +/-- Complete interval computation for depth 13, residue 3380. -/ +theorem bounds_13_3380 : exactInterval 13 3380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3380 : oddCount 3380 13 = 5 ∧ acceleratedOrbit 13 3380 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3380) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3380.1, data_13_3380.2] + +/-- Complete interval computation for depth 13, residue 3381. -/ +theorem bounds_13_3381 : exactInterval 13 3381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3381 : oddCount 3381 13 = 5 ∧ acceleratedOrbit 13 3381 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3381) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3381.1, data_13_3381.2] + +/-- Complete interval computation for depth 13, residue 3382. -/ +theorem bounds_13_3382 : exactInterval 13 3382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3382 : oddCount 3382 13 = 8 ∧ acceleratedOrbit 13 3382 = 2711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3382) = 3 ^ 8 * m + 2711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3382.1, data_13_3382.2] + +/-- Complete interval computation for depth 13, residue 3383. -/ +theorem bounds_13_3383 : exactInterval 13 3383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3383 : oddCount 3383 13 = 8 ∧ acceleratedOrbit 13 3383 = 2711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3383) = 3 ^ 8 * m + 2711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3383.1, data_13_3383.2] + +end Collatz.Research.StoppingAtlas.Batch0687 From d0f3b6eb5655491aae75e67c2f5eda3b9d3d6854 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:31 +0530 Subject: [PATCH 0688/1001] proof: certify atlas Batch0688 (13:3384 to 13:3398) --- Collatz/Research/StoppingAtlas/Batch0688.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0688.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0688.lean b/Collatz/Research/StoppingAtlas/Batch0688.lean new file mode 100644 index 00000000..722d1ef0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0688.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0688 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3384. -/ +theorem bounds_13_3384 : exactInterval 13 3384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3384 : oddCount 3384 13 = 6 ∧ acceleratedOrbit 13 3384 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3384) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3384.1, data_13_3384.2] + +/-- Complete interval computation for depth 13, residue 3385. -/ +theorem bounds_13_3385 : exactInterval 13 3385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3385 : oddCount 3385 13 = 9 ∧ acceleratedOrbit 13 3385 = 8140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3385) = 3 ^ 9 * m + 8140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3385.1, data_13_3385.2] + +/-- Complete interval computation for depth 13, residue 3386. -/ +theorem bounds_13_3386 : exactInterval 13 3386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3386 : oddCount 3386 13 = 6 ∧ acceleratedOrbit 13 3386 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3386) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3386.1, data_13_3386.2] + +/-- Complete interval computation for depth 13, residue 3387. -/ +theorem bounds_13_3387 : exactInterval 13 3387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3387 : oddCount 3387 13 = 5 ∧ acceleratedOrbit 13 3387 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3387) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3387.1, data_13_3387.2] + +/-- Complete interval computation for depth 13, residue 3388. -/ +theorem bounds_13_3388 : exactInterval 13 3388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3388 : oddCount 3388 13 = 6 ∧ acceleratedOrbit 13 3388 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3388) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3388.1, data_13_3388.2] + +/-- Complete interval computation for depth 13, residue 3389. -/ +theorem bounds_13_3389 : exactInterval 13 3389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3389 : oddCount 3389 13 = 6 ∧ acceleratedOrbit 13 3389 = 302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3389) = 3 ^ 6 * m + 302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3389.1, data_13_3389.2] + +/-- Complete interval computation for depth 13, residue 3390. -/ +theorem bounds_13_3390 : exactInterval 13 3390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3390 : oddCount 3390 13 = 10 ∧ acceleratedOrbit 13 3390 = 24452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3390) = 3 ^ 10 * m + 24452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3390.1, data_13_3390.2] + +/-- Complete interval computation for depth 13, residue 3391. -/ +theorem bounds_13_3391 : exactInterval 13 3391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3391 : oddCount 3391 13 = 10 ∧ acceleratedOrbit 13 3391 = 24452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3391) = 3 ^ 10 * m + 24452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3391.1, data_13_3391.2] + +/-- Complete interval computation for depth 13, residue 3392. -/ +theorem bounds_13_3392 : exactInterval 13 3392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3392 : oddCount 3392 13 = 2 ∧ acceleratedOrbit 13 3392 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3392) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3392.1, data_13_3392.2] + +/-- Complete interval computation for depth 13, residue 3393. -/ +theorem bounds_13_3393 : exactInterval 13 3393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3393 : oddCount 3393 13 = 5 ∧ acceleratedOrbit 13 3393 = 101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3393) = 3 ^ 5 * m + 101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3393.1, data_13_3393.2] + +/-- Complete interval computation for depth 13, residue 3394. -/ +theorem bounds_13_3394 : exactInterval 13 3394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3394 : oddCount 3394 13 = 7 ∧ acceleratedOrbit 13 3394 = 908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3394) = 3 ^ 7 * m + 908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3394.1, data_13_3394.2] + +/-- Complete interval computation for depth 13, residue 3395. -/ +theorem bounds_13_3395 : exactInterval 13 3395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3395 : oddCount 3395 13 = 7 ∧ acceleratedOrbit 13 3395 = 908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3395) = 3 ^ 7 * m + 908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3395.1, data_13_3395.2] + +/-- Complete interval computation for depth 13, residue 3396. -/ +theorem bounds_13_3396 : exactInterval 13 3396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3396 : oddCount 3396 13 = 7 ∧ acceleratedOrbit 13 3396 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3396) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3396.1, data_13_3396.2] + +/-- Complete interval computation for depth 13, residue 3397. -/ +theorem bounds_13_3397 : exactInterval 13 3397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3397 : oddCount 3397 13 = 7 ∧ acceleratedOrbit 13 3397 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3397) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3397.1, data_13_3397.2] + +/-- Complete interval computation for depth 13, residue 3398. -/ +theorem bounds_13_3398 : exactInterval 13 3398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3398 : oddCount 3398 13 = 7 ∧ acceleratedOrbit 13 3398 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3398) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3398.1, data_13_3398.2] + +end Collatz.Research.StoppingAtlas.Batch0688 From c21f30f67b189349a424e0b29d0271354a28fdda Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:32 +0530 Subject: [PATCH 0689/1001] proof: certify atlas Batch0689 (13:3399 to 13:3414) --- Collatz/Research/StoppingAtlas/Batch0689.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0689.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0689.lean b/Collatz/Research/StoppingAtlas/Batch0689.lean new file mode 100644 index 00000000..b3ecaaa3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0689.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0689 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3399. -/ +theorem bounds_13_3399 : exactInterval 13 3399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3399 : oddCount 3399 13 = 9 ∧ acceleratedOrbit 13 3399 = 8171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3399) = 3 ^ 9 * m + 8171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3399.1, data_13_3399.2] + +/-- Complete interval computation for depth 13, residue 3400. -/ +theorem bounds_13_3400 : exactInterval 13 3400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3400 : oddCount 3400 13 = 7 ∧ acceleratedOrbit 13 3400 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3400) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3400.1, data_13_3400.2] + +/-- Complete interval computation for depth 13, residue 3401. -/ +theorem bounds_13_3401 : exactInterval 13 3401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3401 : oddCount 3401 13 = 9 ∧ acceleratedOrbit 13 3401 = 8180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3401) = 3 ^ 9 * m + 8180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3401.1, data_13_3401.2] + +/-- Complete interval computation for depth 13, residue 3402. -/ +theorem bounds_13_3402 : exactInterval 13 3402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3402 : oddCount 3402 13 = 7 ∧ acceleratedOrbit 13 3402 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3402) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3402.1, data_13_3402.2] + +/-- Complete interval computation for depth 13, residue 3403. -/ +theorem bounds_13_3403 : exactInterval 13 3403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3403 : oddCount 3403 13 = 7 ∧ acceleratedOrbit 13 3403 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3403) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3403.1, data_13_3403.2] + +/-- Complete interval computation for depth 13, residue 3404. -/ +theorem bounds_13_3404 : exactInterval 13 3404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3404 : oddCount 3404 13 = 7 ∧ acceleratedOrbit 13 3404 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3404) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3404.1, data_13_3404.2] + +/-- Complete interval computation for depth 13, residue 3405. -/ +theorem bounds_13_3405 : exactInterval 13 3405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3405 : oddCount 3405 13 = 7 ∧ acceleratedOrbit 13 3405 = 911 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3405) = 3 ^ 7 * m + 911 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3405.1, data_13_3405.2] + +/-- Complete interval computation for depth 13, residue 3406. -/ +theorem bounds_13_3406 : exactInterval 13 3406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3406 : oddCount 3406 13 = 7 ∧ acceleratedOrbit 13 3406 = 910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3406) = 3 ^ 7 * m + 910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3406.1, data_13_3406.2] + +/-- Complete interval computation for depth 13, residue 3407. -/ +theorem bounds_13_3407 : exactInterval 13 3407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3407 : oddCount 3407 13 = 7 ∧ acceleratedOrbit 13 3407 = 910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3407) = 3 ^ 7 * m + 910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3407.1, data_13_3407.2] + +/-- Complete interval computation for depth 13, residue 3408. -/ +theorem bounds_13_3408 : exactInterval 13 3408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3408 : oddCount 3408 13 = 2 ∧ acceleratedOrbit 13 3408 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3408) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3408.1, data_13_3408.2] + +/-- Complete interval computation for depth 13, residue 3409. -/ +theorem bounds_13_3409 : exactInterval 13 3409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3409 : oddCount 3409 13 = 9 ∧ acceleratedOrbit 13 3409 = 8201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3409) = 3 ^ 9 * m + 8201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3409.1, data_13_3409.2] + +/-- Complete interval computation for depth 13, residue 3410. -/ +theorem bounds_13_3410 : exactInterval 13 3410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3410 : oddCount 3410 13 = 9 ∧ acceleratedOrbit 13 3410 = 8201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3410) = 3 ^ 9 * m + 8201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3410.1, data_13_3410.2] + +/-- Complete interval computation for depth 13, residue 3411. -/ +theorem bounds_13_3411 : exactInterval 13 3411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3411 : oddCount 3411 13 = 9 ∧ acceleratedOrbit 13 3411 = 8201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3411) = 3 ^ 9 * m + 8201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3411.1, data_13_3411.2] + +/-- Complete interval computation for depth 13, residue 3412. -/ +theorem bounds_13_3412 : exactInterval 13 3412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3412 : oddCount 3412 13 = 2 ∧ acceleratedOrbit 13 3412 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3412) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3412.1, data_13_3412.2] + +/-- Complete interval computation for depth 13, residue 3413. -/ +theorem bounds_13_3413 : exactInterval 13 3413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3413 : oddCount 3413 13 = 2 ∧ acceleratedOrbit 13 3413 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3413) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3413.1, data_13_3413.2] + +/-- Complete interval computation for depth 13, residue 3414. -/ +theorem bounds_13_3414 : exactInterval 13 3414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3414 : oddCount 3414 13 = 7 ∧ acceleratedOrbit 13 3414 = 913 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3414) = 3 ^ 7 * m + 913 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3414.1, data_13_3414.2] + +end Collatz.Research.StoppingAtlas.Batch0689 From f1cba97f8c573803520ec43e99cf1d46ea842f96 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:34 +0530 Subject: [PATCH 0690/1001] proof: certify atlas Batch0690 (13:3415 to 13:3429) --- Collatz/Research/StoppingAtlas/Batch0690.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0690.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0690.lean b/Collatz/Research/StoppingAtlas/Batch0690.lean new file mode 100644 index 00000000..51967a51 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0690.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0690 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3415. -/ +theorem bounds_13_3415 : exactInterval 13 3415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3415 : oddCount 3415 13 = 7 ∧ acceleratedOrbit 13 3415 = 913 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3415) = 3 ^ 7 * m + 913 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3415.1, data_13_3415.2] + +/-- Complete interval computation for depth 13, residue 3416. -/ +theorem bounds_13_3416 : exactInterval 13 3416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3416 : oddCount 3416 13 = 7 ∧ acceleratedOrbit 13 3416 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3416) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3416.1, data_13_3416.2] + +/-- Complete interval computation for depth 13, residue 3417. -/ +theorem bounds_13_3417 : exactInterval 13 3417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3417 : oddCount 3417 13 = 6 ∧ acceleratedOrbit 13 3417 = 305 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3417) = 3 ^ 6 * m + 305 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3417.1, data_13_3417.2] + +/-- Complete interval computation for depth 13, residue 3418. -/ +theorem bounds_13_3418 : exactInterval 13 3418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3418 : oddCount 3418 13 = 7 ∧ acceleratedOrbit 13 3418 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3418) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3418.1, data_13_3418.2] + +/-- Complete interval computation for depth 13, residue 3419. -/ +theorem bounds_13_3419 : exactInterval 13 3419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3419 : oddCount 3419 13 = 8 ∧ acceleratedOrbit 13 3419 = 2740 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3419) = 3 ^ 8 * m + 2740 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3419.1, data_13_3419.2] + +/-- Complete interval computation for depth 13, residue 3420. -/ +theorem bounds_13_3420 : exactInterval 13 3420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3420 : oddCount 3420 13 = 7 ∧ acceleratedOrbit 13 3420 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3420) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3420.1, data_13_3420.2] + +/-- Complete interval computation for depth 13, residue 3421. -/ +theorem bounds_13_3421 : exactInterval 13 3421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3421 : oddCount 3421 13 = 7 ∧ acceleratedOrbit 13 3421 = 917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3421) = 3 ^ 7 * m + 917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3421.1, data_13_3421.2] + +/-- Complete interval computation for depth 13, residue 3422. -/ +theorem bounds_13_3422 : exactInterval 13 3422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3422 : oddCount 3422 13 = 8 ∧ acceleratedOrbit 13 3422 = 2744 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3422) = 3 ^ 8 * m + 2744 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3422.1, data_13_3422.2] + +/-- Complete interval computation for depth 13, residue 3423. -/ +theorem bounds_13_3423 : exactInterval 13 3423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3423 : oddCount 3423 13 = 8 ∧ acceleratedOrbit 13 3423 = 2744 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3423) = 3 ^ 8 * m + 2744 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3423.1, data_13_3423.2] + +/-- Complete interval computation for depth 13, residue 3424. -/ +theorem bounds_13_3424 : exactInterval 13 3424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3424 : oddCount 3424 13 = 5 ∧ acceleratedOrbit 13 3424 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3424) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3424.1, data_13_3424.2] + +/-- Complete interval computation for depth 13, residue 3425. -/ +theorem bounds_13_3425 : exactInterval 13 3425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3425 : oddCount 3425 13 = 6 ∧ acceleratedOrbit 13 3425 = 305 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3425) = 3 ^ 6 * m + 305 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3425.1, data_13_3425.2] + +/-- Complete interval computation for depth 13, residue 3426. -/ +theorem bounds_13_3426 : exactInterval 13 3426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3426 : oddCount 3426 13 = 4 ∧ acceleratedOrbit 13 3426 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3426) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3426.1, data_13_3426.2] + +/-- Complete interval computation for depth 13, residue 3427. -/ +theorem bounds_13_3427 : exactInterval 13 3427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3427 : oddCount 3427 13 = 4 ∧ acceleratedOrbit 13 3427 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3427) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3427.1, data_13_3427.2] + +/-- Complete interval computation for depth 13, residue 3428. -/ +theorem bounds_13_3428 : exactInterval 13 3428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3428 : oddCount 3428 13 = 4 ∧ acceleratedOrbit 13 3428 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3428) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3428.1, data_13_3428.2] + +/-- Complete interval computation for depth 13, residue 3429. -/ +theorem bounds_13_3429 : exactInterval 13 3429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3429 : oddCount 3429 13 = 4 ∧ acceleratedOrbit 13 3429 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3429) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3429.1, data_13_3429.2] + +end Collatz.Research.StoppingAtlas.Batch0690 From a4bcb5e19415e1b1a37cdae63740de0dceced06e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:35 +0530 Subject: [PATCH 0691/1001] proof: certify atlas Batch0691 (13:3430 to 13:3444) --- Collatz/Research/StoppingAtlas/Batch0691.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0691.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0691.lean b/Collatz/Research/StoppingAtlas/Batch0691.lean new file mode 100644 index 00000000..ebc3d4eb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0691.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0691 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3430. -/ +theorem bounds_13_3430 : exactInterval 13 3430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3430 : oddCount 3430 13 = 4 ∧ acceleratedOrbit 13 3430 = 34 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3430) = 3 ^ 4 * m + 34 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3430.1, data_13_3430.2] + +/-- Complete interval computation for depth 13, residue 3431. -/ +theorem bounds_13_3431 : exactInterval 13 3431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3431 : oddCount 3431 13 = 11 ∧ acceleratedOrbit 13 3431 = 74222 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3431) = 3 ^ 11 * m + 74222 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3431.1, data_13_3431.2] + +/-- Complete interval computation for depth 13, residue 3432. -/ +theorem bounds_13_3432 : exactInterval 13 3432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3432 : oddCount 3432 13 = 5 ∧ acceleratedOrbit 13 3432 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3432) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3432.1, data_13_3432.2] + +/-- Complete interval computation for depth 13, residue 3433. -/ +theorem bounds_13_3433 : exactInterval 13 3433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3433 : oddCount 3433 13 = 8 ∧ acceleratedOrbit 13 3433 = 2753 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3433) = 3 ^ 8 * m + 2753 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3433.1, data_13_3433.2] + +/-- Complete interval computation for depth 13, residue 3434. -/ +theorem bounds_13_3434 : exactInterval 13 3434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3434 : oddCount 3434 13 = 5 ∧ acceleratedOrbit 13 3434 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3434) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3434.1, data_13_3434.2] + +/-- Complete interval computation for depth 13, residue 3435. -/ +theorem bounds_13_3435 : exactInterval 13 3435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3435 : oddCount 3435 13 = 9 ∧ acceleratedOrbit 13 3435 = 8261 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3435) = 3 ^ 9 * m + 8261 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3435.1, data_13_3435.2] + +/-- Complete interval computation for depth 13, residue 3436. -/ +theorem bounds_13_3436 : exactInterval 13 3436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3436 : oddCount 3436 13 = 7 ∧ acceleratedOrbit 13 3436 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3436) = 3 ^ 7 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3436.1, data_13_3436.2] + +/-- Complete interval computation for depth 13, residue 3437. -/ +theorem bounds_13_3437 : exactInterval 13 3437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3437 : oddCount 3437 13 = 7 ∧ acceleratedOrbit 13 3437 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3437) = 3 ^ 7 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3437.1, data_13_3437.2] + +/-- Complete interval computation for depth 13, residue 3438. -/ +theorem bounds_13_3438 : exactInterval 13 3438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3438 : oddCount 3438 13 = 7 ∧ acceleratedOrbit 13 3438 = 919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3438) = 3 ^ 7 * m + 919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3438.1, data_13_3438.2] + +/-- Complete interval computation for depth 13, residue 3439. -/ +theorem bounds_13_3439 : exactInterval 13 3439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3439 : oddCount 3439 13 = 8 ∧ acceleratedOrbit 13 3439 = 2756 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3439) = 3 ^ 8 * m + 2756 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3439.1, data_13_3439.2] + +/-- Complete interval computation for depth 13, residue 3440. -/ +theorem bounds_13_3440 : exactInterval 13 3440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3440 : oddCount 3440 13 = 5 ∧ acceleratedOrbit 13 3440 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3440) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3440.1, data_13_3440.2] + +/-- Complete interval computation for depth 13, residue 3441. -/ +theorem bounds_13_3441 : exactInterval 13 3441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3441 : oddCount 3441 13 = 5 ∧ acceleratedOrbit 13 3441 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3441) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3441.1, data_13_3441.2] + +/-- Complete interval computation for depth 13, residue 3442. -/ +theorem bounds_13_3442 : exactInterval 13 3442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3442 : oddCount 3442 13 = 6 ∧ acceleratedOrbit 13 3442 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3442) = 3 ^ 6 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3442.1, data_13_3442.2] + +/-- Complete interval computation for depth 13, residue 3443. -/ +theorem bounds_13_3443 : exactInterval 13 3443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3443 : oddCount 3443 13 = 6 ∧ acceleratedOrbit 13 3443 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3443) = 3 ^ 6 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3443.1, data_13_3443.2] + +/-- Complete interval computation for depth 13, residue 3444. -/ +theorem bounds_13_3444 : exactInterval 13 3444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3444 : oddCount 3444 13 = 5 ∧ acceleratedOrbit 13 3444 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3444) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3444.1, data_13_3444.2] + +end Collatz.Research.StoppingAtlas.Batch0691 From 8495d5c74c4c94169c4de786a0f0606fe80718e5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:36 +0530 Subject: [PATCH 0692/1001] proof: certify atlas Batch0692 (13:3445 to 13:3460) --- Collatz/Research/StoppingAtlas/Batch0692.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0692.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0692.lean b/Collatz/Research/StoppingAtlas/Batch0692.lean new file mode 100644 index 00000000..d02d1bc5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0692.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0692 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3445. -/ +theorem bounds_13_3445 : exactInterval 13 3445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3445 : oddCount 3445 13 = 5 ∧ acceleratedOrbit 13 3445 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3445) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3445.1, data_13_3445.2] + +/-- Complete interval computation for depth 13, residue 3446. -/ +theorem bounds_13_3446 : exactInterval 13 3446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3446 : oddCount 3446 13 = 6 ∧ acceleratedOrbit 13 3446 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3446) = 3 ^ 6 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3446.1, data_13_3446.2] + +/-- Complete interval computation for depth 13, residue 3447. -/ +theorem bounds_13_3447 : exactInterval 13 3447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3447 : oddCount 3447 13 = 6 ∧ acceleratedOrbit 13 3447 = 307 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3447) = 3 ^ 6 * m + 307 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3447.1, data_13_3447.2] + +/-- Complete interval computation for depth 13, residue 3448. -/ +theorem bounds_13_3448 : exactInterval 13 3448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3448 : oddCount 3448 13 = 6 ∧ acceleratedOrbit 13 3448 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3448) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3448.1, data_13_3448.2] + +/-- Complete interval computation for depth 13, residue 3449. -/ +theorem bounds_13_3449 : exactInterval 13 3449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3449 : oddCount 3449 13 = 8 ∧ acceleratedOrbit 13 3449 = 2764 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3449) = 3 ^ 8 * m + 2764 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3449.1, data_13_3449.2] + +/-- Complete interval computation for depth 13, residue 3450. -/ +theorem bounds_13_3450 : exactInterval 13 3450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3450 : oddCount 3450 13 = 6 ∧ acceleratedOrbit 13 3450 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3450) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3450.1, data_13_3450.2] + +/-- Complete interval computation for depth 13, residue 3451. -/ +theorem bounds_13_3451 : exactInterval 13 3451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3451 : oddCount 3451 13 = 7 ∧ acceleratedOrbit 13 3451 = 922 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3451) = 3 ^ 7 * m + 922 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3451.1, data_13_3451.2] + +/-- Complete interval computation for depth 13, residue 3452. -/ +theorem bounds_13_3452 : exactInterval 13 3452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3452 : oddCount 3452 13 = 6 ∧ acceleratedOrbit 13 3452 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3452) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3452.1, data_13_3452.2] + +/-- Complete interval computation for depth 13, residue 3453. -/ +theorem bounds_13_3453 : exactInterval 13 3453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3453 : oddCount 3453 13 = 6 ∧ acceleratedOrbit 13 3453 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3453) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3453.1, data_13_3453.2] + +/-- Complete interval computation for depth 13, residue 3454. -/ +theorem bounds_13_3454 : exactInterval 13 3454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3454 : oddCount 3454 13 = 8 ∧ acceleratedOrbit 13 3454 = 2768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3454) = 3 ^ 8 * m + 2768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3454.1, data_13_3454.2] + +/-- Complete interval computation for depth 13, residue 3455. -/ +theorem bounds_13_3455 : exactInterval 13 3455 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3455) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3455 : oddCount 3455 13 = 8 ∧ acceleratedOrbit 13 3455 = 2768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3455) = 3 ^ 8 * m + 2768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3455.1, data_13_3455.2] + +/-- Complete interval computation for depth 13, residue 3456. -/ +theorem bounds_13_3456 : exactInterval 13 3456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3456 : oddCount 3456 13 = 5 ∧ acceleratedOrbit 13 3456 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3456) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3456.1, data_13_3456.2] + +/-- Complete interval computation for depth 13, residue 3457. -/ +theorem bounds_13_3457 : exactInterval 13 3457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3457 : oddCount 3457 13 = 6 ∧ acceleratedOrbit 13 3457 = 308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3457) = 3 ^ 6 * m + 308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3457.1, data_13_3457.2] + +/-- Complete interval computation for depth 13, residue 3458. -/ +theorem bounds_13_3458 : exactInterval 13 3458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3458 : oddCount 3458 13 = 5 ∧ acceleratedOrbit 13 3458 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3458) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3458.1, data_13_3458.2] + +/-- Complete interval computation for depth 13, residue 3459. -/ +theorem bounds_13_3459 : exactInterval 13 3459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3459 : oddCount 3459 13 = 5 ∧ acceleratedOrbit 13 3459 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3459) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3459.1, data_13_3459.2] + +/-- Complete interval computation for depth 13, residue 3460. -/ +theorem bounds_13_3460 : exactInterval 13 3460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3460 : oddCount 3460 13 = 8 ∧ acceleratedOrbit 13 3460 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3460) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3460.1, data_13_3460.2] + +end Collatz.Research.StoppingAtlas.Batch0692 From b0315c2531ad9cf7f089c1fb8148c79c8843285f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:36 +0530 Subject: [PATCH 0693/1001] proof: certify atlas Batch0693 (13:3461 to 13:3475) --- Collatz/Research/StoppingAtlas/Batch0693.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0693.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0693.lean b/Collatz/Research/StoppingAtlas/Batch0693.lean new file mode 100644 index 00000000..c74dfa8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0693.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0693 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3461. -/ +theorem bounds_13_3461 : exactInterval 13 3461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3461 : oddCount 3461 13 = 8 ∧ acceleratedOrbit 13 3461 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3461) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3461.1, data_13_3461.2] + +/-- Complete interval computation for depth 13, residue 3462. -/ +theorem bounds_13_3462 : exactInterval 13 3462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3462 : oddCount 3462 13 = 8 ∧ acceleratedOrbit 13 3462 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3462) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3462.1, data_13_3462.2] + +/-- Complete interval computation for depth 13, residue 3463. -/ +theorem bounds_13_3463 : exactInterval 13 3463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3463 : oddCount 3463 13 = 5 ∧ acceleratedOrbit 13 3463 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3463) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3463.1, data_13_3463.2] + +/-- Complete interval computation for depth 13, residue 3464. -/ +theorem bounds_13_3464 : exactInterval 13 3464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3464 : oddCount 3464 13 = 4 ∧ acceleratedOrbit 13 3464 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3464) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3464.1, data_13_3464.2] + +/-- Complete interval computation for depth 13, residue 3465. -/ +theorem bounds_13_3465 : exactInterval 13 3465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3465 : oddCount 3465 13 = 7 ∧ acceleratedOrbit 13 3465 = 926 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3465) = 3 ^ 7 * m + 926 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3465.1, data_13_3465.2] + +/-- Complete interval computation for depth 13, residue 3466. -/ +theorem bounds_13_3466 : exactInterval 13 3466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3466 : oddCount 3466 13 = 4 ∧ acceleratedOrbit 13 3466 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3466) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3466.1, data_13_3466.2] + +/-- Complete interval computation for depth 13, residue 3467. -/ +theorem bounds_13_3467 : exactInterval 13 3467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3467 : oddCount 3467 13 = 8 ∧ acceleratedOrbit 13 3467 = 2780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3467) = 3 ^ 8 * m + 2780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3467.1, data_13_3467.2] + +/-- Complete interval computation for depth 13, residue 3468. -/ +theorem bounds_13_3468 : exactInterval 13 3468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3468 : oddCount 3468 13 = 4 ∧ acceleratedOrbit 13 3468 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3468) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3468.1, data_13_3468.2] + +/-- Complete interval computation for depth 13, residue 3469. -/ +theorem bounds_13_3469 : exactInterval 13 3469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3469 : oddCount 3469 13 = 4 ∧ acceleratedOrbit 13 3469 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3469) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3469.1, data_13_3469.2] + +/-- Complete interval computation for depth 13, residue 3470. -/ +theorem bounds_13_3470 : exactInterval 13 3470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3470 : oddCount 3470 13 = 5 ∧ acceleratedOrbit 13 3470 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3470) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3470.1, data_13_3470.2] + +/-- Complete interval computation for depth 13, residue 3471. -/ +theorem bounds_13_3471 : exactInterval 13 3471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3471 : oddCount 3471 13 = 5 ∧ acceleratedOrbit 13 3471 = 103 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3471) = 3 ^ 5 * m + 103 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3471.1, data_13_3471.2] + +/-- Complete interval computation for depth 13, residue 3472. -/ +theorem bounds_13_3472 : exactInterval 13 3472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3472 : oddCount 3472 13 = 4 ∧ acceleratedOrbit 13 3472 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3472) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3472.1, data_13_3472.2] + +/-- Complete interval computation for depth 13, residue 3473. -/ +theorem bounds_13_3473 : exactInterval 13 3473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3473 : oddCount 3473 13 = 6 ∧ acceleratedOrbit 13 3473 = 310 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3473) = 3 ^ 6 * m + 310 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3473.1, data_13_3473.2] + +/-- Complete interval computation for depth 13, residue 3474. -/ +theorem bounds_13_3474 : exactInterval 13 3474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3474 : oddCount 3474 13 = 6 ∧ acceleratedOrbit 13 3474 = 310 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3474) = 3 ^ 6 * m + 310 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3474.1, data_13_3474.2] + +/-- Complete interval computation for depth 13, residue 3475. -/ +theorem bounds_13_3475 : exactInterval 13 3475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3475 : oddCount 3475 13 = 6 ∧ acceleratedOrbit 13 3475 = 310 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3475) = 3 ^ 6 * m + 310 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3475.1, data_13_3475.2] + +end Collatz.Research.StoppingAtlas.Batch0693 From 515476b5b60b0fb181f2dcc8652e9e11e75c494d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:39 +0530 Subject: [PATCH 0694/1001] proof: certify atlas Batch0694 (13:3476 to 13:3490) --- Collatz/Research/StoppingAtlas/Batch0694.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0694.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0694.lean b/Collatz/Research/StoppingAtlas/Batch0694.lean new file mode 100644 index 00000000..6bfb729f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0694.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0694 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3476. -/ +theorem bounds_13_3476 : exactInterval 13 3476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3476 : oddCount 3476 13 = 4 ∧ acceleratedOrbit 13 3476 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3476) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3476.1, data_13_3476.2] + +/-- Complete interval computation for depth 13, residue 3477. -/ +theorem bounds_13_3477 : exactInterval 13 3477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3477 : oddCount 3477 13 = 4 ∧ acceleratedOrbit 13 3477 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3477) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3477.1, data_13_3477.2] + +/-- Complete interval computation for depth 13, residue 3478. -/ +theorem bounds_13_3478 : exactInterval 13 3478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3478 : oddCount 3478 13 = 7 ∧ acceleratedOrbit 13 3478 = 931 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3478) = 3 ^ 7 * m + 931 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3478.1, data_13_3478.2] + +/-- Complete interval computation for depth 13, residue 3479. -/ +theorem bounds_13_3479 : exactInterval 13 3479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3479 : oddCount 3479 13 = 7 ∧ acceleratedOrbit 13 3479 = 931 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3479) = 3 ^ 7 * m + 931 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3479.1, data_13_3479.2] + +/-- Complete interval computation for depth 13, residue 3480. -/ +theorem bounds_13_3480 : exactInterval 13 3480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3480 : oddCount 3480 13 = 4 ∧ acceleratedOrbit 13 3480 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3480) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3480.1, data_13_3480.2] + +/-- Complete interval computation for depth 13, residue 3481. -/ +theorem bounds_13_3481 : exactInterval 13 3481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3481 : oddCount 3481 13 = 7 ∧ acceleratedOrbit 13 3481 = 931 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3481) = 3 ^ 7 * m + 931 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3481.1, data_13_3481.2] + +/-- Complete interval computation for depth 13, residue 3482. -/ +theorem bounds_13_3482 : exactInterval 13 3482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3482 : oddCount 3482 13 = 4 ∧ acceleratedOrbit 13 3482 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3482) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3482.1, data_13_3482.2] + +/-- Complete interval computation for depth 13, residue 3483. -/ +theorem bounds_13_3483 : exactInterval 13 3483 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3483) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3483 : oddCount 3483 13 = 8 ∧ acceleratedOrbit 13 3483 = 2791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3483) = 3 ^ 8 * m + 2791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3483.1, data_13_3483.2] + +/-- Complete interval computation for depth 13, residue 3484. -/ +theorem bounds_13_3484 : exactInterval 13 3484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3484 : oddCount 3484 13 = 9 ∧ acceleratedOrbit 13 3484 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3484) = 3 ^ 9 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3484.1, data_13_3484.2] + +/-- Complete interval computation for depth 13, residue 3485. -/ +theorem bounds_13_3485 : exactInterval 13 3485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3485 : oddCount 3485 13 = 9 ∧ acceleratedOrbit 13 3485 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3485) = 3 ^ 9 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3485.1, data_13_3485.2] + +/-- Complete interval computation for depth 13, residue 3486. -/ +theorem bounds_13_3486 : exactInterval 13 3486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3486 : oddCount 3486 13 = 9 ∧ acceleratedOrbit 13 3486 = 8383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3486) = 3 ^ 9 * m + 8383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3486.1, data_13_3486.2] + +/-- Complete interval computation for depth 13, residue 3487. -/ +theorem bounds_13_3487 : exactInterval 13 3487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3487 : oddCount 3487 13 = 9 ∧ acceleratedOrbit 13 3487 = 8381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3487) = 3 ^ 9 * m + 8381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3487.1, data_13_3487.2] + +/-- Complete interval computation for depth 13, residue 3488. -/ +theorem bounds_13_3488 : exactInterval 13 3488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3488 : oddCount 3488 13 = 5 ∧ acceleratedOrbit 13 3488 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3488) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3488.1, data_13_3488.2] + +/-- Complete interval computation for depth 13, residue 3489. -/ +theorem bounds_13_3489 : exactInterval 13 3489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3489 : oddCount 3489 13 = 8 ∧ acceleratedOrbit 13 3489 = 2798 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3489) = 3 ^ 8 * m + 2798 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3489.1, data_13_3489.2] + +/-- Complete interval computation for depth 13, residue 3490. -/ +theorem bounds_13_3490 : exactInterval 13 3490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3490 : oddCount 3490 13 = 7 ∧ acceleratedOrbit 13 3490 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3490) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3490.1, data_13_3490.2] + +end Collatz.Research.StoppingAtlas.Batch0694 From db20779e7afea39e78196a6c1c202ac945625daf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:39 +0530 Subject: [PATCH 0695/1001] proof: certify atlas Batch0695 (13:3491 to 13:3506) --- Collatz/Research/StoppingAtlas/Batch0695.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0695.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0695.lean b/Collatz/Research/StoppingAtlas/Batch0695.lean new file mode 100644 index 00000000..b2781227 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0695.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0695 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3491. -/ +theorem bounds_13_3491 : exactInterval 13 3491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3491 : oddCount 3491 13 = 7 ∧ acceleratedOrbit 13 3491 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3491) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3491.1, data_13_3491.2] + +/-- Complete interval computation for depth 13, residue 3492. -/ +theorem bounds_13_3492 : exactInterval 13 3492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3492 : oddCount 3492 13 = 7 ∧ acceleratedOrbit 13 3492 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3492) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3492.1, data_13_3492.2] + +/-- Complete interval computation for depth 13, residue 3493. -/ +theorem bounds_13_3493 : exactInterval 13 3493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3493 : oddCount 3493 13 = 7 ∧ acceleratedOrbit 13 3493 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3493) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3493.1, data_13_3493.2] + +/-- Complete interval computation for depth 13, residue 3494. -/ +theorem bounds_13_3494 : exactInterval 13 3494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3494 : oddCount 3494 13 = 7 ∧ acceleratedOrbit 13 3494 = 935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3494) = 3 ^ 7 * m + 935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3494.1, data_13_3494.2] + +/-- Complete interval computation for depth 13, residue 3495. -/ +theorem bounds_13_3495 : exactInterval 13 3495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3495 : oddCount 3495 13 = 8 ∧ acceleratedOrbit 13 3495 = 2801 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3495) = 3 ^ 8 * m + 2801 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3495.1, data_13_3495.2] + +/-- Complete interval computation for depth 13, residue 3496. -/ +theorem bounds_13_3496 : exactInterval 13 3496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3496 : oddCount 3496 13 = 5 ∧ acceleratedOrbit 13 3496 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3496) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3496.1, data_13_3496.2] + +/-- Complete interval computation for depth 13, residue 3497. -/ +theorem bounds_13_3497 : exactInterval 13 3497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3497 : oddCount 3497 13 = 7 ∧ acceleratedOrbit 13 3497 = 934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3497) = 3 ^ 7 * m + 934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3497.1, data_13_3497.2] + +/-- Complete interval computation for depth 13, residue 3498. -/ +theorem bounds_13_3498 : exactInterval 13 3498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3498 : oddCount 3498 13 = 5 ∧ acceleratedOrbit 13 3498 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3498) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3498.1, data_13_3498.2] + +/-- Complete interval computation for depth 13, residue 3499. -/ +theorem bounds_13_3499 : exactInterval 13 3499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3499 : oddCount 3499 13 = 9 ∧ acceleratedOrbit 13 3499 = 8414 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3499) = 3 ^ 9 * m + 8414 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3499.1, data_13_3499.2] + +/-- Complete interval computation for depth 13, residue 3500. -/ +theorem bounds_13_3500 : exactInterval 13 3500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3500 : oddCount 3500 13 = 5 ∧ acceleratedOrbit 13 3500 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3500) = 3 ^ 5 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3500.1, data_13_3500.2] + +/-- Complete interval computation for depth 13, residue 3501. -/ +theorem bounds_13_3501 : exactInterval 13 3501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3501 : oddCount 3501 13 = 5 ∧ acceleratedOrbit 13 3501 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3501) = 3 ^ 5 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3501.1, data_13_3501.2] + +/-- Complete interval computation for depth 13, residue 3502. -/ +theorem bounds_13_3502 : exactInterval 13 3502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3502 : oddCount 3502 13 = 5 ∧ acceleratedOrbit 13 3502 = 104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3502) = 3 ^ 5 * m + 104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3502.1, data_13_3502.2] + +/-- Complete interval computation for depth 13, residue 3503. -/ +theorem bounds_13_3503 : exactInterval 13 3503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3503 : oddCount 3503 13 = 9 ∧ acceleratedOrbit 13 3503 = 8423 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3503) = 3 ^ 9 * m + 8423 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3503.1, data_13_3503.2] + +/-- Complete interval computation for depth 13, residue 3504. -/ +theorem bounds_13_3504 : exactInterval 13 3504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3504 : oddCount 3504 13 = 6 ∧ acceleratedOrbit 13 3504 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3504) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3504.1, data_13_3504.2] + +/-- Complete interval computation for depth 13, residue 3505. -/ +theorem bounds_13_3505 : exactInterval 13 3505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3505 : oddCount 3505 13 = 6 ∧ acceleratedOrbit 13 3505 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3505) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3505.1, data_13_3505.2] + +/-- Complete interval computation for depth 13, residue 3506. -/ +theorem bounds_13_3506 : exactInterval 13 3506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3506 : oddCount 3506 13 = 6 ∧ acceleratedOrbit 13 3506 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3506) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3506.1, data_13_3506.2] + +end Collatz.Research.StoppingAtlas.Batch0695 From 41a1ba5e9c60fcb3d9bcf9e9b6f6909008400160 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:40 +0530 Subject: [PATCH 0696/1001] proof: certify atlas Batch0696 (13:3507 to 13:3521) --- Collatz/Research/StoppingAtlas/Batch0696.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0696.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0696.lean b/Collatz/Research/StoppingAtlas/Batch0696.lean new file mode 100644 index 00000000..285e7e2b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0696.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0696 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3507. -/ +theorem bounds_13_3507 : exactInterval 13 3507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3507 : oddCount 3507 13 = 6 ∧ acceleratedOrbit 13 3507 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3507) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3507.1, data_13_3507.2] + +/-- Complete interval computation for depth 13, residue 3508. -/ +theorem bounds_13_3508 : exactInterval 13 3508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3508 : oddCount 3508 13 = 6 ∧ acceleratedOrbit 13 3508 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3508) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3508.1, data_13_3508.2] + +/-- Complete interval computation for depth 13, residue 3509. -/ +theorem bounds_13_3509 : exactInterval 13 3509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3509 : oddCount 3509 13 = 6 ∧ acceleratedOrbit 13 3509 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3509) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3509.1, data_13_3509.2] + +/-- Complete interval computation for depth 13, residue 3510. -/ +theorem bounds_13_3510 : exactInterval 13 3510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3510 : oddCount 3510 13 = 7 ∧ acceleratedOrbit 13 3510 = 938 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3510) = 3 ^ 7 * m + 938 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3510.1, data_13_3510.2] + +/-- Complete interval computation for depth 13, residue 3511. -/ +theorem bounds_13_3511 : exactInterval 13 3511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3511 : oddCount 3511 13 = 7 ∧ acceleratedOrbit 13 3511 = 938 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3511) = 3 ^ 7 * m + 938 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3511.1, data_13_3511.2] + +/-- Complete interval computation for depth 13, residue 3512. -/ +theorem bounds_13_3512 : exactInterval 13 3512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3512 : oddCount 3512 13 = 6 ∧ acceleratedOrbit 13 3512 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3512) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3512.1, data_13_3512.2] + +/-- Complete interval computation for depth 13, residue 3513. -/ +theorem bounds_13_3513 : exactInterval 13 3513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3513 : oddCount 3513 13 = 6 ∧ acceleratedOrbit 13 3513 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3513) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3513.1, data_13_3513.2] + +/-- Complete interval computation for depth 13, residue 3514. -/ +theorem bounds_13_3514 : exactInterval 13 3514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3514 : oddCount 3514 13 = 6 ∧ acceleratedOrbit 13 3514 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3514) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3514.1, data_13_3514.2] + +/-- Complete interval computation for depth 13, residue 3515. -/ +theorem bounds_13_3515 : exactInterval 13 3515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3515 : oddCount 3515 13 = 6 ∧ acceleratedOrbit 13 3515 = 313 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3515) = 3 ^ 6 * m + 313 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3515.1, data_13_3515.2] + +/-- Complete interval computation for depth 13, residue 3516. -/ +theorem bounds_13_3516 : exactInterval 13 3516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3516 : oddCount 3516 13 = 7 ∧ acceleratedOrbit 13 3516 = 940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3516) = 3 ^ 7 * m + 940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3516.1, data_13_3516.2] + +/-- Complete interval computation for depth 13, residue 3517. -/ +theorem bounds_13_3517 : exactInterval 13 3517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3517 : oddCount 3517 13 = 7 ∧ acceleratedOrbit 13 3517 = 940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3517) = 3 ^ 7 * m + 940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3517.1, data_13_3517.2] + +/-- Complete interval computation for depth 13, residue 3518. -/ +theorem bounds_13_3518 : exactInterval 13 3518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3518 : oddCount 3518 13 = 7 ∧ acceleratedOrbit 13 3518 = 940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3518) = 3 ^ 7 * m + 940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3518.1, data_13_3518.2] + +/-- Complete interval computation for depth 13, residue 3519. -/ +theorem bounds_13_3519 : exactInterval 13 3519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3519 : oddCount 3519 13 = 10 ∧ acceleratedOrbit 13 3519 = 25373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3519) = 3 ^ 10 * m + 25373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3519.1, data_13_3519.2] + +/-- Complete interval computation for depth 13, residue 3520. -/ +theorem bounds_13_3520 : exactInterval 13 3520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3520 : oddCount 3520 13 = 5 ∧ acceleratedOrbit 13 3520 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3520) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3520.1, data_13_3520.2] + +/-- Complete interval computation for depth 13, residue 3521. -/ +theorem bounds_13_3521 : exactInterval 13 3521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3521 : oddCount 3521 13 = 8 ∧ acceleratedOrbit 13 3521 = 2825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3521) = 3 ^ 8 * m + 2825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3521.1, data_13_3521.2] + +end Collatz.Research.StoppingAtlas.Batch0696 From 7691ab47b1bb53e7052612c414e8c3b0aad18560 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:40 +0530 Subject: [PATCH 0697/1001] proof: certify atlas Batch0697 (13:3522 to 13:3536) --- Collatz/Research/StoppingAtlas/Batch0697.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0697.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0697.lean b/Collatz/Research/StoppingAtlas/Batch0697.lean new file mode 100644 index 00000000..6068389b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0697.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0697 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3522. -/ +theorem bounds_13_3522 : exactInterval 13 3522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3522 : oddCount 3522 13 = 8 ∧ acceleratedOrbit 13 3522 = 2825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3522) = 3 ^ 8 * m + 2825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3522.1, data_13_3522.2] + +/-- Complete interval computation for depth 13, residue 3523. -/ +theorem bounds_13_3523 : exactInterval 13 3523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3523 : oddCount 3523 13 = 8 ∧ acceleratedOrbit 13 3523 = 2825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3523) = 3 ^ 8 * m + 2825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3523.1, data_13_3523.2] + +/-- Complete interval computation for depth 13, residue 3524. -/ +theorem bounds_13_3524 : exactInterval 13 3524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3524 : oddCount 3524 13 = 5 ∧ acceleratedOrbit 13 3524 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3524) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3524.1, data_13_3524.2] + +/-- Complete interval computation for depth 13, residue 3525. -/ +theorem bounds_13_3525 : exactInterval 13 3525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3525 : oddCount 3525 13 = 5 ∧ acceleratedOrbit 13 3525 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3525) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3525.1, data_13_3525.2] + +/-- Complete interval computation for depth 13, residue 3526. -/ +theorem bounds_13_3526 : exactInterval 13 3526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3526 : oddCount 3526 13 = 5 ∧ acceleratedOrbit 13 3526 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3526) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3526.1, data_13_3526.2] + +/-- Complete interval computation for depth 13, residue 3527. -/ +theorem bounds_13_3527 : exactInterval 13 3527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3527 : oddCount 3527 13 = 6 ∧ acceleratedOrbit 13 3527 = 314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3527) = 3 ^ 6 * m + 314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3527.1, data_13_3527.2] + +/-- Complete interval computation for depth 13, residue 3528. -/ +theorem bounds_13_3528 : exactInterval 13 3528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3528 : oddCount 3528 13 = 4 ∧ acceleratedOrbit 13 3528 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3528) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3528.1, data_13_3528.2] + +/-- Complete interval computation for depth 13, residue 3529. -/ +theorem bounds_13_3529 : exactInterval 13 3529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3529 : oddCount 3529 13 = 7 ∧ acceleratedOrbit 13 3529 = 944 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3529) = 3 ^ 7 * m + 944 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3529.1, data_13_3529.2] + +/-- Complete interval computation for depth 13, residue 3530. -/ +theorem bounds_13_3530 : exactInterval 13 3530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3530 : oddCount 3530 13 = 4 ∧ acceleratedOrbit 13 3530 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3530) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3530.1, data_13_3530.2] + +/-- Complete interval computation for depth 13, residue 3531. -/ +theorem bounds_13_3531 : exactInterval 13 3531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3531 : oddCount 3531 13 = 8 ∧ acceleratedOrbit 13 3531 = 2834 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3531) = 3 ^ 8 * m + 2834 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3531.1, data_13_3531.2] + +/-- Complete interval computation for depth 13, residue 3532. -/ +theorem bounds_13_3532 : exactInterval 13 3532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3532 : oddCount 3532 13 = 4 ∧ acceleratedOrbit 13 3532 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3532) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3532.1, data_13_3532.2] + +/-- Complete interval computation for depth 13, residue 3533. -/ +theorem bounds_13_3533 : exactInterval 13 3533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3533 : oddCount 3533 13 = 4 ∧ acceleratedOrbit 13 3533 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3533) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3533.1, data_13_3533.2] + +/-- Complete interval computation for depth 13, residue 3534. -/ +theorem bounds_13_3534 : exactInterval 13 3534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3534 : oddCount 3534 13 = 9 ∧ acceleratedOrbit 13 3534 = 8498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3534) = 3 ^ 9 * m + 8498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3534.1, data_13_3534.2] + +/-- Complete interval computation for depth 13, residue 3535. -/ +theorem bounds_13_3535 : exactInterval 13 3535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3535 : oddCount 3535 13 = 9 ∧ acceleratedOrbit 13 3535 = 8498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3535) = 3 ^ 9 * m + 8498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3535.1, data_13_3535.2] + +/-- Complete interval computation for depth 13, residue 3536. -/ +theorem bounds_13_3536 : exactInterval 13 3536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3536 : oddCount 3536 13 = 5 ∧ acceleratedOrbit 13 3536 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3536) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3536.1, data_13_3536.2] + +end Collatz.Research.StoppingAtlas.Batch0697 From 1376866bf2328495e89deb47bbdf7c48b8b1b005 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:42 +0530 Subject: [PATCH 0698/1001] proof: certify atlas Batch0698 (13:3537 to 13:3552) --- Collatz/Research/StoppingAtlas/Batch0698.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0698.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0698.lean b/Collatz/Research/StoppingAtlas/Batch0698.lean new file mode 100644 index 00000000..cbfb707b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0698.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0698 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3537. -/ +theorem bounds_13_3537 : exactInterval 13 3537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3537 : oddCount 3537 13 = 4 ∧ acceleratedOrbit 13 3537 = 35 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3537) = 3 ^ 4 * m + 35 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3537.1, data_13_3537.2] + +/-- Complete interval computation for depth 13, residue 3538. -/ +theorem bounds_13_3538 : exactInterval 13 3538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3538 : oddCount 3538 13 = 8 ∧ acceleratedOrbit 13 3538 = 2837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3538) = 3 ^ 8 * m + 2837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3538.1, data_13_3538.2] + +/-- Complete interval computation for depth 13, residue 3539. -/ +theorem bounds_13_3539 : exactInterval 13 3539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3539 : oddCount 3539 13 = 8 ∧ acceleratedOrbit 13 3539 = 2837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3539) = 3 ^ 8 * m + 2837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3539.1, data_13_3539.2] + +/-- Complete interval computation for depth 13, residue 3540. -/ +theorem bounds_13_3540 : exactInterval 13 3540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3540 : oddCount 3540 13 = 5 ∧ acceleratedOrbit 13 3540 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3540) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3540.1, data_13_3540.2] + +/-- Complete interval computation for depth 13, residue 3541. -/ +theorem bounds_13_3541 : exactInterval 13 3541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3541 : oddCount 3541 13 = 5 ∧ acceleratedOrbit 13 3541 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3541) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3541.1, data_13_3541.2] + +/-- Complete interval computation for depth 13, residue 3542. -/ +theorem bounds_13_3542 : exactInterval 13 3542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3542 : oddCount 3542 13 = 7 ∧ acceleratedOrbit 13 3542 = 947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3542) = 3 ^ 7 * m + 947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3542.1, data_13_3542.2] + +/-- Complete interval computation for depth 13, residue 3543. -/ +theorem bounds_13_3543 : exactInterval 13 3543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3543 : oddCount 3543 13 = 7 ∧ acceleratedOrbit 13 3543 = 947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3543) = 3 ^ 7 * m + 947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3543.1, data_13_3543.2] + +/-- Complete interval computation for depth 13, residue 3544. -/ +theorem bounds_13_3544 : exactInterval 13 3544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3544 : oddCount 3544 13 = 6 ∧ acceleratedOrbit 13 3544 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3544) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3544.1, data_13_3544.2] + +/-- Complete interval computation for depth 13, residue 3545. -/ +theorem bounds_13_3545 : exactInterval 13 3545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3545 : oddCount 3545 13 = 6 ∧ acceleratedOrbit 13 3545 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3545) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3545.1, data_13_3545.2] + +/-- Complete interval computation for depth 13, residue 3546. -/ +theorem bounds_13_3546 : exactInterval 13 3546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3546 : oddCount 3546 13 = 6 ∧ acceleratedOrbit 13 3546 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3546) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3546.1, data_13_3546.2] + +/-- Complete interval computation for depth 13, residue 3547. -/ +theorem bounds_13_3547 : exactInterval 13 3547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3547 : oddCount 3547 13 = 6 ∧ acceleratedOrbit 13 3547 = 316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3547) = 3 ^ 6 * m + 316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3547.1, data_13_3547.2] + +/-- Complete interval computation for depth 13, residue 3548. -/ +theorem bounds_13_3548 : exactInterval 13 3548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3548 : oddCount 3548 13 = 6 ∧ acceleratedOrbit 13 3548 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3548) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3548.1, data_13_3548.2] + +/-- Complete interval computation for depth 13, residue 3549. -/ +theorem bounds_13_3549 : exactInterval 13 3549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3549 : oddCount 3549 13 = 6 ∧ acceleratedOrbit 13 3549 = 317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3549) = 3 ^ 6 * m + 317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3549.1, data_13_3549.2] + +/-- Complete interval computation for depth 13, residue 3550. -/ +theorem bounds_13_3550 : exactInterval 13 3550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3550 : oddCount 3550 13 = 8 ∧ acceleratedOrbit 13 3550 = 2845 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3550) = 3 ^ 8 * m + 2845 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3550.1, data_13_3550.2] + +/-- Complete interval computation for depth 13, residue 3551. -/ +theorem bounds_13_3551 : exactInterval 13 3551 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3551) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3551 : oddCount 3551 13 = 8 ∧ acceleratedOrbit 13 3551 = 2845 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3551) = 3 ^ 8 * m + 2845 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3551.1, data_13_3551.2] + +/-- Complete interval computation for depth 13, residue 3552. -/ +theorem bounds_13_3552 : exactInterval 13 3552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3552 : oddCount 3552 13 = 6 ∧ acceleratedOrbit 13 3552 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3552) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3552.1, data_13_3552.2] + +end Collatz.Research.StoppingAtlas.Batch0698 From c13de49ff62facbac6bfd0e77c7184cba633597a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:43 +0530 Subject: [PATCH 0699/1001] proof: certify atlas Batch0699 (13:3553 to 13:3567) --- Collatz/Research/StoppingAtlas/Batch0699.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0699.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0699.lean b/Collatz/Research/StoppingAtlas/Batch0699.lean new file mode 100644 index 00000000..27cabc00 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0699.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0699 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3553. -/ +theorem bounds_13_3553 : exactInterval 13 3553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3553 : oddCount 3553 13 = 8 ∧ acceleratedOrbit 13 3553 = 2848 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3553) = 3 ^ 8 * m + 2848 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3553.1, data_13_3553.2] + +/-- Complete interval computation for depth 13, residue 3554. -/ +theorem bounds_13_3554 : exactInterval 13 3554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3554 : oddCount 3554 13 = 5 ∧ acceleratedOrbit 13 3554 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3554) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3554.1, data_13_3554.2] + +/-- Complete interval computation for depth 13, residue 3555. -/ +theorem bounds_13_3555 : exactInterval 13 3555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3555 : oddCount 3555 13 = 5 ∧ acceleratedOrbit 13 3555 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3555) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3555.1, data_13_3555.2] + +/-- Complete interval computation for depth 13, residue 3556. -/ +theorem bounds_13_3556 : exactInterval 13 3556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3556 : oddCount 3556 13 = 8 ∧ acceleratedOrbit 13 3556 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3556) = 3 ^ 8 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3556.1, data_13_3556.2] + +/-- Complete interval computation for depth 13, residue 3557. -/ +theorem bounds_13_3557 : exactInterval 13 3557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3557 : oddCount 3557 13 = 8 ∧ acceleratedOrbit 13 3557 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3557) = 3 ^ 8 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3557.1, data_13_3557.2] + +/-- Complete interval computation for depth 13, residue 3558. -/ +theorem bounds_13_3558 : exactInterval 13 3558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3558 : oddCount 3558 13 = 8 ∧ acceleratedOrbit 13 3558 = 2855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3558) = 3 ^ 8 * m + 2855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3558.1, data_13_3558.2] + +/-- Complete interval computation for depth 13, residue 3559. -/ +theorem bounds_13_3559 : exactInterval 13 3559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3559 : oddCount 3559 13 = 8 ∧ acceleratedOrbit 13 3559 = 2852 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3559) = 3 ^ 8 * m + 2852 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3559.1, data_13_3559.2] + +/-- Complete interval computation for depth 13, residue 3560. -/ +theorem bounds_13_3560 : exactInterval 13 3560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3560 : oddCount 3560 13 = 6 ∧ acceleratedOrbit 13 3560 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3560) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3560.1, data_13_3560.2] + +/-- Complete interval computation for depth 13, residue 3561. -/ +theorem bounds_13_3561 : exactInterval 13 3561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3561 : oddCount 3561 13 = 9 ∧ acceleratedOrbit 13 3561 = 8561 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3561) = 3 ^ 9 * m + 8561 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3561.1, data_13_3561.2] + +/-- Complete interval computation for depth 13, residue 3562. -/ +theorem bounds_13_3562 : exactInterval 13 3562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3562 : oddCount 3562 13 = 6 ∧ acceleratedOrbit 13 3562 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3562) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3562.1, data_13_3562.2] + +/-- Complete interval computation for depth 13, residue 3563. -/ +theorem bounds_13_3563 : exactInterval 13 3563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3563 : oddCount 3563 13 = 10 ∧ acceleratedOrbit 13 3563 = 25697 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3563) = 3 ^ 10 * m + 25697 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3563.1, data_13_3563.2] + +/-- Complete interval computation for depth 13, residue 3564. -/ +theorem bounds_13_3564 : exactInterval 13 3564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3564 : oddCount 3564 13 = 8 ∧ acceleratedOrbit 13 3564 = 2861 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3564) = 3 ^ 8 * m + 2861 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3564.1, data_13_3564.2] + +/-- Complete interval computation for depth 13, residue 3565. -/ +theorem bounds_13_3565 : exactInterval 13 3565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3565 : oddCount 3565 13 = 8 ∧ acceleratedOrbit 13 3565 = 2861 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3565) = 3 ^ 8 * m + 2861 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3565.1, data_13_3565.2] + +/-- Complete interval computation for depth 13, residue 3566. -/ +theorem bounds_13_3566 : exactInterval 13 3566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3566 : oddCount 3566 13 = 8 ∧ acceleratedOrbit 13 3566 = 2861 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3566) = 3 ^ 8 * m + 2861 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3566.1, data_13_3566.2] + +/-- Complete interval computation for depth 13, residue 3567. -/ +theorem bounds_13_3567 : exactInterval 13 3567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3567 : oddCount 3567 13 = 10 ∧ acceleratedOrbit 13 3567 = 25721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3567) = 3 ^ 10 * m + 25721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3567.1, data_13_3567.2] + +end Collatz.Research.StoppingAtlas.Batch0699 From 84f19f001fae6dc5df261bf2efb24579bdc0c4bf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:43 +0530 Subject: [PATCH 0700/1001] proof: certify atlas Batch0700 (13:3568 to 13:3583) --- Collatz/Research/StoppingAtlas/Batch0700.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0700.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0700.lean b/Collatz/Research/StoppingAtlas/Batch0700.lean new file mode 100644 index 00000000..62ff944e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0700.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0700 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3568. -/ +theorem bounds_13_3568 : exactInterval 13 3568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3568 : oddCount 3568 13 = 6 ∧ acceleratedOrbit 13 3568 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3568) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3568.1, data_13_3568.2] + +/-- Complete interval computation for depth 13, residue 3569. -/ +theorem bounds_13_3569 : exactInterval 13 3569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3569 : oddCount 3569 13 = 6 ∧ acceleratedOrbit 13 3569 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3569) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3569.1, data_13_3569.2] + +/-- Complete interval computation for depth 13, residue 3570. -/ +theorem bounds_13_3570 : exactInterval 13 3570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3570 : oddCount 3570 13 = 5 ∧ acceleratedOrbit 13 3570 = 106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3570) = 3 ^ 5 * m + 106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3570.1, data_13_3570.2] + +/-- Complete interval computation for depth 13, residue 3571. -/ +theorem bounds_13_3571 : exactInterval 13 3571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3571 : oddCount 3571 13 = 5 ∧ acceleratedOrbit 13 3571 = 106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3571) = 3 ^ 5 * m + 106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3571.1, data_13_3571.2] + +/-- Complete interval computation for depth 13, residue 3572. -/ +theorem bounds_13_3572 : exactInterval 13 3572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3572 : oddCount 3572 13 = 6 ∧ acceleratedOrbit 13 3572 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3572) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3572.1, data_13_3572.2] + +/-- Complete interval computation for depth 13, residue 3573. -/ +theorem bounds_13_3573 : exactInterval 13 3573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3573 : oddCount 3573 13 = 6 ∧ acceleratedOrbit 13 3573 = 319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3573) = 3 ^ 6 * m + 319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3573.1, data_13_3573.2] + +/-- Complete interval computation for depth 13, residue 3574. -/ +theorem bounds_13_3574 : exactInterval 13 3574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3574 : oddCount 3574 13 = 7 ∧ acceleratedOrbit 13 3574 = 955 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3574) = 3 ^ 7 * m + 955 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3574.1, data_13_3574.2] + +/-- Complete interval computation for depth 13, residue 3575. -/ +theorem bounds_13_3575 : exactInterval 13 3575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3575 : oddCount 3575 13 = 7 ∧ acceleratedOrbit 13 3575 = 955 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3575) = 3 ^ 7 * m + 955 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3575.1, data_13_3575.2] + +/-- Complete interval computation for depth 13, residue 3576. -/ +theorem bounds_13_3576 : exactInterval 13 3576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3576 : oddCount 3576 13 = 9 ∧ acceleratedOrbit 13 3576 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3576) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3576.1, data_13_3576.2] + +/-- Complete interval computation for depth 13, residue 3577. -/ +theorem bounds_13_3577 : exactInterval 13 3577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3577 : oddCount 3577 13 = 7 ∧ acceleratedOrbit 13 3577 = 956 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3577) = 3 ^ 7 * m + 956 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3577.1, data_13_3577.2] + +/-- Complete interval computation for depth 13, residue 3578. -/ +theorem bounds_13_3578 : exactInterval 13 3578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3578 : oddCount 3578 13 = 9 ∧ acceleratedOrbit 13 3578 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3578) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3578.1, data_13_3578.2] + +/-- Complete interval computation for depth 13, residue 3579. -/ +theorem bounds_13_3579 : exactInterval 13 3579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3579 : oddCount 3579 13 = 7 ∧ acceleratedOrbit 13 3579 = 956 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3579) = 3 ^ 7 * m + 956 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3579.1, data_13_3579.2] + +/-- Complete interval computation for depth 13, residue 3580. -/ +theorem bounds_13_3580 : exactInterval 13 3580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3580 : oddCount 3580 13 = 9 ∧ acceleratedOrbit 13 3580 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3580) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3580.1, data_13_3580.2] + +/-- Complete interval computation for depth 13, residue 3581. -/ +theorem bounds_13_3581 : exactInterval 13 3581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3581 : oddCount 3581 13 = 9 ∧ acceleratedOrbit 13 3581 = 8612 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3581) = 3 ^ 9 * m + 8612 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3581.1, data_13_3581.2] + +/-- Complete interval computation for depth 13, residue 3582. -/ +theorem bounds_13_3582 : exactInterval 13 3582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3582 : oddCount 3582 13 = 10 ∧ acceleratedOrbit 13 3582 = 25834 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3582) = 3 ^ 10 * m + 25834 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3582.1, data_13_3582.2] + +/-- Complete interval computation for depth 13, residue 3583. -/ +theorem bounds_13_3583 : exactInterval 13 3583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3583 : oddCount 3583 13 = 10 ∧ acceleratedOrbit 13 3583 = 25834 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3583) = 3 ^ 10 * m + 25834 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3583.1, data_13_3583.2] + +end Collatz.Research.StoppingAtlas.Batch0700 From 7bc7645b4528abb1081471dc431147c5cb935d7d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:44 +0530 Subject: [PATCH 0701/1001] proof: certify atlas Batch0701 (13:3584 to 13:3598) --- Collatz/Research/StoppingAtlas/Batch0701.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0701.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0701.lean b/Collatz/Research/StoppingAtlas/Batch0701.lean new file mode 100644 index 00000000..eb9dcac5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0701.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0701 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3584. -/ +theorem bounds_13_3584 : exactInterval 13 3584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3584 : oddCount 3584 13 = 3 ∧ acceleratedOrbit 13 3584 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3584) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3584.1, data_13_3584.2] + +/-- Complete interval computation for depth 13, residue 3585. -/ +theorem bounds_13_3585 : exactInterval 13 3585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3585 : oddCount 3585 13 = 8 ∧ acceleratedOrbit 13 3585 = 2875 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3585) = 3 ^ 8 * m + 2875 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3585.1, data_13_3585.2] + +/-- Complete interval computation for depth 13, residue 3586. -/ +theorem bounds_13_3586 : exactInterval 13 3586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3586 : oddCount 3586 13 = 5 ∧ acceleratedOrbit 13 3586 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3586) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3586.1, data_13_3586.2] + +/-- Complete interval computation for depth 13, residue 3587. -/ +theorem bounds_13_3587 : exactInterval 13 3587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3587 : oddCount 3587 13 = 5 ∧ acceleratedOrbit 13 3587 = 107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3587) = 3 ^ 5 * m + 107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3587.1, data_13_3587.2] + +/-- Complete interval computation for depth 13, residue 3588. -/ +theorem bounds_13_3588 : exactInterval 13 3588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3588 : oddCount 3588 13 = 7 ∧ acceleratedOrbit 13 3588 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3588) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3588.1, data_13_3588.2] + +/-- Complete interval computation for depth 13, residue 3589. -/ +theorem bounds_13_3589 : exactInterval 13 3589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3589 : oddCount 3589 13 = 7 ∧ acceleratedOrbit 13 3589 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3589) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3589.1, data_13_3589.2] + +/-- Complete interval computation for depth 13, residue 3590. -/ +theorem bounds_13_3590 : exactInterval 13 3590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3590 : oddCount 3590 13 = 7 ∧ acceleratedOrbit 13 3590 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3590) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3590.1, data_13_3590.2] + +/-- Complete interval computation for depth 13, residue 3591. -/ +theorem bounds_13_3591 : exactInterval 13 3591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3591 : oddCount 3591 13 = 8 ∧ acceleratedOrbit 13 3591 = 2879 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3591) = 3 ^ 8 * m + 2879 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3591.1, data_13_3591.2] + +/-- Complete interval computation for depth 13, residue 3592. -/ +theorem bounds_13_3592 : exactInterval 13 3592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3592 : oddCount 3592 13 = 6 ∧ acceleratedOrbit 13 3592 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3592) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3592.1, data_13_3592.2] + +/-- Complete interval computation for depth 13, residue 3593. -/ +theorem bounds_13_3593 : exactInterval 13 3593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3593 : oddCount 3593 13 = 6 ∧ acceleratedOrbit 13 3593 = 320 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3593) = 3 ^ 6 * m + 320 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3593.1, data_13_3593.2] + +/-- Complete interval computation for depth 13, residue 3594. -/ +theorem bounds_13_3594 : exactInterval 13 3594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3594 : oddCount 3594 13 = 6 ∧ acceleratedOrbit 13 3594 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3594) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3594.1, data_13_3594.2] + +/-- Complete interval computation for depth 13, residue 3595. -/ +theorem bounds_13_3595 : exactInterval 13 3595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3595 : oddCount 3595 13 = 7 ∧ acceleratedOrbit 13 3595 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3595) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3595.1, data_13_3595.2] + +/-- Complete interval computation for depth 13, residue 3596. -/ +theorem bounds_13_3596 : exactInterval 13 3596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3596 : oddCount 3596 13 = 6 ∧ acceleratedOrbit 13 3596 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3596) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3596.1, data_13_3596.2] + +/-- Complete interval computation for depth 13, residue 3597. -/ +theorem bounds_13_3597 : exactInterval 13 3597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3597 : oddCount 3597 13 = 6 ∧ acceleratedOrbit 13 3597 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3597) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3597.1, data_13_3597.2] + +/-- Complete interval computation for depth 13, residue 3598. -/ +theorem bounds_13_3598 : exactInterval 13 3598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3598 : oddCount 3598 13 = 7 ∧ acceleratedOrbit 13 3598 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3598) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3598.1, data_13_3598.2] + +end Collatz.Research.StoppingAtlas.Batch0701 From caa32535e78ce4d38056fc7b819c5d7d1438481f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:46 +0530 Subject: [PATCH 0702/1001] proof: certify atlas Batch0702 (13:3599 to 13:3613) --- Collatz/Research/StoppingAtlas/Batch0702.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0702.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0702.lean b/Collatz/Research/StoppingAtlas/Batch0702.lean new file mode 100644 index 00000000..4770f612 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0702.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0702 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3599. -/ +theorem bounds_13_3599 : exactInterval 13 3599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3599 : oddCount 3599 13 = 7 ∧ acceleratedOrbit 13 3599 = 962 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3599) = 3 ^ 7 * m + 962 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3599.1, data_13_3599.2] + +/-- Complete interval computation for depth 13, residue 3600. -/ +theorem bounds_13_3600 : exactInterval 13 3600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3600 : oddCount 3600 13 = 7 ∧ acceleratedOrbit 13 3600 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3600) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3600.1, data_13_3600.2] + +/-- Complete interval computation for depth 13, residue 3601. -/ +theorem bounds_13_3601 : exactInterval 13 3601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3601 : oddCount 3601 13 = 6 ∧ acceleratedOrbit 13 3601 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3601) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3601.1, data_13_3601.2] + +/-- Complete interval computation for depth 13, residue 3602. -/ +theorem bounds_13_3602 : exactInterval 13 3602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3602 : oddCount 3602 13 = 9 ∧ acceleratedOrbit 13 3602 = 8666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3602) = 3 ^ 9 * m + 8666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3602.1, data_13_3602.2] + +/-- Complete interval computation for depth 13, residue 3603. -/ +theorem bounds_13_3603 : exactInterval 13 3603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3603 : oddCount 3603 13 = 9 ∧ acceleratedOrbit 13 3603 = 8666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3603) = 3 ^ 9 * m + 8666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3603.1, data_13_3603.2] + +/-- Complete interval computation for depth 13, residue 3604. -/ +theorem bounds_13_3604 : exactInterval 13 3604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3604 : oddCount 3604 13 = 7 ∧ acceleratedOrbit 13 3604 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3604) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3604.1, data_13_3604.2] + +/-- Complete interval computation for depth 13, residue 3605. -/ +theorem bounds_13_3605 : exactInterval 13 3605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3605 : oddCount 3605 13 = 7 ∧ acceleratedOrbit 13 3605 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3605) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3605.1, data_13_3605.2] + +/-- Complete interval computation for depth 13, residue 3606. -/ +theorem bounds_13_3606 : exactInterval 13 3606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3606 : oddCount 3606 13 = 7 ∧ acceleratedOrbit 13 3606 = 965 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3606) = 3 ^ 7 * m + 965 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3606.1, data_13_3606.2] + +/-- Complete interval computation for depth 13, residue 3607. -/ +theorem bounds_13_3607 : exactInterval 13 3607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3607) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3607 : oddCount 3607 13 = 7 ∧ acceleratedOrbit 13 3607 = 965 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3607) = 3 ^ 7 * m + 965 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3607.1, data_13_3607.2] + +/-- Complete interval computation for depth 13, residue 3608. -/ +theorem bounds_13_3608 : exactInterval 13 3608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3608 : oddCount 3608 13 = 7 ∧ acceleratedOrbit 13 3608 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3608) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3608.1, data_13_3608.2] + +/-- Complete interval computation for depth 13, residue 3609. -/ +theorem bounds_13_3609 : exactInterval 13 3609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3609 : oddCount 3609 13 = 7 ∧ acceleratedOrbit 13 3609 = 965 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3609) = 3 ^ 7 * m + 965 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3609.1, data_13_3609.2] + +/-- Complete interval computation for depth 13, residue 3610. -/ +theorem bounds_13_3610 : exactInterval 13 3610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3610 : oddCount 3610 13 = 7 ∧ acceleratedOrbit 13 3610 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3610) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3610.1, data_13_3610.2] + +/-- Complete interval computation for depth 13, residue 3611. -/ +theorem bounds_13_3611 : exactInterval 13 3611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3611 : oddCount 3611 13 = 9 ∧ acceleratedOrbit 13 3611 = 8680 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3611) = 3 ^ 9 * m + 8680 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3611.1, data_13_3611.2] + +/-- Complete interval computation for depth 13, residue 3612. -/ +theorem bounds_13_3612 : exactInterval 13 3612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3612 : oddCount 3612 13 = 6 ∧ acceleratedOrbit 13 3612 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3612) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3612.1, data_13_3612.2] + +/-- Complete interval computation for depth 13, residue 3613. -/ +theorem bounds_13_3613 : exactInterval 13 3613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3613 : oddCount 3613 13 = 6 ∧ acceleratedOrbit 13 3613 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3613) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3613.1, data_13_3613.2] + +end Collatz.Research.StoppingAtlas.Batch0702 From c6e47dde212ff5246df1886f46919192ddd41c59 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:47 +0530 Subject: [PATCH 0703/1001] proof: certify atlas Batch0703 (13:3614 to 13:3629) --- Collatz/Research/StoppingAtlas/Batch0703.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0703.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0703.lean b/Collatz/Research/StoppingAtlas/Batch0703.lean new file mode 100644 index 00000000..34c469ad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0703.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0703 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3614. -/ +theorem bounds_13_3614 : exactInterval 13 3614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3614 : oddCount 3614 13 = 6 ∧ acceleratedOrbit 13 3614 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3614) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3614.1, data_13_3614.2] + +/-- Complete interval computation for depth 13, residue 3615. -/ +theorem bounds_13_3615 : exactInterval 13 3615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3615 : oddCount 3615 13 = 9 ∧ acceleratedOrbit 13 3615 = 8689 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3615) = 3 ^ 9 * m + 8689 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3615.1, data_13_3615.2] + +/-- Complete interval computation for depth 13, residue 3616. -/ +theorem bounds_13_3616 : exactInterval 13 3616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3616 : oddCount 3616 13 = 2 ∧ acceleratedOrbit 13 3616 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3616) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3616.1, data_13_3616.2] + +/-- Complete interval computation for depth 13, residue 3617. -/ +theorem bounds_13_3617 : exactInterval 13 3617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3617 : oddCount 3617 13 = 7 ∧ acceleratedOrbit 13 3617 = 967 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3617) = 3 ^ 7 * m + 967 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3617.1, data_13_3617.2] + +/-- Complete interval computation for depth 13, residue 3618. -/ +theorem bounds_13_3618 : exactInterval 13 3618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3618 : oddCount 3618 13 = 7 ∧ acceleratedOrbit 13 3618 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3618) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3618.1, data_13_3618.2] + +/-- Complete interval computation for depth 13, residue 3619. -/ +theorem bounds_13_3619 : exactInterval 13 3619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3619 : oddCount 3619 13 = 7 ∧ acceleratedOrbit 13 3619 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3619) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3619.1, data_13_3619.2] + +/-- Complete interval computation for depth 13, residue 3620. -/ +theorem bounds_13_3620 : exactInterval 13 3620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3620 : oddCount 3620 13 = 8 ∧ acceleratedOrbit 13 3620 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3620) = 3 ^ 8 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3620.1, data_13_3620.2] + +/-- Complete interval computation for depth 13, residue 3621. -/ +theorem bounds_13_3621 : exactInterval 13 3621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3621 : oddCount 3621 13 = 8 ∧ acceleratedOrbit 13 3621 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3621) = 3 ^ 8 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3621.1, data_13_3621.2] + +/-- Complete interval computation for depth 13, residue 3622. -/ +theorem bounds_13_3622 : exactInterval 13 3622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3622 : oddCount 3622 13 = 8 ∧ acceleratedOrbit 13 3622 = 2906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3622) = 3 ^ 8 * m + 2906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3622.1, data_13_3622.2] + +/-- Complete interval computation for depth 13, residue 3623. -/ +theorem bounds_13_3623 : exactInterval 13 3623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3623 : oddCount 3623 13 = 6 ∧ acceleratedOrbit 13 3623 = 323 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3623) = 3 ^ 6 * m + 323 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3623.1, data_13_3623.2] + +/-- Complete interval computation for depth 13, residue 3624. -/ +theorem bounds_13_3624 : exactInterval 13 3624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3624 : oddCount 3624 13 = 2 ∧ acceleratedOrbit 13 3624 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3624) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3624.1, data_13_3624.2] + +/-- Complete interval computation for depth 13, residue 3625. -/ +theorem bounds_13_3625 : exactInterval 13 3625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3625 : oddCount 3625 13 = 9 ∧ acceleratedOrbit 13 3625 = 8714 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3625) = 3 ^ 9 * m + 8714 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3625.1, data_13_3625.2] + +/-- Complete interval computation for depth 13, residue 3626. -/ +theorem bounds_13_3626 : exactInterval 13 3626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3626 : oddCount 3626 13 = 2 ∧ acceleratedOrbit 13 3626 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3626) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3626.1, data_13_3626.2] + +/-- Complete interval computation for depth 13, residue 3627. -/ +theorem bounds_13_3627 : exactInterval 13 3627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3627 : oddCount 3627 13 = 7 ∧ acceleratedOrbit 13 3627 = 971 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3627) = 3 ^ 7 * m + 971 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3627.1, data_13_3627.2] + +/-- Complete interval computation for depth 13, residue 3628. -/ +theorem bounds_13_3628 : exactInterval 13 3628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3628 : oddCount 3628 13 = 8 ∧ acceleratedOrbit 13 3628 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3628) = 3 ^ 8 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3628.1, data_13_3628.2] + +/-- Complete interval computation for depth 13, residue 3629. -/ +theorem bounds_13_3629 : exactInterval 13 3629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3629 : oddCount 3629 13 = 8 ∧ acceleratedOrbit 13 3629 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3629) = 3 ^ 8 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3629.1, data_13_3629.2] + +end Collatz.Research.StoppingAtlas.Batch0703 From 9a5d8838abb75394ef3833bac551e979a6be8201 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:48 +0530 Subject: [PATCH 0704/1001] proof: certify atlas Batch0704 (13:3630 to 13:3644) --- Collatz/Research/StoppingAtlas/Batch0704.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0704.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0704.lean b/Collatz/Research/StoppingAtlas/Batch0704.lean new file mode 100644 index 00000000..31ffcd1b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0704.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0704 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3630. -/ +theorem bounds_13_3630 : exactInterval 13 3630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3630 : oddCount 3630 13 = 8 ∧ acceleratedOrbit 13 3630 = 2915 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3630) = 3 ^ 8 * m + 2915 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3630.1, data_13_3630.2] + +/-- Complete interval computation for depth 13, residue 3631. -/ +theorem bounds_13_3631 : exactInterval 13 3631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3631) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3631 : oddCount 3631 13 = 10 ∧ acceleratedOrbit 13 3631 = 26183 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3631) = 3 ^ 10 * m + 26183 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3631.1, data_13_3631.2] + +/-- Complete interval computation for depth 13, residue 3632. -/ +theorem bounds_13_3632 : exactInterval 13 3632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3632 : oddCount 3632 13 = 2 ∧ acceleratedOrbit 13 3632 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3632) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3632.1, data_13_3632.2] + +/-- Complete interval computation for depth 13, residue 3633. -/ +theorem bounds_13_3633 : exactInterval 13 3633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3633 : oddCount 3633 13 = 9 ∧ acceleratedOrbit 13 3633 = 8747 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3633) = 3 ^ 9 * m + 8747 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3633.1, data_13_3633.2] + +/-- Complete interval computation for depth 13, residue 3634. -/ +theorem bounds_13_3634 : exactInterval 13 3634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3634 : oddCount 3634 13 = 9 ∧ acceleratedOrbit 13 3634 = 8747 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3634) = 3 ^ 9 * m + 8747 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3634.1, data_13_3634.2] + +/-- Complete interval computation for depth 13, residue 3635. -/ +theorem bounds_13_3635 : exactInterval 13 3635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3635 : oddCount 3635 13 = 9 ∧ acceleratedOrbit 13 3635 = 8747 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3635) = 3 ^ 9 * m + 8747 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3635.1, data_13_3635.2] + +/-- Complete interval computation for depth 13, residue 3636. -/ +theorem bounds_13_3636 : exactInterval 13 3636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3636 : oddCount 3636 13 = 2 ∧ acceleratedOrbit 13 3636 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3636) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3636.1, data_13_3636.2] + +/-- Complete interval computation for depth 13, residue 3637. -/ +theorem bounds_13_3637 : exactInterval 13 3637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3637 : oddCount 3637 13 = 2 ∧ acceleratedOrbit 13 3637 = 4 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3637) = 3 ^ 2 * m + 4 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3637.1, data_13_3637.2] + +/-- Complete interval computation for depth 13, residue 3638. -/ +theorem bounds_13_3638 : exactInterval 13 3638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3638 : oddCount 3638 13 = 11 ∧ acceleratedOrbit 13 3638 = 78731 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3638) = 3 ^ 11 * m + 78731 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3638.1, data_13_3638.2] + +/-- Complete interval computation for depth 13, residue 3639. -/ +theorem bounds_13_3639 : exactInterval 13 3639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3639 : oddCount 3639 13 = 11 ∧ acceleratedOrbit 13 3639 = 78731 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3639) = 3 ^ 11 * m + 78731 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3639.1, data_13_3639.2] + +/-- Complete interval computation for depth 13, residue 3640. -/ +theorem bounds_13_3640 : exactInterval 13 3640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3640 : oddCount 3640 13 = 6 ∧ acceleratedOrbit 13 3640 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3640) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3640.1, data_13_3640.2] + +/-- Complete interval computation for depth 13, residue 3641. -/ +theorem bounds_13_3641 : exactInterval 13 3641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3641 : oddCount 3641 13 = 7 ∧ acceleratedOrbit 13 3641 = 973 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3641) = 3 ^ 7 * m + 973 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3641.1, data_13_3641.2] + +/-- Complete interval computation for depth 13, residue 3642. -/ +theorem bounds_13_3642 : exactInterval 13 3642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3642 : oddCount 3642 13 = 6 ∧ acceleratedOrbit 13 3642 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3642) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3642.1, data_13_3642.2] + +/-- Complete interval computation for depth 13, residue 3643. -/ +theorem bounds_13_3643 : exactInterval 13 3643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3643 : oddCount 3643 13 = 7 ∧ acceleratedOrbit 13 3643 = 974 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3643) = 3 ^ 7 * m + 974 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3643.1, data_13_3643.2] + +/-- Complete interval computation for depth 13, residue 3644. -/ +theorem bounds_13_3644 : exactInterval 13 3644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3644 : oddCount 3644 13 = 6 ∧ acceleratedOrbit 13 3644 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3644) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3644.1, data_13_3644.2] + +end Collatz.Research.StoppingAtlas.Batch0704 From fe1a919ee10a5e79559e29c8e5d9cbecaa0b004c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:48 +0530 Subject: [PATCH 0705/1001] proof: certify atlas Batch0705 (13:3645 to 13:3659) --- Collatz/Research/StoppingAtlas/Batch0705.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0705.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0705.lean b/Collatz/Research/StoppingAtlas/Batch0705.lean new file mode 100644 index 00000000..be54ff04 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0705.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0705 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3645. -/ +theorem bounds_13_3645 : exactInterval 13 3645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3645 : oddCount 3645 13 = 6 ∧ acceleratedOrbit 13 3645 = 325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3645) = 3 ^ 6 * m + 325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3645.1, data_13_3645.2] + +/-- Complete interval computation for depth 13, residue 3646. -/ +theorem bounds_13_3646 : exactInterval 13 3646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3646 : oddCount 3646 13 = 7 ∧ acceleratedOrbit 13 3646 = 974 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3646) = 3 ^ 7 * m + 974 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3646.1, data_13_3646.2] + +/-- Complete interval computation for depth 13, residue 3647. -/ +theorem bounds_13_3647 : exactInterval 13 3647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3647 : oddCount 3647 13 = 7 ∧ acceleratedOrbit 13 3647 = 974 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3647) = 3 ^ 7 * m + 974 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3647.1, data_13_3647.2] + +/-- Complete interval computation for depth 13, residue 3648. -/ +theorem bounds_13_3648 : exactInterval 13 3648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3648 : oddCount 3648 13 = 4 ∧ acceleratedOrbit 13 3648 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3648) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3648.1, data_13_3648.2] + +/-- Complete interval computation for depth 13, residue 3649. -/ +theorem bounds_13_3649 : exactInterval 13 3649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3649 : oddCount 3649 13 = 6 ∧ acceleratedOrbit 13 3649 = 326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3649) = 3 ^ 6 * m + 326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3649.1, data_13_3649.2] + +/-- Complete interval computation for depth 13, residue 3650. -/ +theorem bounds_13_3650 : exactInterval 13 3650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3650 : oddCount 3650 13 = 6 ∧ acceleratedOrbit 13 3650 = 326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3650) = 3 ^ 6 * m + 326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3650.1, data_13_3650.2] + +/-- Complete interval computation for depth 13, residue 3651. -/ +theorem bounds_13_3651 : exactInterval 13 3651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3651 : oddCount 3651 13 = 6 ∧ acceleratedOrbit 13 3651 = 326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3651) = 3 ^ 6 * m + 326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3651.1, data_13_3651.2] + +/-- Complete interval computation for depth 13, residue 3652. -/ +theorem bounds_13_3652 : exactInterval 13 3652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3652 : oddCount 3652 13 = 5 ∧ acceleratedOrbit 13 3652 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3652) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3652.1, data_13_3652.2] + +/-- Complete interval computation for depth 13, residue 3653. -/ +theorem bounds_13_3653 : exactInterval 13 3653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3653 : oddCount 3653 13 = 5 ∧ acceleratedOrbit 13 3653 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3653) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3653.1, data_13_3653.2] + +/-- Complete interval computation for depth 13, residue 3654. -/ +theorem bounds_13_3654 : exactInterval 13 3654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3654 : oddCount 3654 13 = 5 ∧ acceleratedOrbit 13 3654 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3654) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3654.1, data_13_3654.2] + +/-- Complete interval computation for depth 13, residue 3655. -/ +theorem bounds_13_3655 : exactInterval 13 3655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3655 : oddCount 3655 13 = 8 ∧ acceleratedOrbit 13 3655 = 2929 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3655) = 3 ^ 8 * m + 2929 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3655.1, data_13_3655.2] + +/-- Complete interval computation for depth 13, residue 3656. -/ +theorem bounds_13_3656 : exactInterval 13 3656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3656 : oddCount 3656 13 = 5 ∧ acceleratedOrbit 13 3656 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3656) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3656.1, data_13_3656.2] + +/-- Complete interval computation for depth 13, residue 3657. -/ +theorem bounds_13_3657 : exactInterval 13 3657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3657 : oddCount 3657 13 = 7 ∧ acceleratedOrbit 13 3657 = 977 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3657) = 3 ^ 7 * m + 977 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3657.1, data_13_3657.2] + +/-- Complete interval computation for depth 13, residue 3658. -/ +theorem bounds_13_3658 : exactInterval 13 3658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3658 : oddCount 3658 13 = 5 ∧ acceleratedOrbit 13 3658 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3658) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3658.1, data_13_3658.2] + +/-- Complete interval computation for depth 13, residue 3659. -/ +theorem bounds_13_3659 : exactInterval 13 3659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3659 : oddCount 3659 13 = 5 ∧ acceleratedOrbit 13 3659 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3659) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3659.1, data_13_3659.2] + +end Collatz.Research.StoppingAtlas.Batch0705 From 6b5366f363f85a40013d68a1da41c62460013d18 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:52 +0530 Subject: [PATCH 0706/1001] proof: certify atlas Batch0706 (13:3660 to 13:3675) --- Collatz/Research/StoppingAtlas/Batch0706.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0706.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0706.lean b/Collatz/Research/StoppingAtlas/Batch0706.lean new file mode 100644 index 00000000..1b9c8f87 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0706.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0706 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3660. -/ +theorem bounds_13_3660 : exactInterval 13 3660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3660 : oddCount 3660 13 = 5 ∧ acceleratedOrbit 13 3660 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3660) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3660.1, data_13_3660.2] + +/-- Complete interval computation for depth 13, residue 3661. -/ +theorem bounds_13_3661 : exactInterval 13 3661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3661 : oddCount 3661 13 = 5 ∧ acceleratedOrbit 13 3661 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3661) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3661.1, data_13_3661.2] + +/-- Complete interval computation for depth 13, residue 3662. -/ +theorem bounds_13_3662 : exactInterval 13 3662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3662 : oddCount 3662 13 = 8 ∧ acceleratedOrbit 13 3662 = 2936 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3662) = 3 ^ 8 * m + 2936 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3662.1, data_13_3662.2] + +/-- Complete interval computation for depth 13, residue 3663. -/ +theorem bounds_13_3663 : exactInterval 13 3663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3663 : oddCount 3663 13 = 8 ∧ acceleratedOrbit 13 3663 = 2936 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3663) = 3 ^ 8 * m + 2936 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3663.1, data_13_3663.2] + +/-- Complete interval computation for depth 13, residue 3664. -/ +theorem bounds_13_3664 : exactInterval 13 3664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3664 : oddCount 3664 13 = 4 ∧ acceleratedOrbit 13 3664 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3664) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3664.1, data_13_3664.2] + +/-- Complete interval computation for depth 13, residue 3665. -/ +theorem bounds_13_3665 : exactInterval 13 3665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3665 : oddCount 3665 13 = 7 ∧ acceleratedOrbit 13 3665 = 980 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3665) = 3 ^ 7 * m + 980 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3665.1, data_13_3665.2] + +/-- Complete interval computation for depth 13, residue 3666. -/ +theorem bounds_13_3666 : exactInterval 13 3666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3666 : oddCount 3666 13 = 7 ∧ acceleratedOrbit 13 3666 = 980 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3666) = 3 ^ 7 * m + 980 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3666.1, data_13_3666.2] + +/-- Complete interval computation for depth 13, residue 3667. -/ +theorem bounds_13_3667 : exactInterval 13 3667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3667 : oddCount 3667 13 = 7 ∧ acceleratedOrbit 13 3667 = 980 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3667) = 3 ^ 7 * m + 980 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3667.1, data_13_3667.2] + +/-- Complete interval computation for depth 13, residue 3668. -/ +theorem bounds_13_3668 : exactInterval 13 3668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3668 : oddCount 3668 13 = 4 ∧ acceleratedOrbit 13 3668 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3668) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3668.1, data_13_3668.2] + +/-- Complete interval computation for depth 13, residue 3669. -/ +theorem bounds_13_3669 : exactInterval 13 3669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3669 : oddCount 3669 13 = 4 ∧ acceleratedOrbit 13 3669 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3669) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3669.1, data_13_3669.2] + +/-- Complete interval computation for depth 13, residue 3670. -/ +theorem bounds_13_3670 : exactInterval 13 3670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3670 : oddCount 3670 13 = 5 ∧ acceleratedOrbit 13 3670 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3670) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3670.1, data_13_3670.2] + +/-- Complete interval computation for depth 13, residue 3671. -/ +theorem bounds_13_3671 : exactInterval 13 3671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3671 : oddCount 3671 13 = 5 ∧ acceleratedOrbit 13 3671 = 109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3671) = 3 ^ 5 * m + 109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3671.1, data_13_3671.2] + +/-- Complete interval computation for depth 13, residue 3672. -/ +theorem bounds_13_3672 : exactInterval 13 3672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3672 : oddCount 3672 13 = 5 ∧ acceleratedOrbit 13 3672 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3672) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3672.1, data_13_3672.2] + +/-- Complete interval computation for depth 13, residue 3673. -/ +theorem bounds_13_3673 : exactInterval 13 3673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3673 : oddCount 3673 13 = 7 ∧ acceleratedOrbit 13 3673 = 982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3673) = 3 ^ 7 * m + 982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3673.1, data_13_3673.2] + +/-- Complete interval computation for depth 13, residue 3674. -/ +theorem bounds_13_3674 : exactInterval 13 3674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3674 : oddCount 3674 13 = 5 ∧ acceleratedOrbit 13 3674 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3674) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3674.1, data_13_3674.2] + +/-- Complete interval computation for depth 13, residue 3675. -/ +theorem bounds_13_3675 : exactInterval 13 3675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3675 : oddCount 3675 13 = 8 ∧ acceleratedOrbit 13 3675 = 2945 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3675) = 3 ^ 8 * m + 2945 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3675.1, data_13_3675.2] + +end Collatz.Research.StoppingAtlas.Batch0706 From 6185ad088cc2ae655e491883c03951ba404f85ef Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:52 +0530 Subject: [PATCH 0707/1001] proof: certify atlas Batch0707 (13:3676 to 13:3690) --- Collatz/Research/StoppingAtlas/Batch0707.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0707.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0707.lean b/Collatz/Research/StoppingAtlas/Batch0707.lean new file mode 100644 index 00000000..bec30ac1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0707.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0707 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3676. -/ +theorem bounds_13_3676 : exactInterval 13 3676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3676 : oddCount 3676 13 = 5 ∧ acceleratedOrbit 13 3676 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3676) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3676.1, data_13_3676.2] + +/-- Complete interval computation for depth 13, residue 3677. -/ +theorem bounds_13_3677 : exactInterval 13 3677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3677 : oddCount 3677 13 = 5 ∧ acceleratedOrbit 13 3677 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3677) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3677.1, data_13_3677.2] + +/-- Complete interval computation for depth 13, residue 3678. -/ +theorem bounds_13_3678 : exactInterval 13 3678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3678 : oddCount 3678 13 = 7 ∧ acceleratedOrbit 13 3678 = 983 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3678) = 3 ^ 7 * m + 983 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3678.1, data_13_3678.2] + +/-- Complete interval computation for depth 13, residue 3679. -/ +theorem bounds_13_3679 : exactInterval 13 3679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3679 : oddCount 3679 13 = 7 ∧ acceleratedOrbit 13 3679 = 983 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3679) = 3 ^ 7 * m + 983 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3679.1, data_13_3679.2] + +/-- Complete interval computation for depth 13, residue 3680. -/ +theorem bounds_13_3680 : exactInterval 13 3680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3680 : oddCount 3680 13 = 4 ∧ acceleratedOrbit 13 3680 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3680) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3680.1, data_13_3680.2] + +/-- Complete interval computation for depth 13, residue 3681. -/ +theorem bounds_13_3681 : exactInterval 13 3681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3681 : oddCount 3681 13 = 6 ∧ acceleratedOrbit 13 3681 = 328 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3681) = 3 ^ 6 * m + 328 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3681.1, data_13_3681.2] + +/-- Complete interval computation for depth 13, residue 3682. -/ +theorem bounds_13_3682 : exactInterval 13 3682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3682 : oddCount 3682 13 = 5 ∧ acceleratedOrbit 13 3682 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3682) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3682.1, data_13_3682.2] + +/-- Complete interval computation for depth 13, residue 3683. -/ +theorem bounds_13_3683 : exactInterval 13 3683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3683 : oddCount 3683 13 = 5 ∧ acceleratedOrbit 13 3683 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3683) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3683.1, data_13_3683.2] + +/-- Complete interval computation for depth 13, residue 3684. -/ +theorem bounds_13_3684 : exactInterval 13 3684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3684 : oddCount 3684 13 = 5 ∧ acceleratedOrbit 13 3684 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3684) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3684.1, data_13_3684.2] + +/-- Complete interval computation for depth 13, residue 3685. -/ +theorem bounds_13_3685 : exactInterval 13 3685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3685 : oddCount 3685 13 = 5 ∧ acceleratedOrbit 13 3685 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3685) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3685.1, data_13_3685.2] + +/-- Complete interval computation for depth 13, residue 3686. -/ +theorem bounds_13_3686 : exactInterval 13 3686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3686 : oddCount 3686 13 = 5 ∧ acceleratedOrbit 13 3686 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3686) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3686.1, data_13_3686.2] + +/-- Complete interval computation for depth 13, residue 3687. -/ +theorem bounds_13_3687 : exactInterval 13 3687 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3687) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3687 : oddCount 3687 13 = 8 ∧ acceleratedOrbit 13 3687 = 2954 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3687) = 3 ^ 8 * m + 2954 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3687.1, data_13_3687.2] + +/-- Complete interval computation for depth 13, residue 3688. -/ +theorem bounds_13_3688 : exactInterval 13 3688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3688 : oddCount 3688 13 = 4 ∧ acceleratedOrbit 13 3688 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3688) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3688.1, data_13_3688.2] + +/-- Complete interval computation for depth 13, residue 3689. -/ +theorem bounds_13_3689 : exactInterval 13 3689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3689 : oddCount 3689 13 = 9 ∧ acceleratedOrbit 13 3689 = 8869 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3689) = 3 ^ 9 * m + 8869 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3689.1, data_13_3689.2] + +/-- Complete interval computation for depth 13, residue 3690. -/ +theorem bounds_13_3690 : exactInterval 13 3690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3690 : oddCount 3690 13 = 4 ∧ acceleratedOrbit 13 3690 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3690) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3690.1, data_13_3690.2] + +end Collatz.Research.StoppingAtlas.Batch0707 From 04bb7207aec49e9d35f17c95d751324d29a4d3b1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:53 +0530 Subject: [PATCH 0708/1001] proof: certify atlas Batch0708 (13:3691 to 13:3705) --- Collatz/Research/StoppingAtlas/Batch0708.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0708.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0708.lean b/Collatz/Research/StoppingAtlas/Batch0708.lean new file mode 100644 index 00000000..c8cfe0ce --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0708.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0708 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3691. -/ +theorem bounds_13_3691 : exactInterval 13 3691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3691 : oddCount 3691 13 = 7 ∧ acceleratedOrbit 13 3691 = 986 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3691) = 3 ^ 7 * m + 986 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3691.1, data_13_3691.2] + +/-- Complete interval computation for depth 13, residue 3692. -/ +theorem bounds_13_3692 : exactInterval 13 3692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3692 : oddCount 3692 13 = 6 ∧ acceleratedOrbit 13 3692 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3692) = 3 ^ 6 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3692.1, data_13_3692.2] + +/-- Complete interval computation for depth 13, residue 3693. -/ +theorem bounds_13_3693 : exactInterval 13 3693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3693 : oddCount 3693 13 = 6 ∧ acceleratedOrbit 13 3693 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3693) = 3 ^ 6 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3693.1, data_13_3693.2] + +/-- Complete interval computation for depth 13, residue 3694. -/ +theorem bounds_13_3694 : exactInterval 13 3694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3694 : oddCount 3694 13 = 6 ∧ acceleratedOrbit 13 3694 = 329 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3694) = 3 ^ 6 * m + 329 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3694.1, data_13_3694.2] + +/-- Complete interval computation for depth 13, residue 3695. -/ +theorem bounds_13_3695 : exactInterval 13 3695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3695 : oddCount 3695 13 = 9 ∧ acceleratedOrbit 13 3695 = 8882 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3695) = 3 ^ 9 * m + 8882 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3695.1, data_13_3695.2] + +/-- Complete interval computation for depth 13, residue 3696. -/ +theorem bounds_13_3696 : exactInterval 13 3696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3696 : oddCount 3696 13 = 7 ∧ acceleratedOrbit 13 3696 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3696) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3696.1, data_13_3696.2] + +/-- Complete interval computation for depth 13, residue 3697. -/ +theorem bounds_13_3697 : exactInterval 13 3697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3697 : oddCount 3697 13 = 4 ∧ acceleratedOrbit 13 3697 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3697) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3697.1, data_13_3697.2] + +/-- Complete interval computation for depth 13, residue 3698. -/ +theorem bounds_13_3698 : exactInterval 13 3698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3698 : oddCount 3698 13 = 7 ∧ acceleratedOrbit 13 3698 = 989 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3698) = 3 ^ 7 * m + 989 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3698.1, data_13_3698.2] + +/-- Complete interval computation for depth 13, residue 3699. -/ +theorem bounds_13_3699 : exactInterval 13 3699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3699 : oddCount 3699 13 = 7 ∧ acceleratedOrbit 13 3699 = 989 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3699) = 3 ^ 7 * m + 989 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3699.1, data_13_3699.2] + +/-- Complete interval computation for depth 13, residue 3700. -/ +theorem bounds_13_3700 : exactInterval 13 3700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3700 : oddCount 3700 13 = 7 ∧ acceleratedOrbit 13 3700 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3700) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3700.1, data_13_3700.2] + +/-- Complete interval computation for depth 13, residue 3701. -/ +theorem bounds_13_3701 : exactInterval 13 3701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3701 : oddCount 3701 13 = 7 ∧ acceleratedOrbit 13 3701 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3701) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3701.1, data_13_3701.2] + +/-- Complete interval computation for depth 13, residue 3702. -/ +theorem bounds_13_3702 : exactInterval 13 3702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3702 : oddCount 3702 13 = 5 ∧ acceleratedOrbit 13 3702 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3702) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3702.1, data_13_3702.2] + +/-- Complete interval computation for depth 13, residue 3703. -/ +theorem bounds_13_3703 : exactInterval 13 3703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3703 : oddCount 3703 13 = 5 ∧ acceleratedOrbit 13 3703 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3703) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3703.1, data_13_3703.2] + +/-- Complete interval computation for depth 13, residue 3704. -/ +theorem bounds_13_3704 : exactInterval 13 3704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3704 : oddCount 3704 13 = 7 ∧ acceleratedOrbit 13 3704 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3704) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3704.1, data_13_3704.2] + +/-- Complete interval computation for depth 13, residue 3705. -/ +theorem bounds_13_3705 : exactInterval 13 3705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3705 : oddCount 3705 13 = 9 ∧ acceleratedOrbit 13 3705 = 8909 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3705) = 3 ^ 9 * m + 8909 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3705.1, data_13_3705.2] + +end Collatz.Research.StoppingAtlas.Batch0708 From e42a86b1ed5e90387fdcce617ed39d1ee9866c6d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:54 +0530 Subject: [PATCH 0709/1001] proof: certify atlas Batch0709 (13:3706 to 13:3721) --- Collatz/Research/StoppingAtlas/Batch0709.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0709.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0709.lean b/Collatz/Research/StoppingAtlas/Batch0709.lean new file mode 100644 index 00000000..a02fa9a6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0709.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0709 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3706. -/ +theorem bounds_13_3706 : exactInterval 13 3706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3706 : oddCount 3706 13 = 7 ∧ acceleratedOrbit 13 3706 = 992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3706) = 3 ^ 7 * m + 992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3706.1, data_13_3706.2] + +/-- Complete interval computation for depth 13, residue 3707. -/ +theorem bounds_13_3707 : exactInterval 13 3707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3707 : oddCount 3707 13 = 5 ∧ acceleratedOrbit 13 3707 = 110 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3707) = 3 ^ 5 * m + 110 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3707.1, data_13_3707.2] + +/-- Complete interval computation for depth 13, residue 3708. -/ +theorem bounds_13_3708 : exactInterval 13 3708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3708 : oddCount 3708 13 = 7 ∧ acceleratedOrbit 13 3708 = 991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3708) = 3 ^ 7 * m + 991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3708.1, data_13_3708.2] + +/-- Complete interval computation for depth 13, residue 3709. -/ +theorem bounds_13_3709 : exactInterval 13 3709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3709 : oddCount 3709 13 = 7 ∧ acceleratedOrbit 13 3709 = 991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3709) = 3 ^ 7 * m + 991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3709.1, data_13_3709.2] + +/-- Complete interval computation for depth 13, residue 3710. -/ +theorem bounds_13_3710 : exactInterval 13 3710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3710 : oddCount 3710 13 = 7 ∧ acceleratedOrbit 13 3710 = 991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3710) = 3 ^ 7 * m + 991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3710.1, data_13_3710.2] + +/-- Complete interval computation for depth 13, residue 3711. -/ +theorem bounds_13_3711 : exactInterval 13 3711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3711 : oddCount 3711 13 = 12 ∧ acceleratedOrbit 13 3711 = 240812 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3711) = 3 ^ 12 * m + 240812 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3711.1, data_13_3711.2] + +/-- Complete interval computation for depth 13, residue 3712. -/ +theorem bounds_13_3712 : exactInterval 13 3712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3712 : oddCount 3712 13 = 3 ∧ acceleratedOrbit 13 3712 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3712) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3712.1, data_13_3712.2] + +/-- Complete interval computation for depth 13, residue 3713. -/ +theorem bounds_13_3713 : exactInterval 13 3713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3713 : oddCount 3713 13 = 9 ∧ acceleratedOrbit 13 3713 = 8930 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3713) = 3 ^ 9 * m + 8930 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3713.1, data_13_3713.2] + +/-- Complete interval computation for depth 13, residue 3714. -/ +theorem bounds_13_3714 : exactInterval 13 3714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3714 : oddCount 3714 13 = 4 ∧ acceleratedOrbit 13 3714 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3714) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3714.1, data_13_3714.2] + +/-- Complete interval computation for depth 13, residue 3715. -/ +theorem bounds_13_3715 : exactInterval 13 3715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3715 : oddCount 3715 13 = 4 ∧ acceleratedOrbit 13 3715 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3715) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3715.1, data_13_3715.2] + +/-- Complete interval computation for depth 13, residue 3716. -/ +theorem bounds_13_3716 : exactInterval 13 3716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3716 : oddCount 3716 13 = 6 ∧ acceleratedOrbit 13 3716 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3716) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3716.1, data_13_3716.2] + +/-- Complete interval computation for depth 13, residue 3717. -/ +theorem bounds_13_3717 : exactInterval 13 3717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3717 : oddCount 3717 13 = 6 ∧ acceleratedOrbit 13 3717 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3717) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3717.1, data_13_3717.2] + +/-- Complete interval computation for depth 13, residue 3718. -/ +theorem bounds_13_3718 : exactInterval 13 3718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3718 : oddCount 3718 13 = 6 ∧ acceleratedOrbit 13 3718 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3718) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3718.1, data_13_3718.2] + +/-- Complete interval computation for depth 13, residue 3719. -/ +theorem bounds_13_3719 : exactInterval 13 3719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3719 : oddCount 3719 13 = 7 ∧ acceleratedOrbit 13 3719 = 994 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3719) = 3 ^ 7 * m + 994 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3719.1, data_13_3719.2] + +/-- Complete interval computation for depth 13, residue 3720. -/ +theorem bounds_13_3720 : exactInterval 13 3720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3720 : oddCount 3720 13 = 4 ∧ acceleratedOrbit 13 3720 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3720) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3720.1, data_13_3720.2] + +/-- Complete interval computation for depth 13, residue 3721. -/ +theorem bounds_13_3721 : exactInterval 13 3721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3721 : oddCount 3721 13 = 10 ∧ acceleratedOrbit 13 3721 = 26837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3721) = 3 ^ 10 * m + 26837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3721.1, data_13_3721.2] + +end Collatz.Research.StoppingAtlas.Batch0709 From d32ae0000cf77344d67dfb8b417c1743b88eff12 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:56 +0530 Subject: [PATCH 0710/1001] proof: certify atlas Batch0710 (13:3722 to 13:3736) --- Collatz/Research/StoppingAtlas/Batch0710.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0710.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0710.lean b/Collatz/Research/StoppingAtlas/Batch0710.lean new file mode 100644 index 00000000..c115dff2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0710.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0710 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3722. -/ +theorem bounds_13_3722 : exactInterval 13 3722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3722 : oddCount 3722 13 = 4 ∧ acceleratedOrbit 13 3722 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3722) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3722.1, data_13_3722.2] + +/-- Complete interval computation for depth 13, residue 3723. -/ +theorem bounds_13_3723 : exactInterval 13 3723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3723 : oddCount 3723 13 = 6 ∧ acceleratedOrbit 13 3723 = 332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3723) = 3 ^ 6 * m + 332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3723.1, data_13_3723.2] + +/-- Complete interval computation for depth 13, residue 3724. -/ +theorem bounds_13_3724 : exactInterval 13 3724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3724 : oddCount 3724 13 = 4 ∧ acceleratedOrbit 13 3724 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3724) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3724.1, data_13_3724.2] + +/-- Complete interval computation for depth 13, residue 3725. -/ +theorem bounds_13_3725 : exactInterval 13 3725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3725 : oddCount 3725 13 = 4 ∧ acceleratedOrbit 13 3725 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3725) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3725.1, data_13_3725.2] + +/-- Complete interval computation for depth 13, residue 3726. -/ +theorem bounds_13_3726 : exactInterval 13 3726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3726 : oddCount 3726 13 = 8 ∧ acceleratedOrbit 13 3726 = 2987 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3726) = 3 ^ 8 * m + 2987 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3726.1, data_13_3726.2] + +/-- Complete interval computation for depth 13, residue 3727. -/ +theorem bounds_13_3727 : exactInterval 13 3727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3727 : oddCount 3727 13 = 8 ∧ acceleratedOrbit 13 3727 = 2987 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3727) = 3 ^ 8 * m + 2987 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3727.1, data_13_3727.2] + +/-- Complete interval computation for depth 13, residue 3728. -/ +theorem bounds_13_3728 : exactInterval 13 3728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3728 : oddCount 3728 13 = 6 ∧ acceleratedOrbit 13 3728 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3728) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3728.1, data_13_3728.2] + +/-- Complete interval computation for depth 13, residue 3729. -/ +theorem bounds_13_3729 : exactInterval 13 3729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3729 : oddCount 3729 13 = 7 ∧ acceleratedOrbit 13 3729 = 998 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3729) = 3 ^ 7 * m + 998 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3729.1, data_13_3729.2] + +/-- Complete interval computation for depth 13, residue 3730. -/ +theorem bounds_13_3730 : exactInterval 13 3730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3730 : oddCount 3730 13 = 7 ∧ acceleratedOrbit 13 3730 = 998 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3730) = 3 ^ 7 * m + 998 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3730.1, data_13_3730.2] + +/-- Complete interval computation for depth 13, residue 3731. -/ +theorem bounds_13_3731 : exactInterval 13 3731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3731 : oddCount 3731 13 = 7 ∧ acceleratedOrbit 13 3731 = 998 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3731) = 3 ^ 7 * m + 998 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3731.1, data_13_3731.2] + +/-- Complete interval computation for depth 13, residue 3732. -/ +theorem bounds_13_3732 : exactInterval 13 3732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3732 : oddCount 3732 13 = 6 ∧ acceleratedOrbit 13 3732 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3732) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3732.1, data_13_3732.2] + +/-- Complete interval computation for depth 13, residue 3733. -/ +theorem bounds_13_3733 : exactInterval 13 3733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3733 : oddCount 3733 13 = 6 ∧ acceleratedOrbit 13 3733 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3733) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3733.1, data_13_3733.2] + +/-- Complete interval computation for depth 13, residue 3734. -/ +theorem bounds_13_3734 : exactInterval 13 3734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3734 : oddCount 3734 13 = 4 ∧ acceleratedOrbit 13 3734 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3734) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3734.1, data_13_3734.2] + +/-- Complete interval computation for depth 13, residue 3735. -/ +theorem bounds_13_3735 : exactInterval 13 3735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3735 : oddCount 3735 13 = 4 ∧ acceleratedOrbit 13 3735 = 37 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3735) = 3 ^ 4 * m + 37 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3735.1, data_13_3735.2] + +/-- Complete interval computation for depth 13, residue 3736. -/ +theorem bounds_13_3736 : exactInterval 13 3736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3736 : oddCount 3736 13 = 6 ∧ acceleratedOrbit 13 3736 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3736) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3736.1, data_13_3736.2] + +end Collatz.Research.StoppingAtlas.Batch0710 From f508ef29f0cbd8f8ef763fbe7aae747847fc12c0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:57 +0530 Subject: [PATCH 0711/1001] proof: certify atlas Batch0711 (13:3737 to 13:3751) --- Collatz/Research/StoppingAtlas/Batch0711.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0711.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0711.lean b/Collatz/Research/StoppingAtlas/Batch0711.lean new file mode 100644 index 00000000..76cae839 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0711.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0711 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3737. -/ +theorem bounds_13_3737 : exactInterval 13 3737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3737 : oddCount 3737 13 = 9 ∧ acceleratedOrbit 13 3737 = 8990 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3737) = 3 ^ 9 * m + 8990 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3737.1, data_13_3737.2] + +/-- Complete interval computation for depth 13, residue 3738. -/ +theorem bounds_13_3738 : exactInterval 13 3738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3738 : oddCount 3738 13 = 6 ∧ acceleratedOrbit 13 3738 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3738) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3738.1, data_13_3738.2] + +/-- Complete interval computation for depth 13, residue 3739. -/ +theorem bounds_13_3739 : exactInterval 13 3739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3739 : oddCount 3739 13 = 10 ∧ acceleratedOrbit 13 3739 = 26963 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3739) = 3 ^ 10 * m + 26963 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3739.1, data_13_3739.2] + +/-- Complete interval computation for depth 13, residue 3740. -/ +theorem bounds_13_3740 : exactInterval 13 3740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3740 : oddCount 3740 13 = 7 ∧ acceleratedOrbit 13 3740 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3740) = 3 ^ 7 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3740.1, data_13_3740.2] + +/-- Complete interval computation for depth 13, residue 3741. -/ +theorem bounds_13_3741 : exactInterval 13 3741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3741 : oddCount 3741 13 = 7 ∧ acceleratedOrbit 13 3741 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3741) = 3 ^ 7 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3741.1, data_13_3741.2] + +/-- Complete interval computation for depth 13, residue 3742. -/ +theorem bounds_13_3742 : exactInterval 13 3742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3742 : oddCount 3742 13 = 7 ∧ acceleratedOrbit 13 3742 = 1000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3742) = 3 ^ 7 * m + 1000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3742.1, data_13_3742.2] + +/-- Complete interval computation for depth 13, residue 3743. -/ +theorem bounds_13_3743 : exactInterval 13 3743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3743 : oddCount 3743 13 = 9 ∧ acceleratedOrbit 13 3743 = 8996 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3743) = 3 ^ 9 * m + 8996 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3743.1, data_13_3743.2] + +/-- Complete interval computation for depth 13, residue 3744. -/ +theorem bounds_13_3744 : exactInterval 13 3744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3744 : oddCount 3744 13 = 3 ∧ acceleratedOrbit 13 3744 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3744) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3744.1, data_13_3744.2] + +/-- Complete interval computation for depth 13, residue 3745. -/ +theorem bounds_13_3745 : exactInterval 13 3745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3745 : oddCount 3745 13 = 7 ∧ acceleratedOrbit 13 3745 = 1001 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3745) = 3 ^ 7 * m + 1001 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3745.1, data_13_3745.2] + +/-- Complete interval computation for depth 13, residue 3746. -/ +theorem bounds_13_3746 : exactInterval 13 3746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3746 : oddCount 3746 13 = 6 ∧ acceleratedOrbit 13 3746 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3746) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3746.1, data_13_3746.2] + +/-- Complete interval computation for depth 13, residue 3747. -/ +theorem bounds_13_3747 : exactInterval 13 3747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3747 : oddCount 3747 13 = 6 ∧ acceleratedOrbit 13 3747 = 334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3747) = 3 ^ 6 * m + 334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3747.1, data_13_3747.2] + +/-- Complete interval computation for depth 13, residue 3748. -/ +theorem bounds_13_3748 : exactInterval 13 3748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3748 : oddCount 3748 13 = 8 ∧ acceleratedOrbit 13 3748 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3748) = 3 ^ 8 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3748.1, data_13_3748.2] + +/-- Complete interval computation for depth 13, residue 3749. -/ +theorem bounds_13_3749 : exactInterval 13 3749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3749 : oddCount 3749 13 = 8 ∧ acceleratedOrbit 13 3749 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3749) = 3 ^ 8 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3749.1, data_13_3749.2] + +/-- Complete interval computation for depth 13, residue 3750. -/ +theorem bounds_13_3750 : exactInterval 13 3750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3750 : oddCount 3750 13 = 8 ∧ acceleratedOrbit 13 3750 = 3007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3750) = 3 ^ 8 * m + 3007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3750.1, data_13_3750.2] + +/-- Complete interval computation for depth 13, residue 3751. -/ +theorem bounds_13_3751 : exactInterval 13 3751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3751 : oddCount 3751 13 = 9 ∧ acceleratedOrbit 13 3751 = 9017 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3751) = 3 ^ 9 * m + 9017 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3751.1, data_13_3751.2] + +end Collatz.Research.StoppingAtlas.Batch0711 From 1a841816bef87b439539e773fdc338ed181bbaa8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:58 +0530 Subject: [PATCH 0712/1001] proof: certify atlas Batch0712 (13:3752 to 13:3767) --- Collatz/Research/StoppingAtlas/Batch0712.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0712.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0712.lean b/Collatz/Research/StoppingAtlas/Batch0712.lean new file mode 100644 index 00000000..13f69e59 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0712.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0712 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3752. -/ +theorem bounds_13_3752 : exactInterval 13 3752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3752 : oddCount 3752 13 = 3 ∧ acceleratedOrbit 13 3752 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3752) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3752.1, data_13_3752.2] + +/-- Complete interval computation for depth 13, residue 3753. -/ +theorem bounds_13_3753 : exactInterval 13 3753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3753 : oddCount 3753 13 = 10 ∧ acceleratedOrbit 13 3753 = 27064 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3753) = 3 ^ 10 * m + 27064 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3753.1, data_13_3753.2] + +/-- Complete interval computation for depth 13, residue 3754. -/ +theorem bounds_13_3754 : exactInterval 13 3754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3754 : oddCount 3754 13 = 3 ∧ acceleratedOrbit 13 3754 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3754) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3754.1, data_13_3754.2] + +/-- Complete interval computation for depth 13, residue 3755. -/ +theorem bounds_13_3755 : exactInterval 13 3755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3755 : oddCount 3755 13 = 8 ∧ acceleratedOrbit 13 3755 = 3010 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3755) = 3 ^ 8 * m + 3010 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3755.1, data_13_3755.2] + +/-- Complete interval computation for depth 13, residue 3756. -/ +theorem bounds_13_3756 : exactInterval 13 3756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3756 : oddCount 3756 13 = 6 ∧ acceleratedOrbit 13 3756 = 335 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3756) = 3 ^ 6 * m + 335 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3756.1, data_13_3756.2] + +/-- Complete interval computation for depth 13, residue 3757. -/ +theorem bounds_13_3757 : exactInterval 13 3757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3757 : oddCount 3757 13 = 6 ∧ acceleratedOrbit 13 3757 = 335 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3757) = 3 ^ 6 * m + 335 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3757.1, data_13_3757.2] + +/-- Complete interval computation for depth 13, residue 3758. -/ +theorem bounds_13_3758 : exactInterval 13 3758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3758 : oddCount 3758 13 = 6 ∧ acceleratedOrbit 13 3758 = 335 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3758) = 3 ^ 6 * m + 335 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3758.1, data_13_3758.2] + +/-- Complete interval computation for depth 13, residue 3759. -/ +theorem bounds_13_3759 : exactInterval 13 3759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3759 : oddCount 3759 13 = 7 ∧ acceleratedOrbit 13 3759 = 1004 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3759) = 3 ^ 7 * m + 1004 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3759.1, data_13_3759.2] + +/-- Complete interval computation for depth 13, residue 3760. -/ +theorem bounds_13_3760 : exactInterval 13 3760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3760 : oddCount 3760 13 = 6 ∧ acceleratedOrbit 13 3760 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3760) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3760.1, data_13_3760.2] + +/-- Complete interval computation for depth 13, residue 3761. -/ +theorem bounds_13_3761 : exactInterval 13 3761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3761 : oddCount 3761 13 = 5 ∧ acceleratedOrbit 13 3761 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3761) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3761.1, data_13_3761.2] + +/-- Complete interval computation for depth 13, residue 3762. -/ +theorem bounds_13_3762 : exactInterval 13 3762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3762 : oddCount 3762 13 = 5 ∧ acceleratedOrbit 13 3762 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3762) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3762.1, data_13_3762.2] + +/-- Complete interval computation for depth 13, residue 3763. -/ +theorem bounds_13_3763 : exactInterval 13 3763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3763 : oddCount 3763 13 = 5 ∧ acceleratedOrbit 13 3763 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3763) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3763.1, data_13_3763.2] + +/-- Complete interval computation for depth 13, residue 3764. -/ +theorem bounds_13_3764 : exactInterval 13 3764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3764 : oddCount 3764 13 = 6 ∧ acceleratedOrbit 13 3764 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3764) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3764.1, data_13_3764.2] + +/-- Complete interval computation for depth 13, residue 3765. -/ +theorem bounds_13_3765 : exactInterval 13 3765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3765 : oddCount 3765 13 = 6 ∧ acceleratedOrbit 13 3765 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3765) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3765.1, data_13_3765.2] + +/-- Complete interval computation for depth 13, residue 3766. -/ +theorem bounds_13_3766 : exactInterval 13 3766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3766 : oddCount 3766 13 = 8 ∧ acceleratedOrbit 13 3766 = 3019 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3766) = 3 ^ 8 * m + 3019 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3766.1, data_13_3766.2] + +/-- Complete interval computation for depth 13, residue 3767. -/ +theorem bounds_13_3767 : exactInterval 13 3767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3767 : oddCount 3767 13 = 8 ∧ acceleratedOrbit 13 3767 = 3019 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3767) = 3 ^ 8 * m + 3019 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3767.1, data_13_3767.2] + +end Collatz.Research.StoppingAtlas.Batch0712 From 0b80cbb131ab0cb50ef16dae1c36b3fe6c49b2eb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:33:59 +0530 Subject: [PATCH 0713/1001] proof: certify atlas Batch0713 (13:3768 to 13:3782) --- Collatz/Research/StoppingAtlas/Batch0713.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0713.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0713.lean b/Collatz/Research/StoppingAtlas/Batch0713.lean new file mode 100644 index 00000000..b16a7867 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0713.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0713 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3768. -/ +theorem bounds_13_3768 : exactInterval 13 3768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3768 : oddCount 3768 13 = 6 ∧ acceleratedOrbit 13 3768 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3768) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3768.1, data_13_3768.2] + +/-- Complete interval computation for depth 13, residue 3769. -/ +theorem bounds_13_3769 : exactInterval 13 3769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3769 : oddCount 3769 13 = 8 ∧ acceleratedOrbit 13 3769 = 3023 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3769) = 3 ^ 8 * m + 3023 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3769.1, data_13_3769.2] + +/-- Complete interval computation for depth 13, residue 3770. -/ +theorem bounds_13_3770 : exactInterval 13 3770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3770 : oddCount 3770 13 = 6 ∧ acceleratedOrbit 13 3770 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3770) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3770.1, data_13_3770.2] + +/-- Complete interval computation for depth 13, residue 3771. -/ +theorem bounds_13_3771 : exactInterval 13 3771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3771 : oddCount 3771 13 = 8 ∧ acceleratedOrbit 13 3771 = 3023 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3771) = 3 ^ 8 * m + 3023 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3771.1, data_13_3771.2] + +/-- Complete interval computation for depth 13, residue 3772. -/ +theorem bounds_13_3772 : exactInterval 13 3772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3772 : oddCount 3772 13 = 5 ∧ acceleratedOrbit 13 3772 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3772) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3772.1, data_13_3772.2] + +/-- Complete interval computation for depth 13, residue 3773. -/ +theorem bounds_13_3773 : exactInterval 13 3773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3773 : oddCount 3773 13 = 5 ∧ acceleratedOrbit 13 3773 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3773) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3773.1, data_13_3773.2] + +/-- Complete interval computation for depth 13, residue 3774. -/ +theorem bounds_13_3774 : exactInterval 13 3774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3774 : oddCount 3774 13 = 5 ∧ acceleratedOrbit 13 3774 = 112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3774) = 3 ^ 5 * m + 112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3774.1, data_13_3774.2] + +/-- Complete interval computation for depth 13, residue 3775. -/ +theorem bounds_13_3775 : exactInterval 13 3775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3775 : oddCount 3775 13 = 9 ∧ acceleratedOrbit 13 3775 = 9073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3775) = 3 ^ 9 * m + 9073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3775.1, data_13_3775.2] + +/-- Complete interval computation for depth 13, residue 3776. -/ +theorem bounds_13_3776 : exactInterval 13 3776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3776 : oddCount 3776 13 = 4 ∧ acceleratedOrbit 13 3776 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3776) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3776.1, data_13_3776.2] + +/-- Complete interval computation for depth 13, residue 3777. -/ +theorem bounds_13_3777 : exactInterval 13 3777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3777 : oddCount 3777 13 = 6 ∧ acceleratedOrbit 13 3777 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3777) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3777.1, data_13_3777.2] + +/-- Complete interval computation for depth 13, residue 3778. -/ +theorem bounds_13_3778 : exactInterval 13 3778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3778 : oddCount 3778 13 = 7 ∧ acceleratedOrbit 13 3778 = 1010 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3778) = 3 ^ 7 * m + 1010 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3778.1, data_13_3778.2] + +/-- Complete interval computation for depth 13, residue 3779. -/ +theorem bounds_13_3779 : exactInterval 13 3779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3779 : oddCount 3779 13 = 7 ∧ acceleratedOrbit 13 3779 = 1010 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3779) = 3 ^ 7 * m + 1010 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3779.1, data_13_3779.2] + +/-- Complete interval computation for depth 13, residue 3780. -/ +theorem bounds_13_3780 : exactInterval 13 3780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3780 : oddCount 3780 13 = 4 ∧ acceleratedOrbit 13 3780 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3780) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3780.1, data_13_3780.2] + +/-- Complete interval computation for depth 13, residue 3781. -/ +theorem bounds_13_3781 : exactInterval 13 3781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3781 : oddCount 3781 13 = 4 ∧ acceleratedOrbit 13 3781 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3781) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3781.1, data_13_3781.2] + +/-- Complete interval computation for depth 13, residue 3782. -/ +theorem bounds_13_3782 : exactInterval 13 3782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3782 : oddCount 3782 13 = 4 ∧ acceleratedOrbit 13 3782 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3782) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3782.1, data_13_3782.2] + +end Collatz.Research.StoppingAtlas.Batch0713 From 47d89727a5b5ad6a4d1bebbca964ceea87f1b5f0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:02 +0530 Subject: [PATCH 0714/1001] proof: certify atlas Batch0714 (13:3783 to 13:3798) --- Collatz/Research/StoppingAtlas/Batch0714.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0714.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0714.lean b/Collatz/Research/StoppingAtlas/Batch0714.lean new file mode 100644 index 00000000..86b28e10 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0714.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0714 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3783. -/ +theorem bounds_13_3783 : exactInterval 13 3783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3783 : oddCount 3783 13 = 6 ∧ acceleratedOrbit 13 3783 = 337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3783) = 3 ^ 6 * m + 337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3783.1, data_13_3783.2] + +/-- Complete interval computation for depth 13, residue 3784. -/ +theorem bounds_13_3784 : exactInterval 13 3784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3784 : oddCount 3784 13 = 4 ∧ acceleratedOrbit 13 3784 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3784) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3784.1, data_13_3784.2] + +/-- Complete interval computation for depth 13, residue 3785. -/ +theorem bounds_13_3785 : exactInterval 13 3785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3785 : oddCount 3785 13 = 7 ∧ acceleratedOrbit 13 3785 = 1012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3785) = 3 ^ 7 * m + 1012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3785.1, data_13_3785.2] + +/-- Complete interval computation for depth 13, residue 3786. -/ +theorem bounds_13_3786 : exactInterval 13 3786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3786 : oddCount 3786 13 = 4 ∧ acceleratedOrbit 13 3786 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3786) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3786.1, data_13_3786.2] + +/-- Complete interval computation for depth 13, residue 3787. -/ +theorem bounds_13_3787 : exactInterval 13 3787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3787 : oddCount 3787 13 = 8 ∧ acceleratedOrbit 13 3787 = 3037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3787) = 3 ^ 8 * m + 3037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3787.1, data_13_3787.2] + +/-- Complete interval computation for depth 13, residue 3788. -/ +theorem bounds_13_3788 : exactInterval 13 3788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3788 : oddCount 3788 13 = 4 ∧ acceleratedOrbit 13 3788 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3788) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3788.1, data_13_3788.2] + +/-- Complete interval computation for depth 13, residue 3789. -/ +theorem bounds_13_3789 : exactInterval 13 3789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3789 : oddCount 3789 13 = 4 ∧ acceleratedOrbit 13 3789 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3789) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3789.1, data_13_3789.2] + +/-- Complete interval computation for depth 13, residue 3790. -/ +theorem bounds_13_3790 : exactInterval 13 3790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3790 : oddCount 3790 13 = 10 ∧ acceleratedOrbit 13 3790 = 27337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3790) = 3 ^ 10 * m + 27337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3790.1, data_13_3790.2] + +/-- Complete interval computation for depth 13, residue 3791. -/ +theorem bounds_13_3791 : exactInterval 13 3791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3791 : oddCount 3791 13 = 10 ∧ acceleratedOrbit 13 3791 = 27337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3791) = 3 ^ 10 * m + 27337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3791.1, data_13_3791.2] + +/-- Complete interval computation for depth 13, residue 3792. -/ +theorem bounds_13_3792 : exactInterval 13 3792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3792 : oddCount 3792 13 = 4 ∧ acceleratedOrbit 13 3792 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3792) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3792.1, data_13_3792.2] + +/-- Complete interval computation for depth 13, residue 3793. -/ +theorem bounds_13_3793 : exactInterval 13 3793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3793 : oddCount 3793 13 = 6 ∧ acceleratedOrbit 13 3793 = 338 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3793) = 3 ^ 6 * m + 338 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3793.1, data_13_3793.2] + +/-- Complete interval computation for depth 13, residue 3794. -/ +theorem bounds_13_3794 : exactInterval 13 3794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3794 : oddCount 3794 13 = 6 ∧ acceleratedOrbit 13 3794 = 338 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3794) = 3 ^ 6 * m + 338 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3794.1, data_13_3794.2] + +/-- Complete interval computation for depth 13, residue 3795. -/ +theorem bounds_13_3795 : exactInterval 13 3795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3795 : oddCount 3795 13 = 6 ∧ acceleratedOrbit 13 3795 = 338 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3795) = 3 ^ 6 * m + 338 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3795.1, data_13_3795.2] + +/-- Complete interval computation for depth 13, residue 3796. -/ +theorem bounds_13_3796 : exactInterval 13 3796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3796 : oddCount 3796 13 = 4 ∧ acceleratedOrbit 13 3796 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3796) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3796.1, data_13_3796.2] + +/-- Complete interval computation for depth 13, residue 3797. -/ +theorem bounds_13_3797 : exactInterval 13 3797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3797 : oddCount 3797 13 = 4 ∧ acceleratedOrbit 13 3797 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3797) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3797.1, data_13_3797.2] + +/-- Complete interval computation for depth 13, residue 3798. -/ +theorem bounds_13_3798 : exactInterval 13 3798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3798 : oddCount 3798 13 = 7 ∧ acceleratedOrbit 13 3798 = 1016 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3798) = 3 ^ 7 * m + 1016 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3798.1, data_13_3798.2] + +end Collatz.Research.StoppingAtlas.Batch0714 From ac69b35b59e674456c5686c19a392c06ffbd7dec Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:02 +0530 Subject: [PATCH 0715/1001] proof: certify atlas Batch0715 (13:3799 to 13:3813) --- Collatz/Research/StoppingAtlas/Batch0715.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0715.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0715.lean b/Collatz/Research/StoppingAtlas/Batch0715.lean new file mode 100644 index 00000000..a1a96f6b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0715.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0715 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3799. -/ +theorem bounds_13_3799 : exactInterval 13 3799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3799 : oddCount 3799 13 = 7 ∧ acceleratedOrbit 13 3799 = 1016 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3799) = 3 ^ 7 * m + 1016 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3799.1, data_13_3799.2] + +/-- Complete interval computation for depth 13, residue 3800. -/ +theorem bounds_13_3800 : exactInterval 13 3800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3800 : oddCount 3800 13 = 5 ∧ acceleratedOrbit 13 3800 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3800) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3800.1, data_13_3800.2] + +/-- Complete interval computation for depth 13, residue 3801. -/ +theorem bounds_13_3801 : exactInterval 13 3801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3801 : oddCount 3801 13 = 5 ∧ acceleratedOrbit 13 3801 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3801) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3801.1, data_13_3801.2] + +/-- Complete interval computation for depth 13, residue 3802. -/ +theorem bounds_13_3802 : exactInterval 13 3802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3802 : oddCount 3802 13 = 5 ∧ acceleratedOrbit 13 3802 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3802) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3802.1, data_13_3802.2] + +/-- Complete interval computation for depth 13, residue 3803. -/ +theorem bounds_13_3803 : exactInterval 13 3803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3803 : oddCount 3803 13 = 9 ∧ acceleratedOrbit 13 3803 = 9143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3803) = 3 ^ 9 * m + 9143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3803.1, data_13_3803.2] + +/-- Complete interval computation for depth 13, residue 3804. -/ +theorem bounds_13_3804 : exactInterval 13 3804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3804 : oddCount 3804 13 = 5 ∧ acceleratedOrbit 13 3804 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3804) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3804.1, data_13_3804.2] + +/-- Complete interval computation for depth 13, residue 3805. -/ +theorem bounds_13_3805 : exactInterval 13 3805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3805 : oddCount 3805 13 = 5 ∧ acceleratedOrbit 13 3805 = 113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3805) = 3 ^ 5 * m + 113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3805.1, data_13_3805.2] + +/-- Complete interval computation for depth 13, residue 3806. -/ +theorem bounds_13_3806 : exactInterval 13 3806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3806 : oddCount 3806 13 = 9 ∧ acceleratedOrbit 13 3806 = 9152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3806) = 3 ^ 9 * m + 9152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3806.1, data_13_3806.2] + +/-- Complete interval computation for depth 13, residue 3807. -/ +theorem bounds_13_3807 : exactInterval 13 3807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3807 : oddCount 3807 13 = 9 ∧ acceleratedOrbit 13 3807 = 9152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3807) = 3 ^ 9 * m + 9152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3807.1, data_13_3807.2] + +/-- Complete interval computation for depth 13, residue 3808. -/ +theorem bounds_13_3808 : exactInterval 13 3808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3808 : oddCount 3808 13 = 4 ∧ acceleratedOrbit 13 3808 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3808) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3808.1, data_13_3808.2] + +/-- Complete interval computation for depth 13, residue 3809. -/ +theorem bounds_13_3809 : exactInterval 13 3809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3809 : oddCount 3809 13 = 8 ∧ acceleratedOrbit 13 3809 = 3053 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3809) = 3 ^ 8 * m + 3053 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3809.1, data_13_3809.2] + +/-- Complete interval computation for depth 13, residue 3810. -/ +theorem bounds_13_3810 : exactInterval 13 3810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3810 : oddCount 3810 13 = 4 ∧ acceleratedOrbit 13 3810 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3810) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3810.1, data_13_3810.2] + +/-- Complete interval computation for depth 13, residue 3811. -/ +theorem bounds_13_3811 : exactInterval 13 3811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3811 : oddCount 3811 13 = 4 ∧ acceleratedOrbit 13 3811 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3811) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3811.1, data_13_3811.2] + +/-- Complete interval computation for depth 13, residue 3812. -/ +theorem bounds_13_3812 : exactInterval 13 3812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3812 : oddCount 3812 13 = 6 ∧ acceleratedOrbit 13 3812 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3812) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3812.1, data_13_3812.2] + +/-- Complete interval computation for depth 13, residue 3813. -/ +theorem bounds_13_3813 : exactInterval 13 3813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3813 : oddCount 3813 13 = 6 ∧ acceleratedOrbit 13 3813 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3813) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3813.1, data_13_3813.2] + +end Collatz.Research.StoppingAtlas.Batch0715 From c3f40a3203adca3adcaf388a73eb774559164adf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:02 +0530 Subject: [PATCH 0716/1001] proof: certify atlas Batch0716 (13:3814 to 13:3828) --- Collatz/Research/StoppingAtlas/Batch0716.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0716.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0716.lean b/Collatz/Research/StoppingAtlas/Batch0716.lean new file mode 100644 index 00000000..6d859800 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0716.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0716 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3814. -/ +theorem bounds_13_3814 : exactInterval 13 3814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3814 : oddCount 3814 13 = 6 ∧ acceleratedOrbit 13 3814 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3814) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3814.1, data_13_3814.2] + +/-- Complete interval computation for depth 13, residue 3815. -/ +theorem bounds_13_3815 : exactInterval 13 3815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3815 : oddCount 3815 13 = 9 ∧ acceleratedOrbit 13 3815 = 9170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3815) = 3 ^ 9 * m + 9170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3815.1, data_13_3815.2] + +/-- Complete interval computation for depth 13, residue 3816. -/ +theorem bounds_13_3816 : exactInterval 13 3816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3816 : oddCount 3816 13 = 4 ∧ acceleratedOrbit 13 3816 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3816) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3816.1, data_13_3816.2] + +/-- Complete interval computation for depth 13, residue 3817. -/ +theorem bounds_13_3817 : exactInterval 13 3817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3817 : oddCount 3817 13 = 8 ∧ acceleratedOrbit 13 3817 = 3059 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3817) = 3 ^ 8 * m + 3059 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3817.1, data_13_3817.2] + +/-- Complete interval computation for depth 13, residue 3818. -/ +theorem bounds_13_3818 : exactInterval 13 3818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3818 : oddCount 3818 13 = 4 ∧ acceleratedOrbit 13 3818 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3818) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3818.1, data_13_3818.2] + +/-- Complete interval computation for depth 13, residue 3819. -/ +theorem bounds_13_3819 : exactInterval 13 3819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3819 : oddCount 3819 13 = 6 ∧ acceleratedOrbit 13 3819 = 340 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3819) = 3 ^ 6 * m + 340 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3819.1, data_13_3819.2] + +/-- Complete interval computation for depth 13, residue 3820. -/ +theorem bounds_13_3820 : exactInterval 13 3820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3820 : oddCount 3820 13 = 6 ∧ acceleratedOrbit 13 3820 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3820) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3820.1, data_13_3820.2] + +/-- Complete interval computation for depth 13, residue 3821. -/ +theorem bounds_13_3821 : exactInterval 13 3821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3821 : oddCount 3821 13 = 6 ∧ acceleratedOrbit 13 3821 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3821) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3821.1, data_13_3821.2] + +/-- Complete interval computation for depth 13, residue 3822. -/ +theorem bounds_13_3822 : exactInterval 13 3822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3822 : oddCount 3822 13 = 6 ∧ acceleratedOrbit 13 3822 = 341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3822) = 3 ^ 6 * m + 341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3822.1, data_13_3822.2] + +/-- Complete interval computation for depth 13, residue 3823. -/ +theorem bounds_13_3823 : exactInterval 13 3823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3823 : oddCount 3823 13 = 10 ∧ acceleratedOrbit 13 3823 = 27566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3823) = 3 ^ 10 * m + 27566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3823.1, data_13_3823.2] + +/-- Complete interval computation for depth 13, residue 3824. -/ +theorem bounds_13_3824 : exactInterval 13 3824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3824 : oddCount 3824 13 = 8 ∧ acceleratedOrbit 13 3824 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3824) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3824.1, data_13_3824.2] + +/-- Complete interval computation for depth 13, residue 3825. -/ +theorem bounds_13_3825 : exactInterval 13 3825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3825 : oddCount 3825 13 = 4 ∧ acceleratedOrbit 13 3825 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3825) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3825.1, data_13_3825.2] + +/-- Complete interval computation for depth 13, residue 3826. -/ +theorem bounds_13_3826 : exactInterval 13 3826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3826 : oddCount 3826 13 = 8 ∧ acceleratedOrbit 13 3826 = 3068 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3826) = 3 ^ 8 * m + 3068 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3826.1, data_13_3826.2] + +/-- Complete interval computation for depth 13, residue 3827. -/ +theorem bounds_13_3827 : exactInterval 13 3827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3827 : oddCount 3827 13 = 8 ∧ acceleratedOrbit 13 3827 = 3068 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3827) = 3 ^ 8 * m + 3068 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3827.1, data_13_3827.2] + +/-- Complete interval computation for depth 13, residue 3828. -/ +theorem bounds_13_3828 : exactInterval 13 3828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3828 : oddCount 3828 13 = 8 ∧ acceleratedOrbit 13 3828 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3828) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3828.1, data_13_3828.2] + +end Collatz.Research.StoppingAtlas.Batch0716 From 5f65087b12c6b51e2fab82f4086f36825372f114 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:04 +0530 Subject: [PATCH 0717/1001] proof: certify atlas Batch0717 (13:3829 to 13:3844) --- Collatz/Research/StoppingAtlas/Batch0717.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0717.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0717.lean b/Collatz/Research/StoppingAtlas/Batch0717.lean new file mode 100644 index 00000000..f250ca8f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0717.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0717 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3829. -/ +theorem bounds_13_3829 : exactInterval 13 3829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3829 : oddCount 3829 13 = 8 ∧ acceleratedOrbit 13 3829 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3829) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3829.1, data_13_3829.2] + +/-- Complete interval computation for depth 13, residue 3830. -/ +theorem bounds_13_3830 : exactInterval 13 3830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3830 : oddCount 3830 13 = 8 ∧ acceleratedOrbit 13 3830 = 3071 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3830) = 3 ^ 8 * m + 3071 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3830.1, data_13_3830.2] + +/-- Complete interval computation for depth 13, residue 3831. -/ +theorem bounds_13_3831 : exactInterval 13 3831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3831 : oddCount 3831 13 = 8 ∧ acceleratedOrbit 13 3831 = 3071 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3831) = 3 ^ 8 * m + 3071 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3831.1, data_13_3831.2] + +/-- Complete interval computation for depth 13, residue 3832. -/ +theorem bounds_13_3832 : exactInterval 13 3832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3832 : oddCount 3832 13 = 8 ∧ acceleratedOrbit 13 3832 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3832) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3832.1, data_13_3832.2] + +/-- Complete interval computation for depth 13, residue 3833. -/ +theorem bounds_13_3833 : exactInterval 13 3833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3833 : oddCount 3833 13 = 7 ∧ acceleratedOrbit 13 3833 = 1025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3833) = 3 ^ 7 * m + 1025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3833.1, data_13_3833.2] + +/-- Complete interval computation for depth 13, residue 3834. -/ +theorem bounds_13_3834 : exactInterval 13 3834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3834 : oddCount 3834 13 = 8 ∧ acceleratedOrbit 13 3834 = 3077 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3834) = 3 ^ 8 * m + 3077 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3834.1, data_13_3834.2] + +/-- Complete interval computation for depth 13, residue 3835. -/ +theorem bounds_13_3835 : exactInterval 13 3835 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3835) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3835 : oddCount 3835 13 = 8 ∧ acceleratedOrbit 13 3835 = 3073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3835) = 3 ^ 8 * m + 3073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3835.1, data_13_3835.2] + +/-- Complete interval computation for depth 13, residue 3836. -/ +theorem bounds_13_3836 : exactInterval 13 3836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3836 : oddCount 3836 13 = 9 ∧ acceleratedOrbit 13 3836 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3836) = 3 ^ 9 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3836.1, data_13_3836.2] + +/-- Complete interval computation for depth 13, residue 3837. -/ +theorem bounds_13_3837 : exactInterval 13 3837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3837 : oddCount 3837 13 = 9 ∧ acceleratedOrbit 13 3837 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3837) = 3 ^ 9 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3837.1, data_13_3837.2] + +/-- Complete interval computation for depth 13, residue 3838. -/ +theorem bounds_13_3838 : exactInterval 13 3838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3838 : oddCount 3838 13 = 9 ∧ acceleratedOrbit 13 3838 = 9227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3838) = 3 ^ 9 * m + 9227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3838.1, data_13_3838.2] + +/-- Complete interval computation for depth 13, residue 3839. -/ +theorem bounds_13_3839 : exactInterval 13 3839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3839 : oddCount 3839 13 = 11 ∧ acceleratedOrbit 13 3839 = 83038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3839) = 3 ^ 11 * m + 83038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3839.1, data_13_3839.2] + +/-- Complete interval computation for depth 13, residue 3840. -/ +theorem bounds_13_3840 : exactInterval 13 3840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3840 : oddCount 3840 13 = 4 ∧ acceleratedOrbit 13 3840 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3840) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3840.1, data_13_3840.2] + +/-- Complete interval computation for depth 13, residue 3841. -/ +theorem bounds_13_3841 : exactInterval 13 3841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3841 : oddCount 3841 13 = 4 ∧ acceleratedOrbit 13 3841 = 38 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3841) = 3 ^ 4 * m + 38 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3841.1, data_13_3841.2] + +/-- Complete interval computation for depth 13, residue 3842. -/ +theorem bounds_13_3842 : exactInterval 13 3842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3842 : oddCount 3842 13 = 7 ∧ acceleratedOrbit 13 3842 = 1028 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3842) = 3 ^ 7 * m + 1028 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3842.1, data_13_3842.2] + +/-- Complete interval computation for depth 13, residue 3843. -/ +theorem bounds_13_3843 : exactInterval 13 3843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3843 : oddCount 3843 13 = 7 ∧ acceleratedOrbit 13 3843 = 1028 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3843) = 3 ^ 7 * m + 1028 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3843.1, data_13_3843.2] + +/-- Complete interval computation for depth 13, residue 3844. -/ +theorem bounds_13_3844 : exactInterval 13 3844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3844 : oddCount 3844 13 = 6 ∧ acceleratedOrbit 13 3844 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3844) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3844.1, data_13_3844.2] + +end Collatz.Research.StoppingAtlas.Batch0717 From c32eec58f21b93b6899b24ed8df610af55bd75ed Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:06 +0530 Subject: [PATCH 0718/1001] proof: certify atlas Batch0718 (13:3845 to 13:3859) --- Collatz/Research/StoppingAtlas/Batch0718.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0718.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0718.lean b/Collatz/Research/StoppingAtlas/Batch0718.lean new file mode 100644 index 00000000..4869af8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0718.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0718 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3845. -/ +theorem bounds_13_3845 : exactInterval 13 3845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3845 : oddCount 3845 13 = 6 ∧ acceleratedOrbit 13 3845 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3845) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3845.1, data_13_3845.2] + +/-- Complete interval computation for depth 13, residue 3846. -/ +theorem bounds_13_3846 : exactInterval 13 3846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3846 : oddCount 3846 13 = 6 ∧ acceleratedOrbit 13 3846 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3846) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3846.1, data_13_3846.2] + +/-- Complete interval computation for depth 13, residue 3847. -/ +theorem bounds_13_3847 : exactInterval 13 3847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3847 : oddCount 3847 13 = 7 ∧ acceleratedOrbit 13 3847 = 1028 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3847) = 3 ^ 7 * m + 1028 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3847.1, data_13_3847.2] + +/-- Complete interval computation for depth 13, residue 3848. -/ +theorem bounds_13_3848 : exactInterval 13 3848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3848 : oddCount 3848 13 = 6 ∧ acceleratedOrbit 13 3848 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3848) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3848.1, data_13_3848.2] + +/-- Complete interval computation for depth 13, residue 3849. -/ +theorem bounds_13_3849 : exactInterval 13 3849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3849 : oddCount 3849 13 = 9 ∧ acceleratedOrbit 13 3849 = 9254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3849) = 3 ^ 9 * m + 9254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3849.1, data_13_3849.2] + +/-- Complete interval computation for depth 13, residue 3850. -/ +theorem bounds_13_3850 : exactInterval 13 3850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3850 : oddCount 3850 13 = 6 ∧ acceleratedOrbit 13 3850 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3850) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3850.1, data_13_3850.2] + +/-- Complete interval computation for depth 13, residue 3851. -/ +theorem bounds_13_3851 : exactInterval 13 3851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3851 : oddCount 3851 13 = 6 ∧ acceleratedOrbit 13 3851 = 343 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3851) = 3 ^ 6 * m + 343 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3851.1, data_13_3851.2] + +/-- Complete interval computation for depth 13, residue 3852. -/ +theorem bounds_13_3852 : exactInterval 13 3852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3852 : oddCount 3852 13 = 6 ∧ acceleratedOrbit 13 3852 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3852) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3852.1, data_13_3852.2] + +/-- Complete interval computation for depth 13, residue 3853. -/ +theorem bounds_13_3853 : exactInterval 13 3853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3853 : oddCount 3853 13 = 6 ∧ acceleratedOrbit 13 3853 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3853) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3853.1, data_13_3853.2] + +/-- Complete interval computation for depth 13, residue 3854. -/ +theorem bounds_13_3854 : exactInterval 13 3854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3854 : oddCount 3854 13 = 6 ∧ acceleratedOrbit 13 3854 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3854) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3854.1, data_13_3854.2] + +/-- Complete interval computation for depth 13, residue 3855. -/ +theorem bounds_13_3855 : exactInterval 13 3855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3855 : oddCount 3855 13 = 6 ∧ acceleratedOrbit 13 3855 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3855) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3855.1, data_13_3855.2] + +/-- Complete interval computation for depth 13, residue 3856. -/ +theorem bounds_13_3856 : exactInterval 13 3856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3856 : oddCount 3856 13 = 3 ∧ acceleratedOrbit 13 3856 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3856) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3856.1, data_13_3856.2] + +/-- Complete interval computation for depth 13, residue 3857. -/ +theorem bounds_13_3857 : exactInterval 13 3857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3857 : oddCount 3857 13 = 6 ∧ acceleratedOrbit 13 3857 = 344 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3857) = 3 ^ 6 * m + 344 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3857.1, data_13_3857.2] + +/-- Complete interval computation for depth 13, residue 3858. -/ +theorem bounds_13_3858 : exactInterval 13 3858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3858 : oddCount 3858 13 = 7 ∧ acceleratedOrbit 13 3858 = 1031 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3858) = 3 ^ 7 * m + 1031 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3858.1, data_13_3858.2] + +/-- Complete interval computation for depth 13, residue 3859. -/ +theorem bounds_13_3859 : exactInterval 13 3859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3859 : oddCount 3859 13 = 7 ∧ acceleratedOrbit 13 3859 = 1031 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3859) = 3 ^ 7 * m + 1031 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3859.1, data_13_3859.2] + +end Collatz.Research.StoppingAtlas.Batch0718 From 26ebea7835a375714fafc552a71f9c2e4520530f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:06 +0530 Subject: [PATCH 0719/1001] proof: certify atlas Batch0719 (13:3860 to 13:3874) --- Collatz/Research/StoppingAtlas/Batch0719.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0719.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0719.lean b/Collatz/Research/StoppingAtlas/Batch0719.lean new file mode 100644 index 00000000..ff2239b4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0719.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0719 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3860. -/ +theorem bounds_13_3860 : exactInterval 13 3860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3860 : oddCount 3860 13 = 3 ∧ acceleratedOrbit 13 3860 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3860) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3860.1, data_13_3860.2] + +/-- Complete interval computation for depth 13, residue 3861. -/ +theorem bounds_13_3861 : exactInterval 13 3861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3861 : oddCount 3861 13 = 3 ∧ acceleratedOrbit 13 3861 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3861) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3861.1, data_13_3861.2] + +/-- Complete interval computation for depth 13, residue 3862. -/ +theorem bounds_13_3862 : exactInterval 13 3862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3862 : oddCount 3862 13 = 8 ∧ acceleratedOrbit 13 3862 = 3098 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3862) = 3 ^ 8 * m + 3098 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3862.1, data_13_3862.2] + +/-- Complete interval computation for depth 13, residue 3863. -/ +theorem bounds_13_3863 : exactInterval 13 3863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3863 : oddCount 3863 13 = 8 ∧ acceleratedOrbit 13 3863 = 3098 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3863) = 3 ^ 8 * m + 3098 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3863.1, data_13_3863.2] + +/-- Complete interval computation for depth 13, residue 3864. -/ +theorem bounds_13_3864 : exactInterval 13 3864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3864 : oddCount 3864 13 = 3 ∧ acceleratedOrbit 13 3864 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3864) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3864.1, data_13_3864.2] + +/-- Complete interval computation for depth 13, residue 3865. -/ +theorem bounds_13_3865 : exactInterval 13 3865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3865 : oddCount 3865 13 = 8 ∧ acceleratedOrbit 13 3865 = 3098 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3865) = 3 ^ 8 * m + 3098 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3865.1, data_13_3865.2] + +/-- Complete interval computation for depth 13, residue 3866. -/ +theorem bounds_13_3866 : exactInterval 13 3866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3866 : oddCount 3866 13 = 3 ∧ acceleratedOrbit 13 3866 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3866) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3866.1, data_13_3866.2] + +/-- Complete interval computation for depth 13, residue 3867. -/ +theorem bounds_13_3867 : exactInterval 13 3867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3867 : oddCount 3867 13 = 10 ∧ acceleratedOrbit 13 3867 = 27884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3867) = 3 ^ 10 * m + 27884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3867.1, data_13_3867.2] + +/-- Complete interval computation for depth 13, residue 3868. -/ +theorem bounds_13_3868 : exactInterval 13 3868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3868 : oddCount 3868 13 = 8 ∧ acceleratedOrbit 13 3868 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3868) = 3 ^ 8 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3868.1, data_13_3868.2] + +/-- Complete interval computation for depth 13, residue 3869. -/ +theorem bounds_13_3869 : exactInterval 13 3869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3869 : oddCount 3869 13 = 8 ∧ acceleratedOrbit 13 3869 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3869) = 3 ^ 8 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3869.1, data_13_3869.2] + +/-- Complete interval computation for depth 13, residue 3870. -/ +theorem bounds_13_3870 : exactInterval 13 3870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3870 : oddCount 3870 13 = 8 ∧ acceleratedOrbit 13 3870 = 3104 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3870) = 3 ^ 8 * m + 3104 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3870.1, data_13_3870.2] + +/-- Complete interval computation for depth 13, residue 3871. -/ +theorem bounds_13_3871 : exactInterval 13 3871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3871 : oddCount 3871 13 = 9 ∧ acceleratedOrbit 13 3871 = 9305 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3871) = 3 ^ 9 * m + 9305 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3871.1, data_13_3871.2] + +/-- Complete interval computation for depth 13, residue 3872. -/ +theorem bounds_13_3872 : exactInterval 13 3872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3872 : oddCount 3872 13 = 6 ∧ acceleratedOrbit 13 3872 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3872) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3872.1, data_13_3872.2] + +/-- Complete interval computation for depth 13, residue 3873. -/ +theorem bounds_13_3873 : exactInterval 13 3873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3873 : oddCount 3873 13 = 5 ∧ acceleratedOrbit 13 3873 = 115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3873) = 3 ^ 5 * m + 115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3873.1, data_13_3873.2] + +/-- Complete interval computation for depth 13, residue 3874. -/ +theorem bounds_13_3874 : exactInterval 13 3874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3874 : oddCount 3874 13 = 6 ∧ acceleratedOrbit 13 3874 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3874) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3874.1, data_13_3874.2] + +end Collatz.Research.StoppingAtlas.Batch0719 From 1aa88094fd288327c843066bd656a4e2a90840c0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:16 +0530 Subject: [PATCH 0720/1001] proof: certify atlas Batch0720 (13:3875 to 13:3890) --- Collatz/Research/StoppingAtlas/Batch0720.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0720.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0720.lean b/Collatz/Research/StoppingAtlas/Batch0720.lean new file mode 100644 index 00000000..ed1ff31d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0720.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0720 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3875. -/ +theorem bounds_13_3875 : exactInterval 13 3875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3875 : oddCount 3875 13 = 6 ∧ acceleratedOrbit 13 3875 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3875) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3875.1, data_13_3875.2] + +/-- Complete interval computation for depth 13, residue 3876. -/ +theorem bounds_13_3876 : exactInterval 13 3876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3876 : oddCount 3876 13 = 6 ∧ acceleratedOrbit 13 3876 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3876) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3876.1, data_13_3876.2] + +/-- Complete interval computation for depth 13, residue 3877. -/ +theorem bounds_13_3877 : exactInterval 13 3877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3877 : oddCount 3877 13 = 6 ∧ acceleratedOrbit 13 3877 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3877) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3877.1, data_13_3877.2] + +/-- Complete interval computation for depth 13, residue 3878. -/ +theorem bounds_13_3878 : exactInterval 13 3878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3878 : oddCount 3878 13 = 6 ∧ acceleratedOrbit 13 3878 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3878) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3878.1, data_13_3878.2] + +/-- Complete interval computation for depth 13, residue 3879. -/ +theorem bounds_13_3879 : exactInterval 13 3879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3879 : oddCount 3879 13 = 7 ∧ acceleratedOrbit 13 3879 = 1036 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3879) = 3 ^ 7 * m + 1036 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3879.1, data_13_3879.2] + +/-- Complete interval computation for depth 13, residue 3880. -/ +theorem bounds_13_3880 : exactInterval 13 3880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3880 : oddCount 3880 13 = 6 ∧ acceleratedOrbit 13 3880 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3880) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3880.1, data_13_3880.2] + +/-- Complete interval computation for depth 13, residue 3881. -/ +theorem bounds_13_3881 : exactInterval 13 3881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3881 : oddCount 3881 13 = 7 ∧ acceleratedOrbit 13 3881 = 1037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3881) = 3 ^ 7 * m + 1037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3881.1, data_13_3881.2] + +/-- Complete interval computation for depth 13, residue 3882. -/ +theorem bounds_13_3882 : exactInterval 13 3882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3882 : oddCount 3882 13 = 6 ∧ acceleratedOrbit 13 3882 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3882) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3882.1, data_13_3882.2] + +/-- Complete interval computation for depth 13, residue 3883. -/ +theorem bounds_13_3883 : exactInterval 13 3883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3883 : oddCount 3883 13 = 6 ∧ acceleratedOrbit 13 3883 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3883) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3883.1, data_13_3883.2] + +/-- Complete interval computation for depth 13, residue 3884. -/ +theorem bounds_13_3884 : exactInterval 13 3884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3884 : oddCount 3884 13 = 5 ∧ acceleratedOrbit 13 3884 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3884) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3884.1, data_13_3884.2] + +/-- Complete interval computation for depth 13, residue 3885. -/ +theorem bounds_13_3885 : exactInterval 13 3885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3885 : oddCount 3885 13 = 5 ∧ acceleratedOrbit 13 3885 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3885) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3885.1, data_13_3885.2] + +/-- Complete interval computation for depth 13, residue 3886. -/ +theorem bounds_13_3886 : exactInterval 13 3886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3886 : oddCount 3886 13 = 5 ∧ acceleratedOrbit 13 3886 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3886) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3886.1, data_13_3886.2] + +/-- Complete interval computation for depth 13, residue 3887. -/ +theorem bounds_13_3887 : exactInterval 13 3887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3887 : oddCount 3887 13 = 6 ∧ acceleratedOrbit 13 3887 = 346 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3887) = 3 ^ 6 * m + 346 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3887.1, data_13_3887.2] + +/-- Complete interval computation for depth 13, residue 3888. -/ +theorem bounds_13_3888 : exactInterval 13 3888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3888 : oddCount 3888 13 = 6 ∧ acceleratedOrbit 13 3888 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3888) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3888.1, data_13_3888.2] + +/-- Complete interval computation for depth 13, residue 3889. -/ +theorem bounds_13_3889 : exactInterval 13 3889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3889 : oddCount 3889 13 = 5 ∧ acceleratedOrbit 13 3889 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3889) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3889.1, data_13_3889.2] + +/-- Complete interval computation for depth 13, residue 3890. -/ +theorem bounds_13_3890 : exactInterval 13 3890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3890 : oddCount 3890 13 = 5 ∧ acceleratedOrbit 13 3890 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3890) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3890.1, data_13_3890.2] + +end Collatz.Research.StoppingAtlas.Batch0720 From c020c82181089953c9d6d0f92824d64ed88704a2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:16 +0530 Subject: [PATCH 0721/1001] proof: certify atlas Batch0721 (13:3891 to 13:3905) --- Collatz/Research/StoppingAtlas/Batch0721.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0721.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0721.lean b/Collatz/Research/StoppingAtlas/Batch0721.lean new file mode 100644 index 00000000..c340792b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0721.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0721 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3891. -/ +theorem bounds_13_3891 : exactInterval 13 3891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3891 : oddCount 3891 13 = 5 ∧ acceleratedOrbit 13 3891 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3891) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3891.1, data_13_3891.2] + +/-- Complete interval computation for depth 13, residue 3892. -/ +theorem bounds_13_3892 : exactInterval 13 3892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3892 : oddCount 3892 13 = 6 ∧ acceleratedOrbit 13 3892 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3892) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3892.1, data_13_3892.2] + +/-- Complete interval computation for depth 13, residue 3893. -/ +theorem bounds_13_3893 : exactInterval 13 3893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3893 : oddCount 3893 13 = 6 ∧ acceleratedOrbit 13 3893 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3893) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3893.1, data_13_3893.2] + +/-- Complete interval computation for depth 13, residue 3894. -/ +theorem bounds_13_3894 : exactInterval 13 3894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3894 : oddCount 3894 13 = 8 ∧ acceleratedOrbit 13 3894 = 3122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3894) = 3 ^ 8 * m + 3122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3894.1, data_13_3894.2] + +/-- Complete interval computation for depth 13, residue 3895. -/ +theorem bounds_13_3895 : exactInterval 13 3895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3895 : oddCount 3895 13 = 8 ∧ acceleratedOrbit 13 3895 = 3122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3895) = 3 ^ 8 * m + 3122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3895.1, data_13_3895.2] + +/-- Complete interval computation for depth 13, residue 3896. -/ +theorem bounds_13_3896 : exactInterval 13 3896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3896 : oddCount 3896 13 = 7 ∧ acceleratedOrbit 13 3896 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3896) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3896.1, data_13_3896.2] + +/-- Complete interval computation for depth 13, residue 3897. -/ +theorem bounds_13_3897 : exactInterval 13 3897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3897 : oddCount 3897 13 = 6 ∧ acceleratedOrbit 13 3897 = 347 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3897) = 3 ^ 6 * m + 347 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3897.1, data_13_3897.2] + +/-- Complete interval computation for depth 13, residue 3898. -/ +theorem bounds_13_3898 : exactInterval 13 3898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3898 : oddCount 3898 13 = 7 ∧ acceleratedOrbit 13 3898 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3898) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3898.1, data_13_3898.2] + +/-- Complete interval computation for depth 13, residue 3899. -/ +theorem bounds_13_3899 : exactInterval 13 3899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3899 : oddCount 3899 13 = 7 ∧ acceleratedOrbit 13 3899 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3899) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3899.1, data_13_3899.2] + +/-- Complete interval computation for depth 13, residue 3900. -/ +theorem bounds_13_3900 : exactInterval 13 3900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3900 : oddCount 3900 13 = 7 ∧ acceleratedOrbit 13 3900 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3900) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3900.1, data_13_3900.2] + +/-- Complete interval computation for depth 13, residue 3901. -/ +theorem bounds_13_3901 : exactInterval 13 3901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3901 : oddCount 3901 13 = 7 ∧ acceleratedOrbit 13 3901 = 1043 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3901) = 3 ^ 7 * m + 1043 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3901.1, data_13_3901.2] + +/-- Complete interval computation for depth 13, residue 3902. -/ +theorem bounds_13_3902 : exactInterval 13 3902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3902 : oddCount 3902 13 = 8 ∧ acceleratedOrbit 13 3902 = 3127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3902) = 3 ^ 8 * m + 3127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3902.1, data_13_3902.2] + +/-- Complete interval computation for depth 13, residue 3903. -/ +theorem bounds_13_3903 : exactInterval 13 3903 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3903) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3903 : oddCount 3903 13 = 8 ∧ acceleratedOrbit 13 3903 = 3127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3903) = 3 ^ 8 * m + 3127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3903.1, data_13_3903.2] + +/-- Complete interval computation for depth 13, residue 3904. -/ +theorem bounds_13_3904 : exactInterval 13 3904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3904 : oddCount 3904 13 = 4 ∧ acceleratedOrbit 13 3904 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3904) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3904.1, data_13_3904.2] + +/-- Complete interval computation for depth 13, residue 3905. -/ +theorem bounds_13_3905 : exactInterval 13 3905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3905 : oddCount 3905 13 = 6 ∧ acceleratedOrbit 13 3905 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3905) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3905.1, data_13_3905.2] + +end Collatz.Research.StoppingAtlas.Batch0721 From b72f7289630fadface48d43a27e915865b0dbe0b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:17 +0530 Subject: [PATCH 0722/1001] proof: certify atlas Batch0722 (13:3906 to 13:3920) --- Collatz/Research/StoppingAtlas/Batch0722.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0722.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0722.lean b/Collatz/Research/StoppingAtlas/Batch0722.lean new file mode 100644 index 00000000..9e2141c4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0722.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0722 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3906. -/ +theorem bounds_13_3906 : exactInterval 13 3906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3906 : oddCount 3906 13 = 5 ∧ acceleratedOrbit 13 3906 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3906) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3906.1, data_13_3906.2] + +/-- Complete interval computation for depth 13, residue 3907. -/ +theorem bounds_13_3907 : exactInterval 13 3907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3907 : oddCount 3907 13 = 5 ∧ acceleratedOrbit 13 3907 = 116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3907) = 3 ^ 5 * m + 116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3907.1, data_13_3907.2] + +/-- Complete interval computation for depth 13, residue 3908. -/ +theorem bounds_13_3908 : exactInterval 13 3908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3908 : oddCount 3908 13 = 6 ∧ acceleratedOrbit 13 3908 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3908) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3908.1, data_13_3908.2] + +/-- Complete interval computation for depth 13, residue 3909. -/ +theorem bounds_13_3909 : exactInterval 13 3909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3909 : oddCount 3909 13 = 6 ∧ acceleratedOrbit 13 3909 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3909) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3909.1, data_13_3909.2] + +/-- Complete interval computation for depth 13, residue 3910. -/ +theorem bounds_13_3910 : exactInterval 13 3910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3910 : oddCount 3910 13 = 6 ∧ acceleratedOrbit 13 3910 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3910) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3910.1, data_13_3910.2] + +/-- Complete interval computation for depth 13, residue 3911. -/ +theorem bounds_13_3911 : exactInterval 13 3911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3911 : oddCount 3911 13 = 8 ∧ acceleratedOrbit 13 3911 = 3134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3911) = 3 ^ 8 * m + 3134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3911.1, data_13_3911.2] + +/-- Complete interval computation for depth 13, residue 3912. -/ +theorem bounds_13_3912 : exactInterval 13 3912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3912 : oddCount 3912 13 = 7 ∧ acceleratedOrbit 13 3912 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3912) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3912.1, data_13_3912.2] + +/-- Complete interval computation for depth 13, residue 3913. -/ +theorem bounds_13_3913 : exactInterval 13 3913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3913 : oddCount 3913 13 = 7 ∧ acceleratedOrbit 13 3913 = 1046 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3913) = 3 ^ 7 * m + 1046 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3913.1, data_13_3913.2] + +/-- Complete interval computation for depth 13, residue 3914. -/ +theorem bounds_13_3914 : exactInterval 13 3914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3914 : oddCount 3914 13 = 7 ∧ acceleratedOrbit 13 3914 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3914) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3914.1, data_13_3914.2] + +/-- Complete interval computation for depth 13, residue 3915. -/ +theorem bounds_13_3915 : exactInterval 13 3915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3915 : oddCount 3915 13 = 6 ∧ acceleratedOrbit 13 3915 = 350 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3915) = 3 ^ 6 * m + 350 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3915.1, data_13_3915.2] + +/-- Complete interval computation for depth 13, residue 3916. -/ +theorem bounds_13_3916 : exactInterval 13 3916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3916 : oddCount 3916 13 = 7 ∧ acceleratedOrbit 13 3916 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3916) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3916.1, data_13_3916.2] + +/-- Complete interval computation for depth 13, residue 3917. -/ +theorem bounds_13_3917 : exactInterval 13 3917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3917 : oddCount 3917 13 = 7 ∧ acceleratedOrbit 13 3917 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3917) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3917.1, data_13_3917.2] + +/-- Complete interval computation for depth 13, residue 3918. -/ +theorem bounds_13_3918 : exactInterval 13 3918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3918 : oddCount 3918 13 = 9 ∧ acceleratedOrbit 13 3918 = 9422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3918) = 3 ^ 9 * m + 9422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3918.1, data_13_3918.2] + +/-- Complete interval computation for depth 13, residue 3919. -/ +theorem bounds_13_3919 : exactInterval 13 3919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3919 : oddCount 3919 13 = 9 ∧ acceleratedOrbit 13 3919 = 9422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3919) = 3 ^ 9 * m + 9422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3919.1, data_13_3919.2] + +/-- Complete interval computation for depth 13, residue 3920. -/ +theorem bounds_13_3920 : exactInterval 13 3920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3920 : oddCount 3920 13 = 4 ∧ acceleratedOrbit 13 3920 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3920) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3920.1, data_13_3920.2] + +end Collatz.Research.StoppingAtlas.Batch0722 From 2dc318472ba3e726e3554ac184ef398702f6bfaf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:17 +0530 Subject: [PATCH 0723/1001] proof: certify atlas Batch0723 (13:3921 to 13:3936) --- Collatz/Research/StoppingAtlas/Batch0723.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0723.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0723.lean b/Collatz/Research/StoppingAtlas/Batch0723.lean new file mode 100644 index 00000000..31255f6a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0723.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0723 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3921. -/ +theorem bounds_13_3921 : exactInterval 13 3921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3921 : oddCount 3921 13 = 7 ∧ acceleratedOrbit 13 3921 = 1048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3921) = 3 ^ 7 * m + 1048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3921.1, data_13_3921.2] + +/-- Complete interval computation for depth 13, residue 3922. -/ +theorem bounds_13_3922 : exactInterval 13 3922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3922 : oddCount 3922 13 = 10 ∧ acceleratedOrbit 13 3922 = 28295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3922) = 3 ^ 10 * m + 28295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3922.1, data_13_3922.2] + +/-- Complete interval computation for depth 13, residue 3923. -/ +theorem bounds_13_3923 : exactInterval 13 3923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3923 : oddCount 3923 13 = 10 ∧ acceleratedOrbit 13 3923 = 28295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3923) = 3 ^ 10 * m + 28295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3923.1, data_13_3923.2] + +/-- Complete interval computation for depth 13, residue 3924. -/ +theorem bounds_13_3924 : exactInterval 13 3924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3924 : oddCount 3924 13 = 4 ∧ acceleratedOrbit 13 3924 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3924) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3924.1, data_13_3924.2] + +/-- Complete interval computation for depth 13, residue 3925. -/ +theorem bounds_13_3925 : exactInterval 13 3925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3925 : oddCount 3925 13 = 4 ∧ acceleratedOrbit 13 3925 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3925) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3925.1, data_13_3925.2] + +/-- Complete interval computation for depth 13, residue 3926. -/ +theorem bounds_13_3926 : exactInterval 13 3926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3926 : oddCount 3926 13 = 8 ∧ acceleratedOrbit 13 3926 = 3149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3926) = 3 ^ 8 * m + 3149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3926.1, data_13_3926.2] + +/-- Complete interval computation for depth 13, residue 3927. -/ +theorem bounds_13_3927 : exactInterval 13 3927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3927 : oddCount 3927 13 = 8 ∧ acceleratedOrbit 13 3927 = 3149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3927) = 3 ^ 8 * m + 3149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3927.1, data_13_3927.2] + +/-- Complete interval computation for depth 13, residue 3928. -/ +theorem bounds_13_3928 : exactInterval 13 3928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3928 : oddCount 3928 13 = 8 ∧ acceleratedOrbit 13 3928 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3928) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3928.1, data_13_3928.2] + +/-- Complete interval computation for depth 13, residue 3929. -/ +theorem bounds_13_3929 : exactInterval 13 3929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3929 : oddCount 3929 13 = 7 ∧ acceleratedOrbit 13 3929 = 1052 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3929) = 3 ^ 7 * m + 1052 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3929.1, data_13_3929.2] + +/-- Complete interval computation for depth 13, residue 3930. -/ +theorem bounds_13_3930 : exactInterval 13 3930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3930 : oddCount 3930 13 = 8 ∧ acceleratedOrbit 13 3930 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3930) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3930.1, data_13_3930.2] + +/-- Complete interval computation for depth 13, residue 3931. -/ +theorem bounds_13_3931 : exactInterval 13 3931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3931 : oddCount 3931 13 = 10 ∧ acceleratedOrbit 13 3931 = 28349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3931) = 3 ^ 10 * m + 28349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3931.1, data_13_3931.2] + +/-- Complete interval computation for depth 13, residue 3932. -/ +theorem bounds_13_3932 : exactInterval 13 3932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3932 : oddCount 3932 13 = 8 ∧ acceleratedOrbit 13 3932 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3932) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3932.1, data_13_3932.2] + +/-- Complete interval computation for depth 13, residue 3933. -/ +theorem bounds_13_3933 : exactInterval 13 3933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3933 : oddCount 3933 13 = 8 ∧ acceleratedOrbit 13 3933 = 3158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3933) = 3 ^ 8 * m + 3158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3933.1, data_13_3933.2] + +/-- Complete interval computation for depth 13, residue 3934. -/ +theorem bounds_13_3934 : exactInterval 13 3934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3934 : oddCount 3934 13 = 7 ∧ acceleratedOrbit 13 3934 = 1052 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3934) = 3 ^ 7 * m + 1052 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3934.1, data_13_3934.2] + +/-- Complete interval computation for depth 13, residue 3935. -/ +theorem bounds_13_3935 : exactInterval 13 3935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3935 : oddCount 3935 13 = 7 ∧ acceleratedOrbit 13 3935 = 1052 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3935) = 3 ^ 7 * m + 1052 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3935.1, data_13_3935.2] + +/-- Complete interval computation for depth 13, residue 3936. -/ +theorem bounds_13_3936 : exactInterval 13 3936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3936 : oddCount 3936 13 = 5 ∧ acceleratedOrbit 13 3936 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3936) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3936.1, data_13_3936.2] + +end Collatz.Research.StoppingAtlas.Batch0723 From 1edf24bcab6a1e5a4f70e3f501d0a5ee2b1952ca Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:18 +0530 Subject: [PATCH 0724/1001] proof: certify atlas Batch0724 (13:3937 to 13:3951) --- Collatz/Research/StoppingAtlas/Batch0724.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0724.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0724.lean b/Collatz/Research/StoppingAtlas/Batch0724.lean new file mode 100644 index 00000000..6944b27b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0724.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0724 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3937. -/ +theorem bounds_13_3937 : exactInterval 13 3937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3937 : oddCount 3937 13 = 9 ∧ acceleratedOrbit 13 3937 = 9467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3937) = 3 ^ 9 * m + 9467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3937.1, data_13_3937.2] + +/-- Complete interval computation for depth 13, residue 3938. -/ +theorem bounds_13_3938 : exactInterval 13 3938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3938 : oddCount 3938 13 = 3 ∧ acceleratedOrbit 13 3938 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3938) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3938.1, data_13_3938.2] + +/-- Complete interval computation for depth 13, residue 3939. -/ +theorem bounds_13_3939 : exactInterval 13 3939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3939 : oddCount 3939 13 = 3 ∧ acceleratedOrbit 13 3939 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3939) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3939.1, data_13_3939.2] + +/-- Complete interval computation for depth 13, residue 3940. -/ +theorem bounds_13_3940 : exactInterval 13 3940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3940 : oddCount 3940 13 = 3 ∧ acceleratedOrbit 13 3940 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3940) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3940.1, data_13_3940.2] + +/-- Complete interval computation for depth 13, residue 3941. -/ +theorem bounds_13_3941 : exactInterval 13 3941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3941 : oddCount 3941 13 = 3 ∧ acceleratedOrbit 13 3941 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3941) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3941.1, data_13_3941.2] + +/-- Complete interval computation for depth 13, residue 3942. -/ +theorem bounds_13_3942 : exactInterval 13 3942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3942 : oddCount 3942 13 = 3 ∧ acceleratedOrbit 13 3942 = 13 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3942) = 3 ^ 3 * m + 13 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3942.1, data_13_3942.2] + +/-- Complete interval computation for depth 13, residue 3943. -/ +theorem bounds_13_3943 : exactInterval 13 3943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3943 : oddCount 3943 13 = 12 ∧ acceleratedOrbit 13 3943 = 255878 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3943) = 3 ^ 12 * m + 255878 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3943.1, data_13_3943.2] + +/-- Complete interval computation for depth 13, residue 3944. -/ +theorem bounds_13_3944 : exactInterval 13 3944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3944 : oddCount 3944 13 = 5 ∧ acceleratedOrbit 13 3944 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3944) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3944.1, data_13_3944.2] + +/-- Complete interval computation for depth 13, residue 3945. -/ +theorem bounds_13_3945 : exactInterval 13 3945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3945 : oddCount 3945 13 = 7 ∧ acceleratedOrbit 13 3945 = 1054 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3945) = 3 ^ 7 * m + 1054 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3945.1, data_13_3945.2] + +/-- Complete interval computation for depth 13, residue 3946. -/ +theorem bounds_13_3946 : exactInterval 13 3946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3946 : oddCount 3946 13 = 5 ∧ acceleratedOrbit 13 3946 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3946) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3946.1, data_13_3946.2] + +/-- Complete interval computation for depth 13, residue 3947. -/ +theorem bounds_13_3947 : exactInterval 13 3947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3947 : oddCount 3947 13 = 7 ∧ acceleratedOrbit 13 3947 = 1055 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3947) = 3 ^ 7 * m + 1055 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3947.1, data_13_3947.2] + +/-- Complete interval computation for depth 13, residue 3948. -/ +theorem bounds_13_3948 : exactInterval 13 3948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3948 : oddCount 3948 13 = 6 ∧ acceleratedOrbit 13 3948 = 352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3948) = 3 ^ 6 * m + 352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3948.1, data_13_3948.2] + +/-- Complete interval computation for depth 13, residue 3949. -/ +theorem bounds_13_3949 : exactInterval 13 3949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3949 : oddCount 3949 13 = 6 ∧ acceleratedOrbit 13 3949 = 352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3949) = 3 ^ 6 * m + 352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3949.1, data_13_3949.2] + +/-- Complete interval computation for depth 13, residue 3950. -/ +theorem bounds_13_3950 : exactInterval 13 3950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3950 : oddCount 3950 13 = 6 ∧ acceleratedOrbit 13 3950 = 352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3950) = 3 ^ 6 * m + 352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3950.1, data_13_3950.2] + +/-- Complete interval computation for depth 13, residue 3951. -/ +theorem bounds_13_3951 : exactInterval 13 3951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3951 : oddCount 3951 13 = 9 ∧ acceleratedOrbit 13 3951 = 9497 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3951) = 3 ^ 9 * m + 9497 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3951.1, data_13_3951.2] + +end Collatz.Research.StoppingAtlas.Batch0724 From 4c6d4c0e465538a928b4bd182d4cb94cc2a0c9e2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:19 +0530 Subject: [PATCH 0725/1001] proof: certify atlas Batch0725 (13:3952 to 13:3967) --- Collatz/Research/StoppingAtlas/Batch0725.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0725.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0725.lean b/Collatz/Research/StoppingAtlas/Batch0725.lean new file mode 100644 index 00000000..24b39f18 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0725.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0725 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3952. -/ +theorem bounds_13_3952 : exactInterval 13 3952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3952 : oddCount 3952 13 = 5 ∧ acceleratedOrbit 13 3952 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3952) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3952.1, data_13_3952.2] + +/-- Complete interval computation for depth 13, residue 3953. -/ +theorem bounds_13_3953 : exactInterval 13 3953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3953 : oddCount 3953 13 = 5 ∧ acceleratedOrbit 13 3953 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3953) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3953.1, data_13_3953.2] + +/-- Complete interval computation for depth 13, residue 3954. -/ +theorem bounds_13_3954 : exactInterval 13 3954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3954 : oddCount 3954 13 = 6 ∧ acceleratedOrbit 13 3954 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3954) = 3 ^ 6 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3954.1, data_13_3954.2] + +/-- Complete interval computation for depth 13, residue 3955. -/ +theorem bounds_13_3955 : exactInterval 13 3955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3955 : oddCount 3955 13 = 6 ∧ acceleratedOrbit 13 3955 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3955) = 3 ^ 6 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3955.1, data_13_3955.2] + +/-- Complete interval computation for depth 13, residue 3956. -/ +theorem bounds_13_3956 : exactInterval 13 3956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3956 : oddCount 3956 13 = 5 ∧ acceleratedOrbit 13 3956 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3956) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3956.1, data_13_3956.2] + +/-- Complete interval computation for depth 13, residue 3957. -/ +theorem bounds_13_3957 : exactInterval 13 3957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3957 : oddCount 3957 13 = 5 ∧ acceleratedOrbit 13 3957 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3957) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3957.1, data_13_3957.2] + +/-- Complete interval computation for depth 13, residue 3958. -/ +theorem bounds_13_3958 : exactInterval 13 3958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3958 : oddCount 3958 13 = 6 ∧ acceleratedOrbit 13 3958 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3958) = 3 ^ 6 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3958.1, data_13_3958.2] + +/-- Complete interval computation for depth 13, residue 3959. -/ +theorem bounds_13_3959 : exactInterval 13 3959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3959 : oddCount 3959 13 = 6 ∧ acceleratedOrbit 13 3959 = 353 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3959) = 3 ^ 6 * m + 353 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3959.1, data_13_3959.2] + +/-- Complete interval computation for depth 13, residue 3960. -/ +theorem bounds_13_3960 : exactInterval 13 3960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3960 : oddCount 3960 13 = 8 ∧ acceleratedOrbit 13 3960 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3960) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3960.1, data_13_3960.2] + +/-- Complete interval computation for depth 13, residue 3961. -/ +theorem bounds_13_3961 : exactInterval 13 3961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3961 : oddCount 3961 13 = 7 ∧ acceleratedOrbit 13 3961 = 1058 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3961) = 3 ^ 7 * m + 1058 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3961.1, data_13_3961.2] + +/-- Complete interval computation for depth 13, residue 3962. -/ +theorem bounds_13_3962 : exactInterval 13 3962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3962 : oddCount 3962 13 = 8 ∧ acceleratedOrbit 13 3962 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3962) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3962.1, data_13_3962.2] + +/-- Complete interval computation for depth 13, residue 3963. -/ +theorem bounds_13_3963 : exactInterval 13 3963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3963 : oddCount 3963 13 = 8 ∧ acceleratedOrbit 13 3963 = 3176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3963) = 3 ^ 8 * m + 3176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3963.1, data_13_3963.2] + +/-- Complete interval computation for depth 13, residue 3964. -/ +theorem bounds_13_3964 : exactInterval 13 3964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3964 : oddCount 3964 13 = 8 ∧ acceleratedOrbit 13 3964 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3964) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3964.1, data_13_3964.2] + +/-- Complete interval computation for depth 13, residue 3965. -/ +theorem bounds_13_3965 : exactInterval 13 3965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3965 : oddCount 3965 13 = 8 ∧ acceleratedOrbit 13 3965 = 3179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3965) = 3 ^ 8 * m + 3179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3965.1, data_13_3965.2] + +/-- Complete interval computation for depth 13, residue 3966. -/ +theorem bounds_13_3966 : exactInterval 13 3966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3966 : oddCount 3966 13 = 8 ∧ acceleratedOrbit 13 3966 = 3178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3966) = 3 ^ 8 * m + 3178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3966.1, data_13_3966.2] + +/-- Complete interval computation for depth 13, residue 3967. -/ +theorem bounds_13_3967 : exactInterval 13 3967 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3967) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3967 : oddCount 3967 13 = 8 ∧ acceleratedOrbit 13 3967 = 3178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3967) = 3 ^ 8 * m + 3178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3967.1, data_13_3967.2] + +end Collatz.Research.StoppingAtlas.Batch0725 From 56249b68fb0924d4fbefdd088d97818c628e88c6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:19 +0530 Subject: [PATCH 0726/1001] proof: certify atlas Batch0726 (13:3968 to 13:3982) --- Collatz/Research/StoppingAtlas/Batch0726.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0726.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0726.lean b/Collatz/Research/StoppingAtlas/Batch0726.lean new file mode 100644 index 00000000..fe2a597d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0726.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0726 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3968. -/ +theorem bounds_13_3968 : exactInterval 13 3968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3968 : oddCount 3968 13 = 5 ∧ acceleratedOrbit 13 3968 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3968) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3968.1, data_13_3968.2] + +/-- Complete interval computation for depth 13, residue 3969. -/ +theorem bounds_13_3969 : exactInterval 13 3969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3969 : oddCount 3969 13 = 7 ∧ acceleratedOrbit 13 3969 = 1061 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3969) = 3 ^ 7 * m + 1061 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3969.1, data_13_3969.2] + +/-- Complete interval computation for depth 13, residue 3970. -/ +theorem bounds_13_3970 : exactInterval 13 3970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3970 : oddCount 3970 13 = 5 ∧ acceleratedOrbit 13 3970 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3970) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3970.1, data_13_3970.2] + +/-- Complete interval computation for depth 13, residue 3971. -/ +theorem bounds_13_3971 : exactInterval 13 3971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3971 : oddCount 3971 13 = 5 ∧ acceleratedOrbit 13 3971 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3971) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3971.1, data_13_3971.2] + +/-- Complete interval computation for depth 13, residue 3972. -/ +theorem bounds_13_3972 : exactInterval 13 3972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3972 : oddCount 3972 13 = 7 ∧ acceleratedOrbit 13 3972 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3972) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3972.1, data_13_3972.2] + +/-- Complete interval computation for depth 13, residue 3973. -/ +theorem bounds_13_3973 : exactInterval 13 3973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3973 : oddCount 3973 13 = 7 ∧ acceleratedOrbit 13 3973 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3973) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3973.1, data_13_3973.2] + +/-- Complete interval computation for depth 13, residue 3974. -/ +theorem bounds_13_3974 : exactInterval 13 3974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3974 : oddCount 3974 13 = 7 ∧ acceleratedOrbit 13 3974 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3974) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3974.1, data_13_3974.2] + +/-- Complete interval computation for depth 13, residue 3975. -/ +theorem bounds_13_3975 : exactInterval 13 3975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3975 : oddCount 3975 13 = 5 ∧ acceleratedOrbit 13 3975 = 118 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3975) = 3 ^ 5 * m + 118 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3975.1, data_13_3975.2] + +/-- Complete interval computation for depth 13, residue 3976. -/ +theorem bounds_13_3976 : exactInterval 13 3976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3976 : oddCount 3976 13 = 4 ∧ acceleratedOrbit 13 3976 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3976) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3976.1, data_13_3976.2] + +/-- Complete interval computation for depth 13, residue 3977. -/ +theorem bounds_13_3977 : exactInterval 13 3977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3977 : oddCount 3977 13 = 8 ∧ acceleratedOrbit 13 3977 = 3187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3977) = 3 ^ 8 * m + 3187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3977.1, data_13_3977.2] + +/-- Complete interval computation for depth 13, residue 3978. -/ +theorem bounds_13_3978 : exactInterval 13 3978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3978 : oddCount 3978 13 = 4 ∧ acceleratedOrbit 13 3978 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3978) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3978.1, data_13_3978.2] + +/-- Complete interval computation for depth 13, residue 3979. -/ +theorem bounds_13_3979 : exactInterval 13 3979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3979 : oddCount 3979 13 = 7 ∧ acceleratedOrbit 13 3979 = 1063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3979) = 3 ^ 7 * m + 1063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3979.1, data_13_3979.2] + +/-- Complete interval computation for depth 13, residue 3980. -/ +theorem bounds_13_3980 : exactInterval 13 3980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3980 : oddCount 3980 13 = 4 ∧ acceleratedOrbit 13 3980 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3980) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3980.1, data_13_3980.2] + +/-- Complete interval computation for depth 13, residue 3981. -/ +theorem bounds_13_3981 : exactInterval 13 3981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3981 : oddCount 3981 13 = 4 ∧ acceleratedOrbit 13 3981 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3981) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3981.1, data_13_3981.2] + +/-- Complete interval computation for depth 13, residue 3982. -/ +theorem bounds_13_3982 : exactInterval 13 3982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3982 : oddCount 3982 13 = 7 ∧ acceleratedOrbit 13 3982 = 1064 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3982) = 3 ^ 7 * m + 1064 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3982.1, data_13_3982.2] + +end Collatz.Research.StoppingAtlas.Batch0726 From 029212c3c7b8533b097d99e67e1b1eb7f3ddcd04 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:22 +0530 Subject: [PATCH 0727/1001] proof: certify atlas Batch0727 (13:3983 to 13:3997) --- Collatz/Research/StoppingAtlas/Batch0727.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0727.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0727.lean b/Collatz/Research/StoppingAtlas/Batch0727.lean new file mode 100644 index 00000000..6e290e55 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0727.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0727 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3983. -/ +theorem bounds_13_3983 : exactInterval 13 3983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3983) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3983 : oddCount 3983 13 = 7 ∧ acceleratedOrbit 13 3983 = 1064 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3983) = 3 ^ 7 * m + 1064 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3983.1, data_13_3983.2] + +/-- Complete interval computation for depth 13, residue 3984. -/ +theorem bounds_13_3984 : exactInterval 13 3984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3984 : oddCount 3984 13 = 5 ∧ acceleratedOrbit 13 3984 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3984) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3984.1, data_13_3984.2] + +/-- Complete interval computation for depth 13, residue 3985. -/ +theorem bounds_13_3985 : exactInterval 13 3985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3985 : oddCount 3985 13 = 7 ∧ acceleratedOrbit 13 3985 = 1066 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3985) = 3 ^ 7 * m + 1066 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3985.1, data_13_3985.2] + +/-- Complete interval computation for depth 13, residue 3986. -/ +theorem bounds_13_3986 : exactInterval 13 3986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3986 : oddCount 3986 13 = 7 ∧ acceleratedOrbit 13 3986 = 1066 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3986) = 3 ^ 7 * m + 1066 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3986.1, data_13_3986.2] + +/-- Complete interval computation for depth 13, residue 3987. -/ +theorem bounds_13_3987 : exactInterval 13 3987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3987 : oddCount 3987 13 = 7 ∧ acceleratedOrbit 13 3987 = 1066 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3987) = 3 ^ 7 * m + 1066 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3987.1, data_13_3987.2] + +/-- Complete interval computation for depth 13, residue 3988. -/ +theorem bounds_13_3988 : exactInterval 13 3988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3988 : oddCount 3988 13 = 5 ∧ acceleratedOrbit 13 3988 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3988) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3988.1, data_13_3988.2] + +/-- Complete interval computation for depth 13, residue 3989. -/ +theorem bounds_13_3989 : exactInterval 13 3989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3989 : oddCount 3989 13 = 5 ∧ acceleratedOrbit 13 3989 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3989) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3989.1, data_13_3989.2] + +/-- Complete interval computation for depth 13, residue 3990. -/ +theorem bounds_13_3990 : exactInterval 13 3990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3990 : oddCount 3990 13 = 5 ∧ acceleratedOrbit 13 3990 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3990) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3990.1, data_13_3990.2] + +/-- Complete interval computation for depth 13, residue 3991. -/ +theorem bounds_13_3991 : exactInterval 13 3991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3991 : oddCount 3991 13 = 5 ∧ acceleratedOrbit 13 3991 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3991) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3991.1, data_13_3991.2] + +/-- Complete interval computation for depth 13, residue 3992. -/ +theorem bounds_13_3992 : exactInterval 13 3992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3992 : oddCount 3992 13 = 5 ∧ acceleratedOrbit 13 3992 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3992) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3992.1, data_13_3992.2] + +/-- Complete interval computation for depth 13, residue 3993. -/ +theorem bounds_13_3993 : exactInterval 13 3993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3993 : oddCount 3993 13 = 5 ∧ acceleratedOrbit 13 3993 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3993) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3993.1, data_13_3993.2] + +/-- Complete interval computation for depth 13, residue 3994. -/ +theorem bounds_13_3994 : exactInterval 13 3994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3994 : oddCount 3994 13 = 5 ∧ acceleratedOrbit 13 3994 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3994) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3994.1, data_13_3994.2] + +/-- Complete interval computation for depth 13, residue 3995. -/ +theorem bounds_13_3995 : exactInterval 13 3995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3995 : oddCount 3995 13 = 7 ∧ acceleratedOrbit 13 3995 = 1067 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3995) = 3 ^ 7 * m + 1067 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3995.1, data_13_3995.2] + +/-- Complete interval computation for depth 13, residue 3996. -/ +theorem bounds_13_3996 : exactInterval 13 3996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3996 : oddCount 3996 13 = 6 ∧ acceleratedOrbit 13 3996 = 356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3996) = 3 ^ 6 * m + 356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3996.1, data_13_3996.2] + +/-- Complete interval computation for depth 13, residue 3997. -/ +theorem bounds_13_3997 : exactInterval 13 3997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3997 : oddCount 3997 13 = 6 ∧ acceleratedOrbit 13 3997 = 356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3997) = 3 ^ 6 * m + 356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3997.1, data_13_3997.2] + +end Collatz.Research.StoppingAtlas.Batch0727 From e631e6bfe219e4c22b8cc683c645def690b829d1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:23 +0530 Subject: [PATCH 0728/1001] proof: certify atlas Batch0728 (13:3998 to 13:4013) --- Collatz/Research/StoppingAtlas/Batch0728.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0728.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0728.lean b/Collatz/Research/StoppingAtlas/Batch0728.lean new file mode 100644 index 00000000..7c03a621 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0728.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0728 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 3998. -/ +theorem bounds_13_3998 : exactInterval 13 3998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3998 : oddCount 3998 13 = 6 ∧ acceleratedOrbit 13 3998 = 356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3998) = 3 ^ 6 * m + 356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3998.1, data_13_3998.2] + +/-- Complete interval computation for depth 13, residue 3999. -/ +theorem bounds_13_3999 : exactInterval 13 3999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_3999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 3999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_3999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_3999 : oddCount 3999 13 = 10 ∧ acceleratedOrbit 13 3999 = 28835 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_3999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 3999) = 3 ^ 10 * m + 28835 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_3999.1, data_13_3999.2] + +/-- Complete interval computation for depth 13, residue 4000. -/ +theorem bounds_13_4000 : exactInterval 13 4000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4000 : oddCount 4000 13 = 5 ∧ acceleratedOrbit 13 4000 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4000) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4000.1, data_13_4000.2] + +/-- Complete interval computation for depth 13, residue 4001. -/ +theorem bounds_13_4001 : exactInterval 13 4001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4001 : oddCount 4001 13 = 7 ∧ acceleratedOrbit 13 4001 = 1070 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4001) = 3 ^ 7 * m + 1070 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4001.1, data_13_4001.2] + +/-- Complete interval computation for depth 13, residue 4002. -/ +theorem bounds_13_4002 : exactInterval 13 4002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4002 : oddCount 4002 13 = 5 ∧ acceleratedOrbit 13 4002 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4002) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4002.1, data_13_4002.2] + +/-- Complete interval computation for depth 13, residue 4003. -/ +theorem bounds_13_4003 : exactInterval 13 4003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4003 : oddCount 4003 13 = 5 ∧ acceleratedOrbit 13 4003 = 119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4003) = 3 ^ 5 * m + 119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4003.1, data_13_4003.2] + +/-- Complete interval computation for depth 13, residue 4004. -/ +theorem bounds_13_4004 : exactInterval 13 4004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4004 : oddCount 4004 13 = 9 ∧ acceleratedOrbit 13 4004 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4004) = 3 ^ 9 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4004.1, data_13_4004.2] + +/-- Complete interval computation for depth 13, residue 4005. -/ +theorem bounds_13_4005 : exactInterval 13 4005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4005 : oddCount 4005 13 = 9 ∧ acceleratedOrbit 13 4005 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4005) = 3 ^ 9 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4005.1, data_13_4005.2] + +/-- Complete interval computation for depth 13, residue 4006. -/ +theorem bounds_13_4006 : exactInterval 13 4006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4006 : oddCount 4006 13 = 9 ∧ acceleratedOrbit 13 4006 = 9638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4006) = 3 ^ 9 * m + 9638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4006.1, data_13_4006.2] + +/-- Complete interval computation for depth 13, residue 4007. -/ +theorem bounds_13_4007 : exactInterval 13 4007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4007 : oddCount 4007 13 = 9 ∧ acceleratedOrbit 13 4007 = 9632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4007) = 3 ^ 9 * m + 9632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4007.1, data_13_4007.2] + +/-- Complete interval computation for depth 13, residue 4008. -/ +theorem bounds_13_4008 : exactInterval 13 4008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4008 : oddCount 4008 13 = 5 ∧ acceleratedOrbit 13 4008 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4008) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4008.1, data_13_4008.2] + +/-- Complete interval computation for depth 13, residue 4009. -/ +theorem bounds_13_4009 : exactInterval 13 4009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4009 : oddCount 4009 13 = 10 ∧ acceleratedOrbit 13 4009 = 28910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4009) = 3 ^ 10 * m + 28910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4009.1, data_13_4009.2] + +/-- Complete interval computation for depth 13, residue 4010. -/ +theorem bounds_13_4010 : exactInterval 13 4010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4010 : oddCount 4010 13 = 5 ∧ acceleratedOrbit 13 4010 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4010) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4010.1, data_13_4010.2] + +/-- Complete interval computation for depth 13, residue 4011. -/ +theorem bounds_13_4011 : exactInterval 13 4011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4011 : oddCount 4011 13 = 8 ∧ acceleratedOrbit 13 4011 = 3215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4011) = 3 ^ 8 * m + 3215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4011.1, data_13_4011.2] + +/-- Complete interval computation for depth 13, residue 4012. -/ +theorem bounds_13_4012 : exactInterval 13 4012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4012 : oddCount 4012 13 = 7 ∧ acceleratedOrbit 13 4012 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4012) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4012.1, data_13_4012.2] + +/-- Complete interval computation for depth 13, residue 4013. -/ +theorem bounds_13_4013 : exactInterval 13 4013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4013 : oddCount 4013 13 = 7 ∧ acceleratedOrbit 13 4013 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4013) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4013.1, data_13_4013.2] + +end Collatz.Research.StoppingAtlas.Batch0728 From 0c4c6ccf528ca2b9fd2dab12691b53831ec77cb3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:23 +0530 Subject: [PATCH 0729/1001] proof: certify atlas Batch0729 (13:4014 to 13:4028) --- Collatz/Research/StoppingAtlas/Batch0729.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0729.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0729.lean b/Collatz/Research/StoppingAtlas/Batch0729.lean new file mode 100644 index 00000000..e9cf1c7a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0729.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0729 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4014. -/ +theorem bounds_13_4014 : exactInterval 13 4014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4014 : oddCount 4014 13 = 7 ∧ acceleratedOrbit 13 4014 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4014) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4014.1, data_13_4014.2] + +/-- Complete interval computation for depth 13, residue 4015. -/ +theorem bounds_13_4015 : exactInterval 13 4015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4015 : oddCount 4015 13 = 7 ∧ acceleratedOrbit 13 4015 = 1073 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4015) = 3 ^ 7 * m + 1073 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4015.1, data_13_4015.2] + +/-- Complete interval computation for depth 13, residue 4016. -/ +theorem bounds_13_4016 : exactInterval 13 4016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4016 : oddCount 4016 13 = 7 ∧ acceleratedOrbit 13 4016 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4016) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4016.1, data_13_4016.2] + +/-- Complete interval computation for depth 13, residue 4017. -/ +theorem bounds_13_4017 : exactInterval 13 4017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4017 : oddCount 4017 13 = 4 ∧ acceleratedOrbit 13 4017 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4017) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4017.1, data_13_4017.2] + +/-- Complete interval computation for depth 13, residue 4018. -/ +theorem bounds_13_4018 : exactInterval 13 4018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4018 : oddCount 4018 13 = 4 ∧ acceleratedOrbit 13 4018 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4018) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4018.1, data_13_4018.2] + +/-- Complete interval computation for depth 13, residue 4019. -/ +theorem bounds_13_4019 : exactInterval 13 4019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4019 : oddCount 4019 13 = 4 ∧ acceleratedOrbit 13 4019 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4019) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4019.1, data_13_4019.2] + +/-- Complete interval computation for depth 13, residue 4020. -/ +theorem bounds_13_4020 : exactInterval 13 4020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4020 : oddCount 4020 13 = 7 ∧ acceleratedOrbit 13 4020 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4020) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4020.1, data_13_4020.2] + +/-- Complete interval computation for depth 13, residue 4021. -/ +theorem bounds_13_4021 : exactInterval 13 4021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4021 : oddCount 4021 13 = 7 ∧ acceleratedOrbit 13 4021 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4021) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4021.1, data_13_4021.2] + +/-- Complete interval computation for depth 13, residue 4022. -/ +theorem bounds_13_4022 : exactInterval 13 4022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4022 : oddCount 4022 13 = 7 ∧ acceleratedOrbit 13 4022 = 1075 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4022) = 3 ^ 7 * m + 1075 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4022.1, data_13_4022.2] + +/-- Complete interval computation for depth 13, residue 4023. -/ +theorem bounds_13_4023 : exactInterval 13 4023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4023) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4023 : oddCount 4023 13 = 7 ∧ acceleratedOrbit 13 4023 = 1075 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4023) = 3 ^ 7 * m + 1075 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4023.1, data_13_4023.2] + +/-- Complete interval computation for depth 13, residue 4024. -/ +theorem bounds_13_4024 : exactInterval 13 4024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4024 : oddCount 4024 13 = 7 ∧ acceleratedOrbit 13 4024 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4024) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4024.1, data_13_4024.2] + +/-- Complete interval computation for depth 13, residue 4025. -/ +theorem bounds_13_4025 : exactInterval 13 4025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4025 : oddCount 4025 13 = 6 ∧ acceleratedOrbit 13 4025 = 359 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4025) = 3 ^ 6 * m + 359 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4025.1, data_13_4025.2] + +/-- Complete interval computation for depth 13, residue 4026. -/ +theorem bounds_13_4026 : exactInterval 13 4026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4026 : oddCount 4026 13 = 7 ∧ acceleratedOrbit 13 4026 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4026) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4026.1, data_13_4026.2] + +/-- Complete interval computation for depth 13, residue 4027. -/ +theorem bounds_13_4027 : exactInterval 13 4027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4027 : oddCount 4027 13 = 6 ∧ acceleratedOrbit 13 4027 = 359 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4027) = 3 ^ 6 * m + 359 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4027.1, data_13_4027.2] + +/-- Complete interval computation for depth 13, residue 4028. -/ +theorem bounds_13_4028 : exactInterval 13 4028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4028 : oddCount 4028 13 = 8 ∧ acceleratedOrbit 13 4028 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4028) = 3 ^ 8 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4028.1, data_13_4028.2] + +end Collatz.Research.StoppingAtlas.Batch0729 From 4c7b92880f89375c33ea5b8f7579243c2eeea935 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:24 +0530 Subject: [PATCH 0730/1001] proof: certify atlas Batch0730 (13:4029 to 13:4043) --- Collatz/Research/StoppingAtlas/Batch0730.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0730.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0730.lean b/Collatz/Research/StoppingAtlas/Batch0730.lean new file mode 100644 index 00000000..5614d04d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0730.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0730 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4029. -/ +theorem bounds_13_4029 : exactInterval 13 4029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4029 : oddCount 4029 13 = 8 ∧ acceleratedOrbit 13 4029 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4029) = 3 ^ 8 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4029.1, data_13_4029.2] + +/-- Complete interval computation for depth 13, residue 4030. -/ +theorem bounds_13_4030 : exactInterval 13 4030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4030 : oddCount 4030 13 = 8 ∧ acceleratedOrbit 13 4030 = 3230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4030) = 3 ^ 8 * m + 3230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4030.1, data_13_4030.2] + +/-- Complete interval computation for depth 13, residue 4031. -/ +theorem bounds_13_4031 : exactInterval 13 4031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4031 : oddCount 4031 13 = 9 ∧ acceleratedOrbit 13 4031 = 9688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4031) = 3 ^ 9 * m + 9688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4031.1, data_13_4031.2] + +/-- Complete interval computation for depth 13, residue 4032. -/ +theorem bounds_13_4032 : exactInterval 13 4032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4032 : oddCount 4032 13 = 6 ∧ acceleratedOrbit 13 4032 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4032) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4032.1, data_13_4032.2] + +/-- Complete interval computation for depth 13, residue 4033. -/ +theorem bounds_13_4033 : exactInterval 13 4033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4033 : oddCount 4033 13 = 7 ∧ acceleratedOrbit 13 4033 = 1079 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4033) = 3 ^ 7 * m + 1079 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4033.1, data_13_4033.2] + +/-- Complete interval computation for depth 13, residue 4034. -/ +theorem bounds_13_4034 : exactInterval 13 4034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4034 : oddCount 4034 13 = 8 ∧ acceleratedOrbit 13 4034 = 3235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4034) = 3 ^ 8 * m + 3235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4034.1, data_13_4034.2] + +/-- Complete interval computation for depth 13, residue 4035. -/ +theorem bounds_13_4035 : exactInterval 13 4035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4035 : oddCount 4035 13 = 8 ∧ acceleratedOrbit 13 4035 = 3235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4035) = 3 ^ 8 * m + 3235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4035.1, data_13_4035.2] + +/-- Complete interval computation for depth 13, residue 4036. -/ +theorem bounds_13_4036 : exactInterval 13 4036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4036 : oddCount 4036 13 = 5 ∧ acceleratedOrbit 13 4036 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4036) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4036.1, data_13_4036.2] + +/-- Complete interval computation for depth 13, residue 4037. -/ +theorem bounds_13_4037 : exactInterval 13 4037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4037 : oddCount 4037 13 = 5 ∧ acceleratedOrbit 13 4037 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4037) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4037.1, data_13_4037.2] + +/-- Complete interval computation for depth 13, residue 4038. -/ +theorem bounds_13_4038 : exactInterval 13 4038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4038 : oddCount 4038 13 = 5 ∧ acceleratedOrbit 13 4038 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4038) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4038.1, data_13_4038.2] + +/-- Complete interval computation for depth 13, residue 4039. -/ +theorem bounds_13_4039 : exactInterval 13 4039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4039 : oddCount 4039 13 = 9 ∧ acceleratedOrbit 13 4039 = 9710 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4039) = 3 ^ 9 * m + 9710 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4039.1, data_13_4039.2] + +/-- Complete interval computation for depth 13, residue 4040. -/ +theorem bounds_13_4040 : exactInterval 13 4040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4040 : oddCount 4040 13 = 6 ∧ acceleratedOrbit 13 4040 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4040) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4040.1, data_13_4040.2] + +/-- Complete interval computation for depth 13, residue 4041. -/ +theorem bounds_13_4041 : exactInterval 13 4041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4041 : oddCount 4041 13 = 9 ∧ acceleratedOrbit 13 4041 = 9719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4041) = 3 ^ 9 * m + 9719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4041.1, data_13_4041.2] + +/-- Complete interval computation for depth 13, residue 4042. -/ +theorem bounds_13_4042 : exactInterval 13 4042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4042 : oddCount 4042 13 = 6 ∧ acceleratedOrbit 13 4042 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4042) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4042.1, data_13_4042.2] + +/-- Complete interval computation for depth 13, residue 4043. -/ +theorem bounds_13_4043 : exactInterval 13 4043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4043 : oddCount 4043 13 = 4 ∧ acceleratedOrbit 13 4043 = 40 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4043) = 3 ^ 4 * m + 40 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4043.1, data_13_4043.2] + +end Collatz.Research.StoppingAtlas.Batch0730 From a6a470b270a017a5428bbbe3d8177480a8ec0b94 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:24 +0530 Subject: [PATCH 0731/1001] proof: certify atlas Batch0731 (13:4044 to 13:4059) --- Collatz/Research/StoppingAtlas/Batch0731.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0731.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0731.lean b/Collatz/Research/StoppingAtlas/Batch0731.lean new file mode 100644 index 00000000..5511b19b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0731.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0731 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4044. -/ +theorem bounds_13_4044 : exactInterval 13 4044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4044 : oddCount 4044 13 = 6 ∧ acceleratedOrbit 13 4044 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4044) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4044.1, data_13_4044.2] + +/-- Complete interval computation for depth 13, residue 4045. -/ +theorem bounds_13_4045 : exactInterval 13 4045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4045 : oddCount 4045 13 = 6 ∧ acceleratedOrbit 13 4045 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4045) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4045.1, data_13_4045.2] + +/-- Complete interval computation for depth 13, residue 4046. -/ +theorem bounds_13_4046 : exactInterval 13 4046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4046 : oddCount 4046 13 = 7 ∧ acceleratedOrbit 13 4046 = 1081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4046) = 3 ^ 7 * m + 1081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4046.1, data_13_4046.2] + +/-- Complete interval computation for depth 13, residue 4047. -/ +theorem bounds_13_4047 : exactInterval 13 4047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4047) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4047 : oddCount 4047 13 = 7 ∧ acceleratedOrbit 13 4047 = 1081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4047) = 3 ^ 7 * m + 1081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4047.1, data_13_4047.2] + +/-- Complete interval computation for depth 13, residue 4048. -/ +theorem bounds_13_4048 : exactInterval 13 4048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4048 : oddCount 4048 13 = 6 ∧ acceleratedOrbit 13 4048 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4048) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4048.1, data_13_4048.2] + +/-- Complete interval computation for depth 13, residue 4049. -/ +theorem bounds_13_4049 : exactInterval 13 4049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4049 : oddCount 4049 13 = 6 ∧ acceleratedOrbit 13 4049 = 361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4049) = 3 ^ 6 * m + 361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4049.1, data_13_4049.2] + +/-- Complete interval computation for depth 13, residue 4050. -/ +theorem bounds_13_4050 : exactInterval 13 4050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4050 : oddCount 4050 13 = 9 ∧ acceleratedOrbit 13 4050 = 9740 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4050) = 3 ^ 9 * m + 9740 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4050.1, data_13_4050.2] + +/-- Complete interval computation for depth 13, residue 4051. -/ +theorem bounds_13_4051 : exactInterval 13 4051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4051 : oddCount 4051 13 = 9 ∧ acceleratedOrbit 13 4051 = 9740 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4051) = 3 ^ 9 * m + 9740 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4051.1, data_13_4051.2] + +/-- Complete interval computation for depth 13, residue 4052. -/ +theorem bounds_13_4052 : exactInterval 13 4052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4052 : oddCount 4052 13 = 6 ∧ acceleratedOrbit 13 4052 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4052) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4052.1, data_13_4052.2] + +/-- Complete interval computation for depth 13, residue 4053. -/ +theorem bounds_13_4053 : exactInterval 13 4053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4053 : oddCount 4053 13 = 6 ∧ acceleratedOrbit 13 4053 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4053) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4053.1, data_13_4053.2] + +/-- Complete interval computation for depth 13, residue 4054. -/ +theorem bounds_13_4054 : exactInterval 13 4054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4054 : oddCount 4054 13 = 8 ∧ acceleratedOrbit 13 4054 = 3250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4054) = 3 ^ 8 * m + 3250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4054.1, data_13_4054.2] + +/-- Complete interval computation for depth 13, residue 4055. -/ +theorem bounds_13_4055 : exactInterval 13 4055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4055 : oddCount 4055 13 = 8 ∧ acceleratedOrbit 13 4055 = 3250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4055) = 3 ^ 8 * m + 3250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4055.1, data_13_4055.2] + +/-- Complete interval computation for depth 13, residue 4056. -/ +theorem bounds_13_4056 : exactInterval 13 4056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4056 : oddCount 4056 13 = 6 ∧ acceleratedOrbit 13 4056 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4056) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4056.1, data_13_4056.2] + +/-- Complete interval computation for depth 13, residue 4057. -/ +theorem bounds_13_4057 : exactInterval 13 4057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4057 : oddCount 4057 13 = 5 ∧ acceleratedOrbit 13 4057 = 121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4057) = 3 ^ 5 * m + 121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4057.1, data_13_4057.2] + +/-- Complete interval computation for depth 13, residue 4058. -/ +theorem bounds_13_4058 : exactInterval 13 4058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4058 : oddCount 4058 13 = 6 ∧ acceleratedOrbit 13 4058 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4058) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4058.1, data_13_4058.2] + +/-- Complete interval computation for depth 13, residue 4059. -/ +theorem bounds_13_4059 : exactInterval 13 4059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4059 : oddCount 4059 13 = 8 ∧ acceleratedOrbit 13 4059 = 3253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4059) = 3 ^ 8 * m + 3253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4059.1, data_13_4059.2] + +end Collatz.Research.StoppingAtlas.Batch0731 From 9328d481fd310d4ae768d152e16357e3e1b91ba4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:25 +0530 Subject: [PATCH 0732/1001] proof: certify atlas Batch0732 (13:4060 to 13:4074) --- Collatz/Research/StoppingAtlas/Batch0732.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0732.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0732.lean b/Collatz/Research/StoppingAtlas/Batch0732.lean new file mode 100644 index 00000000..e1630651 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0732.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0732 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4060. -/ +theorem bounds_13_4060 : exactInterval 13 4060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4060 : oddCount 4060 13 = 6 ∧ acceleratedOrbit 13 4060 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4060) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4060.1, data_13_4060.2] + +/-- Complete interval computation for depth 13, residue 4061. -/ +theorem bounds_13_4061 : exactInterval 13 4061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4061 : oddCount 4061 13 = 6 ∧ acceleratedOrbit 13 4061 = 362 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4061) = 3 ^ 6 * m + 362 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4061.1, data_13_4061.2] + +/-- Complete interval computation for depth 13, residue 4062. -/ +theorem bounds_13_4062 : exactInterval 13 4062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4062 : oddCount 4062 13 = 7 ∧ acceleratedOrbit 13 4062 = 1085 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4062) = 3 ^ 7 * m + 1085 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4062.1, data_13_4062.2] + +/-- Complete interval computation for depth 13, residue 4063. -/ +theorem bounds_13_4063 : exactInterval 13 4063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4063 : oddCount 4063 13 = 7 ∧ acceleratedOrbit 13 4063 = 1085 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4063) = 3 ^ 7 * m + 1085 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4063.1, data_13_4063.2] + +/-- Complete interval computation for depth 13, residue 4064. -/ +theorem bounds_13_4064 : exactInterval 13 4064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4064 : oddCount 4064 13 = 7 ∧ acceleratedOrbit 13 4064 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4064) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4064.1, data_13_4064.2] + +/-- Complete interval computation for depth 13, residue 4065. -/ +theorem bounds_13_4065 : exactInterval 13 4065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4065 : oddCount 4065 13 = 10 ∧ acceleratedOrbit 13 4065 = 29321 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4065) = 3 ^ 10 * m + 29321 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4065.1, data_13_4065.2] + +/-- Complete interval computation for depth 13, residue 4066. -/ +theorem bounds_13_4066 : exactInterval 13 4066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4066 : oddCount 4066 13 = 6 ∧ acceleratedOrbit 13 4066 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4066) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4066.1, data_13_4066.2] + +/-- Complete interval computation for depth 13, residue 4067. -/ +theorem bounds_13_4067 : exactInterval 13 4067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4067 : oddCount 4067 13 = 6 ∧ acceleratedOrbit 13 4067 = 364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4067) = 3 ^ 6 * m + 364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4067.1, data_13_4067.2] + +/-- Complete interval computation for depth 13, residue 4068. -/ +theorem bounds_13_4068 : exactInterval 13 4068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4068 : oddCount 4068 13 = 8 ∧ acceleratedOrbit 13 4068 = 3266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4068) = 3 ^ 8 * m + 3266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4068.1, data_13_4068.2] + +/-- Complete interval computation for depth 13, residue 4069. -/ +theorem bounds_13_4069 : exactInterval 13 4069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4069 : oddCount 4069 13 = 8 ∧ acceleratedOrbit 13 4069 = 3266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4069) = 3 ^ 8 * m + 3266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4069.1, data_13_4069.2] + +/-- Complete interval computation for depth 13, residue 4070. -/ +theorem bounds_13_4070 : exactInterval 13 4070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4070 : oddCount 4070 13 = 8 ∧ acceleratedOrbit 13 4070 = 3266 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4070) = 3 ^ 8 * m + 3266 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4070.1, data_13_4070.2] + +/-- Complete interval computation for depth 13, residue 4071. -/ +theorem bounds_13_4071 : exactInterval 13 4071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4071 : oddCount 4071 13 = 8 ∧ acceleratedOrbit 13 4071 = 3262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4071) = 3 ^ 8 * m + 3262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4071.1, data_13_4071.2] + +/-- Complete interval computation for depth 13, residue 4072. -/ +theorem bounds_13_4072 : exactInterval 13 4072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4072 : oddCount 4072 13 = 7 ∧ acceleratedOrbit 13 4072 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4072) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4072.1, data_13_4072.2] + +/-- Complete interval computation for depth 13, residue 4073. -/ +theorem bounds_13_4073 : exactInterval 13 4073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4073 : oddCount 4073 13 = 9 ∧ acceleratedOrbit 13 4073 = 9791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4073) = 3 ^ 9 * m + 9791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4073.1, data_13_4073.2] + +/-- Complete interval computation for depth 13, residue 4074. -/ +theorem bounds_13_4074 : exactInterval 13 4074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4074 : oddCount 4074 13 = 7 ∧ acceleratedOrbit 13 4074 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4074) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4074.1, data_13_4074.2] + +end Collatz.Research.StoppingAtlas.Batch0732 From b724dff18ee3a8fc2a87f6fc3eb8f81af819bd57 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:25 +0530 Subject: [PATCH 0733/1001] proof: certify atlas Batch0733 (13:4075 to 13:4089) --- Collatz/Research/StoppingAtlas/Batch0733.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0733.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0733.lean b/Collatz/Research/StoppingAtlas/Batch0733.lean new file mode 100644 index 00000000..f511cc14 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0733.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0733 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4075. -/ +theorem bounds_13_4075 : exactInterval 13 4075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4075 : oddCount 4075 13 = 9 ∧ acceleratedOrbit 13 4075 = 9796 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4075) = 3 ^ 9 * m + 9796 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4075.1, data_13_4075.2] + +/-- Complete interval computation for depth 13, residue 4076. -/ +theorem bounds_13_4076 : exactInterval 13 4076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4076 : oddCount 4076 13 = 7 ∧ acceleratedOrbit 13 4076 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4076) = 3 ^ 7 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4076.1, data_13_4076.2] + +/-- Complete interval computation for depth 13, residue 4077. -/ +theorem bounds_13_4077 : exactInterval 13 4077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4077 : oddCount 4077 13 = 7 ∧ acceleratedOrbit 13 4077 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4077) = 3 ^ 7 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4077.1, data_13_4077.2] + +/-- Complete interval computation for depth 13, residue 4078. -/ +theorem bounds_13_4078 : exactInterval 13 4078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4078 : oddCount 4078 13 = 7 ∧ acceleratedOrbit 13 4078 = 1090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4078) = 3 ^ 7 * m + 1090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4078.1, data_13_4078.2] + +/-- Complete interval computation for depth 13, residue 4079. -/ +theorem bounds_13_4079 : exactInterval 13 4079 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4079) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4079 : oddCount 4079 13 = 8 ∧ acceleratedOrbit 13 4079 = 3268 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4079) = 3 ^ 8 * m + 3268 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4079.1, data_13_4079.2] + +/-- Complete interval computation for depth 13, residue 4080. -/ +theorem bounds_13_4080 : exactInterval 13 4080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4080 : oddCount 4080 13 = 8 ∧ acceleratedOrbit 13 4080 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4080) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4080.1, data_13_4080.2] + +/-- Complete interval computation for depth 13, residue 4081. -/ +theorem bounds_13_4081 : exactInterval 13 4081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4081 : oddCount 4081 13 = 7 ∧ acceleratedOrbit 13 4081 = 1093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4081) = 3 ^ 7 * m + 1093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4081.1, data_13_4081.2] + +/-- Complete interval computation for depth 13, residue 4082. -/ +theorem bounds_13_4082 : exactInterval 13 4082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4082 : oddCount 4082 13 = 7 ∧ acceleratedOrbit 13 4082 = 1091 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4082) = 3 ^ 7 * m + 1091 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4082.1, data_13_4082.2] + +/-- Complete interval computation for depth 13, residue 4083. -/ +theorem bounds_13_4083 : exactInterval 13 4083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4083 : oddCount 4083 13 = 7 ∧ acceleratedOrbit 13 4083 = 1091 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4083) = 3 ^ 7 * m + 1091 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4083.1, data_13_4083.2] + +/-- Complete interval computation for depth 13, residue 4084. -/ +theorem bounds_13_4084 : exactInterval 13 4084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4084 : oddCount 4084 13 = 8 ∧ acceleratedOrbit 13 4084 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4084) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4084.1, data_13_4084.2] + +/-- Complete interval computation for depth 13, residue 4085. -/ +theorem bounds_13_4085 : exactInterval 13 4085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4085 : oddCount 4085 13 = 8 ∧ acceleratedOrbit 13 4085 = 3280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4085) = 3 ^ 8 * m + 3280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4085.1, data_13_4085.2] + +/-- Complete interval computation for depth 13, residue 4086. -/ +theorem bounds_13_4086 : exactInterval 13 4086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4086 : oddCount 4086 13 = 9 ∧ acceleratedOrbit 13 4086 = 9827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4086) = 3 ^ 9 * m + 9827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4086.1, data_13_4086.2] + +/-- Complete interval computation for depth 13, residue 4087. -/ +theorem bounds_13_4087 : exactInterval 13 4087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4087 : oddCount 4087 13 = 9 ∧ acceleratedOrbit 13 4087 = 9827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4087) = 3 ^ 9 * m + 9827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4087.1, data_13_4087.2] + +/-- Complete interval computation for depth 13, residue 4088. -/ +theorem bounds_13_4088 : exactInterval 13 4088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4088 : oddCount 4088 13 = 9 ∧ acceleratedOrbit 13 4088 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4088) = 3 ^ 9 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4088.1, data_13_4088.2] + +/-- Complete interval computation for depth 13, residue 4089. -/ +theorem bounds_13_4089 : exactInterval 13 4089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4089 : oddCount 4089 13 = 8 ∧ acceleratedOrbit 13 4089 = 3277 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4089) = 3 ^ 8 * m + 3277 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4089.1, data_13_4089.2] + +end Collatz.Research.StoppingAtlas.Batch0733 From 92a3aa214c31d332447470c236d08da42a63ccd3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:25 +0530 Subject: [PATCH 0734/1001] proof: certify atlas Batch0734 (13:4090 to 13:4105) --- Collatz/Research/StoppingAtlas/Batch0734.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0734.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0734.lean b/Collatz/Research/StoppingAtlas/Batch0734.lean new file mode 100644 index 00000000..bc81c396 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0734.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0734 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4090. -/ +theorem bounds_13_4090 : exactInterval 13 4090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4090 : oddCount 4090 13 = 9 ∧ acceleratedOrbit 13 4090 = 9841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4090) = 3 ^ 9 * m + 9841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4090.1, data_13_4090.2] + +/-- Complete interval computation for depth 13, residue 4091. -/ +theorem bounds_13_4091 : exactInterval 13 4091 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4091) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4091 : oddCount 4091 13 = 8 ∧ acceleratedOrbit 13 4091 = 3278 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4091) = 3 ^ 8 * m + 3278 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4091.1, data_13_4091.2] + +/-- Complete interval computation for depth 13, residue 4092. -/ +theorem bounds_13_4092 : exactInterval 13 4092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4092 : oddCount 4092 13 = 10 ∧ acceleratedOrbit 13 4092 = 29524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4092) = 3 ^ 10 * m + 29524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4092.1, data_13_4092.2] + +/-- Complete interval computation for depth 13, residue 4093. -/ +theorem bounds_13_4093 : exactInterval 13 4093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4093 : oddCount 4093 13 = 10 ∧ acceleratedOrbit 13 4093 = 29524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4093) = 3 ^ 10 * m + 29524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4093.1, data_13_4093.2] + +/-- Complete interval computation for depth 13, residue 4094. -/ +theorem bounds_13_4094 : exactInterval 13 4094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4094 : oddCount 4094 13 = 11 ∧ acceleratedOrbit 13 4094 = 88573 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4094) = 3 ^ 11 * m + 88573 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4094.1, data_13_4094.2] + +/-- Complete interval computation for depth 13, residue 4095. -/ +theorem bounds_13_4095 : exactInterval 13 4095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4095 : oddCount 4095 13 = 12 ∧ acceleratedOrbit 13 4095 = 265720 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4095) = 3 ^ 12 * m + 265720 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4095.1, data_13_4095.2] + +/-- Complete interval computation for depth 13, residue 4096. -/ +theorem bounds_13_4096 : exactInterval 13 4096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4096 : oddCount 4096 13 = 1 ∧ acceleratedOrbit 13 4096 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4096) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4096.1, data_13_4096.2] + +/-- Complete interval computation for depth 13, residue 4097. -/ +theorem bounds_13_4097 : exactInterval 13 4097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4097 : oddCount 4097 13 = 6 ∧ acceleratedOrbit 13 4097 = 365 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4097) = 3 ^ 6 * m + 365 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4097.1, data_13_4097.2] + +/-- Complete interval computation for depth 13, residue 4098. -/ +theorem bounds_13_4098 : exactInterval 13 4098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4098 : oddCount 4098 13 = 7 ∧ acceleratedOrbit 13 4098 = 1097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4098) = 3 ^ 7 * m + 1097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4098.1, data_13_4098.2] + +/-- Complete interval computation for depth 13, residue 4099. -/ +theorem bounds_13_4099 : exactInterval 13 4099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4099 : oddCount 4099 13 = 7 ∧ acceleratedOrbit 13 4099 = 1097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4099) = 3 ^ 7 * m + 1097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4099.1, data_13_4099.2] + +/-- Complete interval computation for depth 13, residue 4100. -/ +theorem bounds_13_4100 : exactInterval 13 4100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4100 : oddCount 4100 13 = 5 ∧ acceleratedOrbit 13 4100 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4100) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4100.1, data_13_4100.2] + +/-- Complete interval computation for depth 13, residue 4101. -/ +theorem bounds_13_4101 : exactInterval 13 4101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4101 : oddCount 4101 13 = 5 ∧ acceleratedOrbit 13 4101 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4101) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4101.1, data_13_4101.2] + +/-- Complete interval computation for depth 13, residue 4102. -/ +theorem bounds_13_4102 : exactInterval 13 4102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4102 : oddCount 4102 13 = 5 ∧ acceleratedOrbit 13 4102 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4102) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4102.1, data_13_4102.2] + +/-- Complete interval computation for depth 13, residue 4103. -/ +theorem bounds_13_4103 : exactInterval 13 4103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4103 : oddCount 4103 13 = 7 ∧ acceleratedOrbit 13 4103 = 1097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4103) = 3 ^ 7 * m + 1097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4103.1, data_13_4103.2] + +/-- Complete interval computation for depth 13, residue 4104. -/ +theorem bounds_13_4104 : exactInterval 13 4104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4104 : oddCount 4104 13 = 6 ∧ acceleratedOrbit 13 4104 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4104) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4104.1, data_13_4104.2] + +/-- Complete interval computation for depth 13, residue 4105. -/ +theorem bounds_13_4105 : exactInterval 13 4105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4105 : oddCount 4105 13 = 7 ∧ acceleratedOrbit 13 4105 = 1097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4105) = 3 ^ 7 * m + 1097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4105.1, data_13_4105.2] + +end Collatz.Research.StoppingAtlas.Batch0734 From ebf6d2be27229873d23d0467aee84eca897930fd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:26 +0530 Subject: [PATCH 0735/1001] proof: certify atlas Batch0735 (13:4106 to 13:4120) --- Collatz/Research/StoppingAtlas/Batch0735.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0735.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0735.lean b/Collatz/Research/StoppingAtlas/Batch0735.lean new file mode 100644 index 00000000..5f89eae4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0735.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0735 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4106. -/ +theorem bounds_13_4106 : exactInterval 13 4106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4106 : oddCount 4106 13 = 6 ∧ acceleratedOrbit 13 4106 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4106) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4106.1, data_13_4106.2] + +/-- Complete interval computation for depth 13, residue 4107. -/ +theorem bounds_13_4107 : exactInterval 13 4107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4107 : oddCount 4107 13 = 5 ∧ acceleratedOrbit 13 4107 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4107) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4107.1, data_13_4107.2] + +/-- Complete interval computation for depth 13, residue 4108. -/ +theorem bounds_13_4108 : exactInterval 13 4108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4108 : oddCount 4108 13 = 6 ∧ acceleratedOrbit 13 4108 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4108) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4108.1, data_13_4108.2] + +/-- Complete interval computation for depth 13, residue 4109. -/ +theorem bounds_13_4109 : exactInterval 13 4109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4109 : oddCount 4109 13 = 6 ∧ acceleratedOrbit 13 4109 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4109) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4109.1, data_13_4109.2] + +/-- Complete interval computation for depth 13, residue 4110. -/ +theorem bounds_13_4110 : exactInterval 13 4110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4110 : oddCount 4110 13 = 5 ∧ acceleratedOrbit 13 4110 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4110) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4110.1, data_13_4110.2] + +/-- Complete interval computation for depth 13, residue 4111. -/ +theorem bounds_13_4111 : exactInterval 13 4111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4111 : oddCount 4111 13 = 5 ∧ acceleratedOrbit 13 4111 = 122 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4111) = 3 ^ 5 * m + 122 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4111.1, data_13_4111.2] + +/-- Complete interval computation for depth 13, residue 4112. -/ +theorem bounds_13_4112 : exactInterval 13 4112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4112 : oddCount 4112 13 = 4 ∧ acceleratedOrbit 13 4112 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4112) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4112.1, data_13_4112.2] + +/-- Complete interval computation for depth 13, residue 4113. -/ +theorem bounds_13_4113 : exactInterval 13 4113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4113 : oddCount 4113 13 = 6 ∧ acceleratedOrbit 13 4113 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4113) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4113.1, data_13_4113.2] + +/-- Complete interval computation for depth 13, residue 4114. -/ +theorem bounds_13_4114 : exactInterval 13 4114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4114 : oddCount 4114 13 = 7 ∧ acceleratedOrbit 13 4114 = 1100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4114) = 3 ^ 7 * m + 1100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4114.1, data_13_4114.2] + +/-- Complete interval computation for depth 13, residue 4115. -/ +theorem bounds_13_4115 : exactInterval 13 4115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4115 : oddCount 4115 13 = 7 ∧ acceleratedOrbit 13 4115 = 1100 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4115) = 3 ^ 7 * m + 1100 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4115.1, data_13_4115.2] + +/-- Complete interval computation for depth 13, residue 4116. -/ +theorem bounds_13_4116 : exactInterval 13 4116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4116 : oddCount 4116 13 = 4 ∧ acceleratedOrbit 13 4116 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4116) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4116.1, data_13_4116.2] + +/-- Complete interval computation for depth 13, residue 4117. -/ +theorem bounds_13_4117 : exactInterval 13 4117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4117 : oddCount 4117 13 = 4 ∧ acceleratedOrbit 13 4117 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4117) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4117.1, data_13_4117.2] + +/-- Complete interval computation for depth 13, residue 4118. -/ +theorem bounds_13_4118 : exactInterval 13 4118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4118 : oddCount 4118 13 = 6 ∧ acceleratedOrbit 13 4118 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4118) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4118.1, data_13_4118.2] + +/-- Complete interval computation for depth 13, residue 4119. -/ +theorem bounds_13_4119 : exactInterval 13 4119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4119 : oddCount 4119 13 = 6 ∧ acceleratedOrbit 13 4119 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4119) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4119.1, data_13_4119.2] + +/-- Complete interval computation for depth 13, residue 4120. -/ +theorem bounds_13_4120 : exactInterval 13 4120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4120 : oddCount 4120 13 = 4 ∧ acceleratedOrbit 13 4120 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4120) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4120.1, data_13_4120.2] + +end Collatz.Research.StoppingAtlas.Batch0735 From a749f1912d033b7287bc170263514bb20c339a58 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:26 +0530 Subject: [PATCH 0736/1001] proof: certify atlas Batch0736 (13:4121 to 13:4135) --- Collatz/Research/StoppingAtlas/Batch0736.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0736.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0736.lean b/Collatz/Research/StoppingAtlas/Batch0736.lean new file mode 100644 index 00000000..117775cc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0736.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0736 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4121. -/ +theorem bounds_13_4121 : exactInterval 13 4121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4121 : oddCount 4121 13 = 6 ∧ acceleratedOrbit 13 4121 = 367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4121) = 3 ^ 6 * m + 367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4121.1, data_13_4121.2] + +/-- Complete interval computation for depth 13, residue 4122. -/ +theorem bounds_13_4122 : exactInterval 13 4122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4122 : oddCount 4122 13 = 4 ∧ acceleratedOrbit 13 4122 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4122) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4122.1, data_13_4122.2] + +/-- Complete interval computation for depth 13, residue 4123. -/ +theorem bounds_13_4123 : exactInterval 13 4123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4123 : oddCount 4123 13 = 9 ∧ acceleratedOrbit 13 4123 = 9910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4123) = 3 ^ 9 * m + 9910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4123.1, data_13_4123.2] + +/-- Complete interval computation for depth 13, residue 4124. -/ +theorem bounds_13_4124 : exactInterval 13 4124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4124 : oddCount 4124 13 = 6 ∧ acceleratedOrbit 13 4124 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4124) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4124.1, data_13_4124.2] + +/-- Complete interval computation for depth 13, residue 4125. -/ +theorem bounds_13_4125 : exactInterval 13 4125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4125 : oddCount 4125 13 = 6 ∧ acceleratedOrbit 13 4125 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4125) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4125.1, data_13_4125.2] + +/-- Complete interval computation for depth 13, residue 4126. -/ +theorem bounds_13_4126 : exactInterval 13 4126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4126 : oddCount 4126 13 = 6 ∧ acceleratedOrbit 13 4126 = 368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4126) = 3 ^ 6 * m + 368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4126.1, data_13_4126.2] + +/-- Complete interval computation for depth 13, residue 4127. -/ +theorem bounds_13_4127 : exactInterval 13 4127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4127 : oddCount 4127 13 = 9 ∧ acceleratedOrbit 13 4127 = 9919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4127) = 3 ^ 9 * m + 9919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4127.1, data_13_4127.2] + +/-- Complete interval computation for depth 13, residue 4128. -/ +theorem bounds_13_4128 : exactInterval 13 4128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4128 : oddCount 4128 13 = 5 ∧ acceleratedOrbit 13 4128 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4128) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4128.1, data_13_4128.2] + +/-- Complete interval computation for depth 13, residue 4129. -/ +theorem bounds_13_4129 : exactInterval 13 4129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4129 : oddCount 4129 13 = 8 ∧ acceleratedOrbit 13 4129 = 3311 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4129) = 3 ^ 8 * m + 3311 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4129.1, data_13_4129.2] + +/-- Complete interval computation for depth 13, residue 4130. -/ +theorem bounds_13_4130 : exactInterval 13 4130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4130 : oddCount 4130 13 = 4 ∧ acceleratedOrbit 13 4130 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4130) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4130.1, data_13_4130.2] + +/-- Complete interval computation for depth 13, residue 4131. -/ +theorem bounds_13_4131 : exactInterval 13 4131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4131 : oddCount 4131 13 = 4 ∧ acceleratedOrbit 13 4131 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4131) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4131.1, data_13_4131.2] + +/-- Complete interval computation for depth 13, residue 4132. -/ +theorem bounds_13_4132 : exactInterval 13 4132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4132 : oddCount 4132 13 = 7 ∧ acceleratedOrbit 13 4132 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4132) = 3 ^ 7 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4132.1, data_13_4132.2] + +/-- Complete interval computation for depth 13, residue 4133. -/ +theorem bounds_13_4133 : exactInterval 13 4133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4133 : oddCount 4133 13 = 7 ∧ acceleratedOrbit 13 4133 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4133) = 3 ^ 7 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4133.1, data_13_4133.2] + +/-- Complete interval computation for depth 13, residue 4134. -/ +theorem bounds_13_4134 : exactInterval 13 4134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4134 : oddCount 4134 13 = 7 ∧ acceleratedOrbit 13 4134 = 1106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4134) = 3 ^ 7 * m + 1106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4134.1, data_13_4134.2] + +/-- Complete interval computation for depth 13, residue 4135. -/ +theorem bounds_13_4135 : exactInterval 13 4135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4135 : oddCount 4135 13 = 8 ∧ acceleratedOrbit 13 4135 = 3314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4135) = 3 ^ 8 * m + 3314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4135.1, data_13_4135.2] + +end Collatz.Research.StoppingAtlas.Batch0736 From 974d051d23ec59512f30fc6c905078b79c5a01e3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:26 +0530 Subject: [PATCH 0737/1001] proof: certify atlas Batch0737 (13:4136 to 13:4151) --- Collatz/Research/StoppingAtlas/Batch0737.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0737.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0737.lean b/Collatz/Research/StoppingAtlas/Batch0737.lean new file mode 100644 index 00000000..06f5e148 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0737.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0737 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4136. -/ +theorem bounds_13_4136 : exactInterval 13 4136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4136 : oddCount 4136 13 = 5 ∧ acceleratedOrbit 13 4136 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4136) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4136.1, data_13_4136.2] + +/-- Complete interval computation for depth 13, residue 4137. -/ +theorem bounds_13_4137 : exactInterval 13 4137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4137 : oddCount 4137 13 = 10 ∧ acceleratedOrbit 13 4137 = 29834 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4137) = 3 ^ 10 * m + 29834 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4137.1, data_13_4137.2] + +/-- Complete interval computation for depth 13, residue 4138. -/ +theorem bounds_13_4138 : exactInterval 13 4138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4138 : oddCount 4138 13 = 5 ∧ acceleratedOrbit 13 4138 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4138) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4138.1, data_13_4138.2] + +/-- Complete interval computation for depth 13, residue 4139. -/ +theorem bounds_13_4139 : exactInterval 13 4139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4139 : oddCount 4139 13 = 8 ∧ acceleratedOrbit 13 4139 = 3320 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4139) = 3 ^ 8 * m + 3320 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4139.1, data_13_4139.2] + +/-- Complete interval computation for depth 13, residue 4140. -/ +theorem bounds_13_4140 : exactInterval 13 4140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4140 : oddCount 4140 13 = 4 ∧ acceleratedOrbit 13 4140 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4140) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4140.1, data_13_4140.2] + +/-- Complete interval computation for depth 13, residue 4141. -/ +theorem bounds_13_4141 : exactInterval 13 4141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4141 : oddCount 4141 13 = 4 ∧ acceleratedOrbit 13 4141 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4141) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4141.1, data_13_4141.2] + +/-- Complete interval computation for depth 13, residue 4142. -/ +theorem bounds_13_4142 : exactInterval 13 4142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4142 : oddCount 4142 13 = 4 ∧ acceleratedOrbit 13 4142 = 41 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4142) = 3 ^ 4 * m + 41 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4142.1, data_13_4142.2] + +/-- Complete interval computation for depth 13, residue 4143. -/ +theorem bounds_13_4143 : exactInterval 13 4143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4143 : oddCount 4143 13 = 9 ∧ acceleratedOrbit 13 4143 = 9958 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4143) = 3 ^ 9 * m + 9958 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4143.1, data_13_4143.2] + +/-- Complete interval computation for depth 13, residue 4144. -/ +theorem bounds_13_4144 : exactInterval 13 4144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4144 : oddCount 4144 13 = 5 ∧ acceleratedOrbit 13 4144 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4144) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4144.1, data_13_4144.2] + +/-- Complete interval computation for depth 13, residue 4145. -/ +theorem bounds_13_4145 : exactInterval 13 4145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4145 : oddCount 4145 13 = 7 ∧ acceleratedOrbit 13 4145 = 1109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4145) = 3 ^ 7 * m + 1109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4145.1, data_13_4145.2] + +/-- Complete interval computation for depth 13, residue 4146. -/ +theorem bounds_13_4146 : exactInterval 13 4146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4146 : oddCount 4146 13 = 7 ∧ acceleratedOrbit 13 4146 = 1109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4146) = 3 ^ 7 * m + 1109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4146.1, data_13_4146.2] + +/-- Complete interval computation for depth 13, residue 4147. -/ +theorem bounds_13_4147 : exactInterval 13 4147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4147 : oddCount 4147 13 = 7 ∧ acceleratedOrbit 13 4147 = 1109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4147) = 3 ^ 7 * m + 1109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4147.1, data_13_4147.2] + +/-- Complete interval computation for depth 13, residue 4148. -/ +theorem bounds_13_4148 : exactInterval 13 4148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4148 : oddCount 4148 13 = 5 ∧ acceleratedOrbit 13 4148 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4148) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4148.1, data_13_4148.2] + +/-- Complete interval computation for depth 13, residue 4149. -/ +theorem bounds_13_4149 : exactInterval 13 4149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4149 : oddCount 4149 13 = 5 ∧ acceleratedOrbit 13 4149 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4149) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4149.1, data_13_4149.2] + +/-- Complete interval computation for depth 13, residue 4150. -/ +theorem bounds_13_4150 : exactInterval 13 4150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4150 : oddCount 4150 13 = 8 ∧ acceleratedOrbit 13 4150 = 3326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4150) = 3 ^ 8 * m + 3326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4150.1, data_13_4150.2] + +/-- Complete interval computation for depth 13, residue 4151. -/ +theorem bounds_13_4151 : exactInterval 13 4151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4151 : oddCount 4151 13 = 8 ∧ acceleratedOrbit 13 4151 = 3326 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4151) = 3 ^ 8 * m + 3326 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4151.1, data_13_4151.2] + +end Collatz.Research.StoppingAtlas.Batch0737 From d67de7c42d962ee3b06941fad2be28370573ecd8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:28 +0530 Subject: [PATCH 0738/1001] proof: certify atlas Batch0738 (13:4152 to 13:4166) --- Collatz/Research/StoppingAtlas/Batch0738.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0738.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0738.lean b/Collatz/Research/StoppingAtlas/Batch0738.lean new file mode 100644 index 00000000..672f0456 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0738.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0738 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4152. -/ +theorem bounds_13_4152 : exactInterval 13 4152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4152 : oddCount 4152 13 = 6 ∧ acceleratedOrbit 13 4152 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4152) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4152.1, data_13_4152.2] + +/-- Complete interval computation for depth 13, residue 4153. -/ +theorem bounds_13_4153 : exactInterval 13 4153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4153 : oddCount 4153 13 = 6 ∧ acceleratedOrbit 13 4153 = 370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4153) = 3 ^ 6 * m + 370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4153.1, data_13_4153.2] + +/-- Complete interval computation for depth 13, residue 4154. -/ +theorem bounds_13_4154 : exactInterval 13 4154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4154 : oddCount 4154 13 = 6 ∧ acceleratedOrbit 13 4154 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4154) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4154.1, data_13_4154.2] + +/-- Complete interval computation for depth 13, residue 4155. -/ +theorem bounds_13_4155 : exactInterval 13 4155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4155 : oddCount 4155 13 = 6 ∧ acceleratedOrbit 13 4155 = 370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4155) = 3 ^ 6 * m + 370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4155.1, data_13_4155.2] + +/-- Complete interval computation for depth 13, residue 4156. -/ +theorem bounds_13_4156 : exactInterval 13 4156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4156 : oddCount 4156 13 = 6 ∧ acceleratedOrbit 13 4156 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4156) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4156.1, data_13_4156.2] + +/-- Complete interval computation for depth 13, residue 4157. -/ +theorem bounds_13_4157 : exactInterval 13 4157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4157 : oddCount 4157 13 = 6 ∧ acceleratedOrbit 13 4157 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4157) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4157.1, data_13_4157.2] + +/-- Complete interval computation for depth 13, residue 4158. -/ +theorem bounds_13_4158 : exactInterval 13 4158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4158 : oddCount 4158 13 = 8 ∧ acceleratedOrbit 13 4158 = 3332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4158) = 3 ^ 8 * m + 3332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4158.1, data_13_4158.2] + +/-- Complete interval computation for depth 13, residue 4159. -/ +theorem bounds_13_4159 : exactInterval 13 4159 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4159) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4159 : oddCount 4159 13 = 8 ∧ acceleratedOrbit 13 4159 = 3332 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4159) = 3 ^ 8 * m + 3332 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4159.1, data_13_4159.2] + +/-- Complete interval computation for depth 13, residue 4160. -/ +theorem bounds_13_4160 : exactInterval 13 4160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4160 : oddCount 4160 13 = 3 ∧ acceleratedOrbit 13 4160 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4160) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4160.1, data_13_4160.2] + +/-- Complete interval computation for depth 13, residue 4161. -/ +theorem bounds_13_4161 : exactInterval 13 4161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4161 : oddCount 4161 13 = 6 ∧ acceleratedOrbit 13 4161 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4161) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4161.1, data_13_4161.2] + +/-- Complete interval computation for depth 13, residue 4162. -/ +theorem bounds_13_4162 : exactInterval 13 4162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4162 : oddCount 4162 13 = 6 ∧ acceleratedOrbit 13 4162 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4162) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4162.1, data_13_4162.2] + +/-- Complete interval computation for depth 13, residue 4163. -/ +theorem bounds_13_4163 : exactInterval 13 4163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4163 : oddCount 4163 13 = 6 ∧ acceleratedOrbit 13 4163 = 371 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4163) = 3 ^ 6 * m + 371 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4163.1, data_13_4163.2] + +/-- Complete interval computation for depth 13, residue 4164. -/ +theorem bounds_13_4164 : exactInterval 13 4164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4164 : oddCount 4164 13 = 5 ∧ acceleratedOrbit 13 4164 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4164) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4164.1, data_13_4164.2] + +/-- Complete interval computation for depth 13, residue 4165. -/ +theorem bounds_13_4165 : exactInterval 13 4165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4165 : oddCount 4165 13 = 5 ∧ acceleratedOrbit 13 4165 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4165) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4165.1, data_13_4165.2] + +/-- Complete interval computation for depth 13, residue 4166. -/ +theorem bounds_13_4166 : exactInterval 13 4166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4166 : oddCount 4166 13 = 5 ∧ acceleratedOrbit 13 4166 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4166) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4166.1, data_13_4166.2] + +end Collatz.Research.StoppingAtlas.Batch0738 From 0b5b321323ee5dfefdaac194906aabeb4416c92e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:29 +0530 Subject: [PATCH 0739/1001] proof: certify atlas Batch0739 (13:4167 to 13:4182) --- Collatz/Research/StoppingAtlas/Batch0739.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0739.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0739.lean b/Collatz/Research/StoppingAtlas/Batch0739.lean new file mode 100644 index 00000000..02a8b1ce --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0739.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0739 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4167. -/ +theorem bounds_13_4167 : exactInterval 13 4167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4167 : oddCount 4167 13 = 10 ∧ acceleratedOrbit 13 4167 = 30050 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4167) = 3 ^ 10 * m + 30050 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4167.1, data_13_4167.2] + +/-- Complete interval computation for depth 13, residue 4168. -/ +theorem bounds_13_4168 : exactInterval 13 4168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4168 : oddCount 4168 13 = 5 ∧ acceleratedOrbit 13 4168 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4168) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4168.1, data_13_4168.2] + +/-- Complete interval computation for depth 13, residue 4169. -/ +theorem bounds_13_4169 : exactInterval 13 4169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4169 : oddCount 4169 13 = 8 ∧ acceleratedOrbit 13 4169 = 3341 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4169) = 3 ^ 8 * m + 3341 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4169.1, data_13_4169.2] + +/-- Complete interval computation for depth 13, residue 4170. -/ +theorem bounds_13_4170 : exactInterval 13 4170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4170 : oddCount 4170 13 = 5 ∧ acceleratedOrbit 13 4170 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4170) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4170.1, data_13_4170.2] + +/-- Complete interval computation for depth 13, residue 4171. -/ +theorem bounds_13_4171 : exactInterval 13 4171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4171 : oddCount 4171 13 = 5 ∧ acceleratedOrbit 13 4171 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4171) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4171.1, data_13_4171.2] + +/-- Complete interval computation for depth 13, residue 4172. -/ +theorem bounds_13_4172 : exactInterval 13 4172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4172 : oddCount 4172 13 = 5 ∧ acceleratedOrbit 13 4172 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4172) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4172.1, data_13_4172.2] + +/-- Complete interval computation for depth 13, residue 4173. -/ +theorem bounds_13_4173 : exactInterval 13 4173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4173 : oddCount 4173 13 = 5 ∧ acceleratedOrbit 13 4173 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4173) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4173.1, data_13_4173.2] + +/-- Complete interval computation for depth 13, residue 4174. -/ +theorem bounds_13_4174 : exactInterval 13 4174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4174 : oddCount 4174 13 = 8 ∧ acceleratedOrbit 13 4174 = 3347 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4174) = 3 ^ 8 * m + 3347 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4174.1, data_13_4174.2] + +/-- Complete interval computation for depth 13, residue 4175. -/ +theorem bounds_13_4175 : exactInterval 13 4175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4175 : oddCount 4175 13 = 8 ∧ acceleratedOrbit 13 4175 = 3347 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4175) = 3 ^ 8 * m + 3347 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4175.1, data_13_4175.2] + +/-- Complete interval computation for depth 13, residue 4176. -/ +theorem bounds_13_4176 : exactInterval 13 4176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4176 : oddCount 4176 13 = 3 ∧ acceleratedOrbit 13 4176 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4176) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4176.1, data_13_4176.2] + +/-- Complete interval computation for depth 13, residue 4177. -/ +theorem bounds_13_4177 : exactInterval 13 4177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4177 : oddCount 4177 13 = 5 ∧ acceleratedOrbit 13 4177 = 124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4177) = 3 ^ 5 * m + 124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4177.1, data_13_4177.2] + +/-- Complete interval computation for depth 13, residue 4178. -/ +theorem bounds_13_4178 : exactInterval 13 4178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4178 : oddCount 4178 13 = 8 ∧ acceleratedOrbit 13 4178 = 3349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4178) = 3 ^ 8 * m + 3349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4178.1, data_13_4178.2] + +/-- Complete interval computation for depth 13, residue 4179. -/ +theorem bounds_13_4179 : exactInterval 13 4179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4179 : oddCount 4179 13 = 8 ∧ acceleratedOrbit 13 4179 = 3349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4179) = 3 ^ 8 * m + 3349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4179.1, data_13_4179.2] + +/-- Complete interval computation for depth 13, residue 4180. -/ +theorem bounds_13_4180 : exactInterval 13 4180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4180 : oddCount 4180 13 = 3 ∧ acceleratedOrbit 13 4180 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4180) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4180.1, data_13_4180.2] + +/-- Complete interval computation for depth 13, residue 4181. -/ +theorem bounds_13_4181 : exactInterval 13 4181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4181 : oddCount 4181 13 = 3 ∧ acceleratedOrbit 13 4181 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4181) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4181.1, data_13_4181.2] + +/-- Complete interval computation for depth 13, residue 4182. -/ +theorem bounds_13_4182 : exactInterval 13 4182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4182 : oddCount 4182 13 = 6 ∧ acceleratedOrbit 13 4182 = 373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4182) = 3 ^ 6 * m + 373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4182.1, data_13_4182.2] + +end Collatz.Research.StoppingAtlas.Batch0739 From 15964c36039e7bb4ff544bcad1afc162c5153129 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:31 +0530 Subject: [PATCH 0740/1001] proof: certify atlas Batch0740 (13:4183 to 13:4197) --- Collatz/Research/StoppingAtlas/Batch0740.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0740.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0740.lean b/Collatz/Research/StoppingAtlas/Batch0740.lean new file mode 100644 index 00000000..cfee081a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0740.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0740 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4183. -/ +theorem bounds_13_4183 : exactInterval 13 4183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4183 : oddCount 4183 13 = 6 ∧ acceleratedOrbit 13 4183 = 373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4183) = 3 ^ 6 * m + 373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4183.1, data_13_4183.2] + +/-- Complete interval computation for depth 13, residue 4184. -/ +theorem bounds_13_4184 : exactInterval 13 4184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4184 : oddCount 4184 13 = 5 ∧ acceleratedOrbit 13 4184 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4184) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4184.1, data_13_4184.2] + +/-- Complete interval computation for depth 13, residue 4185. -/ +theorem bounds_13_4185 : exactInterval 13 4185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4185 : oddCount 4185 13 = 6 ∧ acceleratedOrbit 13 4185 = 373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4185) = 3 ^ 6 * m + 373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4185.1, data_13_4185.2] + +/-- Complete interval computation for depth 13, residue 4186. -/ +theorem bounds_13_4186 : exactInterval 13 4186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4186 : oddCount 4186 13 = 5 ∧ acceleratedOrbit 13 4186 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4186) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4186.1, data_13_4186.2] + +/-- Complete interval computation for depth 13, residue 4187. -/ +theorem bounds_13_4187 : exactInterval 13 4187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4187 : oddCount 4187 13 = 9 ∧ acceleratedOrbit 13 4187 = 10064 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4187) = 3 ^ 9 * m + 10064 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4187.1, data_13_4187.2] + +/-- Complete interval computation for depth 13, residue 4188. -/ +theorem bounds_13_4188 : exactInterval 13 4188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4188 : oddCount 4188 13 = 5 ∧ acceleratedOrbit 13 4188 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4188) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4188.1, data_13_4188.2] + +/-- Complete interval computation for depth 13, residue 4189. -/ +theorem bounds_13_4189 : exactInterval 13 4189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4189 : oddCount 4189 13 = 5 ∧ acceleratedOrbit 13 4189 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4189) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4189.1, data_13_4189.2] + +/-- Complete interval computation for depth 13, residue 4190. -/ +theorem bounds_13_4190 : exactInterval 13 4190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4190 : oddCount 4190 13 = 8 ∧ acceleratedOrbit 13 4190 = 3358 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4190) = 3 ^ 8 * m + 3358 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4190.1, data_13_4190.2] + +/-- Complete interval computation for depth 13, residue 4191. -/ +theorem bounds_13_4191 : exactInterval 13 4191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4191) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4191 : oddCount 4191 13 = 8 ∧ acceleratedOrbit 13 4191 = 3358 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4191) = 3 ^ 8 * m + 3358 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4191.1, data_13_4191.2] + +/-- Complete interval computation for depth 13, residue 4192. -/ +theorem bounds_13_4192 : exactInterval 13 4192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4192 : oddCount 4192 13 = 3 ∧ acceleratedOrbit 13 4192 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4192) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4192.1, data_13_4192.2] + +/-- Complete interval computation for depth 13, residue 4193. -/ +theorem bounds_13_4193 : exactInterval 13 4193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4193 : oddCount 4193 13 = 8 ∧ acceleratedOrbit 13 4193 = 3361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4193) = 3 ^ 8 * m + 3361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4193.1, data_13_4193.2] + +/-- Complete interval computation for depth 13, residue 4194. -/ +theorem bounds_13_4194 : exactInterval 13 4194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4194 : oddCount 4194 13 = 7 ∧ acceleratedOrbit 13 4194 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4194) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4194.1, data_13_4194.2] + +/-- Complete interval computation for depth 13, residue 4195. -/ +theorem bounds_13_4195 : exactInterval 13 4195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4195 : oddCount 4195 13 = 7 ∧ acceleratedOrbit 13 4195 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4195) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4195.1, data_13_4195.2] + +/-- Complete interval computation for depth 13, residue 4196. -/ +theorem bounds_13_4196 : exactInterval 13 4196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4196 : oddCount 4196 13 = 7 ∧ acceleratedOrbit 13 4196 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4196) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4196.1, data_13_4196.2] + +/-- Complete interval computation for depth 13, residue 4197. -/ +theorem bounds_13_4197 : exactInterval 13 4197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4197 : oddCount 4197 13 = 7 ∧ acceleratedOrbit 13 4197 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4197) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4197.1, data_13_4197.2] + +end Collatz.Research.StoppingAtlas.Batch0740 From 1c0a118e9d9a1a1392a47278517e8721de91d004 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:31 +0530 Subject: [PATCH 0741/1001] proof: certify atlas Batch0741 (13:4198 to 13:4212) --- Collatz/Research/StoppingAtlas/Batch0741.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0741.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0741.lean b/Collatz/Research/StoppingAtlas/Batch0741.lean new file mode 100644 index 00000000..bd76b5f2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0741.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0741 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4198. -/ +theorem bounds_13_4198 : exactInterval 13 4198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4198 : oddCount 4198 13 = 7 ∧ acceleratedOrbit 13 4198 = 1124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4198) = 3 ^ 7 * m + 1124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4198.1, data_13_4198.2] + +/-- Complete interval computation for depth 13, residue 4199. -/ +theorem bounds_13_4199 : exactInterval 13 4199 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4199) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4199 : oddCount 4199 13 = 8 ∧ acceleratedOrbit 13 4199 = 3364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4199) = 3 ^ 8 * m + 3364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4199.1, data_13_4199.2] + +/-- Complete interval computation for depth 13, residue 4200. -/ +theorem bounds_13_4200 : exactInterval 13 4200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4200 : oddCount 4200 13 = 3 ∧ acceleratedOrbit 13 4200 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4200) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4200.1, data_13_4200.2] + +/-- Complete interval computation for depth 13, residue 4201. -/ +theorem bounds_13_4201 : exactInterval 13 4201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4201 : oddCount 4201 13 = 6 ∧ acceleratedOrbit 13 4201 = 374 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4201) = 3 ^ 6 * m + 374 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4201.1, data_13_4201.2] + +/-- Complete interval computation for depth 13, residue 4202. -/ +theorem bounds_13_4202 : exactInterval 13 4202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4202 : oddCount 4202 13 = 3 ∧ acceleratedOrbit 13 4202 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4202) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4202.1, data_13_4202.2] + +/-- Complete interval computation for depth 13, residue 4203. -/ +theorem bounds_13_4203 : exactInterval 13 4203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4203 : oddCount 4203 13 = 8 ∧ acceleratedOrbit 13 4203 = 3368 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4203) = 3 ^ 8 * m + 3368 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4203.1, data_13_4203.2] + +/-- Complete interval computation for depth 13, residue 4204. -/ +theorem bounds_13_4204 : exactInterval 13 4204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4204 : oddCount 4204 13 = 9 ∧ acceleratedOrbit 13 4204 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4204) = 3 ^ 9 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4204.1, data_13_4204.2] + +/-- Complete interval computation for depth 13, residue 4205. -/ +theorem bounds_13_4205 : exactInterval 13 4205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4205 : oddCount 4205 13 = 9 ∧ acceleratedOrbit 13 4205 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4205) = 3 ^ 9 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4205.1, data_13_4205.2] + +/-- Complete interval computation for depth 13, residue 4206. -/ +theorem bounds_13_4206 : exactInterval 13 4206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4206 : oddCount 4206 13 = 9 ∧ acceleratedOrbit 13 4206 = 10115 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4206) = 3 ^ 9 * m + 10115 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4206.1, data_13_4206.2] + +/-- Complete interval computation for depth 13, residue 4207. -/ +theorem bounds_13_4207 : exactInterval 13 4207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4207 : oddCount 4207 13 = 10 ∧ acceleratedOrbit 13 4207 = 30334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4207) = 3 ^ 10 * m + 30334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4207.1, data_13_4207.2] + +/-- Complete interval computation for depth 13, residue 4208. -/ +theorem bounds_13_4208 : exactInterval 13 4208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4208 : oddCount 4208 13 = 6 ∧ acceleratedOrbit 13 4208 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4208) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4208.1, data_13_4208.2] + +/-- Complete interval computation for depth 13, residue 4209. -/ +theorem bounds_13_4209 : exactInterval 13 4209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4209 : oddCount 4209 13 = 3 ∧ acceleratedOrbit 13 4209 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4209) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4209.1, data_13_4209.2] + +/-- Complete interval computation for depth 13, residue 4210. -/ +theorem bounds_13_4210 : exactInterval 13 4210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4210 : oddCount 4210 13 = 5 ∧ acceleratedOrbit 13 4210 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4210) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4210.1, data_13_4210.2] + +/-- Complete interval computation for depth 13, residue 4211. -/ +theorem bounds_13_4211 : exactInterval 13 4211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4211 : oddCount 4211 13 = 5 ∧ acceleratedOrbit 13 4211 = 125 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4211) = 3 ^ 5 * m + 125 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4211.1, data_13_4211.2] + +/-- Complete interval computation for depth 13, residue 4212. -/ +theorem bounds_13_4212 : exactInterval 13 4212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4212 : oddCount 4212 13 = 6 ∧ acceleratedOrbit 13 4212 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4212) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4212.1, data_13_4212.2] + +end Collatz.Research.StoppingAtlas.Batch0741 From cc8b2b472b0b89a51d8ea79d17fa3e360813d43d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:32 +0530 Subject: [PATCH 0742/1001] proof: certify atlas Batch0742 (13:4213 to 13:4228) --- Collatz/Research/StoppingAtlas/Batch0742.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0742.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0742.lean b/Collatz/Research/StoppingAtlas/Batch0742.lean new file mode 100644 index 00000000..3d93a706 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0742.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0742 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4213. -/ +theorem bounds_13_4213 : exactInterval 13 4213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4213 : oddCount 4213 13 = 6 ∧ acceleratedOrbit 13 4213 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4213) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4213.1, data_13_4213.2] + +/-- Complete interval computation for depth 13, residue 4214. -/ +theorem bounds_13_4214 : exactInterval 13 4214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4214 : oddCount 4214 13 = 7 ∧ acceleratedOrbit 13 4214 = 1127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4214) = 3 ^ 7 * m + 1127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4214.1, data_13_4214.2] + +/-- Complete interval computation for depth 13, residue 4215. -/ +theorem bounds_13_4215 : exactInterval 13 4215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4215) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4215 : oddCount 4215 13 = 7 ∧ acceleratedOrbit 13 4215 = 1127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4215) = 3 ^ 7 * m + 1127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4215.1, data_13_4215.2] + +/-- Complete interval computation for depth 13, residue 4216. -/ +theorem bounds_13_4216 : exactInterval 13 4216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4216 : oddCount 4216 13 = 6 ∧ acceleratedOrbit 13 4216 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4216) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4216.1, data_13_4216.2] + +/-- Complete interval computation for depth 13, residue 4217. -/ +theorem bounds_13_4217 : exactInterval 13 4217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4217 : oddCount 4217 13 = 9 ∧ acceleratedOrbit 13 4217 = 10138 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4217) = 3 ^ 9 * m + 10138 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4217.1, data_13_4217.2] + +/-- Complete interval computation for depth 13, residue 4218. -/ +theorem bounds_13_4218 : exactInterval 13 4218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4218 : oddCount 4218 13 = 6 ∧ acceleratedOrbit 13 4218 = 377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4218) = 3 ^ 6 * m + 377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4218.1, data_13_4218.2] + +/-- Complete interval computation for depth 13, residue 4219. -/ +theorem bounds_13_4219 : exactInterval 13 4219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4219 : oddCount 4219 13 = 7 ∧ acceleratedOrbit 13 4219 = 1127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4219) = 3 ^ 7 * m + 1127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4219.1, data_13_4219.2] + +/-- Complete interval computation for depth 13, residue 4220. -/ +theorem bounds_13_4220 : exactInterval 13 4220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4220 : oddCount 4220 13 = 9 ∧ acceleratedOrbit 13 4220 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4220) = 3 ^ 9 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4220.1, data_13_4220.2] + +/-- Complete interval computation for depth 13, residue 4221. -/ +theorem bounds_13_4221 : exactInterval 13 4221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4221 : oddCount 4221 13 = 9 ∧ acceleratedOrbit 13 4221 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4221) = 3 ^ 9 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4221.1, data_13_4221.2] + +/-- Complete interval computation for depth 13, residue 4222. -/ +theorem bounds_13_4222 : exactInterval 13 4222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4222 : oddCount 4222 13 = 9 ∧ acceleratedOrbit 13 4222 = 10151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4222) = 3 ^ 9 * m + 10151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4222.1, data_13_4222.2] + +/-- Complete interval computation for depth 13, residue 4223. -/ +theorem bounds_13_4223 : exactInterval 13 4223 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4223) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4223 : oddCount 4223 13 = 8 ∧ acceleratedOrbit 13 4223 = 3383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4223) = 3 ^ 8 * m + 3383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4223.1, data_13_4223.2] + +/-- Complete interval computation for depth 13, residue 4224. -/ +theorem bounds_13_4224 : exactInterval 13 4224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4224 : oddCount 4224 13 = 4 ∧ acceleratedOrbit 13 4224 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4224) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4224.1, data_13_4224.2] + +/-- Complete interval computation for depth 13, residue 4225. -/ +theorem bounds_13_4225 : exactInterval 13 4225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4225 : oddCount 4225 13 = 7 ∧ acceleratedOrbit 13 4225 = 1129 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4225) = 3 ^ 7 * m + 1129 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4225.1, data_13_4225.2] + +/-- Complete interval computation for depth 13, residue 4226. -/ +theorem bounds_13_4226 : exactInterval 13 4226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4226 : oddCount 4226 13 = 7 ∧ acceleratedOrbit 13 4226 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4226) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4226.1, data_13_4226.2] + +/-- Complete interval computation for depth 13, residue 4227. -/ +theorem bounds_13_4227 : exactInterval 13 4227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4227 : oddCount 4227 13 = 7 ∧ acceleratedOrbit 13 4227 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4227) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4227.1, data_13_4227.2] + +/-- Complete interval computation for depth 13, residue 4228. -/ +theorem bounds_13_4228 : exactInterval 13 4228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4228 : oddCount 4228 13 = 7 ∧ acceleratedOrbit 13 4228 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4228) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4228.1, data_13_4228.2] + +end Collatz.Research.StoppingAtlas.Batch0742 From eb65e2da027ae9e05d406c361287bf6db03d8e12 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:33 +0530 Subject: [PATCH 0743/1001] proof: certify atlas Batch0743 (13:4229 to 13:4243) --- Collatz/Research/StoppingAtlas/Batch0743.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0743.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0743.lean b/Collatz/Research/StoppingAtlas/Batch0743.lean new file mode 100644 index 00000000..64630f18 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0743.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0743 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4229. -/ +theorem bounds_13_4229 : exactInterval 13 4229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4229 : oddCount 4229 13 = 7 ∧ acceleratedOrbit 13 4229 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4229) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4229.1, data_13_4229.2] + +/-- Complete interval computation for depth 13, residue 4230. -/ +theorem bounds_13_4230 : exactInterval 13 4230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4230 : oddCount 4230 13 = 7 ∧ acceleratedOrbit 13 4230 = 1133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4230) = 3 ^ 7 * m + 1133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4230.1, data_13_4230.2] + +/-- Complete interval computation for depth 13, residue 4231. -/ +theorem bounds_13_4231 : exactInterval 13 4231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4231 : oddCount 4231 13 = 8 ∧ acceleratedOrbit 13 4231 = 3392 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4231) = 3 ^ 8 * m + 3392 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4231.1, data_13_4231.2] + +/-- Complete interval computation for depth 13, residue 4232. -/ +theorem bounds_13_4232 : exactInterval 13 4232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4232 : oddCount 4232 13 = 3 ∧ acceleratedOrbit 13 4232 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4232) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4232.1, data_13_4232.2] + +/-- Complete interval computation for depth 13, residue 4233. -/ +theorem bounds_13_4233 : exactInterval 13 4233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4233 : oddCount 4233 13 = 10 ∧ acceleratedOrbit 13 4233 = 30527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4233) = 3 ^ 10 * m + 30527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4233.1, data_13_4233.2] + +/-- Complete interval computation for depth 13, residue 4234. -/ +theorem bounds_13_4234 : exactInterval 13 4234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4234 : oddCount 4234 13 = 3 ∧ acceleratedOrbit 13 4234 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4234) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4234.1, data_13_4234.2] + +/-- Complete interval computation for depth 13, residue 4235. -/ +theorem bounds_13_4235 : exactInterval 13 4235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4235 : oddCount 4235 13 = 8 ∧ acceleratedOrbit 13 4235 = 3395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4235) = 3 ^ 8 * m + 3395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4235.1, data_13_4235.2] + +/-- Complete interval computation for depth 13, residue 4236. -/ +theorem bounds_13_4236 : exactInterval 13 4236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4236 : oddCount 4236 13 = 3 ∧ acceleratedOrbit 13 4236 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4236) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4236.1, data_13_4236.2] + +/-- Complete interval computation for depth 13, residue 4237. -/ +theorem bounds_13_4237 : exactInterval 13 4237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4237 : oddCount 4237 13 = 3 ∧ acceleratedOrbit 13 4237 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4237) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4237.1, data_13_4237.2] + +/-- Complete interval computation for depth 13, residue 4238. -/ +theorem bounds_13_4238 : exactInterval 13 4238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4238 : oddCount 4238 13 = 8 ∧ acceleratedOrbit 13 4238 = 3397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4238) = 3 ^ 8 * m + 3397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4238.1, data_13_4238.2] + +/-- Complete interval computation for depth 13, residue 4239. -/ +theorem bounds_13_4239 : exactInterval 13 4239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4239 : oddCount 4239 13 = 8 ∧ acceleratedOrbit 13 4239 = 3397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4239) = 3 ^ 8 * m + 3397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4239.1, data_13_4239.2] + +/-- Complete interval computation for depth 13, residue 4240. -/ +theorem bounds_13_4240 : exactInterval 13 4240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4240 : oddCount 4240 13 = 6 ∧ acceleratedOrbit 13 4240 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4240) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4240.1, data_13_4240.2] + +/-- Complete interval computation for depth 13, residue 4241. -/ +theorem bounds_13_4241 : exactInterval 13 4241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4241 : oddCount 4241 13 = 9 ∧ acceleratedOrbit 13 4241 = 10205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4241) = 3 ^ 9 * m + 10205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4241.1, data_13_4241.2] + +/-- Complete interval computation for depth 13, residue 4242. -/ +theorem bounds_13_4242 : exactInterval 13 4242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4242 : oddCount 4242 13 = 9 ∧ acceleratedOrbit 13 4242 = 10205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4242) = 3 ^ 9 * m + 10205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4242.1, data_13_4242.2] + +/-- Complete interval computation for depth 13, residue 4243. -/ +theorem bounds_13_4243 : exactInterval 13 4243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4243 : oddCount 4243 13 = 9 ∧ acceleratedOrbit 13 4243 = 10205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4243) = 3 ^ 9 * m + 10205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4243.1, data_13_4243.2] + +end Collatz.Research.StoppingAtlas.Batch0743 From 14e1d527f82d563b5ca1925cf247d8fb49f165c6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:33 +0530 Subject: [PATCH 0744/1001] proof: certify atlas Batch0744 (13:4244 to 13:4258) --- Collatz/Research/StoppingAtlas/Batch0744.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0744.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0744.lean b/Collatz/Research/StoppingAtlas/Batch0744.lean new file mode 100644 index 00000000..8a5e3b1c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0744.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0744 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4244. -/ +theorem bounds_13_4244 : exactInterval 13 4244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4244 : oddCount 4244 13 = 6 ∧ acceleratedOrbit 13 4244 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4244) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4244.1, data_13_4244.2] + +/-- Complete interval computation for depth 13, residue 4245. -/ +theorem bounds_13_4245 : exactInterval 13 4245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4245 : oddCount 4245 13 = 6 ∧ acceleratedOrbit 13 4245 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4245) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4245.1, data_13_4245.2] + +/-- Complete interval computation for depth 13, residue 4246. -/ +theorem bounds_13_4246 : exactInterval 13 4246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4246 : oddCount 4246 13 = 3 ∧ acceleratedOrbit 13 4246 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4246) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4246.1, data_13_4246.2] + +/-- Complete interval computation for depth 13, residue 4247. -/ +theorem bounds_13_4247 : exactInterval 13 4247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4247 : oddCount 4247 13 = 3 ∧ acceleratedOrbit 13 4247 = 14 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4247) = 3 ^ 3 * m + 14 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4247.1, data_13_4247.2] + +/-- Complete interval computation for depth 13, residue 4248. -/ +theorem bounds_13_4248 : exactInterval 13 4248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4248 : oddCount 4248 13 = 6 ∧ acceleratedOrbit 13 4248 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4248) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4248.1, data_13_4248.2] + +/-- Complete interval computation for depth 13, residue 4249. -/ +theorem bounds_13_4249 : exactInterval 13 4249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4249 : oddCount 4249 13 = 7 ∧ acceleratedOrbit 13 4249 = 1136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4249) = 3 ^ 7 * m + 1136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4249.1, data_13_4249.2] + +/-- Complete interval computation for depth 13, residue 4250. -/ +theorem bounds_13_4250 : exactInterval 13 4250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4250 : oddCount 4250 13 = 6 ∧ acceleratedOrbit 13 4250 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4250) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4250.1, data_13_4250.2] + +/-- Complete interval computation for depth 13, residue 4251. -/ +theorem bounds_13_4251 : exactInterval 13 4251 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4251) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4251 : oddCount 4251 13 = 8 ∧ acceleratedOrbit 13 4251 = 3406 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4251) = 3 ^ 8 * m + 3406 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4251.1, data_13_4251.2] + +/-- Complete interval computation for depth 13, residue 4252. -/ +theorem bounds_13_4252 : exactInterval 13 4252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4252 : oddCount 4252 13 = 6 ∧ acceleratedOrbit 13 4252 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4252) = 3 ^ 6 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4252.1, data_13_4252.2] + +/-- Complete interval computation for depth 13, residue 4253. -/ +theorem bounds_13_4253 : exactInterval 13 4253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4253 : oddCount 4253 13 = 6 ∧ acceleratedOrbit 13 4253 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4253) = 3 ^ 6 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4253.1, data_13_4253.2] + +/-- Complete interval computation for depth 13, residue 4254. -/ +theorem bounds_13_4254 : exactInterval 13 4254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4254 : oddCount 4254 13 = 6 ∧ acceleratedOrbit 13 4254 = 379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4254) = 3 ^ 6 * m + 379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4254.1, data_13_4254.2] + +/-- Complete interval computation for depth 13, residue 4255. -/ +theorem bounds_13_4255 : exactInterval 13 4255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4255 : oddCount 4255 13 = 11 ∧ acceleratedOrbit 13 4255 = 92036 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4255) = 3 ^ 11 * m + 92036 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4255.1, data_13_4255.2] + +/-- Complete interval computation for depth 13, residue 4256. -/ +theorem bounds_13_4256 : exactInterval 13 4256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4256 : oddCount 4256 13 = 4 ∧ acceleratedOrbit 13 4256 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4256) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4256.1, data_13_4256.2] + +/-- Complete interval computation for depth 13, residue 4257. -/ +theorem bounds_13_4257 : exactInterval 13 4257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4257 : oddCount 4257 13 = 8 ∧ acceleratedOrbit 13 4257 = 3412 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4257) = 3 ^ 8 * m + 3412 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4257.1, data_13_4257.2] + +/-- Complete interval computation for depth 13, residue 4258. -/ +theorem bounds_13_4258 : exactInterval 13 4258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4258 : oddCount 4258 13 = 6 ∧ acceleratedOrbit 13 4258 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4258) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4258.1, data_13_4258.2] + +end Collatz.Research.StoppingAtlas.Batch0744 From c40d0cf176222e113e82d93a92d99dc556cca0e4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:37 +0530 Subject: [PATCH 0745/1001] proof: certify atlas Batch0745 (13:4259 to 13:4274) --- Collatz/Research/StoppingAtlas/Batch0745.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0745.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0745.lean b/Collatz/Research/StoppingAtlas/Batch0745.lean new file mode 100644 index 00000000..76dd11be --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0745.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0745 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4259. -/ +theorem bounds_13_4259 : exactInterval 13 4259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4259 : oddCount 4259 13 = 6 ∧ acceleratedOrbit 13 4259 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4259) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4259.1, data_13_4259.2] + +/-- Complete interval computation for depth 13, residue 4260. -/ +theorem bounds_13_4260 : exactInterval 13 4260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4260 : oddCount 4260 13 = 7 ∧ acceleratedOrbit 13 4260 = 1139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4260) = 3 ^ 7 * m + 1139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4260.1, data_13_4260.2] + +/-- Complete interval computation for depth 13, residue 4261. -/ +theorem bounds_13_4261 : exactInterval 13 4261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4261 : oddCount 4261 13 = 7 ∧ acceleratedOrbit 13 4261 = 1139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4261) = 3 ^ 7 * m + 1139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4261.1, data_13_4261.2] + +/-- Complete interval computation for depth 13, residue 4262. -/ +theorem bounds_13_4262 : exactInterval 13 4262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4262 : oddCount 4262 13 = 7 ∧ acceleratedOrbit 13 4262 = 1139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4262) = 3 ^ 7 * m + 1139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4262.1, data_13_4262.2] + +/-- Complete interval computation for depth 13, residue 4263. -/ +theorem bounds_13_4263 : exactInterval 13 4263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4263 : oddCount 4263 13 = 10 ∧ acceleratedOrbit 13 4263 = 30739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4263) = 3 ^ 10 * m + 30739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4263.1, data_13_4263.2] + +/-- Complete interval computation for depth 13, residue 4264. -/ +theorem bounds_13_4264 : exactInterval 13 4264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4264 : oddCount 4264 13 = 4 ∧ acceleratedOrbit 13 4264 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4264) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4264.1, data_13_4264.2] + +/-- Complete interval computation for depth 13, residue 4265. -/ +theorem bounds_13_4265 : exactInterval 13 4265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4265 : oddCount 4265 13 = 10 ∧ acceleratedOrbit 13 4265 = 30755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4265) = 3 ^ 10 * m + 30755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4265.1, data_13_4265.2] + +/-- Complete interval computation for depth 13, residue 4266. -/ +theorem bounds_13_4266 : exactInterval 13 4266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4266 : oddCount 4266 13 = 4 ∧ acceleratedOrbit 13 4266 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4266) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4266.1, data_13_4266.2] + +/-- Complete interval computation for depth 13, residue 4267. -/ +theorem bounds_13_4267 : exactInterval 13 4267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4267 : oddCount 4267 13 = 6 ∧ acceleratedOrbit 13 4267 = 380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4267) = 3 ^ 6 * m + 380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4267.1, data_13_4267.2] + +/-- Complete interval computation for depth 13, residue 4268. -/ +theorem bounds_13_4268 : exactInterval 13 4268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4268 : oddCount 4268 13 = 5 ∧ acceleratedOrbit 13 4268 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4268) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4268.1, data_13_4268.2] + +/-- Complete interval computation for depth 13, residue 4269. -/ +theorem bounds_13_4269 : exactInterval 13 4269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4269 : oddCount 4269 13 = 5 ∧ acceleratedOrbit 13 4269 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4269) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4269.1, data_13_4269.2] + +/-- Complete interval computation for depth 13, residue 4270. -/ +theorem bounds_13_4270 : exactInterval 13 4270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4270 : oddCount 4270 13 = 5 ∧ acceleratedOrbit 13 4270 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4270) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4270.1, data_13_4270.2] + +/-- Complete interval computation for depth 13, residue 4271. -/ +theorem bounds_13_4271 : exactInterval 13 4271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4271 : oddCount 4271 13 = 8 ∧ acceleratedOrbit 13 4271 = 3422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4271) = 3 ^ 8 * m + 3422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4271.1, data_13_4271.2] + +/-- Complete interval computation for depth 13, residue 4272. -/ +theorem bounds_13_4272 : exactInterval 13 4272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4272 : oddCount 4272 13 = 5 ∧ acceleratedOrbit 13 4272 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4272) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4272.1, data_13_4272.2] + +/-- Complete interval computation for depth 13, residue 4273. -/ +theorem bounds_13_4273 : exactInterval 13 4273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4273 : oddCount 4273 13 = 5 ∧ acceleratedOrbit 13 4273 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4273) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4273.1, data_13_4273.2] + +/-- Complete interval computation for depth 13, residue 4274. -/ +theorem bounds_13_4274 : exactInterval 13 4274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4274 : oddCount 4274 13 = 5 ∧ acceleratedOrbit 13 4274 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4274) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4274.1, data_13_4274.2] + +end Collatz.Research.StoppingAtlas.Batch0745 From 9d760c122076f2aa7bb79cb851571220a36fee62 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:38 +0530 Subject: [PATCH 0746/1001] proof: certify atlas Batch0746 (13:4275 to 13:4289) --- Collatz/Research/StoppingAtlas/Batch0746.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0746.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0746.lean b/Collatz/Research/StoppingAtlas/Batch0746.lean new file mode 100644 index 00000000..c5dccfb9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0746.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0746 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4275. -/ +theorem bounds_13_4275 : exactInterval 13 4275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4275 : oddCount 4275 13 = 5 ∧ acceleratedOrbit 13 4275 = 127 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4275) = 3 ^ 5 * m + 127 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4275.1, data_13_4275.2] + +/-- Complete interval computation for depth 13, residue 4276. -/ +theorem bounds_13_4276 : exactInterval 13 4276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4276 : oddCount 4276 13 = 5 ∧ acceleratedOrbit 13 4276 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4276) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4276.1, data_13_4276.2] + +/-- Complete interval computation for depth 13, residue 4277. -/ +theorem bounds_13_4277 : exactInterval 13 4277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4277 : oddCount 4277 13 = 5 ∧ acceleratedOrbit 13 4277 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4277) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4277.1, data_13_4277.2] + +/-- Complete interval computation for depth 13, residue 4278. -/ +theorem bounds_13_4278 : exactInterval 13 4278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4278 : oddCount 4278 13 = 10 ∧ acceleratedOrbit 13 4278 = 30860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4278) = 3 ^ 10 * m + 30860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4278.1, data_13_4278.2] + +/-- Complete interval computation for depth 13, residue 4279. -/ +theorem bounds_13_4279 : exactInterval 13 4279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4279 : oddCount 4279 13 = 10 ∧ acceleratedOrbit 13 4279 = 30860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4279) = 3 ^ 10 * m + 30860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4279.1, data_13_4279.2] + +/-- Complete interval computation for depth 13, residue 4280. -/ +theorem bounds_13_4280 : exactInterval 13 4280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4280 : oddCount 4280 13 = 5 ∧ acceleratedOrbit 13 4280 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4280) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4280.1, data_13_4280.2] + +/-- Complete interval computation for depth 13, residue 4281. -/ +theorem bounds_13_4281 : exactInterval 13 4281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4281 : oddCount 4281 13 = 7 ∧ acceleratedOrbit 13 4281 = 1144 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4281) = 3 ^ 7 * m + 1144 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4281.1, data_13_4281.2] + +/-- Complete interval computation for depth 13, residue 4282. -/ +theorem bounds_13_4282 : exactInterval 13 4282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4282 : oddCount 4282 13 = 5 ∧ acceleratedOrbit 13 4282 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4282) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4282.1, data_13_4282.2] + +/-- Complete interval computation for depth 13, residue 4283. -/ +theorem bounds_13_4283 : exactInterval 13 4283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4283 : oddCount 4283 13 = 7 ∧ acceleratedOrbit 13 4283 = 1144 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4283) = 3 ^ 7 * m + 1144 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4283.1, data_13_4283.2] + +/-- Complete interval computation for depth 13, residue 4284. -/ +theorem bounds_13_4284 : exactInterval 13 4284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4284 : oddCount 4284 13 = 7 ∧ acceleratedOrbit 13 4284 = 1145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4284) = 3 ^ 7 * m + 1145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4284.1, data_13_4284.2] + +/-- Complete interval computation for depth 13, residue 4285. -/ +theorem bounds_13_4285 : exactInterval 13 4285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4285 : oddCount 4285 13 = 7 ∧ acceleratedOrbit 13 4285 = 1145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4285) = 3 ^ 7 * m + 1145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4285.1, data_13_4285.2] + +/-- Complete interval computation for depth 13, residue 4286. -/ +theorem bounds_13_4286 : exactInterval 13 4286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4286 : oddCount 4286 13 = 7 ∧ acceleratedOrbit 13 4286 = 1145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4286) = 3 ^ 7 * m + 1145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4286.1, data_13_4286.2] + +/-- Complete interval computation for depth 13, residue 4287. -/ +theorem bounds_13_4287 : exactInterval 13 4287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4287 : oddCount 4287 13 = 9 ∧ acceleratedOrbit 13 4287 = 10304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4287) = 3 ^ 9 * m + 10304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4287.1, data_13_4287.2] + +/-- Complete interval computation for depth 13, residue 4288. -/ +theorem bounds_13_4288 : exactInterval 13 4288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4288 : oddCount 4288 13 = 4 ∧ acceleratedOrbit 13 4288 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4288) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4288.1, data_13_4288.2] + +/-- Complete interval computation for depth 13, residue 4289. -/ +theorem bounds_13_4289 : exactInterval 13 4289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4289 : oddCount 4289 13 = 7 ∧ acceleratedOrbit 13 4289 = 1147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4289) = 3 ^ 7 * m + 1147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4289.1, data_13_4289.2] + +end Collatz.Research.StoppingAtlas.Batch0746 From b07e7afec9827505199c0bf9bc8047285f428fa2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:39 +0530 Subject: [PATCH 0747/1001] proof: certify atlas Batch0747 (13:4290 to 13:4304) --- Collatz/Research/StoppingAtlas/Batch0747.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0747.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0747.lean b/Collatz/Research/StoppingAtlas/Batch0747.lean new file mode 100644 index 00000000..8fdf41b7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0747.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0747 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4290. -/ +theorem bounds_13_4290 : exactInterval 13 4290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4290 : oddCount 4290 13 = 7 ∧ acceleratedOrbit 13 4290 = 1147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4290) = 3 ^ 7 * m + 1147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4290.1, data_13_4290.2] + +/-- Complete interval computation for depth 13, residue 4291. -/ +theorem bounds_13_4291 : exactInterval 13 4291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4291 : oddCount 4291 13 = 7 ∧ acceleratedOrbit 13 4291 = 1147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4291) = 3 ^ 7 * m + 1147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4291.1, data_13_4291.2] + +/-- Complete interval computation for depth 13, residue 4292. -/ +theorem bounds_13_4292 : exactInterval 13 4292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4292 : oddCount 4292 13 = 5 ∧ acceleratedOrbit 13 4292 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4292) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4292.1, data_13_4292.2] + +/-- Complete interval computation for depth 13, residue 4293. -/ +theorem bounds_13_4293 : exactInterval 13 4293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4293 : oddCount 4293 13 = 5 ∧ acceleratedOrbit 13 4293 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4293) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4293.1, data_13_4293.2] + +/-- Complete interval computation for depth 13, residue 4294. -/ +theorem bounds_13_4294 : exactInterval 13 4294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4294 : oddCount 4294 13 = 5 ∧ acceleratedOrbit 13 4294 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4294) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4294.1, data_13_4294.2] + +/-- Complete interval computation for depth 13, residue 4295. -/ +theorem bounds_13_4295 : exactInterval 13 4295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4295 : oddCount 4295 13 = 8 ∧ acceleratedOrbit 13 4295 = 3442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4295) = 3 ^ 8 * m + 3442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4295.1, data_13_4295.2] + +/-- Complete interval computation for depth 13, residue 4296. -/ +theorem bounds_13_4296 : exactInterval 13 4296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4296 : oddCount 4296 13 = 5 ∧ acceleratedOrbit 13 4296 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4296) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4296.1, data_13_4296.2] + +/-- Complete interval computation for depth 13, residue 4297. -/ +theorem bounds_13_4297 : exactInterval 13 4297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4297 : oddCount 4297 13 = 5 ∧ acceleratedOrbit 13 4297 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4297) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4297.1, data_13_4297.2] + +/-- Complete interval computation for depth 13, residue 4298. -/ +theorem bounds_13_4298 : exactInterval 13 4298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4298 : oddCount 4298 13 = 5 ∧ acceleratedOrbit 13 4298 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4298) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4298.1, data_13_4298.2] + +/-- Complete interval computation for depth 13, residue 4299. -/ +theorem bounds_13_4299 : exactInterval 13 4299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4299 : oddCount 4299 13 = 6 ∧ acceleratedOrbit 13 4299 = 383 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4299) = 3 ^ 6 * m + 383 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4299.1, data_13_4299.2] + +/-- Complete interval computation for depth 13, residue 4300. -/ +theorem bounds_13_4300 : exactInterval 13 4300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4300 : oddCount 4300 13 = 5 ∧ acceleratedOrbit 13 4300 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4300) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4300.1, data_13_4300.2] + +/-- Complete interval computation for depth 13, residue 4301. -/ +theorem bounds_13_4301 : exactInterval 13 4301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4301 : oddCount 4301 13 = 5 ∧ acceleratedOrbit 13 4301 = 128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4301) = 3 ^ 5 * m + 128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4301.1, data_13_4301.2] + +/-- Complete interval computation for depth 13, residue 4302. -/ +theorem bounds_13_4302 : exactInterval 13 4302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4302 : oddCount 4302 13 = 9 ∧ acceleratedOrbit 13 4302 = 10343 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4302) = 3 ^ 9 * m + 10343 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4302.1, data_13_4302.2] + +/-- Complete interval computation for depth 13, residue 4303. -/ +theorem bounds_13_4303 : exactInterval 13 4303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4303 : oddCount 4303 13 = 9 ∧ acceleratedOrbit 13 4303 = 10343 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4303) = 3 ^ 9 * m + 10343 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4303.1, data_13_4303.2] + +/-- Complete interval computation for depth 13, residue 4304. -/ +theorem bounds_13_4304 : exactInterval 13 4304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4304 : oddCount 4304 13 = 4 ∧ acceleratedOrbit 13 4304 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4304) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4304.1, data_13_4304.2] + +end Collatz.Research.StoppingAtlas.Batch0747 From 371259335e267ecd56d1a746593ac4c75bfcb1e4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:45 +0530 Subject: [PATCH 0748/1001] proof: certify atlas Batch0748 (13:4305 to 13:4320) --- Collatz/Research/StoppingAtlas/Batch0748.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0748.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0748.lean b/Collatz/Research/StoppingAtlas/Batch0748.lean new file mode 100644 index 00000000..d4a7df94 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0748.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0748 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4305. -/ +theorem bounds_13_4305 : exactInterval 13 4305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4305 : oddCount 4305 13 = 7 ∧ acceleratedOrbit 13 4305 = 1151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4305) = 3 ^ 7 * m + 1151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4305.1, data_13_4305.2] + +/-- Complete interval computation for depth 13, residue 4306. -/ +theorem bounds_13_4306 : exactInterval 13 4306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4306 : oddCount 4306 13 = 7 ∧ acceleratedOrbit 13 4306 = 1151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4306) = 3 ^ 7 * m + 1151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4306.1, data_13_4306.2] + +/-- Complete interval computation for depth 13, residue 4307. -/ +theorem bounds_13_4307 : exactInterval 13 4307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4307 : oddCount 4307 13 = 7 ∧ acceleratedOrbit 13 4307 = 1151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4307) = 3 ^ 7 * m + 1151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4307.1, data_13_4307.2] + +/-- Complete interval computation for depth 13, residue 4308. -/ +theorem bounds_13_4308 : exactInterval 13 4308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4308 : oddCount 4308 13 = 4 ∧ acceleratedOrbit 13 4308 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4308) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4308.1, data_13_4308.2] + +/-- Complete interval computation for depth 13, residue 4309. -/ +theorem bounds_13_4309 : exactInterval 13 4309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4309 : oddCount 4309 13 = 4 ∧ acceleratedOrbit 13 4309 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4309) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4309.1, data_13_4309.2] + +/-- Complete interval computation for depth 13, residue 4310. -/ +theorem bounds_13_4310 : exactInterval 13 4310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4310 : oddCount 4310 13 = 9 ∧ acceleratedOrbit 13 4310 = 10367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4310) = 3 ^ 9 * m + 10367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4310.1, data_13_4310.2] + +/-- Complete interval computation for depth 13, residue 4311. -/ +theorem bounds_13_4311 : exactInterval 13 4311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4311 : oddCount 4311 13 = 9 ∧ acceleratedOrbit 13 4311 = 10367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4311) = 3 ^ 9 * m + 10367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4311.1, data_13_4311.2] + +/-- Complete interval computation for depth 13, residue 4312. -/ +theorem bounds_13_4312 : exactInterval 13 4312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4312 : oddCount 4312 13 = 7 ∧ acceleratedOrbit 13 4312 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4312) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4312.1, data_13_4312.2] + +/-- Complete interval computation for depth 13, residue 4313. -/ +theorem bounds_13_4313 : exactInterval 13 4313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4313 : oddCount 4313 13 = 7 ∧ acceleratedOrbit 13 4313 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4313) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4313.1, data_13_4313.2] + +/-- Complete interval computation for depth 13, residue 4314. -/ +theorem bounds_13_4314 : exactInterval 13 4314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4314 : oddCount 4314 13 = 7 ∧ acceleratedOrbit 13 4314 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4314) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4314.1, data_13_4314.2] + +/-- Complete interval computation for depth 13, residue 4315. -/ +theorem bounds_13_4315 : exactInterval 13 4315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4315 : oddCount 4315 13 = 8 ∧ acceleratedOrbit 13 4315 = 3458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4315) = 3 ^ 8 * m + 3458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4315.1, data_13_4315.2] + +/-- Complete interval computation for depth 13, residue 4316. -/ +theorem bounds_13_4316 : exactInterval 13 4316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4316 : oddCount 4316 13 = 7 ∧ acceleratedOrbit 13 4316 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4316) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4316.1, data_13_4316.2] + +/-- Complete interval computation for depth 13, residue 4317. -/ +theorem bounds_13_4317 : exactInterval 13 4317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4317 : oddCount 4317 13 = 7 ∧ acceleratedOrbit 13 4317 = 1154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4317) = 3 ^ 7 * m + 1154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4317.1, data_13_4317.2] + +/-- Complete interval computation for depth 13, residue 4318. -/ +theorem bounds_13_4318 : exactInterval 13 4318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4318 : oddCount 4318 13 = 9 ∧ acceleratedOrbit 13 4318 = 10381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4318) = 3 ^ 9 * m + 10381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4318.1, data_13_4318.2] + +/-- Complete interval computation for depth 13, residue 4319. -/ +theorem bounds_13_4319 : exactInterval 13 4319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4319 : oddCount 4319 13 = 9 ∧ acceleratedOrbit 13 4319 = 10381 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4319) = 3 ^ 9 * m + 10381 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4319.1, data_13_4319.2] + +/-- Complete interval computation for depth 13, residue 4320. -/ +theorem bounds_13_4320 : exactInterval 13 4320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4320 : oddCount 4320 13 = 4 ∧ acceleratedOrbit 13 4320 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4320) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4320.1, data_13_4320.2] + +end Collatz.Research.StoppingAtlas.Batch0748 From aacfaa1a3edd7f2b4eeacae3c7317a2eee77dd9e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:46 +0530 Subject: [PATCH 0749/1001] proof: certify atlas Batch0749 (13:4321 to 13:4335) --- Collatz/Research/StoppingAtlas/Batch0749.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0749.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0749.lean b/Collatz/Research/StoppingAtlas/Batch0749.lean new file mode 100644 index 00000000..38367877 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0749.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0749 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4321. -/ +theorem bounds_13_4321 : exactInterval 13 4321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4321 : oddCount 4321 13 = 9 ∧ acceleratedOrbit 13 4321 = 10388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4321) = 3 ^ 9 * m + 10388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4321.1, data_13_4321.2] + +/-- Complete interval computation for depth 13, residue 4322. -/ +theorem bounds_13_4322 : exactInterval 13 4322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4322 : oddCount 4322 13 = 4 ∧ acceleratedOrbit 13 4322 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4322) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4322.1, data_13_4322.2] + +/-- Complete interval computation for depth 13, residue 4323. -/ +theorem bounds_13_4323 : exactInterval 13 4323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4323 : oddCount 4323 13 = 4 ∧ acceleratedOrbit 13 4323 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4323) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4323.1, data_13_4323.2] + +/-- Complete interval computation for depth 13, residue 4324. -/ +theorem bounds_13_4324 : exactInterval 13 4324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4324 : oddCount 4324 13 = 6 ∧ acceleratedOrbit 13 4324 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4324) = 3 ^ 6 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4324.1, data_13_4324.2] + +/-- Complete interval computation for depth 13, residue 4325. -/ +theorem bounds_13_4325 : exactInterval 13 4325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4325 : oddCount 4325 13 = 6 ∧ acceleratedOrbit 13 4325 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4325) = 3 ^ 6 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4325.1, data_13_4325.2] + +/-- Complete interval computation for depth 13, residue 4326. -/ +theorem bounds_13_4326 : exactInterval 13 4326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4326 : oddCount 4326 13 = 6 ∧ acceleratedOrbit 13 4326 = 386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4326) = 3 ^ 6 * m + 386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4326.1, data_13_4326.2] + +/-- Complete interval computation for depth 13, residue 4327. -/ +theorem bounds_13_4327 : exactInterval 13 4327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4327 : oddCount 4327 13 = 8 ∧ acceleratedOrbit 13 4327 = 3467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4327) = 3 ^ 8 * m + 3467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4327.1, data_13_4327.2] + +/-- Complete interval computation for depth 13, residue 4328. -/ +theorem bounds_13_4328 : exactInterval 13 4328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4328 : oddCount 4328 13 = 4 ∧ acceleratedOrbit 13 4328 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4328) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4328.1, data_13_4328.2] + +/-- Complete interval computation for depth 13, residue 4329. -/ +theorem bounds_13_4329 : exactInterval 13 4329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4329 : oddCount 4329 13 = 8 ∧ acceleratedOrbit 13 4329 = 3469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4329) = 3 ^ 8 * m + 3469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4329.1, data_13_4329.2] + +/-- Complete interval computation for depth 13, residue 4330. -/ +theorem bounds_13_4330 : exactInterval 13 4330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4330 : oddCount 4330 13 = 4 ∧ acceleratedOrbit 13 4330 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4330) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4330.1, data_13_4330.2] + +/-- Complete interval computation for depth 13, residue 4331. -/ +theorem bounds_13_4331 : exactInterval 13 4331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4331 : oddCount 4331 13 = 9 ∧ acceleratedOrbit 13 4331 = 10412 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4331) = 3 ^ 9 * m + 10412 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4331.1, data_13_4331.2] + +/-- Complete interval computation for depth 13, residue 4332. -/ +theorem bounds_13_4332 : exactInterval 13 4332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4332 : oddCount 4332 13 = 7 ∧ acceleratedOrbit 13 4332 = 1160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4332) = 3 ^ 7 * m + 1160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4332.1, data_13_4332.2] + +/-- Complete interval computation for depth 13, residue 4333. -/ +theorem bounds_13_4333 : exactInterval 13 4333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4333 : oddCount 4333 13 = 7 ∧ acceleratedOrbit 13 4333 = 1160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4333) = 3 ^ 7 * m + 1160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4333.1, data_13_4333.2] + +/-- Complete interval computation for depth 13, residue 4334. -/ +theorem bounds_13_4334 : exactInterval 13 4334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4334 : oddCount 4334 13 = 7 ∧ acceleratedOrbit 13 4334 = 1160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4334) = 3 ^ 7 * m + 1160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4334.1, data_13_4334.2] + +/-- Complete interval computation for depth 13, residue 4335. -/ +theorem bounds_13_4335 : exactInterval 13 4335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4335 : oddCount 4335 13 = 10 ∧ acceleratedOrbit 13 4335 = 31256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4335) = 3 ^ 10 * m + 31256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4335.1, data_13_4335.2] + +end Collatz.Research.StoppingAtlas.Batch0749 From e6536be0aec09dfd59f6a03ec40174dc8118428f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:48 +0530 Subject: [PATCH 0750/1001] proof: certify atlas Batch0750 (13:4336 to 13:4351) --- Collatz/Research/StoppingAtlas/Batch0750.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0750.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0750.lean b/Collatz/Research/StoppingAtlas/Batch0750.lean new file mode 100644 index 00000000..34e25acc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0750.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0750 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4336. -/ +theorem bounds_13_4336 : exactInterval 13 4336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4336 : oddCount 4336 13 = 4 ∧ acceleratedOrbit 13 4336 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4336) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4336.1, data_13_4336.2] + +/-- Complete interval computation for depth 13, residue 4337. -/ +theorem bounds_13_4337 : exactInterval 13 4337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4337 : oddCount 4337 13 = 4 ∧ acceleratedOrbit 13 4337 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4337) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4337.1, data_13_4337.2] + +/-- Complete interval computation for depth 13, residue 4338. -/ +theorem bounds_13_4338 : exactInterval 13 4338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4338 : oddCount 4338 13 = 8 ∧ acceleratedOrbit 13 4338 = 3478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4338) = 3 ^ 8 * m + 3478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4338.1, data_13_4338.2] + +/-- Complete interval computation for depth 13, residue 4339. -/ +theorem bounds_13_4339 : exactInterval 13 4339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4339 : oddCount 4339 13 = 8 ∧ acceleratedOrbit 13 4339 = 3478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4339) = 3 ^ 8 * m + 3478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4339.1, data_13_4339.2] + +/-- Complete interval computation for depth 13, residue 4340. -/ +theorem bounds_13_4340 : exactInterval 13 4340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4340 : oddCount 4340 13 = 4 ∧ acceleratedOrbit 13 4340 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4340) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4340.1, data_13_4340.2] + +/-- Complete interval computation for depth 13, residue 4341. -/ +theorem bounds_13_4341 : exactInterval 13 4341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4341 : oddCount 4341 13 = 4 ∧ acceleratedOrbit 13 4341 = 43 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4341) = 3 ^ 4 * m + 43 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4341.1, data_13_4341.2] + +/-- Complete interval computation for depth 13, residue 4342. -/ +theorem bounds_13_4342 : exactInterval 13 4342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4342 : oddCount 4342 13 = 8 ∧ acceleratedOrbit 13 4342 = 3482 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4342) = 3 ^ 8 * m + 3482 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4342.1, data_13_4342.2] + +/-- Complete interval computation for depth 13, residue 4343. -/ +theorem bounds_13_4343 : exactInterval 13 4343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4343 : oddCount 4343 13 = 8 ∧ acceleratedOrbit 13 4343 = 3482 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4343) = 3 ^ 8 * m + 3482 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4343.1, data_13_4343.2] + +/-- Complete interval computation for depth 13, residue 4344. -/ +theorem bounds_13_4344 : exactInterval 13 4344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4344 : oddCount 4344 13 = 7 ∧ acceleratedOrbit 13 4344 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4344) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4344.1, data_13_4344.2] + +/-- Complete interval computation for depth 13, residue 4345. -/ +theorem bounds_13_4345 : exactInterval 13 4345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4345 : oddCount 4345 13 = 9 ∧ acceleratedOrbit 13 4345 = 10448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4345) = 3 ^ 9 * m + 10448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4345.1, data_13_4345.2] + +/-- Complete interval computation for depth 13, residue 4346. -/ +theorem bounds_13_4346 : exactInterval 13 4346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4346 : oddCount 4346 13 = 7 ∧ acceleratedOrbit 13 4346 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4346) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4346.1, data_13_4346.2] + +/-- Complete interval computation for depth 13, residue 4347. -/ +theorem bounds_13_4347 : exactInterval 13 4347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4347 : oddCount 4347 13 = 11 ∧ acceleratedOrbit 13 4347 = 94040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4347) = 3 ^ 11 * m + 94040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4347.1, data_13_4347.2] + +/-- Complete interval computation for depth 13, residue 4348. -/ +theorem bounds_13_4348 : exactInterval 13 4348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4348 : oddCount 4348 13 = 7 ∧ acceleratedOrbit 13 4348 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4348) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4348.1, data_13_4348.2] + +/-- Complete interval computation for depth 13, residue 4349. -/ +theorem bounds_13_4349 : exactInterval 13 4349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4349 : oddCount 4349 13 = 7 ∧ acceleratedOrbit 13 4349 = 1162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4349) = 3 ^ 7 * m + 1162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4349.1, data_13_4349.2] + +/-- Complete interval computation for depth 13, residue 4350. -/ +theorem bounds_13_4350 : exactInterval 13 4350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4350 : oddCount 4350 13 = 9 ∧ acceleratedOrbit 13 4350 = 10457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4350) = 3 ^ 9 * m + 10457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4350.1, data_13_4350.2] + +/-- Complete interval computation for depth 13, residue 4351. -/ +theorem bounds_13_4351 : exactInterval 13 4351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4351 : oddCount 4351 13 = 9 ∧ acceleratedOrbit 13 4351 = 10457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4351) = 3 ^ 9 * m + 10457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4351.1, data_13_4351.2] + +end Collatz.Research.StoppingAtlas.Batch0750 From 9772484e42127b389fb99cb260f85325244b6405 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:55 +0530 Subject: [PATCH 0751/1001] proof: certify atlas Batch0751 (13:4352 to 13:4366) --- Collatz/Research/StoppingAtlas/Batch0751.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0751.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0751.lean b/Collatz/Research/StoppingAtlas/Batch0751.lean new file mode 100644 index 00000000..f9382632 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0751.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0751 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4352. -/ +theorem bounds_13_4352 : exactInterval 13 4352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4352 : oddCount 4352 13 = 2 ∧ acceleratedOrbit 13 4352 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4352) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4352.1, data_13_4352.2] + +/-- Complete interval computation for depth 13, residue 4353. -/ +theorem bounds_13_4353 : exactInterval 13 4353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4353 : oddCount 4353 13 = 6 ∧ acceleratedOrbit 13 4353 = 388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4353) = 3 ^ 6 * m + 388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4353.1, data_13_4353.2] + +/-- Complete interval computation for depth 13, residue 4354. -/ +theorem bounds_13_4354 : exactInterval 13 4354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4354 : oddCount 4354 13 = 6 ∧ acceleratedOrbit 13 4354 = 388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4354) = 3 ^ 6 * m + 388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4354.1, data_13_4354.2] + +/-- Complete interval computation for depth 13, residue 4355. -/ +theorem bounds_13_4355 : exactInterval 13 4355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4355 : oddCount 4355 13 = 6 ∧ acceleratedOrbit 13 4355 = 388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4355) = 3 ^ 6 * m + 388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4355.1, data_13_4355.2] + +/-- Complete interval computation for depth 13, residue 4356. -/ +theorem bounds_13_4356 : exactInterval 13 4356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4356 : oddCount 4356 13 = 5 ∧ acceleratedOrbit 13 4356 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4356) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4356.1, data_13_4356.2] + +/-- Complete interval computation for depth 13, residue 4357. -/ +theorem bounds_13_4357 : exactInterval 13 4357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4357 : oddCount 4357 13 = 5 ∧ acceleratedOrbit 13 4357 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4357) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4357.1, data_13_4357.2] + +/-- Complete interval computation for depth 13, residue 4358. -/ +theorem bounds_13_4358 : exactInterval 13 4358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4358 : oddCount 4358 13 = 5 ∧ acceleratedOrbit 13 4358 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4358) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4358.1, data_13_4358.2] + +/-- Complete interval computation for depth 13, residue 4359. -/ +theorem bounds_13_4359 : exactInterval 13 4359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4359 : oddCount 4359 13 = 8 ∧ acceleratedOrbit 13 4359 = 3493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4359) = 3 ^ 8 * m + 3493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4359.1, data_13_4359.2] + +/-- Complete interval computation for depth 13, residue 4360. -/ +theorem bounds_13_4360 : exactInterval 13 4360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4360 : oddCount 4360 13 = 5 ∧ acceleratedOrbit 13 4360 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4360) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4360.1, data_13_4360.2] + +/-- Complete interval computation for depth 13, residue 4361. -/ +theorem bounds_13_4361 : exactInterval 13 4361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4361 : oddCount 4361 13 = 7 ∧ acceleratedOrbit 13 4361 = 1165 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4361) = 3 ^ 7 * m + 1165 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4361.1, data_13_4361.2] + +/-- Complete interval computation for depth 13, residue 4362. -/ +theorem bounds_13_4362 : exactInterval 13 4362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4362 : oddCount 4362 13 = 5 ∧ acceleratedOrbit 13 4362 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4362) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4362.1, data_13_4362.2] + +/-- Complete interval computation for depth 13, residue 4363. -/ +theorem bounds_13_4363 : exactInterval 13 4363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4363 : oddCount 4363 13 = 6 ∧ acceleratedOrbit 13 4363 = 389 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4363) = 3 ^ 6 * m + 389 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4363.1, data_13_4363.2] + +/-- Complete interval computation for depth 13, residue 4364. -/ +theorem bounds_13_4364 : exactInterval 13 4364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4364 : oddCount 4364 13 = 5 ∧ acceleratedOrbit 13 4364 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4364) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4364.1, data_13_4364.2] + +/-- Complete interval computation for depth 13, residue 4365. -/ +theorem bounds_13_4365 : exactInterval 13 4365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4365 : oddCount 4365 13 = 5 ∧ acceleratedOrbit 13 4365 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4365) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4365.1, data_13_4365.2] + +/-- Complete interval computation for depth 13, residue 4366. -/ +theorem bounds_13_4366 : exactInterval 13 4366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4366 : oddCount 4366 13 = 6 ∧ acceleratedOrbit 13 4366 = 389 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4366) = 3 ^ 6 * m + 389 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4366.1, data_13_4366.2] + +end Collatz.Research.StoppingAtlas.Batch0751 From f2a060799b46b839b61d32854096739e5f3af688 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:55 +0530 Subject: [PATCH 0752/1001] proof: certify atlas Batch0752 (13:4367 to 13:4381) --- Collatz/Research/StoppingAtlas/Batch0752.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0752.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0752.lean b/Collatz/Research/StoppingAtlas/Batch0752.lean new file mode 100644 index 00000000..54a0ab9b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0752.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0752 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4367. -/ +theorem bounds_13_4367 : exactInterval 13 4367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4367 : oddCount 4367 13 = 6 ∧ acceleratedOrbit 13 4367 = 389 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4367) = 3 ^ 6 * m + 389 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4367.1, data_13_4367.2] + +/-- Complete interval computation for depth 13, residue 4368. -/ +theorem bounds_13_4368 : exactInterval 13 4368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4368 : oddCount 4368 13 = 4 ∧ acceleratedOrbit 13 4368 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4368) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4368.1, data_13_4368.2] + +/-- Complete interval computation for depth 13, residue 4369. -/ +theorem bounds_13_4369 : exactInterval 13 4369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4369 : oddCount 4369 13 = 5 ∧ acceleratedOrbit 13 4369 = 130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4369) = 3 ^ 5 * m + 130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4369.1, data_13_4369.2] + +/-- Complete interval computation for depth 13, residue 4370. -/ +theorem bounds_13_4370 : exactInterval 13 4370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4370 : oddCount 4370 13 = 8 ∧ acceleratedOrbit 13 4370 = 3503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4370) = 3 ^ 8 * m + 3503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4370.1, data_13_4370.2] + +/-- Complete interval computation for depth 13, residue 4371. -/ +theorem bounds_13_4371 : exactInterval 13 4371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4371 : oddCount 4371 13 = 8 ∧ acceleratedOrbit 13 4371 = 3503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4371) = 3 ^ 8 * m + 3503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4371.1, data_13_4371.2] + +/-- Complete interval computation for depth 13, residue 4372. -/ +theorem bounds_13_4372 : exactInterval 13 4372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4372 : oddCount 4372 13 = 4 ∧ acceleratedOrbit 13 4372 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4372) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4372.1, data_13_4372.2] + +/-- Complete interval computation for depth 13, residue 4373. -/ +theorem bounds_13_4373 : exactInterval 13 4373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4373 : oddCount 4373 13 = 4 ∧ acceleratedOrbit 13 4373 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4373) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4373.1, data_13_4373.2] + +/-- Complete interval computation for depth 13, residue 4374. -/ +theorem bounds_13_4374 : exactInterval 13 4374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4374 : oddCount 4374 13 = 8 ∧ acceleratedOrbit 13 4374 = 3509 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4374) = 3 ^ 8 * m + 3509 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4374.1, data_13_4374.2] + +/-- Complete interval computation for depth 13, residue 4375. -/ +theorem bounds_13_4375 : exactInterval 13 4375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4375) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4375 : oddCount 4375 13 = 8 ∧ acceleratedOrbit 13 4375 = 3509 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4375) = 3 ^ 8 * m + 3509 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4375.1, data_13_4375.2] + +/-- Complete interval computation for depth 13, residue 4376. -/ +theorem bounds_13_4376 : exactInterval 13 4376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4376 : oddCount 4376 13 = 4 ∧ acceleratedOrbit 13 4376 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4376) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4376.1, data_13_4376.2] + +/-- Complete interval computation for depth 13, residue 4377. -/ +theorem bounds_13_4377 : exactInterval 13 4377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4377 : oddCount 4377 13 = 8 ∧ acceleratedOrbit 13 4377 = 3509 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4377) = 3 ^ 8 * m + 3509 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4377.1, data_13_4377.2] + +/-- Complete interval computation for depth 13, residue 4378. -/ +theorem bounds_13_4378 : exactInterval 13 4378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4378 : oddCount 4378 13 = 4 ∧ acceleratedOrbit 13 4378 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4378) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4378.1, data_13_4378.2] + +/-- Complete interval computation for depth 13, residue 4379. -/ +theorem bounds_13_4379 : exactInterval 13 4379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4379 : oddCount 4379 13 = 9 ∧ acceleratedOrbit 13 4379 = 10525 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4379) = 3 ^ 9 * m + 10525 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4379.1, data_13_4379.2] + +/-- Complete interval computation for depth 13, residue 4380. -/ +theorem bounds_13_4380 : exactInterval 13 4380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4380 : oddCount 4380 13 = 7 ∧ acceleratedOrbit 13 4380 = 1171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4380) = 3 ^ 7 * m + 1171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4380.1, data_13_4380.2] + +/-- Complete interval computation for depth 13, residue 4381. -/ +theorem bounds_13_4381 : exactInterval 13 4381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4381 : oddCount 4381 13 = 7 ∧ acceleratedOrbit 13 4381 = 1171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4381) = 3 ^ 7 * m + 1171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4381.1, data_13_4381.2] + +end Collatz.Research.StoppingAtlas.Batch0752 From 418aecad2faadf4fe6422fc40d18e4259090259e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:34:59 +0530 Subject: [PATCH 0753/1001] proof: certify atlas Batch0753 (13:4382 to 13:4397) --- Collatz/Research/StoppingAtlas/Batch0753.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0753.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0753.lean b/Collatz/Research/StoppingAtlas/Batch0753.lean new file mode 100644 index 00000000..ae619b97 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0753.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0753 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4382. -/ +theorem bounds_13_4382 : exactInterval 13 4382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4382 : oddCount 4382 13 = 7 ∧ acceleratedOrbit 13 4382 = 1171 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4382) = 3 ^ 7 * m + 1171 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4382.1, data_13_4382.2] + +/-- Complete interval computation for depth 13, residue 4383. -/ +theorem bounds_13_4383 : exactInterval 13 4383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4383 : oddCount 4383 13 = 8 ∧ acceleratedOrbit 13 4383 = 3512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4383) = 3 ^ 8 * m + 3512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4383.1, data_13_4383.2] + +/-- Complete interval computation for depth 13, residue 4384. -/ +theorem bounds_13_4384 : exactInterval 13 4384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4384 : oddCount 4384 13 = 6 ∧ acceleratedOrbit 13 4384 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4384) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4384.1, data_13_4384.2] + +/-- Complete interval computation for depth 13, residue 4385. -/ +theorem bounds_13_4385 : exactInterval 13 4385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4385 : oddCount 4385 13 = 6 ∧ acceleratedOrbit 13 4385 = 391 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4385) = 3 ^ 6 * m + 391 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4385.1, data_13_4385.2] + +/-- Complete interval computation for depth 13, residue 4386. -/ +theorem bounds_13_4386 : exactInterval 13 4386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4386 : oddCount 4386 13 = 7 ∧ acceleratedOrbit 13 4386 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4386) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4386.1, data_13_4386.2] + +/-- Complete interval computation for depth 13, residue 4387. -/ +theorem bounds_13_4387 : exactInterval 13 4387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4387 : oddCount 4387 13 = 7 ∧ acceleratedOrbit 13 4387 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4387) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4387.1, data_13_4387.2] + +/-- Complete interval computation for depth 13, residue 4388. -/ +theorem bounds_13_4388 : exactInterval 13 4388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4388 : oddCount 4388 13 = 7 ∧ acceleratedOrbit 13 4388 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4388) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4388.1, data_13_4388.2] + +/-- Complete interval computation for depth 13, residue 4389. -/ +theorem bounds_13_4389 : exactInterval 13 4389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4389 : oddCount 4389 13 = 7 ∧ acceleratedOrbit 13 4389 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4389) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4389.1, data_13_4389.2] + +/-- Complete interval computation for depth 13, residue 4390. -/ +theorem bounds_13_4390 : exactInterval 13 4390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4390 : oddCount 4390 13 = 7 ∧ acceleratedOrbit 13 4390 = 1174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4390) = 3 ^ 7 * m + 1174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4390.1, data_13_4390.2] + +/-- Complete interval computation for depth 13, residue 4391. -/ +theorem bounds_13_4391 : exactInterval 13 4391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4391 : oddCount 4391 13 = 9 ∧ acceleratedOrbit 13 4391 = 10556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4391) = 3 ^ 9 * m + 10556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4391.1, data_13_4391.2] + +/-- Complete interval computation for depth 13, residue 4392. -/ +theorem bounds_13_4392 : exactInterval 13 4392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4392 : oddCount 4392 13 = 6 ∧ acceleratedOrbit 13 4392 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4392) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4392.1, data_13_4392.2] + +/-- Complete interval computation for depth 13, residue 4393. -/ +theorem bounds_13_4393 : exactInterval 13 4393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4393 : oddCount 4393 13 = 8 ∧ acceleratedOrbit 13 4393 = 3520 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4393) = 3 ^ 8 * m + 3520 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4393.1, data_13_4393.2] + +/-- Complete interval computation for depth 13, residue 4394. -/ +theorem bounds_13_4394 : exactInterval 13 4394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4394 : oddCount 4394 13 = 6 ∧ acceleratedOrbit 13 4394 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4394) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4394.1, data_13_4394.2] + +/-- Complete interval computation for depth 13, residue 4395. -/ +theorem bounds_13_4395 : exactInterval 13 4395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4395 : oddCount 4395 13 = 8 ∧ acceleratedOrbit 13 4395 = 3523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4395) = 3 ^ 8 * m + 3523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4395.1, data_13_4395.2] + +/-- Complete interval computation for depth 13, residue 4396. -/ +theorem bounds_13_4396 : exactInterval 13 4396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4396 : oddCount 4396 13 = 4 ∧ acceleratedOrbit 13 4396 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4396) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4396.1, data_13_4396.2] + +/-- Complete interval computation for depth 13, residue 4397. -/ +theorem bounds_13_4397 : exactInterval 13 4397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4397 : oddCount 4397 13 = 4 ∧ acceleratedOrbit 13 4397 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4397) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4397.1, data_13_4397.2] + +end Collatz.Research.StoppingAtlas.Batch0753 From f7e2be3b26d7ad716c6d0e6833aca33ddb58ebab Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:03 +0530 Subject: [PATCH 0754/1001] proof: certify atlas Batch0754 (13:4398 to 13:4412) --- Collatz/Research/StoppingAtlas/Batch0754.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0754.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0754.lean b/Collatz/Research/StoppingAtlas/Batch0754.lean new file mode 100644 index 00000000..e2a8edaf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0754.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0754 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4398. -/ +theorem bounds_13_4398 : exactInterval 13 4398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4398 : oddCount 4398 13 = 4 ∧ acceleratedOrbit 13 4398 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4398) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4398.1, data_13_4398.2] + +/-- Complete interval computation for depth 13, residue 4399. -/ +theorem bounds_13_4399 : exactInterval 13 4399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4399 : oddCount 4399 13 = 9 ∧ acceleratedOrbit 13 4399 = 10574 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4399) = 3 ^ 9 * m + 10574 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4399.1, data_13_4399.2] + +/-- Complete interval computation for depth 13, residue 4400. -/ +theorem bounds_13_4400 : exactInterval 13 4400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4400 : oddCount 4400 13 = 6 ∧ acceleratedOrbit 13 4400 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4400) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4400.1, data_13_4400.2] + +/-- Complete interval computation for depth 13, residue 4401. -/ +theorem bounds_13_4401 : exactInterval 13 4401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4401 : oddCount 4401 13 = 7 ∧ acceleratedOrbit 13 4401 = 1178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4401) = 3 ^ 7 * m + 1178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4401.1, data_13_4401.2] + +/-- Complete interval computation for depth 13, residue 4402. -/ +theorem bounds_13_4402 : exactInterval 13 4402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4402 : oddCount 4402 13 = 7 ∧ acceleratedOrbit 13 4402 = 1178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4402) = 3 ^ 7 * m + 1178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4402.1, data_13_4402.2] + +/-- Complete interval computation for depth 13, residue 4403. -/ +theorem bounds_13_4403 : exactInterval 13 4403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4403 : oddCount 4403 13 = 7 ∧ acceleratedOrbit 13 4403 = 1178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4403) = 3 ^ 7 * m + 1178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4403.1, data_13_4403.2] + +/-- Complete interval computation for depth 13, residue 4404. -/ +theorem bounds_13_4404 : exactInterval 13 4404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4404 : oddCount 4404 13 = 6 ∧ acceleratedOrbit 13 4404 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4404) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4404.1, data_13_4404.2] + +/-- Complete interval computation for depth 13, residue 4405. -/ +theorem bounds_13_4405 : exactInterval 13 4405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4405 : oddCount 4405 13 = 6 ∧ acceleratedOrbit 13 4405 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4405) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4405.1, data_13_4405.2] + +/-- Complete interval computation for depth 13, residue 4406. -/ +theorem bounds_13_4406 : exactInterval 13 4406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4406 : oddCount 4406 13 = 7 ∧ acceleratedOrbit 13 4406 = 1177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4406) = 3 ^ 7 * m + 1177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4406.1, data_13_4406.2] + +/-- Complete interval computation for depth 13, residue 4407. -/ +theorem bounds_13_4407 : exactInterval 13 4407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4407 : oddCount 4407 13 = 7 ∧ acceleratedOrbit 13 4407 = 1177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4407) = 3 ^ 7 * m + 1177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4407.1, data_13_4407.2] + +/-- Complete interval computation for depth 13, residue 4408. -/ +theorem bounds_13_4408 : exactInterval 13 4408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4408 : oddCount 4408 13 = 5 ∧ acceleratedOrbit 13 4408 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4408) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4408.1, data_13_4408.2] + +/-- Complete interval computation for depth 13, residue 4409. -/ +theorem bounds_13_4409 : exactInterval 13 4409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4409 : oddCount 4409 13 = 9 ∧ acceleratedOrbit 13 4409 = 10601 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4409) = 3 ^ 9 * m + 10601 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4409.1, data_13_4409.2] + +/-- Complete interval computation for depth 13, residue 4410. -/ +theorem bounds_13_4410 : exactInterval 13 4410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4410 : oddCount 4410 13 = 5 ∧ acceleratedOrbit 13 4410 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4410) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4410.1, data_13_4410.2] + +/-- Complete interval computation for depth 13, residue 4411. -/ +theorem bounds_13_4411 : exactInterval 13 4411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4411 : oddCount 4411 13 = 5 ∧ acceleratedOrbit 13 4411 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4411) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4411.1, data_13_4411.2] + +/-- Complete interval computation for depth 13, residue 4412. -/ +theorem bounds_13_4412 : exactInterval 13 4412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4412 : oddCount 4412 13 = 5 ∧ acceleratedOrbit 13 4412 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4412) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4412.1, data_13_4412.2] + +end Collatz.Research.StoppingAtlas.Batch0754 From d2d172d0979fdb6438130f6861f55c65518817c0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:05 +0530 Subject: [PATCH 0755/1001] proof: certify atlas Batch0755 (13:4413 to 13:4427) --- Collatz/Research/StoppingAtlas/Batch0755.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0755.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0755.lean b/Collatz/Research/StoppingAtlas/Batch0755.lean new file mode 100644 index 00000000..3c8a8c1e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0755.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0755 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4413. -/ +theorem bounds_13_4413 : exactInterval 13 4413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4413 : oddCount 4413 13 = 5 ∧ acceleratedOrbit 13 4413 = 131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4413) = 3 ^ 5 * m + 131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4413.1, data_13_4413.2] + +/-- Complete interval computation for depth 13, residue 4414. -/ +theorem bounds_13_4414 : exactInterval 13 4414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4414 : oddCount 4414 13 = 11 ∧ acceleratedOrbit 13 4414 = 95498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4414) = 3 ^ 11 * m + 95498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4414.1, data_13_4414.2] + +/-- Complete interval computation for depth 13, residue 4415. -/ +theorem bounds_13_4415 : exactInterval 13 4415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4415 : oddCount 4415 13 = 11 ∧ acceleratedOrbit 13 4415 = 95498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4415) = 3 ^ 11 * m + 95498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4415.1, data_13_4415.2] + +/-- Complete interval computation for depth 13, residue 4416. -/ +theorem bounds_13_4416 : exactInterval 13 4416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4416 : oddCount 4416 13 = 2 ∧ acceleratedOrbit 13 4416 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4416) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4416.1, data_13_4416.2] + +/-- Complete interval computation for depth 13, residue 4417. -/ +theorem bounds_13_4417 : exactInterval 13 4417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4417 : oddCount 4417 13 = 6 ∧ acceleratedOrbit 13 4417 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4417) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4417.1, data_13_4417.2] + +/-- Complete interval computation for depth 13, residue 4418. -/ +theorem bounds_13_4418 : exactInterval 13 4418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4418 : oddCount 4418 13 = 7 ∧ acceleratedOrbit 13 4418 = 1181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4418) = 3 ^ 7 * m + 1181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4418.1, data_13_4418.2] + +/-- Complete interval computation for depth 13, residue 4419. -/ +theorem bounds_13_4419 : exactInterval 13 4419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4419 : oddCount 4419 13 = 7 ∧ acceleratedOrbit 13 4419 = 1181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4419) = 3 ^ 7 * m + 1181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4419.1, data_13_4419.2] + +/-- Complete interval computation for depth 13, residue 4420. -/ +theorem bounds_13_4420 : exactInterval 13 4420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4420 : oddCount 4420 13 = 6 ∧ acceleratedOrbit 13 4420 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4420) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4420.1, data_13_4420.2] + +/-- Complete interval computation for depth 13, residue 4421. -/ +theorem bounds_13_4421 : exactInterval 13 4421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4421 : oddCount 4421 13 = 6 ∧ acceleratedOrbit 13 4421 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4421) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4421.1, data_13_4421.2] + +/-- Complete interval computation for depth 13, residue 4422. -/ +theorem bounds_13_4422 : exactInterval 13 4422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4422 : oddCount 4422 13 = 6 ∧ acceleratedOrbit 13 4422 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4422) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4422.1, data_13_4422.2] + +/-- Complete interval computation for depth 13, residue 4423. -/ +theorem bounds_13_4423 : exactInterval 13 4423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4423 : oddCount 4423 13 = 9 ∧ acceleratedOrbit 13 4423 = 10631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4423) = 3 ^ 9 * m + 10631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4423.1, data_13_4423.2] + +/-- Complete interval computation for depth 13, residue 4424. -/ +theorem bounds_13_4424 : exactInterval 13 4424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4424 : oddCount 4424 13 = 8 ∧ acceleratedOrbit 13 4424 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4424) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4424.1, data_13_4424.2] + +/-- Complete interval computation for depth 13, residue 4425. -/ +theorem bounds_13_4425 : exactInterval 13 4425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4425 : oddCount 4425 13 = 6 ∧ acceleratedOrbit 13 4425 = 394 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4425) = 3 ^ 6 * m + 394 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4425.1, data_13_4425.2] + +/-- Complete interval computation for depth 13, residue 4426. -/ +theorem bounds_13_4426 : exactInterval 13 4426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4426 : oddCount 4426 13 = 8 ∧ acceleratedOrbit 13 4426 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4426) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4426.1, data_13_4426.2] + +/-- Complete interval computation for depth 13, residue 4427. -/ +theorem bounds_13_4427 : exactInterval 13 4427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4427 : oddCount 4427 13 = 6 ∧ acceleratedOrbit 13 4427 = 395 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4427) = 3 ^ 6 * m + 395 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4427.1, data_13_4427.2] + +end Collatz.Research.StoppingAtlas.Batch0755 From b2aa30f016fcdb5f6c7f6eb0e0803ec915487f86 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:19 +0530 Subject: [PATCH 0756/1001] proof: certify atlas Batch0756 (13:4428 to 13:4443) --- Collatz/Research/StoppingAtlas/Batch0756.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0756.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0756.lean b/Collatz/Research/StoppingAtlas/Batch0756.lean new file mode 100644 index 00000000..2a9f0613 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0756.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0756 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4428. -/ +theorem bounds_13_4428 : exactInterval 13 4428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4428 : oddCount 4428 13 = 8 ∧ acceleratedOrbit 13 4428 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4428) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4428.1, data_13_4428.2] + +/-- Complete interval computation for depth 13, residue 4429. -/ +theorem bounds_13_4429 : exactInterval 13 4429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4429 : oddCount 4429 13 = 8 ∧ acceleratedOrbit 13 4429 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4429) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4429.1, data_13_4429.2] + +/-- Complete interval computation for depth 13, residue 4430. -/ +theorem bounds_13_4430 : exactInterval 13 4430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4430 : oddCount 4430 13 = 9 ∧ acceleratedOrbit 13 4430 = 10651 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4430) = 3 ^ 9 * m + 10651 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4430.1, data_13_4430.2] + +/-- Complete interval computation for depth 13, residue 4431. -/ +theorem bounds_13_4431 : exactInterval 13 4431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4431 : oddCount 4431 13 = 9 ∧ acceleratedOrbit 13 4431 = 10651 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4431) = 3 ^ 9 * m + 10651 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4431.1, data_13_4431.2] + +/-- Complete interval computation for depth 13, residue 4432. -/ +theorem bounds_13_4432 : exactInterval 13 4432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4432 : oddCount 4432 13 = 2 ∧ acceleratedOrbit 13 4432 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4432) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4432.1, data_13_4432.2] + +/-- Complete interval computation for depth 13, residue 4433. -/ +theorem bounds_13_4433 : exactInterval 13 4433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4433 : oddCount 4433 13 = 8 ∧ acceleratedOrbit 13 4433 = 3554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4433) = 3 ^ 8 * m + 3554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4433.1, data_13_4433.2] + +/-- Complete interval computation for depth 13, residue 4434. -/ +theorem bounds_13_4434 : exactInterval 13 4434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4434 : oddCount 4434 13 = 10 ∧ acceleratedOrbit 13 4434 = 31985 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4434) = 3 ^ 10 * m + 31985 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4434.1, data_13_4434.2] + +/-- Complete interval computation for depth 13, residue 4435. -/ +theorem bounds_13_4435 : exactInterval 13 4435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4435 : oddCount 4435 13 = 10 ∧ acceleratedOrbit 13 4435 = 31985 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4435) = 3 ^ 10 * m + 31985 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4435.1, data_13_4435.2] + +/-- Complete interval computation for depth 13, residue 4436. -/ +theorem bounds_13_4436 : exactInterval 13 4436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4436 : oddCount 4436 13 = 2 ∧ acceleratedOrbit 13 4436 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4436) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4436.1, data_13_4436.2] + +/-- Complete interval computation for depth 13, residue 4437. -/ +theorem bounds_13_4437 : exactInterval 13 4437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4437 : oddCount 4437 13 = 2 ∧ acceleratedOrbit 13 4437 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4437) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4437.1, data_13_4437.2] + +/-- Complete interval computation for depth 13, residue 4438. -/ +theorem bounds_13_4438 : exactInterval 13 4438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4438 : oddCount 4438 13 = 7 ∧ acceleratedOrbit 13 4438 = 1187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4438) = 3 ^ 7 * m + 1187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4438.1, data_13_4438.2] + +/-- Complete interval computation for depth 13, residue 4439. -/ +theorem bounds_13_4439 : exactInterval 13 4439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4439 : oddCount 4439 13 = 7 ∧ acceleratedOrbit 13 4439 = 1187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4439) = 3 ^ 7 * m + 1187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4439.1, data_13_4439.2] + +/-- Complete interval computation for depth 13, residue 4440. -/ +theorem bounds_13_4440 : exactInterval 13 4440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4440 : oddCount 4440 13 = 4 ∧ acceleratedOrbit 13 4440 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4440) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4440.1, data_13_4440.2] + +/-- Complete interval computation for depth 13, residue 4441. -/ +theorem bounds_13_4441 : exactInterval 13 4441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4441 : oddCount 4441 13 = 8 ∧ acceleratedOrbit 13 4441 = 3563 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4441) = 3 ^ 8 * m + 3563 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4441.1, data_13_4441.2] + +/-- Complete interval computation for depth 13, residue 4442. -/ +theorem bounds_13_4442 : exactInterval 13 4442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4442 : oddCount 4442 13 = 4 ∧ acceleratedOrbit 13 4442 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4442) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4442.1, data_13_4442.2] + +/-- Complete interval computation for depth 13, residue 4443. -/ +theorem bounds_13_4443 : exactInterval 13 4443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4443 : oddCount 4443 13 = 7 ∧ acceleratedOrbit 13 4443 = 1187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4443) = 3 ^ 7 * m + 1187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4443.1, data_13_4443.2] + +end Collatz.Research.StoppingAtlas.Batch0756 From acec9bc35a25fc53446bd5864931fc2d25e86014 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:50 +0530 Subject: [PATCH 0757/1001] proof: certify atlas Batch0757 (13:4444 to 13:4458) --- Collatz/Research/StoppingAtlas/Batch0757.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0757.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0757.lean b/Collatz/Research/StoppingAtlas/Batch0757.lean new file mode 100644 index 00000000..c84554c3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0757.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0757 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4444. -/ +theorem bounds_13_4444 : exactInterval 13 4444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4444 : oddCount 4444 13 = 4 ∧ acceleratedOrbit 13 4444 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4444) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4444.1, data_13_4444.2] + +/-- Complete interval computation for depth 13, residue 4445. -/ +theorem bounds_13_4445 : exactInterval 13 4445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4445 : oddCount 4445 13 = 4 ∧ acceleratedOrbit 13 4445 = 44 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4445) = 3 ^ 4 * m + 44 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4445.1, data_13_4445.2] + +/-- Complete interval computation for depth 13, residue 4446. -/ +theorem bounds_13_4446 : exactInterval 13 4446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4446 : oddCount 4446 13 = 9 ∧ acceleratedOrbit 13 4446 = 10691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4446) = 3 ^ 9 * m + 10691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4446.1, data_13_4446.2] + +/-- Complete interval computation for depth 13, residue 4447. -/ +theorem bounds_13_4447 : exactInterval 13 4447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4447 : oddCount 4447 13 = 9 ∧ acceleratedOrbit 13 4447 = 10691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4447) = 3 ^ 9 * m + 10691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4447.1, data_13_4447.2] + +/-- Complete interval computation for depth 13, residue 4448. -/ +theorem bounds_13_4448 : exactInterval 13 4448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4448 : oddCount 4448 13 = 5 ∧ acceleratedOrbit 13 4448 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4448) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4448.1, data_13_4448.2] + +/-- Complete interval computation for depth 13, residue 4449. -/ +theorem bounds_13_4449 : exactInterval 13 4449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4449 : oddCount 4449 13 = 8 ∧ acceleratedOrbit 13 4449 = 3566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4449) = 3 ^ 8 * m + 3566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4449.1, data_13_4449.2] + +/-- Complete interval computation for depth 13, residue 4450. -/ +theorem bounds_13_4450 : exactInterval 13 4450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4450 : oddCount 4450 13 = 6 ∧ acceleratedOrbit 13 4450 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4450) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4450.1, data_13_4450.2] + +/-- Complete interval computation for depth 13, residue 4451. -/ +theorem bounds_13_4451 : exactInterval 13 4451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4451 : oddCount 4451 13 = 6 ∧ acceleratedOrbit 13 4451 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4451) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4451.1, data_13_4451.2] + +/-- Complete interval computation for depth 13, residue 4452. -/ +theorem bounds_13_4452 : exactInterval 13 4452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4452 : oddCount 4452 13 = 6 ∧ acceleratedOrbit 13 4452 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4452) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4452.1, data_13_4452.2] + +/-- Complete interval computation for depth 13, residue 4453. -/ +theorem bounds_13_4453 : exactInterval 13 4453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4453 : oddCount 4453 13 = 6 ∧ acceleratedOrbit 13 4453 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4453) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4453.1, data_13_4453.2] + +/-- Complete interval computation for depth 13, residue 4454. -/ +theorem bounds_13_4454 : exactInterval 13 4454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4454 : oddCount 4454 13 = 6 ∧ acceleratedOrbit 13 4454 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4454) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4454.1, data_13_4454.2] + +/-- Complete interval computation for depth 13, residue 4455. -/ +theorem bounds_13_4455 : exactInterval 13 4455 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4455) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4455 : oddCount 4455 13 = 8 ∧ acceleratedOrbit 13 4455 = 3569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4455) = 3 ^ 8 * m + 3569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4455.1, data_13_4455.2] + +/-- Complete interval computation for depth 13, residue 4456. -/ +theorem bounds_13_4456 : exactInterval 13 4456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4456 : oddCount 4456 13 = 5 ∧ acceleratedOrbit 13 4456 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4456) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4456.1, data_13_4456.2] + +/-- Complete interval computation for depth 13, residue 4457. -/ +theorem bounds_13_4457 : exactInterval 13 4457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4457 : oddCount 4457 13 = 6 ∧ acceleratedOrbit 13 4457 = 397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4457) = 3 ^ 6 * m + 397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4457.1, data_13_4457.2] + +/-- Complete interval computation for depth 13, residue 4458. -/ +theorem bounds_13_4458 : exactInterval 13 4458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4458 : oddCount 4458 13 = 5 ∧ acceleratedOrbit 13 4458 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4458) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4458.1, data_13_4458.2] + +end Collatz.Research.StoppingAtlas.Batch0757 From 77a204574cf36ab96e0e8ab6f286021d2514665e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:50 +0530 Subject: [PATCH 0758/1001] proof: certify atlas Batch0758 (13:4459 to 13:4473) --- Collatz/Research/StoppingAtlas/Batch0758.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0758.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0758.lean b/Collatz/Research/StoppingAtlas/Batch0758.lean new file mode 100644 index 00000000..ce1f5d4e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0758.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0758 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4459. -/ +theorem bounds_13_4459 : exactInterval 13 4459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4459 : oddCount 4459 13 = 6 ∧ acceleratedOrbit 13 4459 = 397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4459) = 3 ^ 6 * m + 397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4459.1, data_13_4459.2] + +/-- Complete interval computation for depth 13, residue 4460. -/ +theorem bounds_13_4460 : exactInterval 13 4460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4460 : oddCount 4460 13 = 8 ∧ acceleratedOrbit 13 4460 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4460) = 3 ^ 8 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4460.1, data_13_4460.2] + +/-- Complete interval computation for depth 13, residue 4461. -/ +theorem bounds_13_4461 : exactInterval 13 4461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4461 : oddCount 4461 13 = 8 ∧ acceleratedOrbit 13 4461 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4461) = 3 ^ 8 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4461.1, data_13_4461.2] + +/-- Complete interval computation for depth 13, residue 4462. -/ +theorem bounds_13_4462 : exactInterval 13 4462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4462 : oddCount 4462 13 = 8 ∧ acceleratedOrbit 13 4462 = 3577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4462) = 3 ^ 8 * m + 3577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4462.1, data_13_4462.2] + +/-- Complete interval computation for depth 13, residue 4463. -/ +theorem bounds_13_4463 : exactInterval 13 4463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4463 : oddCount 4463 13 = 7 ∧ acceleratedOrbit 13 4463 = 1192 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4463) = 3 ^ 7 * m + 1192 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4463.1, data_13_4463.2] + +/-- Complete interval computation for depth 13, residue 4464. -/ +theorem bounds_13_4464 : exactInterval 13 4464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4464 : oddCount 4464 13 = 5 ∧ acceleratedOrbit 13 4464 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4464) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4464.1, data_13_4464.2] + +/-- Complete interval computation for depth 13, residue 4465. -/ +theorem bounds_13_4465 : exactInterval 13 4465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4465 : oddCount 4465 13 = 5 ∧ acceleratedOrbit 13 4465 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4465) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4465.1, data_13_4465.2] + +/-- Complete interval computation for depth 13, residue 4466. -/ +theorem bounds_13_4466 : exactInterval 13 4466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4466 : oddCount 4466 13 = 6 ∧ acceleratedOrbit 13 4466 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4466) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4466.1, data_13_4466.2] + +/-- Complete interval computation for depth 13, residue 4467. -/ +theorem bounds_13_4467 : exactInterval 13 4467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4467 : oddCount 4467 13 = 6 ∧ acceleratedOrbit 13 4467 = 398 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4467) = 3 ^ 6 * m + 398 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4467.1, data_13_4467.2] + +/-- Complete interval computation for depth 13, residue 4468. -/ +theorem bounds_13_4468 : exactInterval 13 4468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4468 : oddCount 4468 13 = 5 ∧ acceleratedOrbit 13 4468 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4468) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4468.1, data_13_4468.2] + +/-- Complete interval computation for depth 13, residue 4469. -/ +theorem bounds_13_4469 : exactInterval 13 4469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4469 : oddCount 4469 13 = 5 ∧ acceleratedOrbit 13 4469 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4469) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4469.1, data_13_4469.2] + +/-- Complete interval computation for depth 13, residue 4470. -/ +theorem bounds_13_4470 : exactInterval 13 4470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4470 : oddCount 4470 13 = 8 ∧ acceleratedOrbit 13 4470 = 3584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4470) = 3 ^ 8 * m + 3584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4470.1, data_13_4470.2] + +/-- Complete interval computation for depth 13, residue 4471. -/ +theorem bounds_13_4471 : exactInterval 13 4471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4471 : oddCount 4471 13 = 8 ∧ acceleratedOrbit 13 4471 = 3584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4471) = 3 ^ 8 * m + 3584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4471.1, data_13_4471.2] + +/-- Complete interval computation for depth 13, residue 4472. -/ +theorem bounds_13_4472 : exactInterval 13 4472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4472 : oddCount 4472 13 = 8 ∧ acceleratedOrbit 13 4472 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4472) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4472.1, data_13_4472.2] + +/-- Complete interval computation for depth 13, residue 4473. -/ +theorem bounds_13_4473 : exactInterval 13 4473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4473 : oddCount 4473 13 = 10 ∧ acceleratedOrbit 13 4473 = 32258 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4473) = 3 ^ 10 * m + 32258 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4473.1, data_13_4473.2] + +end Collatz.Research.StoppingAtlas.Batch0758 From f87e634f2b3520e9dbe1b6788e0858cb6188c327 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:50 +0530 Subject: [PATCH 0759/1001] proof: certify atlas Batch0759 (13:4474 to 13:4489) --- Collatz/Research/StoppingAtlas/Batch0759.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0759.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0759.lean b/Collatz/Research/StoppingAtlas/Batch0759.lean new file mode 100644 index 00000000..47fc3986 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0759.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0759 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4474. -/ +theorem bounds_13_4474 : exactInterval 13 4474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4474 : oddCount 4474 13 = 8 ∧ acceleratedOrbit 13 4474 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4474) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4474.1, data_13_4474.2] + +/-- Complete interval computation for depth 13, residue 4475. -/ +theorem bounds_13_4475 : exactInterval 13 4475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4475 : oddCount 4475 13 = 8 ∧ acceleratedOrbit 13 4475 = 3586 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4475) = 3 ^ 8 * m + 3586 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4475.1, data_13_4475.2] + +/-- Complete interval computation for depth 13, residue 4476. -/ +theorem bounds_13_4476 : exactInterval 13 4476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4476 : oddCount 4476 13 = 8 ∧ acceleratedOrbit 13 4476 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4476) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4476.1, data_13_4476.2] + +/-- Complete interval computation for depth 13, residue 4477. -/ +theorem bounds_13_4477 : exactInterval 13 4477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4477 : oddCount 4477 13 = 8 ∧ acceleratedOrbit 13 4477 = 3590 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4477) = 3 ^ 8 * m + 3590 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4477.1, data_13_4477.2] + +/-- Complete interval computation for depth 13, residue 4478. -/ +theorem bounds_13_4478 : exactInterval 13 4478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4478 : oddCount 4478 13 = 7 ∧ acceleratedOrbit 13 4478 = 1196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4478) = 3 ^ 7 * m + 1196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4478.1, data_13_4478.2] + +/-- Complete interval computation for depth 13, residue 4479. -/ +theorem bounds_13_4479 : exactInterval 13 4479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4479 : oddCount 4479 13 = 7 ∧ acceleratedOrbit 13 4479 = 1196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4479) = 3 ^ 7 * m + 1196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4479.1, data_13_4479.2] + +/-- Complete interval computation for depth 13, residue 4480. -/ +theorem bounds_13_4480 : exactInterval 13 4480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4480 : oddCount 4480 13 = 2 ∧ acceleratedOrbit 13 4480 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4480) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4480.1, data_13_4480.2] + +/-- Complete interval computation for depth 13, residue 4481. -/ +theorem bounds_13_4481 : exactInterval 13 4481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4481 : oddCount 4481 13 = 5 ∧ acceleratedOrbit 13 4481 = 133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4481) = 3 ^ 5 * m + 133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4481.1, data_13_4481.2] + +/-- Complete interval computation for depth 13, residue 4482. -/ +theorem bounds_13_4482 : exactInterval 13 4482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4482 : oddCount 4482 13 = 6 ∧ acceleratedOrbit 13 4482 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4482) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4482.1, data_13_4482.2] + +/-- Complete interval computation for depth 13, residue 4483. -/ +theorem bounds_13_4483 : exactInterval 13 4483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4483 : oddCount 4483 13 = 6 ∧ acceleratedOrbit 13 4483 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4483) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4483.1, data_13_4483.2] + +/-- Complete interval computation for depth 13, residue 4484. -/ +theorem bounds_13_4484 : exactInterval 13 4484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4484 : oddCount 4484 13 = 6 ∧ acceleratedOrbit 13 4484 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4484) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4484.1, data_13_4484.2] + +/-- Complete interval computation for depth 13, residue 4485. -/ +theorem bounds_13_4485 : exactInterval 13 4485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4485 : oddCount 4485 13 = 6 ∧ acceleratedOrbit 13 4485 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4485) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4485.1, data_13_4485.2] + +/-- Complete interval computation for depth 13, residue 4486. -/ +theorem bounds_13_4486 : exactInterval 13 4486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4486 : oddCount 4486 13 = 6 ∧ acceleratedOrbit 13 4486 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4486) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4486.1, data_13_4486.2] + +/-- Complete interval computation for depth 13, residue 4487. -/ +theorem bounds_13_4487 : exactInterval 13 4487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4487 : oddCount 4487 13 = 6 ∧ acceleratedOrbit 13 4487 = 400 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4487) = 3 ^ 6 * m + 400 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4487.1, data_13_4487.2] + +/-- Complete interval computation for depth 13, residue 4488. -/ +theorem bounds_13_4488 : exactInterval 13 4488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4488 : oddCount 4488 13 = 6 ∧ acceleratedOrbit 13 4488 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4488) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4488.1, data_13_4488.2] + +/-- Complete interval computation for depth 13, residue 4489. -/ +theorem bounds_13_4489 : exactInterval 13 4489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4489 : oddCount 4489 13 = 7 ∧ acceleratedOrbit 13 4489 = 1199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4489) = 3 ^ 7 * m + 1199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4489.1, data_13_4489.2] + +end Collatz.Research.StoppingAtlas.Batch0759 From c61878fe710eec18f2da8d7198cf8e22d5de1ff9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:50 +0530 Subject: [PATCH 0760/1001] proof: certify atlas Batch0760 (13:4490 to 13:4504) --- Collatz/Research/StoppingAtlas/Batch0760.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0760.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0760.lean b/Collatz/Research/StoppingAtlas/Batch0760.lean new file mode 100644 index 00000000..fbe1fbc9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0760.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0760 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4490. -/ +theorem bounds_13_4490 : exactInterval 13 4490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4490 : oddCount 4490 13 = 6 ∧ acceleratedOrbit 13 4490 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4490) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4490.1, data_13_4490.2] + +/-- Complete interval computation for depth 13, residue 4491. -/ +theorem bounds_13_4491 : exactInterval 13 4491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4491 : oddCount 4491 13 = 9 ∧ acceleratedOrbit 13 4491 = 10799 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4491) = 3 ^ 9 * m + 10799 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4491.1, data_13_4491.2] + +/-- Complete interval computation for depth 13, residue 4492. -/ +theorem bounds_13_4492 : exactInterval 13 4492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4492 : oddCount 4492 13 = 6 ∧ acceleratedOrbit 13 4492 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4492) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4492.1, data_13_4492.2] + +/-- Complete interval computation for depth 13, residue 4493. -/ +theorem bounds_13_4493 : exactInterval 13 4493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4493 : oddCount 4493 13 = 6 ∧ acceleratedOrbit 13 4493 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4493) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4493.1, data_13_4493.2] + +/-- Complete interval computation for depth 13, residue 4494. -/ +theorem bounds_13_4494 : exactInterval 13 4494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4494 : oddCount 4494 13 = 7 ∧ acceleratedOrbit 13 4494 = 1201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4494) = 3 ^ 7 * m + 1201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4494.1, data_13_4494.2] + +/-- Complete interval computation for depth 13, residue 4495. -/ +theorem bounds_13_4495 : exactInterval 13 4495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4495 : oddCount 4495 13 = 7 ∧ acceleratedOrbit 13 4495 = 1201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4495) = 3 ^ 7 * m + 1201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4495.1, data_13_4495.2] + +/-- Complete interval computation for depth 13, residue 4496. -/ +theorem bounds_13_4496 : exactInterval 13 4496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4496 : oddCount 4496 13 = 6 ∧ acceleratedOrbit 13 4496 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4496) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4496.1, data_13_4496.2] + +/-- Complete interval computation for depth 13, residue 4497. -/ +theorem bounds_13_4497 : exactInterval 13 4497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4497 : oddCount 4497 13 = 5 ∧ acceleratedOrbit 13 4497 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4497) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4497.1, data_13_4497.2] + +/-- Complete interval computation for depth 13, residue 4498. -/ +theorem bounds_13_4498 : exactInterval 13 4498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4498 : oddCount 4498 13 = 5 ∧ acceleratedOrbit 13 4498 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4498) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4498.1, data_13_4498.2] + +/-- Complete interval computation for depth 13, residue 4499. -/ +theorem bounds_13_4499 : exactInterval 13 4499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4499 : oddCount 4499 13 = 5 ∧ acceleratedOrbit 13 4499 = 134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4499) = 3 ^ 5 * m + 134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4499.1, data_13_4499.2] + +/-- Complete interval computation for depth 13, residue 4500. -/ +theorem bounds_13_4500 : exactInterval 13 4500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4500 : oddCount 4500 13 = 6 ∧ acceleratedOrbit 13 4500 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4500) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4500.1, data_13_4500.2] + +/-- Complete interval computation for depth 13, residue 4501. -/ +theorem bounds_13_4501 : exactInterval 13 4501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4501 : oddCount 4501 13 = 6 ∧ acceleratedOrbit 13 4501 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4501) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4501.1, data_13_4501.2] + +/-- Complete interval computation for depth 13, residue 4502. -/ +theorem bounds_13_4502 : exactInterval 13 4502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4502 : oddCount 4502 13 = 7 ∧ acceleratedOrbit 13 4502 = 1205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4502) = 3 ^ 7 * m + 1205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4502.1, data_13_4502.2] + +/-- Complete interval computation for depth 13, residue 4503. -/ +theorem bounds_13_4503 : exactInterval 13 4503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4503 : oddCount 4503 13 = 7 ∧ acceleratedOrbit 13 4503 = 1205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4503) = 3 ^ 7 * m + 1205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4503.1, data_13_4503.2] + +/-- Complete interval computation for depth 13, residue 4504. -/ +theorem bounds_13_4504 : exactInterval 13 4504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4504 : oddCount 4504 13 = 6 ∧ acceleratedOrbit 13 4504 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4504) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4504.1, data_13_4504.2] + +end Collatz.Research.StoppingAtlas.Batch0760 From 434a1d867c6b62cbcb1b040e381c88555bd4a379 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:51 +0530 Subject: [PATCH 0761/1001] proof: certify atlas Batch0761 (13:4505 to 13:4519) --- Collatz/Research/StoppingAtlas/Batch0761.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0761.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0761.lean b/Collatz/Research/StoppingAtlas/Batch0761.lean new file mode 100644 index 00000000..cad117ba --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0761.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0761 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4505. -/ +theorem bounds_13_4505 : exactInterval 13 4505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4505 : oddCount 4505 13 = 7 ∧ acceleratedOrbit 13 4505 = 1205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4505) = 3 ^ 7 * m + 1205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4505.1, data_13_4505.2] + +/-- Complete interval computation for depth 13, residue 4506. -/ +theorem bounds_13_4506 : exactInterval 13 4506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4506 : oddCount 4506 13 = 6 ∧ acceleratedOrbit 13 4506 = 404 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4506) = 3 ^ 6 * m + 404 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4506.1, data_13_4506.2] + +/-- Complete interval computation for depth 13, residue 4507. -/ +theorem bounds_13_4507 : exactInterval 13 4507 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4507) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4507 : oddCount 4507 13 = 8 ∧ acceleratedOrbit 13 4507 = 3611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4507) = 3 ^ 8 * m + 3611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4507.1, data_13_4507.2] + +/-- Complete interval computation for depth 13, residue 4508. -/ +theorem bounds_13_4508 : exactInterval 13 4508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4508 : oddCount 4508 13 = 9 ∧ acceleratedOrbit 13 4508 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4508) = 3 ^ 9 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4508.1, data_13_4508.2] + +/-- Complete interval computation for depth 13, residue 4509. -/ +theorem bounds_13_4509 : exactInterval 13 4509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4509 : oddCount 4509 13 = 9 ∧ acceleratedOrbit 13 4509 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4509) = 3 ^ 9 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4509.1, data_13_4509.2] + +/-- Complete interval computation for depth 13, residue 4510. -/ +theorem bounds_13_4510 : exactInterval 13 4510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4510 : oddCount 4510 13 = 9 ∧ acceleratedOrbit 13 4510 = 10844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4510) = 3 ^ 9 * m + 10844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4510.1, data_13_4510.2] + +/-- Complete interval computation for depth 13, residue 4511. -/ +theorem bounds_13_4511 : exactInterval 13 4511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4511 : oddCount 4511 13 = 10 ∧ acceleratedOrbit 13 4511 = 32525 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4511) = 3 ^ 10 * m + 32525 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4511.1, data_13_4511.2] + +/-- Complete interval computation for depth 13, residue 4512. -/ +theorem bounds_13_4512 : exactInterval 13 4512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4512 : oddCount 4512 13 = 2 ∧ acceleratedOrbit 13 4512 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4512) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4512.1, data_13_4512.2] + +/-- Complete interval computation for depth 13, residue 4513. -/ +theorem bounds_13_4513 : exactInterval 13 4513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4513 : oddCount 4513 13 = 9 ∧ acceleratedOrbit 13 4513 = 10853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4513) = 3 ^ 9 * m + 10853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4513.1, data_13_4513.2] + +/-- Complete interval computation for depth 13, residue 4514. -/ +theorem bounds_13_4514 : exactInterval 13 4514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4514 : oddCount 4514 13 = 7 ∧ acceleratedOrbit 13 4514 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4514) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4514.1, data_13_4514.2] + +/-- Complete interval computation for depth 13, residue 4515. -/ +theorem bounds_13_4515 : exactInterval 13 4515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4515 : oddCount 4515 13 = 7 ∧ acceleratedOrbit 13 4515 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4515) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4515.1, data_13_4515.2] + +/-- Complete interval computation for depth 13, residue 4516. -/ +theorem bounds_13_4516 : exactInterval 13 4516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4516 : oddCount 4516 13 = 7 ∧ acceleratedOrbit 13 4516 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4516) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4516.1, data_13_4516.2] + +/-- Complete interval computation for depth 13, residue 4517. -/ +theorem bounds_13_4517 : exactInterval 13 4517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4517 : oddCount 4517 13 = 7 ∧ acceleratedOrbit 13 4517 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4517) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4517.1, data_13_4517.2] + +/-- Complete interval computation for depth 13, residue 4518. -/ +theorem bounds_13_4518 : exactInterval 13 4518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4518 : oddCount 4518 13 = 7 ∧ acceleratedOrbit 13 4518 = 1208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4518) = 3 ^ 7 * m + 1208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4518.1, data_13_4518.2] + +/-- Complete interval computation for depth 13, residue 4519. -/ +theorem bounds_13_4519 : exactInterval 13 4519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4519 : oddCount 4519 13 = 7 ∧ acceleratedOrbit 13 4519 = 1207 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4519) = 3 ^ 7 * m + 1207 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4519.1, data_13_4519.2] + +end Collatz.Research.StoppingAtlas.Batch0761 From 0a0fadf833595818c96e3469dad30d5f44f65f05 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:51 +0530 Subject: [PATCH 0762/1001] proof: certify atlas Batch0762 (13:4520 to 13:4535) --- Collatz/Research/StoppingAtlas/Batch0762.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0762.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0762.lean b/Collatz/Research/StoppingAtlas/Batch0762.lean new file mode 100644 index 00000000..b4fed8f6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0762.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0762 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4520. -/ +theorem bounds_13_4520 : exactInterval 13 4520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4520 : oddCount 4520 13 = 2 ∧ acceleratedOrbit 13 4520 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4520) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4520.1, data_13_4520.2] + +/-- Complete interval computation for depth 13, residue 4521. -/ +theorem bounds_13_4521 : exactInterval 13 4521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4521 : oddCount 4521 13 = 9 ∧ acceleratedOrbit 13 4521 = 10867 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4521) = 3 ^ 9 * m + 10867 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4521.1, data_13_4521.2] + +/-- Complete interval computation for depth 13, residue 4522. -/ +theorem bounds_13_4522 : exactInterval 13 4522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4522 : oddCount 4522 13 = 2 ∧ acceleratedOrbit 13 4522 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4522) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4522.1, data_13_4522.2] + +/-- Complete interval computation for depth 13, residue 4523. -/ +theorem bounds_13_4523 : exactInterval 13 4523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4523 : oddCount 4523 13 = 9 ∧ acceleratedOrbit 13 4523 = 10874 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4523) = 3 ^ 9 * m + 10874 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4523.1, data_13_4523.2] + +/-- Complete interval computation for depth 13, residue 4524. -/ +theorem bounds_13_4524 : exactInterval 13 4524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4524 : oddCount 4524 13 = 7 ∧ acceleratedOrbit 13 4524 = 1210 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4524) = 3 ^ 7 * m + 1210 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4524.1, data_13_4524.2] + +/-- Complete interval computation for depth 13, residue 4525. -/ +theorem bounds_13_4525 : exactInterval 13 4525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4525 : oddCount 4525 13 = 7 ∧ acceleratedOrbit 13 4525 = 1210 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4525) = 3 ^ 7 * m + 1210 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4525.1, data_13_4525.2] + +/-- Complete interval computation for depth 13, residue 4526. -/ +theorem bounds_13_4526 : exactInterval 13 4526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4526 : oddCount 4526 13 = 7 ∧ acceleratedOrbit 13 4526 = 1210 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4526) = 3 ^ 7 * m + 1210 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4526.1, data_13_4526.2] + +/-- Complete interval computation for depth 13, residue 4527. -/ +theorem bounds_13_4527 : exactInterval 13 4527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4527 : oddCount 4527 13 = 6 ∧ acceleratedOrbit 13 4527 = 403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4527) = 3 ^ 6 * m + 403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4527.1, data_13_4527.2] + +/-- Complete interval computation for depth 13, residue 4528. -/ +theorem bounds_13_4528 : exactInterval 13 4528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4528 : oddCount 4528 13 = 8 ∧ acceleratedOrbit 13 4528 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4528) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4528.1, data_13_4528.2] + +/-- Complete interval computation for depth 13, residue 4529. -/ +theorem bounds_13_4529 : exactInterval 13 4529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4529 : oddCount 4529 13 = 7 ∧ acceleratedOrbit 13 4529 = 1214 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4529) = 3 ^ 7 * m + 1214 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4529.1, data_13_4529.2] + +/-- Complete interval computation for depth 13, residue 4530. -/ +theorem bounds_13_4530 : exactInterval 13 4530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4530 : oddCount 4530 13 = 7 ∧ acceleratedOrbit 13 4530 = 1214 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4530) = 3 ^ 7 * m + 1214 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4530.1, data_13_4530.2] + +/-- Complete interval computation for depth 13, residue 4531. -/ +theorem bounds_13_4531 : exactInterval 13 4531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4531 : oddCount 4531 13 = 7 ∧ acceleratedOrbit 13 4531 = 1214 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4531) = 3 ^ 7 * m + 1214 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4531.1, data_13_4531.2] + +/-- Complete interval computation for depth 13, residue 4532. -/ +theorem bounds_13_4532 : exactInterval 13 4532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4532 : oddCount 4532 13 = 8 ∧ acceleratedOrbit 13 4532 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4532) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4532.1, data_13_4532.2] + +/-- Complete interval computation for depth 13, residue 4533. -/ +theorem bounds_13_4533 : exactInterval 13 4533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4533 : oddCount 4533 13 = 8 ∧ acceleratedOrbit 13 4533 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4533) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4533.1, data_13_4533.2] + +/-- Complete interval computation for depth 13, residue 4534. -/ +theorem bounds_13_4534 : exactInterval 13 4534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4534 : oddCount 4534 13 = 8 ∧ acceleratedOrbit 13 4534 = 3635 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4534) = 3 ^ 8 * m + 3635 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4534.1, data_13_4534.2] + +/-- Complete interval computation for depth 13, residue 4535. -/ +theorem bounds_13_4535 : exactInterval 13 4535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4535 : oddCount 4535 13 = 8 ∧ acceleratedOrbit 13 4535 = 3635 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4535) = 3 ^ 8 * m + 3635 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4535.1, data_13_4535.2] + +end Collatz.Research.StoppingAtlas.Batch0762 From 252767342a61e6ded28fbb980f805bad4a55eb41 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:51 +0530 Subject: [PATCH 0763/1001] proof: certify atlas Batch0763 (13:4536 to 13:4550) --- Collatz/Research/StoppingAtlas/Batch0763.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0763.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0763.lean b/Collatz/Research/StoppingAtlas/Batch0763.lean new file mode 100644 index 00000000..5bc7c193 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0763.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0763 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4536. -/ +theorem bounds_13_4536 : exactInterval 13 4536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4536 : oddCount 4536 13 = 8 ∧ acceleratedOrbit 13 4536 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4536) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4536.1, data_13_4536.2] + +/-- Complete interval computation for depth 13, residue 4537. -/ +theorem bounds_13_4537 : exactInterval 13 4537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4537 : oddCount 4537 13 = 7 ∧ acceleratedOrbit 13 4537 = 1214 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4537) = 3 ^ 7 * m + 1214 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4537.1, data_13_4537.2] + +/-- Complete interval computation for depth 13, residue 4538. -/ +theorem bounds_13_4538 : exactInterval 13 4538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4538 : oddCount 4538 13 = 8 ∧ acceleratedOrbit 13 4538 = 3644 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4538) = 3 ^ 8 * m + 3644 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4538.1, data_13_4538.2] + +/-- Complete interval computation for depth 13, residue 4539. -/ +theorem bounds_13_4539 : exactInterval 13 4539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4539 : oddCount 4539 13 = 8 ∧ acceleratedOrbit 13 4539 = 3638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4539) = 3 ^ 8 * m + 3638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4539.1, data_13_4539.2] + +/-- Complete interval computation for depth 13, residue 4540. -/ +theorem bounds_13_4540 : exactInterval 13 4540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4540 : oddCount 4540 13 = 8 ∧ acceleratedOrbit 13 4540 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4540) = 3 ^ 8 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4540.1, data_13_4540.2] + +/-- Complete interval computation for depth 13, residue 4541. -/ +theorem bounds_13_4541 : exactInterval 13 4541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4541 : oddCount 4541 13 = 8 ∧ acceleratedOrbit 13 4541 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4541) = 3 ^ 8 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4541.1, data_13_4541.2] + +/-- Complete interval computation for depth 13, residue 4542. -/ +theorem bounds_13_4542 : exactInterval 13 4542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4542 : oddCount 4542 13 = 8 ∧ acceleratedOrbit 13 4542 = 3640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4542) = 3 ^ 8 * m + 3640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4542.1, data_13_4542.2] + +/-- Complete interval computation for depth 13, residue 4543. -/ +theorem bounds_13_4543 : exactInterval 13 4543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4543 : oddCount 4543 13 = 9 ∧ acceleratedOrbit 13 4543 = 10918 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4543) = 3 ^ 9 * m + 10918 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4543.1, data_13_4543.2] + +/-- Complete interval computation for depth 13, residue 4544. -/ +theorem bounds_13_4544 : exactInterval 13 4544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4544 : oddCount 4544 13 = 5 ∧ acceleratedOrbit 13 4544 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4544) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4544.1, data_13_4544.2] + +/-- Complete interval computation for depth 13, residue 4545. -/ +theorem bounds_13_4545 : exactInterval 13 4545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4545 : oddCount 4545 13 = 9 ∧ acceleratedOrbit 13 4545 = 10934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4545) = 3 ^ 9 * m + 10934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4545.1, data_13_4545.2] + +/-- Complete interval computation for depth 13, residue 4546. -/ +theorem bounds_13_4546 : exactInterval 13 4546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4546 : oddCount 4546 13 = 10 ∧ acceleratedOrbit 13 4546 = 32804 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4546) = 3 ^ 10 * m + 32804 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4546.1, data_13_4546.2] + +/-- Complete interval computation for depth 13, residue 4547. -/ +theorem bounds_13_4547 : exactInterval 13 4547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4547 : oddCount 4547 13 = 10 ∧ acceleratedOrbit 13 4547 = 32804 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4547) = 3 ^ 10 * m + 32804 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4547.1, data_13_4547.2] + +/-- Complete interval computation for depth 13, residue 4548. -/ +theorem bounds_13_4548 : exactInterval 13 4548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4548 : oddCount 4548 13 = 2 ∧ acceleratedOrbit 13 4548 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4548) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4548.1, data_13_4548.2] + +/-- Complete interval computation for depth 13, residue 4549. -/ +theorem bounds_13_4549 : exactInterval 13 4549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4549 : oddCount 4549 13 = 2 ∧ acceleratedOrbit 13 4549 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4549) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4549.1, data_13_4549.2] + +/-- Complete interval computation for depth 13, residue 4550. -/ +theorem bounds_13_4550 : exactInterval 13 4550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4550 : oddCount 4550 13 = 2 ∧ acceleratedOrbit 13 4550 = 5 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4550) = 3 ^ 2 * m + 5 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4550.1, data_13_4550.2] + +end Collatz.Research.StoppingAtlas.Batch0763 From d369948eaa95380af835e8a88143d0a74e84882b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:51 +0530 Subject: [PATCH 0764/1001] proof: certify atlas Batch0764 (13:4551 to 13:4566) --- Collatz/Research/StoppingAtlas/Batch0764.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0764.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0764.lean b/Collatz/Research/StoppingAtlas/Batch0764.lean new file mode 100644 index 00000000..83d717a7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0764.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0764 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4551. -/ +theorem bounds_13_4551 : exactInterval 13 4551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4551 : oddCount 4551 13 = 8 ∧ acceleratedOrbit 13 4551 = 3647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4551) = 3 ^ 8 * m + 3647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4551.1, data_13_4551.2] + +/-- Complete interval computation for depth 13, residue 4552. -/ +theorem bounds_13_4552 : exactInterval 13 4552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4552 : oddCount 4552 13 = 6 ∧ acceleratedOrbit 13 4552 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4552) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4552.1, data_13_4552.2] + +/-- Complete interval computation for depth 13, residue 4553. -/ +theorem bounds_13_4553 : exactInterval 13 4553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4553 : oddCount 4553 13 = 7 ∧ acceleratedOrbit 13 4553 = 1217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4553) = 3 ^ 7 * m + 1217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4553.1, data_13_4553.2] + +/-- Complete interval computation for depth 13, residue 4554. -/ +theorem bounds_13_4554 : exactInterval 13 4554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4554 : oddCount 4554 13 = 6 ∧ acceleratedOrbit 13 4554 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4554) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4554.1, data_13_4554.2] + +/-- Complete interval computation for depth 13, residue 4555. -/ +theorem bounds_13_4555 : exactInterval 13 4555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4555 : oddCount 4555 13 = 6 ∧ acceleratedOrbit 13 4555 = 406 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4555) = 3 ^ 6 * m + 406 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4555.1, data_13_4555.2] + +/-- Complete interval computation for depth 13, residue 4556. -/ +theorem bounds_13_4556 : exactInterval 13 4556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4556 : oddCount 4556 13 = 6 ∧ acceleratedOrbit 13 4556 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4556) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4556.1, data_13_4556.2] + +/-- Complete interval computation for depth 13, residue 4557. -/ +theorem bounds_13_4557 : exactInterval 13 4557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4557 : oddCount 4557 13 = 6 ∧ acceleratedOrbit 13 4557 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4557) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4557.1, data_13_4557.2] + +/-- Complete interval computation for depth 13, residue 4558. -/ +theorem bounds_13_4558 : exactInterval 13 4558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4558 : oddCount 4558 13 = 8 ∧ acceleratedOrbit 13 4558 = 3653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4558) = 3 ^ 8 * m + 3653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4558.1, data_13_4558.2] + +/-- Complete interval computation for depth 13, residue 4559. -/ +theorem bounds_13_4559 : exactInterval 13 4559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4559 : oddCount 4559 13 = 8 ∧ acceleratedOrbit 13 4559 = 3653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4559) = 3 ^ 8 * m + 3653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4559.1, data_13_4559.2] + +/-- Complete interval computation for depth 13, residue 4560. -/ +theorem bounds_13_4560 : exactInterval 13 4560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4560 : oddCount 4560 13 = 5 ∧ acceleratedOrbit 13 4560 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4560) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4560.1, data_13_4560.2] + +/-- Complete interval computation for depth 13, residue 4561. -/ +theorem bounds_13_4561 : exactInterval 13 4561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4561 : oddCount 4561 13 = 6 ∧ acceleratedOrbit 13 4561 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4561) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4561.1, data_13_4561.2] + +/-- Complete interval computation for depth 13, residue 4562. -/ +theorem bounds_13_4562 : exactInterval 13 4562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4562 : oddCount 4562 13 = 7 ∧ acceleratedOrbit 13 4562 = 1219 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4562) = 3 ^ 7 * m + 1219 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4562.1, data_13_4562.2] + +/-- Complete interval computation for depth 13, residue 4563. -/ +theorem bounds_13_4563 : exactInterval 13 4563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4563 : oddCount 4563 13 = 7 ∧ acceleratedOrbit 13 4563 = 1219 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4563) = 3 ^ 7 * m + 1219 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4563.1, data_13_4563.2] + +/-- Complete interval computation for depth 13, residue 4564. -/ +theorem bounds_13_4564 : exactInterval 13 4564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4564 : oddCount 4564 13 = 5 ∧ acceleratedOrbit 13 4564 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4564) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4564.1, data_13_4564.2] + +/-- Complete interval computation for depth 13, residue 4565. -/ +theorem bounds_13_4565 : exactInterval 13 4565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4565 : oddCount 4565 13 = 5 ∧ acceleratedOrbit 13 4565 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4565) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4565.1, data_13_4565.2] + +/-- Complete interval computation for depth 13, residue 4566. -/ +theorem bounds_13_4566 : exactInterval 13 4566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4566 : oddCount 4566 13 = 7 ∧ acceleratedOrbit 13 4566 = 1220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4566) = 3 ^ 7 * m + 1220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4566.1, data_13_4566.2] + +end Collatz.Research.StoppingAtlas.Batch0764 From 267a9e62ccb72799ad734bc9fb8e1244455b37a1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:51 +0530 Subject: [PATCH 0765/1001] proof: certify atlas Batch0765 (13:4567 to 13:4581) --- Collatz/Research/StoppingAtlas/Batch0765.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0765.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0765.lean b/Collatz/Research/StoppingAtlas/Batch0765.lean new file mode 100644 index 00000000..825775bf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0765.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0765 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4567. -/ +theorem bounds_13_4567 : exactInterval 13 4567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4567 : oddCount 4567 13 = 7 ∧ acceleratedOrbit 13 4567 = 1220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4567) = 3 ^ 7 * m + 1220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4567.1, data_13_4567.2] + +/-- Complete interval computation for depth 13, residue 4568. -/ +theorem bounds_13_4568 : exactInterval 13 4568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4568 : oddCount 4568 13 = 5 ∧ acceleratedOrbit 13 4568 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4568) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4568.1, data_13_4568.2] + +/-- Complete interval computation for depth 13, residue 4569. -/ +theorem bounds_13_4569 : exactInterval 13 4569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4569 : oddCount 4569 13 = 5 ∧ acceleratedOrbit 13 4569 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4569) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4569.1, data_13_4569.2] + +/-- Complete interval computation for depth 13, residue 4570. -/ +theorem bounds_13_4570 : exactInterval 13 4570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4570 : oddCount 4570 13 = 5 ∧ acceleratedOrbit 13 4570 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4570) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4570.1, data_13_4570.2] + +/-- Complete interval computation for depth 13, residue 4571. -/ +theorem bounds_13_4571 : exactInterval 13 4571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4571 : oddCount 4571 13 = 6 ∧ acceleratedOrbit 13 4571 = 407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4571) = 3 ^ 6 * m + 407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4571.1, data_13_4571.2] + +/-- Complete interval computation for depth 13, residue 4572. -/ +theorem bounds_13_4572 : exactInterval 13 4572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4572 : oddCount 4572 13 = 5 ∧ acceleratedOrbit 13 4572 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4572) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4572.1, data_13_4572.2] + +/-- Complete interval computation for depth 13, residue 4573. -/ +theorem bounds_13_4573 : exactInterval 13 4573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4573 : oddCount 4573 13 = 5 ∧ acceleratedOrbit 13 4573 = 136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4573) = 3 ^ 5 * m + 136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4573.1, data_13_4573.2] + +/-- Complete interval computation for depth 13, residue 4574. -/ +theorem bounds_13_4574 : exactInterval 13 4574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4574 : oddCount 4574 13 = 10 ∧ acceleratedOrbit 13 4574 = 32987 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4574) = 3 ^ 10 * m + 32987 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4574.1, data_13_4574.2] + +/-- Complete interval computation for depth 13, residue 4575. -/ +theorem bounds_13_4575 : exactInterval 13 4575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4575 : oddCount 4575 13 = 10 ∧ acceleratedOrbit 13 4575 = 32987 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4575) = 3 ^ 10 * m + 32987 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4575.1, data_13_4575.2] + +/-- Complete interval computation for depth 13, residue 4576. -/ +theorem bounds_13_4576 : exactInterval 13 4576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4576 : oddCount 4576 13 = 5 ∧ acceleratedOrbit 13 4576 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4576) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4576.1, data_13_4576.2] + +/-- Complete interval computation for depth 13, residue 4577. -/ +theorem bounds_13_4577 : exactInterval 13 4577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4577 : oddCount 4577 13 = 7 ∧ acceleratedOrbit 13 4577 = 1223 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4577) = 3 ^ 7 * m + 1223 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4577.1, data_13_4577.2] + +/-- Complete interval computation for depth 13, residue 4578. -/ +theorem bounds_13_4578 : exactInterval 13 4578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4578 : oddCount 4578 13 = 5 ∧ acceleratedOrbit 13 4578 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4578) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4578.1, data_13_4578.2] + +/-- Complete interval computation for depth 13, residue 4579. -/ +theorem bounds_13_4579 : exactInterval 13 4579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4579 : oddCount 4579 13 = 5 ∧ acceleratedOrbit 13 4579 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4579) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4579.1, data_13_4579.2] + +/-- Complete interval computation for depth 13, residue 4580. -/ +theorem bounds_13_4580 : exactInterval 13 4580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4580 : oddCount 4580 13 = 7 ∧ acceleratedOrbit 13 4580 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4580) = 3 ^ 7 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4580.1, data_13_4580.2] + +/-- Complete interval computation for depth 13, residue 4581. -/ +theorem bounds_13_4581 : exactInterval 13 4581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4581 : oddCount 4581 13 = 7 ∧ acceleratedOrbit 13 4581 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4581) = 3 ^ 7 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4581.1, data_13_4581.2] + +end Collatz.Research.StoppingAtlas.Batch0765 From ab1920243ca41b2927c9bb46b081b260d3efe684 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:51 +0530 Subject: [PATCH 0766/1001] proof: certify atlas Batch0766 (13:4582 to 13:4596) --- Collatz/Research/StoppingAtlas/Batch0766.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0766.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0766.lean b/Collatz/Research/StoppingAtlas/Batch0766.lean new file mode 100644 index 00000000..2605b6b5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0766.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0766 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4582. -/ +theorem bounds_13_4582 : exactInterval 13 4582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4582 : oddCount 4582 13 = 7 ∧ acceleratedOrbit 13 4582 = 1225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4582) = 3 ^ 7 * m + 1225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4582.1, data_13_4582.2] + +/-- Complete interval computation for depth 13, residue 4583. -/ +theorem bounds_13_4583 : exactInterval 13 4583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4583 : oddCount 4583 13 = 10 ∧ acceleratedOrbit 13 4583 = 33047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4583) = 3 ^ 10 * m + 33047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4583.1, data_13_4583.2] + +/-- Complete interval computation for depth 13, residue 4584. -/ +theorem bounds_13_4584 : exactInterval 13 4584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4584 : oddCount 4584 13 = 5 ∧ acceleratedOrbit 13 4584 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4584) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4584.1, data_13_4584.2] + +/-- Complete interval computation for depth 13, residue 4585. -/ +theorem bounds_13_4585 : exactInterval 13 4585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4585 : oddCount 4585 13 = 8 ∧ acceleratedOrbit 13 4585 = 3674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4585) = 3 ^ 8 * m + 3674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4585.1, data_13_4585.2] + +/-- Complete interval computation for depth 13, residue 4586. -/ +theorem bounds_13_4586 : exactInterval 13 4586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4586 : oddCount 4586 13 = 5 ∧ acceleratedOrbit 13 4586 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4586) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4586.1, data_13_4586.2] + +/-- Complete interval computation for depth 13, residue 4587. -/ +theorem bounds_13_4587 : exactInterval 13 4587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4587 : oddCount 4587 13 = 9 ∧ acceleratedOrbit 13 4587 = 11026 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4587) = 3 ^ 9 * m + 11026 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4587.1, data_13_4587.2] + +/-- Complete interval computation for depth 13, residue 4588. -/ +theorem bounds_13_4588 : exactInterval 13 4588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4588 : oddCount 4588 13 = 6 ∧ acceleratedOrbit 13 4588 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4588) = 3 ^ 6 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4588.1, data_13_4588.2] + +/-- Complete interval computation for depth 13, residue 4589. -/ +theorem bounds_13_4589 : exactInterval 13 4589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4589 : oddCount 4589 13 = 6 ∧ acceleratedOrbit 13 4589 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4589) = 3 ^ 6 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4589.1, data_13_4589.2] + +/-- Complete interval computation for depth 13, residue 4590. -/ +theorem bounds_13_4590 : exactInterval 13 4590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4590 : oddCount 4590 13 = 6 ∧ acceleratedOrbit 13 4590 = 409 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4590) = 3 ^ 6 * m + 409 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4590.1, data_13_4590.2] + +/-- Complete interval computation for depth 13, residue 4591. -/ +theorem bounds_13_4591 : exactInterval 13 4591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4591 : oddCount 4591 13 = 11 ∧ acceleratedOrbit 13 4591 = 99305 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4591) = 3 ^ 11 * m + 99305 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4591.1, data_13_4591.2] + +/-- Complete interval computation for depth 13, residue 4592. -/ +theorem bounds_13_4592 : exactInterval 13 4592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4592 : oddCount 4592 13 = 6 ∧ acceleratedOrbit 13 4592 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4592) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4592.1, data_13_4592.2] + +/-- Complete interval computation for depth 13, residue 4593. -/ +theorem bounds_13_4593 : exactInterval 13 4593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4593 : oddCount 4593 13 = 5 ∧ acceleratedOrbit 13 4593 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4593) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4593.1, data_13_4593.2] + +/-- Complete interval computation for depth 13, residue 4594. -/ +theorem bounds_13_4594 : exactInterval 13 4594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4594 : oddCount 4594 13 = 7 ∧ acceleratedOrbit 13 4594 = 1228 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4594) = 3 ^ 7 * m + 1228 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4594.1, data_13_4594.2] + +/-- Complete interval computation for depth 13, residue 4595. -/ +theorem bounds_13_4595 : exactInterval 13 4595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4595 : oddCount 4595 13 = 7 ∧ acceleratedOrbit 13 4595 = 1228 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4595) = 3 ^ 7 * m + 1228 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4595.1, data_13_4595.2] + +/-- Complete interval computation for depth 13, residue 4596. -/ +theorem bounds_13_4596 : exactInterval 13 4596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4596 : oddCount 4596 13 = 6 ∧ acceleratedOrbit 13 4596 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4596) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4596.1, data_13_4596.2] + +end Collatz.Research.StoppingAtlas.Batch0766 From 32a747e6577fe4bb53524455b78153c66a72f252 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:52 +0530 Subject: [PATCH 0767/1001] proof: certify atlas Batch0767 (13:4597 to 13:4612) --- Collatz/Research/StoppingAtlas/Batch0767.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0767.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0767.lean b/Collatz/Research/StoppingAtlas/Batch0767.lean new file mode 100644 index 00000000..27497b3a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0767.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0767 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4597. -/ +theorem bounds_13_4597 : exactInterval 13 4597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4597 : oddCount 4597 13 = 6 ∧ acceleratedOrbit 13 4597 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4597) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4597.1, data_13_4597.2] + +/-- Complete interval computation for depth 13, residue 4598. -/ +theorem bounds_13_4598 : exactInterval 13 4598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4598 : oddCount 4598 13 = 9 ∧ acceleratedOrbit 13 4598 = 11056 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4598) = 3 ^ 9 * m + 11056 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4598.1, data_13_4598.2] + +/-- Complete interval computation for depth 13, residue 4599. -/ +theorem bounds_13_4599 : exactInterval 13 4599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4599 : oddCount 4599 13 = 9 ∧ acceleratedOrbit 13 4599 = 11056 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4599) = 3 ^ 9 * m + 11056 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4599.1, data_13_4599.2] + +/-- Complete interval computation for depth 13, residue 4600. -/ +theorem bounds_13_4600 : exactInterval 13 4600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4600 : oddCount 4600 13 = 6 ∧ acceleratedOrbit 13 4600 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4600) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4600.1, data_13_4600.2] + +/-- Complete interval computation for depth 13, residue 4601. -/ +theorem bounds_13_4601 : exactInterval 13 4601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4601 : oddCount 4601 13 = 7 ∧ acceleratedOrbit 13 4601 = 1229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4601) = 3 ^ 7 * m + 1229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4601.1, data_13_4601.2] + +/-- Complete interval computation for depth 13, residue 4602. -/ +theorem bounds_13_4602 : exactInterval 13 4602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4602 : oddCount 4602 13 = 6 ∧ acceleratedOrbit 13 4602 = 410 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4602) = 3 ^ 6 * m + 410 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4602.1, data_13_4602.2] + +/-- Complete interval computation for depth 13, residue 4603. -/ +theorem bounds_13_4603 : exactInterval 13 4603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4603 : oddCount 4603 13 = 8 ∧ acceleratedOrbit 13 4603 = 3689 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4603) = 3 ^ 8 * m + 3689 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4603.1, data_13_4603.2] + +/-- Complete interval computation for depth 13, residue 4604. -/ +theorem bounds_13_4604 : exactInterval 13 4604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4604 : oddCount 4604 13 = 9 ∧ acceleratedOrbit 13 4604 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4604) = 3 ^ 9 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4604.1, data_13_4604.2] + +/-- Complete interval computation for depth 13, residue 4605. -/ +theorem bounds_13_4605 : exactInterval 13 4605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4605 : oddCount 4605 13 = 9 ∧ acceleratedOrbit 13 4605 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4605) = 3 ^ 9 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4605.1, data_13_4605.2] + +/-- Complete interval computation for depth 13, residue 4606. -/ +theorem bounds_13_4606 : exactInterval 13 4606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4606 : oddCount 4606 13 = 9 ∧ acceleratedOrbit 13 4606 = 11072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4606) = 3 ^ 9 * m + 11072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4606.1, data_13_4606.2] + +/-- Complete interval computation for depth 13, residue 4607. -/ +theorem bounds_13_4607 : exactInterval 13 4607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4607) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4607 : oddCount 4607 13 = 10 ∧ acceleratedOrbit 13 4607 = 33215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4607) = 3 ^ 10 * m + 33215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4607.1, data_13_4607.2] + +/-- Complete interval computation for depth 13, residue 4608. -/ +theorem bounds_13_4608 : exactInterval 13 4608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4608 : oddCount 4608 13 = 3 ∧ acceleratedOrbit 13 4608 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4608) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4608.1, data_13_4608.2] + +/-- Complete interval computation for depth 13, residue 4609. -/ +theorem bounds_13_4609 : exactInterval 13 4609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4609 : oddCount 4609 13 = 7 ∧ acceleratedOrbit 13 4609 = 1232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4609) = 3 ^ 7 * m + 1232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4609.1, data_13_4609.2] + +/-- Complete interval computation for depth 13, residue 4610. -/ +theorem bounds_13_4610 : exactInterval 13 4610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4610 : oddCount 4610 13 = 5 ∧ acceleratedOrbit 13 4610 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4610) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4610.1, data_13_4610.2] + +/-- Complete interval computation for depth 13, residue 4611. -/ +theorem bounds_13_4611 : exactInterval 13 4611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4611 : oddCount 4611 13 = 5 ∧ acceleratedOrbit 13 4611 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4611) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4611.1, data_13_4611.2] + +/-- Complete interval computation for depth 13, residue 4612. -/ +theorem bounds_13_4612 : exactInterval 13 4612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4612 : oddCount 4612 13 = 7 ∧ acceleratedOrbit 13 4612 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4612) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4612.1, data_13_4612.2] + +end Collatz.Research.StoppingAtlas.Batch0767 From 768843726ab0b2240ba89fcbf099810ec53ae202 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:52 +0530 Subject: [PATCH 0768/1001] proof: certify atlas Batch0768 (13:4613 to 13:4627) --- Collatz/Research/StoppingAtlas/Batch0768.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0768.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0768.lean b/Collatz/Research/StoppingAtlas/Batch0768.lean new file mode 100644 index 00000000..9616de10 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0768.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0768 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4613. -/ +theorem bounds_13_4613 : exactInterval 13 4613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4613 : oddCount 4613 13 = 7 ∧ acceleratedOrbit 13 4613 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4613) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4613.1, data_13_4613.2] + +/-- Complete interval computation for depth 13, residue 4614. -/ +theorem bounds_13_4614 : exactInterval 13 4614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4614 : oddCount 4614 13 = 7 ∧ acceleratedOrbit 13 4614 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4614) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4614.1, data_13_4614.2] + +/-- Complete interval computation for depth 13, residue 4615. -/ +theorem bounds_13_4615 : exactInterval 13 4615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4615 : oddCount 4615 13 = 9 ∧ acceleratedOrbit 13 4615 = 11096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4615) = 3 ^ 9 * m + 11096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4615.1, data_13_4615.2] + +/-- Complete interval computation for depth 13, residue 4616. -/ +theorem bounds_13_4616 : exactInterval 13 4616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4616 : oddCount 4616 13 = 4 ∧ acceleratedOrbit 13 4616 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4616) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4616.1, data_13_4616.2] + +/-- Complete interval computation for depth 13, residue 4617. -/ +theorem bounds_13_4617 : exactInterval 13 4617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4617 : oddCount 4617 13 = 5 ∧ acceleratedOrbit 13 4617 = 137 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4617) = 3 ^ 5 * m + 137 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4617.1, data_13_4617.2] + +/-- Complete interval computation for depth 13, residue 4618. -/ +theorem bounds_13_4618 : exactInterval 13 4618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4618 : oddCount 4618 13 = 4 ∧ acceleratedOrbit 13 4618 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4618) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4618.1, data_13_4618.2] + +/-- Complete interval computation for depth 13, residue 4619. -/ +theorem bounds_13_4619 : exactInterval 13 4619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4619 : oddCount 4619 13 = 7 ∧ acceleratedOrbit 13 4619 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4619) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4619.1, data_13_4619.2] + +/-- Complete interval computation for depth 13, residue 4620. -/ +theorem bounds_13_4620 : exactInterval 13 4620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4620 : oddCount 4620 13 = 4 ∧ acceleratedOrbit 13 4620 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4620) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4620.1, data_13_4620.2] + +/-- Complete interval computation for depth 13, residue 4621. -/ +theorem bounds_13_4621 : exactInterval 13 4621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4621 : oddCount 4621 13 = 4 ∧ acceleratedOrbit 13 4621 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4621) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4621.1, data_13_4621.2] + +/-- Complete interval computation for depth 13, residue 4622. -/ +theorem bounds_13_4622 : exactInterval 13 4622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4622 : oddCount 4622 13 = 7 ∧ acceleratedOrbit 13 4622 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4622) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4622.1, data_13_4622.2] + +/-- Complete interval computation for depth 13, residue 4623. -/ +theorem bounds_13_4623 : exactInterval 13 4623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4623 : oddCount 4623 13 = 7 ∧ acceleratedOrbit 13 4623 = 1235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4623) = 3 ^ 7 * m + 1235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4623.1, data_13_4623.2] + +/-- Complete interval computation for depth 13, residue 4624. -/ +theorem bounds_13_4624 : exactInterval 13 4624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4624 : oddCount 4624 13 = 4 ∧ acceleratedOrbit 13 4624 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4624) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4624.1, data_13_4624.2] + +/-- Complete interval computation for depth 13, residue 4625. -/ +theorem bounds_13_4625 : exactInterval 13 4625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4625 : oddCount 4625 13 = 4 ∧ acceleratedOrbit 13 4625 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4625) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4625.1, data_13_4625.2] + +/-- Complete interval computation for depth 13, residue 4626. -/ +theorem bounds_13_4626 : exactInterval 13 4626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4626 : oddCount 4626 13 = 6 ∧ acceleratedOrbit 13 4626 = 412 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4626) = 3 ^ 6 * m + 412 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4626.1, data_13_4626.2] + +/-- Complete interval computation for depth 13, residue 4627. -/ +theorem bounds_13_4627 : exactInterval 13 4627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4627 : oddCount 4627 13 = 6 ∧ acceleratedOrbit 13 4627 = 412 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4627) = 3 ^ 6 * m + 412 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4627.1, data_13_4627.2] + +end Collatz.Research.StoppingAtlas.Batch0768 From 187a30ae0e6d425b5ea060eadfdb4e11092d95ef Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:52 +0530 Subject: [PATCH 0769/1001] proof: certify atlas Batch0769 (13:4628 to 13:4642) --- Collatz/Research/StoppingAtlas/Batch0769.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0769.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0769.lean b/Collatz/Research/StoppingAtlas/Batch0769.lean new file mode 100644 index 00000000..a8606c48 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0769.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0769 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4628. -/ +theorem bounds_13_4628 : exactInterval 13 4628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4628 : oddCount 4628 13 = 4 ∧ acceleratedOrbit 13 4628 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4628) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4628.1, data_13_4628.2] + +/-- Complete interval computation for depth 13, residue 4629. -/ +theorem bounds_13_4629 : exactInterval 13 4629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4629 : oddCount 4629 13 = 4 ∧ acceleratedOrbit 13 4629 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4629) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4629.1, data_13_4629.2] + +/-- Complete interval computation for depth 13, residue 4630. -/ +theorem bounds_13_4630 : exactInterval 13 4630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4630 : oddCount 4630 13 = 6 ∧ acceleratedOrbit 13 4630 = 413 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4630) = 3 ^ 6 * m + 413 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4630.1, data_13_4630.2] + +/-- Complete interval computation for depth 13, residue 4631. -/ +theorem bounds_13_4631 : exactInterval 13 4631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4631) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4631 : oddCount 4631 13 = 6 ∧ acceleratedOrbit 13 4631 = 413 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4631) = 3 ^ 6 * m + 413 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4631.1, data_13_4631.2] + +/-- Complete interval computation for depth 13, residue 4632. -/ +theorem bounds_13_4632 : exactInterval 13 4632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4632 : oddCount 4632 13 = 4 ∧ acceleratedOrbit 13 4632 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4632) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4632.1, data_13_4632.2] + +/-- Complete interval computation for depth 13, residue 4633. -/ +theorem bounds_13_4633 : exactInterval 13 4633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4633 : oddCount 4633 13 = 6 ∧ acceleratedOrbit 13 4633 = 413 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4633) = 3 ^ 6 * m + 413 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4633.1, data_13_4633.2] + +/-- Complete interval computation for depth 13, residue 4634. -/ +theorem bounds_13_4634 : exactInterval 13 4634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4634 : oddCount 4634 13 = 4 ∧ acceleratedOrbit 13 4634 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4634) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4634.1, data_13_4634.2] + +/-- Complete interval computation for depth 13, residue 4635. -/ +theorem bounds_13_4635 : exactInterval 13 4635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4635 : oddCount 4635 13 = 9 ∧ acceleratedOrbit 13 4635 = 11141 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4635) = 3 ^ 9 * m + 11141 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4635.1, data_13_4635.2] + +/-- Complete interval computation for depth 13, residue 4636. -/ +theorem bounds_13_4636 : exactInterval 13 4636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4636 : oddCount 4636 13 = 7 ∧ acceleratedOrbit 13 4636 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4636) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4636.1, data_13_4636.2] + +/-- Complete interval computation for depth 13, residue 4637. -/ +theorem bounds_13_4637 : exactInterval 13 4637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4637 : oddCount 4637 13 = 7 ∧ acceleratedOrbit 13 4637 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4637) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4637.1, data_13_4637.2] + +/-- Complete interval computation for depth 13, residue 4638. -/ +theorem bounds_13_4638 : exactInterval 13 4638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4638 : oddCount 4638 13 = 7 ∧ acceleratedOrbit 13 4638 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4638) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4638.1, data_13_4638.2] + +/-- Complete interval computation for depth 13, residue 4639. -/ +theorem bounds_13_4639 : exactInterval 13 4639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4639 : oddCount 4639 13 = 9 ∧ acceleratedOrbit 13 4639 = 11150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4639) = 3 ^ 9 * m + 11150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4639.1, data_13_4639.2] + +/-- Complete interval computation for depth 13, residue 4640. -/ +theorem bounds_13_4640 : exactInterval 13 4640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4640 : oddCount 4640 13 = 4 ∧ acceleratedOrbit 13 4640 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4640) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4640.1, data_13_4640.2] + +/-- Complete interval computation for depth 13, residue 4641. -/ +theorem bounds_13_4641 : exactInterval 13 4641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4641 : oddCount 4641 13 = 7 ∧ acceleratedOrbit 13 4641 = 1241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4641) = 3 ^ 7 * m + 1241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4641.1, data_13_4641.2] + +/-- Complete interval computation for depth 13, residue 4642. -/ +theorem bounds_13_4642 : exactInterval 13 4642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4642 : oddCount 4642 13 = 4 ∧ acceleratedOrbit 13 4642 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4642) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4642.1, data_13_4642.2] + +end Collatz.Research.StoppingAtlas.Batch0769 From ce22f12b6227ae2e1c9c352bd705fdc3cc08dc01 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:52 +0530 Subject: [PATCH 0770/1001] proof: certify atlas Batch0770 (13:4643 to 13:4658) --- Collatz/Research/StoppingAtlas/Batch0770.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0770.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0770.lean b/Collatz/Research/StoppingAtlas/Batch0770.lean new file mode 100644 index 00000000..8516127c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0770.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0770 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4643. -/ +theorem bounds_13_4643 : exactInterval 13 4643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4643 : oddCount 4643 13 = 4 ∧ acceleratedOrbit 13 4643 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4643) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4643.1, data_13_4643.2] + +/-- Complete interval computation for depth 13, residue 4644. -/ +theorem bounds_13_4644 : exactInterval 13 4644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4644 : oddCount 4644 13 = 9 ∧ acceleratedOrbit 13 4644 = 11177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4644) = 3 ^ 9 * m + 11177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4644.1, data_13_4644.2] + +/-- Complete interval computation for depth 13, residue 4645. -/ +theorem bounds_13_4645 : exactInterval 13 4645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4645 : oddCount 4645 13 = 9 ∧ acceleratedOrbit 13 4645 = 11177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4645) = 3 ^ 9 * m + 11177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4645.1, data_13_4645.2] + +/-- Complete interval computation for depth 13, residue 4646. -/ +theorem bounds_13_4646 : exactInterval 13 4646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4646 : oddCount 4646 13 = 9 ∧ acceleratedOrbit 13 4646 = 11177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4646) = 3 ^ 9 * m + 11177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4646.1, data_13_4646.2] + +/-- Complete interval computation for depth 13, residue 4647. -/ +theorem bounds_13_4647 : exactInterval 13 4647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4647 : oddCount 4647 13 = 8 ∧ acceleratedOrbit 13 4647 = 3725 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4647) = 3 ^ 8 * m + 3725 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4647.1, data_13_4647.2] + +/-- Complete interval computation for depth 13, residue 4648. -/ +theorem bounds_13_4648 : exactInterval 13 4648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4648 : oddCount 4648 13 = 4 ∧ acceleratedOrbit 13 4648 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4648) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4648.1, data_13_4648.2] + +/-- Complete interval computation for depth 13, residue 4649. -/ +theorem bounds_13_4649 : exactInterval 13 4649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4649 : oddCount 4649 13 = 10 ∧ acceleratedOrbit 13 4649 = 33524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4649) = 3 ^ 10 * m + 33524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4649.1, data_13_4649.2] + +/-- Complete interval computation for depth 13, residue 4650. -/ +theorem bounds_13_4650 : exactInterval 13 4650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4650 : oddCount 4650 13 = 4 ∧ acceleratedOrbit 13 4650 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4650) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4650.1, data_13_4650.2] + +/-- Complete interval computation for depth 13, residue 4651. -/ +theorem bounds_13_4651 : exactInterval 13 4651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4651 : oddCount 4651 13 = 4 ∧ acceleratedOrbit 13 4651 = 46 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4651) = 3 ^ 4 * m + 46 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4651.1, data_13_4651.2] + +/-- Complete interval computation for depth 13, residue 4652. -/ +theorem bounds_13_4652 : exactInterval 13 4652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4652 : oddCount 4652 13 = 6 ∧ acceleratedOrbit 13 4652 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4652) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4652.1, data_13_4652.2] + +/-- Complete interval computation for depth 13, residue 4653. -/ +theorem bounds_13_4653 : exactInterval 13 4653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4653 : oddCount 4653 13 = 6 ∧ acceleratedOrbit 13 4653 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4653) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4653.1, data_13_4653.2] + +/-- Complete interval computation for depth 13, residue 4654. -/ +theorem bounds_13_4654 : exactInterval 13 4654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4654 : oddCount 4654 13 = 6 ∧ acceleratedOrbit 13 4654 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4654) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4654.1, data_13_4654.2] + +/-- Complete interval computation for depth 13, residue 4655. -/ +theorem bounds_13_4655 : exactInterval 13 4655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4655 : oddCount 4655 13 = 9 ∧ acceleratedOrbit 13 4655 = 11188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4655) = 3 ^ 9 * m + 11188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4655.1, data_13_4655.2] + +/-- Complete interval computation for depth 13, residue 4656. -/ +theorem bounds_13_4656 : exactInterval 13 4656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4656 : oddCount 4656 13 = 4 ∧ acceleratedOrbit 13 4656 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4656) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4656.1, data_13_4656.2] + +/-- Complete interval computation for depth 13, residue 4657. -/ +theorem bounds_13_4657 : exactInterval 13 4657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4657 : oddCount 4657 13 = 6 ∧ acceleratedOrbit 13 4657 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4657) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4657.1, data_13_4657.2] + +/-- Complete interval computation for depth 13, residue 4658. -/ +theorem bounds_13_4658 : exactInterval 13 4658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4658 : oddCount 4658 13 = 6 ∧ acceleratedOrbit 13 4658 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4658) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4658.1, data_13_4658.2] + +end Collatz.Research.StoppingAtlas.Batch0770 From b95ea423d33559b8a404e9bb4b5358d3ff978588 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:52 +0530 Subject: [PATCH 0771/1001] proof: certify atlas Batch0771 (13:4659 to 13:4673) --- Collatz/Research/StoppingAtlas/Batch0771.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0771.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0771.lean b/Collatz/Research/StoppingAtlas/Batch0771.lean new file mode 100644 index 00000000..6aa69b40 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0771.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0771 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4659. -/ +theorem bounds_13_4659 : exactInterval 13 4659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4659 : oddCount 4659 13 = 6 ∧ acceleratedOrbit 13 4659 = 415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4659) = 3 ^ 6 * m + 415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4659.1, data_13_4659.2] + +/-- Complete interval computation for depth 13, residue 4660. -/ +theorem bounds_13_4660 : exactInterval 13 4660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4660 : oddCount 4660 13 = 4 ∧ acceleratedOrbit 13 4660 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4660) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4660.1, data_13_4660.2] + +/-- Complete interval computation for depth 13, residue 4661. -/ +theorem bounds_13_4661 : exactInterval 13 4661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4661 : oddCount 4661 13 = 4 ∧ acceleratedOrbit 13 4661 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4661) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4661.1, data_13_4661.2] + +/-- Complete interval computation for depth 13, residue 4662. -/ +theorem bounds_13_4662 : exactInterval 13 4662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4662 : oddCount 4662 13 = 8 ∧ acceleratedOrbit 13 4662 = 3736 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4662) = 3 ^ 8 * m + 3736 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4662.1, data_13_4662.2] + +/-- Complete interval computation for depth 13, residue 4663. -/ +theorem bounds_13_4663 : exactInterval 13 4663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4663 : oddCount 4663 13 = 8 ∧ acceleratedOrbit 13 4663 = 3736 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4663) = 3 ^ 8 * m + 3736 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4663.1, data_13_4663.2] + +/-- Complete interval computation for depth 13, residue 4664. -/ +theorem bounds_13_4664 : exactInterval 13 4664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4664 : oddCount 4664 13 = 6 ∧ acceleratedOrbit 13 4664 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4664) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4664.1, data_13_4664.2] + +/-- Complete interval computation for depth 13, residue 4665. -/ +theorem bounds_13_4665 : exactInterval 13 4665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4665 : oddCount 4665 13 = 8 ∧ acceleratedOrbit 13 4665 = 3739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4665) = 3 ^ 8 * m + 3739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4665.1, data_13_4665.2] + +/-- Complete interval computation for depth 13, residue 4666. -/ +theorem bounds_13_4666 : exactInterval 13 4666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4666 : oddCount 4666 13 = 6 ∧ acceleratedOrbit 13 4666 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4666) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4666.1, data_13_4666.2] + +/-- Complete interval computation for depth 13, residue 4667. -/ +theorem bounds_13_4667 : exactInterval 13 4667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4667 : oddCount 4667 13 = 6 ∧ acceleratedOrbit 13 4667 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4667) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4667.1, data_13_4667.2] + +/-- Complete interval computation for depth 13, residue 4668. -/ +theorem bounds_13_4668 : exactInterval 13 4668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4668 : oddCount 4668 13 = 6 ∧ acceleratedOrbit 13 4668 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4668) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4668.1, data_13_4668.2] + +/-- Complete interval computation for depth 13, residue 4669. -/ +theorem bounds_13_4669 : exactInterval 13 4669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4669 : oddCount 4669 13 = 6 ∧ acceleratedOrbit 13 4669 = 416 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4669) = 3 ^ 6 * m + 416 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4669.1, data_13_4669.2] + +/-- Complete interval computation for depth 13, residue 4670. -/ +theorem bounds_13_4670 : exactInterval 13 4670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4670 : oddCount 4670 13 = 8 ∧ acceleratedOrbit 13 4670 = 3743 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4670) = 3 ^ 8 * m + 3743 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4670.1, data_13_4670.2] + +/-- Complete interval computation for depth 13, residue 4671. -/ +theorem bounds_13_4671 : exactInterval 13 4671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4671 : oddCount 4671 13 = 8 ∧ acceleratedOrbit 13 4671 = 3743 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4671) = 3 ^ 8 * m + 3743 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4671.1, data_13_4671.2] + +/-- Complete interval computation for depth 13, residue 4672. -/ +theorem bounds_13_4672 : exactInterval 13 4672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4672 : oddCount 4672 13 = 4 ∧ acceleratedOrbit 13 4672 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4672) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4672.1, data_13_4672.2] + +/-- Complete interval computation for depth 13, residue 4673. -/ +theorem bounds_13_4673 : exactInterval 13 4673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4673 : oddCount 4673 13 = 5 ∧ acceleratedOrbit 13 4673 = 139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4673) = 3 ^ 5 * m + 139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4673.1, data_13_4673.2] + +end Collatz.Research.StoppingAtlas.Batch0771 From 4000d69127de9858782c68f3e4f05c24bcfa5674 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:53 +0530 Subject: [PATCH 0772/1001] proof: certify atlas Batch0772 (13:4674 to 13:4688) --- Collatz/Research/StoppingAtlas/Batch0772.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0772.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0772.lean b/Collatz/Research/StoppingAtlas/Batch0772.lean new file mode 100644 index 00000000..e1a699bd --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0772.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0772 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4674. -/ +theorem bounds_13_4674 : exactInterval 13 4674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4674 : oddCount 4674 13 = 5 ∧ acceleratedOrbit 13 4674 = 139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4674) = 3 ^ 5 * m + 139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4674.1, data_13_4674.2] + +/-- Complete interval computation for depth 13, residue 4675. -/ +theorem bounds_13_4675 : exactInterval 13 4675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4675 : oddCount 4675 13 = 5 ∧ acceleratedOrbit 13 4675 = 139 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4675) = 3 ^ 5 * m + 139 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4675.1, data_13_4675.2] + +/-- Complete interval computation for depth 13, residue 4676. -/ +theorem bounds_13_4676 : exactInterval 13 4676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4676 : oddCount 4676 13 = 6 ∧ acceleratedOrbit 13 4676 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4676) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4676.1, data_13_4676.2] + +/-- Complete interval computation for depth 13, residue 4677. -/ +theorem bounds_13_4677 : exactInterval 13 4677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4677 : oddCount 4677 13 = 6 ∧ acceleratedOrbit 13 4677 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4677) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4677.1, data_13_4677.2] + +/-- Complete interval computation for depth 13, residue 4678. -/ +theorem bounds_13_4678 : exactInterval 13 4678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4678 : oddCount 4678 13 = 6 ∧ acceleratedOrbit 13 4678 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4678) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4678.1, data_13_4678.2] + +/-- Complete interval computation for depth 13, residue 4679. -/ +theorem bounds_13_4679 : exactInterval 13 4679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4679 : oddCount 4679 13 = 7 ∧ acceleratedOrbit 13 4679 = 1250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4679) = 3 ^ 7 * m + 1250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4679.1, data_13_4679.2] + +/-- Complete interval computation for depth 13, residue 4680. -/ +theorem bounds_13_4680 : exactInterval 13 4680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4680 : oddCount 4680 13 = 6 ∧ acceleratedOrbit 13 4680 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4680) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4680.1, data_13_4680.2] + +/-- Complete interval computation for depth 13, residue 4681. -/ +theorem bounds_13_4681 : exactInterval 13 4681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4681 : oddCount 4681 13 = 8 ∧ acceleratedOrbit 13 4681 = 3752 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4681) = 3 ^ 8 * m + 3752 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4681.1, data_13_4681.2] + +/-- Complete interval computation for depth 13, residue 4682. -/ +theorem bounds_13_4682 : exactInterval 13 4682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4682 : oddCount 4682 13 = 6 ∧ acceleratedOrbit 13 4682 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4682) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4682.1, data_13_4682.2] + +/-- Complete interval computation for depth 13, residue 4683. -/ +theorem bounds_13_4683 : exactInterval 13 4683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4683 : oddCount 4683 13 = 6 ∧ acceleratedOrbit 13 4683 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4683) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4683.1, data_13_4683.2] + +/-- Complete interval computation for depth 13, residue 4684. -/ +theorem bounds_13_4684 : exactInterval 13 4684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4684 : oddCount 4684 13 = 6 ∧ acceleratedOrbit 13 4684 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4684) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4684.1, data_13_4684.2] + +/-- Complete interval computation for depth 13, residue 4685. -/ +theorem bounds_13_4685 : exactInterval 13 4685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4685 : oddCount 4685 13 = 6 ∧ acceleratedOrbit 13 4685 = 418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4685) = 3 ^ 6 * m + 418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4685.1, data_13_4685.2] + +/-- Complete interval computation for depth 13, residue 4686. -/ +theorem bounds_13_4686 : exactInterval 13 4686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4686 : oddCount 4686 13 = 7 ∧ acceleratedOrbit 13 4686 = 1252 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4686) = 3 ^ 7 * m + 1252 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4686.1, data_13_4686.2] + +/-- Complete interval computation for depth 13, residue 4687. -/ +theorem bounds_13_4687 : exactInterval 13 4687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4687 : oddCount 4687 13 = 7 ∧ acceleratedOrbit 13 4687 = 1252 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4687) = 3 ^ 7 * m + 1252 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4687.1, data_13_4687.2] + +/-- Complete interval computation for depth 13, residue 4688. -/ +theorem bounds_13_4688 : exactInterval 13 4688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4688 : oddCount 4688 13 = 4 ∧ acceleratedOrbit 13 4688 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4688) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4688.1, data_13_4688.2] + +end Collatz.Research.StoppingAtlas.Batch0772 From 9c1033b32f0e0e85766425bb4e2f883fbb0cd12e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:54 +0530 Subject: [PATCH 0773/1001] proof: certify atlas Batch0773 (13:4689 to 13:4704) --- Collatz/Research/StoppingAtlas/Batch0773.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0773.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0773.lean b/Collatz/Research/StoppingAtlas/Batch0773.lean new file mode 100644 index 00000000..c2a7d0da --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0773.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0773 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4689. -/ +theorem bounds_13_4689 : exactInterval 13 4689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4689 : oddCount 4689 13 = 7 ∧ acceleratedOrbit 13 4689 = 1253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4689) = 3 ^ 7 * m + 1253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4689.1, data_13_4689.2] + +/-- Complete interval computation for depth 13, residue 4690. -/ +theorem bounds_13_4690 : exactInterval 13 4690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4690 : oddCount 4690 13 = 7 ∧ acceleratedOrbit 13 4690 = 1253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4690) = 3 ^ 7 * m + 1253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4690.1, data_13_4690.2] + +/-- Complete interval computation for depth 13, residue 4691. -/ +theorem bounds_13_4691 : exactInterval 13 4691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4691 : oddCount 4691 13 = 7 ∧ acceleratedOrbit 13 4691 = 1253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4691) = 3 ^ 7 * m + 1253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4691.1, data_13_4691.2] + +/-- Complete interval computation for depth 13, residue 4692. -/ +theorem bounds_13_4692 : exactInterval 13 4692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4692 : oddCount 4692 13 = 4 ∧ acceleratedOrbit 13 4692 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4692) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4692.1, data_13_4692.2] + +/-- Complete interval computation for depth 13, residue 4693. -/ +theorem bounds_13_4693 : exactInterval 13 4693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4693 : oddCount 4693 13 = 4 ∧ acceleratedOrbit 13 4693 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4693) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4693.1, data_13_4693.2] + +/-- Complete interval computation for depth 13, residue 4694. -/ +theorem bounds_13_4694 : exactInterval 13 4694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4694 : oddCount 4694 13 = 7 ∧ acceleratedOrbit 13 4694 = 1255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4694) = 3 ^ 7 * m + 1255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4694.1, data_13_4694.2] + +/-- Complete interval computation for depth 13, residue 4695. -/ +theorem bounds_13_4695 : exactInterval 13 4695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4695 : oddCount 4695 13 = 7 ∧ acceleratedOrbit 13 4695 = 1255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4695) = 3 ^ 7 * m + 1255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4695.1, data_13_4695.2] + +/-- Complete interval computation for depth 13, residue 4696. -/ +theorem bounds_13_4696 : exactInterval 13 4696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4696 : oddCount 4696 13 = 4 ∧ acceleratedOrbit 13 4696 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4696) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4696.1, data_13_4696.2] + +/-- Complete interval computation for depth 13, residue 4697. -/ +theorem bounds_13_4697 : exactInterval 13 4697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4697 : oddCount 4697 13 = 8 ∧ acceleratedOrbit 13 4697 = 3766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4697) = 3 ^ 8 * m + 3766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4697.1, data_13_4697.2] + +/-- Complete interval computation for depth 13, residue 4698. -/ +theorem bounds_13_4698 : exactInterval 13 4698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4698 : oddCount 4698 13 = 4 ∧ acceleratedOrbit 13 4698 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4698) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4698.1, data_13_4698.2] + +/-- Complete interval computation for depth 13, residue 4699. -/ +theorem bounds_13_4699 : exactInterval 13 4699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4699 : oddCount 4699 13 = 10 ∧ acceleratedOrbit 13 4699 = 33884 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4699) = 3 ^ 10 * m + 33884 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4699.1, data_13_4699.2] + +/-- Complete interval computation for depth 13, residue 4700. -/ +theorem bounds_13_4700 : exactInterval 13 4700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4700 : oddCount 4700 13 = 4 ∧ acceleratedOrbit 13 4700 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4700) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4700.1, data_13_4700.2] + +/-- Complete interval computation for depth 13, residue 4701. -/ +theorem bounds_13_4701 : exactInterval 13 4701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4701 : oddCount 4701 13 = 4 ∧ acceleratedOrbit 13 4701 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4701) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4701.1, data_13_4701.2] + +/-- Complete interval computation for depth 13, residue 4702. -/ +theorem bounds_13_4702 : exactInterval 13 4702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4702 : oddCount 4702 13 = 7 ∧ acceleratedOrbit 13 4702 = 1256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4702) = 3 ^ 7 * m + 1256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4702.1, data_13_4702.2] + +/-- Complete interval computation for depth 13, residue 4703. -/ +theorem bounds_13_4703 : exactInterval 13 4703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4703 : oddCount 4703 13 = 7 ∧ acceleratedOrbit 13 4703 = 1256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4703) = 3 ^ 7 * m + 1256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4703.1, data_13_4703.2] + +/-- Complete interval computation for depth 13, residue 4704. -/ +theorem bounds_13_4704 : exactInterval 13 4704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4704 : oddCount 4704 13 = 4 ∧ acceleratedOrbit 13 4704 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4704) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4704.1, data_13_4704.2] + +end Collatz.Research.StoppingAtlas.Batch0773 From c81fa1970780359c64d195d149fd5f4d48f7a322 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:54 +0530 Subject: [PATCH 0774/1001] proof: certify atlas Batch0774 (13:4705 to 13:4719) --- Collatz/Research/StoppingAtlas/Batch0774.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0774.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0774.lean b/Collatz/Research/StoppingAtlas/Batch0774.lean new file mode 100644 index 00000000..fa017ed7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0774.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0774 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4705. -/ +theorem bounds_13_4705 : exactInterval 13 4705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4705 : oddCount 4705 13 = 6 ∧ acceleratedOrbit 13 4705 = 419 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4705) = 3 ^ 6 * m + 419 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4705.1, data_13_4705.2] + +/-- Complete interval computation for depth 13, residue 4706. -/ +theorem bounds_13_4706 : exactInterval 13 4706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4706 : oddCount 4706 13 = 5 ∧ acceleratedOrbit 13 4706 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4706) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4706.1, data_13_4706.2] + +/-- Complete interval computation for depth 13, residue 4707. -/ +theorem bounds_13_4707 : exactInterval 13 4707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4707 : oddCount 4707 13 = 5 ∧ acceleratedOrbit 13 4707 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4707) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4707.1, data_13_4707.2] + +/-- Complete interval computation for depth 13, residue 4708. -/ +theorem bounds_13_4708 : exactInterval 13 4708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4708 : oddCount 4708 13 = 5 ∧ acceleratedOrbit 13 4708 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4708) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4708.1, data_13_4708.2] + +/-- Complete interval computation for depth 13, residue 4709. -/ +theorem bounds_13_4709 : exactInterval 13 4709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4709 : oddCount 4709 13 = 5 ∧ acceleratedOrbit 13 4709 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4709) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4709.1, data_13_4709.2] + +/-- Complete interval computation for depth 13, residue 4710. -/ +theorem bounds_13_4710 : exactInterval 13 4710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4710 : oddCount 4710 13 = 5 ∧ acceleratedOrbit 13 4710 = 140 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4710) = 3 ^ 5 * m + 140 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4710.1, data_13_4710.2] + +/-- Complete interval computation for depth 13, residue 4711. -/ +theorem bounds_13_4711 : exactInterval 13 4711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4711 : oddCount 4711 13 = 7 ∧ acceleratedOrbit 13 4711 = 1258 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4711) = 3 ^ 7 * m + 1258 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4711.1, data_13_4711.2] + +/-- Complete interval computation for depth 13, residue 4712. -/ +theorem bounds_13_4712 : exactInterval 13 4712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4712 : oddCount 4712 13 = 4 ∧ acceleratedOrbit 13 4712 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4712) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4712.1, data_13_4712.2] + +/-- Complete interval computation for depth 13, residue 4713. -/ +theorem bounds_13_4713 : exactInterval 13 4713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4713 : oddCount 4713 13 = 9 ∧ acceleratedOrbit 13 4713 = 11330 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4713) = 3 ^ 9 * m + 11330 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4713.1, data_13_4713.2] + +/-- Complete interval computation for depth 13, residue 4714. -/ +theorem bounds_13_4714 : exactInterval 13 4714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4714 : oddCount 4714 13 = 4 ∧ acceleratedOrbit 13 4714 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4714) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4714.1, data_13_4714.2] + +/-- Complete interval computation for depth 13, residue 4715. -/ +theorem bounds_13_4715 : exactInterval 13 4715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4715 : oddCount 4715 13 = 8 ∧ acceleratedOrbit 13 4715 = 3779 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4715) = 3 ^ 8 * m + 3779 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4715.1, data_13_4715.2] + +/-- Complete interval computation for depth 13, residue 4716. -/ +theorem bounds_13_4716 : exactInterval 13 4716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4716 : oddCount 4716 13 = 8 ∧ acceleratedOrbit 13 4716 = 3782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4716) = 3 ^ 8 * m + 3782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4716.1, data_13_4716.2] + +/-- Complete interval computation for depth 13, residue 4717. -/ +theorem bounds_13_4717 : exactInterval 13 4717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4717 : oddCount 4717 13 = 8 ∧ acceleratedOrbit 13 4717 = 3782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4717) = 3 ^ 8 * m + 3782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4717.1, data_13_4717.2] + +/-- Complete interval computation for depth 13, residue 4718. -/ +theorem bounds_13_4718 : exactInterval 13 4718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4718 : oddCount 4718 13 = 8 ∧ acceleratedOrbit 13 4718 = 3782 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4718) = 3 ^ 8 * m + 3782 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4718.1, data_13_4718.2] + +/-- Complete interval computation for depth 13, residue 4719. -/ +theorem bounds_13_4719 : exactInterval 13 4719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4719 : oddCount 4719 13 = 9 ∧ acceleratedOrbit 13 4719 = 11342 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4719) = 3 ^ 9 * m + 11342 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4719.1, data_13_4719.2] + +end Collatz.Research.StoppingAtlas.Batch0774 From f170829641677747b421d57ba9b8b38a7f8cd59d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:54 +0530 Subject: [PATCH 0775/1001] proof: certify atlas Batch0775 (13:4720 to 13:4735) --- Collatz/Research/StoppingAtlas/Batch0775.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0775.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0775.lean b/Collatz/Research/StoppingAtlas/Batch0775.lean new file mode 100644 index 00000000..b5b93255 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0775.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0775 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4720. -/ +theorem bounds_13_4720 : exactInterval 13 4720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4720 : oddCount 4720 13 = 6 ∧ acceleratedOrbit 13 4720 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4720) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4720.1, data_13_4720.2] + +/-- Complete interval computation for depth 13, residue 4721. -/ +theorem bounds_13_4721 : exactInterval 13 4721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4721 : oddCount 4721 13 = 4 ∧ acceleratedOrbit 13 4721 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4721) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4721.1, data_13_4721.2] + +/-- Complete interval computation for depth 13, residue 4722. -/ +theorem bounds_13_4722 : exactInterval 13 4722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4722 : oddCount 4722 13 = 7 ∧ acceleratedOrbit 13 4722 = 1262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4722) = 3 ^ 7 * m + 1262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4722.1, data_13_4722.2] + +/-- Complete interval computation for depth 13, residue 4723. -/ +theorem bounds_13_4723 : exactInterval 13 4723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4723 : oddCount 4723 13 = 7 ∧ acceleratedOrbit 13 4723 = 1262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4723) = 3 ^ 7 * m + 1262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4723.1, data_13_4723.2] + +/-- Complete interval computation for depth 13, residue 4724. -/ +theorem bounds_13_4724 : exactInterval 13 4724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4724 : oddCount 4724 13 = 6 ∧ acceleratedOrbit 13 4724 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4724) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4724.1, data_13_4724.2] + +/-- Complete interval computation for depth 13, residue 4725. -/ +theorem bounds_13_4725 : exactInterval 13 4725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4725 : oddCount 4725 13 = 6 ∧ acceleratedOrbit 13 4725 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4725) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4725.1, data_13_4725.2] + +/-- Complete interval computation for depth 13, residue 4726. -/ +theorem bounds_13_4726 : exactInterval 13 4726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4726 : oddCount 4726 13 = 6 ∧ acceleratedOrbit 13 4726 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4726) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4726.1, data_13_4726.2] + +/-- Complete interval computation for depth 13, residue 4727. -/ +theorem bounds_13_4727 : exactInterval 13 4727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4727 : oddCount 4727 13 = 6 ∧ acceleratedOrbit 13 4727 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4727) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4727.1, data_13_4727.2] + +/-- Complete interval computation for depth 13, residue 4728. -/ +theorem bounds_13_4728 : exactInterval 13 4728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4728 : oddCount 4728 13 = 6 ∧ acceleratedOrbit 13 4728 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4728) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4728.1, data_13_4728.2] + +/-- Complete interval computation for depth 13, residue 4729. -/ +theorem bounds_13_4729 : exactInterval 13 4729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4729 : oddCount 4729 13 = 6 ∧ acceleratedOrbit 13 4729 = 421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4729) = 3 ^ 6 * m + 421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4729.1, data_13_4729.2] + +/-- Complete interval computation for depth 13, residue 4730. -/ +theorem bounds_13_4730 : exactInterval 13 4730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4730 : oddCount 4730 13 = 6 ∧ acceleratedOrbit 13 4730 = 422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4730) = 3 ^ 6 * m + 422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4730.1, data_13_4730.2] + +/-- Complete interval computation for depth 13, residue 4731. -/ +theorem bounds_13_4731 : exactInterval 13 4731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4731 : oddCount 4731 13 = 7 ∧ acceleratedOrbit 13 4731 = 1264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4731) = 3 ^ 7 * m + 1264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4731.1, data_13_4731.2] + +/-- Complete interval computation for depth 13, residue 4732. -/ +theorem bounds_13_4732 : exactInterval 13 4732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4732 : oddCount 4732 13 = 9 ∧ acceleratedOrbit 13 4732 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4732) = 3 ^ 9 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4732.1, data_13_4732.2] + +/-- Complete interval computation for depth 13, residue 4733. -/ +theorem bounds_13_4733 : exactInterval 13 4733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4733 : oddCount 4733 13 = 9 ∧ acceleratedOrbit 13 4733 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4733) = 3 ^ 9 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4733.1, data_13_4733.2] + +/-- Complete interval computation for depth 13, residue 4734. -/ +theorem bounds_13_4734 : exactInterval 13 4734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4734 : oddCount 4734 13 = 9 ∧ acceleratedOrbit 13 4734 = 11380 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4734) = 3 ^ 9 * m + 11380 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4734.1, data_13_4734.2] + +/-- Complete interval computation for depth 13, residue 4735. -/ +theorem bounds_13_4735 : exactInterval 13 4735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4735 : oddCount 4735 13 = 10 ∧ acceleratedOrbit 13 4735 = 34138 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4735) = 3 ^ 10 * m + 34138 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4735.1, data_13_4735.2] + +end Collatz.Research.StoppingAtlas.Batch0775 From 5862cd49859bc9ba2cf53fcd93c8de396da7f859 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:54 +0530 Subject: [PATCH 0776/1001] proof: certify atlas Batch0776 (13:4736 to 13:4750) --- Collatz/Research/StoppingAtlas/Batch0776.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0776.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0776.lean b/Collatz/Research/StoppingAtlas/Batch0776.lean new file mode 100644 index 00000000..436e95a4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0776.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0776 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4736. -/ +theorem bounds_13_4736 : exactInterval 13 4736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4736 : oddCount 4736 13 = 3 ∧ acceleratedOrbit 13 4736 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4736) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4736.1, data_13_4736.2] + +/-- Complete interval computation for depth 13, residue 4737. -/ +theorem bounds_13_4737 : exactInterval 13 4737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4737 : oddCount 4737 13 = 8 ∧ acceleratedOrbit 13 4737 = 3797 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4737) = 3 ^ 8 * m + 3797 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4737.1, data_13_4737.2] + +/-- Complete interval computation for depth 13, residue 4738. -/ +theorem bounds_13_4738 : exactInterval 13 4738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4738 : oddCount 4738 13 = 4 ∧ acceleratedOrbit 13 4738 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4738) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4738.1, data_13_4738.2] + +/-- Complete interval computation for depth 13, residue 4739. -/ +theorem bounds_13_4739 : exactInterval 13 4739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4739 : oddCount 4739 13 = 4 ∧ acceleratedOrbit 13 4739 = 47 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4739) = 3 ^ 4 * m + 47 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4739.1, data_13_4739.2] + +/-- Complete interval computation for depth 13, residue 4740. -/ +theorem bounds_13_4740 : exactInterval 13 4740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4740 : oddCount 4740 13 = 8 ∧ acceleratedOrbit 13 4740 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4740) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4740.1, data_13_4740.2] + +/-- Complete interval computation for depth 13, residue 4741. -/ +theorem bounds_13_4741 : exactInterval 13 4741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4741 : oddCount 4741 13 = 8 ∧ acceleratedOrbit 13 4741 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4741) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4741.1, data_13_4741.2] + +/-- Complete interval computation for depth 13, residue 4742. -/ +theorem bounds_13_4742 : exactInterval 13 4742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4742 : oddCount 4742 13 = 8 ∧ acceleratedOrbit 13 4742 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4742) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4742.1, data_13_4742.2] + +/-- Complete interval computation for depth 13, residue 4743. -/ +theorem bounds_13_4743 : exactInterval 13 4743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4743 : oddCount 4743 13 = 7 ∧ acceleratedOrbit 13 4743 = 1268 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4743) = 3 ^ 7 * m + 1268 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4743.1, data_13_4743.2] + +/-- Complete interval computation for depth 13, residue 4744. -/ +theorem bounds_13_4744 : exactInterval 13 4744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4744 : oddCount 4744 13 = 6 ∧ acceleratedOrbit 13 4744 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4744) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4744.1, data_13_4744.2] + +/-- Complete interval computation for depth 13, residue 4745. -/ +theorem bounds_13_4745 : exactInterval 13 4745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4745 : oddCount 4745 13 = 8 ∧ acceleratedOrbit 13 4745 = 3802 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4745) = 3 ^ 8 * m + 3802 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4745.1, data_13_4745.2] + +/-- Complete interval computation for depth 13, residue 4746. -/ +theorem bounds_13_4746 : exactInterval 13 4746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4746 : oddCount 4746 13 = 6 ∧ acceleratedOrbit 13 4746 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4746) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4746.1, data_13_4746.2] + +/-- Complete interval computation for depth 13, residue 4747. -/ +theorem bounds_13_4747 : exactInterval 13 4747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4747 : oddCount 4747 13 = 8 ∧ acceleratedOrbit 13 4747 = 3806 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4747) = 3 ^ 8 * m + 3806 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4747.1, data_13_4747.2] + +/-- Complete interval computation for depth 13, residue 4748. -/ +theorem bounds_13_4748 : exactInterval 13 4748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4748 : oddCount 4748 13 = 6 ∧ acceleratedOrbit 13 4748 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4748) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4748.1, data_13_4748.2] + +/-- Complete interval computation for depth 13, residue 4749. -/ +theorem bounds_13_4749 : exactInterval 13 4749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4749 : oddCount 4749 13 = 6 ∧ acceleratedOrbit 13 4749 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4749) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4749.1, data_13_4749.2] + +/-- Complete interval computation for depth 13, residue 4750. -/ +theorem bounds_13_4750 : exactInterval 13 4750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4750 : oddCount 4750 13 = 10 ∧ acceleratedOrbit 13 4750 = 34262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4750) = 3 ^ 10 * m + 34262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4750.1, data_13_4750.2] + +end Collatz.Research.StoppingAtlas.Batch0776 From 9d1d6b9e33e38065607e759fc227a87082fbdcf4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:55 +0530 Subject: [PATCH 0777/1001] proof: certify atlas Batch0777 (13:4751 to 13:4765) --- Collatz/Research/StoppingAtlas/Batch0777.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0777.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0777.lean b/Collatz/Research/StoppingAtlas/Batch0777.lean new file mode 100644 index 00000000..0f4a1373 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0777.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0777 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4751. -/ +theorem bounds_13_4751 : exactInterval 13 4751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4751 : oddCount 4751 13 = 10 ∧ acceleratedOrbit 13 4751 = 34262 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4751) = 3 ^ 10 * m + 34262 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4751.1, data_13_4751.2] + +/-- Complete interval computation for depth 13, residue 4752. -/ +theorem bounds_13_4752 : exactInterval 13 4752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4752 : oddCount 4752 13 = 6 ∧ acceleratedOrbit 13 4752 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4752) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4752.1, data_13_4752.2] + +/-- Complete interval computation for depth 13, residue 4753. -/ +theorem bounds_13_4753 : exactInterval 13 4753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4753 : oddCount 4753 13 = 7 ∧ acceleratedOrbit 13 4753 = 1271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4753) = 3 ^ 7 * m + 1271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4753.1, data_13_4753.2] + +/-- Complete interval computation for depth 13, residue 4754. -/ +theorem bounds_13_4754 : exactInterval 13 4754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4754 : oddCount 4754 13 = 7 ∧ acceleratedOrbit 13 4754 = 1271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4754) = 3 ^ 7 * m + 1271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4754.1, data_13_4754.2] + +/-- Complete interval computation for depth 13, residue 4755. -/ +theorem bounds_13_4755 : exactInterval 13 4755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4755 : oddCount 4755 13 = 7 ∧ acceleratedOrbit 13 4755 = 1271 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4755) = 3 ^ 7 * m + 1271 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4755.1, data_13_4755.2] + +/-- Complete interval computation for depth 13, residue 4756. -/ +theorem bounds_13_4756 : exactInterval 13 4756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4756 : oddCount 4756 13 = 6 ∧ acceleratedOrbit 13 4756 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4756) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4756.1, data_13_4756.2] + +/-- Complete interval computation for depth 13, residue 4757. -/ +theorem bounds_13_4757 : exactInterval 13 4757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4757 : oddCount 4757 13 = 6 ∧ acceleratedOrbit 13 4757 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4757) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4757.1, data_13_4757.2] + +/-- Complete interval computation for depth 13, residue 4758. -/ +theorem bounds_13_4758 : exactInterval 13 4758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4758 : oddCount 4758 13 = 6 ∧ acceleratedOrbit 13 4758 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4758) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4758.1, data_13_4758.2] + +/-- Complete interval computation for depth 13, residue 4759. -/ +theorem bounds_13_4759 : exactInterval 13 4759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4759 : oddCount 4759 13 = 6 ∧ acceleratedOrbit 13 4759 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4759) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4759.1, data_13_4759.2] + +/-- Complete interval computation for depth 13, residue 4760. -/ +theorem bounds_13_4760 : exactInterval 13 4760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4760 : oddCount 4760 13 = 6 ∧ acceleratedOrbit 13 4760 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4760) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4760.1, data_13_4760.2] + +/-- Complete interval computation for depth 13, residue 4761. -/ +theorem bounds_13_4761 : exactInterval 13 4761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4761 : oddCount 4761 13 = 6 ∧ acceleratedOrbit 13 4761 = 424 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4761) = 3 ^ 6 * m + 424 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4761.1, data_13_4761.2] + +/-- Complete interval computation for depth 13, residue 4762. -/ +theorem bounds_13_4762 : exactInterval 13 4762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4762 : oddCount 4762 13 = 6 ∧ acceleratedOrbit 13 4762 = 425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4762) = 3 ^ 6 * m + 425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4762.1, data_13_4762.2] + +/-- Complete interval computation for depth 13, residue 4763. -/ +theorem bounds_13_4763 : exactInterval 13 4763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4763 : oddCount 4763 13 = 11 ∧ acceleratedOrbit 13 4763 = 103031 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4763) = 3 ^ 11 * m + 103031 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4763.1, data_13_4763.2] + +/-- Complete interval computation for depth 13, residue 4764. -/ +theorem bounds_13_4764 : exactInterval 13 4764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4764 : oddCount 4764 13 = 8 ∧ acceleratedOrbit 13 4764 = 3820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4764) = 3 ^ 8 * m + 3820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4764.1, data_13_4764.2] + +/-- Complete interval computation for depth 13, residue 4765. -/ +theorem bounds_13_4765 : exactInterval 13 4765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4765 : oddCount 4765 13 = 8 ∧ acceleratedOrbit 13 4765 = 3820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4765) = 3 ^ 8 * m + 3820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4765.1, data_13_4765.2] + +end Collatz.Research.StoppingAtlas.Batch0777 From 215ffb812c568f3d159415503194d519c2ba9833 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:35:58 +0530 Subject: [PATCH 0778/1001] proof: certify atlas Batch0778 (13:4766 to 13:4781) --- Collatz/Research/StoppingAtlas/Batch0778.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0778.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0778.lean b/Collatz/Research/StoppingAtlas/Batch0778.lean new file mode 100644 index 00000000..8bda3f0b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0778.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0778 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4766. -/ +theorem bounds_13_4766 : exactInterval 13 4766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4766 : oddCount 4766 13 = 8 ∧ acceleratedOrbit 13 4766 = 3820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4766) = 3 ^ 8 * m + 3820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4766.1, data_13_4766.2] + +/-- Complete interval computation for depth 13, residue 4767. -/ +theorem bounds_13_4767 : exactInterval 13 4767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4767 : oddCount 4767 13 = 10 ∧ acceleratedOrbit 13 4767 = 34370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4767) = 3 ^ 10 * m + 34370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4767.1, data_13_4767.2] + +/-- Complete interval computation for depth 13, residue 4768. -/ +theorem bounds_13_4768 : exactInterval 13 4768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4768 : oddCount 4768 13 = 3 ∧ acceleratedOrbit 13 4768 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4768) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4768.1, data_13_4768.2] + +/-- Complete interval computation for depth 13, residue 4769. -/ +theorem bounds_13_4769 : exactInterval 13 4769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4769 : oddCount 4769 13 = 7 ∧ acceleratedOrbit 13 4769 = 1274 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4769) = 3 ^ 7 * m + 1274 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4769.1, data_13_4769.2] + +/-- Complete interval computation for depth 13, residue 4770. -/ +theorem bounds_13_4770 : exactInterval 13 4770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4770 : oddCount 4770 13 = 8 ∧ acceleratedOrbit 13 4770 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4770) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4770.1, data_13_4770.2] + +/-- Complete interval computation for depth 13, residue 4771. -/ +theorem bounds_13_4771 : exactInterval 13 4771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4771 : oddCount 4771 13 = 8 ∧ acceleratedOrbit 13 4771 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4771) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4771.1, data_13_4771.2] + +/-- Complete interval computation for depth 13, residue 4772. -/ +theorem bounds_13_4772 : exactInterval 13 4772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4772 : oddCount 4772 13 = 8 ∧ acceleratedOrbit 13 4772 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4772) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4772.1, data_13_4772.2] + +/-- Complete interval computation for depth 13, residue 4773. -/ +theorem bounds_13_4773 : exactInterval 13 4773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4773 : oddCount 4773 13 = 8 ∧ acceleratedOrbit 13 4773 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4773) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4773.1, data_13_4773.2] + +/-- Complete interval computation for depth 13, residue 4774. -/ +theorem bounds_13_4774 : exactInterval 13 4774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4774 : oddCount 4774 13 = 8 ∧ acceleratedOrbit 13 4774 = 3827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4774) = 3 ^ 8 * m + 3827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4774.1, data_13_4774.2] + +/-- Complete interval computation for depth 13, residue 4775. -/ +theorem bounds_13_4775 : exactInterval 13 4775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4775 : oddCount 4775 13 = 9 ∧ acceleratedOrbit 13 4775 = 11477 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4775) = 3 ^ 9 * m + 11477 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4775.1, data_13_4775.2] + +/-- Complete interval computation for depth 13, residue 4776. -/ +theorem bounds_13_4776 : exactInterval 13 4776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4776 : oddCount 4776 13 = 3 ∧ acceleratedOrbit 13 4776 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4776) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4776.1, data_13_4776.2] + +/-- Complete interval computation for depth 13, residue 4777. -/ +theorem bounds_13_4777 : exactInterval 13 4777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4777 : oddCount 4777 13 = 10 ∧ acceleratedOrbit 13 4777 = 34445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4777) = 3 ^ 10 * m + 34445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4777.1, data_13_4777.2] + +/-- Complete interval computation for depth 13, residue 4778. -/ +theorem bounds_13_4778 : exactInterval 13 4778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4778 : oddCount 4778 13 = 3 ∧ acceleratedOrbit 13 4778 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4778) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4778.1, data_13_4778.2] + +/-- Complete interval computation for depth 13, residue 4779. -/ +theorem bounds_13_4779 : exactInterval 13 4779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4779 : oddCount 4779 13 = 7 ∧ acceleratedOrbit 13 4779 = 1277 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4779) = 3 ^ 7 * m + 1277 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4779.1, data_13_4779.2] + +/-- Complete interval computation for depth 13, residue 4780. -/ +theorem bounds_13_4780 : exactInterval 13 4780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4780 : oddCount 4780 13 = 5 ∧ acceleratedOrbit 13 4780 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4780) = 3 ^ 5 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4780.1, data_13_4780.2] + +/-- Complete interval computation for depth 13, residue 4781. -/ +theorem bounds_13_4781 : exactInterval 13 4781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4781 : oddCount 4781 13 = 5 ∧ acceleratedOrbit 13 4781 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4781) = 3 ^ 5 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4781.1, data_13_4781.2] + +end Collatz.Research.StoppingAtlas.Batch0778 From c5b551464b2fcaa00261602ef194c3b8cdbac83e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:36:01 +0530 Subject: [PATCH 0779/1001] proof: certify atlas Batch0779 (13:4782 to 13:4796) --- Collatz/Research/StoppingAtlas/Batch0779.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0779.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0779.lean b/Collatz/Research/StoppingAtlas/Batch0779.lean new file mode 100644 index 00000000..6a67cd60 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0779.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0779 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4782. -/ +theorem bounds_13_4782 : exactInterval 13 4782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4782 : oddCount 4782 13 = 5 ∧ acceleratedOrbit 13 4782 = 142 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4782) = 3 ^ 5 * m + 142 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4782.1, data_13_4782.2] + +/-- Complete interval computation for depth 13, residue 4783. -/ +theorem bounds_13_4783 : exactInterval 13 4783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4783 : oddCount 4783 13 = 8 ∧ acceleratedOrbit 13 4783 = 3833 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4783) = 3 ^ 8 * m + 3833 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4783.1, data_13_4783.2] + +/-- Complete interval computation for depth 13, residue 4784. -/ +theorem bounds_13_4784 : exactInterval 13 4784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4784 : oddCount 4784 13 = 5 ∧ acceleratedOrbit 13 4784 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4784) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4784.1, data_13_4784.2] + +/-- Complete interval computation for depth 13, residue 4785. -/ +theorem bounds_13_4785 : exactInterval 13 4785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4785 : oddCount 4785 13 = 6 ∧ acceleratedOrbit 13 4785 = 427 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4785) = 3 ^ 6 * m + 427 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4785.1, data_13_4785.2] + +/-- Complete interval computation for depth 13, residue 4786. -/ +theorem bounds_13_4786 : exactInterval 13 4786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4786 : oddCount 4786 13 = 6 ∧ acceleratedOrbit 13 4786 = 427 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4786) = 3 ^ 6 * m + 427 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4786.1, data_13_4786.2] + +/-- Complete interval computation for depth 13, residue 4787. -/ +theorem bounds_13_4787 : exactInterval 13 4787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4787 : oddCount 4787 13 = 6 ∧ acceleratedOrbit 13 4787 = 427 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4787) = 3 ^ 6 * m + 427 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4787.1, data_13_4787.2] + +/-- Complete interval computation for depth 13, residue 4788. -/ +theorem bounds_13_4788 : exactInterval 13 4788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4788 : oddCount 4788 13 = 5 ∧ acceleratedOrbit 13 4788 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4788) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4788.1, data_13_4788.2] + +/-- Complete interval computation for depth 13, residue 4789. -/ +theorem bounds_13_4789 : exactInterval 13 4789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4789 : oddCount 4789 13 = 5 ∧ acceleratedOrbit 13 4789 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4789) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4789.1, data_13_4789.2] + +/-- Complete interval computation for depth 13, residue 4790. -/ +theorem bounds_13_4790 : exactInterval 13 4790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4790 : oddCount 4790 13 = 7 ∧ acceleratedOrbit 13 4790 = 1280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4790) = 3 ^ 7 * m + 1280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4790.1, data_13_4790.2] + +/-- Complete interval computation for depth 13, residue 4791. -/ +theorem bounds_13_4791 : exactInterval 13 4791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4791 : oddCount 4791 13 = 7 ∧ acceleratedOrbit 13 4791 = 1280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4791) = 3 ^ 7 * m + 1280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4791.1, data_13_4791.2] + +/-- Complete interval computation for depth 13, residue 4792. -/ +theorem bounds_13_4792 : exactInterval 13 4792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4792 : oddCount 4792 13 = 5 ∧ acceleratedOrbit 13 4792 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4792) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4792.1, data_13_4792.2] + +/-- Complete interval computation for depth 13, residue 4793. -/ +theorem bounds_13_4793 : exactInterval 13 4793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4793 : oddCount 4793 13 = 6 ∧ acceleratedOrbit 13 4793 = 427 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4793) = 3 ^ 6 * m + 427 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4793.1, data_13_4793.2] + +/-- Complete interval computation for depth 13, residue 4794. -/ +theorem bounds_13_4794 : exactInterval 13 4794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4794 : oddCount 4794 13 = 5 ∧ acceleratedOrbit 13 4794 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4794) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4794.1, data_13_4794.2] + +/-- Complete interval computation for depth 13, residue 4795. -/ +theorem bounds_13_4795 : exactInterval 13 4795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4795 : oddCount 4795 13 = 9 ∧ acceleratedOrbit 13 4795 = 11528 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4795) = 3 ^ 9 * m + 11528 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4795.1, data_13_4795.2] + +/-- Complete interval computation for depth 13, residue 4796. -/ +theorem bounds_13_4796 : exactInterval 13 4796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4796 : oddCount 4796 13 = 7 ∧ acceleratedOrbit 13 4796 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4796) = 3 ^ 7 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4796.1, data_13_4796.2] + +end Collatz.Research.StoppingAtlas.Batch0779 From a5be34fd15da6a9eee8bf54adf4ab4e5e3d45d27 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:36:02 +0530 Subject: [PATCH 0780/1001] proof: certify atlas Batch0780 (13:4797 to 13:4811) --- Collatz/Research/StoppingAtlas/Batch0780.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0780.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0780.lean b/Collatz/Research/StoppingAtlas/Batch0780.lean new file mode 100644 index 00000000..fb4d6543 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0780.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0780 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4797. -/ +theorem bounds_13_4797 : exactInterval 13 4797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4797 : oddCount 4797 13 = 7 ∧ acceleratedOrbit 13 4797 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4797) = 3 ^ 7 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4797.1, data_13_4797.2] + +/-- Complete interval computation for depth 13, residue 4798. -/ +theorem bounds_13_4798 : exactInterval 13 4798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4798 : oddCount 4798 13 = 7 ∧ acceleratedOrbit 13 4798 = 1282 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4798) = 3 ^ 7 * m + 1282 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4798.1, data_13_4798.2] + +/-- Complete interval computation for depth 13, residue 4799. -/ +theorem bounds_13_4799 : exactInterval 13 4799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4799 : oddCount 4799 13 = 10 ∧ acceleratedOrbit 13 4799 = 34600 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4799) = 3 ^ 10 * m + 34600 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4799.1, data_13_4799.2] + +/-- Complete interval computation for depth 13, residue 4800. -/ +theorem bounds_13_4800 : exactInterval 13 4800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4800 : oddCount 4800 13 = 3 ∧ acceleratedOrbit 13 4800 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4800) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4800.1, data_13_4800.2] + +/-- Complete interval computation for depth 13, residue 4801. -/ +theorem bounds_13_4801 : exactInterval 13 4801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4801 : oddCount 4801 13 = 5 ∧ acceleratedOrbit 13 4801 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4801) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4801.1, data_13_4801.2] + +/-- Complete interval computation for depth 13, residue 4802. -/ +theorem bounds_13_4802 : exactInterval 13 4802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4802 : oddCount 4802 13 = 8 ∧ acceleratedOrbit 13 4802 = 3851 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4802) = 3 ^ 8 * m + 3851 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4802.1, data_13_4802.2] + +/-- Complete interval computation for depth 13, residue 4803. -/ +theorem bounds_13_4803 : exactInterval 13 4803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4803 : oddCount 4803 13 = 8 ∧ acceleratedOrbit 13 4803 = 3851 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4803) = 3 ^ 8 * m + 3851 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4803.1, data_13_4803.2] + +/-- Complete interval computation for depth 13, residue 4804. -/ +theorem bounds_13_4804 : exactInterval 13 4804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4804 : oddCount 4804 13 = 6 ∧ acceleratedOrbit 13 4804 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4804) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4804.1, data_13_4804.2] + +/-- Complete interval computation for depth 13, residue 4805. -/ +theorem bounds_13_4805 : exactInterval 13 4805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4805 : oddCount 4805 13 = 6 ∧ acceleratedOrbit 13 4805 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4805) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4805.1, data_13_4805.2] + +/-- Complete interval computation for depth 13, residue 4806. -/ +theorem bounds_13_4806 : exactInterval 13 4806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4806 : oddCount 4806 13 = 6 ∧ acceleratedOrbit 13 4806 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4806) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4806.1, data_13_4806.2] + +/-- Complete interval computation for depth 13, residue 4807. -/ +theorem bounds_13_4807 : exactInterval 13 4807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4807 : oddCount 4807 13 = 6 ∧ acceleratedOrbit 13 4807 = 428 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4807) = 3 ^ 6 * m + 428 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4807.1, data_13_4807.2] + +/-- Complete interval computation for depth 13, residue 4808. -/ +theorem bounds_13_4808 : exactInterval 13 4808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4808 : oddCount 4808 13 = 6 ∧ acceleratedOrbit 13 4808 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4808) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4808.1, data_13_4808.2] + +/-- Complete interval computation for depth 13, residue 4809. -/ +theorem bounds_13_4809 : exactInterval 13 4809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4809 : oddCount 4809 13 = 7 ∧ acceleratedOrbit 13 4809 = 1286 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4809) = 3 ^ 7 * m + 1286 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4809.1, data_13_4809.2] + +/-- Complete interval computation for depth 13, residue 4810. -/ +theorem bounds_13_4810 : exactInterval 13 4810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4810 : oddCount 4810 13 = 6 ∧ acceleratedOrbit 13 4810 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4810) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4810.1, data_13_4810.2] + +/-- Complete interval computation for depth 13, residue 4811. -/ +theorem bounds_13_4811 : exactInterval 13 4811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4811 : oddCount 4811 13 = 7 ∧ acceleratedOrbit 13 4811 = 1286 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4811) = 3 ^ 7 * m + 1286 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4811.1, data_13_4811.2] + +end Collatz.Research.StoppingAtlas.Batch0780 From 52f8ac15979168562261aec66ecd56311c1dd456 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:36:02 +0530 Subject: [PATCH 0781/1001] proof: certify atlas Batch0781 (13:4812 to 13:4827) --- Collatz/Research/StoppingAtlas/Batch0781.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0781.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0781.lean b/Collatz/Research/StoppingAtlas/Batch0781.lean new file mode 100644 index 00000000..818e9013 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0781.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0781 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4812. -/ +theorem bounds_13_4812 : exactInterval 13 4812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4812 : oddCount 4812 13 = 6 ∧ acceleratedOrbit 13 4812 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4812) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4812.1, data_13_4812.2] + +/-- Complete interval computation for depth 13, residue 4813. -/ +theorem bounds_13_4813 : exactInterval 13 4813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4813 : oddCount 4813 13 = 6 ∧ acceleratedOrbit 13 4813 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4813) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4813.1, data_13_4813.2] + +/-- Complete interval computation for depth 13, residue 4814. -/ +theorem bounds_13_4814 : exactInterval 13 4814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4814 : oddCount 4814 13 = 9 ∧ acceleratedOrbit 13 4814 = 11573 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4814) = 3 ^ 9 * m + 11573 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4814.1, data_13_4814.2] + +/-- Complete interval computation for depth 13, residue 4815. -/ +theorem bounds_13_4815 : exactInterval 13 4815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4815 : oddCount 4815 13 = 9 ∧ acceleratedOrbit 13 4815 = 11573 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4815) = 3 ^ 9 * m + 11573 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4815.1, data_13_4815.2] + +/-- Complete interval computation for depth 13, residue 4816. -/ +theorem bounds_13_4816 : exactInterval 13 4816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4816 : oddCount 4816 13 = 3 ∧ acceleratedOrbit 13 4816 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4816) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4816.1, data_13_4816.2] + +/-- Complete interval computation for depth 13, residue 4817. -/ +theorem bounds_13_4817 : exactInterval 13 4817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4817 : oddCount 4817 13 = 5 ∧ acceleratedOrbit 13 4817 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4817) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4817.1, data_13_4817.2] + +/-- Complete interval computation for depth 13, residue 4818. -/ +theorem bounds_13_4818 : exactInterval 13 4818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4818 : oddCount 4818 13 = 5 ∧ acceleratedOrbit 13 4818 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4818) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4818.1, data_13_4818.2] + +/-- Complete interval computation for depth 13, residue 4819. -/ +theorem bounds_13_4819 : exactInterval 13 4819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4819 : oddCount 4819 13 = 5 ∧ acceleratedOrbit 13 4819 = 143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4819) = 3 ^ 5 * m + 143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4819.1, data_13_4819.2] + +/-- Complete interval computation for depth 13, residue 4820. -/ +theorem bounds_13_4820 : exactInterval 13 4820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4820 : oddCount 4820 13 = 3 ∧ acceleratedOrbit 13 4820 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4820) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4820.1, data_13_4820.2] + +/-- Complete interval computation for depth 13, residue 4821. -/ +theorem bounds_13_4821 : exactInterval 13 4821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4821 : oddCount 4821 13 = 3 ∧ acceleratedOrbit 13 4821 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4821) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4821.1, data_13_4821.2] + +/-- Complete interval computation for depth 13, residue 4822. -/ +theorem bounds_13_4822 : exactInterval 13 4822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4822 : oddCount 4822 13 = 7 ∧ acceleratedOrbit 13 4822 = 1289 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4822) = 3 ^ 7 * m + 1289 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4822.1, data_13_4822.2] + +/-- Complete interval computation for depth 13, residue 4823. -/ +theorem bounds_13_4823 : exactInterval 13 4823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4823 : oddCount 4823 13 = 7 ∧ acceleratedOrbit 13 4823 = 1289 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4823) = 3 ^ 7 * m + 1289 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4823.1, data_13_4823.2] + +/-- Complete interval computation for depth 13, residue 4824. -/ +theorem bounds_13_4824 : exactInterval 13 4824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4824 : oddCount 4824 13 = 7 ∧ acceleratedOrbit 13 4824 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4824) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4824.1, data_13_4824.2] + +/-- Complete interval computation for depth 13, residue 4825. -/ +theorem bounds_13_4825 : exactInterval 13 4825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4825 : oddCount 4825 13 = 6 ∧ acceleratedOrbit 13 4825 = 431 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4825) = 3 ^ 6 * m + 431 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4825.1, data_13_4825.2] + +/-- Complete interval computation for depth 13, residue 4826. -/ +theorem bounds_13_4826 : exactInterval 13 4826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4826 : oddCount 4826 13 = 7 ∧ acceleratedOrbit 13 4826 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4826) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4826.1, data_13_4826.2] + +/-- Complete interval computation for depth 13, residue 4827. -/ +theorem bounds_13_4827 : exactInterval 13 4827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4827 : oddCount 4827 13 = 9 ∧ acceleratedOrbit 13 4827 = 11603 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4827) = 3 ^ 9 * m + 11603 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4827.1, data_13_4827.2] + +end Collatz.Research.StoppingAtlas.Batch0781 From db868a5e50f994d4650319b7dc99476581ceec2c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:57 +0530 Subject: [PATCH 0782/1001] proof: certify atlas Batch0782 (13:4828 to 13:4842) --- Collatz/Research/StoppingAtlas/Batch0782.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0782.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0782.lean b/Collatz/Research/StoppingAtlas/Batch0782.lean new file mode 100644 index 00000000..45a70f4f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0782.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0782 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4828. -/ +theorem bounds_13_4828 : exactInterval 13 4828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4828 : oddCount 4828 13 = 7 ∧ acceleratedOrbit 13 4828 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4828) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4828.1, data_13_4828.2] + +/-- Complete interval computation for depth 13, residue 4829. -/ +theorem bounds_13_4829 : exactInterval 13 4829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4829 : oddCount 4829 13 = 7 ∧ acceleratedOrbit 13 4829 = 1291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4829) = 3 ^ 7 * m + 1291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4829.1, data_13_4829.2] + +/-- Complete interval computation for depth 13, residue 4830. -/ +theorem bounds_13_4830 : exactInterval 13 4830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4830 : oddCount 4830 13 = 6 ∧ acceleratedOrbit 13 4830 = 430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4830) = 3 ^ 6 * m + 430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4830.1, data_13_4830.2] + +/-- Complete interval computation for depth 13, residue 4831. -/ +theorem bounds_13_4831 : exactInterval 13 4831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4831 : oddCount 4831 13 = 6 ∧ acceleratedOrbit 13 4831 = 430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4831) = 3 ^ 6 * m + 430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4831.1, data_13_4831.2] + +/-- Complete interval computation for depth 13, residue 4832. -/ +theorem bounds_13_4832 : exactInterval 13 4832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4832 : oddCount 4832 13 = 3 ∧ acceleratedOrbit 13 4832 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4832) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4832.1, data_13_4832.2] + +/-- Complete interval computation for depth 13, residue 4833. -/ +theorem bounds_13_4833 : exactInterval 13 4833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4833 : oddCount 4833 13 = 10 ∧ acceleratedOrbit 13 4833 = 34856 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4833) = 3 ^ 10 * m + 34856 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4833.1, data_13_4833.2] + +/-- Complete interval computation for depth 13, residue 4834. -/ +theorem bounds_13_4834 : exactInterval 13 4834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4834 : oddCount 4834 13 = 3 ∧ acceleratedOrbit 13 4834 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4834) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4834.1, data_13_4834.2] + +/-- Complete interval computation for depth 13, residue 4835. -/ +theorem bounds_13_4835 : exactInterval 13 4835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4835 : oddCount 4835 13 = 3 ∧ acceleratedOrbit 13 4835 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4835) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4835.1, data_13_4835.2] + +/-- Complete interval computation for depth 13, residue 4836. -/ +theorem bounds_13_4836 : exactInterval 13 4836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4836 : oddCount 4836 13 = 7 ∧ acceleratedOrbit 13 4836 = 1295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4836) = 3 ^ 7 * m + 1295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4836.1, data_13_4836.2] + +/-- Complete interval computation for depth 13, residue 4837. -/ +theorem bounds_13_4837 : exactInterval 13 4837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4837 : oddCount 4837 13 = 7 ∧ acceleratedOrbit 13 4837 = 1295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4837) = 3 ^ 7 * m + 1295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4837.1, data_13_4837.2] + +/-- Complete interval computation for depth 13, residue 4838. -/ +theorem bounds_13_4838 : exactInterval 13 4838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4838 : oddCount 4838 13 = 7 ∧ acceleratedOrbit 13 4838 = 1295 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4838) = 3 ^ 7 * m + 1295 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4838.1, data_13_4838.2] + +/-- Complete interval computation for depth 13, residue 4839. -/ +theorem bounds_13_4839 : exactInterval 13 4839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4839 : oddCount 4839 13 = 9 ∧ acceleratedOrbit 13 4839 = 11630 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4839) = 3 ^ 9 * m + 11630 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4839.1, data_13_4839.2] + +/-- Complete interval computation for depth 13, residue 4840. -/ +theorem bounds_13_4840 : exactInterval 13 4840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4840 : oddCount 4840 13 = 3 ∧ acceleratedOrbit 13 4840 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4840) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4840.1, data_13_4840.2] + +/-- Complete interval computation for depth 13, residue 4841. -/ +theorem bounds_13_4841 : exactInterval 13 4841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4841 : oddCount 4841 13 = 10 ∧ acceleratedOrbit 13 4841 = 34910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4841) = 3 ^ 10 * m + 34910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4841.1, data_13_4841.2] + +/-- Complete interval computation for depth 13, residue 4842. -/ +theorem bounds_13_4842 : exactInterval 13 4842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4842 : oddCount 4842 13 = 3 ∧ acceleratedOrbit 13 4842 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4842) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4842.1, data_13_4842.2] + +end Collatz.Research.StoppingAtlas.Batch0782 From e9476c6ccec23105344f9e90e2091f3dc16bfe59 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:58 +0530 Subject: [PATCH 0783/1001] proof: certify atlas Batch0783 (13:4843 to 13:4857) --- Collatz/Research/StoppingAtlas/Batch0783.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0783.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0783.lean b/Collatz/Research/StoppingAtlas/Batch0783.lean new file mode 100644 index 00000000..00062c06 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0783.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0783 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4843. -/ +theorem bounds_13_4843 : exactInterval 13 4843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4843 : oddCount 4843 13 = 8 ∧ acceleratedOrbit 13 4843 = 3881 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4843) = 3 ^ 8 * m + 3881 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4843.1, data_13_4843.2] + +/-- Complete interval computation for depth 13, residue 4844. -/ +theorem bounds_13_4844 : exactInterval 13 4844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4844 : oddCount 4844 13 = 8 ∧ acceleratedOrbit 13 4844 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4844) = 3 ^ 8 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4844.1, data_13_4844.2] + +/-- Complete interval computation for depth 13, residue 4845. -/ +theorem bounds_13_4845 : exactInterval 13 4845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4845 : oddCount 4845 13 = 8 ∧ acceleratedOrbit 13 4845 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4845) = 3 ^ 8 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4845.1, data_13_4845.2] + +/-- Complete interval computation for depth 13, residue 4846. -/ +theorem bounds_13_4846 : exactInterval 13 4846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4846 : oddCount 4846 13 = 8 ∧ acceleratedOrbit 13 4846 = 3887 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4846) = 3 ^ 8 * m + 3887 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4846.1, data_13_4846.2] + +/-- Complete interval computation for depth 13, residue 4847. -/ +theorem bounds_13_4847 : exactInterval 13 4847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4847 : oddCount 4847 13 = 11 ∧ acceleratedOrbit 13 4847 = 104840 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4847) = 3 ^ 11 * m + 104840 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4847.1, data_13_4847.2] + +/-- Complete interval computation for depth 13, residue 4848. -/ +theorem bounds_13_4848 : exactInterval 13 4848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4848 : oddCount 4848 13 = 6 ∧ acceleratedOrbit 13 4848 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4848) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4848.1, data_13_4848.2] + +/-- Complete interval computation for depth 13, residue 4849. -/ +theorem bounds_13_4849 : exactInterval 13 4849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4849 : oddCount 4849 13 = 3 ∧ acceleratedOrbit 13 4849 = 16 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4849) = 3 ^ 3 * m + 16 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4849.1, data_13_4849.2] + +/-- Complete interval computation for depth 13, residue 4850. -/ +theorem bounds_13_4850 : exactInterval 13 4850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4850 : oddCount 4850 13 = 10 ∧ acceleratedOrbit 13 4850 = 34991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4850) = 3 ^ 10 * m + 34991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4850.1, data_13_4850.2] + +/-- Complete interval computation for depth 13, residue 4851. -/ +theorem bounds_13_4851 : exactInterval 13 4851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4851 : oddCount 4851 13 = 10 ∧ acceleratedOrbit 13 4851 = 34991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4851) = 3 ^ 10 * m + 34991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4851.1, data_13_4851.2] + +/-- Complete interval computation for depth 13, residue 4852. -/ +theorem bounds_13_4852 : exactInterval 13 4852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4852 : oddCount 4852 13 = 6 ∧ acceleratedOrbit 13 4852 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4852) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4852.1, data_13_4852.2] + +/-- Complete interval computation for depth 13, residue 4853. -/ +theorem bounds_13_4853 : exactInterval 13 4853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4853 : oddCount 4853 13 = 6 ∧ acceleratedOrbit 13 4853 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4853) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4853.1, data_13_4853.2] + +/-- Complete interval computation for depth 13, residue 4854. -/ +theorem bounds_13_4854 : exactInterval 13 4854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4854 : oddCount 4854 13 = 7 ∧ acceleratedOrbit 13 4854 = 1297 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4854) = 3 ^ 7 * m + 1297 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4854.1, data_13_4854.2] + +/-- Complete interval computation for depth 13, residue 4855. -/ +theorem bounds_13_4855 : exactInterval 13 4855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4855 : oddCount 4855 13 = 7 ∧ acceleratedOrbit 13 4855 = 1297 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4855) = 3 ^ 7 * m + 1297 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4855.1, data_13_4855.2] + +/-- Complete interval computation for depth 13, residue 4856. -/ +theorem bounds_13_4856 : exactInterval 13 4856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4856 : oddCount 4856 13 = 6 ∧ acceleratedOrbit 13 4856 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4856) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4856.1, data_13_4856.2] + +/-- Complete interval computation for depth 13, residue 4857. -/ +theorem bounds_13_4857 : exactInterval 13 4857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4857 : oddCount 4857 13 = 7 ∧ acceleratedOrbit 13 4857 = 1298 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4857) = 3 ^ 7 * m + 1298 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4857.1, data_13_4857.2] + +end Collatz.Research.StoppingAtlas.Batch0783 From 145be75a52604aa4dfbecfcb7587dc773666cede Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:58 +0530 Subject: [PATCH 0784/1001] proof: certify atlas Batch0784 (13:4858 to 13:4873) --- Collatz/Research/StoppingAtlas/Batch0784.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0784.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0784.lean b/Collatz/Research/StoppingAtlas/Batch0784.lean new file mode 100644 index 00000000..ed3078c4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0784.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0784 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4858. -/ +theorem bounds_13_4858 : exactInterval 13 4858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4858 : oddCount 4858 13 = 6 ∧ acceleratedOrbit 13 4858 = 433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4858) = 3 ^ 6 * m + 433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4858.1, data_13_4858.2] + +/-- Complete interval computation for depth 13, residue 4859. -/ +theorem bounds_13_4859 : exactInterval 13 4859 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4859) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4859 : oddCount 4859 13 = 8 ∧ acceleratedOrbit 13 4859 = 3893 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4859) = 3 ^ 8 * m + 3893 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4859.1, data_13_4859.2] + +/-- Complete interval computation for depth 13, residue 4860. -/ +theorem bounds_13_4860 : exactInterval 13 4860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4860 : oddCount 4860 13 = 8 ∧ acceleratedOrbit 13 4860 = 3896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4860) = 3 ^ 8 * m + 3896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4860.1, data_13_4860.2] + +/-- Complete interval computation for depth 13, residue 4861. -/ +theorem bounds_13_4861 : exactInterval 13 4861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4861 : oddCount 4861 13 = 8 ∧ acceleratedOrbit 13 4861 = 3896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4861) = 3 ^ 8 * m + 3896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4861.1, data_13_4861.2] + +/-- Complete interval computation for depth 13, residue 4862. -/ +theorem bounds_13_4862 : exactInterval 13 4862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4862 : oddCount 4862 13 = 8 ∧ acceleratedOrbit 13 4862 = 3896 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4862) = 3 ^ 8 * m + 3896 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4862.1, data_13_4862.2] + +/-- Complete interval computation for depth 13, residue 4863. -/ +theorem bounds_13_4863 : exactInterval 13 4863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4863 : oddCount 4863 13 = 11 ∧ acceleratedOrbit 13 4863 = 105182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4863) = 3 ^ 11 * m + 105182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4863.1, data_13_4863.2] + +/-- Complete interval computation for depth 13, residue 4864. -/ +theorem bounds_13_4864 : exactInterval 13 4864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4864 : oddCount 4864 13 = 3 ∧ acceleratedOrbit 13 4864 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4864) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4864.1, data_13_4864.2] + +/-- Complete interval computation for depth 13, residue 4865. -/ +theorem bounds_13_4865 : exactInterval 13 4865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4865 : oddCount 4865 13 = 6 ∧ acceleratedOrbit 13 4865 = 434 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4865) = 3 ^ 6 * m + 434 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4865.1, data_13_4865.2] + +/-- Complete interval computation for depth 13, residue 4866. -/ +theorem bounds_13_4866 : exactInterval 13 4866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4866 : oddCount 4866 13 = 6 ∧ acceleratedOrbit 13 4866 = 434 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4866) = 3 ^ 6 * m + 434 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4866.1, data_13_4866.2] + +/-- Complete interval computation for depth 13, residue 4867. -/ +theorem bounds_13_4867 : exactInterval 13 4867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4867 : oddCount 4867 13 = 6 ∧ acceleratedOrbit 13 4867 = 434 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4867) = 3 ^ 6 * m + 434 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4867.1, data_13_4867.2] + +/-- Complete interval computation for depth 13, residue 4868. -/ +theorem bounds_13_4868 : exactInterval 13 4868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4868 : oddCount 4868 13 = 5 ∧ acceleratedOrbit 13 4868 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4868) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4868.1, data_13_4868.2] + +/-- Complete interval computation for depth 13, residue 4869. -/ +theorem bounds_13_4869 : exactInterval 13 4869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4869 : oddCount 4869 13 = 5 ∧ acceleratedOrbit 13 4869 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4869) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4869.1, data_13_4869.2] + +/-- Complete interval computation for depth 13, residue 4870. -/ +theorem bounds_13_4870 : exactInterval 13 4870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4870 : oddCount 4870 13 = 5 ∧ acceleratedOrbit 13 4870 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4870) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4870.1, data_13_4870.2] + +/-- Complete interval computation for depth 13, residue 4871. -/ +theorem bounds_13_4871 : exactInterval 13 4871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4871 : oddCount 4871 13 = 7 ∧ acceleratedOrbit 13 4871 = 1301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4871) = 3 ^ 7 * m + 1301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4871.1, data_13_4871.2] + +/-- Complete interval computation for depth 13, residue 4872. -/ +theorem bounds_13_4872 : exactInterval 13 4872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4872 : oddCount 4872 13 = 5 ∧ acceleratedOrbit 13 4872 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4872) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4872.1, data_13_4872.2] + +/-- Complete interval computation for depth 13, residue 4873. -/ +theorem bounds_13_4873 : exactInterval 13 4873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4873 : oddCount 4873 13 = 8 ∧ acceleratedOrbit 13 4873 = 3905 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4873) = 3 ^ 8 * m + 3905 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4873.1, data_13_4873.2] + +end Collatz.Research.StoppingAtlas.Batch0784 From b7ab8280599eddaeb3f46697593fac5acba67189 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:58 +0530 Subject: [PATCH 0785/1001] proof: certify atlas Batch0785 (13:4874 to 13:4888) --- Collatz/Research/StoppingAtlas/Batch0785.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0785.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0785.lean b/Collatz/Research/StoppingAtlas/Batch0785.lean new file mode 100644 index 00000000..c6edf440 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0785.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0785 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4874. -/ +theorem bounds_13_4874 : exactInterval 13 4874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4874 : oddCount 4874 13 = 5 ∧ acceleratedOrbit 13 4874 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4874) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4874.1, data_13_4874.2] + +/-- Complete interval computation for depth 13, residue 4875. -/ +theorem bounds_13_4875 : exactInterval 13 4875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4875 : oddCount 4875 13 = 8 ∧ acceleratedOrbit 13 4875 = 3908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4875) = 3 ^ 8 * m + 3908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4875.1, data_13_4875.2] + +/-- Complete interval computation for depth 13, residue 4876. -/ +theorem bounds_13_4876 : exactInterval 13 4876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4876 : oddCount 4876 13 = 5 ∧ acceleratedOrbit 13 4876 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4876) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4876.1, data_13_4876.2] + +/-- Complete interval computation for depth 13, residue 4877. -/ +theorem bounds_13_4877 : exactInterval 13 4877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4877 : oddCount 4877 13 = 5 ∧ acceleratedOrbit 13 4877 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4877) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4877.1, data_13_4877.2] + +/-- Complete interval computation for depth 13, residue 4878. -/ +theorem bounds_13_4878 : exactInterval 13 4878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4878 : oddCount 4878 13 = 5 ∧ acceleratedOrbit 13 4878 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4878) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4878.1, data_13_4878.2] + +/-- Complete interval computation for depth 13, residue 4879. -/ +theorem bounds_13_4879 : exactInterval 13 4879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4879 : oddCount 4879 13 = 5 ∧ acceleratedOrbit 13 4879 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4879) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4879.1, data_13_4879.2] + +/-- Complete interval computation for depth 13, residue 4880. -/ +theorem bounds_13_4880 : exactInterval 13 4880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4880 : oddCount 4880 13 = 4 ∧ acceleratedOrbit 13 4880 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4880) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4880.1, data_13_4880.2] + +/-- Complete interval computation for depth 13, residue 4881. -/ +theorem bounds_13_4881 : exactInterval 13 4881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4881 : oddCount 4881 13 = 5 ∧ acceleratedOrbit 13 4881 = 145 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4881) = 3 ^ 5 * m + 145 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4881.1, data_13_4881.2] + +/-- Complete interval computation for depth 13, residue 4882. -/ +theorem bounds_13_4882 : exactInterval 13 4882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4882 : oddCount 4882 13 = 8 ∧ acceleratedOrbit 13 4882 = 3914 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4882) = 3 ^ 8 * m + 3914 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4882.1, data_13_4882.2] + +/-- Complete interval computation for depth 13, residue 4883. -/ +theorem bounds_13_4883 : exactInterval 13 4883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4883 : oddCount 4883 13 = 8 ∧ acceleratedOrbit 13 4883 = 3914 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4883) = 3 ^ 8 * m + 3914 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4883.1, data_13_4883.2] + +/-- Complete interval computation for depth 13, residue 4884. -/ +theorem bounds_13_4884 : exactInterval 13 4884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4884 : oddCount 4884 13 = 4 ∧ acceleratedOrbit 13 4884 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4884) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4884.1, data_13_4884.2] + +/-- Complete interval computation for depth 13, residue 4885. -/ +theorem bounds_13_4885 : exactInterval 13 4885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4885 : oddCount 4885 13 = 4 ∧ acceleratedOrbit 13 4885 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4885) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4885.1, data_13_4885.2] + +/-- Complete interval computation for depth 13, residue 4886. -/ +theorem bounds_13_4886 : exactInterval 13 4886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4886 : oddCount 4886 13 = 7 ∧ acceleratedOrbit 13 4886 = 1306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4886) = 3 ^ 7 * m + 1306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4886.1, data_13_4886.2] + +/-- Complete interval computation for depth 13, residue 4887. -/ +theorem bounds_13_4887 : exactInterval 13 4887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4887 : oddCount 4887 13 = 7 ∧ acceleratedOrbit 13 4887 = 1306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4887) = 3 ^ 7 * m + 1306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4887.1, data_13_4887.2] + +/-- Complete interval computation for depth 13, residue 4888. -/ +theorem bounds_13_4888 : exactInterval 13 4888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4888 : oddCount 4888 13 = 4 ∧ acceleratedOrbit 13 4888 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4888) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4888.1, data_13_4888.2] + +end Collatz.Research.StoppingAtlas.Batch0785 From 353fb93394d3da4a74b28638e85bcfe7566aa104 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0786/1001] proof: certify atlas Batch0786 (13:4889 to 13:4903) --- Collatz/Research/StoppingAtlas/Batch0786.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0786.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0786.lean b/Collatz/Research/StoppingAtlas/Batch0786.lean new file mode 100644 index 00000000..a3778e15 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0786.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0786 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4889. -/ +theorem bounds_13_4889 : exactInterval 13 4889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4889 : oddCount 4889 13 = 7 ∧ acceleratedOrbit 13 4889 = 1306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4889) = 3 ^ 7 * m + 1306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4889.1, data_13_4889.2] + +/-- Complete interval computation for depth 13, residue 4890. -/ +theorem bounds_13_4890 : exactInterval 13 4890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4890 : oddCount 4890 13 = 4 ∧ acceleratedOrbit 13 4890 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4890) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4890.1, data_13_4890.2] + +/-- Complete interval computation for depth 13, residue 4891. -/ +theorem bounds_13_4891 : exactInterval 13 4891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4891 : oddCount 4891 13 = 9 ∧ acceleratedOrbit 13 4891 = 11755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4891) = 3 ^ 9 * m + 11755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4891.1, data_13_4891.2] + +/-- Complete interval computation for depth 13, residue 4892. -/ +theorem bounds_13_4892 : exactInterval 13 4892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4892 : oddCount 4892 13 = 6 ∧ acceleratedOrbit 13 4892 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4892) = 3 ^ 6 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4892.1, data_13_4892.2] + +/-- Complete interval computation for depth 13, residue 4893. -/ +theorem bounds_13_4893 : exactInterval 13 4893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4893 : oddCount 4893 13 = 6 ∧ acceleratedOrbit 13 4893 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4893) = 3 ^ 6 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4893.1, data_13_4893.2] + +/-- Complete interval computation for depth 13, residue 4894. -/ +theorem bounds_13_4894 : exactInterval 13 4894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4894 : oddCount 4894 13 = 6 ∧ acceleratedOrbit 13 4894 = 436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4894) = 3 ^ 6 * m + 436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4894.1, data_13_4894.2] + +/-- Complete interval computation for depth 13, residue 4895. -/ +theorem bounds_13_4895 : exactInterval 13 4895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4895 : oddCount 4895 13 = 9 ∧ acceleratedOrbit 13 4895 = 11765 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4895) = 3 ^ 9 * m + 11765 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4895.1, data_13_4895.2] + +/-- Complete interval computation for depth 13, residue 4896. -/ +theorem bounds_13_4896 : exactInterval 13 4896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4896 : oddCount 4896 13 = 4 ∧ acceleratedOrbit 13 4896 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4896) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4896.1, data_13_4896.2] + +/-- Complete interval computation for depth 13, residue 4897. -/ +theorem bounds_13_4897 : exactInterval 13 4897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4897 : oddCount 4897 13 = 7 ∧ acceleratedOrbit 13 4897 = 1309 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4897) = 3 ^ 7 * m + 1309 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4897.1, data_13_4897.2] + +/-- Complete interval computation for depth 13, residue 4898. -/ +theorem bounds_13_4898 : exactInterval 13 4898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4898 : oddCount 4898 13 = 5 ∧ acceleratedOrbit 13 4898 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4898) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4898.1, data_13_4898.2] + +/-- Complete interval computation for depth 13, residue 4899. -/ +theorem bounds_13_4899 : exactInterval 13 4899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4899 : oddCount 4899 13 = 5 ∧ acceleratedOrbit 13 4899 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4899) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4899.1, data_13_4899.2] + +/-- Complete interval computation for depth 13, residue 4900. -/ +theorem bounds_13_4900 : exactInterval 13 4900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4900 : oddCount 4900 13 = 5 ∧ acceleratedOrbit 13 4900 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4900) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4900.1, data_13_4900.2] + +/-- Complete interval computation for depth 13, residue 4901. -/ +theorem bounds_13_4901 : exactInterval 13 4901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4901 : oddCount 4901 13 = 5 ∧ acceleratedOrbit 13 4901 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4901) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4901.1, data_13_4901.2] + +/-- Complete interval computation for depth 13, residue 4902. -/ +theorem bounds_13_4902 : exactInterval 13 4902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4902 : oddCount 4902 13 = 5 ∧ acceleratedOrbit 13 4902 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4902) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4902.1, data_13_4902.2] + +/-- Complete interval computation for depth 13, residue 4903. -/ +theorem bounds_13_4903 : exactInterval 13 4903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4903 : oddCount 4903 13 = 9 ∧ acceleratedOrbit 13 4903 = 11785 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4903) = 3 ^ 9 * m + 11785 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4903.1, data_13_4903.2] + +end Collatz.Research.StoppingAtlas.Batch0786 From e805145c7f69ed1e2c941c12cebb73466217a75f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0787/1001] proof: certify atlas Batch0787 (13:4904 to 13:4919) --- Collatz/Research/StoppingAtlas/Batch0787.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0787.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0787.lean b/Collatz/Research/StoppingAtlas/Batch0787.lean new file mode 100644 index 00000000..94e5d2fc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0787.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0787 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4904. -/ +theorem bounds_13_4904 : exactInterval 13 4904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4904 : oddCount 4904 13 = 4 ∧ acceleratedOrbit 13 4904 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4904) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4904.1, data_13_4904.2] + +/-- Complete interval computation for depth 13, residue 4905. -/ +theorem bounds_13_4905 : exactInterval 13 4905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4905 : oddCount 4905 13 = 7 ∧ acceleratedOrbit 13 4905 = 1310 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4905) = 3 ^ 7 * m + 1310 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4905.1, data_13_4905.2] + +/-- Complete interval computation for depth 13, residue 4906. -/ +theorem bounds_13_4906 : exactInterval 13 4906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4906 : oddCount 4906 13 = 4 ∧ acceleratedOrbit 13 4906 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4906) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4906.1, data_13_4906.2] + +/-- Complete interval computation for depth 13, residue 4907. -/ +theorem bounds_13_4907 : exactInterval 13 4907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4907 : oddCount 4907 13 = 6 ∧ acceleratedOrbit 13 4907 = 437 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4907) = 3 ^ 6 * m + 437 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4907.1, data_13_4907.2] + +/-- Complete interval computation for depth 13, residue 4908. -/ +theorem bounds_13_4908 : exactInterval 13 4908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4908 : oddCount 4908 13 = 5 ∧ acceleratedOrbit 13 4908 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4908) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4908.1, data_13_4908.2] + +/-- Complete interval computation for depth 13, residue 4909. -/ +theorem bounds_13_4909 : exactInterval 13 4909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4909 : oddCount 4909 13 = 5 ∧ acceleratedOrbit 13 4909 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4909) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4909.1, data_13_4909.2] + +/-- Complete interval computation for depth 13, residue 4910. -/ +theorem bounds_13_4910 : exactInterval 13 4910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4910 : oddCount 4910 13 = 5 ∧ acceleratedOrbit 13 4910 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4910) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4910.1, data_13_4910.2] + +/-- Complete interval computation for depth 13, residue 4911. -/ +theorem bounds_13_4911 : exactInterval 13 4911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4911 : oddCount 4911 13 = 8 ∧ acceleratedOrbit 13 4911 = 3935 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4911) = 3 ^ 8 * m + 3935 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4911.1, data_13_4911.2] + +/-- Complete interval computation for depth 13, residue 4912. -/ +theorem bounds_13_4912 : exactInterval 13 4912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4912 : oddCount 4912 13 = 4 ∧ acceleratedOrbit 13 4912 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4912) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4912.1, data_13_4912.2] + +/-- Complete interval computation for depth 13, residue 4913. -/ +theorem bounds_13_4913 : exactInterval 13 4913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4913 : oddCount 4913 13 = 5 ∧ acceleratedOrbit 13 4913 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4913) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4913.1, data_13_4913.2] + +/-- Complete interval computation for depth 13, residue 4914. -/ +theorem bounds_13_4914 : exactInterval 13 4914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4914 : oddCount 4914 13 = 5 ∧ acceleratedOrbit 13 4914 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4914) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4914.1, data_13_4914.2] + +/-- Complete interval computation for depth 13, residue 4915. -/ +theorem bounds_13_4915 : exactInterval 13 4915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4915 : oddCount 4915 13 = 5 ∧ acceleratedOrbit 13 4915 = 146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4915) = 3 ^ 5 * m + 146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4915.1, data_13_4915.2] + +/-- Complete interval computation for depth 13, residue 4916. -/ +theorem bounds_13_4916 : exactInterval 13 4916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4916 : oddCount 4916 13 = 4 ∧ acceleratedOrbit 13 4916 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4916) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4916.1, data_13_4916.2] + +/-- Complete interval computation for depth 13, residue 4917. -/ +theorem bounds_13_4917 : exactInterval 13 4917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4917 : oddCount 4917 13 = 4 ∧ acceleratedOrbit 13 4917 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4917) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4917.1, data_13_4917.2] + +/-- Complete interval computation for depth 13, residue 4918. -/ +theorem bounds_13_4918 : exactInterval 13 4918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4918 : oddCount 4918 13 = 9 ∧ acceleratedOrbit 13 4918 = 11825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4918) = 3 ^ 9 * m + 11825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4918.1, data_13_4918.2] + +/-- Complete interval computation for depth 13, residue 4919. -/ +theorem bounds_13_4919 : exactInterval 13 4919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4919 : oddCount 4919 13 = 9 ∧ acceleratedOrbit 13 4919 = 11825 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4919) = 3 ^ 9 * m + 11825 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4919.1, data_13_4919.2] + +end Collatz.Research.StoppingAtlas.Batch0787 From eedf797dee4fd9e5440a661f88a2f7e923870a3f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0788/1001] proof: certify atlas Batch0788 (13:4920 to 13:4934) --- Collatz/Research/StoppingAtlas/Batch0788.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0788.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0788.lean b/Collatz/Research/StoppingAtlas/Batch0788.lean new file mode 100644 index 00000000..ba675e0c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0788.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0788 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4920. -/ +theorem bounds_13_4920 : exactInterval 13 4920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4920 : oddCount 4920 13 = 7 ∧ acceleratedOrbit 13 4920 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4920) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4920.1, data_13_4920.2] + +/-- Complete interval computation for depth 13, residue 4921. -/ +theorem bounds_13_4921 : exactInterval 13 4921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4921 : oddCount 4921 13 = 8 ∧ acceleratedOrbit 13 4921 = 3944 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4921) = 3 ^ 8 * m + 3944 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4921.1, data_13_4921.2] + +/-- Complete interval computation for depth 13, residue 4922. -/ +theorem bounds_13_4922 : exactInterval 13 4922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4922 : oddCount 4922 13 = 7 ∧ acceleratedOrbit 13 4922 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4922) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4922.1, data_13_4922.2] + +/-- Complete interval computation for depth 13, residue 4923. -/ +theorem bounds_13_4923 : exactInterval 13 4923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4923 : oddCount 4923 13 = 7 ∧ acceleratedOrbit 13 4923 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4923) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4923.1, data_13_4923.2] + +/-- Complete interval computation for depth 13, residue 4924. -/ +theorem bounds_13_4924 : exactInterval 13 4924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4924 : oddCount 4924 13 = 7 ∧ acceleratedOrbit 13 4924 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4924) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4924.1, data_13_4924.2] + +/-- Complete interval computation for depth 13, residue 4925. -/ +theorem bounds_13_4925 : exactInterval 13 4925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4925 : oddCount 4925 13 = 7 ∧ acceleratedOrbit 13 4925 = 1316 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4925) = 3 ^ 7 * m + 1316 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4925.1, data_13_4925.2] + +/-- Complete interval computation for depth 13, residue 4926. -/ +theorem bounds_13_4926 : exactInterval 13 4926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4926 : oddCount 4926 13 = 8 ∧ acceleratedOrbit 13 4926 = 3947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4926) = 3 ^ 8 * m + 3947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4926.1, data_13_4926.2] + +/-- Complete interval computation for depth 13, residue 4927. -/ +theorem bounds_13_4927 : exactInterval 13 4927 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4927) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4927 : oddCount 4927 13 = 8 ∧ acceleratedOrbit 13 4927 = 3947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4927) = 3 ^ 8 * m + 3947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4927.1, data_13_4927.2] + +/-- Complete interval computation for depth 13, residue 4928. -/ +theorem bounds_13_4928 : exactInterval 13 4928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4928 : oddCount 4928 13 = 3 ∧ acceleratedOrbit 13 4928 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4928) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4928.1, data_13_4928.2] + +/-- Complete interval computation for depth 13, residue 4929. -/ +theorem bounds_13_4929 : exactInterval 13 4929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4929 : oddCount 4929 13 = 4 ∧ acceleratedOrbit 13 4929 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4929) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4929.1, data_13_4929.2] + +/-- Complete interval computation for depth 13, residue 4930. -/ +theorem bounds_13_4930 : exactInterval 13 4930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4930 : oddCount 4930 13 = 7 ∧ acceleratedOrbit 13 4930 = 1318 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4930) = 3 ^ 7 * m + 1318 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4930.1, data_13_4930.2] + +/-- Complete interval computation for depth 13, residue 4931. -/ +theorem bounds_13_4931 : exactInterval 13 4931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4931 : oddCount 4931 13 = 7 ∧ acceleratedOrbit 13 4931 = 1318 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4931) = 3 ^ 7 * m + 1318 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4931.1, data_13_4931.2] + +/-- Complete interval computation for depth 13, residue 4932. -/ +theorem bounds_13_4932 : exactInterval 13 4932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4932 : oddCount 4932 13 = 7 ∧ acceleratedOrbit 13 4932 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4932) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4932.1, data_13_4932.2] + +/-- Complete interval computation for depth 13, residue 4933. -/ +theorem bounds_13_4933 : exactInterval 13 4933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4933 : oddCount 4933 13 = 7 ∧ acceleratedOrbit 13 4933 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4933) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4933.1, data_13_4933.2] + +/-- Complete interval computation for depth 13, residue 4934. -/ +theorem bounds_13_4934 : exactInterval 13 4934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4934 : oddCount 4934 13 = 7 ∧ acceleratedOrbit 13 4934 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4934) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4934.1, data_13_4934.2] + +end Collatz.Research.StoppingAtlas.Batch0788 From 1e91d764f0e2d34569edc59f8383df2e26454398 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0789/1001] proof: certify atlas Batch0789 (13:4935 to 13:4950) --- Collatz/Research/StoppingAtlas/Batch0789.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0789.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0789.lean b/Collatz/Research/StoppingAtlas/Batch0789.lean new file mode 100644 index 00000000..81176d8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0789.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0789 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4935. -/ +theorem bounds_13_4935 : exactInterval 13 4935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4935 : oddCount 4935 13 = 10 ∧ acceleratedOrbit 13 4935 = 35585 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4935) = 3 ^ 10 * m + 35585 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4935.1, data_13_4935.2] + +/-- Complete interval computation for depth 13, residue 4936. -/ +theorem bounds_13_4936 : exactInterval 13 4936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4936 : oddCount 4936 13 = 7 ∧ acceleratedOrbit 13 4936 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4936) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4936.1, data_13_4936.2] + +/-- Complete interval computation for depth 13, residue 4937. -/ +theorem bounds_13_4937 : exactInterval 13 4937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4937 : oddCount 4937 13 = 6 ∧ acceleratedOrbit 13 4937 = 440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4937) = 3 ^ 6 * m + 440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4937.1, data_13_4937.2] + +/-- Complete interval computation for depth 13, residue 4938. -/ +theorem bounds_13_4938 : exactInterval 13 4938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4938 : oddCount 4938 13 = 7 ∧ acceleratedOrbit 13 4938 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4938) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4938.1, data_13_4938.2] + +/-- Complete interval computation for depth 13, residue 4939. -/ +theorem bounds_13_4939 : exactInterval 13 4939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4939 : oddCount 4939 13 = 7 ∧ acceleratedOrbit 13 4939 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4939) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4939.1, data_13_4939.2] + +/-- Complete interval computation for depth 13, residue 4940. -/ +theorem bounds_13_4940 : exactInterval 13 4940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4940 : oddCount 4940 13 = 7 ∧ acceleratedOrbit 13 4940 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4940) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4940.1, data_13_4940.2] + +/-- Complete interval computation for depth 13, residue 4941. -/ +theorem bounds_13_4941 : exactInterval 13 4941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4941 : oddCount 4941 13 = 7 ∧ acceleratedOrbit 13 4941 = 1322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4941) = 3 ^ 7 * m + 1322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4941.1, data_13_4941.2] + +/-- Complete interval computation for depth 13, residue 4942. -/ +theorem bounds_13_4942 : exactInterval 13 4942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4942 : oddCount 4942 13 = 6 ∧ acceleratedOrbit 13 4942 = 440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4942) = 3 ^ 6 * m + 440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4942.1, data_13_4942.2] + +/-- Complete interval computation for depth 13, residue 4943. -/ +theorem bounds_13_4943 : exactInterval 13 4943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4943 : oddCount 4943 13 = 6 ∧ acceleratedOrbit 13 4943 = 440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4943) = 3 ^ 6 * m + 440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4943.1, data_13_4943.2] + +/-- Complete interval computation for depth 13, residue 4944. -/ +theorem bounds_13_4944 : exactInterval 13 4944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4944 : oddCount 4944 13 = 3 ∧ acceleratedOrbit 13 4944 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4944) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4944.1, data_13_4944.2] + +/-- Complete interval computation for depth 13, residue 4945. -/ +theorem bounds_13_4945 : exactInterval 13 4945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4945 : oddCount 4945 13 = 8 ∧ acceleratedOrbit 13 4945 = 3964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4945) = 3 ^ 8 * m + 3964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4945.1, data_13_4945.2] + +/-- Complete interval computation for depth 13, residue 4946. -/ +theorem bounds_13_4946 : exactInterval 13 4946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4946 : oddCount 4946 13 = 8 ∧ acceleratedOrbit 13 4946 = 3964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4946) = 3 ^ 8 * m + 3964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4946.1, data_13_4946.2] + +/-- Complete interval computation for depth 13, residue 4947. -/ +theorem bounds_13_4947 : exactInterval 13 4947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4947 : oddCount 4947 13 = 8 ∧ acceleratedOrbit 13 4947 = 3964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4947) = 3 ^ 8 * m + 3964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4947.1, data_13_4947.2] + +/-- Complete interval computation for depth 13, residue 4948. -/ +theorem bounds_13_4948 : exactInterval 13 4948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4948 : oddCount 4948 13 = 3 ∧ acceleratedOrbit 13 4948 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4948) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4948.1, data_13_4948.2] + +/-- Complete interval computation for depth 13, residue 4949. -/ +theorem bounds_13_4949 : exactInterval 13 4949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4949 : oddCount 4949 13 = 3 ∧ acceleratedOrbit 13 4949 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4949) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4949.1, data_13_4949.2] + +/-- Complete interval computation for depth 13, residue 4950. -/ +theorem bounds_13_4950 : exactInterval 13 4950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4950 : oddCount 4950 13 = 9 ∧ acceleratedOrbit 13 4950 = 11906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4950) = 3 ^ 9 * m + 11906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4950.1, data_13_4950.2] + +end Collatz.Research.StoppingAtlas.Batch0789 From 53f95079b215e4abc6bb244a54ea6218dea7996b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0790/1001] proof: certify atlas Batch0790 (13:4951 to 13:4965) --- Collatz/Research/StoppingAtlas/Batch0790.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0790.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0790.lean b/Collatz/Research/StoppingAtlas/Batch0790.lean new file mode 100644 index 00000000..e8fc5d32 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0790.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0790 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4951. -/ +theorem bounds_13_4951 : exactInterval 13 4951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4951 : oddCount 4951 13 = 9 ∧ acceleratedOrbit 13 4951 = 11906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4951) = 3 ^ 9 * m + 11906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4951.1, data_13_4951.2] + +/-- Complete interval computation for depth 13, residue 4952. -/ +theorem bounds_13_4952 : exactInterval 13 4952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4952 : oddCount 4952 13 = 6 ∧ acceleratedOrbit 13 4952 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4952) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4952.1, data_13_4952.2] + +/-- Complete interval computation for depth 13, residue 4953. -/ +theorem bounds_13_4953 : exactInterval 13 4953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4953 : oddCount 4953 13 = 4 ∧ acceleratedOrbit 13 4953 = 49 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4953) = 3 ^ 4 * m + 49 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4953.1, data_13_4953.2] + +/-- Complete interval computation for depth 13, residue 4954. -/ +theorem bounds_13_4954 : exactInterval 13 4954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4954 : oddCount 4954 13 = 6 ∧ acceleratedOrbit 13 4954 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4954) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4954.1, data_13_4954.2] + +/-- Complete interval computation for depth 13, residue 4955. -/ +theorem bounds_13_4955 : exactInterval 13 4955 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4955) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4955 : oddCount 4955 13 = 8 ∧ acceleratedOrbit 13 4955 = 3970 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4955) = 3 ^ 8 * m + 3970 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4955.1, data_13_4955.2] + +/-- Complete interval computation for depth 13, residue 4956. -/ +theorem bounds_13_4956 : exactInterval 13 4956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4956 : oddCount 4956 13 = 6 ∧ acceleratedOrbit 13 4956 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4956) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4956.1, data_13_4956.2] + +/-- Complete interval computation for depth 13, residue 4957. -/ +theorem bounds_13_4957 : exactInterval 13 4957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4957 : oddCount 4957 13 = 6 ∧ acceleratedOrbit 13 4957 = 442 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4957) = 3 ^ 6 * m + 442 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4957.1, data_13_4957.2] + +/-- Complete interval computation for depth 13, residue 4958. -/ +theorem bounds_13_4958 : exactInterval 13 4958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4958 : oddCount 4958 13 = 7 ∧ acceleratedOrbit 13 4958 = 1325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4958) = 3 ^ 7 * m + 1325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4958.1, data_13_4958.2] + +/-- Complete interval computation for depth 13, residue 4959. -/ +theorem bounds_13_4959 : exactInterval 13 4959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4959 : oddCount 4959 13 = 7 ∧ acceleratedOrbit 13 4959 = 1325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4959) = 3 ^ 7 * m + 1325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4959.1, data_13_4959.2] + +/-- Complete interval computation for depth 13, residue 4960. -/ +theorem bounds_13_4960 : exactInterval 13 4960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4960 : oddCount 4960 13 = 6 ∧ acceleratedOrbit 13 4960 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4960) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4960.1, data_13_4960.2] + +/-- Complete interval computation for depth 13, residue 4961. -/ +theorem bounds_13_4961 : exactInterval 13 4961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4961 : oddCount 4961 13 = 9 ∧ acceleratedOrbit 13 4961 = 11927 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4961) = 3 ^ 9 * m + 11927 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4961.1, data_13_4961.2] + +/-- Complete interval computation for depth 13, residue 4962. -/ +theorem bounds_13_4962 : exactInterval 13 4962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4962 : oddCount 4962 13 = 5 ∧ acceleratedOrbit 13 4962 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4962) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4962.1, data_13_4962.2] + +/-- Complete interval computation for depth 13, residue 4963. -/ +theorem bounds_13_4963 : exactInterval 13 4963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4963 : oddCount 4963 13 = 5 ∧ acceleratedOrbit 13 4963 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4963) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4963.1, data_13_4963.2] + +/-- Complete interval computation for depth 13, residue 4964. -/ +theorem bounds_13_4964 : exactInterval 13 4964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4964 : oddCount 4964 13 = 5 ∧ acceleratedOrbit 13 4964 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4964) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4964.1, data_13_4964.2] + +/-- Complete interval computation for depth 13, residue 4965. -/ +theorem bounds_13_4965 : exactInterval 13 4965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4965 : oddCount 4965 13 = 5 ∧ acceleratedOrbit 13 4965 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4965) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4965.1, data_13_4965.2] + +end Collatz.Research.StoppingAtlas.Batch0790 From 342d4415ab61456d34303ebbade5dd6e2974ee10 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0791/1001] proof: certify atlas Batch0791 (13:4966 to 13:4980) --- Collatz/Research/StoppingAtlas/Batch0791.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0791.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0791.lean b/Collatz/Research/StoppingAtlas/Batch0791.lean new file mode 100644 index 00000000..c68c473c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0791.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0791 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4966. -/ +theorem bounds_13_4966 : exactInterval 13 4966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4966 : oddCount 4966 13 = 5 ∧ acceleratedOrbit 13 4966 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4966) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4966.1, data_13_4966.2] + +/-- Complete interval computation for depth 13, residue 4967. -/ +theorem bounds_13_4967 : exactInterval 13 4967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4967) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4967 : oddCount 4967 13 = 10 ∧ acceleratedOrbit 13 4967 = 35812 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4967) = 3 ^ 10 * m + 35812 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4967.1, data_13_4967.2] + +/-- Complete interval computation for depth 13, residue 4968. -/ +theorem bounds_13_4968 : exactInterval 13 4968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4968 : oddCount 4968 13 = 6 ∧ acceleratedOrbit 13 4968 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4968) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4968.1, data_13_4968.2] + +/-- Complete interval computation for depth 13, residue 4969. -/ +theorem bounds_13_4969 : exactInterval 13 4969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4969 : oddCount 4969 13 = 8 ∧ acceleratedOrbit 13 4969 = 3982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4969) = 3 ^ 8 * m + 3982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4969.1, data_13_4969.2] + +/-- Complete interval computation for depth 13, residue 4970. -/ +theorem bounds_13_4970 : exactInterval 13 4970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4970 : oddCount 4970 13 = 6 ∧ acceleratedOrbit 13 4970 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4970) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4970.1, data_13_4970.2] + +/-- Complete interval computation for depth 13, residue 4971. -/ +theorem bounds_13_4971 : exactInterval 13 4971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4971 : oddCount 4971 13 = 6 ∧ acceleratedOrbit 13 4971 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4971) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4971.1, data_13_4971.2] + +/-- Complete interval computation for depth 13, residue 4972. -/ +theorem bounds_13_4972 : exactInterval 13 4972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4972 : oddCount 4972 13 = 6 ∧ acceleratedOrbit 13 4972 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4972) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4972.1, data_13_4972.2] + +/-- Complete interval computation for depth 13, residue 4973. -/ +theorem bounds_13_4973 : exactInterval 13 4973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4973 : oddCount 4973 13 = 6 ∧ acceleratedOrbit 13 4973 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4973) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4973.1, data_13_4973.2] + +/-- Complete interval computation for depth 13, residue 4974. -/ +theorem bounds_13_4974 : exactInterval 13 4974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4974 : oddCount 4974 13 = 6 ∧ acceleratedOrbit 13 4974 = 443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4974) = 3 ^ 6 * m + 443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4974.1, data_13_4974.2] + +/-- Complete interval computation for depth 13, residue 4975. -/ +theorem bounds_13_4975 : exactInterval 13 4975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4975 : oddCount 4975 13 = 8 ∧ acceleratedOrbit 13 4975 = 3986 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4975) = 3 ^ 8 * m + 3986 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4975.1, data_13_4975.2] + +/-- Complete interval computation for depth 13, residue 4976. -/ +theorem bounds_13_4976 : exactInterval 13 4976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4976 : oddCount 4976 13 = 6 ∧ acceleratedOrbit 13 4976 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4976) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4976.1, data_13_4976.2] + +/-- Complete interval computation for depth 13, residue 4977. -/ +theorem bounds_13_4977 : exactInterval 13 4977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4977 : oddCount 4977 13 = 6 ∧ acceleratedOrbit 13 4977 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4977) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4977.1, data_13_4977.2] + +/-- Complete interval computation for depth 13, residue 4978. -/ +theorem bounds_13_4978 : exactInterval 13 4978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4978 : oddCount 4978 13 = 5 ∧ acceleratedOrbit 13 4978 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4978) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4978.1, data_13_4978.2] + +/-- Complete interval computation for depth 13, residue 4979. -/ +theorem bounds_13_4979 : exactInterval 13 4979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4979 : oddCount 4979 13 = 5 ∧ acceleratedOrbit 13 4979 = 148 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4979) = 3 ^ 5 * m + 148 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4979.1, data_13_4979.2] + +/-- Complete interval computation for depth 13, residue 4980. -/ +theorem bounds_13_4980 : exactInterval 13 4980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4980 : oddCount 4980 13 = 6 ∧ acceleratedOrbit 13 4980 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4980) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4980.1, data_13_4980.2] + +end Collatz.Research.StoppingAtlas.Batch0791 From 1b6049b835edc80dea477b8ea6c4f2a4aa3777a0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0792/1001] proof: certify atlas Batch0792 (13:4981 to 13:4996) --- Collatz/Research/StoppingAtlas/Batch0792.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0792.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0792.lean b/Collatz/Research/StoppingAtlas/Batch0792.lean new file mode 100644 index 00000000..e8254eeb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0792.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0792 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4981. -/ +theorem bounds_13_4981 : exactInterval 13 4981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4981 : oddCount 4981 13 = 6 ∧ acceleratedOrbit 13 4981 = 445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4981) = 3 ^ 6 * m + 445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4981.1, data_13_4981.2] + +/-- Complete interval computation for depth 13, residue 4982. -/ +theorem bounds_13_4982 : exactInterval 13 4982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4982 : oddCount 4982 13 = 8 ∧ acceleratedOrbit 13 4982 = 3995 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4982) = 3 ^ 8 * m + 3995 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4982.1, data_13_4982.2] + +/-- Complete interval computation for depth 13, residue 4983. -/ +theorem bounds_13_4983 : exactInterval 13 4983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4983) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4983 : oddCount 4983 13 = 8 ∧ acceleratedOrbit 13 4983 = 3995 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4983) = 3 ^ 8 * m + 3995 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4983.1, data_13_4983.2] + +/-- Complete interval computation for depth 13, residue 4984. -/ +theorem bounds_13_4984 : exactInterval 13 4984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4984 : oddCount 4984 13 = 7 ∧ acceleratedOrbit 13 4984 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4984) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4984.1, data_13_4984.2] + +/-- Complete interval computation for depth 13, residue 4985. -/ +theorem bounds_13_4985 : exactInterval 13 4985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4985 : oddCount 4985 13 = 9 ∧ acceleratedOrbit 13 4985 = 11983 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4985) = 3 ^ 9 * m + 11983 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4985.1, data_13_4985.2] + +/-- Complete interval computation for depth 13, residue 4986. -/ +theorem bounds_13_4986 : exactInterval 13 4986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4986 : oddCount 4986 13 = 7 ∧ acceleratedOrbit 13 4986 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4986) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4986.1, data_13_4986.2] + +/-- Complete interval computation for depth 13, residue 4987. -/ +theorem bounds_13_4987 : exactInterval 13 4987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4987 : oddCount 4987 13 = 10 ∧ acceleratedOrbit 13 4987 = 35963 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4987) = 3 ^ 10 * m + 35963 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4987.1, data_13_4987.2] + +/-- Complete interval computation for depth 13, residue 4988. -/ +theorem bounds_13_4988 : exactInterval 13 4988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4988 : oddCount 4988 13 = 7 ∧ acceleratedOrbit 13 4988 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4988) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4988.1, data_13_4988.2] + +/-- Complete interval computation for depth 13, residue 4989. -/ +theorem bounds_13_4989 : exactInterval 13 4989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4989 : oddCount 4989 13 = 7 ∧ acceleratedOrbit 13 4989 = 1333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4989) = 3 ^ 7 * m + 1333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4989.1, data_13_4989.2] + +/-- Complete interval computation for depth 13, residue 4990. -/ +theorem bounds_13_4990 : exactInterval 13 4990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4990 : oddCount 4990 13 = 10 ∧ acceleratedOrbit 13 4990 = 35984 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4990) = 3 ^ 10 * m + 35984 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4990.1, data_13_4990.2] + +/-- Complete interval computation for depth 13, residue 4991. -/ +theorem bounds_13_4991 : exactInterval 13 4991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4991 : oddCount 4991 13 = 10 ∧ acceleratedOrbit 13 4991 = 35984 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4991) = 3 ^ 10 * m + 35984 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4991.1, data_13_4991.2] + +/-- Complete interval computation for depth 13, residue 4992. -/ +theorem bounds_13_4992 : exactInterval 13 4992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4992 : oddCount 4992 13 = 5 ∧ acceleratedOrbit 13 4992 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4992) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4992.1, data_13_4992.2] + +/-- Complete interval computation for depth 13, residue 4993. -/ +theorem bounds_13_4993 : exactInterval 13 4993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4993 : oddCount 4993 13 = 7 ∧ acceleratedOrbit 13 4993 = 1334 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4993) = 3 ^ 7 * m + 1334 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4993.1, data_13_4993.2] + +/-- Complete interval computation for depth 13, residue 4994. -/ +theorem bounds_13_4994 : exactInterval 13 4994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4994 : oddCount 4994 13 = 7 ∧ acceleratedOrbit 13 4994 = 1336 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4994) = 3 ^ 7 * m + 1336 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4994.1, data_13_4994.2] + +/-- Complete interval computation for depth 13, residue 4995. -/ +theorem bounds_13_4995 : exactInterval 13 4995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4995 : oddCount 4995 13 = 7 ∧ acceleratedOrbit 13 4995 = 1336 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4995) = 3 ^ 7 * m + 1336 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4995.1, data_13_4995.2] + +/-- Complete interval computation for depth 13, residue 4996. -/ +theorem bounds_13_4996 : exactInterval 13 4996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4996 : oddCount 4996 13 = 8 ∧ acceleratedOrbit 13 4996 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4996) = 3 ^ 8 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4996.1, data_13_4996.2] + +end Collatz.Research.StoppingAtlas.Batch0792 From 906b7d23496a3bc58530a71f71601fc003938727 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:38:59 +0530 Subject: [PATCH 0793/1001] proof: certify atlas Batch0793 (13:4997 to 13:5011) --- Collatz/Research/StoppingAtlas/Batch0793.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0793.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0793.lean b/Collatz/Research/StoppingAtlas/Batch0793.lean new file mode 100644 index 00000000..a0ebb58c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0793.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0793 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 4997. -/ +theorem bounds_13_4997 : exactInterval 13 4997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4997 : oddCount 4997 13 = 8 ∧ acceleratedOrbit 13 4997 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4997) = 3 ^ 8 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4997.1, data_13_4997.2] + +/-- Complete interval computation for depth 13, residue 4998. -/ +theorem bounds_13_4998 : exactInterval 13 4998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4998 : oddCount 4998 13 = 8 ∧ acceleratedOrbit 13 4998 = 4009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4998) = 3 ^ 8 * m + 4009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4998.1, data_13_4998.2] + +/-- Complete interval computation for depth 13, residue 4999. -/ +theorem bounds_13_4999 : exactInterval 13 4999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_4999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 4999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_4999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_4999 : oddCount 4999 13 = 7 ∧ acceleratedOrbit 13 4999 = 1336 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_4999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 4999) = 3 ^ 7 * m + 1336 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_4999.1, data_13_4999.2] + +/-- Complete interval computation for depth 13, residue 5000. -/ +theorem bounds_13_5000 : exactInterval 13 5000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5000 : oddCount 5000 13 = 3 ∧ acceleratedOrbit 13 5000 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5000) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5000.1, data_13_5000.2] + +/-- Complete interval computation for depth 13, residue 5001. -/ +theorem bounds_13_5001 : exactInterval 13 5001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5001 : oddCount 5001 13 = 8 ∧ acceleratedOrbit 13 5001 = 4007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5001) = 3 ^ 8 * m + 4007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5001.1, data_13_5001.2] + +/-- Complete interval computation for depth 13, residue 5002. -/ +theorem bounds_13_5002 : exactInterval 13 5002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5002 : oddCount 5002 13 = 3 ∧ acceleratedOrbit 13 5002 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5002) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5002.1, data_13_5002.2] + +/-- Complete interval computation for depth 13, residue 5003. -/ +theorem bounds_13_5003 : exactInterval 13 5003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5003 : oddCount 5003 13 = 9 ∧ acceleratedOrbit 13 5003 = 12028 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5003) = 3 ^ 9 * m + 12028 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5003.1, data_13_5003.2] + +/-- Complete interval computation for depth 13, residue 5004. -/ +theorem bounds_13_5004 : exactInterval 13 5004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5004 : oddCount 5004 13 = 3 ∧ acceleratedOrbit 13 5004 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5004) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5004.1, data_13_5004.2] + +/-- Complete interval computation for depth 13, residue 5005. -/ +theorem bounds_13_5005 : exactInterval 13 5005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5005 : oddCount 5005 13 = 3 ∧ acceleratedOrbit 13 5005 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5005) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5005.1, data_13_5005.2] + +/-- Complete interval computation for depth 13, residue 5006. -/ +theorem bounds_13_5006 : exactInterval 13 5006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5006 : oddCount 5006 13 = 8 ∧ acceleratedOrbit 13 5006 = 4013 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5006) = 3 ^ 8 * m + 4013 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5006.1, data_13_5006.2] + +/-- Complete interval computation for depth 13, residue 5007. -/ +theorem bounds_13_5007 : exactInterval 13 5007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5007 : oddCount 5007 13 = 8 ∧ acceleratedOrbit 13 5007 = 4013 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5007) = 3 ^ 8 * m + 4013 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5007.1, data_13_5007.2] + +/-- Complete interval computation for depth 13, residue 5008. -/ +theorem bounds_13_5008 : exactInterval 13 5008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5008 : oddCount 5008 13 = 6 ∧ acceleratedOrbit 13 5008 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5008) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5008.1, data_13_5008.2] + +/-- Complete interval computation for depth 13, residue 5009. -/ +theorem bounds_13_5009 : exactInterval 13 5009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5009 : oddCount 5009 13 = 7 ∧ acceleratedOrbit 13 5009 = 1340 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5009) = 3 ^ 7 * m + 1340 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5009.1, data_13_5009.2] + +/-- Complete interval computation for depth 13, residue 5010. -/ +theorem bounds_13_5010 : exactInterval 13 5010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5010 : oddCount 5010 13 = 7 ∧ acceleratedOrbit 13 5010 = 1340 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5010) = 3 ^ 7 * m + 1340 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5010.1, data_13_5010.2] + +/-- Complete interval computation for depth 13, residue 5011. -/ +theorem bounds_13_5011 : exactInterval 13 5011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5011 : oddCount 5011 13 = 7 ∧ acceleratedOrbit 13 5011 = 1340 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5011) = 3 ^ 7 * m + 1340 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5011.1, data_13_5011.2] + +end Collatz.Research.StoppingAtlas.Batch0793 From 8fb61bfd73f7419cae61d4fa21aeb1aedc0d8849 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:00 +0530 Subject: [PATCH 0794/1001] proof: certify atlas Batch0794 (13:5012 to 13:5026) --- Collatz/Research/StoppingAtlas/Batch0794.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0794.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0794.lean b/Collatz/Research/StoppingAtlas/Batch0794.lean new file mode 100644 index 00000000..e61ff384 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0794.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0794 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5012. -/ +theorem bounds_13_5012 : exactInterval 13 5012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5012 : oddCount 5012 13 = 6 ∧ acceleratedOrbit 13 5012 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5012) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5012.1, data_13_5012.2] + +/-- Complete interval computation for depth 13, residue 5013. -/ +theorem bounds_13_5013 : exactInterval 13 5013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5013 : oddCount 5013 13 = 6 ∧ acceleratedOrbit 13 5013 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5013) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5013.1, data_13_5013.2] + +/-- Complete interval computation for depth 13, residue 5014. -/ +theorem bounds_13_5014 : exactInterval 13 5014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5014 : oddCount 5014 13 = 5 ∧ acceleratedOrbit 13 5014 = 149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5014) = 3 ^ 5 * m + 149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5014.1, data_13_5014.2] + +/-- Complete interval computation for depth 13, residue 5015. -/ +theorem bounds_13_5015 : exactInterval 13 5015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5015 : oddCount 5015 13 = 5 ∧ acceleratedOrbit 13 5015 = 149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5015) = 3 ^ 5 * m + 149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5015.1, data_13_5015.2] + +/-- Complete interval computation for depth 13, residue 5016. -/ +theorem bounds_13_5016 : exactInterval 13 5016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5016 : oddCount 5016 13 = 6 ∧ acceleratedOrbit 13 5016 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5016) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5016.1, data_13_5016.2] + +/-- Complete interval computation for depth 13, residue 5017. -/ +theorem bounds_13_5017 : exactInterval 13 5017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5017 : oddCount 5017 13 = 5 ∧ acceleratedOrbit 13 5017 = 149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5017) = 3 ^ 5 * m + 149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5017.1, data_13_5017.2] + +/-- Complete interval computation for depth 13, residue 5018. -/ +theorem bounds_13_5018 : exactInterval 13 5018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5018 : oddCount 5018 13 = 6 ∧ acceleratedOrbit 13 5018 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5018) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5018.1, data_13_5018.2] + +/-- Complete interval computation for depth 13, residue 5019. -/ +theorem bounds_13_5019 : exactInterval 13 5019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5019 : oddCount 5019 13 = 8 ∧ acceleratedOrbit 13 5019 = 4022 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5019) = 3 ^ 8 * m + 4022 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5019.1, data_13_5019.2] + +/-- Complete interval computation for depth 13, residue 5020. -/ +theorem bounds_13_5020 : exactInterval 13 5020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5020 : oddCount 5020 13 = 8 ∧ acceleratedOrbit 13 5020 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5020) = 3 ^ 8 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5020.1, data_13_5020.2] + +/-- Complete interval computation for depth 13, residue 5021. -/ +theorem bounds_13_5021 : exactInterval 13 5021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5021 : oddCount 5021 13 = 8 ∧ acceleratedOrbit 13 5021 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5021) = 3 ^ 8 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5021.1, data_13_5021.2] + +/-- Complete interval computation for depth 13, residue 5022. -/ +theorem bounds_13_5022 : exactInterval 13 5022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5022 : oddCount 5022 13 = 8 ∧ acceleratedOrbit 13 5022 = 4025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5022) = 3 ^ 8 * m + 4025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5022.1, data_13_5022.2] + +/-- Complete interval computation for depth 13, residue 5023. -/ +theorem bounds_13_5023 : exactInterval 13 5023 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5023) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5023 : oddCount 5023 13 = 8 ∧ acceleratedOrbit 13 5023 = 4024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5023) = 3 ^ 8 * m + 4024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5023.1, data_13_5023.2] + +/-- Complete interval computation for depth 13, residue 5024. -/ +theorem bounds_13_5024 : exactInterval 13 5024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5024 : oddCount 5024 13 = 5 ∧ acceleratedOrbit 13 5024 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5024) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5024.1, data_13_5024.2] + +/-- Complete interval computation for depth 13, residue 5025. -/ +theorem bounds_13_5025 : exactInterval 13 5025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5025 : oddCount 5025 13 = 7 ∧ acceleratedOrbit 13 5025 = 1343 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5025) = 3 ^ 7 * m + 1343 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5025.1, data_13_5025.2] + +/-- Complete interval computation for depth 13, residue 5026. -/ +theorem bounds_13_5026 : exactInterval 13 5026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5026 : oddCount 5026 13 = 6 ∧ acceleratedOrbit 13 5026 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5026) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5026.1, data_13_5026.2] + +end Collatz.Research.StoppingAtlas.Batch0794 From a0d2dfaa6c2081be6826bc62cdbade9fd1617618 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:00 +0530 Subject: [PATCH 0795/1001] proof: certify atlas Batch0795 (13:5027 to 13:5042) --- Collatz/Research/StoppingAtlas/Batch0795.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0795.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0795.lean b/Collatz/Research/StoppingAtlas/Batch0795.lean new file mode 100644 index 00000000..9a0ef754 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0795.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0795 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5027. -/ +theorem bounds_13_5027 : exactInterval 13 5027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5027 : oddCount 5027 13 = 6 ∧ acceleratedOrbit 13 5027 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5027) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5027.1, data_13_5027.2] + +/-- Complete interval computation for depth 13, residue 5028. -/ +theorem bounds_13_5028 : exactInterval 13 5028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5028 : oddCount 5028 13 = 6 ∧ acceleratedOrbit 13 5028 = 448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5028) = 3 ^ 6 * m + 448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5028.1, data_13_5028.2] + +/-- Complete interval computation for depth 13, residue 5029. -/ +theorem bounds_13_5029 : exactInterval 13 5029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5029 : oddCount 5029 13 = 6 ∧ acceleratedOrbit 13 5029 = 448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5029) = 3 ^ 6 * m + 448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5029.1, data_13_5029.2] + +/-- Complete interval computation for depth 13, residue 5030. -/ +theorem bounds_13_5030 : exactInterval 13 5030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5030 : oddCount 5030 13 = 6 ∧ acceleratedOrbit 13 5030 = 448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5030) = 3 ^ 6 * m + 448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5030.1, data_13_5030.2] + +/-- Complete interval computation for depth 13, residue 5031. -/ +theorem bounds_13_5031 : exactInterval 13 5031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5031 : oddCount 5031 13 = 8 ∧ acceleratedOrbit 13 5031 = 4031 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5031) = 3 ^ 8 * m + 4031 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5031.1, data_13_5031.2] + +/-- Complete interval computation for depth 13, residue 5032. -/ +theorem bounds_13_5032 : exactInterval 13 5032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5032 : oddCount 5032 13 = 5 ∧ acceleratedOrbit 13 5032 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5032) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5032.1, data_13_5032.2] + +/-- Complete interval computation for depth 13, residue 5033. -/ +theorem bounds_13_5033 : exactInterval 13 5033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5033 : oddCount 5033 13 = 9 ∧ acceleratedOrbit 13 5033 = 12097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5033) = 3 ^ 9 * m + 12097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5033.1, data_13_5033.2] + +/-- Complete interval computation for depth 13, residue 5034. -/ +theorem bounds_13_5034 : exactInterval 13 5034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5034 : oddCount 5034 13 = 5 ∧ acceleratedOrbit 13 5034 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5034) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5034.1, data_13_5034.2] + +/-- Complete interval computation for depth 13, residue 5035. -/ +theorem bounds_13_5035 : exactInterval 13 5035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5035 : oddCount 5035 13 = 7 ∧ acceleratedOrbit 13 5035 = 1345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5035) = 3 ^ 7 * m + 1345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5035.1, data_13_5035.2] + +/-- Complete interval computation for depth 13, residue 5036. -/ +theorem bounds_13_5036 : exactInterval 13 5036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5036 : oddCount 5036 13 = 8 ∧ acceleratedOrbit 13 5036 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5036) = 3 ^ 8 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5036.1, data_13_5036.2] + +/-- Complete interval computation for depth 13, residue 5037. -/ +theorem bounds_13_5037 : exactInterval 13 5037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5037 : oddCount 5037 13 = 8 ∧ acceleratedOrbit 13 5037 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5037) = 3 ^ 8 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5037.1, data_13_5037.2] + +/-- Complete interval computation for depth 13, residue 5038. -/ +theorem bounds_13_5038 : exactInterval 13 5038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5038 : oddCount 5038 13 = 8 ∧ acceleratedOrbit 13 5038 = 4040 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5038) = 3 ^ 8 * m + 4040 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5038.1, data_13_5038.2] + +/-- Complete interval computation for depth 13, residue 5039. -/ +theorem bounds_13_5039 : exactInterval 13 5039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5039 : oddCount 5039 13 = 6 ∧ acceleratedOrbit 13 5039 = 449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5039) = 3 ^ 6 * m + 449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5039.1, data_13_5039.2] + +/-- Complete interval computation for depth 13, residue 5040. -/ +theorem bounds_13_5040 : exactInterval 13 5040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5040 : oddCount 5040 13 = 4 ∧ acceleratedOrbit 13 5040 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5040) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5040.1, data_13_5040.2] + +/-- Complete interval computation for depth 13, residue 5041. -/ +theorem bounds_13_5041 : exactInterval 13 5041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5041 : oddCount 5041 13 = 4 ∧ acceleratedOrbit 13 5041 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5041) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5041.1, data_13_5041.2] + +/-- Complete interval computation for depth 13, residue 5042. -/ +theorem bounds_13_5042 : exactInterval 13 5042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5042 : oddCount 5042 13 = 4 ∧ acceleratedOrbit 13 5042 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5042) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5042.1, data_13_5042.2] + +end Collatz.Research.StoppingAtlas.Batch0795 From c7def46f3f2982331bbabc802d6f6f31d98d161f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:00 +0530 Subject: [PATCH 0796/1001] proof: certify atlas Batch0796 (13:5043 to 13:5057) --- Collatz/Research/StoppingAtlas/Batch0796.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0796.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0796.lean b/Collatz/Research/StoppingAtlas/Batch0796.lean new file mode 100644 index 00000000..df4579dc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0796.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0796 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5043. -/ +theorem bounds_13_5043 : exactInterval 13 5043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5043 : oddCount 5043 13 = 4 ∧ acceleratedOrbit 13 5043 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5043) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5043.1, data_13_5043.2] + +/-- Complete interval computation for depth 13, residue 5044. -/ +theorem bounds_13_5044 : exactInterval 13 5044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5044 : oddCount 5044 13 = 4 ∧ acceleratedOrbit 13 5044 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5044) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5044.1, data_13_5044.2] + +/-- Complete interval computation for depth 13, residue 5045. -/ +theorem bounds_13_5045 : exactInterval 13 5045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5045 : oddCount 5045 13 = 4 ∧ acceleratedOrbit 13 5045 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5045) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5045.1, data_13_5045.2] + +/-- Complete interval computation for depth 13, residue 5046. -/ +theorem bounds_13_5046 : exactInterval 13 5046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5046 : oddCount 5046 13 = 7 ∧ acceleratedOrbit 13 5046 = 1349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5046) = 3 ^ 7 * m + 1349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5046.1, data_13_5046.2] + +/-- Complete interval computation for depth 13, residue 5047. -/ +theorem bounds_13_5047 : exactInterval 13 5047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5047) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5047 : oddCount 5047 13 = 7 ∧ acceleratedOrbit 13 5047 = 1349 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5047) = 3 ^ 7 * m + 1349 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5047.1, data_13_5047.2] + +/-- Complete interval computation for depth 13, residue 5048. -/ +theorem bounds_13_5048 : exactInterval 13 5048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5048 : oddCount 5048 13 = 4 ∧ acceleratedOrbit 13 5048 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5048) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5048.1, data_13_5048.2] + +/-- Complete interval computation for depth 13, residue 5049. -/ +theorem bounds_13_5049 : exactInterval 13 5049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5049 : oddCount 5049 13 = 8 ∧ acceleratedOrbit 13 5049 = 4049 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5049) = 3 ^ 8 * m + 4049 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5049.1, data_13_5049.2] + +/-- Complete interval computation for depth 13, residue 5050. -/ +theorem bounds_13_5050 : exactInterval 13 5050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5050 : oddCount 5050 13 = 4 ∧ acceleratedOrbit 13 5050 = 50 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5050) = 3 ^ 4 * m + 50 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5050.1, data_13_5050.2] + +/-- Complete interval computation for depth 13, residue 5051. -/ +theorem bounds_13_5051 : exactInterval 13 5051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5051 : oddCount 5051 13 = 8 ∧ acceleratedOrbit 13 5051 = 4049 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5051) = 3 ^ 8 * m + 4049 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5051.1, data_13_5051.2] + +/-- Complete interval computation for depth 13, residue 5052. -/ +theorem bounds_13_5052 : exactInterval 13 5052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5052 : oddCount 5052 13 = 10 ∧ acceleratedOrbit 13 5052 = 36449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5052) = 3 ^ 10 * m + 36449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5052.1, data_13_5052.2] + +/-- Complete interval computation for depth 13, residue 5053. -/ +theorem bounds_13_5053 : exactInterval 13 5053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5053 : oddCount 5053 13 = 10 ∧ acceleratedOrbit 13 5053 = 36449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5053) = 3 ^ 10 * m + 36449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5053.1, data_13_5053.2] + +/-- Complete interval computation for depth 13, residue 5054. -/ +theorem bounds_13_5054 : exactInterval 13 5054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5054 : oddCount 5054 13 = 10 ∧ acceleratedOrbit 13 5054 = 36449 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5054) = 3 ^ 10 * m + 36449 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5054.1, data_13_5054.2] + +/-- Complete interval computation for depth 13, residue 5055. -/ +theorem bounds_13_5055 : exactInterval 13 5055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5055 : oddCount 5055 13 = 10 ∧ acceleratedOrbit 13 5055 = 36445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5055) = 3 ^ 10 * m + 36445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5055.1, data_13_5055.2] + +/-- Complete interval computation for depth 13, residue 5056. -/ +theorem bounds_13_5056 : exactInterval 13 5056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5056 : oddCount 5056 13 = 5 ∧ acceleratedOrbit 13 5056 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5056) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5056.1, data_13_5056.2] + +/-- Complete interval computation for depth 13, residue 5057. -/ +theorem bounds_13_5057 : exactInterval 13 5057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5057 : oddCount 5057 13 = 7 ∧ acceleratedOrbit 13 5057 = 1352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5057) = 3 ^ 7 * m + 1352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5057.1, data_13_5057.2] + +end Collatz.Research.StoppingAtlas.Batch0796 From 370505b02fde828a627ee0aa9eefa43d915dbd28 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:00 +0530 Subject: [PATCH 0797/1001] proof: certify atlas Batch0797 (13:5058 to 13:5072) --- Collatz/Research/StoppingAtlas/Batch0797.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0797.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0797.lean b/Collatz/Research/StoppingAtlas/Batch0797.lean new file mode 100644 index 00000000..4aafc38a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0797.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0797 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5058. -/ +theorem bounds_13_5058 : exactInterval 13 5058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5058 : oddCount 5058 13 = 7 ∧ acceleratedOrbit 13 5058 = 1352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5058) = 3 ^ 7 * m + 1352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5058.1, data_13_5058.2] + +/-- Complete interval computation for depth 13, residue 5059. -/ +theorem bounds_13_5059 : exactInterval 13 5059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5059 : oddCount 5059 13 = 7 ∧ acceleratedOrbit 13 5059 = 1352 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5059) = 3 ^ 7 * m + 1352 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5059.1, data_13_5059.2] + +/-- Complete interval computation for depth 13, residue 5060. -/ +theorem bounds_13_5060 : exactInterval 13 5060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5060 : oddCount 5060 13 = 5 ∧ acceleratedOrbit 13 5060 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5060) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5060.1, data_13_5060.2] + +/-- Complete interval computation for depth 13, residue 5061. -/ +theorem bounds_13_5061 : exactInterval 13 5061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5061 : oddCount 5061 13 = 5 ∧ acceleratedOrbit 13 5061 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5061) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5061.1, data_13_5061.2] + +/-- Complete interval computation for depth 13, residue 5062. -/ +theorem bounds_13_5062 : exactInterval 13 5062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5062 : oddCount 5062 13 = 5 ∧ acceleratedOrbit 13 5062 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5062) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5062.1, data_13_5062.2] + +/-- Complete interval computation for depth 13, residue 5063. -/ +theorem bounds_13_5063 : exactInterval 13 5063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5063 : oddCount 5063 13 = 9 ∧ acceleratedOrbit 13 5063 = 12170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5063) = 3 ^ 9 * m + 12170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5063.1, data_13_5063.2] + +/-- Complete interval computation for depth 13, residue 5064. -/ +theorem bounds_13_5064 : exactInterval 13 5064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5064 : oddCount 5064 13 = 6 ∧ acceleratedOrbit 13 5064 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5064) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5064.1, data_13_5064.2] + +/-- Complete interval computation for depth 13, residue 5065. -/ +theorem bounds_13_5065 : exactInterval 13 5065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5065 : oddCount 5065 13 = 6 ∧ acceleratedOrbit 13 5065 = 451 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5065) = 3 ^ 6 * m + 451 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5065.1, data_13_5065.2] + +/-- Complete interval computation for depth 13, residue 5066. -/ +theorem bounds_13_5066 : exactInterval 13 5066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5066 : oddCount 5066 13 = 6 ∧ acceleratedOrbit 13 5066 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5066) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5066.1, data_13_5066.2] + +/-- Complete interval computation for depth 13, residue 5067. -/ +theorem bounds_13_5067 : exactInterval 13 5067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5067 : oddCount 5067 13 = 6 ∧ acceleratedOrbit 13 5067 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5067) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5067.1, data_13_5067.2] + +/-- Complete interval computation for depth 13, residue 5068. -/ +theorem bounds_13_5068 : exactInterval 13 5068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5068 : oddCount 5068 13 = 6 ∧ acceleratedOrbit 13 5068 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5068) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5068.1, data_13_5068.2] + +/-- Complete interval computation for depth 13, residue 5069. -/ +theorem bounds_13_5069 : exactInterval 13 5069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5069 : oddCount 5069 13 = 6 ∧ acceleratedOrbit 13 5069 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5069) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5069.1, data_13_5069.2] + +/-- Complete interval computation for depth 13, residue 5070. -/ +theorem bounds_13_5070 : exactInterval 13 5070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5070 : oddCount 5070 13 = 8 ∧ acceleratedOrbit 13 5070 = 4063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5070) = 3 ^ 8 * m + 4063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5070.1, data_13_5070.2] + +/-- Complete interval computation for depth 13, residue 5071. -/ +theorem bounds_13_5071 : exactInterval 13 5071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5071 : oddCount 5071 13 = 8 ∧ acceleratedOrbit 13 5071 = 4063 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5071) = 3 ^ 8 * m + 4063 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5071.1, data_13_5071.2] + +/-- Complete interval computation for depth 13, residue 5072. -/ +theorem bounds_13_5072 : exactInterval 13 5072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5072 : oddCount 5072 13 = 5 ∧ acceleratedOrbit 13 5072 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5072) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5072.1, data_13_5072.2] + +end Collatz.Research.StoppingAtlas.Batch0797 From e9f0369ab07589b3eba4ae3f34fa72d89231c6b6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:00 +0530 Subject: [PATCH 0798/1001] proof: certify atlas Batch0798 (13:5073 to 13:5088) --- Collatz/Research/StoppingAtlas/Batch0798.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0798.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0798.lean b/Collatz/Research/StoppingAtlas/Batch0798.lean new file mode 100644 index 00000000..b449d56f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0798.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0798 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5073. -/ +theorem bounds_13_5073 : exactInterval 13 5073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5073 : oddCount 5073 13 = 6 ∧ acceleratedOrbit 13 5073 = 452 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5073) = 3 ^ 6 * m + 452 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5073.1, data_13_5073.2] + +/-- Complete interval computation for depth 13, residue 5074. -/ +theorem bounds_13_5074 : exactInterval 13 5074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5074 : oddCount 5074 13 = 8 ∧ acceleratedOrbit 13 5074 = 4067 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5074) = 3 ^ 8 * m + 4067 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5074.1, data_13_5074.2] + +/-- Complete interval computation for depth 13, residue 5075. -/ +theorem bounds_13_5075 : exactInterval 13 5075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5075 : oddCount 5075 13 = 8 ∧ acceleratedOrbit 13 5075 = 4067 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5075) = 3 ^ 8 * m + 4067 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5075.1, data_13_5075.2] + +/-- Complete interval computation for depth 13, residue 5076. -/ +theorem bounds_13_5076 : exactInterval 13 5076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5076 : oddCount 5076 13 = 5 ∧ acceleratedOrbit 13 5076 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5076) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5076.1, data_13_5076.2] + +/-- Complete interval computation for depth 13, residue 5077. -/ +theorem bounds_13_5077 : exactInterval 13 5077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5077 : oddCount 5077 13 = 5 ∧ acceleratedOrbit 13 5077 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5077) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5077.1, data_13_5077.2] + +/-- Complete interval computation for depth 13, residue 5078. -/ +theorem bounds_13_5078 : exactInterval 13 5078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5078 : oddCount 5078 13 = 8 ∧ acceleratedOrbit 13 5078 = 4070 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5078) = 3 ^ 8 * m + 4070 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5078.1, data_13_5078.2] + +/-- Complete interval computation for depth 13, residue 5079. -/ +theorem bounds_13_5079 : exactInterval 13 5079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5079) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5079 : oddCount 5079 13 = 8 ∧ acceleratedOrbit 13 5079 = 4070 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5079) = 3 ^ 8 * m + 4070 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5079.1, data_13_5079.2] + +/-- Complete interval computation for depth 13, residue 5080. -/ +theorem bounds_13_5080 : exactInterval 13 5080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5080 : oddCount 5080 13 = 5 ∧ acceleratedOrbit 13 5080 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5080) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5080.1, data_13_5080.2] + +/-- Complete interval computation for depth 13, residue 5081. -/ +theorem bounds_13_5081 : exactInterval 13 5081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5081 : oddCount 5081 13 = 5 ∧ acceleratedOrbit 13 5081 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5081) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5081.1, data_13_5081.2] + +/-- Complete interval computation for depth 13, residue 5082. -/ +theorem bounds_13_5082 : exactInterval 13 5082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5082 : oddCount 5082 13 = 5 ∧ acceleratedOrbit 13 5082 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5082) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5082.1, data_13_5082.2] + +/-- Complete interval computation for depth 13, residue 5083. -/ +theorem bounds_13_5083 : exactInterval 13 5083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5083 : oddCount 5083 13 = 7 ∧ acceleratedOrbit 13 5083 = 1358 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5083) = 3 ^ 7 * m + 1358 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5083.1, data_13_5083.2] + +/-- Complete interval computation for depth 13, residue 5084. -/ +theorem bounds_13_5084 : exactInterval 13 5084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5084 : oddCount 5084 13 = 5 ∧ acceleratedOrbit 13 5084 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5084) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5084.1, data_13_5084.2] + +/-- Complete interval computation for depth 13, residue 5085. -/ +theorem bounds_13_5085 : exactInterval 13 5085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5085 : oddCount 5085 13 = 5 ∧ acceleratedOrbit 13 5085 = 151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5085) = 3 ^ 5 * m + 151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5085.1, data_13_5085.2] + +/-- Complete interval computation for depth 13, residue 5086. -/ +theorem bounds_13_5086 : exactInterval 13 5086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5086 : oddCount 5086 13 = 9 ∧ acceleratedOrbit 13 5086 = 12226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5086) = 3 ^ 9 * m + 12226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5086.1, data_13_5086.2] + +/-- Complete interval computation for depth 13, residue 5087. -/ +theorem bounds_13_5087 : exactInterval 13 5087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5087 : oddCount 5087 13 = 9 ∧ acceleratedOrbit 13 5087 = 12226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5087) = 3 ^ 9 * m + 12226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5087.1, data_13_5087.2] + +/-- Complete interval computation for depth 13, residue 5088. -/ +theorem bounds_13_5088 : exactInterval 13 5088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5088 : oddCount 5088 13 = 7 ∧ acceleratedOrbit 13 5088 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5088) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5088.1, data_13_5088.2] + +end Collatz.Research.StoppingAtlas.Batch0798 From d4eee43b8f2e51088b9162b5056beb4b362dad34 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:00 +0530 Subject: [PATCH 0799/1001] proof: certify atlas Batch0799 (13:5089 to 13:5103) --- Collatz/Research/StoppingAtlas/Batch0799.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0799.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0799.lean b/Collatz/Research/StoppingAtlas/Batch0799.lean new file mode 100644 index 00000000..ea0659fa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0799.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0799 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5089. -/ +theorem bounds_13_5089 : exactInterval 13 5089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5089 : oddCount 5089 13 = 8 ∧ acceleratedOrbit 13 5089 = 4078 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5089) = 3 ^ 8 * m + 4078 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5089.1, data_13_5089.2] + +/-- Complete interval computation for depth 13, residue 5090. -/ +theorem bounds_13_5090 : exactInterval 13 5090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5090 : oddCount 5090 13 = 5 ∧ acceleratedOrbit 13 5090 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5090) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5090.1, data_13_5090.2] + +/-- Complete interval computation for depth 13, residue 5091. -/ +theorem bounds_13_5091 : exactInterval 13 5091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5091 : oddCount 5091 13 = 5 ∧ acceleratedOrbit 13 5091 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5091) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5091.1, data_13_5091.2] + +/-- Complete interval computation for depth 13, residue 5092. -/ +theorem bounds_13_5092 : exactInterval 13 5092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5092 : oddCount 5092 13 = 6 ∧ acceleratedOrbit 13 5092 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5092) = 3 ^ 6 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5092.1, data_13_5092.2] + +/-- Complete interval computation for depth 13, residue 5093. -/ +theorem bounds_13_5093 : exactInterval 13 5093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5093 : oddCount 5093 13 = 6 ∧ acceleratedOrbit 13 5093 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5093) = 3 ^ 6 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5093.1, data_13_5093.2] + +/-- Complete interval computation for depth 13, residue 5094. -/ +theorem bounds_13_5094 : exactInterval 13 5094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5094 : oddCount 5094 13 = 6 ∧ acceleratedOrbit 13 5094 = 454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5094) = 3 ^ 6 * m + 454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5094.1, data_13_5094.2] + +/-- Complete interval computation for depth 13, residue 5095. -/ +theorem bounds_13_5095 : exactInterval 13 5095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5095 : oddCount 5095 13 = 7 ∧ acceleratedOrbit 13 5095 = 1361 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5095) = 3 ^ 7 * m + 1361 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5095.1, data_13_5095.2] + +/-- Complete interval computation for depth 13, residue 5096. -/ +theorem bounds_13_5096 : exactInterval 13 5096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5096 : oddCount 5096 13 = 7 ∧ acceleratedOrbit 13 5096 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5096) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5096.1, data_13_5096.2] + +/-- Complete interval computation for depth 13, residue 5097. -/ +theorem bounds_13_5097 : exactInterval 13 5097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5097 : oddCount 5097 13 = 9 ∧ acceleratedOrbit 13 5097 = 12251 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5097) = 3 ^ 9 * m + 12251 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5097.1, data_13_5097.2] + +/-- Complete interval computation for depth 13, residue 5098. -/ +theorem bounds_13_5098 : exactInterval 13 5098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5098 : oddCount 5098 13 = 7 ∧ acceleratedOrbit 13 5098 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5098) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5098.1, data_13_5098.2] + +/-- Complete interval computation for depth 13, residue 5099. -/ +theorem bounds_13_5099 : exactInterval 13 5099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5099 : oddCount 5099 13 = 9 ∧ acceleratedOrbit 13 5099 = 12257 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5099) = 3 ^ 9 * m + 12257 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5099.1, data_13_5099.2] + +/-- Complete interval computation for depth 13, residue 5100. -/ +theorem bounds_13_5100 : exactInterval 13 5100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5100 : oddCount 5100 13 = 8 ∧ acceleratedOrbit 13 5100 = 4090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5100) = 3 ^ 8 * m + 4090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5100.1, data_13_5100.2] + +/-- Complete interval computation for depth 13, residue 5101. -/ +theorem bounds_13_5101 : exactInterval 13 5101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5101 : oddCount 5101 13 = 8 ∧ acceleratedOrbit 13 5101 = 4090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5101) = 3 ^ 8 * m + 4090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5101.1, data_13_5101.2] + +/-- Complete interval computation for depth 13, residue 5102. -/ +theorem bounds_13_5102 : exactInterval 13 5102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5102 : oddCount 5102 13 = 8 ∧ acceleratedOrbit 13 5102 = 4090 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5102) = 3 ^ 8 * m + 4090 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5102.1, data_13_5102.2] + +/-- Complete interval computation for depth 13, residue 5103. -/ +theorem bounds_13_5103 : exactInterval 13 5103 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5103) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5103 : oddCount 5103 13 = 8 ∧ acceleratedOrbit 13 5103 = 4088 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5103) = 3 ^ 8 * m + 4088 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5103.1, data_13_5103.2] + +end Collatz.Research.StoppingAtlas.Batch0799 From 1a8ee1eb9f6b6c4a25366bf060accfb27284e5b3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:01 +0530 Subject: [PATCH 0800/1001] proof: certify atlas Batch0800 (13:5104 to 13:5119) --- Collatz/Research/StoppingAtlas/Batch0800.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0800.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0800.lean b/Collatz/Research/StoppingAtlas/Batch0800.lean new file mode 100644 index 00000000..ac444ef7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0800.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0800 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5104. -/ +theorem bounds_13_5104 : exactInterval 13 5104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5104 : oddCount 5104 13 = 7 ∧ acceleratedOrbit 13 5104 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5104) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5104.1, data_13_5104.2] + +/-- Complete interval computation for depth 13, residue 5105. -/ +theorem bounds_13_5105 : exactInterval 13 5105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5105 : oddCount 5105 13 = 7 ∧ acceleratedOrbit 13 5105 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5105) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5105.1, data_13_5105.2] + +/-- Complete interval computation for depth 13, residue 5106. -/ +theorem bounds_13_5106 : exactInterval 13 5106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5106 : oddCount 5106 13 = 8 ∧ acceleratedOrbit 13 5106 = 4094 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5106) = 3 ^ 8 * m + 4094 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5106.1, data_13_5106.2] + +/-- Complete interval computation for depth 13, residue 5107. -/ +theorem bounds_13_5107 : exactInterval 13 5107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5107 : oddCount 5107 13 = 8 ∧ acceleratedOrbit 13 5107 = 4094 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5107) = 3 ^ 8 * m + 4094 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5107.1, data_13_5107.2] + +/-- Complete interval computation for depth 13, residue 5108. -/ +theorem bounds_13_5108 : exactInterval 13 5108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5108 : oddCount 5108 13 = 7 ∧ acceleratedOrbit 13 5108 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5108) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5108.1, data_13_5108.2] + +/-- Complete interval computation for depth 13, residue 5109. -/ +theorem bounds_13_5109 : exactInterval 13 5109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5109 : oddCount 5109 13 = 7 ∧ acceleratedOrbit 13 5109 = 1367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5109) = 3 ^ 7 * m + 1367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5109.1, data_13_5109.2] + +/-- Complete interval computation for depth 13, residue 5110. -/ +theorem bounds_13_5110 : exactInterval 13 5110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5110 : oddCount 5110 13 = 6 ∧ acceleratedOrbit 13 5110 = 455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5110) = 3 ^ 6 * m + 455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5110.1, data_13_5110.2] + +/-- Complete interval computation for depth 13, residue 5111. -/ +theorem bounds_13_5111 : exactInterval 13 5111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5111 : oddCount 5111 13 = 6 ∧ acceleratedOrbit 13 5111 = 455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5111) = 3 ^ 6 * m + 455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5111.1, data_13_5111.2] + +/-- Complete interval computation for depth 13, residue 5112. -/ +theorem bounds_13_5112 : exactInterval 13 5112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5112 : oddCount 5112 13 = 9 ∧ acceleratedOrbit 13 5112 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5112) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5112.1, data_13_5112.2] + +/-- Complete interval computation for depth 13, residue 5113. -/ +theorem bounds_13_5113 : exactInterval 13 5113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5113 : oddCount 5113 13 = 8 ∧ acceleratedOrbit 13 5113 = 4097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5113) = 3 ^ 8 * m + 4097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5113.1, data_13_5113.2] + +/-- Complete interval computation for depth 13, residue 5114. -/ +theorem bounds_13_5114 : exactInterval 13 5114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5114 : oddCount 5114 13 = 9 ∧ acceleratedOrbit 13 5114 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5114) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5114.1, data_13_5114.2] + +/-- Complete interval computation for depth 13, residue 5115. -/ +theorem bounds_13_5115 : exactInterval 13 5115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5115 : oddCount 5115 13 = 7 ∧ acceleratedOrbit 13 5115 = 1366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5115) = 3 ^ 7 * m + 1366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5115.1, data_13_5115.2] + +/-- Complete interval computation for depth 13, residue 5116. -/ +theorem bounds_13_5116 : exactInterval 13 5116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5116 : oddCount 5116 13 = 9 ∧ acceleratedOrbit 13 5116 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5116) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5116.1, data_13_5116.2] + +/-- Complete interval computation for depth 13, residue 5117. -/ +theorem bounds_13_5117 : exactInterval 13 5117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5117 : oddCount 5117 13 = 9 ∧ acceleratedOrbit 13 5117 = 12302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5117) = 3 ^ 9 * m + 12302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5117.1, data_13_5117.2] + +/-- Complete interval computation for depth 13, residue 5118. -/ +theorem bounds_13_5118 : exactInterval 13 5118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5118 : oddCount 5118 13 = 11 ∧ acceleratedOrbit 13 5118 = 110717 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5118) = 3 ^ 11 * m + 110717 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5118.1, data_13_5118.2] + +/-- Complete interval computation for depth 13, residue 5119. -/ +theorem bounds_13_5119 : exactInterval 13 5119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5119 : oddCount 5119 13 = 11 ∧ acceleratedOrbit 13 5119 = 110717 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5119) = 3 ^ 11 * m + 110717 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5119.1, data_13_5119.2] + +end Collatz.Research.StoppingAtlas.Batch0800 From 3d696b897b7a9a4f9f60320a836ee8780556367a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:01 +0530 Subject: [PATCH 0801/1001] proof: certify atlas Batch0801 (13:5120 to 13:5134) --- Collatz/Research/StoppingAtlas/Batch0801.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0801.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0801.lean b/Collatz/Research/StoppingAtlas/Batch0801.lean new file mode 100644 index 00000000..e481dce9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0801.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0801 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5120. -/ +theorem bounds_13_5120 : exactInterval 13 5120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5120 : oddCount 5120 13 = 1 ∧ acceleratedOrbit 13 5120 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5120) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5120.1, data_13_5120.2] + +/-- Complete interval computation for depth 13, residue 5121. -/ +theorem bounds_13_5121 : exactInterval 13 5121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5121 : oddCount 5121 13 = 5 ∧ acceleratedOrbit 13 5121 = 152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5121) = 3 ^ 5 * m + 152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5121.1, data_13_5121.2] + +/-- Complete interval computation for depth 13, residue 5122. -/ +theorem bounds_13_5122 : exactInterval 13 5122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5122 : oddCount 5122 13 = 7 ∧ acceleratedOrbit 13 5122 = 1370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5122) = 3 ^ 7 * m + 1370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5122.1, data_13_5122.2] + +/-- Complete interval computation for depth 13, residue 5123. -/ +theorem bounds_13_5123 : exactInterval 13 5123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5123 : oddCount 5123 13 = 7 ∧ acceleratedOrbit 13 5123 = 1370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5123) = 3 ^ 7 * m + 1370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5123.1, data_13_5123.2] + +/-- Complete interval computation for depth 13, residue 5124. -/ +theorem bounds_13_5124 : exactInterval 13 5124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5124 : oddCount 5124 13 = 6 ∧ acceleratedOrbit 13 5124 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5124) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5124.1, data_13_5124.2] + +/-- Complete interval computation for depth 13, residue 5125. -/ +theorem bounds_13_5125 : exactInterval 13 5125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5125 : oddCount 5125 13 = 6 ∧ acceleratedOrbit 13 5125 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5125) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5125.1, data_13_5125.2] + +/-- Complete interval computation for depth 13, residue 5126. -/ +theorem bounds_13_5126 : exactInterval 13 5126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5126 : oddCount 5126 13 = 6 ∧ acceleratedOrbit 13 5126 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5126) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5126.1, data_13_5126.2] + +/-- Complete interval computation for depth 13, residue 5127. -/ +theorem bounds_13_5127 : exactInterval 13 5127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5127 : oddCount 5127 13 = 7 ∧ acceleratedOrbit 13 5127 = 1370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5127) = 3 ^ 7 * m + 1370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5127.1, data_13_5127.2] + +/-- Complete interval computation for depth 13, residue 5128. -/ +theorem bounds_13_5128 : exactInterval 13 5128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5128 : oddCount 5128 13 = 7 ∧ acceleratedOrbit 13 5128 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5128) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5128.1, data_13_5128.2] + +/-- Complete interval computation for depth 13, residue 5129. -/ +theorem bounds_13_5129 : exactInterval 13 5129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5129 : oddCount 5129 13 = 7 ∧ acceleratedOrbit 13 5129 = 1370 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5129) = 3 ^ 7 * m + 1370 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5129.1, data_13_5129.2] + +/-- Complete interval computation for depth 13, residue 5130. -/ +theorem bounds_13_5130 : exactInterval 13 5130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5130 : oddCount 5130 13 = 7 ∧ acceleratedOrbit 13 5130 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5130) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5130.1, data_13_5130.2] + +/-- Complete interval computation for depth 13, residue 5131. -/ +theorem bounds_13_5131 : exactInterval 13 5131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5131 : oddCount 5131 13 = 6 ∧ acceleratedOrbit 13 5131 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5131) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5131.1, data_13_5131.2] + +/-- Complete interval computation for depth 13, residue 5132. -/ +theorem bounds_13_5132 : exactInterval 13 5132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5132 : oddCount 5132 13 = 7 ∧ acceleratedOrbit 13 5132 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5132) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5132.1, data_13_5132.2] + +/-- Complete interval computation for depth 13, residue 5133. -/ +theorem bounds_13_5133 : exactInterval 13 5133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5133 : oddCount 5133 13 = 7 ∧ acceleratedOrbit 13 5133 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5133) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5133.1, data_13_5133.2] + +/-- Complete interval computation for depth 13, residue 5134. -/ +theorem bounds_13_5134 : exactInterval 13 5134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5134 : oddCount 5134 13 = 7 ∧ acceleratedOrbit 13 5134 = 1372 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5134) = 3 ^ 7 * m + 1372 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5134.1, data_13_5134.2] + +end Collatz.Research.StoppingAtlas.Batch0801 From d820d578b9b2a4ad43c3e000c7ac19060c81bf7b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:01 +0530 Subject: [PATCH 0802/1001] proof: certify atlas Batch0802 (13:5135 to 13:5149) --- Collatz/Research/StoppingAtlas/Batch0802.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0802.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0802.lean b/Collatz/Research/StoppingAtlas/Batch0802.lean new file mode 100644 index 00000000..65e4269a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0802.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0802 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5135. -/ +theorem bounds_13_5135 : exactInterval 13 5135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5135 : oddCount 5135 13 = 7 ∧ acceleratedOrbit 13 5135 = 1372 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5135) = 3 ^ 7 * m + 1372 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5135.1, data_13_5135.2] + +/-- Complete interval computation for depth 13, residue 5136. -/ +theorem bounds_13_5136 : exactInterval 13 5136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5136 : oddCount 5136 13 = 3 ∧ acceleratedOrbit 13 5136 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5136) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5136.1, data_13_5136.2] + +/-- Complete interval computation for depth 13, residue 5137. -/ +theorem bounds_13_5137 : exactInterval 13 5137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5137 : oddCount 5137 13 = 7 ∧ acceleratedOrbit 13 5137 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5137) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5137.1, data_13_5137.2] + +/-- Complete interval computation for depth 13, residue 5138. -/ +theorem bounds_13_5138 : exactInterval 13 5138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5138 : oddCount 5138 13 = 6 ∧ acceleratedOrbit 13 5138 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5138) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5138.1, data_13_5138.2] + +/-- Complete interval computation for depth 13, residue 5139. -/ +theorem bounds_13_5139 : exactInterval 13 5139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5139 : oddCount 5139 13 = 6 ∧ acceleratedOrbit 13 5139 = 458 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5139) = 3 ^ 6 * m + 458 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5139.1, data_13_5139.2] + +/-- Complete interval computation for depth 13, residue 5140. -/ +theorem bounds_13_5140 : exactInterval 13 5140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5140 : oddCount 5140 13 = 3 ∧ acceleratedOrbit 13 5140 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5140) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5140.1, data_13_5140.2] + +/-- Complete interval computation for depth 13, residue 5141. -/ +theorem bounds_13_5141 : exactInterval 13 5141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5141 : oddCount 5141 13 = 3 ∧ acceleratedOrbit 13 5141 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5141) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5141.1, data_13_5141.2] + +/-- Complete interval computation for depth 13, residue 5142. -/ +theorem bounds_13_5142 : exactInterval 13 5142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5142 : oddCount 5142 13 = 7 ∧ acceleratedOrbit 13 5142 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5142) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5142.1, data_13_5142.2] + +/-- Complete interval computation for depth 13, residue 5143. -/ +theorem bounds_13_5143 : exactInterval 13 5143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5143 : oddCount 5143 13 = 7 ∧ acceleratedOrbit 13 5143 = 1376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5143) = 3 ^ 7 * m + 1376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5143.1, data_13_5143.2] + +/-- Complete interval computation for depth 13, residue 5144. -/ +theorem bounds_13_5144 : exactInterval 13 5144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5144 : oddCount 5144 13 = 3 ∧ acceleratedOrbit 13 5144 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5144) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5144.1, data_13_5144.2] + +/-- Complete interval computation for depth 13, residue 5145. -/ +theorem bounds_13_5145 : exactInterval 13 5145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5145 : oddCount 5145 13 = 8 ∧ acceleratedOrbit 13 5145 = 4124 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5145) = 3 ^ 8 * m + 4124 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5145.1, data_13_5145.2] + +/-- Complete interval computation for depth 13, residue 5146. -/ +theorem bounds_13_5146 : exactInterval 13 5146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5146 : oddCount 5146 13 = 3 ∧ acceleratedOrbit 13 5146 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5146) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5146.1, data_13_5146.2] + +/-- Complete interval computation for depth 13, residue 5147. -/ +theorem bounds_13_5147 : exactInterval 13 5147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5147 : oddCount 5147 13 = 10 ∧ acceleratedOrbit 13 5147 = 37111 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5147) = 3 ^ 10 * m + 37111 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5147.1, data_13_5147.2] + +/-- Complete interval computation for depth 13, residue 5148. -/ +theorem bounds_13_5148 : exactInterval 13 5148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5148 : oddCount 5148 13 = 8 ∧ acceleratedOrbit 13 5148 = 4130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5148) = 3 ^ 8 * m + 4130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5148.1, data_13_5148.2] + +/-- Complete interval computation for depth 13, residue 5149. -/ +theorem bounds_13_5149 : exactInterval 13 5149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5149 : oddCount 5149 13 = 8 ∧ acceleratedOrbit 13 5149 = 4130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5149) = 3 ^ 8 * m + 4130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5149.1, data_13_5149.2] + +end Collatz.Research.StoppingAtlas.Batch0802 From dc8438ff94978f72d820f7b5f7f1d5f754b8b3d4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:01 +0530 Subject: [PATCH 0803/1001] proof: certify atlas Batch0803 (13:5150 to 13:5165) --- Collatz/Research/StoppingAtlas/Batch0803.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0803.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0803.lean b/Collatz/Research/StoppingAtlas/Batch0803.lean new file mode 100644 index 00000000..b6478dff --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0803.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0803 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5150. -/ +theorem bounds_13_5150 : exactInterval 13 5150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5150 : oddCount 5150 13 = 8 ∧ acceleratedOrbit 13 5150 = 4130 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5150) = 3 ^ 8 * m + 4130 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5150.1, data_13_5150.2] + +/-- Complete interval computation for depth 13, residue 5151. -/ +theorem bounds_13_5151 : exactInterval 13 5151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5151 : oddCount 5151 13 = 10 ∧ acceleratedOrbit 13 5151 = 37138 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5151) = 3 ^ 10 * m + 37138 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5151.1, data_13_5151.2] + +/-- Complete interval computation for depth 13, residue 5152. -/ +theorem bounds_13_5152 : exactInterval 13 5152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5152 : oddCount 5152 13 = 5 ∧ acceleratedOrbit 13 5152 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5152) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5152.1, data_13_5152.2] + +/-- Complete interval computation for depth 13, residue 5153. -/ +theorem bounds_13_5153 : exactInterval 13 5153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5153 : oddCount 5153 13 = 9 ∧ acceleratedOrbit 13 5153 = 12392 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5153) = 3 ^ 9 * m + 12392 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5153.1, data_13_5153.2] + +/-- Complete interval computation for depth 13, residue 5154. -/ +theorem bounds_13_5154 : exactInterval 13 5154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5154 : oddCount 5154 13 = 3 ∧ acceleratedOrbit 13 5154 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5154) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5154.1, data_13_5154.2] + +/-- Complete interval computation for depth 13, residue 5155. -/ +theorem bounds_13_5155 : exactInterval 13 5155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5155 : oddCount 5155 13 = 3 ∧ acceleratedOrbit 13 5155 = 17 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5155) = 3 ^ 3 * m + 17 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5155.1, data_13_5155.2] + +/-- Complete interval computation for depth 13, residue 5156. -/ +theorem bounds_13_5156 : exactInterval 13 5156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5156 : oddCount 5156 13 = 7 ∧ acceleratedOrbit 13 5156 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5156) = 3 ^ 7 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5156.1, data_13_5156.2] + +/-- Complete interval computation for depth 13, residue 5157. -/ +theorem bounds_13_5157 : exactInterval 13 5157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5157 : oddCount 5157 13 = 7 ∧ acceleratedOrbit 13 5157 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5157) = 3 ^ 7 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5157.1, data_13_5157.2] + +/-- Complete interval computation for depth 13, residue 5158. -/ +theorem bounds_13_5158 : exactInterval 13 5158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5158 : oddCount 5158 13 = 7 ∧ acceleratedOrbit 13 5158 = 1379 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5158) = 3 ^ 7 * m + 1379 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5158.1, data_13_5158.2] + +/-- Complete interval computation for depth 13, residue 5159. -/ +theorem bounds_13_5159 : exactInterval 13 5159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5159 : oddCount 5159 13 = 7 ∧ acceleratedOrbit 13 5159 = 1378 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5159) = 3 ^ 7 * m + 1378 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5159.1, data_13_5159.2] + +/-- Complete interval computation for depth 13, residue 5160. -/ +theorem bounds_13_5160 : exactInterval 13 5160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5160 : oddCount 5160 13 = 5 ∧ acceleratedOrbit 13 5160 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5160) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5160.1, data_13_5160.2] + +/-- Complete interval computation for depth 13, residue 5161. -/ +theorem bounds_13_5161 : exactInterval 13 5161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5161 : oddCount 5161 13 = 8 ∧ acceleratedOrbit 13 5161 = 4135 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5161) = 3 ^ 8 * m + 4135 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5161.1, data_13_5161.2] + +/-- Complete interval computation for depth 13, residue 5162. -/ +theorem bounds_13_5162 : exactInterval 13 5162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5162 : oddCount 5162 13 = 5 ∧ acceleratedOrbit 13 5162 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5162) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5162.1, data_13_5162.2] + +/-- Complete interval computation for depth 13, residue 5163. -/ +theorem bounds_13_5163 : exactInterval 13 5163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5163 : oddCount 5163 13 = 6 ∧ acceleratedOrbit 13 5163 = 460 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5163) = 3 ^ 6 * m + 460 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5163.1, data_13_5163.2] + +/-- Complete interval computation for depth 13, residue 5164. -/ +theorem bounds_13_5164 : exactInterval 13 5164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5164 : oddCount 5164 13 = 6 ∧ acceleratedOrbit 13 5164 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5164) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5164.1, data_13_5164.2] + +/-- Complete interval computation for depth 13, residue 5165. -/ +theorem bounds_13_5165 : exactInterval 13 5165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5165 : oddCount 5165 13 = 6 ∧ acceleratedOrbit 13 5165 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5165) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5165.1, data_13_5165.2] + +end Collatz.Research.StoppingAtlas.Batch0803 From eb188562bc077e81c408d7cb2d65f11bd8cb2b2e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:01 +0530 Subject: [PATCH 0804/1001] proof: certify atlas Batch0804 (13:5166 to 13:5180) --- Collatz/Research/StoppingAtlas/Batch0804.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0804.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0804.lean b/Collatz/Research/StoppingAtlas/Batch0804.lean new file mode 100644 index 00000000..237ce8aa --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0804.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0804 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5166. -/ +theorem bounds_13_5166 : exactInterval 13 5166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5166 : oddCount 5166 13 = 6 ∧ acceleratedOrbit 13 5166 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5166) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5166.1, data_13_5166.2] + +/-- Complete interval computation for depth 13, residue 5167. -/ +theorem bounds_13_5167 : exactInterval 13 5167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5167 : oddCount 5167 13 = 9 ∧ acceleratedOrbit 13 5167 = 12419 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5167) = 3 ^ 9 * m + 12419 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5167.1, data_13_5167.2] + +/-- Complete interval computation for depth 13, residue 5168. -/ +theorem bounds_13_5168 : exactInterval 13 5168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5168 : oddCount 5168 13 = 5 ∧ acceleratedOrbit 13 5168 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5168) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5168.1, data_13_5168.2] + +/-- Complete interval computation for depth 13, residue 5169. -/ +theorem bounds_13_5169 : exactInterval 13 5169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5169 : oddCount 5169 13 = 6 ∧ acceleratedOrbit 13 5169 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5169) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5169.1, data_13_5169.2] + +/-- Complete interval computation for depth 13, residue 5170. -/ +theorem bounds_13_5170 : exactInterval 13 5170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5170 : oddCount 5170 13 = 6 ∧ acceleratedOrbit 13 5170 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5170) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5170.1, data_13_5170.2] + +/-- Complete interval computation for depth 13, residue 5171. -/ +theorem bounds_13_5171 : exactInterval 13 5171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5171 : oddCount 5171 13 = 6 ∧ acceleratedOrbit 13 5171 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5171) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5171.1, data_13_5171.2] + +/-- Complete interval computation for depth 13, residue 5172. -/ +theorem bounds_13_5172 : exactInterval 13 5172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5172 : oddCount 5172 13 = 5 ∧ acceleratedOrbit 13 5172 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5172) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5172.1, data_13_5172.2] + +/-- Complete interval computation for depth 13, residue 5173. -/ +theorem bounds_13_5173 : exactInterval 13 5173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5173 : oddCount 5173 13 = 5 ∧ acceleratedOrbit 13 5173 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5173) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5173.1, data_13_5173.2] + +/-- Complete interval computation for depth 13, residue 5174. -/ +theorem bounds_13_5174 : exactInterval 13 5174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5174 : oddCount 5174 13 = 7 ∧ acceleratedOrbit 13 5174 = 1382 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5174) = 3 ^ 7 * m + 1382 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5174.1, data_13_5174.2] + +/-- Complete interval computation for depth 13, residue 5175. -/ +theorem bounds_13_5175 : exactInterval 13 5175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5175 : oddCount 5175 13 = 7 ∧ acceleratedOrbit 13 5175 = 1382 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5175) = 3 ^ 7 * m + 1382 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5175.1, data_13_5175.2] + +/-- Complete interval computation for depth 13, residue 5176. -/ +theorem bounds_13_5176 : exactInterval 13 5176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5176 : oddCount 5176 13 = 5 ∧ acceleratedOrbit 13 5176 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5176) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5176.1, data_13_5176.2] + +/-- Complete interval computation for depth 13, residue 5177. -/ +theorem bounds_13_5177 : exactInterval 13 5177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5177 : oddCount 5177 13 = 6 ∧ acceleratedOrbit 13 5177 = 461 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5177) = 3 ^ 6 * m + 461 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5177.1, data_13_5177.2] + +/-- Complete interval computation for depth 13, residue 5178. -/ +theorem bounds_13_5178 : exactInterval 13 5178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5178 : oddCount 5178 13 = 5 ∧ acceleratedOrbit 13 5178 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5178) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5178.1, data_13_5178.2] + +/-- Complete interval computation for depth 13, residue 5179. -/ +theorem bounds_13_5179 : exactInterval 13 5179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5179 : oddCount 5179 13 = 8 ∧ acceleratedOrbit 13 5179 = 4151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5179) = 3 ^ 8 * m + 4151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5179.1, data_13_5179.2] + +/-- Complete interval computation for depth 13, residue 5180. -/ +theorem bounds_13_5180 : exactInterval 13 5180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5180 : oddCount 5180 13 = 5 ∧ acceleratedOrbit 13 5180 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5180) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5180.1, data_13_5180.2] + +end Collatz.Research.StoppingAtlas.Batch0804 From 3570646ea9854bec1f9b90f7432fc6d19edbc923 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:01 +0530 Subject: [PATCH 0805/1001] proof: certify atlas Batch0805 (13:5181 to 13:5195) --- Collatz/Research/StoppingAtlas/Batch0805.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0805.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0805.lean b/Collatz/Research/StoppingAtlas/Batch0805.lean new file mode 100644 index 00000000..2ace5f8d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0805.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0805 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5181. -/ +theorem bounds_13_5181 : exactInterval 13 5181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5181 : oddCount 5181 13 = 5 ∧ acceleratedOrbit 13 5181 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5181) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5181.1, data_13_5181.2] + +/-- Complete interval computation for depth 13, residue 5182. -/ +theorem bounds_13_5182 : exactInterval 13 5182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5182 : oddCount 5182 13 = 7 ∧ acceleratedOrbit 13 5182 = 1384 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5182) = 3 ^ 7 * m + 1384 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5182.1, data_13_5182.2] + +/-- Complete interval computation for depth 13, residue 5183. -/ +theorem bounds_13_5183 : exactInterval 13 5183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5183 : oddCount 5183 13 = 7 ∧ acceleratedOrbit 13 5183 = 1384 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5183) = 3 ^ 7 * m + 1384 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5183.1, data_13_5183.2] + +/-- Complete interval computation for depth 13, residue 5184. -/ +theorem bounds_13_5184 : exactInterval 13 5184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5184 : oddCount 5184 13 = 4 ∧ acceleratedOrbit 13 5184 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5184) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5184.1, data_13_5184.2] + +/-- Complete interval computation for depth 13, residue 5185. -/ +theorem bounds_13_5185 : exactInterval 13 5185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5185 : oddCount 5185 13 = 5 ∧ acceleratedOrbit 13 5185 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5185) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5185.1, data_13_5185.2] + +/-- Complete interval computation for depth 13, residue 5186. -/ +theorem bounds_13_5186 : exactInterval 13 5186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5186 : oddCount 5186 13 = 5 ∧ acceleratedOrbit 13 5186 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5186) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5186.1, data_13_5186.2] + +/-- Complete interval computation for depth 13, residue 5187. -/ +theorem bounds_13_5187 : exactInterval 13 5187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5187 : oddCount 5187 13 = 5 ∧ acceleratedOrbit 13 5187 = 154 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5187) = 3 ^ 5 * m + 154 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5187.1, data_13_5187.2] + +/-- Complete interval computation for depth 13, residue 5188. -/ +theorem bounds_13_5188 : exactInterval 13 5188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5188 : oddCount 5188 13 = 5 ∧ acceleratedOrbit 13 5188 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5188) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5188.1, data_13_5188.2] + +/-- Complete interval computation for depth 13, residue 5189. -/ +theorem bounds_13_5189 : exactInterval 13 5189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5189 : oddCount 5189 13 = 5 ∧ acceleratedOrbit 13 5189 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5189) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5189.1, data_13_5189.2] + +/-- Complete interval computation for depth 13, residue 5190. -/ +theorem bounds_13_5190 : exactInterval 13 5190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5190 : oddCount 5190 13 = 5 ∧ acceleratedOrbit 13 5190 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5190) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5190.1, data_13_5190.2] + +/-- Complete interval computation for depth 13, residue 5191. -/ +theorem bounds_13_5191 : exactInterval 13 5191 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5191) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5191 : oddCount 5191 13 = 8 ∧ acceleratedOrbit 13 5191 = 4159 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5191) = 3 ^ 8 * m + 4159 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5191.1, data_13_5191.2] + +/-- Complete interval computation for depth 13, residue 5192. -/ +theorem bounds_13_5192 : exactInterval 13 5192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5192 : oddCount 5192 13 = 7 ∧ acceleratedOrbit 13 5192 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5192) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5192.1, data_13_5192.2] + +/-- Complete interval computation for depth 13, residue 5193. -/ +theorem bounds_13_5193 : exactInterval 13 5193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5193 : oddCount 5193 13 = 7 ∧ acceleratedOrbit 13 5193 = 1387 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5193) = 3 ^ 7 * m + 1387 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5193.1, data_13_5193.2] + +/-- Complete interval computation for depth 13, residue 5194. -/ +theorem bounds_13_5194 : exactInterval 13 5194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5194 : oddCount 5194 13 = 7 ∧ acceleratedOrbit 13 5194 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5194) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5194.1, data_13_5194.2] + +/-- Complete interval computation for depth 13, residue 5195. -/ +theorem bounds_13_5195 : exactInterval 13 5195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5195 : oddCount 5195 13 = 5 ∧ acceleratedOrbit 13 5195 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5195) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5195.1, data_13_5195.2] + +end Collatz.Research.StoppingAtlas.Batch0805 From 0f4a5f17cab56019a47ccee46e6c323499f01c98 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0806/1001] proof: certify atlas Batch0806 (13:5196 to 13:5211) --- Collatz/Research/StoppingAtlas/Batch0806.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0806.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0806.lean b/Collatz/Research/StoppingAtlas/Batch0806.lean new file mode 100644 index 00000000..7cc02f51 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0806.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0806 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5196. -/ +theorem bounds_13_5196 : exactInterval 13 5196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5196 : oddCount 5196 13 = 7 ∧ acceleratedOrbit 13 5196 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5196) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5196.1, data_13_5196.2] + +/-- Complete interval computation for depth 13, residue 5197. -/ +theorem bounds_13_5197 : exactInterval 13 5197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5197 : oddCount 5197 13 = 7 ∧ acceleratedOrbit 13 5197 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5197) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5197.1, data_13_5197.2] + +/-- Complete interval computation for depth 13, residue 5198. -/ +theorem bounds_13_5198 : exactInterval 13 5198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5198 : oddCount 5198 13 = 6 ∧ acceleratedOrbit 13 5198 = 463 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5198) = 3 ^ 6 * m + 463 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5198.1, data_13_5198.2] + +/-- Complete interval computation for depth 13, residue 5199. -/ +theorem bounds_13_5199 : exactInterval 13 5199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5199 : oddCount 5199 13 = 6 ∧ acceleratedOrbit 13 5199 = 463 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5199) = 3 ^ 6 * m + 463 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5199.1, data_13_5199.2] + +/-- Complete interval computation for depth 13, residue 5200. -/ +theorem bounds_13_5200 : exactInterval 13 5200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5200 : oddCount 5200 13 = 4 ∧ acceleratedOrbit 13 5200 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5200) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5200.1, data_13_5200.2] + +/-- Complete interval computation for depth 13, residue 5201. -/ +theorem bounds_13_5201 : exactInterval 13 5201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5201 : oddCount 5201 13 = 7 ∧ acceleratedOrbit 13 5201 = 1390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5201) = 3 ^ 7 * m + 1390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5201.1, data_13_5201.2] + +/-- Complete interval computation for depth 13, residue 5202. -/ +theorem bounds_13_5202 : exactInterval 13 5202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5202 : oddCount 5202 13 = 8 ∧ acceleratedOrbit 13 5202 = 4169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5202) = 3 ^ 8 * m + 4169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5202.1, data_13_5202.2] + +/-- Complete interval computation for depth 13, residue 5203. -/ +theorem bounds_13_5203 : exactInterval 13 5203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5203 : oddCount 5203 13 = 8 ∧ acceleratedOrbit 13 5203 = 4169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5203) = 3 ^ 8 * m + 4169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5203.1, data_13_5203.2] + +/-- Complete interval computation for depth 13, residue 5204. -/ +theorem bounds_13_5204 : exactInterval 13 5204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5204 : oddCount 5204 13 = 4 ∧ acceleratedOrbit 13 5204 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5204) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5204.1, data_13_5204.2] + +/-- Complete interval computation for depth 13, residue 5205. -/ +theorem bounds_13_5205 : exactInterval 13 5205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5205 : oddCount 5205 13 = 4 ∧ acceleratedOrbit 13 5205 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5205) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5205.1, data_13_5205.2] + +/-- Complete interval computation for depth 13, residue 5206. -/ +theorem bounds_13_5206 : exactInterval 13 5206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5206 : oddCount 5206 13 = 5 ∧ acceleratedOrbit 13 5206 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5206) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5206.1, data_13_5206.2] + +/-- Complete interval computation for depth 13, residue 5207. -/ +theorem bounds_13_5207 : exactInterval 13 5207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5207 : oddCount 5207 13 = 5 ∧ acceleratedOrbit 13 5207 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5207) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5207.1, data_13_5207.2] + +/-- Complete interval computation for depth 13, residue 5208. -/ +theorem bounds_13_5208 : exactInterval 13 5208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5208 : oddCount 5208 13 = 5 ∧ acceleratedOrbit 13 5208 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5208) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5208.1, data_13_5208.2] + +/-- Complete interval computation for depth 13, residue 5209. -/ +theorem bounds_13_5209 : exactInterval 13 5209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5209 : oddCount 5209 13 = 6 ∧ acceleratedOrbit 13 5209 = 464 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5209) = 3 ^ 6 * m + 464 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5209.1, data_13_5209.2] + +/-- Complete interval computation for depth 13, residue 5210. -/ +theorem bounds_13_5210 : exactInterval 13 5210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5210 : oddCount 5210 13 = 5 ∧ acceleratedOrbit 13 5210 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5210) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5210.1, data_13_5210.2] + +/-- Complete interval computation for depth 13, residue 5211. -/ +theorem bounds_13_5211 : exactInterval 13 5211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5211 : oddCount 5211 13 = 10 ∧ acceleratedOrbit 13 5211 = 37574 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5211) = 3 ^ 10 * m + 37574 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5211.1, data_13_5211.2] + +end Collatz.Research.StoppingAtlas.Batch0806 From 978b51174498b9774c004b186e257ca7ea458545 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0807/1001] proof: certify atlas Batch0807 (13:5212 to 13:5226) --- Collatz/Research/StoppingAtlas/Batch0807.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0807.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0807.lean b/Collatz/Research/StoppingAtlas/Batch0807.lean new file mode 100644 index 00000000..45170253 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0807.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0807 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5212. -/ +theorem bounds_13_5212 : exactInterval 13 5212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5212 : oddCount 5212 13 = 5 ∧ acceleratedOrbit 13 5212 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5212) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5212.1, data_13_5212.2] + +/-- Complete interval computation for depth 13, residue 5213. -/ +theorem bounds_13_5213 : exactInterval 13 5213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5213 : oddCount 5213 13 = 5 ∧ acceleratedOrbit 13 5213 = 155 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5213) = 3 ^ 5 * m + 155 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5213.1, data_13_5213.2] + +/-- Complete interval computation for depth 13, residue 5214. -/ +theorem bounds_13_5214 : exactInterval 13 5214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5214 : oddCount 5214 13 = 8 ∧ acceleratedOrbit 13 5214 = 4178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5214) = 3 ^ 8 * m + 4178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5214.1, data_13_5214.2] + +/-- Complete interval computation for depth 13, residue 5215. -/ +theorem bounds_13_5215 : exactInterval 13 5215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5215) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5215 : oddCount 5215 13 = 8 ∧ acceleratedOrbit 13 5215 = 4178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5215) = 3 ^ 8 * m + 4178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5215.1, data_13_5215.2] + +/-- Complete interval computation for depth 13, residue 5216. -/ +theorem bounds_13_5216 : exactInterval 13 5216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5216 : oddCount 5216 13 = 4 ∧ acceleratedOrbit 13 5216 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5216) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5216.1, data_13_5216.2] + +/-- Complete interval computation for depth 13, residue 5217. -/ +theorem bounds_13_5217 : exactInterval 13 5217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5217 : oddCount 5217 13 = 7 ∧ acceleratedOrbit 13 5217 = 1394 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5217) = 3 ^ 7 * m + 1394 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5217.1, data_13_5217.2] + +/-- Complete interval computation for depth 13, residue 5218. -/ +theorem bounds_13_5218 : exactInterval 13 5218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5218 : oddCount 5218 13 = 7 ∧ acceleratedOrbit 13 5218 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5218) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5218.1, data_13_5218.2] + +/-- Complete interval computation for depth 13, residue 5219. -/ +theorem bounds_13_5219 : exactInterval 13 5219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5219 : oddCount 5219 13 = 7 ∧ acceleratedOrbit 13 5219 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5219) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5219.1, data_13_5219.2] + +/-- Complete interval computation for depth 13, residue 5220. -/ +theorem bounds_13_5220 : exactInterval 13 5220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5220 : oddCount 5220 13 = 7 ∧ acceleratedOrbit 13 5220 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5220) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5220.1, data_13_5220.2] + +/-- Complete interval computation for depth 13, residue 5221. -/ +theorem bounds_13_5221 : exactInterval 13 5221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5221 : oddCount 5221 13 = 7 ∧ acceleratedOrbit 13 5221 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5221) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5221.1, data_13_5221.2] + +/-- Complete interval computation for depth 13, residue 5222. -/ +theorem bounds_13_5222 : exactInterval 13 5222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5222 : oddCount 5222 13 = 7 ∧ acceleratedOrbit 13 5222 = 1397 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5222) = 3 ^ 7 * m + 1397 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5222.1, data_13_5222.2] + +/-- Complete interval computation for depth 13, residue 5223. -/ +theorem bounds_13_5223 : exactInterval 13 5223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5223 : oddCount 5223 13 = 10 ∧ acceleratedOrbit 13 5223 = 37658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5223) = 3 ^ 10 * m + 37658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5223.1, data_13_5223.2] + +/-- Complete interval computation for depth 13, residue 5224. -/ +theorem bounds_13_5224 : exactInterval 13 5224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5224 : oddCount 5224 13 = 4 ∧ acceleratedOrbit 13 5224 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5224) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5224.1, data_13_5224.2] + +/-- Complete interval computation for depth 13, residue 5225. -/ +theorem bounds_13_5225 : exactInterval 13 5225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5225 : oddCount 5225 13 = 8 ∧ acceleratedOrbit 13 5225 = 4187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5225) = 3 ^ 8 * m + 4187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5225.1, data_13_5225.2] + +/-- Complete interval computation for depth 13, residue 5226. -/ +theorem bounds_13_5226 : exactInterval 13 5226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5226 : oddCount 5226 13 = 4 ∧ acceleratedOrbit 13 5226 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5226) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5226.1, data_13_5226.2] + +end Collatz.Research.StoppingAtlas.Batch0807 From 517279250215ce98374955044b2ca4ba3f1469e2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0808/1001] proof: certify atlas Batch0808 (13:5227 to 13:5241) --- Collatz/Research/StoppingAtlas/Batch0808.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0808.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0808.lean b/Collatz/Research/StoppingAtlas/Batch0808.lean new file mode 100644 index 00000000..1dcc7317 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0808.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0808 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5227. -/ +theorem bounds_13_5227 : exactInterval 13 5227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5227 : oddCount 5227 13 = 7 ∧ acceleratedOrbit 13 5227 = 1396 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5227) = 3 ^ 7 * m + 1396 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5227.1, data_13_5227.2] + +/-- Complete interval computation for depth 13, residue 5228. -/ +theorem bounds_13_5228 : exactInterval 13 5228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5228 : oddCount 5228 13 = 9 ∧ acceleratedOrbit 13 5228 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5228) = 3 ^ 9 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5228.1, data_13_5228.2] + +/-- Complete interval computation for depth 13, residue 5229. -/ +theorem bounds_13_5229 : exactInterval 13 5229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5229 : oddCount 5229 13 = 9 ∧ acceleratedOrbit 13 5229 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5229) = 3 ^ 9 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5229.1, data_13_5229.2] + +/-- Complete interval computation for depth 13, residue 5230. -/ +theorem bounds_13_5230 : exactInterval 13 5230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5230 : oddCount 5230 13 = 9 ∧ acceleratedOrbit 13 5230 = 12575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5230) = 3 ^ 9 * m + 12575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5230.1, data_13_5230.2] + +/-- Complete interval computation for depth 13, residue 5231. -/ +theorem bounds_13_5231 : exactInterval 13 5231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5231 : oddCount 5231 13 = 9 ∧ acceleratedOrbit 13 5231 = 12572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5231) = 3 ^ 9 * m + 12572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5231.1, data_13_5231.2] + +/-- Complete interval computation for depth 13, residue 5232. -/ +theorem bounds_13_5232 : exactInterval 13 5232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5232 : oddCount 5232 13 = 7 ∧ acceleratedOrbit 13 5232 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5232) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5232.1, data_13_5232.2] + +/-- Complete interval computation for depth 13, residue 5233. -/ +theorem bounds_13_5233 : exactInterval 13 5233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5233 : oddCount 5233 13 = 4 ∧ acceleratedOrbit 13 5233 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5233) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5233.1, data_13_5233.2] + +/-- Complete interval computation for depth 13, residue 5234. -/ +theorem bounds_13_5234 : exactInterval 13 5234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5234 : oddCount 5234 13 = 7 ∧ acceleratedOrbit 13 5234 = 1399 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5234) = 3 ^ 7 * m + 1399 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5234.1, data_13_5234.2] + +/-- Complete interval computation for depth 13, residue 5235. -/ +theorem bounds_13_5235 : exactInterval 13 5235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5235 : oddCount 5235 13 = 7 ∧ acceleratedOrbit 13 5235 = 1399 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5235) = 3 ^ 7 * m + 1399 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5235.1, data_13_5235.2] + +/-- Complete interval computation for depth 13, residue 5236. -/ +theorem bounds_13_5236 : exactInterval 13 5236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5236 : oddCount 5236 13 = 7 ∧ acceleratedOrbit 13 5236 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5236) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5236.1, data_13_5236.2] + +/-- Complete interval computation for depth 13, residue 5237. -/ +theorem bounds_13_5237 : exactInterval 13 5237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5237 : oddCount 5237 13 = 7 ∧ acceleratedOrbit 13 5237 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5237) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5237.1, data_13_5237.2] + +/-- Complete interval computation for depth 13, residue 5238. -/ +theorem bounds_13_5238 : exactInterval 13 5238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5238 : oddCount 5238 13 = 6 ∧ acceleratedOrbit 13 5238 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5238) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5238.1, data_13_5238.2] + +/-- Complete interval computation for depth 13, residue 5239. -/ +theorem bounds_13_5239 : exactInterval 13 5239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5239 : oddCount 5239 13 = 6 ∧ acceleratedOrbit 13 5239 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5239) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5239.1, data_13_5239.2] + +/-- Complete interval computation for depth 13, residue 5240. -/ +theorem bounds_13_5240 : exactInterval 13 5240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5240 : oddCount 5240 13 = 7 ∧ acceleratedOrbit 13 5240 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5240) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5240.1, data_13_5240.2] + +/-- Complete interval computation for depth 13, residue 5241. -/ +theorem bounds_13_5241 : exactInterval 13 5241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5241 : oddCount 5241 13 = 9 ∧ acceleratedOrbit 13 5241 = 12599 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5241) = 3 ^ 9 * m + 12599 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5241.1, data_13_5241.2] + +end Collatz.Research.StoppingAtlas.Batch0808 From 511e5d16e667f654a523d7131fa4489b985102d8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0809/1001] proof: certify atlas Batch0809 (13:5242 to 13:5257) --- Collatz/Research/StoppingAtlas/Batch0809.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0809.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0809.lean b/Collatz/Research/StoppingAtlas/Batch0809.lean new file mode 100644 index 00000000..83105be9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0809.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0809 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5242. -/ +theorem bounds_13_5242 : exactInterval 13 5242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5242 : oddCount 5242 13 = 7 ∧ acceleratedOrbit 13 5242 = 1403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5242) = 3 ^ 7 * m + 1403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5242.1, data_13_5242.2] + +/-- Complete interval computation for depth 13, residue 5243. -/ +theorem bounds_13_5243 : exactInterval 13 5243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5243 : oddCount 5243 13 = 8 ∧ acceleratedOrbit 13 5243 = 4202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5243) = 3 ^ 8 * m + 4202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5243.1, data_13_5243.2] + +/-- Complete interval computation for depth 13, residue 5244. -/ +theorem bounds_13_5244 : exactInterval 13 5244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5244 : oddCount 5244 13 = 6 ∧ acceleratedOrbit 13 5244 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5244) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5244.1, data_13_5244.2] + +/-- Complete interval computation for depth 13, residue 5245. -/ +theorem bounds_13_5245 : exactInterval 13 5245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5245 : oddCount 5245 13 = 6 ∧ acceleratedOrbit 13 5245 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5245) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5245.1, data_13_5245.2] + +/-- Complete interval computation for depth 13, residue 5246. -/ +theorem bounds_13_5246 : exactInterval 13 5246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5246 : oddCount 5246 13 = 6 ∧ acceleratedOrbit 13 5246 = 467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5246) = 3 ^ 6 * m + 467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5246.1, data_13_5246.2] + +/-- Complete interval computation for depth 13, residue 5247. -/ +theorem bounds_13_5247 : exactInterval 13 5247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5247 : oddCount 5247 13 = 10 ∧ acceleratedOrbit 13 5247 = 37829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5247) = 3 ^ 10 * m + 37829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5247.1, data_13_5247.2] + +/-- Complete interval computation for depth 13, residue 5248. -/ +theorem bounds_13_5248 : exactInterval 13 5248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5248 : oddCount 5248 13 = 5 ∧ acceleratedOrbit 13 5248 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5248) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5248.1, data_13_5248.2] + +/-- Complete interval computation for depth 13, residue 5249. -/ +theorem bounds_13_5249 : exactInterval 13 5249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5249 : oddCount 5249 13 = 8 ∧ acceleratedOrbit 13 5249 = 4207 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5249) = 3 ^ 8 * m + 4207 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5249.1, data_13_5249.2] + +/-- Complete interval computation for depth 13, residue 5250. -/ +theorem bounds_13_5250 : exactInterval 13 5250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5250 : oddCount 5250 13 = 4 ∧ acceleratedOrbit 13 5250 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5250) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5250.1, data_13_5250.2] + +/-- Complete interval computation for depth 13, residue 5251. -/ +theorem bounds_13_5251 : exactInterval 13 5251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5251 : oddCount 5251 13 = 4 ∧ acceleratedOrbit 13 5251 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5251) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5251.1, data_13_5251.2] + +/-- Complete interval computation for depth 13, residue 5252. -/ +theorem bounds_13_5252 : exactInterval 13 5252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5252 : oddCount 5252 13 = 4 ∧ acceleratedOrbit 13 5252 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5252) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5252.1, data_13_5252.2] + +/-- Complete interval computation for depth 13, residue 5253. -/ +theorem bounds_13_5253 : exactInterval 13 5253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5253 : oddCount 5253 13 = 4 ∧ acceleratedOrbit 13 5253 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5253) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5253.1, data_13_5253.2] + +/-- Complete interval computation for depth 13, residue 5254. -/ +theorem bounds_13_5254 : exactInterval 13 5254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5254 : oddCount 5254 13 = 4 ∧ acceleratedOrbit 13 5254 = 52 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5254) = 3 ^ 4 * m + 52 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5254.1, data_13_5254.2] + +/-- Complete interval computation for depth 13, residue 5255. -/ +theorem bounds_13_5255 : exactInterval 13 5255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5255 : oddCount 5255 13 = 9 ∧ acceleratedOrbit 13 5255 = 12635 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5255) = 3 ^ 9 * m + 12635 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5255.1, data_13_5255.2] + +/-- Complete interval computation for depth 13, residue 5256. -/ +theorem bounds_13_5256 : exactInterval 13 5256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5256 : oddCount 5256 13 = 5 ∧ acceleratedOrbit 13 5256 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5256) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5256.1, data_13_5256.2] + +/-- Complete interval computation for depth 13, residue 5257. -/ +theorem bounds_13_5257 : exactInterval 13 5257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5257 : oddCount 5257 13 = 11 ∧ acceleratedOrbit 13 5257 = 113723 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5257) = 3 ^ 11 * m + 113723 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5257.1, data_13_5257.2] + +end Collatz.Research.StoppingAtlas.Batch0809 From b4a7386a2ebcadc78ab7846f357c21c52162859b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0810/1001] proof: certify atlas Batch0810 (13:5258 to 13:5272) --- Collatz/Research/StoppingAtlas/Batch0810.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0810.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0810.lean b/Collatz/Research/StoppingAtlas/Batch0810.lean new file mode 100644 index 00000000..1921a4ff --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0810.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0810 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5258. -/ +theorem bounds_13_5258 : exactInterval 13 5258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5258 : oddCount 5258 13 = 5 ∧ acceleratedOrbit 13 5258 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5258) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5258.1, data_13_5258.2] + +/-- Complete interval computation for depth 13, residue 5259. -/ +theorem bounds_13_5259 : exactInterval 13 5259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5259 : oddCount 5259 13 = 7 ∧ acceleratedOrbit 13 5259 = 1405 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5259) = 3 ^ 7 * m + 1405 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5259.1, data_13_5259.2] + +/-- Complete interval computation for depth 13, residue 5260. -/ +theorem bounds_13_5260 : exactInterval 13 5260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5260 : oddCount 5260 13 = 5 ∧ acceleratedOrbit 13 5260 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5260) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5260.1, data_13_5260.2] + +/-- Complete interval computation for depth 13, residue 5261. -/ +theorem bounds_13_5261 : exactInterval 13 5261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5261 : oddCount 5261 13 = 5 ∧ acceleratedOrbit 13 5261 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5261) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5261.1, data_13_5261.2] + +/-- Complete interval computation for depth 13, residue 5262. -/ +theorem bounds_13_5262 : exactInterval 13 5262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5262 : oddCount 5262 13 = 7 ∧ acceleratedOrbit 13 5262 = 1406 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5262) = 3 ^ 7 * m + 1406 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5262.1, data_13_5262.2] + +/-- Complete interval computation for depth 13, residue 5263. -/ +theorem bounds_13_5263 : exactInterval 13 5263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5263 : oddCount 5263 13 = 7 ∧ acceleratedOrbit 13 5263 = 1406 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5263) = 3 ^ 7 * m + 1406 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5263.1, data_13_5263.2] + +/-- Complete interval computation for depth 13, residue 5264. -/ +theorem bounds_13_5264 : exactInterval 13 5264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5264 : oddCount 5264 13 = 5 ∧ acceleratedOrbit 13 5264 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5264) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5264.1, data_13_5264.2] + +/-- Complete interval computation for depth 13, residue 5265. -/ +theorem bounds_13_5265 : exactInterval 13 5265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5265 : oddCount 5265 13 = 6 ∧ acceleratedOrbit 13 5265 = 469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5265) = 3 ^ 6 * m + 469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5265.1, data_13_5265.2] + +/-- Complete interval computation for depth 13, residue 5266. -/ +theorem bounds_13_5266 : exactInterval 13 5266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5266 : oddCount 5266 13 = 6 ∧ acceleratedOrbit 13 5266 = 469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5266) = 3 ^ 6 * m + 469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5266.1, data_13_5266.2] + +/-- Complete interval computation for depth 13, residue 5267. -/ +theorem bounds_13_5267 : exactInterval 13 5267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5267 : oddCount 5267 13 = 6 ∧ acceleratedOrbit 13 5267 = 469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5267) = 3 ^ 6 * m + 469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5267.1, data_13_5267.2] + +/-- Complete interval computation for depth 13, residue 5268. -/ +theorem bounds_13_5268 : exactInterval 13 5268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5268 : oddCount 5268 13 = 5 ∧ acceleratedOrbit 13 5268 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5268) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5268.1, data_13_5268.2] + +/-- Complete interval computation for depth 13, residue 5269. -/ +theorem bounds_13_5269 : exactInterval 13 5269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5269 : oddCount 5269 13 = 5 ∧ acceleratedOrbit 13 5269 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5269) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5269.1, data_13_5269.2] + +/-- Complete interval computation for depth 13, residue 5270. -/ +theorem bounds_13_5270 : exactInterval 13 5270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5270 : oddCount 5270 13 = 5 ∧ acceleratedOrbit 13 5270 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5270) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5270.1, data_13_5270.2] + +/-- Complete interval computation for depth 13, residue 5271. -/ +theorem bounds_13_5271 : exactInterval 13 5271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5271 : oddCount 5271 13 = 5 ∧ acceleratedOrbit 13 5271 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5271) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5271.1, data_13_5271.2] + +/-- Complete interval computation for depth 13, residue 5272. -/ +theorem bounds_13_5272 : exactInterval 13 5272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5272 : oddCount 5272 13 = 5 ∧ acceleratedOrbit 13 5272 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5272) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5272.1, data_13_5272.2] + +end Collatz.Research.StoppingAtlas.Batch0810 From be60390d72bc0addf0f8bf1c083c54d499227ee8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0811/1001] proof: certify atlas Batch0811 (13:5273 to 13:5287) --- Collatz/Research/StoppingAtlas/Batch0811.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0811.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0811.lean b/Collatz/Research/StoppingAtlas/Batch0811.lean new file mode 100644 index 00000000..78b50be9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0811.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0811 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5273. -/ +theorem bounds_13_5273 : exactInterval 13 5273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5273 : oddCount 5273 13 = 6 ∧ acceleratedOrbit 13 5273 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5273) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5273.1, data_13_5273.2] + +/-- Complete interval computation for depth 13, residue 5274. -/ +theorem bounds_13_5274 : exactInterval 13 5274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5274 : oddCount 5274 13 = 5 ∧ acceleratedOrbit 13 5274 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5274) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5274.1, data_13_5274.2] + +/-- Complete interval computation for depth 13, residue 5275. -/ +theorem bounds_13_5275 : exactInterval 13 5275 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5275) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5275 : oddCount 5275 13 = 8 ∧ acceleratedOrbit 13 5275 = 4226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5275) = 3 ^ 8 * m + 4226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5275.1, data_13_5275.2] + +/-- Complete interval computation for depth 13, residue 5276. -/ +theorem bounds_13_5276 : exactInterval 13 5276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5276 : oddCount 5276 13 = 6 ∧ acceleratedOrbit 13 5276 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5276) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5276.1, data_13_5276.2] + +/-- Complete interval computation for depth 13, residue 5277. -/ +theorem bounds_13_5277 : exactInterval 13 5277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5277 : oddCount 5277 13 = 6 ∧ acceleratedOrbit 13 5277 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5277) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5277.1, data_13_5277.2] + +/-- Complete interval computation for depth 13, residue 5278. -/ +theorem bounds_13_5278 : exactInterval 13 5278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5278 : oddCount 5278 13 = 6 ∧ acceleratedOrbit 13 5278 = 470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5278) = 3 ^ 6 * m + 470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5278.1, data_13_5278.2] + +/-- Complete interval computation for depth 13, residue 5279. -/ +theorem bounds_13_5279 : exactInterval 13 5279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5279 : oddCount 5279 13 = 10 ∧ acceleratedOrbit 13 5279 = 38060 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5279) = 3 ^ 10 * m + 38060 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5279.1, data_13_5279.2] + +/-- Complete interval computation for depth 13, residue 5280. -/ +theorem bounds_13_5280 : exactInterval 13 5280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5280 : oddCount 5280 13 = 5 ∧ acceleratedOrbit 13 5280 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5280) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5280.1, data_13_5280.2] + +/-- Complete interval computation for depth 13, residue 5281. -/ +theorem bounds_13_5281 : exactInterval 13 5281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5281 : oddCount 5281 13 = 8 ∧ acceleratedOrbit 13 5281 = 4232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5281) = 3 ^ 8 * m + 4232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5281.1, data_13_5281.2] + +/-- Complete interval computation for depth 13, residue 5282. -/ +theorem bounds_13_5282 : exactInterval 13 5282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5282 : oddCount 5282 13 = 8 ∧ acceleratedOrbit 13 5282 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5282) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5282.1, data_13_5282.2] + +/-- Complete interval computation for depth 13, residue 5283. -/ +theorem bounds_13_5283 : exactInterval 13 5283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5283 : oddCount 5283 13 = 8 ∧ acceleratedOrbit 13 5283 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5283) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5283.1, data_13_5283.2] + +/-- Complete interval computation for depth 13, residue 5284. -/ +theorem bounds_13_5284 : exactInterval 13 5284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5284 : oddCount 5284 13 = 8 ∧ acceleratedOrbit 13 5284 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5284) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5284.1, data_13_5284.2] + +/-- Complete interval computation for depth 13, residue 5285. -/ +theorem bounds_13_5285 : exactInterval 13 5285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5285 : oddCount 5285 13 = 8 ∧ acceleratedOrbit 13 5285 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5285) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5285.1, data_13_5285.2] + +/-- Complete interval computation for depth 13, residue 5286. -/ +theorem bounds_13_5286 : exactInterval 13 5286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5286 : oddCount 5286 13 = 8 ∧ acceleratedOrbit 13 5286 = 4238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5286) = 3 ^ 8 * m + 4238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5286.1, data_13_5286.2] + +/-- Complete interval computation for depth 13, residue 5287. -/ +theorem bounds_13_5287 : exactInterval 13 5287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5287 : oddCount 5287 13 = 9 ∧ acceleratedOrbit 13 5287 = 12707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5287) = 3 ^ 9 * m + 12707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5287.1, data_13_5287.2] + +end Collatz.Research.StoppingAtlas.Batch0811 From 563a598ffaee445b3f9a6e9a95e799b941ef17c2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0812/1001] proof: certify atlas Batch0812 (13:5288 to 13:5303) --- Collatz/Research/StoppingAtlas/Batch0812.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0812.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0812.lean b/Collatz/Research/StoppingAtlas/Batch0812.lean new file mode 100644 index 00000000..5bc9b305 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0812.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0812 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5288. -/ +theorem bounds_13_5288 : exactInterval 13 5288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5288 : oddCount 5288 13 = 5 ∧ acceleratedOrbit 13 5288 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5288) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5288.1, data_13_5288.2] + +/-- Complete interval computation for depth 13, residue 5289. -/ +theorem bounds_13_5289 : exactInterval 13 5289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5289 : oddCount 5289 13 = 9 ∧ acceleratedOrbit 13 5289 = 12712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5289) = 3 ^ 9 * m + 12712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5289.1, data_13_5289.2] + +/-- Complete interval computation for depth 13, residue 5290. -/ +theorem bounds_13_5290 : exactInterval 13 5290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5290 : oddCount 5290 13 = 5 ∧ acceleratedOrbit 13 5290 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5290) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5290.1, data_13_5290.2] + +/-- Complete interval computation for depth 13, residue 5291. -/ +theorem bounds_13_5291 : exactInterval 13 5291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5291 : oddCount 5291 13 = 5 ∧ acceleratedOrbit 13 5291 = 157 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5291) = 3 ^ 5 * m + 157 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5291.1, data_13_5291.2] + +/-- Complete interval computation for depth 13, residue 5292. -/ +theorem bounds_13_5292 : exactInterval 13 5292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5292 : oddCount 5292 13 = 6 ∧ acceleratedOrbit 13 5292 = 472 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5292) = 3 ^ 6 * m + 472 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5292.1, data_13_5292.2] + +/-- Complete interval computation for depth 13, residue 5293. -/ +theorem bounds_13_5293 : exactInterval 13 5293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5293 : oddCount 5293 13 = 6 ∧ acceleratedOrbit 13 5293 = 472 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5293) = 3 ^ 6 * m + 472 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5293.1, data_13_5293.2] + +/-- Complete interval computation for depth 13, residue 5294. -/ +theorem bounds_13_5294 : exactInterval 13 5294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5294 : oddCount 5294 13 = 6 ∧ acceleratedOrbit 13 5294 = 472 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5294) = 3 ^ 6 * m + 472 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5294.1, data_13_5294.2] + +/-- Complete interval computation for depth 13, residue 5295. -/ +theorem bounds_13_5295 : exactInterval 13 5295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5295 : oddCount 5295 13 = 7 ∧ acceleratedOrbit 13 5295 = 1414 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5295) = 3 ^ 7 * m + 1414 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5295.1, data_13_5295.2] + +/-- Complete interval computation for depth 13, residue 5296. -/ +theorem bounds_13_5296 : exactInterval 13 5296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5296 : oddCount 5296 13 = 4 ∧ acceleratedOrbit 13 5296 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5296) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5296.1, data_13_5296.2] + +/-- Complete interval computation for depth 13, residue 5297. -/ +theorem bounds_13_5297 : exactInterval 13 5297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5297 : oddCount 5297 13 = 7 ∧ acceleratedOrbit 13 5297 = 1417 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5297) = 3 ^ 7 * m + 1417 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5297.1, data_13_5297.2] + +/-- Complete interval computation for depth 13, residue 5298. -/ +theorem bounds_13_5298 : exactInterval 13 5298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5298 : oddCount 5298 13 = 7 ∧ acceleratedOrbit 13 5298 = 1417 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5298) = 3 ^ 7 * m + 1417 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5298.1, data_13_5298.2] + +/-- Complete interval computation for depth 13, residue 5299. -/ +theorem bounds_13_5299 : exactInterval 13 5299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5299 : oddCount 5299 13 = 7 ∧ acceleratedOrbit 13 5299 = 1417 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5299) = 3 ^ 7 * m + 1417 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5299.1, data_13_5299.2] + +/-- Complete interval computation for depth 13, residue 5300. -/ +theorem bounds_13_5300 : exactInterval 13 5300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5300 : oddCount 5300 13 = 4 ∧ acceleratedOrbit 13 5300 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5300) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5300.1, data_13_5300.2] + +/-- Complete interval computation for depth 13, residue 5301. -/ +theorem bounds_13_5301 : exactInterval 13 5301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5301 : oddCount 5301 13 = 4 ∧ acceleratedOrbit 13 5301 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5301) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5301.1, data_13_5301.2] + +/-- Complete interval computation for depth 13, residue 5302. -/ +theorem bounds_13_5302 : exactInterval 13 5302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5302 : oddCount 5302 13 = 8 ∧ acceleratedOrbit 13 5302 = 4249 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5302) = 3 ^ 8 * m + 4249 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5302.1, data_13_5302.2] + +/-- Complete interval computation for depth 13, residue 5303. -/ +theorem bounds_13_5303 : exactInterval 13 5303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5303 : oddCount 5303 13 = 8 ∧ acceleratedOrbit 13 5303 = 4249 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5303) = 3 ^ 8 * m + 4249 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5303.1, data_13_5303.2] + +end Collatz.Research.StoppingAtlas.Batch0812 From e23f187da564ac634256911b35998c60b1332c08 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:02 +0530 Subject: [PATCH 0813/1001] proof: certify atlas Batch0813 (13:5304 to 13:5318) --- Collatz/Research/StoppingAtlas/Batch0813.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0813.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0813.lean b/Collatz/Research/StoppingAtlas/Batch0813.lean new file mode 100644 index 00000000..2c3cb9c3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0813.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0813 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5304. -/ +theorem bounds_13_5304 : exactInterval 13 5304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5304 : oddCount 5304 13 = 4 ∧ acceleratedOrbit 13 5304 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5304) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5304.1, data_13_5304.2] + +/-- Complete interval computation for depth 13, residue 5305. -/ +theorem bounds_13_5305 : exactInterval 13 5305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5305 : oddCount 5305 13 = 8 ∧ acceleratedOrbit 13 5305 = 4252 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5305) = 3 ^ 8 * m + 4252 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5305.1, data_13_5305.2] + +/-- Complete interval computation for depth 13, residue 5306. -/ +theorem bounds_13_5306 : exactInterval 13 5306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5306 : oddCount 5306 13 = 4 ∧ acceleratedOrbit 13 5306 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5306) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5306.1, data_13_5306.2] + +/-- Complete interval computation for depth 13, residue 5307. -/ +theorem bounds_13_5307 : exactInterval 13 5307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5307 : oddCount 5307 13 = 9 ∧ acceleratedOrbit 13 5307 = 12757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5307) = 3 ^ 9 * m + 12757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5307.1, data_13_5307.2] + +/-- Complete interval computation for depth 13, residue 5308. -/ +theorem bounds_13_5308 : exactInterval 13 5308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5308 : oddCount 5308 13 = 8 ∧ acceleratedOrbit 13 5308 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5308) = 3 ^ 8 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5308.1, data_13_5308.2] + +/-- Complete interval computation for depth 13, residue 5309. -/ +theorem bounds_13_5309 : exactInterval 13 5309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5309 : oddCount 5309 13 = 8 ∧ acceleratedOrbit 13 5309 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5309) = 3 ^ 8 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5309.1, data_13_5309.2] + +/-- Complete interval computation for depth 13, residue 5310. -/ +theorem bounds_13_5310 : exactInterval 13 5310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5310 : oddCount 5310 13 = 8 ∧ acceleratedOrbit 13 5310 = 4256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5310) = 3 ^ 8 * m + 4256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5310.1, data_13_5310.2] + +/-- Complete interval computation for depth 13, residue 5311. -/ +theorem bounds_13_5311 : exactInterval 13 5311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5311 : oddCount 5311 13 = 9 ∧ acceleratedOrbit 13 5311 = 12764 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5311) = 3 ^ 9 * m + 12764 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5311.1, data_13_5311.2] + +/-- Complete interval computation for depth 13, residue 5312. -/ +theorem bounds_13_5312 : exactInterval 13 5312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5312 : oddCount 5312 13 = 5 ∧ acceleratedOrbit 13 5312 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5312) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5312.1, data_13_5312.2] + +/-- Complete interval computation for depth 13, residue 5313. -/ +theorem bounds_13_5313 : exactInterval 13 5313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5313 : oddCount 5313 13 = 7 ∧ acceleratedOrbit 13 5313 = 1421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5313) = 3 ^ 7 * m + 1421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5313.1, data_13_5313.2] + +/-- Complete interval computation for depth 13, residue 5314. -/ +theorem bounds_13_5314 : exactInterval 13 5314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5314 : oddCount 5314 13 = 7 ∧ acceleratedOrbit 13 5314 = 1421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5314) = 3 ^ 7 * m + 1421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5314.1, data_13_5314.2] + +/-- Complete interval computation for depth 13, residue 5315. -/ +theorem bounds_13_5315 : exactInterval 13 5315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5315 : oddCount 5315 13 = 7 ∧ acceleratedOrbit 13 5315 = 1421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5315) = 3 ^ 7 * m + 1421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5315.1, data_13_5315.2] + +/-- Complete interval computation for depth 13, residue 5316. -/ +theorem bounds_13_5316 : exactInterval 13 5316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5316 : oddCount 5316 13 = 6 ∧ acceleratedOrbit 13 5316 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5316) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5316.1, data_13_5316.2] + +/-- Complete interval computation for depth 13, residue 5317. -/ +theorem bounds_13_5317 : exactInterval 13 5317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5317 : oddCount 5317 13 = 6 ∧ acceleratedOrbit 13 5317 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5317) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5317.1, data_13_5317.2] + +/-- Complete interval computation for depth 13, residue 5318. -/ +theorem bounds_13_5318 : exactInterval 13 5318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5318 : oddCount 5318 13 = 6 ∧ acceleratedOrbit 13 5318 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5318) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5318.1, data_13_5318.2] + +end Collatz.Research.StoppingAtlas.Batch0813 From a9936a86387572eb0239f2d9843f5c3bc20e8616 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:03 +0530 Subject: [PATCH 0814/1001] proof: certify atlas Batch0814 (13:5319 to 13:5334) --- Collatz/Research/StoppingAtlas/Batch0814.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0814.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0814.lean b/Collatz/Research/StoppingAtlas/Batch0814.lean new file mode 100644 index 00000000..af3c484b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0814.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0814 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5319. -/ +theorem bounds_13_5319 : exactInterval 13 5319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5319 : oddCount 5319 13 = 7 ∧ acceleratedOrbit 13 5319 = 1421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5319) = 3 ^ 7 * m + 1421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5319.1, data_13_5319.2] + +/-- Complete interval computation for depth 13, residue 5320. -/ +theorem bounds_13_5320 : exactInterval 13 5320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5320 : oddCount 5320 13 = 6 ∧ acceleratedOrbit 13 5320 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5320) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5320.1, data_13_5320.2] + +/-- Complete interval computation for depth 13, residue 5321. -/ +theorem bounds_13_5321 : exactInterval 13 5321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5321 : oddCount 5321 13 = 5 ∧ acceleratedOrbit 13 5321 = 158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5321) = 3 ^ 5 * m + 158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5321.1, data_13_5321.2] + +/-- Complete interval computation for depth 13, residue 5322. -/ +theorem bounds_13_5322 : exactInterval 13 5322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5322 : oddCount 5322 13 = 6 ∧ acceleratedOrbit 13 5322 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5322) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5322.1, data_13_5322.2] + +/-- Complete interval computation for depth 13, residue 5323. -/ +theorem bounds_13_5323 : exactInterval 13 5323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5323 : oddCount 5323 13 = 5 ∧ acceleratedOrbit 13 5323 = 158 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5323) = 3 ^ 5 * m + 158 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5323.1, data_13_5323.2] + +/-- Complete interval computation for depth 13, residue 5324. -/ +theorem bounds_13_5324 : exactInterval 13 5324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5324 : oddCount 5324 13 = 6 ∧ acceleratedOrbit 13 5324 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5324) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5324.1, data_13_5324.2] + +/-- Complete interval computation for depth 13, residue 5325. -/ +theorem bounds_13_5325 : exactInterval 13 5325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5325 : oddCount 5325 13 = 6 ∧ acceleratedOrbit 13 5325 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5325) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5325.1, data_13_5325.2] + +/-- Complete interval computation for depth 13, residue 5326. -/ +theorem bounds_13_5326 : exactInterval 13 5326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5326 : oddCount 5326 13 = 8 ∧ acceleratedOrbit 13 5326 = 4268 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5326) = 3 ^ 8 * m + 4268 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5326.1, data_13_5326.2] + +/-- Complete interval computation for depth 13, residue 5327. -/ +theorem bounds_13_5327 : exactInterval 13 5327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5327 : oddCount 5327 13 = 8 ∧ acceleratedOrbit 13 5327 = 4268 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5327) = 3 ^ 8 * m + 4268 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5327.1, data_13_5327.2] + +/-- Complete interval computation for depth 13, residue 5328. -/ +theorem bounds_13_5328 : exactInterval 13 5328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5328 : oddCount 5328 13 = 5 ∧ acceleratedOrbit 13 5328 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5328) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5328.1, data_13_5328.2] + +/-- Complete interval computation for depth 13, residue 5329. -/ +theorem bounds_13_5329 : exactInterval 13 5329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5329 : oddCount 5329 13 = 7 ∧ acceleratedOrbit 13 5329 = 1424 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5329) = 3 ^ 7 * m + 1424 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5329.1, data_13_5329.2] + +/-- Complete interval computation for depth 13, residue 5330. -/ +theorem bounds_13_5330 : exactInterval 13 5330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5330 : oddCount 5330 13 = 7 ∧ acceleratedOrbit 13 5330 = 1424 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5330) = 3 ^ 7 * m + 1424 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5330.1, data_13_5330.2] + +/-- Complete interval computation for depth 13, residue 5331. -/ +theorem bounds_13_5331 : exactInterval 13 5331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5331 : oddCount 5331 13 = 7 ∧ acceleratedOrbit 13 5331 = 1424 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5331) = 3 ^ 7 * m + 1424 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5331.1, data_13_5331.2] + +/-- Complete interval computation for depth 13, residue 5332. -/ +theorem bounds_13_5332 : exactInterval 13 5332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5332 : oddCount 5332 13 = 5 ∧ acceleratedOrbit 13 5332 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5332) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5332.1, data_13_5332.2] + +/-- Complete interval computation for depth 13, residue 5333. -/ +theorem bounds_13_5333 : exactInterval 13 5333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5333 : oddCount 5333 13 = 5 ∧ acceleratedOrbit 13 5333 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5333) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5333.1, data_13_5333.2] + +/-- Complete interval computation for depth 13, residue 5334. -/ +theorem bounds_13_5334 : exactInterval 13 5334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5334 : oddCount 5334 13 = 6 ∧ acceleratedOrbit 13 5334 = 475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5334) = 3 ^ 6 * m + 475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5334.1, data_13_5334.2] + +end Collatz.Research.StoppingAtlas.Batch0814 From a9884f6d6e7036318a43e8c7076e2abc5675d73d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:03 +0530 Subject: [PATCH 0815/1001] proof: certify atlas Batch0815 (13:5335 to 13:5349) --- Collatz/Research/StoppingAtlas/Batch0815.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0815.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0815.lean b/Collatz/Research/StoppingAtlas/Batch0815.lean new file mode 100644 index 00000000..c42b666e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0815.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0815 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5335. -/ +theorem bounds_13_5335 : exactInterval 13 5335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5335 : oddCount 5335 13 = 6 ∧ acceleratedOrbit 13 5335 = 475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5335) = 3 ^ 6 * m + 475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5335.1, data_13_5335.2] + +/-- Complete interval computation for depth 13, residue 5336. -/ +theorem bounds_13_5336 : exactInterval 13 5336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5336 : oddCount 5336 13 = 8 ∧ acceleratedOrbit 13 5336 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5336) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5336.1, data_13_5336.2] + +/-- Complete interval computation for depth 13, residue 5337. -/ +theorem bounds_13_5337 : exactInterval 13 5337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5337 : oddCount 5337 13 = 6 ∧ acceleratedOrbit 13 5337 = 476 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5337) = 3 ^ 6 * m + 476 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5337.1, data_13_5337.2] + +/-- Complete interval computation for depth 13, residue 5338. -/ +theorem bounds_13_5338 : exactInterval 13 5338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5338 : oddCount 5338 13 = 8 ∧ acceleratedOrbit 13 5338 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5338) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5338.1, data_13_5338.2] + +/-- Complete interval computation for depth 13, residue 5339. -/ +theorem bounds_13_5339 : exactInterval 13 5339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5339 : oddCount 5339 13 = 7 ∧ acceleratedOrbit 13 5339 = 1426 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5339) = 3 ^ 7 * m + 1426 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5339.1, data_13_5339.2] + +/-- Complete interval computation for depth 13, residue 5340. -/ +theorem bounds_13_5340 : exactInterval 13 5340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5340 : oddCount 5340 13 = 8 ∧ acceleratedOrbit 13 5340 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5340) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5340.1, data_13_5340.2] + +/-- Complete interval computation for depth 13, residue 5341. -/ +theorem bounds_13_5341 : exactInterval 13 5341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5341 : oddCount 5341 13 = 8 ∧ acceleratedOrbit 13 5341 = 4283 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5341) = 3 ^ 8 * m + 4283 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5341.1, data_13_5341.2] + +/-- Complete interval computation for depth 13, residue 5342. -/ +theorem bounds_13_5342 : exactInterval 13 5342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5342 : oddCount 5342 13 = 9 ∧ acceleratedOrbit 13 5342 = 12842 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5342) = 3 ^ 9 * m + 12842 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5342.1, data_13_5342.2] + +/-- Complete interval computation for depth 13, residue 5343. -/ +theorem bounds_13_5343 : exactInterval 13 5343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5343 : oddCount 5343 13 = 9 ∧ acceleratedOrbit 13 5343 = 12842 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5343) = 3 ^ 9 * m + 12842 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5343.1, data_13_5343.2] + +/-- Complete interval computation for depth 13, residue 5344. -/ +theorem bounds_13_5344 : exactInterval 13 5344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5344 : oddCount 5344 13 = 6 ∧ acceleratedOrbit 13 5344 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5344) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5344.1, data_13_5344.2] + +/-- Complete interval computation for depth 13, residue 5345. -/ +theorem bounds_13_5345 : exactInterval 13 5345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5345 : oddCount 5345 13 = 10 ∧ acceleratedOrbit 13 5345 = 38546 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5345) = 3 ^ 10 * m + 38546 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5345.1, data_13_5345.2] + +/-- Complete interval computation for depth 13, residue 5346. -/ +theorem bounds_13_5346 : exactInterval 13 5346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5346 : oddCount 5346 13 = 5 ∧ acceleratedOrbit 13 5346 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5346) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5346.1, data_13_5346.2] + +/-- Complete interval computation for depth 13, residue 5347. -/ +theorem bounds_13_5347 : exactInterval 13 5347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5347 : oddCount 5347 13 = 5 ∧ acceleratedOrbit 13 5347 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5347) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5347.1, data_13_5347.2] + +/-- Complete interval computation for depth 13, residue 5348. -/ +theorem bounds_13_5348 : exactInterval 13 5348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5348 : oddCount 5348 13 = 8 ∧ acceleratedOrbit 13 5348 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5348) = 3 ^ 8 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5348.1, data_13_5348.2] + +/-- Complete interval computation for depth 13, residue 5349. -/ +theorem bounds_13_5349 : exactInterval 13 5349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5349 : oddCount 5349 13 = 8 ∧ acceleratedOrbit 13 5349 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5349) = 3 ^ 8 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5349.1, data_13_5349.2] + +end Collatz.Research.StoppingAtlas.Batch0815 From ea222d207e04471a653eddec3ae164c268506709 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:03 +0530 Subject: [PATCH 0816/1001] proof: certify atlas Batch0816 (13:5350 to 13:5364) --- Collatz/Research/StoppingAtlas/Batch0816.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0816.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0816.lean b/Collatz/Research/StoppingAtlas/Batch0816.lean new file mode 100644 index 00000000..2efe36da --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0816.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0816 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5350. -/ +theorem bounds_13_5350 : exactInterval 13 5350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5350 : oddCount 5350 13 = 8 ∧ acceleratedOrbit 13 5350 = 4292 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5350) = 3 ^ 8 * m + 4292 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5350.1, data_13_5350.2] + +/-- Complete interval computation for depth 13, residue 5351. -/ +theorem bounds_13_5351 : exactInterval 13 5351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5351 : oddCount 5351 13 = 10 ∧ acceleratedOrbit 13 5351 = 38582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5351) = 3 ^ 10 * m + 38582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5351.1, data_13_5351.2] + +/-- Complete interval computation for depth 13, residue 5352. -/ +theorem bounds_13_5352 : exactInterval 13 5352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5352 : oddCount 5352 13 = 6 ∧ acceleratedOrbit 13 5352 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5352) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5352.1, data_13_5352.2] + +/-- Complete interval computation for depth 13, residue 5353. -/ +theorem bounds_13_5353 : exactInterval 13 5353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5353 : oddCount 5353 13 = 7 ∧ acceleratedOrbit 13 5353 = 1430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5353) = 3 ^ 7 * m + 1430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5353.1, data_13_5353.2] + +/-- Complete interval computation for depth 13, residue 5354. -/ +theorem bounds_13_5354 : exactInterval 13 5354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5354 : oddCount 5354 13 = 6 ∧ acceleratedOrbit 13 5354 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5354) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5354.1, data_13_5354.2] + +/-- Complete interval computation for depth 13, residue 5355. -/ +theorem bounds_13_5355 : exactInterval 13 5355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5355 : oddCount 5355 13 = 9 ∧ acceleratedOrbit 13 5355 = 12872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5355) = 3 ^ 9 * m + 12872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5355.1, data_13_5355.2] + +/-- Complete interval computation for depth 13, residue 5356. -/ +theorem bounds_13_5356 : exactInterval 13 5356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5356 : oddCount 5356 13 = 4 ∧ acceleratedOrbit 13 5356 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5356) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5356.1, data_13_5356.2] + +/-- Complete interval computation for depth 13, residue 5357. -/ +theorem bounds_13_5357 : exactInterval 13 5357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5357 : oddCount 5357 13 = 4 ∧ acceleratedOrbit 13 5357 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5357) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5357.1, data_13_5357.2] + +/-- Complete interval computation for depth 13, residue 5358. -/ +theorem bounds_13_5358 : exactInterval 13 5358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5358 : oddCount 5358 13 = 4 ∧ acceleratedOrbit 13 5358 = 53 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5358) = 3 ^ 4 * m + 53 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5358.1, data_13_5358.2] + +/-- Complete interval computation for depth 13, residue 5359. -/ +theorem bounds_13_5359 : exactInterval 13 5359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5359 : oddCount 5359 13 = 12 ∧ acceleratedOrbit 13 5359 = 347732 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5359) = 3 ^ 12 * m + 347732 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5359.1, data_13_5359.2] + +/-- Complete interval computation for depth 13, residue 5360. -/ +theorem bounds_13_5360 : exactInterval 13 5360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5360 : oddCount 5360 13 = 6 ∧ acceleratedOrbit 13 5360 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5360) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5360.1, data_13_5360.2] + +/-- Complete interval computation for depth 13, residue 5361. -/ +theorem bounds_13_5361 : exactInterval 13 5361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5361 : oddCount 5361 13 = 6 ∧ acceleratedOrbit 13 5361 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5361) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5361.1, data_13_5361.2] + +/-- Complete interval computation for depth 13, residue 5362. -/ +theorem bounds_13_5362 : exactInterval 13 5362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5362 : oddCount 5362 13 = 7 ∧ acceleratedOrbit 13 5362 = 1433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5362) = 3 ^ 7 * m + 1433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5362.1, data_13_5362.2] + +/-- Complete interval computation for depth 13, residue 5363. -/ +theorem bounds_13_5363 : exactInterval 13 5363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5363 : oddCount 5363 13 = 7 ∧ acceleratedOrbit 13 5363 = 1433 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5363) = 3 ^ 7 * m + 1433 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5363.1, data_13_5363.2] + +/-- Complete interval computation for depth 13, residue 5364. -/ +theorem bounds_13_5364 : exactInterval 13 5364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5364 : oddCount 5364 13 = 6 ∧ acceleratedOrbit 13 5364 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5364) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5364.1, data_13_5364.2] + +end Collatz.Research.StoppingAtlas.Batch0816 From 784c4f51007006243df30971c5a4d772fb85225c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:03 +0530 Subject: [PATCH 0817/1001] proof: certify atlas Batch0817 (13:5365 to 13:5380) --- Collatz/Research/StoppingAtlas/Batch0817.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0817.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0817.lean b/Collatz/Research/StoppingAtlas/Batch0817.lean new file mode 100644 index 00000000..9b93740f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0817.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0817 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5365. -/ +theorem bounds_13_5365 : exactInterval 13 5365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5365 : oddCount 5365 13 = 6 ∧ acceleratedOrbit 13 5365 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5365) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5365.1, data_13_5365.2] + +/-- Complete interval computation for depth 13, residue 5366. -/ +theorem bounds_13_5366 : exactInterval 13 5366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5366 : oddCount 5366 13 = 6 ∧ acceleratedOrbit 13 5366 = 478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5366) = 3 ^ 6 * m + 478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5366.1, data_13_5366.2] + +/-- Complete interval computation for depth 13, residue 5367. -/ +theorem bounds_13_5367 : exactInterval 13 5367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5367 : oddCount 5367 13 = 6 ∧ acceleratedOrbit 13 5367 = 478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5367) = 3 ^ 6 * m + 478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5367.1, data_13_5367.2] + +/-- Complete interval computation for depth 13, residue 5368. -/ +theorem bounds_13_5368 : exactInterval 13 5368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5368 : oddCount 5368 13 = 8 ∧ acceleratedOrbit 13 5368 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5368) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5368.1, data_13_5368.2] + +/-- Complete interval computation for depth 13, residue 5369. -/ +theorem bounds_13_5369 : exactInterval 13 5369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5369 : oddCount 5369 13 = 6 ∧ acceleratedOrbit 13 5369 = 478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5369) = 3 ^ 6 * m + 478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5369.1, data_13_5369.2] + +/-- Complete interval computation for depth 13, residue 5370. -/ +theorem bounds_13_5370 : exactInterval 13 5370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5370 : oddCount 5370 13 = 8 ∧ acceleratedOrbit 13 5370 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5370) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5370.1, data_13_5370.2] + +/-- Complete interval computation for depth 13, residue 5371. -/ +theorem bounds_13_5371 : exactInterval 13 5371 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5371) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5371 : oddCount 5371 13 = 8 ∧ acceleratedOrbit 13 5371 = 4303 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5371) = 3 ^ 8 * m + 4303 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5371.1, data_13_5371.2] + +/-- Complete interval computation for depth 13, residue 5372. -/ +theorem bounds_13_5372 : exactInterval 13 5372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5372 : oddCount 5372 13 = 8 ∧ acceleratedOrbit 13 5372 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5372) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5372.1, data_13_5372.2] + +/-- Complete interval computation for depth 13, residue 5373. -/ +theorem bounds_13_5373 : exactInterval 13 5373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5373 : oddCount 5373 13 = 8 ∧ acceleratedOrbit 13 5373 = 4306 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5373) = 3 ^ 8 * m + 4306 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5373.1, data_13_5373.2] + +/-- Complete interval computation for depth 13, residue 5374. -/ +theorem bounds_13_5374 : exactInterval 13 5374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5374 : oddCount 5374 13 = 9 ∧ acceleratedOrbit 13 5374 = 12917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5374) = 3 ^ 9 * m + 12917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5374.1, data_13_5374.2] + +/-- Complete interval computation for depth 13, residue 5375. -/ +theorem bounds_13_5375 : exactInterval 13 5375 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5375) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5375 : oddCount 5375 13 = 9 ∧ acceleratedOrbit 13 5375 = 12917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5375) = 3 ^ 9 * m + 12917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5375.1, data_13_5375.2] + +/-- Complete interval computation for depth 13, residue 5376. -/ +theorem bounds_13_5376 : exactInterval 13 5376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5376 : oddCount 5376 13 = 1 ∧ acceleratedOrbit 13 5376 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5376) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5376.1, data_13_5376.2] + +/-- Complete interval computation for depth 13, residue 5377. -/ +theorem bounds_13_5377 : exactInterval 13 5377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5377 : oddCount 5377 13 = 6 ∧ acceleratedOrbit 13 5377 = 479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5377) = 3 ^ 6 * m + 479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5377.1, data_13_5377.2] + +/-- Complete interval computation for depth 13, residue 5378. -/ +theorem bounds_13_5378 : exactInterval 13 5378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5378 : oddCount 5378 13 = 8 ∧ acceleratedOrbit 13 5378 = 4313 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5378) = 3 ^ 8 * m + 4313 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5378.1, data_13_5378.2] + +/-- Complete interval computation for depth 13, residue 5379. -/ +theorem bounds_13_5379 : exactInterval 13 5379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5379 : oddCount 5379 13 = 8 ∧ acceleratedOrbit 13 5379 = 4313 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5379) = 3 ^ 8 * m + 4313 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5379.1, data_13_5379.2] + +/-- Complete interval computation for depth 13, residue 5380. -/ +theorem bounds_13_5380 : exactInterval 13 5380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5380 : oddCount 5380 13 = 5 ∧ acceleratedOrbit 13 5380 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5380) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5380.1, data_13_5380.2] + +end Collatz.Research.StoppingAtlas.Batch0817 From 7550f57047c72abea445e5ee544bb8bf2f757a25 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:03 +0530 Subject: [PATCH 0818/1001] proof: certify atlas Batch0818 (13:5381 to 13:5395) --- Collatz/Research/StoppingAtlas/Batch0818.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0818.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0818.lean b/Collatz/Research/StoppingAtlas/Batch0818.lean new file mode 100644 index 00000000..59db6219 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0818.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0818 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5381. -/ +theorem bounds_13_5381 : exactInterval 13 5381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5381 : oddCount 5381 13 = 5 ∧ acceleratedOrbit 13 5381 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5381) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5381.1, data_13_5381.2] + +/-- Complete interval computation for depth 13, residue 5382. -/ +theorem bounds_13_5382 : exactInterval 13 5382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5382 : oddCount 5382 13 = 5 ∧ acceleratedOrbit 13 5382 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5382) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5382.1, data_13_5382.2] + +/-- Complete interval computation for depth 13, residue 5383. -/ +theorem bounds_13_5383 : exactInterval 13 5383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5383 : oddCount 5383 13 = 8 ∧ acceleratedOrbit 13 5383 = 4313 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5383) = 3 ^ 8 * m + 4313 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5383.1, data_13_5383.2] + +/-- Complete interval computation for depth 13, residue 5384. -/ +theorem bounds_13_5384 : exactInterval 13 5384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5384 : oddCount 5384 13 = 6 ∧ acceleratedOrbit 13 5384 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5384) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5384.1, data_13_5384.2] + +/-- Complete interval computation for depth 13, residue 5385. -/ +theorem bounds_13_5385 : exactInterval 13 5385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5385 : oddCount 5385 13 = 8 ∧ acceleratedOrbit 13 5385 = 4315 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5385) = 3 ^ 8 * m + 4315 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5385.1, data_13_5385.2] + +/-- Complete interval computation for depth 13, residue 5386. -/ +theorem bounds_13_5386 : exactInterval 13 5386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5386 : oddCount 5386 13 = 6 ∧ acceleratedOrbit 13 5386 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5386) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5386.1, data_13_5386.2] + +/-- Complete interval computation for depth 13, residue 5387. -/ +theorem bounds_13_5387 : exactInterval 13 5387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5387 : oddCount 5387 13 = 8 ∧ acceleratedOrbit 13 5387 = 4319 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5387) = 3 ^ 8 * m + 4319 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5387.1, data_13_5387.2] + +/-- Complete interval computation for depth 13, residue 5388. -/ +theorem bounds_13_5388 : exactInterval 13 5388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5388 : oddCount 5388 13 = 6 ∧ acceleratedOrbit 13 5388 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5388) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5388.1, data_13_5388.2] + +/-- Complete interval computation for depth 13, residue 5389. -/ +theorem bounds_13_5389 : exactInterval 13 5389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5389 : oddCount 5389 13 = 6 ∧ acceleratedOrbit 13 5389 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5389) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5389.1, data_13_5389.2] + +/-- Complete interval computation for depth 13, residue 5390. -/ +theorem bounds_13_5390 : exactInterval 13 5390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5390 : oddCount 5390 13 = 5 ∧ acceleratedOrbit 13 5390 = 160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5390) = 3 ^ 5 * m + 160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5390.1, data_13_5390.2] + +/-- Complete interval computation for depth 13, residue 5391. -/ +theorem bounds_13_5391 : exactInterval 13 5391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5391 : oddCount 5391 13 = 5 ∧ acceleratedOrbit 13 5391 = 160 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5391) = 3 ^ 5 * m + 160 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5391.1, data_13_5391.2] + +/-- Complete interval computation for depth 13, residue 5392. -/ +theorem bounds_13_5392 : exactInterval 13 5392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5392 : oddCount 5392 13 = 6 ∧ acceleratedOrbit 13 5392 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5392) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5392.1, data_13_5392.2] + +/-- Complete interval computation for depth 13, residue 5393. -/ +theorem bounds_13_5393 : exactInterval 13 5393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5393 : oddCount 5393 13 = 6 ∧ acceleratedOrbit 13 5393 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5393) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5393.1, data_13_5393.2] + +/-- Complete interval computation for depth 13, residue 5394. -/ +theorem bounds_13_5394 : exactInterval 13 5394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5394 : oddCount 5394 13 = 7 ∧ acceleratedOrbit 13 5394 = 1441 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5394) = 3 ^ 7 * m + 1441 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5394.1, data_13_5394.2] + +/-- Complete interval computation for depth 13, residue 5395. -/ +theorem bounds_13_5395 : exactInterval 13 5395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5395 : oddCount 5395 13 = 7 ∧ acceleratedOrbit 13 5395 = 1441 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5395) = 3 ^ 7 * m + 1441 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5395.1, data_13_5395.2] + +end Collatz.Research.StoppingAtlas.Batch0818 From 3cb19dacb4b5ad4f6622d235b35cdc306f76456d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:03 +0530 Subject: [PATCH 0819/1001] proof: certify atlas Batch0819 (13:5396 to 13:5410) --- Collatz/Research/StoppingAtlas/Batch0819.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0819.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0819.lean b/Collatz/Research/StoppingAtlas/Batch0819.lean new file mode 100644 index 00000000..c6ff4360 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0819.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0819 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5396. -/ +theorem bounds_13_5396 : exactInterval 13 5396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5396 : oddCount 5396 13 = 6 ∧ acceleratedOrbit 13 5396 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5396) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5396.1, data_13_5396.2] + +/-- Complete interval computation for depth 13, residue 5397. -/ +theorem bounds_13_5397 : exactInterval 13 5397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5397 : oddCount 5397 13 = 6 ∧ acceleratedOrbit 13 5397 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5397) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5397.1, data_13_5397.2] + +/-- Complete interval computation for depth 13, residue 5398. -/ +theorem bounds_13_5398 : exactInterval 13 5398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5398 : oddCount 5398 13 = 6 ∧ acceleratedOrbit 13 5398 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5398) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5398.1, data_13_5398.2] + +/-- Complete interval computation for depth 13, residue 5399. -/ +theorem bounds_13_5399 : exactInterval 13 5399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5399 : oddCount 5399 13 = 6 ∧ acceleratedOrbit 13 5399 = 481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5399) = 3 ^ 6 * m + 481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5399.1, data_13_5399.2] + +/-- Complete interval computation for depth 13, residue 5400. -/ +theorem bounds_13_5400 : exactInterval 13 5400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5400 : oddCount 5400 13 = 6 ∧ acceleratedOrbit 13 5400 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5400) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5400.1, data_13_5400.2] + +/-- Complete interval computation for depth 13, residue 5401. -/ +theorem bounds_13_5401 : exactInterval 13 5401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5401 : oddCount 5401 13 = 9 ∧ acceleratedOrbit 13 5401 = 12986 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5401) = 3 ^ 9 * m + 12986 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5401.1, data_13_5401.2] + +/-- Complete interval computation for depth 13, residue 5402. -/ +theorem bounds_13_5402 : exactInterval 13 5402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5402 : oddCount 5402 13 = 6 ∧ acceleratedOrbit 13 5402 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5402) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5402.1, data_13_5402.2] + +/-- Complete interval computation for depth 13, residue 5403. -/ +theorem bounds_13_5403 : exactInterval 13 5403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5403 : oddCount 5403 13 = 10 ∧ acceleratedOrbit 13 5403 = 38956 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5403) = 3 ^ 10 * m + 38956 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5403.1, data_13_5403.2] + +/-- Complete interval computation for depth 13, residue 5404. -/ +theorem bounds_13_5404 : exactInterval 13 5404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5404 : oddCount 5404 13 = 8 ∧ acceleratedOrbit 13 5404 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5404) = 3 ^ 8 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5404.1, data_13_5404.2] + +/-- Complete interval computation for depth 13, residue 5405. -/ +theorem bounds_13_5405 : exactInterval 13 5405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5405 : oddCount 5405 13 = 8 ∧ acceleratedOrbit 13 5405 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5405) = 3 ^ 8 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5405.1, data_13_5405.2] + +/-- Complete interval computation for depth 13, residue 5406. -/ +theorem bounds_13_5406 : exactInterval 13 5406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5406 : oddCount 5406 13 = 8 ∧ acceleratedOrbit 13 5406 = 4333 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5406) = 3 ^ 8 * m + 4333 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5406.1, data_13_5406.2] + +/-- Complete interval computation for depth 13, residue 5407. -/ +theorem bounds_13_5407 : exactInterval 13 5407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5407 : oddCount 5407 13 = 7 ∧ acceleratedOrbit 13 5407 = 1444 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5407) = 3 ^ 7 * m + 1444 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5407.1, data_13_5407.2] + +/-- Complete interval computation for depth 13, residue 5408. -/ +theorem bounds_13_5408 : exactInterval 13 5408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5408 : oddCount 5408 13 = 7 ∧ acceleratedOrbit 13 5408 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5408) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5408.1, data_13_5408.2] + +/-- Complete interval computation for depth 13, residue 5409. -/ +theorem bounds_13_5409 : exactInterval 13 5409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5409 : oddCount 5409 13 = 5 ∧ acceleratedOrbit 13 5409 = 161 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5409) = 3 ^ 5 * m + 161 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5409.1, data_13_5409.2] + +/-- Complete interval computation for depth 13, residue 5410. -/ +theorem bounds_13_5410 : exactInterval 13 5410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5410 : oddCount 5410 13 = 7 ∧ acceleratedOrbit 13 5410 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5410) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5410.1, data_13_5410.2] + +end Collatz.Research.StoppingAtlas.Batch0819 From b02cebeabce2071e4b7c4620fa8fabe306ec676e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:04 +0530 Subject: [PATCH 0820/1001] proof: certify atlas Batch0820 (13:5411 to 13:5426) --- Collatz/Research/StoppingAtlas/Batch0820.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0820.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0820.lean b/Collatz/Research/StoppingAtlas/Batch0820.lean new file mode 100644 index 00000000..2959a058 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0820.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0820 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5411. -/ +theorem bounds_13_5411 : exactInterval 13 5411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5411 : oddCount 5411 13 = 7 ∧ acceleratedOrbit 13 5411 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5411) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5411.1, data_13_5411.2] + +/-- Complete interval computation for depth 13, residue 5412. -/ +theorem bounds_13_5412 : exactInterval 13 5412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5412 : oddCount 5412 13 = 7 ∧ acceleratedOrbit 13 5412 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5412) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5412.1, data_13_5412.2] + +/-- Complete interval computation for depth 13, residue 5413. -/ +theorem bounds_13_5413 : exactInterval 13 5413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5413 : oddCount 5413 13 = 7 ∧ acceleratedOrbit 13 5413 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5413) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5413.1, data_13_5413.2] + +/-- Complete interval computation for depth 13, residue 5414. -/ +theorem bounds_13_5414 : exactInterval 13 5414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5414 : oddCount 5414 13 = 7 ∧ acceleratedOrbit 13 5414 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5414) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5414.1, data_13_5414.2] + +/-- Complete interval computation for depth 13, residue 5415. -/ +theorem bounds_13_5415 : exactInterval 13 5415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5415 : oddCount 5415 13 = 6 ∧ acceleratedOrbit 13 5415 = 482 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5415) = 3 ^ 6 * m + 482 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5415.1, data_13_5415.2] + +/-- Complete interval computation for depth 13, residue 5416. -/ +theorem bounds_13_5416 : exactInterval 13 5416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5416 : oddCount 5416 13 = 7 ∧ acceleratedOrbit 13 5416 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5416) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5416.1, data_13_5416.2] + +/-- Complete interval computation for depth 13, residue 5417. -/ +theorem bounds_13_5417 : exactInterval 13 5417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5417 : oddCount 5417 13 = 8 ∧ acceleratedOrbit 13 5417 = 4340 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5417) = 3 ^ 8 * m + 4340 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5417.1, data_13_5417.2] + +/-- Complete interval computation for depth 13, residue 5418. -/ +theorem bounds_13_5418 : exactInterval 13 5418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5418 : oddCount 5418 13 = 7 ∧ acceleratedOrbit 13 5418 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5418) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5418.1, data_13_5418.2] + +/-- Complete interval computation for depth 13, residue 5419. -/ +theorem bounds_13_5419 : exactInterval 13 5419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5419 : oddCount 5419 13 = 7 ∧ acceleratedOrbit 13 5419 = 1448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5419) = 3 ^ 7 * m + 1448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5419.1, data_13_5419.2] + +/-- Complete interval computation for depth 13, residue 5420. -/ +theorem bounds_13_5420 : exactInterval 13 5420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5420 : oddCount 5420 13 = 6 ∧ acceleratedOrbit 13 5420 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5420) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5420.1, data_13_5420.2] + +/-- Complete interval computation for depth 13, residue 5421. -/ +theorem bounds_13_5421 : exactInterval 13 5421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5421 : oddCount 5421 13 = 6 ∧ acceleratedOrbit 13 5421 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5421) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5421.1, data_13_5421.2] + +/-- Complete interval computation for depth 13, residue 5422. -/ +theorem bounds_13_5422 : exactInterval 13 5422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5422 : oddCount 5422 13 = 6 ∧ acceleratedOrbit 13 5422 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5422) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5422.1, data_13_5422.2] + +/-- Complete interval computation for depth 13, residue 5423. -/ +theorem bounds_13_5423 : exactInterval 13 5423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5423 : oddCount 5423 13 = 9 ∧ acceleratedOrbit 13 5423 = 13034 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5423) = 3 ^ 9 * m + 13034 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5423.1, data_13_5423.2] + +/-- Complete interval computation for depth 13, residue 5424. -/ +theorem bounds_13_5424 : exactInterval 13 5424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5424 : oddCount 5424 13 = 7 ∧ acceleratedOrbit 13 5424 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5424) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5424.1, data_13_5424.2] + +/-- Complete interval computation for depth 13, residue 5425. -/ +theorem bounds_13_5425 : exactInterval 13 5425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5425 : oddCount 5425 13 = 7 ∧ acceleratedOrbit 13 5425 = 1451 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5425) = 3 ^ 7 * m + 1451 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5425.1, data_13_5425.2] + +/-- Complete interval computation for depth 13, residue 5426. -/ +theorem bounds_13_5426 : exactInterval 13 5426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5426 : oddCount 5426 13 = 7 ∧ acceleratedOrbit 13 5426 = 1451 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5426) = 3 ^ 7 * m + 1451 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5426.1, data_13_5426.2] + +end Collatz.Research.StoppingAtlas.Batch0820 From bc16c1ce99445c8bd202b9ec9dd624759254d3d6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:04 +0530 Subject: [PATCH 0821/1001] proof: certify atlas Batch0821 (13:5427 to 13:5441) --- Collatz/Research/StoppingAtlas/Batch0821.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0821.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0821.lean b/Collatz/Research/StoppingAtlas/Batch0821.lean new file mode 100644 index 00000000..2175245b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0821.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0821 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5427. -/ +theorem bounds_13_5427 : exactInterval 13 5427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5427 : oddCount 5427 13 = 7 ∧ acceleratedOrbit 13 5427 = 1451 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5427) = 3 ^ 7 * m + 1451 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5427.1, data_13_5427.2] + +/-- Complete interval computation for depth 13, residue 5428. -/ +theorem bounds_13_5428 : exactInterval 13 5428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5428 : oddCount 5428 13 = 7 ∧ acceleratedOrbit 13 5428 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5428) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5428.1, data_13_5428.2] + +/-- Complete interval computation for depth 13, residue 5429. -/ +theorem bounds_13_5429 : exactInterval 13 5429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5429 : oddCount 5429 13 = 7 ∧ acceleratedOrbit 13 5429 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5429) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5429.1, data_13_5429.2] + +/-- Complete interval computation for depth 13, residue 5430. -/ +theorem bounds_13_5430 : exactInterval 13 5430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5430 : oddCount 5430 13 = 9 ∧ acceleratedOrbit 13 5430 = 13054 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5430) = 3 ^ 9 * m + 13054 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5430.1, data_13_5430.2] + +/-- Complete interval computation for depth 13, residue 5431. -/ +theorem bounds_13_5431 : exactInterval 13 5431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5431 : oddCount 5431 13 = 9 ∧ acceleratedOrbit 13 5431 = 13054 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5431) = 3 ^ 9 * m + 13054 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5431.1, data_13_5431.2] + +/-- Complete interval computation for depth 13, residue 5432. -/ +theorem bounds_13_5432 : exactInterval 13 5432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5432 : oddCount 5432 13 = 7 ∧ acceleratedOrbit 13 5432 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5432) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5432.1, data_13_5432.2] + +/-- Complete interval computation for depth 13, residue 5433. -/ +theorem bounds_13_5433 : exactInterval 13 5433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5433 : oddCount 5433 13 = 9 ∧ acceleratedOrbit 13 5433 = 13061 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5433) = 3 ^ 9 * m + 13061 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5433.1, data_13_5433.2] + +/-- Complete interval computation for depth 13, residue 5434. -/ +theorem bounds_13_5434 : exactInterval 13 5434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5434 : oddCount 5434 13 = 7 ∧ acceleratedOrbit 13 5434 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5434) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5434.1, data_13_5434.2] + +/-- Complete interval computation for depth 13, residue 5435. -/ +theorem bounds_13_5435 : exactInterval 13 5435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5435 : oddCount 5435 13 = 6 ∧ acceleratedOrbit 13 5435 = 485 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5435) = 3 ^ 6 * m + 485 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5435.1, data_13_5435.2] + +/-- Complete interval computation for depth 13, residue 5436. -/ +theorem bounds_13_5436 : exactInterval 13 5436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5436 : oddCount 5436 13 = 7 ∧ acceleratedOrbit 13 5436 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5436) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5436.1, data_13_5436.2] + +/-- Complete interval computation for depth 13, residue 5437. -/ +theorem bounds_13_5437 : exactInterval 13 5437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5437 : oddCount 5437 13 = 7 ∧ acceleratedOrbit 13 5437 = 1453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5437) = 3 ^ 7 * m + 1453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5437.1, data_13_5437.2] + +/-- Complete interval computation for depth 13, residue 5438. -/ +theorem bounds_13_5438 : exactInterval 13 5438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5438 : oddCount 5438 13 = 8 ∧ acceleratedOrbit 13 5438 = 4357 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5438) = 3 ^ 8 * m + 4357 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5438.1, data_13_5438.2] + +/-- Complete interval computation for depth 13, residue 5439. -/ +theorem bounds_13_5439 : exactInterval 13 5439 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5439) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5439 : oddCount 5439 13 = 8 ∧ acceleratedOrbit 13 5439 = 4357 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5439) = 3 ^ 8 * m + 4357 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5439.1, data_13_5439.2] + +/-- Complete interval computation for depth 13, residue 5440. -/ +theorem bounds_13_5440 : exactInterval 13 5440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5440 : oddCount 5440 13 = 1 ∧ acceleratedOrbit 13 5440 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5440) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5440.1, data_13_5440.2] + +/-- Complete interval computation for depth 13, residue 5441. -/ +theorem bounds_13_5441 : exactInterval 13 5441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5441 : oddCount 5441 13 = 7 ∧ acceleratedOrbit 13 5441 = 1457 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5441) = 3 ^ 7 * m + 1457 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5441.1, data_13_5441.2] + +end Collatz.Research.StoppingAtlas.Batch0821 From a58672b1f0b64d9a0d694d1b9092bfbc40bb6437 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:04 +0530 Subject: [PATCH 0822/1001] proof: certify atlas Batch0822 (13:5442 to 13:5456) --- Collatz/Research/StoppingAtlas/Batch0822.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0822.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0822.lean b/Collatz/Research/StoppingAtlas/Batch0822.lean new file mode 100644 index 00000000..bf0f9d80 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0822.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0822 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5442. -/ +theorem bounds_13_5442 : exactInterval 13 5442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5442 : oddCount 5442 13 = 8 ∧ acceleratedOrbit 13 5442 = 4364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5442) = 3 ^ 8 * m + 4364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5442.1, data_13_5442.2] + +/-- Complete interval computation for depth 13, residue 5443. -/ +theorem bounds_13_5443 : exactInterval 13 5443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5443 : oddCount 5443 13 = 8 ∧ acceleratedOrbit 13 5443 = 4364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5443) = 3 ^ 8 * m + 4364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5443.1, data_13_5443.2] + +/-- Complete interval computation for depth 13, residue 5444. -/ +theorem bounds_13_5444 : exactInterval 13 5444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5444 : oddCount 5444 13 = 8 ∧ acceleratedOrbit 13 5444 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5444) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5444.1, data_13_5444.2] + +/-- Complete interval computation for depth 13, residue 5445. -/ +theorem bounds_13_5445 : exactInterval 13 5445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5445 : oddCount 5445 13 = 8 ∧ acceleratedOrbit 13 5445 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5445) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5445.1, data_13_5445.2] + +/-- Complete interval computation for depth 13, residue 5446. -/ +theorem bounds_13_5446 : exactInterval 13 5446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5446 : oddCount 5446 13 = 8 ∧ acceleratedOrbit 13 5446 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5446) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5446.1, data_13_5446.2] + +/-- Complete interval computation for depth 13, residue 5447. -/ +theorem bounds_13_5447 : exactInterval 13 5447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5447 : oddCount 5447 13 = 10 ∧ acceleratedOrbit 13 5447 = 39275 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5447) = 3 ^ 10 * m + 39275 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5447.1, data_13_5447.2] + +/-- Complete interval computation for depth 13, residue 5448. -/ +theorem bounds_13_5448 : exactInterval 13 5448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5448 : oddCount 5448 13 = 9 ∧ acceleratedOrbit 13 5448 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5448) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5448.1, data_13_5448.2] + +/-- Complete interval computation for depth 13, residue 5449. -/ +theorem bounds_13_5449 : exactInterval 13 5449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5449 : oddCount 5449 13 = 8 ∧ acceleratedOrbit 13 5449 = 4367 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5449) = 3 ^ 8 * m + 4367 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5449.1, data_13_5449.2] + +/-- Complete interval computation for depth 13, residue 5450. -/ +theorem bounds_13_5450 : exactInterval 13 5450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5450 : oddCount 5450 13 = 9 ∧ acceleratedOrbit 13 5450 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5450) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5450.1, data_13_5450.2] + +/-- Complete interval computation for depth 13, residue 5451. -/ +theorem bounds_13_5451 : exactInterval 13 5451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5451 : oddCount 5451 13 = 8 ∧ acceleratedOrbit 13 5451 = 4373 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5451) = 3 ^ 8 * m + 4373 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5451.1, data_13_5451.2] + +/-- Complete interval computation for depth 13, residue 5452. -/ +theorem bounds_13_5452 : exactInterval 13 5452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5452 : oddCount 5452 13 = 9 ∧ acceleratedOrbit 13 5452 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5452) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5452.1, data_13_5452.2] + +/-- Complete interval computation for depth 13, residue 5453. -/ +theorem bounds_13_5453 : exactInterval 13 5453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5453 : oddCount 5453 13 = 9 ∧ acceleratedOrbit 13 5453 = 13121 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5453) = 3 ^ 9 * m + 13121 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5453.1, data_13_5453.2] + +/-- Complete interval computation for depth 13, residue 5454. -/ +theorem bounds_13_5454 : exactInterval 13 5454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5454 : oddCount 5454 13 = 9 ∧ acceleratedOrbit 13 5454 = 13112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5454) = 3 ^ 9 * m + 13112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5454.1, data_13_5454.2] + +/-- Complete interval computation for depth 13, residue 5455. -/ +theorem bounds_13_5455 : exactInterval 13 5455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5455) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5455 : oddCount 5455 13 = 9 ∧ acceleratedOrbit 13 5455 = 13112 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5455) = 3 ^ 9 * m + 13112 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5455.1, data_13_5455.2] + +/-- Complete interval computation for depth 13, residue 5456. -/ +theorem bounds_13_5456 : exactInterval 13 5456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5456 : oddCount 5456 13 = 1 ∧ acceleratedOrbit 13 5456 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5456) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5456.1, data_13_5456.2] + +end Collatz.Research.StoppingAtlas.Batch0822 From 4433fc3b2ca92a6f1b7ad93c155344b533fce702 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:04 +0530 Subject: [PATCH 0823/1001] proof: certify atlas Batch0823 (13:5457 to 13:5472) --- Collatz/Research/StoppingAtlas/Batch0823.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0823.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0823.lean b/Collatz/Research/StoppingAtlas/Batch0823.lean new file mode 100644 index 00000000..ecfd6555 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0823.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0823 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5457. -/ +theorem bounds_13_5457 : exactInterval 13 5457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5457 : oddCount 5457 13 = 10 ∧ acceleratedOrbit 13 5457 = 39365 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5457) = 3 ^ 10 * m + 39365 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5457.1, data_13_5457.2] + +/-- Complete interval computation for depth 13, residue 5458. -/ +theorem bounds_13_5458 : exactInterval 13 5458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5458 : oddCount 5458 13 = 11 ∧ acceleratedOrbit 13 5458 = 118097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5458) = 3 ^ 11 * m + 118097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5458.1, data_13_5458.2] + +/-- Complete interval computation for depth 13, residue 5459. -/ +theorem bounds_13_5459 : exactInterval 13 5459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5459 : oddCount 5459 13 = 11 ∧ acceleratedOrbit 13 5459 = 118097 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5459) = 3 ^ 11 * m + 118097 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5459.1, data_13_5459.2] + +/-- Complete interval computation for depth 13, residue 5460. -/ +theorem bounds_13_5460 : exactInterval 13 5460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5460 : oddCount 5460 13 = 1 ∧ acceleratedOrbit 13 5460 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5460) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5460.1, data_13_5460.2] + +/-- Complete interval computation for depth 13, residue 5461. -/ +theorem bounds_13_5461 : exactInterval 13 5461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5461 : oddCount 5461 13 = 1 ∧ acceleratedOrbit 13 5461 = 2 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5461) = 3 ^ 1 * m + 2 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5461.1, data_13_5461.2] + +/-- Complete interval computation for depth 13, residue 5462. -/ +theorem bounds_13_5462 : exactInterval 13 5462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5462 : oddCount 5462 13 = 7 ∧ acceleratedOrbit 13 5462 = 1460 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5462) = 3 ^ 7 * m + 1460 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5462.1, data_13_5462.2] + +/-- Complete interval computation for depth 13, residue 5463. -/ +theorem bounds_13_5463 : exactInterval 13 5463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5463 : oddCount 5463 13 = 7 ∧ acceleratedOrbit 13 5463 = 1460 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5463) = 3 ^ 7 * m + 1460 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5463.1, data_13_5463.2] + +/-- Complete interval computation for depth 13, residue 5464. -/ +theorem bounds_13_5464 : exactInterval 13 5464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5464 : oddCount 5464 13 = 6 ∧ acceleratedOrbit 13 5464 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5464) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5464.1, data_13_5464.2] + +/-- Complete interval computation for depth 13, residue 5465. -/ +theorem bounds_13_5465 : exactInterval 13 5465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5465 : oddCount 5465 13 = 6 ∧ acceleratedOrbit 13 5465 = 487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5465) = 3 ^ 6 * m + 487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5465.1, data_13_5465.2] + +/-- Complete interval computation for depth 13, residue 5466. -/ +theorem bounds_13_5466 : exactInterval 13 5466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5466 : oddCount 5466 13 = 6 ∧ acceleratedOrbit 13 5466 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5466) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5466.1, data_13_5466.2] + +/-- Complete interval computation for depth 13, residue 5467. -/ +theorem bounds_13_5467 : exactInterval 13 5467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5467 : oddCount 5467 13 = 7 ∧ acceleratedOrbit 13 5467 = 1460 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5467) = 3 ^ 7 * m + 1460 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5467.1, data_13_5467.2] + +/-- Complete interval computation for depth 13, residue 5468. -/ +theorem bounds_13_5468 : exactInterval 13 5468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5468 : oddCount 5468 13 = 6 ∧ acceleratedOrbit 13 5468 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5468) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5468.1, data_13_5468.2] + +/-- Complete interval computation for depth 13, residue 5469. -/ +theorem bounds_13_5469 : exactInterval 13 5469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5469 : oddCount 5469 13 = 6 ∧ acceleratedOrbit 13 5469 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5469) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5469.1, data_13_5469.2] + +/-- Complete interval computation for depth 13, residue 5470. -/ +theorem bounds_13_5470 : exactInterval 13 5470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5470 : oddCount 5470 13 = 6 ∧ acceleratedOrbit 13 5470 = 487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5470) = 3 ^ 6 * m + 487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5470.1, data_13_5470.2] + +/-- Complete interval computation for depth 13, residue 5471. -/ +theorem bounds_13_5471 : exactInterval 13 5471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5471 : oddCount 5471 13 = 6 ∧ acceleratedOrbit 13 5471 = 487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5471) = 3 ^ 6 * m + 487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5471.1, data_13_5471.2] + +/-- Complete interval computation for depth 13, residue 5472. -/ +theorem bounds_13_5472 : exactInterval 13 5472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5472 : oddCount 5472 13 = 5 ∧ acceleratedOrbit 13 5472 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5472) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5472.1, data_13_5472.2] + +end Collatz.Research.StoppingAtlas.Batch0823 From 97f3b0ae9a41fb31f3e8c0bafb66b7b184545b4b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:04 +0530 Subject: [PATCH 0824/1001] proof: certify atlas Batch0824 (13:5473 to 13:5487) --- Collatz/Research/StoppingAtlas/Batch0824.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0824.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0824.lean b/Collatz/Research/StoppingAtlas/Batch0824.lean new file mode 100644 index 00000000..e6a7c67b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0824.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0824 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5473. -/ +theorem bounds_13_5473 : exactInterval 13 5473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5473 : oddCount 5473 13 = 7 ∧ acceleratedOrbit 13 5473 = 1462 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5473) = 3 ^ 7 * m + 1462 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5473.1, data_13_5473.2] + +/-- Complete interval computation for depth 13, residue 5474. -/ +theorem bounds_13_5474 : exactInterval 13 5474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5474 : oddCount 5474 13 = 5 ∧ acceleratedOrbit 13 5474 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5474) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5474.1, data_13_5474.2] + +/-- Complete interval computation for depth 13, residue 5475. -/ +theorem bounds_13_5475 : exactInterval 13 5475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5475 : oddCount 5475 13 = 5 ∧ acceleratedOrbit 13 5475 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5475) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5475.1, data_13_5475.2] + +/-- Complete interval computation for depth 13, residue 5476. -/ +theorem bounds_13_5476 : exactInterval 13 5476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5476 : oddCount 5476 13 = 5 ∧ acceleratedOrbit 13 5476 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5476) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5476.1, data_13_5476.2] + +/-- Complete interval computation for depth 13, residue 5477. -/ +theorem bounds_13_5477 : exactInterval 13 5477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5477 : oddCount 5477 13 = 5 ∧ acceleratedOrbit 13 5477 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5477) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5477.1, data_13_5477.2] + +/-- Complete interval computation for depth 13, residue 5478. -/ +theorem bounds_13_5478 : exactInterval 13 5478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5478 : oddCount 5478 13 = 5 ∧ acceleratedOrbit 13 5478 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5478) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5478.1, data_13_5478.2] + +/-- Complete interval computation for depth 13, residue 5479. -/ +theorem bounds_13_5479 : exactInterval 13 5479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5479 : oddCount 5479 13 = 10 ∧ acceleratedOrbit 13 5479 = 39503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5479) = 3 ^ 10 * m + 39503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5479.1, data_13_5479.2] + +/-- Complete interval computation for depth 13, residue 5480. -/ +theorem bounds_13_5480 : exactInterval 13 5480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5480 : oddCount 5480 13 = 5 ∧ acceleratedOrbit 13 5480 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5480) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5480.1, data_13_5480.2] + +/-- Complete interval computation for depth 13, residue 5481. -/ +theorem bounds_13_5481 : exactInterval 13 5481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5481 : oddCount 5481 13 = 6 ∧ acceleratedOrbit 13 5481 = 488 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5481) = 3 ^ 6 * m + 488 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5481.1, data_13_5481.2] + +/-- Complete interval computation for depth 13, residue 5482. -/ +theorem bounds_13_5482 : exactInterval 13 5482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5482 : oddCount 5482 13 = 5 ∧ acceleratedOrbit 13 5482 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5482) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5482.1, data_13_5482.2] + +/-- Complete interval computation for depth 13, residue 5483. -/ +theorem bounds_13_5483 : exactInterval 13 5483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5483 : oddCount 5483 13 = 8 ∧ acceleratedOrbit 13 5483 = 4394 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5483) = 3 ^ 8 * m + 4394 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5483.1, data_13_5483.2] + +/-- Complete interval computation for depth 13, residue 5484. -/ +theorem bounds_13_5484 : exactInterval 13 5484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5484 : oddCount 5484 13 = 7 ∧ acceleratedOrbit 13 5484 = 1466 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5484) = 3 ^ 7 * m + 1466 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5484.1, data_13_5484.2] + +/-- Complete interval computation for depth 13, residue 5485. -/ +theorem bounds_13_5485 : exactInterval 13 5485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5485 : oddCount 5485 13 = 7 ∧ acceleratedOrbit 13 5485 = 1466 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5485) = 3 ^ 7 * m + 1466 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5485.1, data_13_5485.2] + +/-- Complete interval computation for depth 13, residue 5486. -/ +theorem bounds_13_5486 : exactInterval 13 5486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5486 : oddCount 5486 13 = 7 ∧ acceleratedOrbit 13 5486 = 1466 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5486) = 3 ^ 7 * m + 1466 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5486.1, data_13_5486.2] + +/-- Complete interval computation for depth 13, residue 5487. -/ +theorem bounds_13_5487 : exactInterval 13 5487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5487 : oddCount 5487 13 = 8 ∧ acceleratedOrbit 13 5487 = 4396 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5487) = 3 ^ 8 * m + 4396 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5487.1, data_13_5487.2] + +end Collatz.Research.StoppingAtlas.Batch0824 From bf2ea7c294b46459d37e9c02d6768514aa68e13d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:04 +0530 Subject: [PATCH 0825/1001] proof: certify atlas Batch0825 (13:5488 to 13:5503) --- Collatz/Research/StoppingAtlas/Batch0825.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0825.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0825.lean b/Collatz/Research/StoppingAtlas/Batch0825.lean new file mode 100644 index 00000000..1ba244da --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0825.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0825 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5488. -/ +theorem bounds_13_5488 : exactInterval 13 5488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5488 : oddCount 5488 13 = 5 ∧ acceleratedOrbit 13 5488 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5488) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5488.1, data_13_5488.2] + +/-- Complete interval computation for depth 13, residue 5489. -/ +theorem bounds_13_5489 : exactInterval 13 5489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5489 : oddCount 5489 13 = 5 ∧ acceleratedOrbit 13 5489 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5489) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5489.1, data_13_5489.2] + +/-- Complete interval computation for depth 13, residue 5490. -/ +theorem bounds_13_5490 : exactInterval 13 5490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5490 : oddCount 5490 13 = 5 ∧ acceleratedOrbit 13 5490 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5490) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5490.1, data_13_5490.2] + +/-- Complete interval computation for depth 13, residue 5491. -/ +theorem bounds_13_5491 : exactInterval 13 5491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5491 : oddCount 5491 13 = 5 ∧ acceleratedOrbit 13 5491 = 163 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5491) = 3 ^ 5 * m + 163 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5491.1, data_13_5491.2] + +/-- Complete interval computation for depth 13, residue 5492. -/ +theorem bounds_13_5492 : exactInterval 13 5492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5492 : oddCount 5492 13 = 5 ∧ acceleratedOrbit 13 5492 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5492) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5492.1, data_13_5492.2] + +/-- Complete interval computation for depth 13, residue 5493. -/ +theorem bounds_13_5493 : exactInterval 13 5493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5493 : oddCount 5493 13 = 5 ∧ acceleratedOrbit 13 5493 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5493) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5493.1, data_13_5493.2] + +/-- Complete interval computation for depth 13, residue 5494. -/ +theorem bounds_13_5494 : exactInterval 13 5494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5494 : oddCount 5494 13 = 7 ∧ acceleratedOrbit 13 5494 = 1468 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5494) = 3 ^ 7 * m + 1468 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5494.1, data_13_5494.2] + +/-- Complete interval computation for depth 13, residue 5495. -/ +theorem bounds_13_5495 : exactInterval 13 5495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5495 : oddCount 5495 13 = 7 ∧ acceleratedOrbit 13 5495 = 1468 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5495) = 3 ^ 7 * m + 1468 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5495.1, data_13_5495.2] + +/-- Complete interval computation for depth 13, residue 5496. -/ +theorem bounds_13_5496 : exactInterval 13 5496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5496 : oddCount 5496 13 = 6 ∧ acceleratedOrbit 13 5496 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5496) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5496.1, data_13_5496.2] + +/-- Complete interval computation for depth 13, residue 5497. -/ +theorem bounds_13_5497 : exactInterval 13 5497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5497 : oddCount 5497 13 = 9 ∧ acceleratedOrbit 13 5497 = 13213 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5497) = 3 ^ 9 * m + 13213 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5497.1, data_13_5497.2] + +/-- Complete interval computation for depth 13, residue 5498. -/ +theorem bounds_13_5498 : exactInterval 13 5498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5498 : oddCount 5498 13 = 6 ∧ acceleratedOrbit 13 5498 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5498) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5498.1, data_13_5498.2] + +/-- Complete interval computation for depth 13, residue 5499. -/ +theorem bounds_13_5499 : exactInterval 13 5499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5499 : oddCount 5499 13 = 7 ∧ acceleratedOrbit 13 5499 = 1469 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5499) = 3 ^ 7 * m + 1469 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5499.1, data_13_5499.2] + +/-- Complete interval computation for depth 13, residue 5500. -/ +theorem bounds_13_5500 : exactInterval 13 5500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5500 : oddCount 5500 13 = 6 ∧ acceleratedOrbit 13 5500 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5500) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5500.1, data_13_5500.2] + +/-- Complete interval computation for depth 13, residue 5501. -/ +theorem bounds_13_5501 : exactInterval 13 5501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5501 : oddCount 5501 13 = 6 ∧ acceleratedOrbit 13 5501 = 490 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5501) = 3 ^ 6 * m + 490 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5501.1, data_13_5501.2] + +/-- Complete interval computation for depth 13, residue 5502. -/ +theorem bounds_13_5502 : exactInterval 13 5502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5502 : oddCount 5502 13 = 9 ∧ acceleratedOrbit 13 5502 = 13225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5502) = 3 ^ 9 * m + 13225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5502.1, data_13_5502.2] + +/-- Complete interval computation for depth 13, residue 5503. -/ +theorem bounds_13_5503 : exactInterval 13 5503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5503 : oddCount 5503 13 = 9 ∧ acceleratedOrbit 13 5503 = 13225 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5503) = 3 ^ 9 * m + 13225 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5503.1, data_13_5503.2] + +end Collatz.Research.StoppingAtlas.Batch0825 From 46cd8a7412c10bca5dc34421d22312c463c6eb66 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:05 +0530 Subject: [PATCH 0826/1001] proof: certify atlas Batch0826 (13:5504 to 13:5518) --- Collatz/Research/StoppingAtlas/Batch0826.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0826.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0826.lean b/Collatz/Research/StoppingAtlas/Batch0826.lean new file mode 100644 index 00000000..c1b8a3f7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0826.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0826 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5504. -/ +theorem bounds_13_5504 : exactInterval 13 5504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5504 : oddCount 5504 13 = 4 ∧ acceleratedOrbit 13 5504 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5504) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5504.1, data_13_5504.2] + +/-- Complete interval computation for depth 13, residue 5505. -/ +theorem bounds_13_5505 : exactInterval 13 5505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5505 : oddCount 5505 13 = 7 ∧ acceleratedOrbit 13 5505 = 1471 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5505) = 3 ^ 7 * m + 1471 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5505.1, data_13_5505.2] + +/-- Complete interval computation for depth 13, residue 5506. -/ +theorem bounds_13_5506 : exactInterval 13 5506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5506 : oddCount 5506 13 = 5 ∧ acceleratedOrbit 13 5506 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5506) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5506.1, data_13_5506.2] + +/-- Complete interval computation for depth 13, residue 5507. -/ +theorem bounds_13_5507 : exactInterval 13 5507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5507 : oddCount 5507 13 = 5 ∧ acceleratedOrbit 13 5507 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5507) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5507.1, data_13_5507.2] + +/-- Complete interval computation for depth 13, residue 5508. -/ +theorem bounds_13_5508 : exactInterval 13 5508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5508 : oddCount 5508 13 = 6 ∧ acceleratedOrbit 13 5508 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5508) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5508.1, data_13_5508.2] + +/-- Complete interval computation for depth 13, residue 5509. -/ +theorem bounds_13_5509 : exactInterval 13 5509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5509 : oddCount 5509 13 = 6 ∧ acceleratedOrbit 13 5509 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5509) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5509.1, data_13_5509.2] + +/-- Complete interval computation for depth 13, residue 5510. -/ +theorem bounds_13_5510 : exactInterval 13 5510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5510 : oddCount 5510 13 = 6 ∧ acceleratedOrbit 13 5510 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5510) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5510.1, data_13_5510.2] + +/-- Complete interval computation for depth 13, residue 5511. -/ +theorem bounds_13_5511 : exactInterval 13 5511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5511 : oddCount 5511 13 = 5 ∧ acceleratedOrbit 13 5511 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5511) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5511.1, data_13_5511.2] + +/-- Complete interval computation for depth 13, residue 5512. -/ +theorem bounds_13_5512 : exactInterval 13 5512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5512 : oddCount 5512 13 = 4 ∧ acceleratedOrbit 13 5512 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5512) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5512.1, data_13_5512.2] + +/-- Complete interval computation for depth 13, residue 5513. -/ +theorem bounds_13_5513 : exactInterval 13 5513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5513 : oddCount 5513 13 = 8 ∧ acceleratedOrbit 13 5513 = 4418 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5513) = 3 ^ 8 * m + 4418 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5513.1, data_13_5513.2] + +/-- Complete interval computation for depth 13, residue 5514. -/ +theorem bounds_13_5514 : exactInterval 13 5514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5514 : oddCount 5514 13 = 4 ∧ acceleratedOrbit 13 5514 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5514) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5514.1, data_13_5514.2] + +/-- Complete interval computation for depth 13, residue 5515. -/ +theorem bounds_13_5515 : exactInterval 13 5515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5515 : oddCount 5515 13 = 6 ∧ acceleratedOrbit 13 5515 = 491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5515) = 3 ^ 6 * m + 491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5515.1, data_13_5515.2] + +/-- Complete interval computation for depth 13, residue 5516. -/ +theorem bounds_13_5516 : exactInterval 13 5516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5516 : oddCount 5516 13 = 4 ∧ acceleratedOrbit 13 5516 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5516) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5516.1, data_13_5516.2] + +/-- Complete interval computation for depth 13, residue 5517. -/ +theorem bounds_13_5517 : exactInterval 13 5517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5517 : oddCount 5517 13 = 4 ∧ acceleratedOrbit 13 5517 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5517) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5517.1, data_13_5517.2] + +/-- Complete interval computation for depth 13, residue 5518. -/ +theorem bounds_13_5518 : exactInterval 13 5518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5518 : oddCount 5518 13 = 7 ∧ acceleratedOrbit 13 5518 = 1475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5518) = 3 ^ 7 * m + 1475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5518.1, data_13_5518.2] + +end Collatz.Research.StoppingAtlas.Batch0826 From f949b2fab421b1d246662abe8497870a500941d3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:05 +0530 Subject: [PATCH 0827/1001] proof: certify atlas Batch0827 (13:5519 to 13:5533) --- Collatz/Research/StoppingAtlas/Batch0827.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0827.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0827.lean b/Collatz/Research/StoppingAtlas/Batch0827.lean new file mode 100644 index 00000000..c8afdccb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0827.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0827 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5519. -/ +theorem bounds_13_5519 : exactInterval 13 5519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5519 : oddCount 5519 13 = 7 ∧ acceleratedOrbit 13 5519 = 1475 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5519) = 3 ^ 7 * m + 1475 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5519.1, data_13_5519.2] + +/-- Complete interval computation for depth 13, residue 5520. -/ +theorem bounds_13_5520 : exactInterval 13 5520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5520 : oddCount 5520 13 = 4 ∧ acceleratedOrbit 13 5520 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5520) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5520.1, data_13_5520.2] + +/-- Complete interval computation for depth 13, residue 5521. -/ +theorem bounds_13_5521 : exactInterval 13 5521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5521 : oddCount 5521 13 = 5 ∧ acceleratedOrbit 13 5521 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5521) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5521.1, data_13_5521.2] + +/-- Complete interval computation for depth 13, residue 5522. -/ +theorem bounds_13_5522 : exactInterval 13 5522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5522 : oddCount 5522 13 = 5 ∧ acceleratedOrbit 13 5522 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5522) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5522.1, data_13_5522.2] + +/-- Complete interval computation for depth 13, residue 5523. -/ +theorem bounds_13_5523 : exactInterval 13 5523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5523 : oddCount 5523 13 = 5 ∧ acceleratedOrbit 13 5523 = 164 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5523) = 3 ^ 5 * m + 164 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5523.1, data_13_5523.2] + +/-- Complete interval computation for depth 13, residue 5524. -/ +theorem bounds_13_5524 : exactInterval 13 5524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5524 : oddCount 5524 13 = 4 ∧ acceleratedOrbit 13 5524 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5524) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5524.1, data_13_5524.2] + +/-- Complete interval computation for depth 13, residue 5525. -/ +theorem bounds_13_5525 : exactInterval 13 5525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5525 : oddCount 5525 13 = 4 ∧ acceleratedOrbit 13 5525 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5525) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5525.1, data_13_5525.2] + +/-- Complete interval computation for depth 13, residue 5526. -/ +theorem bounds_13_5526 : exactInterval 13 5526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5526 : oddCount 5526 13 = 7 ∧ acceleratedOrbit 13 5526 = 1478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5526) = 3 ^ 7 * m + 1478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5526.1, data_13_5526.2] + +/-- Complete interval computation for depth 13, residue 5527. -/ +theorem bounds_13_5527 : exactInterval 13 5527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5527 : oddCount 5527 13 = 7 ∧ acceleratedOrbit 13 5527 = 1478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5527) = 3 ^ 7 * m + 1478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5527.1, data_13_5527.2] + +/-- Complete interval computation for depth 13, residue 5528. -/ +theorem bounds_13_5528 : exactInterval 13 5528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5528 : oddCount 5528 13 = 4 ∧ acceleratedOrbit 13 5528 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5528) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5528.1, data_13_5528.2] + +/-- Complete interval computation for depth 13, residue 5529. -/ +theorem bounds_13_5529 : exactInterval 13 5529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5529 : oddCount 5529 13 = 7 ∧ acceleratedOrbit 13 5529 = 1478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5529) = 3 ^ 7 * m + 1478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5529.1, data_13_5529.2] + +/-- Complete interval computation for depth 13, residue 5530. -/ +theorem bounds_13_5530 : exactInterval 13 5530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5530 : oddCount 5530 13 = 4 ∧ acceleratedOrbit 13 5530 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5530) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5530.1, data_13_5530.2] + +/-- Complete interval computation for depth 13, residue 5531. -/ +theorem bounds_13_5531 : exactInterval 13 5531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5531 : oddCount 5531 13 = 7 ∧ acceleratedOrbit 13 5531 = 1477 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5531) = 3 ^ 7 * m + 1477 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5531.1, data_13_5531.2] + +/-- Complete interval computation for depth 13, residue 5532. -/ +theorem bounds_13_5532 : exactInterval 13 5532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5532 : oddCount 5532 13 = 9 ∧ acceleratedOrbit 13 5532 = 13304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5532) = 3 ^ 9 * m + 13304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5532.1, data_13_5532.2] + +/-- Complete interval computation for depth 13, residue 5533. -/ +theorem bounds_13_5533 : exactInterval 13 5533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5533 : oddCount 5533 13 = 9 ∧ acceleratedOrbit 13 5533 = 13304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5533) = 3 ^ 9 * m + 13304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5533.1, data_13_5533.2] + +end Collatz.Research.StoppingAtlas.Batch0827 From 5d2d289883cfed903923e85e285abb8c1118c7cb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:05 +0530 Subject: [PATCH 0828/1001] proof: certify atlas Batch0828 (13:5534 to 13:5549) --- Collatz/Research/StoppingAtlas/Batch0828.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0828.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0828.lean b/Collatz/Research/StoppingAtlas/Batch0828.lean new file mode 100644 index 00000000..a8ede8bb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0828.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0828 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5534. -/ +theorem bounds_13_5534 : exactInterval 13 5534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5534 : oddCount 5534 13 = 9 ∧ acceleratedOrbit 13 5534 = 13304 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5534) = 3 ^ 9 * m + 13304 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5534.1, data_13_5534.2] + +/-- Complete interval computation for depth 13, residue 5535. -/ +theorem bounds_13_5535 : exactInterval 13 5535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5535 : oddCount 5535 13 = 11 ∧ acceleratedOrbit 13 5535 = 119717 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5535) = 3 ^ 11 * m + 119717 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5535.1, data_13_5535.2] + +/-- Complete interval computation for depth 13, residue 5536. -/ +theorem bounds_13_5536 : exactInterval 13 5536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5536 : oddCount 5536 13 = 4 ∧ acceleratedOrbit 13 5536 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5536) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5536.1, data_13_5536.2] + +/-- Complete interval computation for depth 13, residue 5537. -/ +theorem bounds_13_5537 : exactInterval 13 5537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5537 : oddCount 5537 13 = 6 ∧ acceleratedOrbit 13 5537 = 493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5537) = 3 ^ 6 * m + 493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5537.1, data_13_5537.2] + +/-- Complete interval computation for depth 13, residue 5538. -/ +theorem bounds_13_5538 : exactInterval 13 5538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5538 : oddCount 5538 13 = 6 ∧ acceleratedOrbit 13 5538 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5538) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5538.1, data_13_5538.2] + +/-- Complete interval computation for depth 13, residue 5539. -/ +theorem bounds_13_5539 : exactInterval 13 5539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5539 : oddCount 5539 13 = 6 ∧ acceleratedOrbit 13 5539 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5539) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5539.1, data_13_5539.2] + +/-- Complete interval computation for depth 13, residue 5540. -/ +theorem bounds_13_5540 : exactInterval 13 5540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5540 : oddCount 5540 13 = 6 ∧ acceleratedOrbit 13 5540 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5540) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5540.1, data_13_5540.2] + +/-- Complete interval computation for depth 13, residue 5541. -/ +theorem bounds_13_5541 : exactInterval 13 5541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5541 : oddCount 5541 13 = 6 ∧ acceleratedOrbit 13 5541 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5541) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5541.1, data_13_5541.2] + +/-- Complete interval computation for depth 13, residue 5542. -/ +theorem bounds_13_5542 : exactInterval 13 5542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5542 : oddCount 5542 13 = 6 ∧ acceleratedOrbit 13 5542 = 494 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5542) = 3 ^ 6 * m + 494 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5542.1, data_13_5542.2] + +/-- Complete interval computation for depth 13, residue 5543. -/ +theorem bounds_13_5543 : exactInterval 13 5543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5543 : oddCount 5543 13 = 8 ∧ acceleratedOrbit 13 5543 = 4441 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5543) = 3 ^ 8 * m + 4441 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5543.1, data_13_5543.2] + +/-- Complete interval computation for depth 13, residue 5544. -/ +theorem bounds_13_5544 : exactInterval 13 5544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5544 : oddCount 5544 13 = 4 ∧ acceleratedOrbit 13 5544 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5544) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5544.1, data_13_5544.2] + +/-- Complete interval computation for depth 13, residue 5545. -/ +theorem bounds_13_5545 : exactInterval 13 5545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5545 : oddCount 5545 13 = 9 ∧ acceleratedOrbit 13 5545 = 13328 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5545) = 3 ^ 9 * m + 13328 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5545.1, data_13_5545.2] + +/-- Complete interval computation for depth 13, residue 5546. -/ +theorem bounds_13_5546 : exactInterval 13 5546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5546 : oddCount 5546 13 = 4 ∧ acceleratedOrbit 13 5546 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5546) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5546.1, data_13_5546.2] + +/-- Complete interval computation for depth 13, residue 5547. -/ +theorem bounds_13_5547 : exactInterval 13 5547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5547 : oddCount 5547 13 = 8 ∧ acceleratedOrbit 13 5547 = 4445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5547) = 3 ^ 8 * m + 4445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5547.1, data_13_5547.2] + +/-- Complete interval computation for depth 13, residue 5548. -/ +theorem bounds_13_5548 : exactInterval 13 5548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5548 : oddCount 5548 13 = 7 ∧ acceleratedOrbit 13 5548 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5548) = 3 ^ 7 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5548.1, data_13_5548.2] + +/-- Complete interval computation for depth 13, residue 5549. -/ +theorem bounds_13_5549 : exactInterval 13 5549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5549 : oddCount 5549 13 = 7 ∧ acceleratedOrbit 13 5549 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5549) = 3 ^ 7 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5549.1, data_13_5549.2] + +end Collatz.Research.StoppingAtlas.Batch0828 From 41541a2087d3ef1f301e2ab513aed3ef5e38b4a3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:05 +0530 Subject: [PATCH 0829/1001] proof: certify atlas Batch0829 (13:5550 to 13:5564) --- Collatz/Research/StoppingAtlas/Batch0829.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0829.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0829.lean b/Collatz/Research/StoppingAtlas/Batch0829.lean new file mode 100644 index 00000000..eba2e2d9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0829.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0829 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5550. -/ +theorem bounds_13_5550 : exactInterval 13 5550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5550 : oddCount 5550 13 = 7 ∧ acceleratedOrbit 13 5550 = 1484 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5550) = 3 ^ 7 * m + 1484 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5550.1, data_13_5550.2] + +/-- Complete interval computation for depth 13, residue 5551. -/ +theorem bounds_13_5551 : exactInterval 13 5551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5551 : oddCount 5551 13 = 8 ∧ acceleratedOrbit 13 5551 = 4448 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5551) = 3 ^ 8 * m + 4448 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5551.1, data_13_5551.2] + +/-- Complete interval computation for depth 13, residue 5552. -/ +theorem bounds_13_5552 : exactInterval 13 5552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5552 : oddCount 5552 13 = 6 ∧ acceleratedOrbit 13 5552 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5552) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5552.1, data_13_5552.2] + +/-- Complete interval computation for depth 13, residue 5553. -/ +theorem bounds_13_5553 : exactInterval 13 5553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5553 : oddCount 5553 13 = 4 ∧ acceleratedOrbit 13 5553 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5553) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5553.1, data_13_5553.2] + +/-- Complete interval computation for depth 13, residue 5554. -/ +theorem bounds_13_5554 : exactInterval 13 5554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5554 : oddCount 5554 13 = 4 ∧ acceleratedOrbit 13 5554 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5554) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5554.1, data_13_5554.2] + +/-- Complete interval computation for depth 13, residue 5555. -/ +theorem bounds_13_5555 : exactInterval 13 5555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5555 : oddCount 5555 13 = 4 ∧ acceleratedOrbit 13 5555 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5555) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5555.1, data_13_5555.2] + +/-- Complete interval computation for depth 13, residue 5556. -/ +theorem bounds_13_5556 : exactInterval 13 5556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5556 : oddCount 5556 13 = 6 ∧ acceleratedOrbit 13 5556 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5556) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5556.1, data_13_5556.2] + +/-- Complete interval computation for depth 13, residue 5557. -/ +theorem bounds_13_5557 : exactInterval 13 5557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5557 : oddCount 5557 13 = 6 ∧ acceleratedOrbit 13 5557 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5557) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5557.1, data_13_5557.2] + +/-- Complete interval computation for depth 13, residue 5558. -/ +theorem bounds_13_5558 : exactInterval 13 5558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5558 : oddCount 5558 13 = 9 ∧ acceleratedOrbit 13 5558 = 13364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5558) = 3 ^ 9 * m + 13364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5558.1, data_13_5558.2] + +/-- Complete interval computation for depth 13, residue 5559. -/ +theorem bounds_13_5559 : exactInterval 13 5559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5559 : oddCount 5559 13 = 9 ∧ acceleratedOrbit 13 5559 = 13364 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5559) = 3 ^ 9 * m + 13364 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5559.1, data_13_5559.2] + +/-- Complete interval computation for depth 13, residue 5560. -/ +theorem bounds_13_5560 : exactInterval 13 5560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5560 : oddCount 5560 13 = 6 ∧ acceleratedOrbit 13 5560 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5560) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5560.1, data_13_5560.2] + +/-- Complete interval computation for depth 13, residue 5561. -/ +theorem bounds_13_5561 : exactInterval 13 5561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5561 : oddCount 5561 13 = 4 ∧ acceleratedOrbit 13 5561 = 55 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5561) = 3 ^ 4 * m + 55 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5561.1, data_13_5561.2] + +/-- Complete interval computation for depth 13, residue 5562. -/ +theorem bounds_13_5562 : exactInterval 13 5562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5562 : oddCount 5562 13 = 6 ∧ acceleratedOrbit 13 5562 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5562) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5562.1, data_13_5562.2] + +/-- Complete interval computation for depth 13, residue 5563. -/ +theorem bounds_13_5563 : exactInterval 13 5563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5563 : oddCount 5563 13 = 7 ∧ acceleratedOrbit 13 5563 = 1486 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5563) = 3 ^ 7 * m + 1486 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5563.1, data_13_5563.2] + +/-- Complete interval computation for depth 13, residue 5564. -/ +theorem bounds_13_5564 : exactInterval 13 5564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5564 : oddCount 5564 13 = 7 ∧ acceleratedOrbit 13 5564 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5564) = 3 ^ 7 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5564.1, data_13_5564.2] + +end Collatz.Research.StoppingAtlas.Batch0829 From 378bcd019fb4810eca889b5fc260c2231a1a2754 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:05 +0530 Subject: [PATCH 0830/1001] proof: certify atlas Batch0830 (13:5565 to 13:5579) --- Collatz/Research/StoppingAtlas/Batch0830.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0830.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0830.lean b/Collatz/Research/StoppingAtlas/Batch0830.lean new file mode 100644 index 00000000..5f8d4b7b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0830.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0830 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5565. -/ +theorem bounds_13_5565 : exactInterval 13 5565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5565 : oddCount 5565 13 = 7 ∧ acceleratedOrbit 13 5565 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5565) = 3 ^ 7 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5565.1, data_13_5565.2] + +/-- Complete interval computation for depth 13, residue 5566. -/ +theorem bounds_13_5566 : exactInterval 13 5566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5566 : oddCount 5566 13 = 7 ∧ acceleratedOrbit 13 5566 = 1487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5566) = 3 ^ 7 * m + 1487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5566.1, data_13_5566.2] + +/-- Complete interval computation for depth 13, residue 5567. -/ +theorem bounds_13_5567 : exactInterval 13 5567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5567 : oddCount 5567 13 = 11 ∧ acceleratedOrbit 13 5567 = 120406 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5567) = 3 ^ 11 * m + 120406 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5567.1, data_13_5567.2] + +/-- Complete interval computation for depth 13, residue 5568. -/ +theorem bounds_13_5568 : exactInterval 13 5568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5568 : oddCount 5568 13 = 4 ∧ acceleratedOrbit 13 5568 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5568) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5568.1, data_13_5568.2] + +/-- Complete interval computation for depth 13, residue 5569. -/ +theorem bounds_13_5569 : exactInterval 13 5569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5569 : oddCount 5569 13 = 6 ∧ acceleratedOrbit 13 5569 = 496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5569) = 3 ^ 6 * m + 496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5569.1, data_13_5569.2] + +/-- Complete interval computation for depth 13, residue 5570. -/ +theorem bounds_13_5570 : exactInterval 13 5570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5570 : oddCount 5570 13 = 8 ∧ acceleratedOrbit 13 5570 = 4465 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5570) = 3 ^ 8 * m + 4465 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5570.1, data_13_5570.2] + +/-- Complete interval computation for depth 13, residue 5571. -/ +theorem bounds_13_5571 : exactInterval 13 5571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5571 : oddCount 5571 13 = 8 ∧ acceleratedOrbit 13 5571 = 4465 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5571) = 3 ^ 8 * m + 4465 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5571.1, data_13_5571.2] + +/-- Complete interval computation for depth 13, residue 5572. -/ +theorem bounds_13_5572 : exactInterval 13 5572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5572 : oddCount 5572 13 = 4 ∧ acceleratedOrbit 13 5572 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5572) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5572.1, data_13_5572.2] + +/-- Complete interval computation for depth 13, residue 5573. -/ +theorem bounds_13_5573 : exactInterval 13 5573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5573 : oddCount 5573 13 = 4 ∧ acceleratedOrbit 13 5573 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5573) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5573.1, data_13_5573.2] + +/-- Complete interval computation for depth 13, residue 5574. -/ +theorem bounds_13_5574 : exactInterval 13 5574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5574 : oddCount 5574 13 = 4 ∧ acceleratedOrbit 13 5574 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5574) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5574.1, data_13_5574.2] + +/-- Complete interval computation for depth 13, residue 5575. -/ +theorem bounds_13_5575 : exactInterval 13 5575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5575 : oddCount 5575 13 = 7 ∧ acceleratedOrbit 13 5575 = 1489 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5575) = 3 ^ 7 * m + 1489 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5575.1, data_13_5575.2] + +/-- Complete interval computation for depth 13, residue 5576. -/ +theorem bounds_13_5576 : exactInterval 13 5576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5576 : oddCount 5576 13 = 5 ∧ acceleratedOrbit 13 5576 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5576) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5576.1, data_13_5576.2] + +/-- Complete interval computation for depth 13, residue 5577. -/ +theorem bounds_13_5577 : exactInterval 13 5577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5577 : oddCount 5577 13 = 6 ∧ acceleratedOrbit 13 5577 = 497 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5577) = 3 ^ 6 * m + 497 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5577.1, data_13_5577.2] + +/-- Complete interval computation for depth 13, residue 5578. -/ +theorem bounds_13_5578 : exactInterval 13 5578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5578 : oddCount 5578 13 = 5 ∧ acceleratedOrbit 13 5578 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5578) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5578.1, data_13_5578.2] + +/-- Complete interval computation for depth 13, residue 5579. -/ +theorem bounds_13_5579 : exactInterval 13 5579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5579 : oddCount 5579 13 = 6 ∧ acceleratedOrbit 13 5579 = 497 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5579) = 3 ^ 6 * m + 497 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5579.1, data_13_5579.2] + +end Collatz.Research.StoppingAtlas.Batch0830 From ae244b7be1c8d49e33eca95d0742f0c75d8da0c1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:06 +0530 Subject: [PATCH 0831/1001] proof: certify atlas Batch0831 (13:5580 to 13:5595) --- Collatz/Research/StoppingAtlas/Batch0831.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0831.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0831.lean b/Collatz/Research/StoppingAtlas/Batch0831.lean new file mode 100644 index 00000000..8506c217 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0831.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0831 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5580. -/ +theorem bounds_13_5580 : exactInterval 13 5580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5580 : oddCount 5580 13 = 5 ∧ acceleratedOrbit 13 5580 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5580) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5580.1, data_13_5580.2] + +/-- Complete interval computation for depth 13, residue 5581. -/ +theorem bounds_13_5581 : exactInterval 13 5581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5581 : oddCount 5581 13 = 5 ∧ acceleratedOrbit 13 5581 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5581) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5581.1, data_13_5581.2] + +/-- Complete interval computation for depth 13, residue 5582. -/ +theorem bounds_13_5582 : exactInterval 13 5582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5582 : oddCount 5582 13 = 10 ∧ acceleratedOrbit 13 5582 = 40256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5582) = 3 ^ 10 * m + 40256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5582.1, data_13_5582.2] + +/-- Complete interval computation for depth 13, residue 5583. -/ +theorem bounds_13_5583 : exactInterval 13 5583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5583 : oddCount 5583 13 = 10 ∧ acceleratedOrbit 13 5583 = 40256 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5583) = 3 ^ 10 * m + 40256 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5583.1, data_13_5583.2] + +/-- Complete interval computation for depth 13, residue 5584. -/ +theorem bounds_13_5584 : exactInterval 13 5584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5584 : oddCount 5584 13 = 4 ∧ acceleratedOrbit 13 5584 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5584) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5584.1, data_13_5584.2] + +/-- Complete interval computation for depth 13, residue 5585. -/ +theorem bounds_13_5585 : exactInterval 13 5585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5585 : oddCount 5585 13 = 5 ∧ acceleratedOrbit 13 5585 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5585) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5585.1, data_13_5585.2] + +/-- Complete interval computation for depth 13, residue 5586. -/ +theorem bounds_13_5586 : exactInterval 13 5586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5586 : oddCount 5586 13 = 8 ∧ acceleratedOrbit 13 5586 = 4477 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5586) = 3 ^ 8 * m + 4477 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5586.1, data_13_5586.2] + +/-- Complete interval computation for depth 13, residue 5587. -/ +theorem bounds_13_5587 : exactInterval 13 5587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5587 : oddCount 5587 13 = 8 ∧ acceleratedOrbit 13 5587 = 4477 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5587) = 3 ^ 8 * m + 4477 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5587.1, data_13_5587.2] + +/-- Complete interval computation for depth 13, residue 5588. -/ +theorem bounds_13_5588 : exactInterval 13 5588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5588 : oddCount 5588 13 = 4 ∧ acceleratedOrbit 13 5588 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5588) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5588.1, data_13_5588.2] + +/-- Complete interval computation for depth 13, residue 5589. -/ +theorem bounds_13_5589 : exactInterval 13 5589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5589 : oddCount 5589 13 = 4 ∧ acceleratedOrbit 13 5589 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5589) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5589.1, data_13_5589.2] + +/-- Complete interval computation for depth 13, residue 5590. -/ +theorem bounds_13_5590 : exactInterval 13 5590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5590 : oddCount 5590 13 = 8 ∧ acceleratedOrbit 13 5590 = 4481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5590) = 3 ^ 8 * m + 4481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5590.1, data_13_5590.2] + +/-- Complete interval computation for depth 13, residue 5591. -/ +theorem bounds_13_5591 : exactInterval 13 5591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5591 : oddCount 5591 13 = 8 ∧ acceleratedOrbit 13 5591 = 4481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5591) = 3 ^ 8 * m + 4481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5591.1, data_13_5591.2] + +/-- Complete interval computation for depth 13, residue 5592. -/ +theorem bounds_13_5592 : exactInterval 13 5592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5592 : oddCount 5592 13 = 6 ∧ acceleratedOrbit 13 5592 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5592) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5592.1, data_13_5592.2] + +/-- Complete interval computation for depth 13, residue 5593. -/ +theorem bounds_13_5593 : exactInterval 13 5593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5593 : oddCount 5593 13 = 6 ∧ acceleratedOrbit 13 5593 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5593) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5593.1, data_13_5593.2] + +/-- Complete interval computation for depth 13, residue 5594. -/ +theorem bounds_13_5594 : exactInterval 13 5594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5594 : oddCount 5594 13 = 6 ∧ acceleratedOrbit 13 5594 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5594) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5594.1, data_13_5594.2] + +/-- Complete interval computation for depth 13, residue 5595. -/ +theorem bounds_13_5595 : exactInterval 13 5595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5595 : oddCount 5595 13 = 5 ∧ acceleratedOrbit 13 5595 = 166 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5595) = 3 ^ 5 * m + 166 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5595.1, data_13_5595.2] + +end Collatz.Research.StoppingAtlas.Batch0831 From c1475b1b6fa91c6ee0b55f259e42abe998a04eac Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:06 +0530 Subject: [PATCH 0832/1001] proof: certify atlas Batch0832 (13:5596 to 13:5610) --- Collatz/Research/StoppingAtlas/Batch0832.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0832.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0832.lean b/Collatz/Research/StoppingAtlas/Batch0832.lean new file mode 100644 index 00000000..0c9c9e72 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0832.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0832 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5596. -/ +theorem bounds_13_5596 : exactInterval 13 5596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5596 : oddCount 5596 13 = 6 ∧ acceleratedOrbit 13 5596 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5596) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5596.1, data_13_5596.2] + +/-- Complete interval computation for depth 13, residue 5597. -/ +theorem bounds_13_5597 : exactInterval 13 5597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5597 : oddCount 5597 13 = 6 ∧ acceleratedOrbit 13 5597 = 499 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5597) = 3 ^ 6 * m + 499 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5597.1, data_13_5597.2] + +/-- Complete interval computation for depth 13, residue 5598. -/ +theorem bounds_13_5598 : exactInterval 13 5598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5598 : oddCount 5598 13 = 9 ∧ acceleratedOrbit 13 5598 = 13456 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5598) = 3 ^ 9 * m + 13456 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5598.1, data_13_5598.2] + +/-- Complete interval computation for depth 13, residue 5599. -/ +theorem bounds_13_5599 : exactInterval 13 5599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5599 : oddCount 5599 13 = 9 ∧ acceleratedOrbit 13 5599 = 13456 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5599) = 3 ^ 9 * m + 13456 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5599.1, data_13_5599.2] + +/-- Complete interval computation for depth 13, residue 5600. -/ +theorem bounds_13_5600 : exactInterval 13 5600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5600 : oddCount 5600 13 = 5 ∧ acceleratedOrbit 13 5600 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5600) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5600.1, data_13_5600.2] + +/-- Complete interval computation for depth 13, residue 5601. -/ +theorem bounds_13_5601 : exactInterval 13 5601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5601 : oddCount 5601 13 = 7 ∧ acceleratedOrbit 13 5601 = 1496 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5601) = 3 ^ 7 * m + 1496 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5601.1, data_13_5601.2] + +/-- Complete interval computation for depth 13, residue 5602. -/ +theorem bounds_13_5602 : exactInterval 13 5602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5602 : oddCount 5602 13 = 4 ∧ acceleratedOrbit 13 5602 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5602) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5602.1, data_13_5602.2] + +/-- Complete interval computation for depth 13, residue 5603. -/ +theorem bounds_13_5603 : exactInterval 13 5603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5603 : oddCount 5603 13 = 4 ∧ acceleratedOrbit 13 5603 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5603) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5603.1, data_13_5603.2] + +/-- Complete interval computation for depth 13, residue 5604. -/ +theorem bounds_13_5604 : exactInterval 13 5604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5604 : oddCount 5604 13 = 8 ∧ acceleratedOrbit 13 5604 = 4495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5604) = 3 ^ 8 * m + 4495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5604.1, data_13_5604.2] + +/-- Complete interval computation for depth 13, residue 5605. -/ +theorem bounds_13_5605 : exactInterval 13 5605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5605 : oddCount 5605 13 = 8 ∧ acceleratedOrbit 13 5605 = 4495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5605) = 3 ^ 8 * m + 4495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5605.1, data_13_5605.2] + +/-- Complete interval computation for depth 13, residue 5606. -/ +theorem bounds_13_5606 : exactInterval 13 5606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5606 : oddCount 5606 13 = 8 ∧ acceleratedOrbit 13 5606 = 4495 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5606) = 3 ^ 8 * m + 4495 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5606.1, data_13_5606.2] + +/-- Complete interval computation for depth 13, residue 5607. -/ +theorem bounds_13_5607 : exactInterval 13 5607 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5607) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5607 : oddCount 5607 13 = 8 ∧ acceleratedOrbit 13 5607 = 4492 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5607) = 3 ^ 8 * m + 4492 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5607.1, data_13_5607.2] + +/-- Complete interval computation for depth 13, residue 5608. -/ +theorem bounds_13_5608 : exactInterval 13 5608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5608 : oddCount 5608 13 = 5 ∧ acceleratedOrbit 13 5608 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5608) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5608.1, data_13_5608.2] + +/-- Complete interval computation for depth 13, residue 5609. -/ +theorem bounds_13_5609 : exactInterval 13 5609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5609 : oddCount 5609 13 = 10 ∧ acceleratedOrbit 13 5609 = 40445 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5609) = 3 ^ 10 * m + 40445 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5609.1, data_13_5609.2] + +/-- Complete interval computation for depth 13, residue 5610. -/ +theorem bounds_13_5610 : exactInterval 13 5610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5610 : oddCount 5610 13 = 5 ∧ acceleratedOrbit 13 5610 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5610) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5610.1, data_13_5610.2] + +end Collatz.Research.StoppingAtlas.Batch0832 From df439829c91ca538a56146f45bcb2159ea7388da Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:06 +0530 Subject: [PATCH 0833/1001] proof: certify atlas Batch0833 (13:5611 to 13:5625) --- Collatz/Research/StoppingAtlas/Batch0833.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0833.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0833.lean b/Collatz/Research/StoppingAtlas/Batch0833.lean new file mode 100644 index 00000000..2b74dc2c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0833.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0833 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5611. -/ +theorem bounds_13_5611 : exactInterval 13 5611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5611 : oddCount 5611 13 = 10 ∧ acceleratedOrbit 13 5611 = 40459 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5611) = 3 ^ 10 * m + 40459 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5611.1, data_13_5611.2] + +/-- Complete interval computation for depth 13, residue 5612. -/ +theorem bounds_13_5612 : exactInterval 13 5612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5612 : oddCount 5612 13 = 6 ∧ acceleratedOrbit 13 5612 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5612) = 3 ^ 6 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5612.1, data_13_5612.2] + +/-- Complete interval computation for depth 13, residue 5613. -/ +theorem bounds_13_5613 : exactInterval 13 5613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5613 : oddCount 5613 13 = 6 ∧ acceleratedOrbit 13 5613 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5613) = 3 ^ 6 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5613.1, data_13_5613.2] + +/-- Complete interval computation for depth 13, residue 5614. -/ +theorem bounds_13_5614 : exactInterval 13 5614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5614 : oddCount 5614 13 = 6 ∧ acceleratedOrbit 13 5614 = 500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5614) = 3 ^ 6 * m + 500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5614.1, data_13_5614.2] + +/-- Complete interval computation for depth 13, residue 5615. -/ +theorem bounds_13_5615 : exactInterval 13 5615 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5615) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5615 : oddCount 5615 13 = 8 ∧ acceleratedOrbit 13 5615 = 4498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5615) = 3 ^ 8 * m + 4498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5615.1, data_13_5615.2] + +/-- Complete interval computation for depth 13, residue 5616. -/ +theorem bounds_13_5616 : exactInterval 13 5616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5616 : oddCount 5616 13 = 5 ∧ acceleratedOrbit 13 5616 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5616) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5616.1, data_13_5616.2] + +/-- Complete interval computation for depth 13, residue 5617. -/ +theorem bounds_13_5617 : exactInterval 13 5617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5617 : oddCount 5617 13 = 5 ∧ acceleratedOrbit 13 5617 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5617) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5617.1, data_13_5617.2] + +/-- Complete interval computation for depth 13, residue 5618. -/ +theorem bounds_13_5618 : exactInterval 13 5618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5618 : oddCount 5618 13 = 7 ∧ acceleratedOrbit 13 5618 = 1502 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5618) = 3 ^ 7 * m + 1502 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5618.1, data_13_5618.2] + +/-- Complete interval computation for depth 13, residue 5619. -/ +theorem bounds_13_5619 : exactInterval 13 5619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5619 : oddCount 5619 13 = 7 ∧ acceleratedOrbit 13 5619 = 1502 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5619) = 3 ^ 7 * m + 1502 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5619.1, data_13_5619.2] + +/-- Complete interval computation for depth 13, residue 5620. -/ +theorem bounds_13_5620 : exactInterval 13 5620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5620 : oddCount 5620 13 = 5 ∧ acceleratedOrbit 13 5620 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5620) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5620.1, data_13_5620.2] + +/-- Complete interval computation for depth 13, residue 5621. -/ +theorem bounds_13_5621 : exactInterval 13 5621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5621 : oddCount 5621 13 = 5 ∧ acceleratedOrbit 13 5621 = 167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5621) = 3 ^ 5 * m + 167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5621.1, data_13_5621.2] + +/-- Complete interval computation for depth 13, residue 5622. -/ +theorem bounds_13_5622 : exactInterval 13 5622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5622 : oddCount 5622 13 = 9 ∧ acceleratedOrbit 13 5622 = 13517 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5622) = 3 ^ 9 * m + 13517 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5622.1, data_13_5622.2] + +/-- Complete interval computation for depth 13, residue 5623. -/ +theorem bounds_13_5623 : exactInterval 13 5623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5623 : oddCount 5623 13 = 9 ∧ acceleratedOrbit 13 5623 = 13517 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5623) = 3 ^ 9 * m + 13517 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5623.1, data_13_5623.2] + +/-- Complete interval computation for depth 13, residue 5624. -/ +theorem bounds_13_5624 : exactInterval 13 5624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5624 : oddCount 5624 13 = 8 ∧ acceleratedOrbit 13 5624 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5624) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5624.1, data_13_5624.2] + +/-- Complete interval computation for depth 13, residue 5625. -/ +theorem bounds_13_5625 : exactInterval 13 5625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5625 : oddCount 5625 13 = 8 ∧ acceleratedOrbit 13 5625 = 4508 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5625) = 3 ^ 8 * m + 4508 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5625.1, data_13_5625.2] + +end Collatz.Research.StoppingAtlas.Batch0833 From ab22800b5d83c639a4acc1eb32e20279ee6cf3f7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:06 +0530 Subject: [PATCH 0834/1001] proof: certify atlas Batch0834 (13:5626 to 13:5641) --- Collatz/Research/StoppingAtlas/Batch0834.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0834.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0834.lean b/Collatz/Research/StoppingAtlas/Batch0834.lean new file mode 100644 index 00000000..3a921880 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0834.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0834 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5626. -/ +theorem bounds_13_5626 : exactInterval 13 5626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5626 : oddCount 5626 13 = 8 ∧ acceleratedOrbit 13 5626 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5626) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5626.1, data_13_5626.2] + +/-- Complete interval computation for depth 13, residue 5627. -/ +theorem bounds_13_5627 : exactInterval 13 5627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5627 : oddCount 5627 13 = 9 ∧ acceleratedOrbit 13 5627 = 13526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5627) = 3 ^ 9 * m + 13526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5627.1, data_13_5627.2] + +/-- Complete interval computation for depth 13, residue 5628. -/ +theorem bounds_13_5628 : exactInterval 13 5628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5628 : oddCount 5628 13 = 8 ∧ acceleratedOrbit 13 5628 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5628) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5628.1, data_13_5628.2] + +/-- Complete interval computation for depth 13, residue 5629. -/ +theorem bounds_13_5629 : exactInterval 13 5629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5629 : oddCount 5629 13 = 8 ∧ acceleratedOrbit 13 5629 = 4511 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5629) = 3 ^ 8 * m + 4511 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5629.1, data_13_5629.2] + +/-- Complete interval computation for depth 13, residue 5630. -/ +theorem bounds_13_5630 : exactInterval 13 5630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5630 : oddCount 5630 13 = 9 ∧ acceleratedOrbit 13 5630 = 13532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5630) = 3 ^ 9 * m + 13532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5630.1, data_13_5630.2] + +/-- Complete interval computation for depth 13, residue 5631. -/ +theorem bounds_13_5631 : exactInterval 13 5631 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5631) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5631 : oddCount 5631 13 = 9 ∧ acceleratedOrbit 13 5631 = 13532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5631) = 3 ^ 9 * m + 13532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5631.1, data_13_5631.2] + +/-- Complete interval computation for depth 13, residue 5632. -/ +theorem bounds_13_5632 : exactInterval 13 5632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5632 : oddCount 5632 13 = 3 ∧ acceleratedOrbit 13 5632 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5632) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5632.1, data_13_5632.2] + +/-- Complete interval computation for depth 13, residue 5633. -/ +theorem bounds_13_5633 : exactInterval 13 5633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5633 : oddCount 5633 13 = 7 ∧ acceleratedOrbit 13 5633 = 1505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5633) = 3 ^ 7 * m + 1505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5633.1, data_13_5633.2] + +/-- Complete interval computation for depth 13, residue 5634. -/ +theorem bounds_13_5634 : exactInterval 13 5634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5634 : oddCount 5634 13 = 6 ∧ acceleratedOrbit 13 5634 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5634) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5634.1, data_13_5634.2] + +/-- Complete interval computation for depth 13, residue 5635. -/ +theorem bounds_13_5635 : exactInterval 13 5635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5635 : oddCount 5635 13 = 6 ∧ acceleratedOrbit 13 5635 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5635) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5635.1, data_13_5635.2] + +/-- Complete interval computation for depth 13, residue 5636. -/ +theorem bounds_13_5636 : exactInterval 13 5636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5636 : oddCount 5636 13 = 6 ∧ acceleratedOrbit 13 5636 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5636) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5636.1, data_13_5636.2] + +/-- Complete interval computation for depth 13, residue 5637. -/ +theorem bounds_13_5637 : exactInterval 13 5637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5637 : oddCount 5637 13 = 6 ∧ acceleratedOrbit 13 5637 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5637) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5637.1, data_13_5637.2] + +/-- Complete interval computation for depth 13, residue 5638. -/ +theorem bounds_13_5638 : exactInterval 13 5638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5638 : oddCount 5638 13 = 6 ∧ acceleratedOrbit 13 5638 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5638) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5638.1, data_13_5638.2] + +/-- Complete interval computation for depth 13, residue 5639. -/ +theorem bounds_13_5639 : exactInterval 13 5639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5639 : oddCount 5639 13 = 6 ∧ acceleratedOrbit 13 5639 = 502 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5639) = 3 ^ 6 * m + 502 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5639.1, data_13_5639.2] + +/-- Complete interval computation for depth 13, residue 5640. -/ +theorem bounds_13_5640 : exactInterval 13 5640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5640 : oddCount 5640 13 = 4 ∧ acceleratedOrbit 13 5640 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5640) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5640.1, data_13_5640.2] + +/-- Complete interval computation for depth 13, residue 5641. -/ +theorem bounds_13_5641 : exactInterval 13 5641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5641 : oddCount 5641 13 = 7 ∧ acceleratedOrbit 13 5641 = 1507 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5641) = 3 ^ 7 * m + 1507 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5641.1, data_13_5641.2] + +end Collatz.Research.StoppingAtlas.Batch0834 From ada9f40eca7596d042c3f8a131237c51f0eca5d0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0835/1001] proof: certify atlas Batch0835 (13:5642 to 13:5656) --- Collatz/Research/StoppingAtlas/Batch0835.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0835.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0835.lean b/Collatz/Research/StoppingAtlas/Batch0835.lean new file mode 100644 index 00000000..57e3c2b5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0835.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0835 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5642. -/ +theorem bounds_13_5642 : exactInterval 13 5642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5642 : oddCount 5642 13 = 4 ∧ acceleratedOrbit 13 5642 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5642) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5642.1, data_13_5642.2] + +/-- Complete interval computation for depth 13, residue 5643. -/ +theorem bounds_13_5643 : exactInterval 13 5643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5643 : oddCount 5643 13 = 6 ∧ acceleratedOrbit 13 5643 = 503 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5643) = 3 ^ 6 * m + 503 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5643.1, data_13_5643.2] + +/-- Complete interval computation for depth 13, residue 5644. -/ +theorem bounds_13_5644 : exactInterval 13 5644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5644 : oddCount 5644 13 = 4 ∧ acceleratedOrbit 13 5644 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5644) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5644.1, data_13_5644.2] + +/-- Complete interval computation for depth 13, residue 5645. -/ +theorem bounds_13_5645 : exactInterval 13 5645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5645 : oddCount 5645 13 = 4 ∧ acceleratedOrbit 13 5645 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5645) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5645.1, data_13_5645.2] + +/-- Complete interval computation for depth 13, residue 5646. -/ +theorem bounds_13_5646 : exactInterval 13 5646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5646 : oddCount 5646 13 = 8 ∧ acceleratedOrbit 13 5646 = 4526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5646) = 3 ^ 8 * m + 4526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5646.1, data_13_5646.2] + +/-- Complete interval computation for depth 13, residue 5647. -/ +theorem bounds_13_5647 : exactInterval 13 5647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5647 : oddCount 5647 13 = 8 ∧ acceleratedOrbit 13 5647 = 4526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5647) = 3 ^ 8 * m + 4526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5647.1, data_13_5647.2] + +/-- Complete interval computation for depth 13, residue 5648. -/ +theorem bounds_13_5648 : exactInterval 13 5648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5648 : oddCount 5648 13 = 6 ∧ acceleratedOrbit 13 5648 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5648) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5648.1, data_13_5648.2] + +/-- Complete interval computation for depth 13, residue 5649. -/ +theorem bounds_13_5649 : exactInterval 13 5649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5649 : oddCount 5649 13 = 4 ∧ acceleratedOrbit 13 5649 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5649) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5649.1, data_13_5649.2] + +/-- Complete interval computation for depth 13, residue 5650. -/ +theorem bounds_13_5650 : exactInterval 13 5650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5650 : oddCount 5650 13 = 8 ∧ acceleratedOrbit 13 5650 = 4529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5650) = 3 ^ 8 * m + 4529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5650.1, data_13_5650.2] + +/-- Complete interval computation for depth 13, residue 5651. -/ +theorem bounds_13_5651 : exactInterval 13 5651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5651 : oddCount 5651 13 = 8 ∧ acceleratedOrbit 13 5651 = 4529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5651) = 3 ^ 8 * m + 4529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5651.1, data_13_5651.2] + +/-- Complete interval computation for depth 13, residue 5652. -/ +theorem bounds_13_5652 : exactInterval 13 5652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5652 : oddCount 5652 13 = 6 ∧ acceleratedOrbit 13 5652 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5652) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5652.1, data_13_5652.2] + +/-- Complete interval computation for depth 13, residue 5653. -/ +theorem bounds_13_5653 : exactInterval 13 5653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5653 : oddCount 5653 13 = 6 ∧ acceleratedOrbit 13 5653 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5653) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5653.1, data_13_5653.2] + +/-- Complete interval computation for depth 13, residue 5654. -/ +theorem bounds_13_5654 : exactInterval 13 5654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5654 : oddCount 5654 13 = 8 ∧ acceleratedOrbit 13 5654 = 4535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5654) = 3 ^ 8 * m + 4535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5654.1, data_13_5654.2] + +/-- Complete interval computation for depth 13, residue 5655. -/ +theorem bounds_13_5655 : exactInterval 13 5655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5655 : oddCount 5655 13 = 8 ∧ acceleratedOrbit 13 5655 = 4535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5655) = 3 ^ 8 * m + 4535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5655.1, data_13_5655.2] + +/-- Complete interval computation for depth 13, residue 5656. -/ +theorem bounds_13_5656 : exactInterval 13 5656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5656 : oddCount 5656 13 = 6 ∧ acceleratedOrbit 13 5656 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5656) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5656.1, data_13_5656.2] + +end Collatz.Research.StoppingAtlas.Batch0835 From f8de4e6c1ed1a2c443df04728683dd92078a225f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0836/1001] proof: certify atlas Batch0836 (13:5657 to 13:5671) --- Collatz/Research/StoppingAtlas/Batch0836.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0836.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0836.lean b/Collatz/Research/StoppingAtlas/Batch0836.lean new file mode 100644 index 00000000..51ff33a2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0836.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0836 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5657. -/ +theorem bounds_13_5657 : exactInterval 13 5657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5657 : oddCount 5657 13 = 8 ∧ acceleratedOrbit 13 5657 = 4535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5657) = 3 ^ 8 * m + 4535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5657.1, data_13_5657.2] + +/-- Complete interval computation for depth 13, residue 5658. -/ +theorem bounds_13_5658 : exactInterval 13 5658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5658 : oddCount 5658 13 = 6 ∧ acceleratedOrbit 13 5658 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5658) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5658.1, data_13_5658.2] + +/-- Complete interval computation for depth 13, residue 5659. -/ +theorem bounds_13_5659 : exactInterval 13 5659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5659 : oddCount 5659 13 = 9 ∧ acceleratedOrbit 13 5659 = 13601 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5659) = 3 ^ 9 * m + 13601 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5659.1, data_13_5659.2] + +/-- Complete interval computation for depth 13, residue 5660. -/ +theorem bounds_13_5660 : exactInterval 13 5660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5660 : oddCount 5660 13 = 4 ∧ acceleratedOrbit 13 5660 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5660) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5660.1, data_13_5660.2] + +/-- Complete interval computation for depth 13, residue 5661. -/ +theorem bounds_13_5661 : exactInterval 13 5661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5661 : oddCount 5661 13 = 4 ∧ acceleratedOrbit 13 5661 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5661) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5661.1, data_13_5661.2] + +/-- Complete interval computation for depth 13, residue 5662. -/ +theorem bounds_13_5662 : exactInterval 13 5662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5662 : oddCount 5662 13 = 4 ∧ acceleratedOrbit 13 5662 = 56 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5662) = 3 ^ 4 * m + 56 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5662.1, data_13_5662.2] + +/-- Complete interval computation for depth 13, residue 5663. -/ +theorem bounds_13_5663 : exactInterval 13 5663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5663 : oddCount 5663 13 = 9 ∧ acceleratedOrbit 13 5663 = 13610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5663) = 3 ^ 9 * m + 13610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5663.1, data_13_5663.2] + +/-- Complete interval computation for depth 13, residue 5664. -/ +theorem bounds_13_5664 : exactInterval 13 5664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5664 : oddCount 5664 13 = 3 ∧ acceleratedOrbit 13 5664 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5664) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5664.1, data_13_5664.2] + +/-- Complete interval computation for depth 13, residue 5665. -/ +theorem bounds_13_5665 : exactInterval 13 5665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5665 : oddCount 5665 13 = 7 ∧ acceleratedOrbit 13 5665 = 1514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5665) = 3 ^ 7 * m + 1514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5665.1, data_13_5665.2] + +/-- Complete interval computation for depth 13, residue 5666. -/ +theorem bounds_13_5666 : exactInterval 13 5666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5666 : oddCount 5666 13 = 6 ∧ acceleratedOrbit 13 5666 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5666) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5666.1, data_13_5666.2] + +/-- Complete interval computation for depth 13, residue 5667. -/ +theorem bounds_13_5667 : exactInterval 13 5667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5667 : oddCount 5667 13 = 6 ∧ acceleratedOrbit 13 5667 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5667) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5667.1, data_13_5667.2] + +/-- Complete interval computation for depth 13, residue 5668. -/ +theorem bounds_13_5668 : exactInterval 13 5668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5668 : oddCount 5668 13 = 6 ∧ acceleratedOrbit 13 5668 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5668) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5668.1, data_13_5668.2] + +/-- Complete interval computation for depth 13, residue 5669. -/ +theorem bounds_13_5669 : exactInterval 13 5669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5669 : oddCount 5669 13 = 6 ∧ acceleratedOrbit 13 5669 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5669) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5669.1, data_13_5669.2] + +/-- Complete interval computation for depth 13, residue 5670. -/ +theorem bounds_13_5670 : exactInterval 13 5670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5670 : oddCount 5670 13 = 6 ∧ acceleratedOrbit 13 5670 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5670) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5670.1, data_13_5670.2] + +/-- Complete interval computation for depth 13, residue 5671. -/ +theorem bounds_13_5671 : exactInterval 13 5671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5671 : oddCount 5671 13 = 6 ∧ acceleratedOrbit 13 5671 = 505 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5671) = 3 ^ 6 * m + 505 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5671.1, data_13_5671.2] + +end Collatz.Research.StoppingAtlas.Batch0836 From 38c392649b0ed907cf3a36f58e1cbdceb041414b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0837/1001] proof: certify atlas Batch0837 (13:5672 to 13:5687) --- Collatz/Research/StoppingAtlas/Batch0837.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0837.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0837.lean b/Collatz/Research/StoppingAtlas/Batch0837.lean new file mode 100644 index 00000000..2811f12b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0837.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0837 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5672. -/ +theorem bounds_13_5672 : exactInterval 13 5672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5672 : oddCount 5672 13 = 3 ∧ acceleratedOrbit 13 5672 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5672) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5672.1, data_13_5672.2] + +/-- Complete interval computation for depth 13, residue 5673. -/ +theorem bounds_13_5673 : exactInterval 13 5673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5673 : oddCount 5673 13 = 11 ∧ acceleratedOrbit 13 5673 = 122714 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5673) = 3 ^ 11 * m + 122714 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5673.1, data_13_5673.2] + +/-- Complete interval computation for depth 13, residue 5674. -/ +theorem bounds_13_5674 : exactInterval 13 5674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5674 : oddCount 5674 13 = 3 ∧ acceleratedOrbit 13 5674 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5674) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5674.1, data_13_5674.2] + +/-- Complete interval computation for depth 13, residue 5675. -/ +theorem bounds_13_5675 : exactInterval 13 5675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5675 : oddCount 5675 13 = 6 ∧ acceleratedOrbit 13 5675 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5675) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5675.1, data_13_5675.2] + +/-- Complete interval computation for depth 13, residue 5676. -/ +theorem bounds_13_5676 : exactInterval 13 5676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5676 : oddCount 5676 13 = 6 ∧ acceleratedOrbit 13 5676 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5676) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5676.1, data_13_5676.2] + +/-- Complete interval computation for depth 13, residue 5677. -/ +theorem bounds_13_5677 : exactInterval 13 5677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5677 : oddCount 5677 13 = 6 ∧ acceleratedOrbit 13 5677 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5677) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5677.1, data_13_5677.2] + +/-- Complete interval computation for depth 13, residue 5678. -/ +theorem bounds_13_5678 : exactInterval 13 5678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5678 : oddCount 5678 13 = 6 ∧ acceleratedOrbit 13 5678 = 506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5678) = 3 ^ 6 * m + 506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5678.1, data_13_5678.2] + +/-- Complete interval computation for depth 13, residue 5679. -/ +theorem bounds_13_5679 : exactInterval 13 5679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5679 : oddCount 5679 13 = 10 ∧ acceleratedOrbit 13 5679 = 40945 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5679) = 3 ^ 10 * m + 40945 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5679.1, data_13_5679.2] + +/-- Complete interval computation for depth 13, residue 5680. -/ +theorem bounds_13_5680 : exactInterval 13 5680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5680 : oddCount 5680 13 = 3 ∧ acceleratedOrbit 13 5680 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5680) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5680.1, data_13_5680.2] + +/-- Complete interval computation for depth 13, residue 5681. -/ +theorem bounds_13_5681 : exactInterval 13 5681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5681 : oddCount 5681 13 = 8 ∧ acceleratedOrbit 13 5681 = 4556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5681) = 3 ^ 8 * m + 4556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5681.1, data_13_5681.2] + +/-- Complete interval computation for depth 13, residue 5682. -/ +theorem bounds_13_5682 : exactInterval 13 5682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5682 : oddCount 5682 13 = 8 ∧ acceleratedOrbit 13 5682 = 4556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5682) = 3 ^ 8 * m + 4556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5682.1, data_13_5682.2] + +/-- Complete interval computation for depth 13, residue 5683. -/ +theorem bounds_13_5683 : exactInterval 13 5683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5683 : oddCount 5683 13 = 8 ∧ acceleratedOrbit 13 5683 = 4556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5683) = 3 ^ 8 * m + 4556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5683.1, data_13_5683.2] + +/-- Complete interval computation for depth 13, residue 5684. -/ +theorem bounds_13_5684 : exactInterval 13 5684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5684 : oddCount 5684 13 = 3 ∧ acceleratedOrbit 13 5684 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5684) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5684.1, data_13_5684.2] + +/-- Complete interval computation for depth 13, residue 5685. -/ +theorem bounds_13_5685 : exactInterval 13 5685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5685 : oddCount 5685 13 = 3 ∧ acceleratedOrbit 13 5685 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5685) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5685.1, data_13_5685.2] + +/-- Complete interval computation for depth 13, residue 5686. -/ +theorem bounds_13_5686 : exactInterval 13 5686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5686 : oddCount 5686 13 = 10 ∧ acceleratedOrbit 13 5686 = 41006 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5686) = 3 ^ 10 * m + 41006 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5686.1, data_13_5686.2] + +/-- Complete interval computation for depth 13, residue 5687. -/ +theorem bounds_13_5687 : exactInterval 13 5687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5687 : oddCount 5687 13 = 10 ∧ acceleratedOrbit 13 5687 = 41006 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5687) = 3 ^ 10 * m + 41006 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5687.1, data_13_5687.2] + +end Collatz.Research.StoppingAtlas.Batch0837 From 355d003c1d7208b3f598f05f2eacb2ebece85be7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0838/1001] proof: certify atlas Batch0838 (13:5688 to 13:5702) --- Collatz/Research/StoppingAtlas/Batch0838.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0838.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0838.lean b/Collatz/Research/StoppingAtlas/Batch0838.lean new file mode 100644 index 00000000..cad557b6 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0838.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0838 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5688. -/ +theorem bounds_13_5688 : exactInterval 13 5688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5688 : oddCount 5688 13 = 5 ∧ acceleratedOrbit 13 5688 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5688) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5688.1, data_13_5688.2] + +/-- Complete interval computation for depth 13, residue 5689. -/ +theorem bounds_13_5689 : exactInterval 13 5689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5689 : oddCount 5689 13 = 7 ∧ acceleratedOrbit 13 5689 = 1520 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5689) = 3 ^ 7 * m + 1520 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5689.1, data_13_5689.2] + +/-- Complete interval computation for depth 13, residue 5690. -/ +theorem bounds_13_5690 : exactInterval 13 5690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5690 : oddCount 5690 13 = 5 ∧ acceleratedOrbit 13 5690 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5690) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5690.1, data_13_5690.2] + +/-- Complete interval computation for depth 13, residue 5691. -/ +theorem bounds_13_5691 : exactInterval 13 5691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5691 : oddCount 5691 13 = 8 ∧ acceleratedOrbit 13 5691 = 4562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5691) = 3 ^ 8 * m + 4562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5691.1, data_13_5691.2] + +/-- Complete interval computation for depth 13, residue 5692. -/ +theorem bounds_13_5692 : exactInterval 13 5692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5692 : oddCount 5692 13 = 5 ∧ acceleratedOrbit 13 5692 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5692) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5692.1, data_13_5692.2] + +/-- Complete interval computation for depth 13, residue 5693. -/ +theorem bounds_13_5693 : exactInterval 13 5693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5693 : oddCount 5693 13 = 5 ∧ acceleratedOrbit 13 5693 = 169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5693) = 3 ^ 5 * m + 169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5693.1, data_13_5693.2] + +/-- Complete interval computation for depth 13, residue 5694. -/ +theorem bounds_13_5694 : exactInterval 13 5694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5694 : oddCount 5694 13 = 9 ∧ acceleratedOrbit 13 5694 = 13688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5694) = 3 ^ 9 * m + 13688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5694.1, data_13_5694.2] + +/-- Complete interval computation for depth 13, residue 5695. -/ +theorem bounds_13_5695 : exactInterval 13 5695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5695 : oddCount 5695 13 = 9 ∧ acceleratedOrbit 13 5695 = 13688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5695) = 3 ^ 9 * m + 13688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5695.1, data_13_5695.2] + +/-- Complete interval computation for depth 13, residue 5696. -/ +theorem bounds_13_5696 : exactInterval 13 5696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5696 : oddCount 5696 13 = 3 ∧ acceleratedOrbit 13 5696 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5696) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5696.1, data_13_5696.2] + +/-- Complete interval computation for depth 13, residue 5697. -/ +theorem bounds_13_5697 : exactInterval 13 5697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5697 : oddCount 5697 13 = 6 ∧ acceleratedOrbit 13 5697 = 508 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5697) = 3 ^ 6 * m + 508 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5697.1, data_13_5697.2] + +/-- Complete interval computation for depth 13, residue 5698. -/ +theorem bounds_13_5698 : exactInterval 13 5698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5698 : oddCount 5698 13 = 6 ∧ acceleratedOrbit 13 5698 = 508 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5698) = 3 ^ 6 * m + 508 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5698.1, data_13_5698.2] + +/-- Complete interval computation for depth 13, residue 5699. -/ +theorem bounds_13_5699 : exactInterval 13 5699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5699 : oddCount 5699 13 = 6 ∧ acceleratedOrbit 13 5699 = 508 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5699) = 3 ^ 6 * m + 508 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5699.1, data_13_5699.2] + +/-- Complete interval computation for depth 13, residue 5700. -/ +theorem bounds_13_5700 : exactInterval 13 5700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5700 : oddCount 5700 13 = 5 ∧ acceleratedOrbit 13 5700 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5700) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5700.1, data_13_5700.2] + +/-- Complete interval computation for depth 13, residue 5701. -/ +theorem bounds_13_5701 : exactInterval 13 5701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5701 : oddCount 5701 13 = 5 ∧ acceleratedOrbit 13 5701 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5701) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5701.1, data_13_5701.2] + +/-- Complete interval computation for depth 13, residue 5702. -/ +theorem bounds_13_5702 : exactInterval 13 5702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5702 : oddCount 5702 13 = 5 ∧ acceleratedOrbit 13 5702 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5702) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5702.1, data_13_5702.2] + +end Collatz.Research.StoppingAtlas.Batch0838 From ad385ede5a1a112ccdb024538403dc9586dfe510 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0839/1001] proof: certify atlas Batch0839 (13:5703 to 13:5718) --- Collatz/Research/StoppingAtlas/Batch0839.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0839.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0839.lean b/Collatz/Research/StoppingAtlas/Batch0839.lean new file mode 100644 index 00000000..91768388 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0839.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0839 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5703. -/ +theorem bounds_13_5703 : exactInterval 13 5703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5703 : oddCount 5703 13 = 7 ∧ acceleratedOrbit 13 5703 = 1523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5703) = 3 ^ 7 * m + 1523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5703.1, data_13_5703.2] + +/-- Complete interval computation for depth 13, residue 5704. -/ +theorem bounds_13_5704 : exactInterval 13 5704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5704 : oddCount 5704 13 = 5 ∧ acceleratedOrbit 13 5704 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5704) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5704.1, data_13_5704.2] + +/-- Complete interval computation for depth 13, residue 5705. -/ +theorem bounds_13_5705 : exactInterval 13 5705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5705 : oddCount 5705 13 = 9 ∧ acceleratedOrbit 13 5705 = 13715 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5705) = 3 ^ 9 * m + 13715 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5705.1, data_13_5705.2] + +/-- Complete interval computation for depth 13, residue 5706. -/ +theorem bounds_13_5706 : exactInterval 13 5706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5706 : oddCount 5706 13 = 5 ∧ acceleratedOrbit 13 5706 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5706) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5706.1, data_13_5706.2] + +/-- Complete interval computation for depth 13, residue 5707. -/ +theorem bounds_13_5707 : exactInterval 13 5707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5707 : oddCount 5707 13 = 5 ∧ acceleratedOrbit 13 5707 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5707) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5707.1, data_13_5707.2] + +/-- Complete interval computation for depth 13, residue 5708. -/ +theorem bounds_13_5708 : exactInterval 13 5708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5708 : oddCount 5708 13 = 5 ∧ acceleratedOrbit 13 5708 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5708) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5708.1, data_13_5708.2] + +/-- Complete interval computation for depth 13, residue 5709. -/ +theorem bounds_13_5709 : exactInterval 13 5709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5709 : oddCount 5709 13 = 5 ∧ acceleratedOrbit 13 5709 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5709) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5709.1, data_13_5709.2] + +/-- Complete interval computation for depth 13, residue 5710. -/ +theorem bounds_13_5710 : exactInterval 13 5710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5710 : oddCount 5710 13 = 8 ∧ acceleratedOrbit 13 5710 = 4576 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5710) = 3 ^ 8 * m + 4576 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5710.1, data_13_5710.2] + +/-- Complete interval computation for depth 13, residue 5711. -/ +theorem bounds_13_5711 : exactInterval 13 5711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5711 : oddCount 5711 13 = 8 ∧ acceleratedOrbit 13 5711 = 4576 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5711) = 3 ^ 8 * m + 4576 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5711.1, data_13_5711.2] + +/-- Complete interval computation for depth 13, residue 5712. -/ +theorem bounds_13_5712 : exactInterval 13 5712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5712 : oddCount 5712 13 = 3 ∧ acceleratedOrbit 13 5712 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5712) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5712.1, data_13_5712.2] + +/-- Complete interval computation for depth 13, residue 5713. -/ +theorem bounds_13_5713 : exactInterval 13 5713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5713 : oddCount 5713 13 = 8 ∧ acceleratedOrbit 13 5713 = 4580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5713) = 3 ^ 8 * m + 4580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5713.1, data_13_5713.2] + +/-- Complete interval computation for depth 13, residue 5714. -/ +theorem bounds_13_5714 : exactInterval 13 5714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5714 : oddCount 5714 13 = 8 ∧ acceleratedOrbit 13 5714 = 4580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5714) = 3 ^ 8 * m + 4580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5714.1, data_13_5714.2] + +/-- Complete interval computation for depth 13, residue 5715. -/ +theorem bounds_13_5715 : exactInterval 13 5715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5715 : oddCount 5715 13 = 8 ∧ acceleratedOrbit 13 5715 = 4580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5715) = 3 ^ 8 * m + 4580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5715.1, data_13_5715.2] + +/-- Complete interval computation for depth 13, residue 5716. -/ +theorem bounds_13_5716 : exactInterval 13 5716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5716 : oddCount 5716 13 = 3 ∧ acceleratedOrbit 13 5716 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5716) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5716.1, data_13_5716.2] + +/-- Complete interval computation for depth 13, residue 5717. -/ +theorem bounds_13_5717 : exactInterval 13 5717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5717 : oddCount 5717 13 = 3 ∧ acceleratedOrbit 13 5717 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5717) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5717.1, data_13_5717.2] + +/-- Complete interval computation for depth 13, residue 5718. -/ +theorem bounds_13_5718 : exactInterval 13 5718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5718 : oddCount 5718 13 = 7 ∧ acceleratedOrbit 13 5718 = 1529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5718) = 3 ^ 7 * m + 1529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5718.1, data_13_5718.2] + +end Collatz.Research.StoppingAtlas.Batch0839 From 45d6d59567eff393c01b45420d101317e307227e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0840/1001] proof: certify atlas Batch0840 (13:5719 to 13:5733) --- Collatz/Research/StoppingAtlas/Batch0840.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0840.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0840.lean b/Collatz/Research/StoppingAtlas/Batch0840.lean new file mode 100644 index 00000000..3097201a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0840.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0840 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5719. -/ +theorem bounds_13_5719 : exactInterval 13 5719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5719 : oddCount 5719 13 = 7 ∧ acceleratedOrbit 13 5719 = 1529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5719) = 3 ^ 7 * m + 1529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5719.1, data_13_5719.2] + +/-- Complete interval computation for depth 13, residue 5720. -/ +theorem bounds_13_5720 : exactInterval 13 5720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5720 : oddCount 5720 13 = 6 ∧ acceleratedOrbit 13 5720 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5720) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5720.1, data_13_5720.2] + +/-- Complete interval computation for depth 13, residue 5721. -/ +theorem bounds_13_5721 : exactInterval 13 5721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5721 : oddCount 5721 13 = 7 ∧ acceleratedOrbit 13 5721 = 1529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5721) = 3 ^ 7 * m + 1529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5721.1, data_13_5721.2] + +/-- Complete interval computation for depth 13, residue 5722. -/ +theorem bounds_13_5722 : exactInterval 13 5722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5722 : oddCount 5722 13 = 6 ∧ acceleratedOrbit 13 5722 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5722) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5722.1, data_13_5722.2] + +/-- Complete interval computation for depth 13, residue 5723. -/ +theorem bounds_13_5723 : exactInterval 13 5723 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5723) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5723 : oddCount 5723 13 = 8 ∧ acceleratedOrbit 13 5723 = 4585 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5723) = 3 ^ 8 * m + 4585 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5723.1, data_13_5723.2] + +/-- Complete interval computation for depth 13, residue 5724. -/ +theorem bounds_13_5724 : exactInterval 13 5724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5724 : oddCount 5724 13 = 6 ∧ acceleratedOrbit 13 5724 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5724) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5724.1, data_13_5724.2] + +/-- Complete interval computation for depth 13, residue 5725. -/ +theorem bounds_13_5725 : exactInterval 13 5725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5725 : oddCount 5725 13 = 6 ∧ acceleratedOrbit 13 5725 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5725) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5725.1, data_13_5725.2] + +/-- Complete interval computation for depth 13, residue 5726. -/ +theorem bounds_13_5726 : exactInterval 13 5726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5726 : oddCount 5726 13 = 8 ∧ acceleratedOrbit 13 5726 = 4589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5726) = 3 ^ 8 * m + 4589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5726.1, data_13_5726.2] + +/-- Complete interval computation for depth 13, residue 5727. -/ +theorem bounds_13_5727 : exactInterval 13 5727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5727 : oddCount 5727 13 = 8 ∧ acceleratedOrbit 13 5727 = 4589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5727) = 3 ^ 8 * m + 4589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5727.1, data_13_5727.2] + +/-- Complete interval computation for depth 13, residue 5728. -/ +theorem bounds_13_5728 : exactInterval 13 5728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5728 : oddCount 5728 13 = 3 ∧ acceleratedOrbit 13 5728 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5728) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5728.1, data_13_5728.2] + +/-- Complete interval computation for depth 13, residue 5729. -/ +theorem bounds_13_5729 : exactInterval 13 5729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5729 : oddCount 5729 13 = 5 ∧ acceleratedOrbit 13 5729 = 170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5729) = 3 ^ 5 * m + 170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5729.1, data_13_5729.2] + +/-- Complete interval computation for depth 13, residue 5730. -/ +theorem bounds_13_5730 : exactInterval 13 5730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5730 : oddCount 5730 13 = 6 ∧ acceleratedOrbit 13 5730 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5730) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5730.1, data_13_5730.2] + +/-- Complete interval computation for depth 13, residue 5731. -/ +theorem bounds_13_5731 : exactInterval 13 5731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5731 : oddCount 5731 13 = 6 ∧ acceleratedOrbit 13 5731 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5731) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5731.1, data_13_5731.2] + +/-- Complete interval computation for depth 13, residue 5732. -/ +theorem bounds_13_5732 : exactInterval 13 5732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5732 : oddCount 5732 13 = 6 ∧ acceleratedOrbit 13 5732 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5732) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5732.1, data_13_5732.2] + +/-- Complete interval computation for depth 13, residue 5733. -/ +theorem bounds_13_5733 : exactInterval 13 5733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5733 : oddCount 5733 13 = 6 ∧ acceleratedOrbit 13 5733 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5733) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5733.1, data_13_5733.2] + +end Collatz.Research.StoppingAtlas.Batch0840 From a315c22de8759f281508f1eb6f52de155442db86 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:07 +0530 Subject: [PATCH 0841/1001] proof: certify atlas Batch0841 (13:5734 to 13:5748) --- Collatz/Research/StoppingAtlas/Batch0841.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0841.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0841.lean b/Collatz/Research/StoppingAtlas/Batch0841.lean new file mode 100644 index 00000000..2c5ef4fb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0841.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0841 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5734. -/ +theorem bounds_13_5734 : exactInterval 13 5734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5734 : oddCount 5734 13 = 6 ∧ acceleratedOrbit 13 5734 = 512 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5734) = 3 ^ 6 * m + 512 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5734.1, data_13_5734.2] + +/-- Complete interval computation for depth 13, residue 5735. -/ +theorem bounds_13_5735 : exactInterval 13 5735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5735 : oddCount 5735 13 = 9 ∧ acceleratedOrbit 13 5735 = 13783 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5735) = 3 ^ 9 * m + 13783 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5735.1, data_13_5735.2] + +/-- Complete interval computation for depth 13, residue 5736. -/ +theorem bounds_13_5736 : exactInterval 13 5736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5736 : oddCount 5736 13 = 3 ∧ acceleratedOrbit 13 5736 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5736) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5736.1, data_13_5736.2] + +/-- Complete interval computation for depth 13, residue 5737. -/ +theorem bounds_13_5737 : exactInterval 13 5737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5737 : oddCount 5737 13 = 9 ∧ acceleratedOrbit 13 5737 = 13790 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5737) = 3 ^ 9 * m + 13790 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5737.1, data_13_5737.2] + +/-- Complete interval computation for depth 13, residue 5738. -/ +theorem bounds_13_5738 : exactInterval 13 5738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5738 : oddCount 5738 13 = 3 ∧ acceleratedOrbit 13 5738 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5738) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5738.1, data_13_5738.2] + +/-- Complete interval computation for depth 13, residue 5739. -/ +theorem bounds_13_5739 : exactInterval 13 5739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5739 : oddCount 5739 13 = 9 ∧ acceleratedOrbit 13 5739 = 13796 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5739) = 3 ^ 9 * m + 13796 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5739.1, data_13_5739.2] + +/-- Complete interval computation for depth 13, residue 5740. -/ +theorem bounds_13_5740 : exactInterval 13 5740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5740 : oddCount 5740 13 = 7 ∧ acceleratedOrbit 13 5740 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5740) = 3 ^ 7 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5740.1, data_13_5740.2] + +/-- Complete interval computation for depth 13, residue 5741. -/ +theorem bounds_13_5741 : exactInterval 13 5741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5741 : oddCount 5741 13 = 7 ∧ acceleratedOrbit 13 5741 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5741) = 3 ^ 7 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5741.1, data_13_5741.2] + +/-- Complete interval computation for depth 13, residue 5742. -/ +theorem bounds_13_5742 : exactInterval 13 5742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5742 : oddCount 5742 13 = 7 ∧ acceleratedOrbit 13 5742 = 1534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5742) = 3 ^ 7 * m + 1534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5742.1, data_13_5742.2] + +/-- Complete interval computation for depth 13, residue 5743. -/ +theorem bounds_13_5743 : exactInterval 13 5743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5743 : oddCount 5743 13 = 8 ∧ acceleratedOrbit 13 5743 = 4601 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5743) = 3 ^ 8 * m + 4601 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5743.1, data_13_5743.2] + +/-- Complete interval computation for depth 13, residue 5744. -/ +theorem bounds_13_5744 : exactInterval 13 5744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5744 : oddCount 5744 13 = 8 ∧ acceleratedOrbit 13 5744 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5744) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5744.1, data_13_5744.2] + +/-- Complete interval computation for depth 13, residue 5745. -/ +theorem bounds_13_5745 : exactInterval 13 5745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5745 : oddCount 5745 13 = 3 ∧ acceleratedOrbit 13 5745 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5745) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5745.1, data_13_5745.2] + +/-- Complete interval computation for depth 13, residue 5746. -/ +theorem bounds_13_5746 : exactInterval 13 5746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5746 : oddCount 5746 13 = 8 ∧ acceleratedOrbit 13 5746 = 4607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5746) = 3 ^ 8 * m + 4607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5746.1, data_13_5746.2] + +/-- Complete interval computation for depth 13, residue 5747. -/ +theorem bounds_13_5747 : exactInterval 13 5747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5747 : oddCount 5747 13 = 8 ∧ acceleratedOrbit 13 5747 = 4607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5747) = 3 ^ 8 * m + 4607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5747.1, data_13_5747.2] + +/-- Complete interval computation for depth 13, residue 5748. -/ +theorem bounds_13_5748 : exactInterval 13 5748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5748 : oddCount 5748 13 = 8 ∧ acceleratedOrbit 13 5748 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5748) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5748.1, data_13_5748.2] + +end Collatz.Research.StoppingAtlas.Batch0841 From 39f5db7ee9f27b8be1f81a5a3fcf260cdc404e4f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:08 +0530 Subject: [PATCH 0842/1001] proof: certify atlas Batch0842 (13:5749 to 13:5764) --- Collatz/Research/StoppingAtlas/Batch0842.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0842.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0842.lean b/Collatz/Research/StoppingAtlas/Batch0842.lean new file mode 100644 index 00000000..6589e90e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0842.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0842 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5749. -/ +theorem bounds_13_5749 : exactInterval 13 5749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5749 : oddCount 5749 13 = 8 ∧ acceleratedOrbit 13 5749 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5749) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5749.1, data_13_5749.2] + +/-- Complete interval computation for depth 13, residue 5750. -/ +theorem bounds_13_5750 : exactInterval 13 5750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5750 : oddCount 5750 13 = 7 ∧ acceleratedOrbit 13 5750 = 1538 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5750) = 3 ^ 7 * m + 1538 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5750.1, data_13_5750.2] + +/-- Complete interval computation for depth 13, residue 5751. -/ +theorem bounds_13_5751 : exactInterval 13 5751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5751 : oddCount 5751 13 = 7 ∧ acceleratedOrbit 13 5751 = 1538 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5751) = 3 ^ 7 * m + 1538 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5751.1, data_13_5751.2] + +/-- Complete interval computation for depth 13, residue 5752. -/ +theorem bounds_13_5752 : exactInterval 13 5752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5752 : oddCount 5752 13 = 8 ∧ acceleratedOrbit 13 5752 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5752) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5752.1, data_13_5752.2] + +/-- Complete interval computation for depth 13, residue 5753. -/ +theorem bounds_13_5753 : exactInterval 13 5753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5753 : oddCount 5753 13 = 8 ∧ acceleratedOrbit 13 5753 = 4610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5753) = 3 ^ 8 * m + 4610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5753.1, data_13_5753.2] + +/-- Complete interval computation for depth 13, residue 5754. -/ +theorem bounds_13_5754 : exactInterval 13 5754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5754 : oddCount 5754 13 = 8 ∧ acceleratedOrbit 13 5754 = 4616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5754) = 3 ^ 8 * m + 4616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5754.1, data_13_5754.2] + +/-- Complete interval computation for depth 13, residue 5755. -/ +theorem bounds_13_5755 : exactInterval 13 5755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5755 : oddCount 5755 13 = 7 ∧ acceleratedOrbit 13 5755 = 1538 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5755) = 3 ^ 7 * m + 1538 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5755.1, data_13_5755.2] + +/-- Complete interval computation for depth 13, residue 5756. -/ +theorem bounds_13_5756 : exactInterval 13 5756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5756 : oddCount 5756 13 = 9 ∧ acceleratedOrbit 13 5756 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5756) = 3 ^ 9 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5756.1, data_13_5756.2] + +/-- Complete interval computation for depth 13, residue 5757. -/ +theorem bounds_13_5757 : exactInterval 13 5757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5757 : oddCount 5757 13 = 9 ∧ acceleratedOrbit 13 5757 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5757) = 3 ^ 9 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5757.1, data_13_5757.2] + +/-- Complete interval computation for depth 13, residue 5758. -/ +theorem bounds_13_5758 : exactInterval 13 5758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5758 : oddCount 5758 13 = 9 ∧ acceleratedOrbit 13 5758 = 13841 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5758) = 3 ^ 9 * m + 13841 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5758.1, data_13_5758.2] + +/-- Complete interval computation for depth 13, residue 5759. -/ +theorem bounds_13_5759 : exactInterval 13 5759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5759 : oddCount 5759 13 = 10 ∧ acceleratedOrbit 13 5759 = 41519 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5759) = 3 ^ 10 * m + 41519 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5759.1, data_13_5759.2] + +/-- Complete interval computation for depth 13, residue 5760. -/ +theorem bounds_13_5760 : exactInterval 13 5760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5760 : oddCount 5760 13 = 3 ∧ acceleratedOrbit 13 5760 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5760) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5760.1, data_13_5760.2] + +/-- Complete interval computation for depth 13, residue 5761. -/ +theorem bounds_13_5761 : exactInterval 13 5761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5761 : oddCount 5761 13 = 10 ∧ acceleratedOrbit 13 5761 = 41552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5761) = 3 ^ 10 * m + 41552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5761.1, data_13_5761.2] + +/-- Complete interval computation for depth 13, residue 5762. -/ +theorem bounds_13_5762 : exactInterval 13 5762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5762 : oddCount 5762 13 = 3 ∧ acceleratedOrbit 13 5762 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5762) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5762.1, data_13_5762.2] + +/-- Complete interval computation for depth 13, residue 5763. -/ +theorem bounds_13_5763 : exactInterval 13 5763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5763 : oddCount 5763 13 = 3 ∧ acceleratedOrbit 13 5763 = 19 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5763) = 3 ^ 3 * m + 19 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5763.1, data_13_5763.2] + +/-- Complete interval computation for depth 13, residue 5764. -/ +theorem bounds_13_5764 : exactInterval 13 5764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5764 : oddCount 5764 13 = 6 ∧ acceleratedOrbit 13 5764 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5764) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5764.1, data_13_5764.2] + +end Collatz.Research.StoppingAtlas.Batch0842 From 49db07c6defc99cc0cbc3fe4003a9bced13b3647 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:08 +0530 Subject: [PATCH 0843/1001] proof: certify atlas Batch0843 (13:5765 to 13:5779) --- Collatz/Research/StoppingAtlas/Batch0843.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0843.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0843.lean b/Collatz/Research/StoppingAtlas/Batch0843.lean new file mode 100644 index 00000000..fc110432 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0843.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0843 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5765. -/ +theorem bounds_13_5765 : exactInterval 13 5765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5765 : oddCount 5765 13 = 6 ∧ acceleratedOrbit 13 5765 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5765) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5765.1, data_13_5765.2] + +/-- Complete interval computation for depth 13, residue 5766. -/ +theorem bounds_13_5766 : exactInterval 13 5766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5766 : oddCount 5766 13 = 6 ∧ acceleratedOrbit 13 5766 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5766) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5766.1, data_13_5766.2] + +/-- Complete interval computation for depth 13, residue 5767. -/ +theorem bounds_13_5767 : exactInterval 13 5767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5767 : oddCount 5767 13 = 7 ∧ acceleratedOrbit 13 5767 = 1541 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5767) = 3 ^ 7 * m + 1541 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5767.1, data_13_5767.2] + +/-- Complete interval computation for depth 13, residue 5768. -/ +theorem bounds_13_5768 : exactInterval 13 5768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5768 : oddCount 5768 13 = 5 ∧ acceleratedOrbit 13 5768 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5768) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5768.1, data_13_5768.2] + +/-- Complete interval computation for depth 13, residue 5769. -/ +theorem bounds_13_5769 : exactInterval 13 5769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5769 : oddCount 5769 13 = 8 ∧ acceleratedOrbit 13 5769 = 4622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5769) = 3 ^ 8 * m + 4622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5769.1, data_13_5769.2] + +/-- Complete interval computation for depth 13, residue 5770. -/ +theorem bounds_13_5770 : exactInterval 13 5770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5770 : oddCount 5770 13 = 5 ∧ acceleratedOrbit 13 5770 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5770) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5770.1, data_13_5770.2] + +/-- Complete interval computation for depth 13, residue 5771. -/ +theorem bounds_13_5771 : exactInterval 13 5771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5771 : oddCount 5771 13 = 6 ∧ acceleratedOrbit 13 5771 = 514 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5771) = 3 ^ 6 * m + 514 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5771.1, data_13_5771.2] + +/-- Complete interval computation for depth 13, residue 5772. -/ +theorem bounds_13_5772 : exactInterval 13 5772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5772 : oddCount 5772 13 = 5 ∧ acceleratedOrbit 13 5772 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5772) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5772.1, data_13_5772.2] + +/-- Complete interval computation for depth 13, residue 5773. -/ +theorem bounds_13_5773 : exactInterval 13 5773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5773 : oddCount 5773 13 = 5 ∧ acceleratedOrbit 13 5773 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5773) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5773.1, data_13_5773.2] + +/-- Complete interval computation for depth 13, residue 5774. -/ +theorem bounds_13_5774 : exactInterval 13 5774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5774 : oddCount 5774 13 = 8 ∧ acceleratedOrbit 13 5774 = 4627 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5774) = 3 ^ 8 * m + 4627 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5774.1, data_13_5774.2] + +/-- Complete interval computation for depth 13, residue 5775. -/ +theorem bounds_13_5775 : exactInterval 13 5775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5775 : oddCount 5775 13 = 8 ∧ acceleratedOrbit 13 5775 = 4627 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5775) = 3 ^ 8 * m + 4627 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5775.1, data_13_5775.2] + +/-- Complete interval computation for depth 13, residue 5776. -/ +theorem bounds_13_5776 : exactInterval 13 5776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5776 : oddCount 5776 13 = 5 ∧ acceleratedOrbit 13 5776 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5776) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5776.1, data_13_5776.2] + +/-- Complete interval computation for depth 13, residue 5777. -/ +theorem bounds_13_5777 : exactInterval 13 5777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5777 : oddCount 5777 13 = 6 ∧ acceleratedOrbit 13 5777 = 515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5777) = 3 ^ 6 * m + 515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5777.1, data_13_5777.2] + +/-- Complete interval computation for depth 13, residue 5778. -/ +theorem bounds_13_5778 : exactInterval 13 5778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5778 : oddCount 5778 13 = 6 ∧ acceleratedOrbit 13 5778 = 515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5778) = 3 ^ 6 * m + 515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5778.1, data_13_5778.2] + +/-- Complete interval computation for depth 13, residue 5779. -/ +theorem bounds_13_5779 : exactInterval 13 5779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5779 : oddCount 5779 13 = 6 ∧ acceleratedOrbit 13 5779 = 515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5779) = 3 ^ 6 * m + 515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5779.1, data_13_5779.2] + +end Collatz.Research.StoppingAtlas.Batch0843 From 3efac762ce2c5fdf801ee325777b2dd8165daf24 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:08 +0530 Subject: [PATCH 0844/1001] proof: certify atlas Batch0844 (13:5780 to 13:5794) --- Collatz/Research/StoppingAtlas/Batch0844.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0844.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0844.lean b/Collatz/Research/StoppingAtlas/Batch0844.lean new file mode 100644 index 00000000..e55fb43b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0844.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0844 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5780. -/ +theorem bounds_13_5780 : exactInterval 13 5780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5780 : oddCount 5780 13 = 5 ∧ acceleratedOrbit 13 5780 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5780) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5780.1, data_13_5780.2] + +/-- Complete interval computation for depth 13, residue 5781. -/ +theorem bounds_13_5781 : exactInterval 13 5781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5781 : oddCount 5781 13 = 5 ∧ acceleratedOrbit 13 5781 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5781) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5781.1, data_13_5781.2] + +/-- Complete interval computation for depth 13, residue 5782. -/ +theorem bounds_13_5782 : exactInterval 13 5782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5782 : oddCount 5782 13 = 5 ∧ acceleratedOrbit 13 5782 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5782) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5782.1, data_13_5782.2] + +/-- Complete interval computation for depth 13, residue 5783. -/ +theorem bounds_13_5783 : exactInterval 13 5783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5783 : oddCount 5783 13 = 5 ∧ acceleratedOrbit 13 5783 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5783) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5783.1, data_13_5783.2] + +/-- Complete interval computation for depth 13, residue 5784. -/ +theorem bounds_13_5784 : exactInterval 13 5784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5784 : oddCount 5784 13 = 5 ∧ acceleratedOrbit 13 5784 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5784) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5784.1, data_13_5784.2] + +/-- Complete interval computation for depth 13, residue 5785. -/ +theorem bounds_13_5785 : exactInterval 13 5785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5785 : oddCount 5785 13 = 8 ∧ acceleratedOrbit 13 5785 = 4637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5785) = 3 ^ 8 * m + 4637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5785.1, data_13_5785.2] + +/-- Complete interval computation for depth 13, residue 5786. -/ +theorem bounds_13_5786 : exactInterval 13 5786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5786 : oddCount 5786 13 = 5 ∧ acceleratedOrbit 13 5786 = 172 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5786) = 3 ^ 5 * m + 172 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5786.1, data_13_5786.2] + +/-- Complete interval computation for depth 13, residue 5787. -/ +theorem bounds_13_5787 : exactInterval 13 5787 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5787) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5787 : oddCount 5787 13 = 8 ∧ acceleratedOrbit 13 5787 = 4636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5787) = 3 ^ 8 * m + 4636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5787.1, data_13_5787.2] + +/-- Complete interval computation for depth 13, residue 5788. -/ +theorem bounds_13_5788 : exactInterval 13 5788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5788 : oddCount 5788 13 = 7 ∧ acceleratedOrbit 13 5788 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5788) = 3 ^ 7 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5788.1, data_13_5788.2] + +/-- Complete interval computation for depth 13, residue 5789. -/ +theorem bounds_13_5789 : exactInterval 13 5789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5789 : oddCount 5789 13 = 7 ∧ acceleratedOrbit 13 5789 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5789) = 3 ^ 7 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5789.1, data_13_5789.2] + +/-- Complete interval computation for depth 13, residue 5790. -/ +theorem bounds_13_5790 : exactInterval 13 5790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5790 : oddCount 5790 13 = 7 ∧ acceleratedOrbit 13 5790 = 1547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5790) = 3 ^ 7 * m + 1547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5790.1, data_13_5790.2] + +/-- Complete interval computation for depth 13, residue 5791. -/ +theorem bounds_13_5791 : exactInterval 13 5791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5791 : oddCount 5791 13 = 11 ∧ acceleratedOrbit 13 5791 = 125252 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5791) = 3 ^ 11 * m + 125252 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5791.1, data_13_5791.2] + +/-- Complete interval computation for depth 13, residue 5792. -/ +theorem bounds_13_5792 : exactInterval 13 5792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5792 : oddCount 5792 13 = 3 ∧ acceleratedOrbit 13 5792 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5792) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5792.1, data_13_5792.2] + +/-- Complete interval computation for depth 13, residue 5793. -/ +theorem bounds_13_5793 : exactInterval 13 5793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5793 : oddCount 5793 13 = 8 ∧ acceleratedOrbit 13 5793 = 4643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5793) = 3 ^ 8 * m + 4643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5793.1, data_13_5793.2] + +/-- Complete interval computation for depth 13, residue 5794. -/ +theorem bounds_13_5794 : exactInterval 13 5794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5794 : oddCount 5794 13 = 7 ∧ acceleratedOrbit 13 5794 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5794) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5794.1, data_13_5794.2] + +end Collatz.Research.StoppingAtlas.Batch0844 From 1d3b782258343eabbf94214b4a09865a97a34f51 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:08 +0530 Subject: [PATCH 0845/1001] proof: certify atlas Batch0845 (13:5795 to 13:5810) --- Collatz/Research/StoppingAtlas/Batch0845.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0845.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0845.lean b/Collatz/Research/StoppingAtlas/Batch0845.lean new file mode 100644 index 00000000..0f311216 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0845.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0845 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5795. -/ +theorem bounds_13_5795 : exactInterval 13 5795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5795 : oddCount 5795 13 = 7 ∧ acceleratedOrbit 13 5795 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5795) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5795.1, data_13_5795.2] + +/-- Complete interval computation for depth 13, residue 5796. -/ +theorem bounds_13_5796 : exactInterval 13 5796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5796 : oddCount 5796 13 = 7 ∧ acceleratedOrbit 13 5796 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5796) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5796.1, data_13_5796.2] + +/-- Complete interval computation for depth 13, residue 5797. -/ +theorem bounds_13_5797 : exactInterval 13 5797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5797 : oddCount 5797 13 = 7 ∧ acceleratedOrbit 13 5797 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5797) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5797.1, data_13_5797.2] + +/-- Complete interval computation for depth 13, residue 5798. -/ +theorem bounds_13_5798 : exactInterval 13 5798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5798 : oddCount 5798 13 = 7 ∧ acceleratedOrbit 13 5798 = 1549 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5798) = 3 ^ 7 * m + 1549 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5798.1, data_13_5798.2] + +/-- Complete interval computation for depth 13, residue 5799. -/ +theorem bounds_13_5799 : exactInterval 13 5799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5799 : oddCount 5799 13 = 8 ∧ acceleratedOrbit 13 5799 = 4646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5799) = 3 ^ 8 * m + 4646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5799.1, data_13_5799.2] + +/-- Complete interval computation for depth 13, residue 5800. -/ +theorem bounds_13_5800 : exactInterval 13 5800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5800 : oddCount 5800 13 = 3 ∧ acceleratedOrbit 13 5800 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5800) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5800.1, data_13_5800.2] + +/-- Complete interval computation for depth 13, residue 5801. -/ +theorem bounds_13_5801 : exactInterval 13 5801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5801 : oddCount 5801 13 = 9 ∧ acceleratedOrbit 13 5801 = 13942 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5801) = 3 ^ 9 * m + 13942 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5801.1, data_13_5801.2] + +/-- Complete interval computation for depth 13, residue 5802. -/ +theorem bounds_13_5802 : exactInterval 13 5802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5802 : oddCount 5802 13 = 3 ∧ acceleratedOrbit 13 5802 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5802) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5802.1, data_13_5802.2] + +/-- Complete interval computation for depth 13, residue 5803. -/ +theorem bounds_13_5803 : exactInterval 13 5803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5803 : oddCount 5803 13 = 7 ∧ acceleratedOrbit 13 5803 = 1550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5803) = 3 ^ 7 * m + 1550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5803.1, data_13_5803.2] + +/-- Complete interval computation for depth 13, residue 5804. -/ +theorem bounds_13_5804 : exactInterval 13 5804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5804 : oddCount 5804 13 = 7 ∧ acceleratedOrbit 13 5804 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5804) = 3 ^ 7 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5804.1, data_13_5804.2] + +/-- Complete interval computation for depth 13, residue 5805. -/ +theorem bounds_13_5805 : exactInterval 13 5805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5805 : oddCount 5805 13 = 7 ∧ acceleratedOrbit 13 5805 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5805) = 3 ^ 7 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5805.1, data_13_5805.2] + +/-- Complete interval computation for depth 13, residue 5806. -/ +theorem bounds_13_5806 : exactInterval 13 5806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5806 : oddCount 5806 13 = 7 ∧ acceleratedOrbit 13 5806 = 1552 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5806) = 3 ^ 7 * m + 1552 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5806.1, data_13_5806.2] + +/-- Complete interval computation for depth 13, residue 5807. -/ +theorem bounds_13_5807 : exactInterval 13 5807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5807 : oddCount 5807 13 = 9 ∧ acceleratedOrbit 13 5807 = 13958 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5807) = 3 ^ 9 * m + 13958 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5807.1, data_13_5807.2] + +/-- Complete interval computation for depth 13, residue 5808. -/ +theorem bounds_13_5808 : exactInterval 13 5808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5808 : oddCount 5808 13 = 5 ∧ acceleratedOrbit 13 5808 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5808) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5808.1, data_13_5808.2] + +/-- Complete interval computation for depth 13, residue 5809. -/ +theorem bounds_13_5809 : exactInterval 13 5809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5809 : oddCount 5809 13 = 5 ∧ acceleratedOrbit 13 5809 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5809) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5809.1, data_13_5809.2] + +/-- Complete interval computation for depth 13, residue 5810. -/ +theorem bounds_13_5810 : exactInterval 13 5810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5810 : oddCount 5810 13 = 5 ∧ acceleratedOrbit 13 5810 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5810) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5810.1, data_13_5810.2] + +end Collatz.Research.StoppingAtlas.Batch0845 From 1efde336c1d43aa7da382fe1a3e46a6486d1192f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:08 +0530 Subject: [PATCH 0846/1001] proof: certify atlas Batch0846 (13:5811 to 13:5825) --- Collatz/Research/StoppingAtlas/Batch0846.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0846.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0846.lean b/Collatz/Research/StoppingAtlas/Batch0846.lean new file mode 100644 index 00000000..f895577e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0846.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0846 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5811. -/ +theorem bounds_13_5811 : exactInterval 13 5811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5811 : oddCount 5811 13 = 5 ∧ acceleratedOrbit 13 5811 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5811) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5811.1, data_13_5811.2] + +/-- Complete interval computation for depth 13, residue 5812. -/ +theorem bounds_13_5812 : exactInterval 13 5812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5812 : oddCount 5812 13 = 5 ∧ acceleratedOrbit 13 5812 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5812) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5812.1, data_13_5812.2] + +/-- Complete interval computation for depth 13, residue 5813. -/ +theorem bounds_13_5813 : exactInterval 13 5813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5813 : oddCount 5813 13 = 5 ∧ acceleratedOrbit 13 5813 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5813) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5813.1, data_13_5813.2] + +/-- Complete interval computation for depth 13, residue 5814. -/ +theorem bounds_13_5814 : exactInterval 13 5814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5814 : oddCount 5814 13 = 7 ∧ acceleratedOrbit 13 5814 = 1553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5814) = 3 ^ 7 * m + 1553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5814.1, data_13_5814.2] + +/-- Complete interval computation for depth 13, residue 5815. -/ +theorem bounds_13_5815 : exactInterval 13 5815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5815 : oddCount 5815 13 = 7 ∧ acceleratedOrbit 13 5815 = 1553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5815) = 3 ^ 7 * m + 1553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5815.1, data_13_5815.2] + +/-- Complete interval computation for depth 13, residue 5816. -/ +theorem bounds_13_5816 : exactInterval 13 5816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5816 : oddCount 5816 13 = 5 ∧ acceleratedOrbit 13 5816 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5816) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5816.1, data_13_5816.2] + +/-- Complete interval computation for depth 13, residue 5817. -/ +theorem bounds_13_5817 : exactInterval 13 5817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5817 : oddCount 5817 13 = 6 ∧ acceleratedOrbit 13 5817 = 518 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5817) = 3 ^ 6 * m + 518 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5817.1, data_13_5817.2] + +/-- Complete interval computation for depth 13, residue 5818. -/ +theorem bounds_13_5818 : exactInterval 13 5818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5818 : oddCount 5818 13 = 5 ∧ acceleratedOrbit 13 5818 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5818) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5818.1, data_13_5818.2] + +/-- Complete interval computation for depth 13, residue 5819. -/ +theorem bounds_13_5819 : exactInterval 13 5819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5819 : oddCount 5819 13 = 6 ∧ acceleratedOrbit 13 5819 = 518 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5819) = 3 ^ 6 * m + 518 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5819.1, data_13_5819.2] + +/-- Complete interval computation for depth 13, residue 5820. -/ +theorem bounds_13_5820 : exactInterval 13 5820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5820 : oddCount 5820 13 = 7 ∧ acceleratedOrbit 13 5820 = 1556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5820) = 3 ^ 7 * m + 1556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5820.1, data_13_5820.2] + +/-- Complete interval computation for depth 13, residue 5821. -/ +theorem bounds_13_5821 : exactInterval 13 5821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5821 : oddCount 5821 13 = 7 ∧ acceleratedOrbit 13 5821 = 1556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5821) = 3 ^ 7 * m + 1556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5821.1, data_13_5821.2] + +/-- Complete interval computation for depth 13, residue 5822. -/ +theorem bounds_13_5822 : exactInterval 13 5822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5822 : oddCount 5822 13 = 7 ∧ acceleratedOrbit 13 5822 = 1556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5822) = 3 ^ 7 * m + 1556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5822.1, data_13_5822.2] + +/-- Complete interval computation for depth 13, residue 5823. -/ +theorem bounds_13_5823 : exactInterval 13 5823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5823 : oddCount 5823 13 = 9 ∧ acceleratedOrbit 13 5823 = 13994 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5823) = 3 ^ 9 * m + 13994 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5823.1, data_13_5823.2] + +/-- Complete interval computation for depth 13, residue 5824. -/ +theorem bounds_13_5824 : exactInterval 13 5824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5824 : oddCount 5824 13 = 5 ∧ acceleratedOrbit 13 5824 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5824) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5824.1, data_13_5824.2] + +/-- Complete interval computation for depth 13, residue 5825. -/ +theorem bounds_13_5825 : exactInterval 13 5825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5825 : oddCount 5825 13 = 5 ∧ acceleratedOrbit 13 5825 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5825) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5825.1, data_13_5825.2] + +end Collatz.Research.StoppingAtlas.Batch0846 From e90262e8e03c1ca76f120ae1c0f2bea8a86ce036 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:08 +0530 Subject: [PATCH 0847/1001] proof: certify atlas Batch0847 (13:5826 to 13:5840) --- Collatz/Research/StoppingAtlas/Batch0847.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0847.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0847.lean b/Collatz/Research/StoppingAtlas/Batch0847.lean new file mode 100644 index 00000000..4c1d7676 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0847.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0847 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5826. -/ +theorem bounds_13_5826 : exactInterval 13 5826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5826 : oddCount 5826 13 = 9 ∧ acceleratedOrbit 13 5826 = 14012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5826) = 3 ^ 9 * m + 14012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5826.1, data_13_5826.2] + +/-- Complete interval computation for depth 13, residue 5827. -/ +theorem bounds_13_5827 : exactInterval 13 5827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5827 : oddCount 5827 13 = 9 ∧ acceleratedOrbit 13 5827 = 14012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5827) = 3 ^ 9 * m + 14012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5827.1, data_13_5827.2] + +/-- Complete interval computation for depth 13, residue 5828. -/ +theorem bounds_13_5828 : exactInterval 13 5828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5828 : oddCount 5828 13 = 4 ∧ acceleratedOrbit 13 5828 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5828) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5828.1, data_13_5828.2] + +/-- Complete interval computation for depth 13, residue 5829. -/ +theorem bounds_13_5829 : exactInterval 13 5829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5829 : oddCount 5829 13 = 4 ∧ acceleratedOrbit 13 5829 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5829) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5829.1, data_13_5829.2] + +/-- Complete interval computation for depth 13, residue 5830. -/ +theorem bounds_13_5830 : exactInterval 13 5830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5830 : oddCount 5830 13 = 4 ∧ acceleratedOrbit 13 5830 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5830) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5830.1, data_13_5830.2] + +/-- Complete interval computation for depth 13, residue 5831. -/ +theorem bounds_13_5831 : exactInterval 13 5831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5831 : oddCount 5831 13 = 5 ∧ acceleratedOrbit 13 5831 = 173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5831) = 3 ^ 5 * m + 173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5831.1, data_13_5831.2] + +/-- Complete interval computation for depth 13, residue 5832. -/ +theorem bounds_13_5832 : exactInterval 13 5832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5832 : oddCount 5832 13 = 4 ∧ acceleratedOrbit 13 5832 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5832) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5832.1, data_13_5832.2] + +/-- Complete interval computation for depth 13, residue 5833. -/ +theorem bounds_13_5833 : exactInterval 13 5833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5833 : oddCount 5833 13 = 7 ∧ acceleratedOrbit 13 5833 = 1559 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5833) = 3 ^ 7 * m + 1559 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5833.1, data_13_5833.2] + +/-- Complete interval computation for depth 13, residue 5834. -/ +theorem bounds_13_5834 : exactInterval 13 5834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5834 : oddCount 5834 13 = 4 ∧ acceleratedOrbit 13 5834 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5834) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5834.1, data_13_5834.2] + +/-- Complete interval computation for depth 13, residue 5835. -/ +theorem bounds_13_5835 : exactInterval 13 5835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5835 : oddCount 5835 13 = 7 ∧ acceleratedOrbit 13 5835 = 1559 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5835) = 3 ^ 7 * m + 1559 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5835.1, data_13_5835.2] + +/-- Complete interval computation for depth 13, residue 5836. -/ +theorem bounds_13_5836 : exactInterval 13 5836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5836 : oddCount 5836 13 = 4 ∧ acceleratedOrbit 13 5836 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5836) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5836.1, data_13_5836.2] + +/-- Complete interval computation for depth 13, residue 5837. -/ +theorem bounds_13_5837 : exactInterval 13 5837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5837 : oddCount 5837 13 = 4 ∧ acceleratedOrbit 13 5837 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5837) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5837.1, data_13_5837.2] + +/-- Complete interval computation for depth 13, residue 5838. -/ +theorem bounds_13_5838 : exactInterval 13 5838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5838 : oddCount 5838 13 = 9 ∧ acceleratedOrbit 13 5838 = 14033 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5838) = 3 ^ 9 * m + 14033 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5838.1, data_13_5838.2] + +/-- Complete interval computation for depth 13, residue 5839. -/ +theorem bounds_13_5839 : exactInterval 13 5839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5839 : oddCount 5839 13 = 9 ∧ acceleratedOrbit 13 5839 = 14033 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5839) = 3 ^ 9 * m + 14033 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5839.1, data_13_5839.2] + +/-- Complete interval computation for depth 13, residue 5840. -/ +theorem bounds_13_5840 : exactInterval 13 5840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5840 : oddCount 5840 13 = 5 ∧ acceleratedOrbit 13 5840 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5840) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5840.1, data_13_5840.2] + +end Collatz.Research.StoppingAtlas.Batch0847 From 31f2772841b420ece4d3eb11903c20366f73a28e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:09 +0530 Subject: [PATCH 0848/1001] proof: certify atlas Batch0848 (13:5841 to 13:5856) --- Collatz/Research/StoppingAtlas/Batch0848.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0848.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0848.lean b/Collatz/Research/StoppingAtlas/Batch0848.lean new file mode 100644 index 00000000..ce60f627 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0848.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0848 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5841. -/ +theorem bounds_13_5841 : exactInterval 13 5841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5841 : oddCount 5841 13 = 7 ∧ acceleratedOrbit 13 5841 = 1561 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5841) = 3 ^ 7 * m + 1561 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5841.1, data_13_5841.2] + +/-- Complete interval computation for depth 13, residue 5842. -/ +theorem bounds_13_5842 : exactInterval 13 5842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5842 : oddCount 5842 13 = 7 ∧ acceleratedOrbit 13 5842 = 1561 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5842) = 3 ^ 7 * m + 1561 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5842.1, data_13_5842.2] + +/-- Complete interval computation for depth 13, residue 5843. -/ +theorem bounds_13_5843 : exactInterval 13 5843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5843 : oddCount 5843 13 = 7 ∧ acceleratedOrbit 13 5843 = 1561 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5843) = 3 ^ 7 * m + 1561 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5843.1, data_13_5843.2] + +/-- Complete interval computation for depth 13, residue 5844. -/ +theorem bounds_13_5844 : exactInterval 13 5844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5844 : oddCount 5844 13 = 5 ∧ acceleratedOrbit 13 5844 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5844) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5844.1, data_13_5844.2] + +/-- Complete interval computation for depth 13, residue 5845. -/ +theorem bounds_13_5845 : exactInterval 13 5845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5845 : oddCount 5845 13 = 5 ∧ acceleratedOrbit 13 5845 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5845) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5845.1, data_13_5845.2] + +/-- Complete interval computation for depth 13, residue 5846. -/ +theorem bounds_13_5846 : exactInterval 13 5846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5846 : oddCount 5846 13 = 6 ∧ acceleratedOrbit 13 5846 = 521 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5846) = 3 ^ 6 * m + 521 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5846.1, data_13_5846.2] + +/-- Complete interval computation for depth 13, residue 5847. -/ +theorem bounds_13_5847 : exactInterval 13 5847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5847 : oddCount 5847 13 = 6 ∧ acceleratedOrbit 13 5847 = 521 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5847) = 3 ^ 6 * m + 521 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5847.1, data_13_5847.2] + +/-- Complete interval computation for depth 13, residue 5848. -/ +theorem bounds_13_5848 : exactInterval 13 5848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5848 : oddCount 5848 13 = 7 ∧ acceleratedOrbit 13 5848 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5848) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5848.1, data_13_5848.2] + +/-- Complete interval computation for depth 13, residue 5849. -/ +theorem bounds_13_5849 : exactInterval 13 5849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5849 : oddCount 5849 13 = 7 ∧ acceleratedOrbit 13 5849 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5849) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5849.1, data_13_5849.2] + +/-- Complete interval computation for depth 13, residue 5850. -/ +theorem bounds_13_5850 : exactInterval 13 5850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5850 : oddCount 5850 13 = 7 ∧ acceleratedOrbit 13 5850 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5850) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5850.1, data_13_5850.2] + +/-- Complete interval computation for depth 13, residue 5851. -/ +theorem bounds_13_5851 : exactInterval 13 5851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5851 : oddCount 5851 13 = 8 ∧ acceleratedOrbit 13 5851 = 4688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5851) = 3 ^ 8 * m + 4688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5851.1, data_13_5851.2] + +/-- Complete interval computation for depth 13, residue 5852. -/ +theorem bounds_13_5852 : exactInterval 13 5852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5852 : oddCount 5852 13 = 7 ∧ acceleratedOrbit 13 5852 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5852) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5852.1, data_13_5852.2] + +/-- Complete interval computation for depth 13, residue 5853. -/ +theorem bounds_13_5853 : exactInterval 13 5853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5853 : oddCount 5853 13 = 7 ∧ acceleratedOrbit 13 5853 = 1565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5853) = 3 ^ 7 * m + 1565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5853.1, data_13_5853.2] + +/-- Complete interval computation for depth 13, residue 5854. -/ +theorem bounds_13_5854 : exactInterval 13 5854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5854 : oddCount 5854 13 = 8 ∧ acceleratedOrbit 13 5854 = 4691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5854) = 3 ^ 8 * m + 4691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5854.1, data_13_5854.2] + +/-- Complete interval computation for depth 13, residue 5855. -/ +theorem bounds_13_5855 : exactInterval 13 5855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5855 : oddCount 5855 13 = 8 ∧ acceleratedOrbit 13 5855 = 4691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5855) = 3 ^ 8 * m + 4691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5855.1, data_13_5855.2] + +/-- Complete interval computation for depth 13, residue 5856. -/ +theorem bounds_13_5856 : exactInterval 13 5856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5856 : oddCount 5856 13 = 5 ∧ acceleratedOrbit 13 5856 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5856) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5856.1, data_13_5856.2] + +end Collatz.Research.StoppingAtlas.Batch0848 From e58ed76ac5b0cc0ee2df15b69361d5f4910cfe14 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:09 +0530 Subject: [PATCH 0849/1001] proof: certify atlas Batch0849 (13:5857 to 13:5871) --- Collatz/Research/StoppingAtlas/Batch0849.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0849.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0849.lean b/Collatz/Research/StoppingAtlas/Batch0849.lean new file mode 100644 index 00000000..b0a4b01e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0849.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0849 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5857. -/ +theorem bounds_13_5857 : exactInterval 13 5857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5857 : oddCount 5857 13 = 8 ∧ acceleratedOrbit 13 5857 = 4693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5857) = 3 ^ 8 * m + 4693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5857.1, data_13_5857.2] + +/-- Complete interval computation for depth 13, residue 5858. -/ +theorem bounds_13_5858 : exactInterval 13 5858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5858 : oddCount 5858 13 = 5 ∧ acceleratedOrbit 13 5858 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5858) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5858.1, data_13_5858.2] + +/-- Complete interval computation for depth 13, residue 5859. -/ +theorem bounds_13_5859 : exactInterval 13 5859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5859 : oddCount 5859 13 = 5 ∧ acceleratedOrbit 13 5859 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5859) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5859.1, data_13_5859.2] + +/-- Complete interval computation for depth 13, residue 5860. -/ +theorem bounds_13_5860 : exactInterval 13 5860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5860 : oddCount 5860 13 = 4 ∧ acceleratedOrbit 13 5860 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5860) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5860.1, data_13_5860.2] + +/-- Complete interval computation for depth 13, residue 5861. -/ +theorem bounds_13_5861 : exactInterval 13 5861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5861 : oddCount 5861 13 = 4 ∧ acceleratedOrbit 13 5861 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5861) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5861.1, data_13_5861.2] + +/-- Complete interval computation for depth 13, residue 5862. -/ +theorem bounds_13_5862 : exactInterval 13 5862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5862 : oddCount 5862 13 = 4 ∧ acceleratedOrbit 13 5862 = 58 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5862) = 3 ^ 4 * m + 58 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5862.1, data_13_5862.2] + +/-- Complete interval computation for depth 13, residue 5863. -/ +theorem bounds_13_5863 : exactInterval 13 5863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5863 : oddCount 5863 13 = 10 ∧ acceleratedOrbit 13 5863 = 42272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5863) = 3 ^ 10 * m + 42272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5863.1, data_13_5863.2] + +/-- Complete interval computation for depth 13, residue 5864. -/ +theorem bounds_13_5864 : exactInterval 13 5864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5864 : oddCount 5864 13 = 5 ∧ acceleratedOrbit 13 5864 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5864) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5864.1, data_13_5864.2] + +/-- Complete interval computation for depth 13, residue 5865. -/ +theorem bounds_13_5865 : exactInterval 13 5865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5865 : oddCount 5865 13 = 8 ∧ acceleratedOrbit 13 5865 = 4699 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5865) = 3 ^ 8 * m + 4699 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5865.1, data_13_5865.2] + +/-- Complete interval computation for depth 13, residue 5866. -/ +theorem bounds_13_5866 : exactInterval 13 5866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5866 : oddCount 5866 13 = 5 ∧ acceleratedOrbit 13 5866 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5866) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5866.1, data_13_5866.2] + +/-- Complete interval computation for depth 13, residue 5867. -/ +theorem bounds_13_5867 : exactInterval 13 5867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5867 : oddCount 5867 13 = 7 ∧ acceleratedOrbit 13 5867 = 1567 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5867) = 3 ^ 7 * m + 1567 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5867.1, data_13_5867.2] + +/-- Complete interval computation for depth 13, residue 5868. -/ +theorem bounds_13_5868 : exactInterval 13 5868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5868 : oddCount 5868 13 = 6 ∧ acceleratedOrbit 13 5868 = 523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5868) = 3 ^ 6 * m + 523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5868.1, data_13_5868.2] + +/-- Complete interval computation for depth 13, residue 5869. -/ +theorem bounds_13_5869 : exactInterval 13 5869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5869 : oddCount 5869 13 = 6 ∧ acceleratedOrbit 13 5869 = 523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5869) = 3 ^ 6 * m + 523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5869.1, data_13_5869.2] + +/-- Complete interval computation for depth 13, residue 5870. -/ +theorem bounds_13_5870 : exactInterval 13 5870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5870 : oddCount 5870 13 = 6 ∧ acceleratedOrbit 13 5870 = 523 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5870) = 3 ^ 6 * m + 523 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5870.1, data_13_5870.2] + +/-- Complete interval computation for depth 13, residue 5871. -/ +theorem bounds_13_5871 : exactInterval 13 5871 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5871) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5871 : oddCount 5871 13 = 8 ∧ acceleratedOrbit 13 5871 = 4703 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5871) = 3 ^ 8 * m + 4703 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5871.1, data_13_5871.2] + +end Collatz.Research.StoppingAtlas.Batch0849 From 3c743916f91947de9345779a8855c6a72be752ee Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:09 +0530 Subject: [PATCH 0850/1001] proof: certify atlas Batch0850 (13:5872 to 13:5887) --- Collatz/Research/StoppingAtlas/Batch0850.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0850.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0850.lean b/Collatz/Research/StoppingAtlas/Batch0850.lean new file mode 100644 index 00000000..f8e95d0f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0850.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0850 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5872. -/ +theorem bounds_13_5872 : exactInterval 13 5872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5872 : oddCount 5872 13 = 6 ∧ acceleratedOrbit 13 5872 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5872) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5872.1, data_13_5872.2] + +/-- Complete interval computation for depth 13, residue 5873. -/ +theorem bounds_13_5873 : exactInterval 13 5873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5873 : oddCount 5873 13 = 5 ∧ acceleratedOrbit 13 5873 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5873) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5873.1, data_13_5873.2] + +/-- Complete interval computation for depth 13, residue 5874. -/ +theorem bounds_13_5874 : exactInterval 13 5874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5874 : oddCount 5874 13 = 8 ∧ acceleratedOrbit 13 5874 = 4708 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5874) = 3 ^ 8 * m + 4708 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5874.1, data_13_5874.2] + +/-- Complete interval computation for depth 13, residue 5875. -/ +theorem bounds_13_5875 : exactInterval 13 5875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5875 : oddCount 5875 13 = 8 ∧ acceleratedOrbit 13 5875 = 4708 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5875) = 3 ^ 8 * m + 4708 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5875.1, data_13_5875.2] + +/-- Complete interval computation for depth 13, residue 5876. -/ +theorem bounds_13_5876 : exactInterval 13 5876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5876 : oddCount 5876 13 = 6 ∧ acceleratedOrbit 13 5876 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5876) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5876.1, data_13_5876.2] + +/-- Complete interval computation for depth 13, residue 5877. -/ +theorem bounds_13_5877 : exactInterval 13 5877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5877 : oddCount 5877 13 = 6 ∧ acceleratedOrbit 13 5877 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5877) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5877.1, data_13_5877.2] + +/-- Complete interval computation for depth 13, residue 5878. -/ +theorem bounds_13_5878 : exactInterval 13 5878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5878 : oddCount 5878 13 = 8 ∧ acceleratedOrbit 13 5878 = 4711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5878) = 3 ^ 8 * m + 4711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5878.1, data_13_5878.2] + +/-- Complete interval computation for depth 13, residue 5879. -/ +theorem bounds_13_5879 : exactInterval 13 5879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5879 : oddCount 5879 13 = 8 ∧ acceleratedOrbit 13 5879 = 4711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5879) = 3 ^ 8 * m + 4711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5879.1, data_13_5879.2] + +/-- Complete interval computation for depth 13, residue 5880. -/ +theorem bounds_13_5880 : exactInterval 13 5880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5880 : oddCount 5880 13 = 6 ∧ acceleratedOrbit 13 5880 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5880) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5880.1, data_13_5880.2] + +/-- Complete interval computation for depth 13, residue 5881. -/ +theorem bounds_13_5881 : exactInterval 13 5881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5881 : oddCount 5881 13 = 6 ∧ acceleratedOrbit 13 5881 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5881) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5881.1, data_13_5881.2] + +/-- Complete interval computation for depth 13, residue 5882. -/ +theorem bounds_13_5882 : exactInterval 13 5882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5882 : oddCount 5882 13 = 6 ∧ acceleratedOrbit 13 5882 = 524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5882) = 3 ^ 6 * m + 524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5882.1, data_13_5882.2] + +/-- Complete interval computation for depth 13, residue 5883. -/ +theorem bounds_13_5883 : exactInterval 13 5883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5883 : oddCount 5883 13 = 7 ∧ acceleratedOrbit 13 5883 = 1571 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5883) = 3 ^ 7 * m + 1571 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5883.1, data_13_5883.2] + +/-- Complete interval computation for depth 13, residue 5884. -/ +theorem bounds_13_5884 : exactInterval 13 5884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5884 : oddCount 5884 13 = 10 ∧ acceleratedOrbit 13 5884 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5884) = 3 ^ 10 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5884.1, data_13_5884.2] + +/-- Complete interval computation for depth 13, residue 5885. -/ +theorem bounds_13_5885 : exactInterval 13 5885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5885 : oddCount 5885 13 = 10 ∧ acceleratedOrbit 13 5885 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5885) = 3 ^ 10 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5885.1, data_13_5885.2] + +/-- Complete interval computation for depth 13, residue 5886. -/ +theorem bounds_13_5886 : exactInterval 13 5886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5886 : oddCount 5886 13 = 10 ∧ acceleratedOrbit 13 5886 = 42443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5886) = 3 ^ 10 * m + 42443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5886.1, data_13_5886.2] + +/-- Complete interval computation for depth 13, residue 5887. -/ +theorem bounds_13_5887 : exactInterval 13 5887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5887 : oddCount 5887 13 = 11 ∧ acceleratedOrbit 13 5887 = 127325 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5887) = 3 ^ 11 * m + 127325 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5887.1, data_13_5887.2] + +end Collatz.Research.StoppingAtlas.Batch0850 From fd4e4ad9fd3aa340e2c71fa7cfcf9e09261a5aad Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:09 +0530 Subject: [PATCH 0851/1001] proof: certify atlas Batch0851 (13:5888 to 13:5902) --- Collatz/Research/StoppingAtlas/Batch0851.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0851.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0851.lean b/Collatz/Research/StoppingAtlas/Batch0851.lean new file mode 100644 index 00000000..55a81b96 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0851.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0851 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5888. -/ +theorem bounds_13_5888 : exactInterval 13 5888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5888 : oddCount 5888 13 = 3 ∧ acceleratedOrbit 13 5888 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5888) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5888.1, data_13_5888.2] + +/-- Complete interval computation for depth 13, residue 5889. -/ +theorem bounds_13_5889 : exactInterval 13 5889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5889 : oddCount 5889 13 = 5 ∧ acceleratedOrbit 13 5889 = 175 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5889) = 3 ^ 5 * m + 175 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5889.1, data_13_5889.2] + +/-- Complete interval computation for depth 13, residue 5890. -/ +theorem bounds_13_5890 : exactInterval 13 5890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5890 : oddCount 5890 13 = 8 ∧ acceleratedOrbit 13 5890 = 4724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5890) = 3 ^ 8 * m + 4724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5890.1, data_13_5890.2] + +/-- Complete interval computation for depth 13, residue 5891. -/ +theorem bounds_13_5891 : exactInterval 13 5891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5891 : oddCount 5891 13 = 8 ∧ acceleratedOrbit 13 5891 = 4724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5891) = 3 ^ 8 * m + 4724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5891.1, data_13_5891.2] + +/-- Complete interval computation for depth 13, residue 5892. -/ +theorem bounds_13_5892 : exactInterval 13 5892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5892 : oddCount 5892 13 = 6 ∧ acceleratedOrbit 13 5892 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5892) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5892.1, data_13_5892.2] + +/-- Complete interval computation for depth 13, residue 5893. -/ +theorem bounds_13_5893 : exactInterval 13 5893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5893 : oddCount 5893 13 = 6 ∧ acceleratedOrbit 13 5893 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5893) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5893.1, data_13_5893.2] + +/-- Complete interval computation for depth 13, residue 5894. -/ +theorem bounds_13_5894 : exactInterval 13 5894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5894 : oddCount 5894 13 = 6 ∧ acceleratedOrbit 13 5894 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5894) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5894.1, data_13_5894.2] + +/-- Complete interval computation for depth 13, residue 5895. -/ +theorem bounds_13_5895 : exactInterval 13 5895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5895 : oddCount 5895 13 = 8 ∧ acceleratedOrbit 13 5895 = 4724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5895) = 3 ^ 8 * m + 4724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5895.1, data_13_5895.2] + +/-- Complete interval computation for depth 13, residue 5896. -/ +theorem bounds_13_5896 : exactInterval 13 5896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5896 : oddCount 5896 13 = 7 ∧ acceleratedOrbit 13 5896 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5896) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5896.1, data_13_5896.2] + +/-- Complete interval computation for depth 13, residue 5897. -/ +theorem bounds_13_5897 : exactInterval 13 5897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5897 : oddCount 5897 13 = 10 ∧ acceleratedOrbit 13 5897 = 42524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5897) = 3 ^ 10 * m + 42524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5897.1, data_13_5897.2] + +/-- Complete interval computation for depth 13, residue 5898. -/ +theorem bounds_13_5898 : exactInterval 13 5898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5898 : oddCount 5898 13 = 7 ∧ acceleratedOrbit 13 5898 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5898) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5898.1, data_13_5898.2] + +/-- Complete interval computation for depth 13, residue 5899. -/ +theorem bounds_13_5899 : exactInterval 13 5899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5899 : oddCount 5899 13 = 7 ∧ acceleratedOrbit 13 5899 = 1576 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5899) = 3 ^ 7 * m + 1576 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5899.1, data_13_5899.2] + +/-- Complete interval computation for depth 13, residue 5900. -/ +theorem bounds_13_5900 : exactInterval 13 5900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5900 : oddCount 5900 13 = 7 ∧ acceleratedOrbit 13 5900 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5900) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5900.1, data_13_5900.2] + +/-- Complete interval computation for depth 13, residue 5901. -/ +theorem bounds_13_5901 : exactInterval 13 5901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5901 : oddCount 5901 13 = 7 ∧ acceleratedOrbit 13 5901 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5901) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5901.1, data_13_5901.2] + +/-- Complete interval computation for depth 13, residue 5902. -/ +theorem bounds_13_5902 : exactInterval 13 5902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5902 : oddCount 5902 13 = 6 ∧ acceleratedOrbit 13 5902 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5902) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5902.1, data_13_5902.2] + +end Collatz.Research.StoppingAtlas.Batch0851 From 02238e870b7ebf6341de00bd7cf713c8d45e23bf Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:09 +0530 Subject: [PATCH 0852/1001] proof: certify atlas Batch0852 (13:5903 to 13:5917) --- Collatz/Research/StoppingAtlas/Batch0852.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0852.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0852.lean b/Collatz/Research/StoppingAtlas/Batch0852.lean new file mode 100644 index 00000000..63293212 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0852.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0852 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5903. -/ +theorem bounds_13_5903 : exactInterval 13 5903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5903 : oddCount 5903 13 = 6 ∧ acceleratedOrbit 13 5903 = 526 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5903) = 3 ^ 6 * m + 526 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5903.1, data_13_5903.2] + +/-- Complete interval computation for depth 13, residue 5904. -/ +theorem bounds_13_5904 : exactInterval 13 5904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5904 : oddCount 5904 13 = 3 ∧ acceleratedOrbit 13 5904 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5904) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5904.1, data_13_5904.2] + +/-- Complete interval computation for depth 13, residue 5905. -/ +theorem bounds_13_5905 : exactInterval 13 5905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5905 : oddCount 5905 13 = 7 ∧ acceleratedOrbit 13 5905 = 1579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5905) = 3 ^ 7 * m + 1579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5905.1, data_13_5905.2] + +/-- Complete interval computation for depth 13, residue 5906. -/ +theorem bounds_13_5906 : exactInterval 13 5906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5906 : oddCount 5906 13 = 9 ∧ acceleratedOrbit 13 5906 = 14201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5906) = 3 ^ 9 * m + 14201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5906.1, data_13_5906.2] + +/-- Complete interval computation for depth 13, residue 5907. -/ +theorem bounds_13_5907 : exactInterval 13 5907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5907 : oddCount 5907 13 = 9 ∧ acceleratedOrbit 13 5907 = 14201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5907) = 3 ^ 9 * m + 14201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5907.1, data_13_5907.2] + +/-- Complete interval computation for depth 13, residue 5908. -/ +theorem bounds_13_5908 : exactInterval 13 5908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5908 : oddCount 5908 13 = 3 ∧ acceleratedOrbit 13 5908 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5908) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5908.1, data_13_5908.2] + +/-- Complete interval computation for depth 13, residue 5909. -/ +theorem bounds_13_5909 : exactInterval 13 5909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5909 : oddCount 5909 13 = 3 ∧ acceleratedOrbit 13 5909 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5909) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5909.1, data_13_5909.2] + +/-- Complete interval computation for depth 13, residue 5910. -/ +theorem bounds_13_5910 : exactInterval 13 5910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5910 : oddCount 5910 13 = 8 ∧ acceleratedOrbit 13 5910 = 4738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5910) = 3 ^ 8 * m + 4738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5910.1, data_13_5910.2] + +/-- Complete interval computation for depth 13, residue 5911. -/ +theorem bounds_13_5911 : exactInterval 13 5911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5911 : oddCount 5911 13 = 8 ∧ acceleratedOrbit 13 5911 = 4738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5911) = 3 ^ 8 * m + 4738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5911.1, data_13_5911.2] + +/-- Complete interval computation for depth 13, residue 5912. -/ +theorem bounds_13_5912 : exactInterval 13 5912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5912 : oddCount 5912 13 = 3 ∧ acceleratedOrbit 13 5912 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5912) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5912.1, data_13_5912.2] + +/-- Complete interval computation for depth 13, residue 5913. -/ +theorem bounds_13_5913 : exactInterval 13 5913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5913 : oddCount 5913 13 = 9 ∧ acceleratedOrbit 13 5913 = 14215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5913) = 3 ^ 9 * m + 14215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5913.1, data_13_5913.2] + +/-- Complete interval computation for depth 13, residue 5914. -/ +theorem bounds_13_5914 : exactInterval 13 5914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5914 : oddCount 5914 13 = 3 ∧ acceleratedOrbit 13 5914 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5914) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5914.1, data_13_5914.2] + +/-- Complete interval computation for depth 13, residue 5915. -/ +theorem bounds_13_5915 : exactInterval 13 5915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5915 : oddCount 5915 13 = 11 ∧ acceleratedOrbit 13 5915 = 127939 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5915) = 3 ^ 11 * m + 127939 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5915.1, data_13_5915.2] + +/-- Complete interval computation for depth 13, residue 5916. -/ +theorem bounds_13_5916 : exactInterval 13 5916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5916 : oddCount 5916 13 = 6 ∧ acceleratedOrbit 13 5916 = 527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5916) = 3 ^ 6 * m + 527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5916.1, data_13_5916.2] + +/-- Complete interval computation for depth 13, residue 5917. -/ +theorem bounds_13_5917 : exactInterval 13 5917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5917 : oddCount 5917 13 = 6 ∧ acceleratedOrbit 13 5917 = 527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5917) = 3 ^ 6 * m + 527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5917.1, data_13_5917.2] + +end Collatz.Research.StoppingAtlas.Batch0852 From c17261956e823397a122193d0d7c08efaf2440da Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:09 +0530 Subject: [PATCH 0853/1001] proof: certify atlas Batch0853 (13:5918 to 13:5933) --- Collatz/Research/StoppingAtlas/Batch0853.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0853.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0853.lean b/Collatz/Research/StoppingAtlas/Batch0853.lean new file mode 100644 index 00000000..f4a65dc3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0853.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0853 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5918. -/ +theorem bounds_13_5918 : exactInterval 13 5918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5918 : oddCount 5918 13 = 6 ∧ acceleratedOrbit 13 5918 = 527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5918) = 3 ^ 6 * m + 527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5918.1, data_13_5918.2] + +/-- Complete interval computation for depth 13, residue 5919. -/ +theorem bounds_13_5919 : exactInterval 13 5919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5919 : oddCount 5919 13 = 8 ∧ acceleratedOrbit 13 5919 = 4742 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5919) = 3 ^ 8 * m + 4742 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5919.1, data_13_5919.2] + +/-- Complete interval computation for depth 13, residue 5920. -/ +theorem bounds_13_5920 : exactInterval 13 5920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5920 : oddCount 5920 13 = 4 ∧ acceleratedOrbit 13 5920 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5920) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5920.1, data_13_5920.2] + +/-- Complete interval computation for depth 13, residue 5921. -/ +theorem bounds_13_5921 : exactInterval 13 5921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5921 : oddCount 5921 13 = 7 ∧ acceleratedOrbit 13 5921 = 1583 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5921) = 3 ^ 7 * m + 1583 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5921.1, data_13_5921.2] + +/-- Complete interval computation for depth 13, residue 5922. -/ +theorem bounds_13_5922 : exactInterval 13 5922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5922 : oddCount 5922 13 = 5 ∧ acceleratedOrbit 13 5922 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5922) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5922.1, data_13_5922.2] + +/-- Complete interval computation for depth 13, residue 5923. -/ +theorem bounds_13_5923 : exactInterval 13 5923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5923 : oddCount 5923 13 = 5 ∧ acceleratedOrbit 13 5923 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5923) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5923.1, data_13_5923.2] + +/-- Complete interval computation for depth 13, residue 5924. -/ +theorem bounds_13_5924 : exactInterval 13 5924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5924 : oddCount 5924 13 = 5 ∧ acceleratedOrbit 13 5924 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5924) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5924.1, data_13_5924.2] + +/-- Complete interval computation for depth 13, residue 5925. -/ +theorem bounds_13_5925 : exactInterval 13 5925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5925 : oddCount 5925 13 = 5 ∧ acceleratedOrbit 13 5925 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5925) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5925.1, data_13_5925.2] + +/-- Complete interval computation for depth 13, residue 5926. -/ +theorem bounds_13_5926 : exactInterval 13 5926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5926 : oddCount 5926 13 = 5 ∧ acceleratedOrbit 13 5926 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5926) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5926.1, data_13_5926.2] + +/-- Complete interval computation for depth 13, residue 5927. -/ +theorem bounds_13_5927 : exactInterval 13 5927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5927 : oddCount 5927 13 = 9 ∧ acceleratedOrbit 13 5927 = 14246 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5927) = 3 ^ 9 * m + 14246 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5927.1, data_13_5927.2] + +/-- Complete interval computation for depth 13, residue 5928. -/ +theorem bounds_13_5928 : exactInterval 13 5928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5928 : oddCount 5928 13 = 4 ∧ acceleratedOrbit 13 5928 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5928) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5928.1, data_13_5928.2] + +/-- Complete interval computation for depth 13, residue 5929. -/ +theorem bounds_13_5929 : exactInterval 13 5929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5929 : oddCount 5929 13 = 8 ∧ acceleratedOrbit 13 5929 = 4751 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5929) = 3 ^ 8 * m + 4751 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5929.1, data_13_5929.2] + +/-- Complete interval computation for depth 13, residue 5930. -/ +theorem bounds_13_5930 : exactInterval 13 5930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5930 : oddCount 5930 13 = 4 ∧ acceleratedOrbit 13 5930 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5930) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5930.1, data_13_5930.2] + +/-- Complete interval computation for depth 13, residue 5931. -/ +theorem bounds_13_5931 : exactInterval 13 5931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5931 : oddCount 5931 13 = 5 ∧ acceleratedOrbit 13 5931 = 176 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5931) = 3 ^ 5 * m + 176 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5931.1, data_13_5931.2] + +/-- Complete interval computation for depth 13, residue 5932. -/ +theorem bounds_13_5932 : exactInterval 13 5932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5932 : oddCount 5932 13 = 6 ∧ acceleratedOrbit 13 5932 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5932) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5932.1, data_13_5932.2] + +/-- Complete interval computation for depth 13, residue 5933. -/ +theorem bounds_13_5933 : exactInterval 13 5933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5933 : oddCount 5933 13 = 6 ∧ acceleratedOrbit 13 5933 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5933) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5933.1, data_13_5933.2] + +end Collatz.Research.StoppingAtlas.Batch0853 From aab42700ebf87317774bb9bef4e5e2c5d40f2317 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:10 +0530 Subject: [PATCH 0854/1001] proof: certify atlas Batch0854 (13:5934 to 13:5948) --- Collatz/Research/StoppingAtlas/Batch0854.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0854.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0854.lean b/Collatz/Research/StoppingAtlas/Batch0854.lean new file mode 100644 index 00000000..da208061 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0854.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0854 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5934. -/ +theorem bounds_13_5934 : exactInterval 13 5934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5934 : oddCount 5934 13 = 6 ∧ acceleratedOrbit 13 5934 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5934) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5934.1, data_13_5934.2] + +/-- Complete interval computation for depth 13, residue 5935. -/ +theorem bounds_13_5935 : exactInterval 13 5935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5935 : oddCount 5935 13 = 7 ∧ acceleratedOrbit 13 5935 = 1585 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5935) = 3 ^ 7 * m + 1585 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5935.1, data_13_5935.2] + +/-- Complete interval computation for depth 13, residue 5936. -/ +theorem bounds_13_5936 : exactInterval 13 5936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5936 : oddCount 5936 13 = 4 ∧ acceleratedOrbit 13 5936 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5936) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5936.1, data_13_5936.2] + +/-- Complete interval computation for depth 13, residue 5937. -/ +theorem bounds_13_5937 : exactInterval 13 5937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5937 : oddCount 5937 13 = 6 ∧ acceleratedOrbit 13 5937 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5937) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5937.1, data_13_5937.2] + +/-- Complete interval computation for depth 13, residue 5938. -/ +theorem bounds_13_5938 : exactInterval 13 5938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5938 : oddCount 5938 13 = 6 ∧ acceleratedOrbit 13 5938 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5938) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5938.1, data_13_5938.2] + +/-- Complete interval computation for depth 13, residue 5939. -/ +theorem bounds_13_5939 : exactInterval 13 5939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5939 : oddCount 5939 13 = 6 ∧ acceleratedOrbit 13 5939 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5939) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5939.1, data_13_5939.2] + +/-- Complete interval computation for depth 13, residue 5940. -/ +theorem bounds_13_5940 : exactInterval 13 5940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5940 : oddCount 5940 13 = 4 ∧ acceleratedOrbit 13 5940 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5940) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5940.1, data_13_5940.2] + +/-- Complete interval computation for depth 13, residue 5941. -/ +theorem bounds_13_5941 : exactInterval 13 5941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5941 : oddCount 5941 13 = 4 ∧ acceleratedOrbit 13 5941 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5941) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5941.1, data_13_5941.2] + +/-- Complete interval computation for depth 13, residue 5942. -/ +theorem bounds_13_5942 : exactInterval 13 5942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5942 : oddCount 5942 13 = 6 ∧ acceleratedOrbit 13 5942 = 529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5942) = 3 ^ 6 * m + 529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5942.1, data_13_5942.2] + +/-- Complete interval computation for depth 13, residue 5943. -/ +theorem bounds_13_5943 : exactInterval 13 5943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5943 : oddCount 5943 13 = 6 ∧ acceleratedOrbit 13 5943 = 529 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5943) = 3 ^ 6 * m + 529 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5943.1, data_13_5943.2] + +/-- Complete interval computation for depth 13, residue 5944. -/ +theorem bounds_13_5944 : exactInterval 13 5944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5944 : oddCount 5944 13 = 8 ∧ acceleratedOrbit 13 5944 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5944) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5944.1, data_13_5944.2] + +/-- Complete interval computation for depth 13, residue 5945. -/ +theorem bounds_13_5945 : exactInterval 13 5945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5945 : oddCount 5945 13 = 7 ∧ acceleratedOrbit 13 5945 = 1588 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5945) = 3 ^ 7 * m + 1588 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5945.1, data_13_5945.2] + +/-- Complete interval computation for depth 13, residue 5946. -/ +theorem bounds_13_5946 : exactInterval 13 5946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5946 : oddCount 5946 13 = 8 ∧ acceleratedOrbit 13 5946 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5946) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5946.1, data_13_5946.2] + +/-- Complete interval computation for depth 13, residue 5947. -/ +theorem bounds_13_5947 : exactInterval 13 5947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5947 : oddCount 5947 13 = 6 ∧ acceleratedOrbit 13 5947 = 530 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5947) = 3 ^ 6 * m + 530 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5947.1, data_13_5947.2] + +/-- Complete interval computation for depth 13, residue 5948. -/ +theorem bounds_13_5948 : exactInterval 13 5948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5948 : oddCount 5948 13 = 8 ∧ acceleratedOrbit 13 5948 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5948) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5948.1, data_13_5948.2] + +end Collatz.Research.StoppingAtlas.Batch0854 From 923475cd3d12322a5723a680f26a778e3ae15f5c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:10 +0530 Subject: [PATCH 0855/1001] proof: certify atlas Batch0855 (13:5949 to 13:5963) --- Collatz/Research/StoppingAtlas/Batch0855.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0855.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0855.lean b/Collatz/Research/StoppingAtlas/Batch0855.lean new file mode 100644 index 00000000..b635fd8c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0855.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0855 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5949. -/ +theorem bounds_13_5949 : exactInterval 13 5949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5949 : oddCount 5949 13 = 8 ∧ acceleratedOrbit 13 5949 = 4769 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5949) = 3 ^ 8 * m + 4769 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5949.1, data_13_5949.2] + +/-- Complete interval computation for depth 13, residue 5950. -/ +theorem bounds_13_5950 : exactInterval 13 5950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5950 : oddCount 5950 13 = 7 ∧ acceleratedOrbit 13 5950 = 1589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5950) = 3 ^ 7 * m + 1589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5950.1, data_13_5950.2] + +/-- Complete interval computation for depth 13, residue 5951. -/ +theorem bounds_13_5951 : exactInterval 13 5951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5951 : oddCount 5951 13 = 7 ∧ acceleratedOrbit 13 5951 = 1589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5951) = 3 ^ 7 * m + 1589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5951.1, data_13_5951.2] + +/-- Complete interval computation for depth 13, residue 5952. -/ +theorem bounds_13_5952 : exactInterval 13 5952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5952 : oddCount 5952 13 = 3 ∧ acceleratedOrbit 13 5952 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5952) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5952.1, data_13_5952.2] + +/-- Complete interval computation for depth 13, residue 5953. -/ +theorem bounds_13_5953 : exactInterval 13 5953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5953 : oddCount 5953 13 = 4 ∧ acceleratedOrbit 13 5953 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5953) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5953.1, data_13_5953.2] + +/-- Complete interval computation for depth 13, residue 5954. -/ +theorem bounds_13_5954 : exactInterval 13 5954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5954 : oddCount 5954 13 = 7 ∧ acceleratedOrbit 13 5954 = 1592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5954) = 3 ^ 7 * m + 1592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5954.1, data_13_5954.2] + +/-- Complete interval computation for depth 13, residue 5955. -/ +theorem bounds_13_5955 : exactInterval 13 5955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5955 : oddCount 5955 13 = 7 ∧ acceleratedOrbit 13 5955 = 1592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5955) = 3 ^ 7 * m + 1592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5955.1, data_13_5955.2] + +/-- Complete interval computation for depth 13, residue 5956. -/ +theorem bounds_13_5956 : exactInterval 13 5956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5956 : oddCount 5956 13 = 4 ∧ acceleratedOrbit 13 5956 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5956) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5956.1, data_13_5956.2] + +/-- Complete interval computation for depth 13, residue 5957. -/ +theorem bounds_13_5957 : exactInterval 13 5957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5957 : oddCount 5957 13 = 4 ∧ acceleratedOrbit 13 5957 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5957) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5957.1, data_13_5957.2] + +/-- Complete interval computation for depth 13, residue 5958. -/ +theorem bounds_13_5958 : exactInterval 13 5958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5958 : oddCount 5958 13 = 4 ∧ acceleratedOrbit 13 5958 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5958) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5958.1, data_13_5958.2] + +/-- Complete interval computation for depth 13, residue 5959. -/ +theorem bounds_13_5959 : exactInterval 13 5959 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5959) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5959 : oddCount 5959 13 = 8 ∧ acceleratedOrbit 13 5959 = 4774 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5959) = 3 ^ 8 * m + 4774 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5959.1, data_13_5959.2] + +/-- Complete interval computation for depth 13, residue 5960. -/ +theorem bounds_13_5960 : exactInterval 13 5960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5960 : oddCount 5960 13 = 7 ∧ acceleratedOrbit 13 5960 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5960) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5960.1, data_13_5960.2] + +/-- Complete interval computation for depth 13, residue 5961. -/ +theorem bounds_13_5961 : exactInterval 13 5961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5961 : oddCount 5961 13 = 8 ∧ acceleratedOrbit 13 5961 = 4778 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5961) = 3 ^ 8 * m + 4778 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5961.1, data_13_5961.2] + +/-- Complete interval computation for depth 13, residue 5962. -/ +theorem bounds_13_5962 : exactInterval 13 5962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5962 : oddCount 5962 13 = 7 ∧ acceleratedOrbit 13 5962 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5962) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5962.1, data_13_5962.2] + +/-- Complete interval computation for depth 13, residue 5963. -/ +theorem bounds_13_5963 : exactInterval 13 5963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5963 : oddCount 5963 13 = 4 ∧ acceleratedOrbit 13 5963 = 59 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5963) = 3 ^ 4 * m + 59 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5963.1, data_13_5963.2] + +end Collatz.Research.StoppingAtlas.Batch0855 From 35ae53265885fd50447b51b16c0a6520a69eaaca Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:10 +0530 Subject: [PATCH 0856/1001] proof: certify atlas Batch0856 (13:5964 to 13:5979) --- Collatz/Research/StoppingAtlas/Batch0856.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0856.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0856.lean b/Collatz/Research/StoppingAtlas/Batch0856.lean new file mode 100644 index 00000000..bd2b2e1c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0856.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0856 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5964. -/ +theorem bounds_13_5964 : exactInterval 13 5964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5964 : oddCount 5964 13 = 7 ∧ acceleratedOrbit 13 5964 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5964) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5964.1, data_13_5964.2] + +/-- Complete interval computation for depth 13, residue 5965. -/ +theorem bounds_13_5965 : exactInterval 13 5965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5965 : oddCount 5965 13 = 7 ∧ acceleratedOrbit 13 5965 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5965) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5965.1, data_13_5965.2] + +/-- Complete interval computation for depth 13, residue 5966. -/ +theorem bounds_13_5966 : exactInterval 13 5966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5966 : oddCount 5966 13 = 8 ∧ acceleratedOrbit 13 5966 = 4781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5966) = 3 ^ 8 * m + 4781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5966.1, data_13_5966.2] + +/-- Complete interval computation for depth 13, residue 5967. -/ +theorem bounds_13_5967 : exactInterval 13 5967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5967) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5967 : oddCount 5967 13 = 8 ∧ acceleratedOrbit 13 5967 = 4781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5967) = 3 ^ 8 * m + 4781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5967.1, data_13_5967.2] + +/-- Complete interval computation for depth 13, residue 5968. -/ +theorem bounds_13_5968 : exactInterval 13 5968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5968 : oddCount 5968 13 = 3 ∧ acceleratedOrbit 13 5968 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5968) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5968.1, data_13_5968.2] + +/-- Complete interval computation for depth 13, residue 5969. -/ +theorem bounds_13_5969 : exactInterval 13 5969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5969 : oddCount 5969 13 = 7 ∧ acceleratedOrbit 13 5969 = 1595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5969) = 3 ^ 7 * m + 1595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5969.1, data_13_5969.2] + +/-- Complete interval computation for depth 13, residue 5970. -/ +theorem bounds_13_5970 : exactInterval 13 5970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5970 : oddCount 5970 13 = 8 ∧ acceleratedOrbit 13 5970 = 4784 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5970) = 3 ^ 8 * m + 4784 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5970.1, data_13_5970.2] + +/-- Complete interval computation for depth 13, residue 5971. -/ +theorem bounds_13_5971 : exactInterval 13 5971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5971 : oddCount 5971 13 = 8 ∧ acceleratedOrbit 13 5971 = 4784 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5971) = 3 ^ 8 * m + 4784 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5971.1, data_13_5971.2] + +/-- Complete interval computation for depth 13, residue 5972. -/ +theorem bounds_13_5972 : exactInterval 13 5972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5972 : oddCount 5972 13 = 3 ∧ acceleratedOrbit 13 5972 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5972) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5972.1, data_13_5972.2] + +/-- Complete interval computation for depth 13, residue 5973. -/ +theorem bounds_13_5973 : exactInterval 13 5973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5973 : oddCount 5973 13 = 3 ∧ acceleratedOrbit 13 5973 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5973) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5973.1, data_13_5973.2] + +/-- Complete interval computation for depth 13, residue 5974. -/ +theorem bounds_13_5974 : exactInterval 13 5974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5974 : oddCount 5974 13 = 6 ∧ acceleratedOrbit 13 5974 = 532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5974) = 3 ^ 6 * m + 532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5974.1, data_13_5974.2] + +/-- Complete interval computation for depth 13, residue 5975. -/ +theorem bounds_13_5975 : exactInterval 13 5975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5975 : oddCount 5975 13 = 6 ∧ acceleratedOrbit 13 5975 = 532 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5975) = 3 ^ 6 * m + 532 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5975.1, data_13_5975.2] + +/-- Complete interval computation for depth 13, residue 5976. -/ +theorem bounds_13_5976 : exactInterval 13 5976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5976 : oddCount 5976 13 = 6 ∧ acceleratedOrbit 13 5976 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5976) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5976.1, data_13_5976.2] + +/-- Complete interval computation for depth 13, residue 5977. -/ +theorem bounds_13_5977 : exactInterval 13 5977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5977 : oddCount 5977 13 = 6 ∧ acceleratedOrbit 13 5977 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5977) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5977.1, data_13_5977.2] + +/-- Complete interval computation for depth 13, residue 5978. -/ +theorem bounds_13_5978 : exactInterval 13 5978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5978 : oddCount 5978 13 = 6 ∧ acceleratedOrbit 13 5978 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5978) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5978.1, data_13_5978.2] + +/-- Complete interval computation for depth 13, residue 5979. -/ +theorem bounds_13_5979 : exactInterval 13 5979 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5979) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5979 : oddCount 5979 13 = 8 ∧ acceleratedOrbit 13 5979 = 4790 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5979) = 3 ^ 8 * m + 4790 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5979.1, data_13_5979.2] + +end Collatz.Research.StoppingAtlas.Batch0856 From e89eb075b1b414c846e1073b8810713f41c2631e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:10 +0530 Subject: [PATCH 0857/1001] proof: certify atlas Batch0857 (13:5980 to 13:5994) --- Collatz/Research/StoppingAtlas/Batch0857.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0857.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0857.lean b/Collatz/Research/StoppingAtlas/Batch0857.lean new file mode 100644 index 00000000..9e83e54f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0857.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0857 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5980. -/ +theorem bounds_13_5980 : exactInterval 13 5980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5980 : oddCount 5980 13 = 6 ∧ acceleratedOrbit 13 5980 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5980) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5980.1, data_13_5980.2] + +/-- Complete interval computation for depth 13, residue 5981. -/ +theorem bounds_13_5981 : exactInterval 13 5981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5981 : oddCount 5981 13 = 6 ∧ acceleratedOrbit 13 5981 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5981) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5981.1, data_13_5981.2] + +/-- Complete interval computation for depth 13, residue 5982. -/ +theorem bounds_13_5982 : exactInterval 13 5982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5982 : oddCount 5982 13 = 6 ∧ acceleratedOrbit 13 5982 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5982) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5982.1, data_13_5982.2] + +/-- Complete interval computation for depth 13, residue 5983. -/ +theorem bounds_13_5983 : exactInterval 13 5983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5983) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5983 : oddCount 5983 13 = 6 ∧ acceleratedOrbit 13 5983 = 533 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5983) = 3 ^ 6 * m + 533 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5983.1, data_13_5983.2] + +/-- Complete interval computation for depth 13, residue 5984. -/ +theorem bounds_13_5984 : exactInterval 13 5984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5984 : oddCount 5984 13 = 5 ∧ acceleratedOrbit 13 5984 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5984) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5984.1, data_13_5984.2] + +/-- Complete interval computation for depth 13, residue 5985. -/ +theorem bounds_13_5985 : exactInterval 13 5985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5985 : oddCount 5985 13 = 8 ∧ acceleratedOrbit 13 5985 = 4796 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5985) = 3 ^ 8 * m + 4796 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5985.1, data_13_5985.2] + +/-- Complete interval computation for depth 13, residue 5986. -/ +theorem bounds_13_5986 : exactInterval 13 5986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5986 : oddCount 5986 13 = 5 ∧ acceleratedOrbit 13 5986 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5986) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5986.1, data_13_5986.2] + +/-- Complete interval computation for depth 13, residue 5987. -/ +theorem bounds_13_5987 : exactInterval 13 5987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5987 : oddCount 5987 13 = 5 ∧ acceleratedOrbit 13 5987 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5987) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5987.1, data_13_5987.2] + +/-- Complete interval computation for depth 13, residue 5988. -/ +theorem bounds_13_5988 : exactInterval 13 5988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5988 : oddCount 5988 13 = 5 ∧ acceleratedOrbit 13 5988 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5988) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5988.1, data_13_5988.2] + +/-- Complete interval computation for depth 13, residue 5989. -/ +theorem bounds_13_5989 : exactInterval 13 5989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5989 : oddCount 5989 13 = 5 ∧ acceleratedOrbit 13 5989 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5989) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5989.1, data_13_5989.2] + +/-- Complete interval computation for depth 13, residue 5990. -/ +theorem bounds_13_5990 : exactInterval 13 5990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5990 : oddCount 5990 13 = 5 ∧ acceleratedOrbit 13 5990 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5990) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5990.1, data_13_5990.2] + +/-- Complete interval computation for depth 13, residue 5991. -/ +theorem bounds_13_5991 : exactInterval 13 5991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5991 : oddCount 5991 13 = 10 ∧ acceleratedOrbit 13 5991 = 43193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5991) = 3 ^ 10 * m + 43193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5991.1, data_13_5991.2] + +/-- Complete interval computation for depth 13, residue 5992. -/ +theorem bounds_13_5992 : exactInterval 13 5992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5992 : oddCount 5992 13 = 5 ∧ acceleratedOrbit 13 5992 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5992) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5992.1, data_13_5992.2] + +/-- Complete interval computation for depth 13, residue 5993. -/ +theorem bounds_13_5993 : exactInterval 13 5993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5993 : oddCount 5993 13 = 7 ∧ acceleratedOrbit 13 5993 = 1601 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5993) = 3 ^ 7 * m + 1601 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5993.1, data_13_5993.2] + +/-- Complete interval computation for depth 13, residue 5994. -/ +theorem bounds_13_5994 : exactInterval 13 5994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5994 : oddCount 5994 13 = 5 ∧ acceleratedOrbit 13 5994 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5994) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5994.1, data_13_5994.2] + +end Collatz.Research.StoppingAtlas.Batch0857 From dc58a4c618d4d5e80206791d7e50a8941a03bc61 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:10 +0530 Subject: [PATCH 0858/1001] proof: certify atlas Batch0858 (13:5995 to 13:6009) --- Collatz/Research/StoppingAtlas/Batch0858.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0858.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0858.lean b/Collatz/Research/StoppingAtlas/Batch0858.lean new file mode 100644 index 00000000..989dc779 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0858.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0858 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 5995. -/ +theorem bounds_13_5995 : exactInterval 13 5995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5995 : oddCount 5995 13 = 8 ∧ acceleratedOrbit 13 5995 = 4805 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5995) = 3 ^ 8 * m + 4805 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5995.1, data_13_5995.2] + +/-- Complete interval computation for depth 13, residue 5996. -/ +theorem bounds_13_5996 : exactInterval 13 5996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5996 : oddCount 5996 13 = 5 ∧ acceleratedOrbit 13 5996 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5996) = 3 ^ 5 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5996.1, data_13_5996.2] + +/-- Complete interval computation for depth 13, residue 5997. -/ +theorem bounds_13_5997 : exactInterval 13 5997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5997 : oddCount 5997 13 = 5 ∧ acceleratedOrbit 13 5997 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5997) = 3 ^ 5 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5997.1, data_13_5997.2] + +/-- Complete interval computation for depth 13, residue 5998. -/ +theorem bounds_13_5998 : exactInterval 13 5998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5998 : oddCount 5998 13 = 5 ∧ acceleratedOrbit 13 5998 = 178 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5998) = 3 ^ 5 * m + 178 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5998.1, data_13_5998.2] + +/-- Complete interval computation for depth 13, residue 5999. -/ +theorem bounds_13_5999 : exactInterval 13 5999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_5999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 5999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_5999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_5999 : oddCount 5999 13 = 10 ∧ acceleratedOrbit 13 5999 = 43253 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_5999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 5999) = 3 ^ 10 * m + 43253 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_5999.1, data_13_5999.2] + +/-- Complete interval computation for depth 13, residue 6000. -/ +theorem bounds_13_6000 : exactInterval 13 6000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6000 : oddCount 6000 13 = 5 ∧ acceleratedOrbit 13 6000 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6000) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6000.1, data_13_6000.2] + +/-- Complete interval computation for depth 13, residue 6001. -/ +theorem bounds_13_6001 : exactInterval 13 6001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6001 : oddCount 6001 13 = 5 ∧ acceleratedOrbit 13 6001 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6001) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6001.1, data_13_6001.2] + +/-- Complete interval computation for depth 13, residue 6002. -/ +theorem bounds_13_6002 : exactInterval 13 6002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6002 : oddCount 6002 13 = 6 ∧ acceleratedOrbit 13 6002 = 535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6002) = 3 ^ 6 * m + 535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6002.1, data_13_6002.2] + +/-- Complete interval computation for depth 13, residue 6003. -/ +theorem bounds_13_6003 : exactInterval 13 6003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6003 : oddCount 6003 13 = 6 ∧ acceleratedOrbit 13 6003 = 535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6003) = 3 ^ 6 * m + 535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6003.1, data_13_6003.2] + +/-- Complete interval computation for depth 13, residue 6004. -/ +theorem bounds_13_6004 : exactInterval 13 6004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6004 : oddCount 6004 13 = 5 ∧ acceleratedOrbit 13 6004 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6004) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6004.1, data_13_6004.2] + +/-- Complete interval computation for depth 13, residue 6005. -/ +theorem bounds_13_6005 : exactInterval 13 6005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6005 : oddCount 6005 13 = 5 ∧ acceleratedOrbit 13 6005 = 179 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6005) = 3 ^ 5 * m + 179 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6005.1, data_13_6005.2] + +/-- Complete interval computation for depth 13, residue 6006. -/ +theorem bounds_13_6006 : exactInterval 13 6006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6006 : oddCount 6006 13 = 6 ∧ acceleratedOrbit 13 6006 = 535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6006) = 3 ^ 6 * m + 535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6006.1, data_13_6006.2] + +/-- Complete interval computation for depth 13, residue 6007. -/ +theorem bounds_13_6007 : exactInterval 13 6007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6007 : oddCount 6007 13 = 6 ∧ acceleratedOrbit 13 6007 = 535 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6007) = 3 ^ 6 * m + 535 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6007.1, data_13_6007.2] + +/-- Complete interval computation for depth 13, residue 6008. -/ +theorem bounds_13_6008 : exactInterval 13 6008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6008 : oddCount 6008 13 = 8 ∧ acceleratedOrbit 13 6008 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6008) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6008.1, data_13_6008.2] + +/-- Complete interval computation for depth 13, residue 6009. -/ +theorem bounds_13_6009 : exactInterval 13 6009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6009 : oddCount 6009 13 = 9 ∧ acceleratedOrbit 13 6009 = 14444 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6009) = 3 ^ 9 * m + 14444 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6009.1, data_13_6009.2] + +end Collatz.Research.StoppingAtlas.Batch0858 From 7898b95447817a6e4cdd895d7dfceba874dfe8d0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:11 +0530 Subject: [PATCH 0859/1001] proof: certify atlas Batch0859 (13:6010 to 13:6025) --- Collatz/Research/StoppingAtlas/Batch0859.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0859.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0859.lean b/Collatz/Research/StoppingAtlas/Batch0859.lean new file mode 100644 index 00000000..89c16b29 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0859.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0859 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6010. -/ +theorem bounds_13_6010 : exactInterval 13 6010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6010 : oddCount 6010 13 = 8 ∧ acceleratedOrbit 13 6010 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6010) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6010.1, data_13_6010.2] + +/-- Complete interval computation for depth 13, residue 6011. -/ +theorem bounds_13_6011 : exactInterval 13 6011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6011 : oddCount 6011 13 = 8 ∧ acceleratedOrbit 13 6011 = 4816 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6011) = 3 ^ 8 * m + 4816 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6011.1, data_13_6011.2] + +/-- Complete interval computation for depth 13, residue 6012. -/ +theorem bounds_13_6012 : exactInterval 13 6012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6012 : oddCount 6012 13 = 8 ∧ acceleratedOrbit 13 6012 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6012) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6012.1, data_13_6012.2] + +/-- Complete interval computation for depth 13, residue 6013. -/ +theorem bounds_13_6013 : exactInterval 13 6013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6013 : oddCount 6013 13 = 8 ∧ acceleratedOrbit 13 6013 = 4819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6013) = 3 ^ 8 * m + 4819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6013.1, data_13_6013.2] + +/-- Complete interval computation for depth 13, residue 6014. -/ +theorem bounds_13_6014 : exactInterval 13 6014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6014 : oddCount 6014 13 = 9 ∧ acceleratedOrbit 13 6014 = 14455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6014) = 3 ^ 9 * m + 14455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6014.1, data_13_6014.2] + +/-- Complete interval computation for depth 13, residue 6015. -/ +theorem bounds_13_6015 : exactInterval 13 6015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6015 : oddCount 6015 13 = 9 ∧ acceleratedOrbit 13 6015 = 14455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6015) = 3 ^ 9 * m + 14455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6015.1, data_13_6015.2] + +/-- Complete interval computation for depth 13, residue 6016. -/ +theorem bounds_13_6016 : exactInterval 13 6016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6016 : oddCount 6016 13 = 5 ∧ acceleratedOrbit 13 6016 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6016) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6016.1, data_13_6016.2] + +/-- Complete interval computation for depth 13, residue 6017. -/ +theorem bounds_13_6017 : exactInterval 13 6017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6017 : oddCount 6017 13 = 8 ∧ acceleratedOrbit 13 6017 = 4823 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6017) = 3 ^ 8 * m + 4823 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6017.1, data_13_6017.2] + +/-- Complete interval computation for depth 13, residue 6018. -/ +theorem bounds_13_6018 : exactInterval 13 6018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6018 : oddCount 6018 13 = 7 ∧ acceleratedOrbit 13 6018 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6018) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6018.1, data_13_6018.2] + +/-- Complete interval computation for depth 13, residue 6019. -/ +theorem bounds_13_6019 : exactInterval 13 6019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6019 : oddCount 6019 13 = 7 ∧ acceleratedOrbit 13 6019 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6019) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6019.1, data_13_6019.2] + +/-- Complete interval computation for depth 13, residue 6020. -/ +theorem bounds_13_6020 : exactInterval 13 6020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6020 : oddCount 6020 13 = 7 ∧ acceleratedOrbit 13 6020 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6020) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6020.1, data_13_6020.2] + +/-- Complete interval computation for depth 13, residue 6021. -/ +theorem bounds_13_6021 : exactInterval 13 6021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6021 : oddCount 6021 13 = 7 ∧ acceleratedOrbit 13 6021 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6021) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6021.1, data_13_6021.2] + +/-- Complete interval computation for depth 13, residue 6022. -/ +theorem bounds_13_6022 : exactInterval 13 6022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6022 : oddCount 6022 13 = 7 ∧ acceleratedOrbit 13 6022 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6022) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6022.1, data_13_6022.2] + +/-- Complete interval computation for depth 13, residue 6023. -/ +theorem bounds_13_6023 : exactInterval 13 6023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6023) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6023 : oddCount 6023 13 = 7 ∧ acceleratedOrbit 13 6023 = 1610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6023) = 3 ^ 7 * m + 1610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6023.1, data_13_6023.2] + +/-- Complete interval computation for depth 13, residue 6024. -/ +theorem bounds_13_6024 : exactInterval 13 6024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6024 : oddCount 6024 13 = 3 ∧ acceleratedOrbit 13 6024 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6024) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6024.1, data_13_6024.2] + +/-- Complete interval computation for depth 13, residue 6025. -/ +theorem bounds_13_6025 : exactInterval 13 6025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6025 : oddCount 6025 13 = 7 ∧ acceleratedOrbit 13 6025 = 1609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6025) = 3 ^ 7 * m + 1609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6025.1, data_13_6025.2] + +end Collatz.Research.StoppingAtlas.Batch0859 From 71a4f8559d3bec4de32a2558a83f0799de6a444f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:11 +0530 Subject: [PATCH 0860/1001] proof: certify atlas Batch0860 (13:6026 to 13:6040) --- Collatz/Research/StoppingAtlas/Batch0860.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0860.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0860.lean b/Collatz/Research/StoppingAtlas/Batch0860.lean new file mode 100644 index 00000000..cad301ed --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0860.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0860 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6026. -/ +theorem bounds_13_6026 : exactInterval 13 6026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6026 : oddCount 6026 13 = 3 ∧ acceleratedOrbit 13 6026 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6026) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6026.1, data_13_6026.2] + +/-- Complete interval computation for depth 13, residue 6027. -/ +theorem bounds_13_6027 : exactInterval 13 6027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6027 : oddCount 6027 13 = 9 ∧ acceleratedOrbit 13 6027 = 14489 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6027) = 3 ^ 9 * m + 14489 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6027.1, data_13_6027.2] + +/-- Complete interval computation for depth 13, residue 6028. -/ +theorem bounds_13_6028 : exactInterval 13 6028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6028 : oddCount 6028 13 = 3 ∧ acceleratedOrbit 13 6028 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6028) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6028.1, data_13_6028.2] + +/-- Complete interval computation for depth 13, residue 6029. -/ +theorem bounds_13_6029 : exactInterval 13 6029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6029 : oddCount 6029 13 = 3 ∧ acceleratedOrbit 13 6029 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6029) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6029.1, data_13_6029.2] + +/-- Complete interval computation for depth 13, residue 6030. -/ +theorem bounds_13_6030 : exactInterval 13 6030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6030 : oddCount 6030 13 = 9 ∧ acceleratedOrbit 13 6030 = 14498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6030) = 3 ^ 9 * m + 14498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6030.1, data_13_6030.2] + +/-- Complete interval computation for depth 13, residue 6031. -/ +theorem bounds_13_6031 : exactInterval 13 6031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6031 : oddCount 6031 13 = 9 ∧ acceleratedOrbit 13 6031 = 14498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6031) = 3 ^ 9 * m + 14498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6031.1, data_13_6031.2] + +/-- Complete interval computation for depth 13, residue 6032. -/ +theorem bounds_13_6032 : exactInterval 13 6032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6032 : oddCount 6032 13 = 7 ∧ acceleratedOrbit 13 6032 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6032) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6032.1, data_13_6032.2] + +/-- Complete interval computation for depth 13, residue 6033. -/ +theorem bounds_13_6033 : exactInterval 13 6033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6033 : oddCount 6033 13 = 7 ∧ acceleratedOrbit 13 6033 = 1613 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6033) = 3 ^ 7 * m + 1613 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6033.1, data_13_6033.2] + +/-- Complete interval computation for depth 13, residue 6034. -/ +theorem bounds_13_6034 : exactInterval 13 6034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6034 : oddCount 6034 13 = 7 ∧ acceleratedOrbit 13 6034 = 1613 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6034) = 3 ^ 7 * m + 1613 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6034.1, data_13_6034.2] + +/-- Complete interval computation for depth 13, residue 6035. -/ +theorem bounds_13_6035 : exactInterval 13 6035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6035 : oddCount 6035 13 = 7 ∧ acceleratedOrbit 13 6035 = 1613 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6035) = 3 ^ 7 * m + 1613 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6035.1, data_13_6035.2] + +/-- Complete interval computation for depth 13, residue 6036. -/ +theorem bounds_13_6036 : exactInterval 13 6036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6036 : oddCount 6036 13 = 7 ∧ acceleratedOrbit 13 6036 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6036) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6036.1, data_13_6036.2] + +/-- Complete interval computation for depth 13, residue 6037. -/ +theorem bounds_13_6037 : exactInterval 13 6037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6037 : oddCount 6037 13 = 7 ∧ acceleratedOrbit 13 6037 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6037) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6037.1, data_13_6037.2] + +/-- Complete interval computation for depth 13, residue 6038. -/ +theorem bounds_13_6038 : exactInterval 13 6038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6038 : oddCount 6038 13 = 6 ∧ acceleratedOrbit 13 6038 = 539 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6038) = 3 ^ 6 * m + 539 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6038.1, data_13_6038.2] + +/-- Complete interval computation for depth 13, residue 6039. -/ +theorem bounds_13_6039 : exactInterval 13 6039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6039 : oddCount 6039 13 = 6 ∧ acceleratedOrbit 13 6039 = 539 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6039) = 3 ^ 6 * m + 539 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6039.1, data_13_6039.2] + +/-- Complete interval computation for depth 13, residue 6040. -/ +theorem bounds_13_6040 : exactInterval 13 6040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6040 : oddCount 6040 13 = 7 ∧ acceleratedOrbit 13 6040 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6040) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6040.1, data_13_6040.2] + +end Collatz.Research.StoppingAtlas.Batch0860 From aa727097d931400f498b50ff06017745d36a3086 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:11 +0530 Subject: [PATCH 0861/1001] proof: certify atlas Batch0861 (13:6041 to 13:6055) --- Collatz/Research/StoppingAtlas/Batch0861.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0861.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0861.lean b/Collatz/Research/StoppingAtlas/Batch0861.lean new file mode 100644 index 00000000..d62d7e2d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0861.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0861 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6041. -/ +theorem bounds_13_6041 : exactInterval 13 6041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6041 : oddCount 6041 13 = 6 ∧ acceleratedOrbit 13 6041 = 539 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6041) = 3 ^ 6 * m + 539 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6041.1, data_13_6041.2] + +/-- Complete interval computation for depth 13, residue 6042. -/ +theorem bounds_13_6042 : exactInterval 13 6042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6042 : oddCount 6042 13 = 7 ∧ acceleratedOrbit 13 6042 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6042) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6042.1, data_13_6042.2] + +/-- Complete interval computation for depth 13, residue 6043. -/ +theorem bounds_13_6043 : exactInterval 13 6043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6043 : oddCount 6043 13 = 9 ∧ acceleratedOrbit 13 6043 = 14525 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6043) = 3 ^ 9 * m + 14525 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6043.1, data_13_6043.2] + +/-- Complete interval computation for depth 13, residue 6044. -/ +theorem bounds_13_6044 : exactInterval 13 6044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6044 : oddCount 6044 13 = 7 ∧ acceleratedOrbit 13 6044 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6044) = 3 ^ 7 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6044.1, data_13_6044.2] + +/-- Complete interval computation for depth 13, residue 6045. -/ +theorem bounds_13_6045 : exactInterval 13 6045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6045 : oddCount 6045 13 = 7 ∧ acceleratedOrbit 13 6045 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6045) = 3 ^ 7 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6045.1, data_13_6045.2] + +/-- Complete interval computation for depth 13, residue 6046. -/ +theorem bounds_13_6046 : exactInterval 13 6046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6046 : oddCount 6046 13 = 7 ∧ acceleratedOrbit 13 6046 = 1615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6046) = 3 ^ 7 * m + 1615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6046.1, data_13_6046.2] + +/-- Complete interval computation for depth 13, residue 6047. -/ +theorem bounds_13_6047 : exactInterval 13 6047 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6047) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6047 : oddCount 6047 13 = 8 ∧ acceleratedOrbit 13 6047 = 4844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6047) = 3 ^ 8 * m + 4844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6047.1, data_13_6047.2] + +/-- Complete interval computation for depth 13, residue 6048. -/ +theorem bounds_13_6048 : exactInterval 13 6048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6048 : oddCount 6048 13 = 5 ∧ acceleratedOrbit 13 6048 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6048) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6048.1, data_13_6048.2] + +/-- Complete interval computation for depth 13, residue 6049. -/ +theorem bounds_13_6049 : exactInterval 13 6049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6049 : oddCount 6049 13 = 6 ∧ acceleratedOrbit 13 6049 = 539 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6049) = 3 ^ 6 * m + 539 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6049.1, data_13_6049.2] + +/-- Complete interval computation for depth 13, residue 6050. -/ +theorem bounds_13_6050 : exactInterval 13 6050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6050 : oddCount 6050 13 = 7 ∧ acceleratedOrbit 13 6050 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6050) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6050.1, data_13_6050.2] + +/-- Complete interval computation for depth 13, residue 6051. -/ +theorem bounds_13_6051 : exactInterval 13 6051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6051 : oddCount 6051 13 = 7 ∧ acceleratedOrbit 13 6051 = 1619 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6051) = 3 ^ 7 * m + 1619 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6051.1, data_13_6051.2] + +/-- Complete interval computation for depth 13, residue 6052. -/ +theorem bounds_13_6052 : exactInterval 13 6052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6052 : oddCount 6052 13 = 8 ∧ acceleratedOrbit 13 6052 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6052) = 3 ^ 8 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6052.1, data_13_6052.2] + +/-- Complete interval computation for depth 13, residue 6053. -/ +theorem bounds_13_6053 : exactInterval 13 6053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6053 : oddCount 6053 13 = 8 ∧ acceleratedOrbit 13 6053 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6053) = 3 ^ 8 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6053.1, data_13_6053.2] + +/-- Complete interval computation for depth 13, residue 6054. -/ +theorem bounds_13_6054 : exactInterval 13 6054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6054 : oddCount 6054 13 = 8 ∧ acceleratedOrbit 13 6054 = 4853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6054) = 3 ^ 8 * m + 4853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6054.1, data_13_6054.2] + +/-- Complete interval computation for depth 13, residue 6055. -/ +theorem bounds_13_6055 : exactInterval 13 6055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6055 : oddCount 6055 13 = 10 ∧ acceleratedOrbit 13 6055 = 43658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6055) = 3 ^ 10 * m + 43658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6055.1, data_13_6055.2] + +end Collatz.Research.StoppingAtlas.Batch0861 From e0af071008f02b10bc960bcef53f6efbd76944b5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:11 +0530 Subject: [PATCH 0862/1001] proof: certify atlas Batch0862 (13:6056 to 13:6071) --- Collatz/Research/StoppingAtlas/Batch0862.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0862.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0862.lean b/Collatz/Research/StoppingAtlas/Batch0862.lean new file mode 100644 index 00000000..2615aa57 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0862.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0862 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6056. -/ +theorem bounds_13_6056 : exactInterval 13 6056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6056 : oddCount 6056 13 = 5 ∧ acceleratedOrbit 13 6056 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6056) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6056.1, data_13_6056.2] + +/-- Complete interval computation for depth 13, residue 6057. -/ +theorem bounds_13_6057 : exactInterval 13 6057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6057 : oddCount 6057 13 = 10 ∧ acceleratedOrbit 13 6057 = 43672 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6057) = 3 ^ 10 * m + 43672 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6057.1, data_13_6057.2] + +/-- Complete interval computation for depth 13, residue 6058. -/ +theorem bounds_13_6058 : exactInterval 13 6058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6058 : oddCount 6058 13 = 5 ∧ acceleratedOrbit 13 6058 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6058) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6058.1, data_13_6058.2] + +/-- Complete interval computation for depth 13, residue 6059. -/ +theorem bounds_13_6059 : exactInterval 13 6059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6059 : oddCount 6059 13 = 8 ∧ acceleratedOrbit 13 6059 = 4855 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6059) = 3 ^ 8 * m + 4855 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6059.1, data_13_6059.2] + +/-- Complete interval computation for depth 13, residue 6060. -/ +theorem bounds_13_6060 : exactInterval 13 6060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6060 : oddCount 6060 13 = 9 ∧ acceleratedOrbit 13 6060 = 14579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6060) = 3 ^ 9 * m + 14579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6060.1, data_13_6060.2] + +/-- Complete interval computation for depth 13, residue 6061. -/ +theorem bounds_13_6061 : exactInterval 13 6061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6061 : oddCount 6061 13 = 9 ∧ acceleratedOrbit 13 6061 = 14579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6061) = 3 ^ 9 * m + 14579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6061.1, data_13_6061.2] + +/-- Complete interval computation for depth 13, residue 6062. -/ +theorem bounds_13_6062 : exactInterval 13 6062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6062 : oddCount 6062 13 = 9 ∧ acceleratedOrbit 13 6062 = 14579 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6062) = 3 ^ 9 * m + 14579 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6062.1, data_13_6062.2] + +/-- Complete interval computation for depth 13, residue 6063. -/ +theorem bounds_13_6063 : exactInterval 13 6063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6063 : oddCount 6063 13 = 8 ∧ acceleratedOrbit 13 6063 = 4859 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6063) = 3 ^ 8 * m + 4859 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6063.1, data_13_6063.2] + +/-- Complete interval computation for depth 13, residue 6064. -/ +theorem bounds_13_6064 : exactInterval 13 6064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6064 : oddCount 6064 13 = 6 ∧ acceleratedOrbit 13 6064 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6064) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6064.1, data_13_6064.2] + +/-- Complete interval computation for depth 13, residue 6065. -/ +theorem bounds_13_6065 : exactInterval 13 6065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6065 : oddCount 6065 13 = 3 ∧ acceleratedOrbit 13 6065 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6065) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6065.1, data_13_6065.2] + +/-- Complete interval computation for depth 13, residue 6066. -/ +theorem bounds_13_6066 : exactInterval 13 6066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6066 : oddCount 6066 13 = 3 ∧ acceleratedOrbit 13 6066 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6066) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6066.1, data_13_6066.2] + +/-- Complete interval computation for depth 13, residue 6067. -/ +theorem bounds_13_6067 : exactInterval 13 6067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6067 : oddCount 6067 13 = 3 ∧ acceleratedOrbit 13 6067 = 20 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6067) = 3 ^ 3 * m + 20 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6067.1, data_13_6067.2] + +/-- Complete interval computation for depth 13, residue 6068. -/ +theorem bounds_13_6068 : exactInterval 13 6068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6068 : oddCount 6068 13 = 6 ∧ acceleratedOrbit 13 6068 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6068) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6068.1, data_13_6068.2] + +/-- Complete interval computation for depth 13, residue 6069. -/ +theorem bounds_13_6069 : exactInterval 13 6069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6069 : oddCount 6069 13 = 6 ∧ acceleratedOrbit 13 6069 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6069) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6069.1, data_13_6069.2] + +/-- Complete interval computation for depth 13, residue 6070. -/ +theorem bounds_13_6070 : exactInterval 13 6070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6070 : oddCount 6070 13 = 7 ∧ acceleratedOrbit 13 6070 = 1622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6070) = 3 ^ 7 * m + 1622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6070.1, data_13_6070.2] + +/-- Complete interval computation for depth 13, residue 6071. -/ +theorem bounds_13_6071 : exactInterval 13 6071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6071 : oddCount 6071 13 = 7 ∧ acceleratedOrbit 13 6071 = 1622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6071) = 3 ^ 7 * m + 1622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6071.1, data_13_6071.2] + +end Collatz.Research.StoppingAtlas.Batch0862 From 98f9f11532e969f536ab67dc40b3875b7b7c7d0f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0863/1001] proof: certify atlas Batch0863 (13:6072 to 13:6086) --- Collatz/Research/StoppingAtlas/Batch0863.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0863.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0863.lean b/Collatz/Research/StoppingAtlas/Batch0863.lean new file mode 100644 index 00000000..a7b8f879 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0863.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0863 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6072. -/ +theorem bounds_13_6072 : exactInterval 13 6072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6072 : oddCount 6072 13 = 6 ∧ acceleratedOrbit 13 6072 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6072) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6072.1, data_13_6072.2] + +/-- Complete interval computation for depth 13, residue 6073. -/ +theorem bounds_13_6073 : exactInterval 13 6073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6073 : oddCount 6073 13 = 6 ∧ acceleratedOrbit 13 6073 = 541 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6073) = 3 ^ 6 * m + 541 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6073.1, data_13_6073.2] + +/-- Complete interval computation for depth 13, residue 6074. -/ +theorem bounds_13_6074 : exactInterval 13 6074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6074 : oddCount 6074 13 = 6 ∧ acceleratedOrbit 13 6074 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6074) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6074.1, data_13_6074.2] + +/-- Complete interval computation for depth 13, residue 6075. -/ +theorem bounds_13_6075 : exactInterval 13 6075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6075 : oddCount 6075 13 = 6 ∧ acceleratedOrbit 13 6075 = 541 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6075) = 3 ^ 6 * m + 541 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6075.1, data_13_6075.2] + +/-- Complete interval computation for depth 13, residue 6076. -/ +theorem bounds_13_6076 : exactInterval 13 6076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6076 : oddCount 6076 13 = 8 ∧ acceleratedOrbit 13 6076 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6076) = 3 ^ 8 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6076.1, data_13_6076.2] + +/-- Complete interval computation for depth 13, residue 6077. -/ +theorem bounds_13_6077 : exactInterval 13 6077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6077 : oddCount 6077 13 = 8 ∧ acceleratedOrbit 13 6077 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6077) = 3 ^ 8 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6077.1, data_13_6077.2] + +/-- Complete interval computation for depth 13, residue 6078. -/ +theorem bounds_13_6078 : exactInterval 13 6078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6078 : oddCount 6078 13 = 8 ∧ acceleratedOrbit 13 6078 = 4870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6078) = 3 ^ 8 * m + 4870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6078.1, data_13_6078.2] + +/-- Complete interval computation for depth 13, residue 6079. -/ +theorem bounds_13_6079 : exactInterval 13 6079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6079) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6079 : oddCount 6079 13 = 9 ∧ acceleratedOrbit 13 6079 = 14609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6079) = 3 ^ 9 * m + 14609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6079.1, data_13_6079.2] + +/-- Complete interval computation for depth 13, residue 6080. -/ +theorem bounds_13_6080 : exactInterval 13 6080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6080 : oddCount 6080 13 = 5 ∧ acceleratedOrbit 13 6080 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6080) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6080.1, data_13_6080.2] + +/-- Complete interval computation for depth 13, residue 6081. -/ +theorem bounds_13_6081 : exactInterval 13 6081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6081 : oddCount 6081 13 = 6 ∧ acceleratedOrbit 13 6081 = 542 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6081) = 3 ^ 6 * m + 542 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6081.1, data_13_6081.2] + +/-- Complete interval computation for depth 13, residue 6082. -/ +theorem bounds_13_6082 : exactInterval 13 6082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6082 : oddCount 6082 13 = 7 ∧ acceleratedOrbit 13 6082 = 1625 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6082) = 3 ^ 7 * m + 1625 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6082.1, data_13_6082.2] + +/-- Complete interval computation for depth 13, residue 6083. -/ +theorem bounds_13_6083 : exactInterval 13 6083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6083 : oddCount 6083 13 = 7 ∧ acceleratedOrbit 13 6083 = 1625 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6083) = 3 ^ 7 * m + 1625 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6083.1, data_13_6083.2] + +/-- Complete interval computation for depth 13, residue 6084. -/ +theorem bounds_13_6084 : exactInterval 13 6084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6084 : oddCount 6084 13 = 5 ∧ acceleratedOrbit 13 6084 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6084) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6084.1, data_13_6084.2] + +/-- Complete interval computation for depth 13, residue 6085. -/ +theorem bounds_13_6085 : exactInterval 13 6085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6085 : oddCount 6085 13 = 5 ∧ acceleratedOrbit 13 6085 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6085) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6085.1, data_13_6085.2] + +/-- Complete interval computation for depth 13, residue 6086. -/ +theorem bounds_13_6086 : exactInterval 13 6086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6086 : oddCount 6086 13 = 5 ∧ acceleratedOrbit 13 6086 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6086) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6086.1, data_13_6086.2] + +end Collatz.Research.StoppingAtlas.Batch0863 From 79278b78e2fb1625ccd26667d9877b51702fd987 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0864/1001] proof: certify atlas Batch0864 (13:6087 to 13:6102) --- Collatz/Research/StoppingAtlas/Batch0864.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0864.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0864.lean b/Collatz/Research/StoppingAtlas/Batch0864.lean new file mode 100644 index 00000000..169be1ad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0864.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0864 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6087. -/ +theorem bounds_13_6087 : exactInterval 13 6087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6087 : oddCount 6087 13 = 8 ∧ acceleratedOrbit 13 6087 = 4877 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6087) = 3 ^ 8 * m + 4877 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6087.1, data_13_6087.2] + +/-- Complete interval computation for depth 13, residue 6088. -/ +theorem bounds_13_6088 : exactInterval 13 6088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6088 : oddCount 6088 13 = 5 ∧ acceleratedOrbit 13 6088 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6088) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6088.1, data_13_6088.2] + +/-- Complete interval computation for depth 13, residue 6089. -/ +theorem bounds_13_6089 : exactInterval 13 6089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6089 : oddCount 6089 13 = 8 ∧ acceleratedOrbit 13 6089 = 4880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6089) = 3 ^ 8 * m + 4880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6089.1, data_13_6089.2] + +/-- Complete interval computation for depth 13, residue 6090. -/ +theorem bounds_13_6090 : exactInterval 13 6090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6090 : oddCount 6090 13 = 5 ∧ acceleratedOrbit 13 6090 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6090) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6090.1, data_13_6090.2] + +/-- Complete interval computation for depth 13, residue 6091. -/ +theorem bounds_13_6091 : exactInterval 13 6091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6091 : oddCount 6091 13 = 5 ∧ acceleratedOrbit 13 6091 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6091) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6091.1, data_13_6091.2] + +/-- Complete interval computation for depth 13, residue 6092. -/ +theorem bounds_13_6092 : exactInterval 13 6092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6092 : oddCount 6092 13 = 5 ∧ acceleratedOrbit 13 6092 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6092) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6092.1, data_13_6092.2] + +/-- Complete interval computation for depth 13, residue 6093. -/ +theorem bounds_13_6093 : exactInterval 13 6093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6093 : oddCount 6093 13 = 5 ∧ acceleratedOrbit 13 6093 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6093) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6093.1, data_13_6093.2] + +/-- Complete interval computation for depth 13, residue 6094. -/ +theorem bounds_13_6094 : exactInterval 13 6094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6094 : oddCount 6094 13 = 7 ∧ acceleratedOrbit 13 6094 = 1628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6094) = 3 ^ 7 * m + 1628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6094.1, data_13_6094.2] + +/-- Complete interval computation for depth 13, residue 6095. -/ +theorem bounds_13_6095 : exactInterval 13 6095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6095 : oddCount 6095 13 = 7 ∧ acceleratedOrbit 13 6095 = 1628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6095) = 3 ^ 7 * m + 1628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6095.1, data_13_6095.2] + +/-- Complete interval computation for depth 13, residue 6096. -/ +theorem bounds_13_6096 : exactInterval 13 6096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6096 : oddCount 6096 13 = 5 ∧ acceleratedOrbit 13 6096 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6096) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6096.1, data_13_6096.2] + +/-- Complete interval computation for depth 13, residue 6097. -/ +theorem bounds_13_6097 : exactInterval 13 6097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6097 : oddCount 6097 13 = 5 ∧ acceleratedOrbit 13 6097 = 181 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6097) = 3 ^ 5 * m + 181 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6097.1, data_13_6097.2] + +/-- Complete interval computation for depth 13, residue 6098. -/ +theorem bounds_13_6098 : exactInterval 13 6098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6098 : oddCount 6098 13 = 10 ∧ acceleratedOrbit 13 6098 = 43982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6098) = 3 ^ 10 * m + 43982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6098.1, data_13_6098.2] + +/-- Complete interval computation for depth 13, residue 6099. -/ +theorem bounds_13_6099 : exactInterval 13 6099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6099 : oddCount 6099 13 = 10 ∧ acceleratedOrbit 13 6099 = 43982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6099) = 3 ^ 10 * m + 43982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6099.1, data_13_6099.2] + +/-- Complete interval computation for depth 13, residue 6100. -/ +theorem bounds_13_6100 : exactInterval 13 6100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6100 : oddCount 6100 13 = 5 ∧ acceleratedOrbit 13 6100 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6100) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6100.1, data_13_6100.2] + +/-- Complete interval computation for depth 13, residue 6101. -/ +theorem bounds_13_6101 : exactInterval 13 6101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6101 : oddCount 6101 13 = 5 ∧ acceleratedOrbit 13 6101 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6101) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6101.1, data_13_6101.2] + +/-- Complete interval computation for depth 13, residue 6102. -/ +theorem bounds_13_6102 : exactInterval 13 6102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6102 : oddCount 6102 13 = 7 ∧ acceleratedOrbit 13 6102 = 1630 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6102) = 3 ^ 7 * m + 1630 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6102.1, data_13_6102.2] + +end Collatz.Research.StoppingAtlas.Batch0864 From ed76e915fddd49d1c765a3596816c792fff503eb Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0865/1001] proof: certify atlas Batch0865 (13:6103 to 13:6117) --- Collatz/Research/StoppingAtlas/Batch0865.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0865.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0865.lean b/Collatz/Research/StoppingAtlas/Batch0865.lean new file mode 100644 index 00000000..1b284b16 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0865.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0865 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6103. -/ +theorem bounds_13_6103 : exactInterval 13 6103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6103 : oddCount 6103 13 = 7 ∧ acceleratedOrbit 13 6103 = 1630 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6103) = 3 ^ 7 * m + 1630 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6103.1, data_13_6103.2] + +/-- Complete interval computation for depth 13, residue 6104. -/ +theorem bounds_13_6104 : exactInterval 13 6104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6104 : oddCount 6104 13 = 7 ∧ acceleratedOrbit 13 6104 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6104) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6104.1, data_13_6104.2] + +/-- Complete interval computation for depth 13, residue 6105. -/ +theorem bounds_13_6105 : exactInterval 13 6105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6105 : oddCount 6105 13 = 5 ∧ acceleratedOrbit 13 6105 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6105) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6105.1, data_13_6105.2] + +/-- Complete interval computation for depth 13, residue 6106. -/ +theorem bounds_13_6106 : exactInterval 13 6106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6106 : oddCount 6106 13 = 7 ∧ acceleratedOrbit 13 6106 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6106) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6106.1, data_13_6106.2] + +/-- Complete interval computation for depth 13, residue 6107. -/ +theorem bounds_13_6107 : exactInterval 13 6107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6107 : oddCount 6107 13 = 7 ∧ acceleratedOrbit 13 6107 = 1631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6107) = 3 ^ 7 * m + 1631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6107.1, data_13_6107.2] + +/-- Complete interval computation for depth 13, residue 6108. -/ +theorem bounds_13_6108 : exactInterval 13 6108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6108 : oddCount 6108 13 = 7 ∧ acceleratedOrbit 13 6108 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6108) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6108.1, data_13_6108.2] + +/-- Complete interval computation for depth 13, residue 6109. -/ +theorem bounds_13_6109 : exactInterval 13 6109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6109 : oddCount 6109 13 = 7 ∧ acceleratedOrbit 13 6109 = 1633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6109) = 3 ^ 7 * m + 1633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6109.1, data_13_6109.2] + +/-- Complete interval computation for depth 13, residue 6110. -/ +theorem bounds_13_6110 : exactInterval 13 6110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6110 : oddCount 6110 13 = 9 ∧ acceleratedOrbit 13 6110 = 14687 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6110) = 3 ^ 9 * m + 14687 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6110.1, data_13_6110.2] + +/-- Complete interval computation for depth 13, residue 6111. -/ +theorem bounds_13_6111 : exactInterval 13 6111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6111 : oddCount 6111 13 = 9 ∧ acceleratedOrbit 13 6111 = 14687 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6111) = 3 ^ 9 * m + 14687 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6111.1, data_13_6111.2] + +/-- Complete interval computation for depth 13, residue 6112. -/ +theorem bounds_13_6112 : exactInterval 13 6112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6112 : oddCount 6112 13 = 7 ∧ acceleratedOrbit 13 6112 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6112) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6112.1, data_13_6112.2] + +/-- Complete interval computation for depth 13, residue 6113. -/ +theorem bounds_13_6113 : exactInterval 13 6113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6113 : oddCount 6113 13 = 8 ∧ acceleratedOrbit 13 6113 = 4898 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6113) = 3 ^ 8 * m + 4898 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6113.1, data_13_6113.2] + +/-- Complete interval computation for depth 13, residue 6114. -/ +theorem bounds_13_6114 : exactInterval 13 6114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6114 : oddCount 6114 13 = 5 ∧ acceleratedOrbit 13 6114 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6114) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6114.1, data_13_6114.2] + +/-- Complete interval computation for depth 13, residue 6115. -/ +theorem bounds_13_6115 : exactInterval 13 6115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6115 : oddCount 6115 13 = 5 ∧ acceleratedOrbit 13 6115 = 182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6115) = 3 ^ 5 * m + 182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6115.1, data_13_6115.2] + +/-- Complete interval computation for depth 13, residue 6116. -/ +theorem bounds_13_6116 : exactInterval 13 6116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6116 : oddCount 6116 13 = 6 ∧ acceleratedOrbit 13 6116 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6116) = 3 ^ 6 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6116.1, data_13_6116.2] + +/-- Complete interval computation for depth 13, residue 6117. -/ +theorem bounds_13_6117 : exactInterval 13 6117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6117 : oddCount 6117 13 = 6 ∧ acceleratedOrbit 13 6117 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6117) = 3 ^ 6 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6117.1, data_13_6117.2] + +end Collatz.Research.StoppingAtlas.Batch0865 From f0bed0ac3df7ec2628c872001868273b1a05139c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0866/1001] proof: certify atlas Batch0866 (13:6118 to 13:6132) --- Collatz/Research/StoppingAtlas/Batch0866.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0866.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0866.lean b/Collatz/Research/StoppingAtlas/Batch0866.lean new file mode 100644 index 00000000..51e52f93 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0866.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0866 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6118. -/ +theorem bounds_13_6118 : exactInterval 13 6118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6118 : oddCount 6118 13 = 6 ∧ acceleratedOrbit 13 6118 = 545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6118) = 3 ^ 6 * m + 545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6118.1, data_13_6118.2] + +/-- Complete interval computation for depth 13, residue 6119. -/ +theorem bounds_13_6119 : exactInterval 13 6119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6119 : oddCount 6119 13 = 7 ∧ acceleratedOrbit 13 6119 = 1634 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6119) = 3 ^ 7 * m + 1634 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6119.1, data_13_6119.2] + +/-- Complete interval computation for depth 13, residue 6120. -/ +theorem bounds_13_6120 : exactInterval 13 6120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6120 : oddCount 6120 13 = 7 ∧ acceleratedOrbit 13 6120 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6120) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6120.1, data_13_6120.2] + +/-- Complete interval computation for depth 13, residue 6121. -/ +theorem bounds_13_6121 : exactInterval 13 6121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6121 : oddCount 6121 13 = 10 ∧ acceleratedOrbit 13 6121 = 44135 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6121) = 3 ^ 10 * m + 44135 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6121.1, data_13_6121.2] + +/-- Complete interval computation for depth 13, residue 6122. -/ +theorem bounds_13_6122 : exactInterval 13 6122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6122 : oddCount 6122 13 = 7 ∧ acceleratedOrbit 13 6122 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6122) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6122.1, data_13_6122.2] + +/-- Complete interval computation for depth 13, residue 6123. -/ +theorem bounds_13_6123 : exactInterval 13 6123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6123 : oddCount 6123 13 = 9 ∧ acceleratedOrbit 13 6123 = 14717 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6123) = 3 ^ 9 * m + 14717 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6123.1, data_13_6123.2] + +/-- Complete interval computation for depth 13, residue 6124. -/ +theorem bounds_13_6124 : exactInterval 13 6124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6124 : oddCount 6124 13 = 7 ∧ acceleratedOrbit 13 6124 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6124) = 3 ^ 7 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6124.1, data_13_6124.2] + +/-- Complete interval computation for depth 13, residue 6125. -/ +theorem bounds_13_6125 : exactInterval 13 6125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6125 : oddCount 6125 13 = 7 ∧ acceleratedOrbit 13 6125 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6125) = 3 ^ 7 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6125.1, data_13_6125.2] + +/-- Complete interval computation for depth 13, residue 6126. -/ +theorem bounds_13_6126 : exactInterval 13 6126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6126 : oddCount 6126 13 = 7 ∧ acceleratedOrbit 13 6126 = 1637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6126) = 3 ^ 7 * m + 1637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6126.1, data_13_6126.2] + +/-- Complete interval computation for depth 13, residue 6127. -/ +theorem bounds_13_6127 : exactInterval 13 6127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6127 : oddCount 6127 13 = 7 ∧ acceleratedOrbit 13 6127 = 1636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6127) = 3 ^ 7 * m + 1636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6127.1, data_13_6127.2] + +/-- Complete interval computation for depth 13, residue 6128. -/ +theorem bounds_13_6128 : exactInterval 13 6128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6128 : oddCount 6128 13 = 7 ∧ acceleratedOrbit 13 6128 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6128) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6128.1, data_13_6128.2] + +/-- Complete interval computation for depth 13, residue 6129. -/ +theorem bounds_13_6129 : exactInterval 13 6129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6129 : oddCount 6129 13 = 7 ∧ acceleratedOrbit 13 6129 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6129) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6129.1, data_13_6129.2] + +/-- Complete interval computation for depth 13, residue 6130. -/ +theorem bounds_13_6130 : exactInterval 13 6130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6130 : oddCount 6130 13 = 9 ∧ acceleratedOrbit 13 6130 = 14741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6130) = 3 ^ 9 * m + 14741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6130.1, data_13_6130.2] + +/-- Complete interval computation for depth 13, residue 6131. -/ +theorem bounds_13_6131 : exactInterval 13 6131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6131 : oddCount 6131 13 = 9 ∧ acceleratedOrbit 13 6131 = 14741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6131) = 3 ^ 9 * m + 14741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6131.1, data_13_6131.2] + +/-- Complete interval computation for depth 13, residue 6132. -/ +theorem bounds_13_6132 : exactInterval 13 6132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6132 : oddCount 6132 13 = 7 ∧ acceleratedOrbit 13 6132 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6132) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6132.1, data_13_6132.2] + +end Collatz.Research.StoppingAtlas.Batch0866 From 5a535fe94f4c322b3d9a4b4a83856d433c6098e5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0867/1001] proof: certify atlas Batch0867 (13:6133 to 13:6148) --- Collatz/Research/StoppingAtlas/Batch0867.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0867.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0867.lean b/Collatz/Research/StoppingAtlas/Batch0867.lean new file mode 100644 index 00000000..0b57a77d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0867.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0867 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6133. -/ +theorem bounds_13_6133 : exactInterval 13 6133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6133 : oddCount 6133 13 = 7 ∧ acceleratedOrbit 13 6133 = 1640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6133) = 3 ^ 7 * m + 1640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6133.1, data_13_6133.2] + +/-- Complete interval computation for depth 13, residue 6134. -/ +theorem bounds_13_6134 : exactInterval 13 6134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6134 : oddCount 6134 13 = 8 ∧ acceleratedOrbit 13 6134 = 4916 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6134) = 3 ^ 8 * m + 4916 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6134.1, data_13_6134.2] + +/-- Complete interval computation for depth 13, residue 6135. -/ +theorem bounds_13_6135 : exactInterval 13 6135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6135 : oddCount 6135 13 = 8 ∧ acceleratedOrbit 13 6135 = 4916 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6135) = 3 ^ 8 * m + 4916 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6135.1, data_13_6135.2] + +/-- Complete interval computation for depth 13, residue 6136. -/ +theorem bounds_13_6136 : exactInterval 13 6136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6136 : oddCount 6136 13 = 9 ∧ acceleratedOrbit 13 6136 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6136) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6136.1, data_13_6136.2] + +/-- Complete interval computation for depth 13, residue 6137. -/ +theorem bounds_13_6137 : exactInterval 13 6137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6137 : oddCount 6137 13 = 7 ∧ acceleratedOrbit 13 6137 = 1639 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6137) = 3 ^ 7 * m + 1639 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6137.1, data_13_6137.2] + +/-- Complete interval computation for depth 13, residue 6138. -/ +theorem bounds_13_6138 : exactInterval 13 6138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6138 : oddCount 6138 13 = 9 ∧ acceleratedOrbit 13 6138 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6138) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6138.1, data_13_6138.2] + +/-- Complete interval computation for depth 13, residue 6139. -/ +theorem bounds_13_6139 : exactInterval 13 6139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6139 : oddCount 6139 13 = 9 ∧ acceleratedOrbit 13 6139 = 14755 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6139) = 3 ^ 9 * m + 14755 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6139.1, data_13_6139.2] + +/-- Complete interval computation for depth 13, residue 6140. -/ +theorem bounds_13_6140 : exactInterval 13 6140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6140 : oddCount 6140 13 = 9 ∧ acceleratedOrbit 13 6140 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6140) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6140.1, data_13_6140.2] + +/-- Complete interval computation for depth 13, residue 6141. -/ +theorem bounds_13_6141 : exactInterval 13 6141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6141 : oddCount 6141 13 = 9 ∧ acceleratedOrbit 13 6141 = 14762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6141) = 3 ^ 9 * m + 14762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6141.1, data_13_6141.2] + +/-- Complete interval computation for depth 13, residue 6142. -/ +theorem bounds_13_6142 : exactInterval 13 6142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6142 : oddCount 6142 13 = 11 ∧ acceleratedOrbit 13 6142 = 132860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6142) = 3 ^ 11 * m + 132860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6142.1, data_13_6142.2] + +/-- Complete interval computation for depth 13, residue 6143. -/ +theorem bounds_13_6143 : exactInterval 13 6143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6143 : oddCount 6143 13 = 11 ∧ acceleratedOrbit 13 6143 = 132860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6143) = 3 ^ 11 * m + 132860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6143.1, data_13_6143.2] + +/-- Complete interval computation for depth 13, residue 6144. -/ +theorem bounds_13_6144 : exactInterval 13 6144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6144 : oddCount 6144 13 = 2 ∧ acceleratedOrbit 13 6144 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6144) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6144.1, data_13_6144.2] + +/-- Complete interval computation for depth 13, residue 6145. -/ +theorem bounds_13_6145 : exactInterval 13 6145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6145 : oddCount 6145 13 = 7 ∧ acceleratedOrbit 13 6145 = 1642 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6145) = 3 ^ 7 * m + 1642 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6145.1, data_13_6145.2] + +/-- Complete interval computation for depth 13, residue 6146. -/ +theorem bounds_13_6146 : exactInterval 13 6146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6146 : oddCount 6146 13 = 6 ∧ acceleratedOrbit 13 6146 = 548 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6146) = 3 ^ 6 * m + 548 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6146.1, data_13_6146.2] + +/-- Complete interval computation for depth 13, residue 6147. -/ +theorem bounds_13_6147 : exactInterval 13 6147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6147 : oddCount 6147 13 = 6 ∧ acceleratedOrbit 13 6147 = 548 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6147) = 3 ^ 6 * m + 548 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6147.1, data_13_6147.2] + +/-- Complete interval computation for depth 13, residue 6148. -/ +theorem bounds_13_6148 : exactInterval 13 6148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6148 : oddCount 6148 13 = 7 ∧ acceleratedOrbit 13 6148 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6148) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6148.1, data_13_6148.2] + +end Collatz.Research.StoppingAtlas.Batch0867 From 7bec75ac138c351491e8748e8159c86ec6e12de1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0868/1001] proof: certify atlas Batch0868 (13:6149 to 13:6163) --- Collatz/Research/StoppingAtlas/Batch0868.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0868.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0868.lean b/Collatz/Research/StoppingAtlas/Batch0868.lean new file mode 100644 index 00000000..ca702f4d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0868.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0868 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6149. -/ +theorem bounds_13_6149 : exactInterval 13 6149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6149 : oddCount 6149 13 = 7 ∧ acceleratedOrbit 13 6149 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6149) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6149.1, data_13_6149.2] + +/-- Complete interval computation for depth 13, residue 6150. -/ +theorem bounds_13_6150 : exactInterval 13 6150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6150 : oddCount 6150 13 = 7 ∧ acceleratedOrbit 13 6150 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6150) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6150.1, data_13_6150.2] + +/-- Complete interval computation for depth 13, residue 6151. -/ +theorem bounds_13_6151 : exactInterval 13 6151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6151 : oddCount 6151 13 = 6 ∧ acceleratedOrbit 13 6151 = 548 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6151) = 3 ^ 6 * m + 548 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6151.1, data_13_6151.2] + +/-- Complete interval computation for depth 13, residue 6152. -/ +theorem bounds_13_6152 : exactInterval 13 6152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6152 : oddCount 6152 13 = 4 ∧ acceleratedOrbit 13 6152 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6152) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6152.1, data_13_6152.2] + +/-- Complete interval computation for depth 13, residue 6153. -/ +theorem bounds_13_6153 : exactInterval 13 6153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6153 : oddCount 6153 13 = 8 ∧ acceleratedOrbit 13 6153 = 4931 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6153) = 3 ^ 8 * m + 4931 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6153.1, data_13_6153.2] + +/-- Complete interval computation for depth 13, residue 6154. -/ +theorem bounds_13_6154 : exactInterval 13 6154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6154 : oddCount 6154 13 = 4 ∧ acceleratedOrbit 13 6154 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6154) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6154.1, data_13_6154.2] + +/-- Complete interval computation for depth 13, residue 6155. -/ +theorem bounds_13_6155 : exactInterval 13 6155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6155 : oddCount 6155 13 = 7 ∧ acceleratedOrbit 13 6155 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6155) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6155.1, data_13_6155.2] + +/-- Complete interval computation for depth 13, residue 6156. -/ +theorem bounds_13_6156 : exactInterval 13 6156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6156 : oddCount 6156 13 = 4 ∧ acceleratedOrbit 13 6156 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6156) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6156.1, data_13_6156.2] + +/-- Complete interval computation for depth 13, residue 6157. -/ +theorem bounds_13_6157 : exactInterval 13 6157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6157 : oddCount 6157 13 = 4 ∧ acceleratedOrbit 13 6157 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6157) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6157.1, data_13_6157.2] + +/-- Complete interval computation for depth 13, residue 6158. -/ +theorem bounds_13_6158 : exactInterval 13 6158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6158 : oddCount 6158 13 = 7 ∧ acceleratedOrbit 13 6158 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6158) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6158.1, data_13_6158.2] + +/-- Complete interval computation for depth 13, residue 6159. -/ +theorem bounds_13_6159 : exactInterval 13 6159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6159 : oddCount 6159 13 = 7 ∧ acceleratedOrbit 13 6159 = 1646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6159) = 3 ^ 7 * m + 1646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6159.1, data_13_6159.2] + +/-- Complete interval computation for depth 13, residue 6160. -/ +theorem bounds_13_6160 : exactInterval 13 6160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6160 : oddCount 6160 13 = 5 ∧ acceleratedOrbit 13 6160 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6160) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6160.1, data_13_6160.2] + +/-- Complete interval computation for depth 13, residue 6161. -/ +theorem bounds_13_6161 : exactInterval 13 6161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6161 : oddCount 6161 13 = 4 ∧ acceleratedOrbit 13 6161 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6161) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6161.1, data_13_6161.2] + +/-- Complete interval computation for depth 13, residue 6162. -/ +theorem bounds_13_6162 : exactInterval 13 6162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6162 : oddCount 6162 13 = 8 ∧ acceleratedOrbit 13 6162 = 4940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6162) = 3 ^ 8 * m + 4940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6162.1, data_13_6162.2] + +/-- Complete interval computation for depth 13, residue 6163. -/ +theorem bounds_13_6163 : exactInterval 13 6163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6163 : oddCount 6163 13 = 8 ∧ acceleratedOrbit 13 6163 = 4940 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6163) = 3 ^ 8 * m + 4940 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6163.1, data_13_6163.2] + +end Collatz.Research.StoppingAtlas.Batch0868 From 70f1b31c9a55f292ca24718522a25d93dad26c45 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:12 +0530 Subject: [PATCH 0869/1001] proof: certify atlas Batch0869 (13:6164 to 13:6178) --- Collatz/Research/StoppingAtlas/Batch0869.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0869.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0869.lean b/Collatz/Research/StoppingAtlas/Batch0869.lean new file mode 100644 index 00000000..96294bc8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0869.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0869 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6164. -/ +theorem bounds_13_6164 : exactInterval 13 6164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6164 : oddCount 6164 13 = 5 ∧ acceleratedOrbit 13 6164 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6164) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6164.1, data_13_6164.2] + +/-- Complete interval computation for depth 13, residue 6165. -/ +theorem bounds_13_6165 : exactInterval 13 6165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6165 : oddCount 6165 13 = 5 ∧ acceleratedOrbit 13 6165 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6165) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6165.1, data_13_6165.2] + +/-- Complete interval computation for depth 13, residue 6166. -/ +theorem bounds_13_6166 : exactInterval 13 6166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6166 : oddCount 6166 13 = 4 ∧ acceleratedOrbit 13 6166 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6166) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6166.1, data_13_6166.2] + +/-- Complete interval computation for depth 13, residue 6167. -/ +theorem bounds_13_6167 : exactInterval 13 6167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6167 : oddCount 6167 13 = 4 ∧ acceleratedOrbit 13 6167 = 61 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6167) = 3 ^ 4 * m + 61 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6167.1, data_13_6167.2] + +/-- Complete interval computation for depth 13, residue 6168. -/ +theorem bounds_13_6168 : exactInterval 13 6168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6168 : oddCount 6168 13 = 5 ∧ acceleratedOrbit 13 6168 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6168) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6168.1, data_13_6168.2] + +/-- Complete interval computation for depth 13, residue 6169. -/ +theorem bounds_13_6169 : exactInterval 13 6169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6169 : oddCount 6169 13 = 7 ∧ acceleratedOrbit 13 6169 = 1648 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6169) = 3 ^ 7 * m + 1648 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6169.1, data_13_6169.2] + +/-- Complete interval computation for depth 13, residue 6170. -/ +theorem bounds_13_6170 : exactInterval 13 6170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6170 : oddCount 6170 13 = 5 ∧ acceleratedOrbit 13 6170 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6170) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6170.1, data_13_6170.2] + +/-- Complete interval computation for depth 13, residue 6171. -/ +theorem bounds_13_6171 : exactInterval 13 6171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6171 : oddCount 6171 13 = 9 ∧ acceleratedOrbit 13 6171 = 14831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6171) = 3 ^ 9 * m + 14831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6171.1, data_13_6171.2] + +/-- Complete interval computation for depth 13, residue 6172. -/ +theorem bounds_13_6172 : exactInterval 13 6172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6172 : oddCount 6172 13 = 6 ∧ acceleratedOrbit 13 6172 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6172) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6172.1, data_13_6172.2] + +/-- Complete interval computation for depth 13, residue 6173. -/ +theorem bounds_13_6173 : exactInterval 13 6173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6173 : oddCount 6173 13 = 6 ∧ acceleratedOrbit 13 6173 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6173) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6173.1, data_13_6173.2] + +/-- Complete interval computation for depth 13, residue 6174. -/ +theorem bounds_13_6174 : exactInterval 13 6174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6174 : oddCount 6174 13 = 6 ∧ acceleratedOrbit 13 6174 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6174) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6174.1, data_13_6174.2] + +/-- Complete interval computation for depth 13, residue 6175. -/ +theorem bounds_13_6175 : exactInterval 13 6175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6175 : oddCount 6175 13 = 9 ∧ acceleratedOrbit 13 6175 = 14840 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6175) = 3 ^ 9 * m + 14840 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6175.1, data_13_6175.2] + +/-- Complete interval computation for depth 13, residue 6176. -/ +theorem bounds_13_6176 : exactInterval 13 6176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6176 : oddCount 6176 13 = 4 ∧ acceleratedOrbit 13 6176 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6176) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6176.1, data_13_6176.2] + +/-- Complete interval computation for depth 13, residue 6177. -/ +theorem bounds_13_6177 : exactInterval 13 6177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6177 : oddCount 6177 13 = 6 ∧ acceleratedOrbit 13 6177 = 550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6177) = 3 ^ 6 * m + 550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6177.1, data_13_6177.2] + +/-- Complete interval computation for depth 13, residue 6178. -/ +theorem bounds_13_6178 : exactInterval 13 6178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6178 : oddCount 6178 13 = 5 ∧ acceleratedOrbit 13 6178 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6178) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6178.1, data_13_6178.2] + +end Collatz.Research.StoppingAtlas.Batch0869 From 25a58fe6717a2e44318ebc3e5898e9be1558f164 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:13 +0530 Subject: [PATCH 0870/1001] proof: certify atlas Batch0870 (13:6179 to 13:6194) --- Collatz/Research/StoppingAtlas/Batch0870.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0870.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0870.lean b/Collatz/Research/StoppingAtlas/Batch0870.lean new file mode 100644 index 00000000..5fc660d7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0870.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0870 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6179. -/ +theorem bounds_13_6179 : exactInterval 13 6179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6179 : oddCount 6179 13 = 5 ∧ acceleratedOrbit 13 6179 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6179) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6179.1, data_13_6179.2] + +/-- Complete interval computation for depth 13, residue 6180. -/ +theorem bounds_13_6180 : exactInterval 13 6180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6180 : oddCount 6180 13 = 6 ∧ acceleratedOrbit 13 6180 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6180) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6180.1, data_13_6180.2] + +/-- Complete interval computation for depth 13, residue 6181. -/ +theorem bounds_13_6181 : exactInterval 13 6181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6181 : oddCount 6181 13 = 6 ∧ acceleratedOrbit 13 6181 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6181) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6181.1, data_13_6181.2] + +/-- Complete interval computation for depth 13, residue 6182. -/ +theorem bounds_13_6182 : exactInterval 13 6182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6182 : oddCount 6182 13 = 6 ∧ acceleratedOrbit 13 6182 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6182) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6182.1, data_13_6182.2] + +/-- Complete interval computation for depth 13, residue 6183. -/ +theorem bounds_13_6183 : exactInterval 13 6183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6183 : oddCount 6183 13 = 8 ∧ acceleratedOrbit 13 6183 = 4954 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6183) = 3 ^ 8 * m + 4954 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6183.1, data_13_6183.2] + +/-- Complete interval computation for depth 13, residue 6184. -/ +theorem bounds_13_6184 : exactInterval 13 6184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6184 : oddCount 6184 13 = 4 ∧ acceleratedOrbit 13 6184 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6184) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6184.1, data_13_6184.2] + +/-- Complete interval computation for depth 13, residue 6185. -/ +theorem bounds_13_6185 : exactInterval 13 6185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6185 : oddCount 6185 13 = 8 ∧ acceleratedOrbit 13 6185 = 4955 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6185) = 3 ^ 8 * m + 4955 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6185.1, data_13_6185.2] + +/-- Complete interval computation for depth 13, residue 6186. -/ +theorem bounds_13_6186 : exactInterval 13 6186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6186 : oddCount 6186 13 = 4 ∧ acceleratedOrbit 13 6186 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6186) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6186.1, data_13_6186.2] + +/-- Complete interval computation for depth 13, residue 6187. -/ +theorem bounds_13_6187 : exactInterval 13 6187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6187 : oddCount 6187 13 = 6 ∧ acceleratedOrbit 13 6187 = 551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6187) = 3 ^ 6 * m + 551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6187.1, data_13_6187.2] + +/-- Complete interval computation for depth 13, residue 6188. -/ +theorem bounds_13_6188 : exactInterval 13 6188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6188 : oddCount 6188 13 = 5 ∧ acceleratedOrbit 13 6188 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6188) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6188.1, data_13_6188.2] + +/-- Complete interval computation for depth 13, residue 6189. -/ +theorem bounds_13_6189 : exactInterval 13 6189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6189 : oddCount 6189 13 = 5 ∧ acceleratedOrbit 13 6189 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6189) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6189.1, data_13_6189.2] + +/-- Complete interval computation for depth 13, residue 6190. -/ +theorem bounds_13_6190 : exactInterval 13 6190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6190 : oddCount 6190 13 = 5 ∧ acceleratedOrbit 13 6190 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6190) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6190.1, data_13_6190.2] + +/-- Complete interval computation for depth 13, residue 6191. -/ +theorem bounds_13_6191 : exactInterval 13 6191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6191) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6191 : oddCount 6191 13 = 9 ∧ acceleratedOrbit 13 6191 = 14879 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6191) = 3 ^ 9 * m + 14879 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6191.1, data_13_6191.2] + +/-- Complete interval computation for depth 13, residue 6192. -/ +theorem bounds_13_6192 : exactInterval 13 6192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6192 : oddCount 6192 13 = 4 ∧ acceleratedOrbit 13 6192 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6192) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6192.1, data_13_6192.2] + +/-- Complete interval computation for depth 13, residue 6193. -/ +theorem bounds_13_6193 : exactInterval 13 6193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6193 : oddCount 6193 13 = 8 ∧ acceleratedOrbit 13 6193 = 4967 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6193) = 3 ^ 8 * m + 4967 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6193.1, data_13_6193.2] + +/-- Complete interval computation for depth 13, residue 6194. -/ +theorem bounds_13_6194 : exactInterval 13 6194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6194 : oddCount 6194 13 = 8 ∧ acceleratedOrbit 13 6194 = 4967 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6194) = 3 ^ 8 * m + 4967 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6194.1, data_13_6194.2] + +end Collatz.Research.StoppingAtlas.Batch0870 From fcb50523fd1d1620bf8dd4a2e60d9b042ca9ae8c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:13 +0530 Subject: [PATCH 0871/1001] proof: certify atlas Batch0871 (13:6195 to 13:6209) --- Collatz/Research/StoppingAtlas/Batch0871.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0871.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0871.lean b/Collatz/Research/StoppingAtlas/Batch0871.lean new file mode 100644 index 00000000..cb0161db --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0871.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0871 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6195. -/ +theorem bounds_13_6195 : exactInterval 13 6195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6195 : oddCount 6195 13 = 8 ∧ acceleratedOrbit 13 6195 = 4967 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6195) = 3 ^ 8 * m + 4967 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6195.1, data_13_6195.2] + +/-- Complete interval computation for depth 13, residue 6196. -/ +theorem bounds_13_6196 : exactInterval 13 6196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6196 : oddCount 6196 13 = 4 ∧ acceleratedOrbit 13 6196 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6196) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6196.1, data_13_6196.2] + +/-- Complete interval computation for depth 13, residue 6197. -/ +theorem bounds_13_6197 : exactInterval 13 6197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6197 : oddCount 6197 13 = 4 ∧ acceleratedOrbit 13 6197 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6197) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6197.1, data_13_6197.2] + +/-- Complete interval computation for depth 13, residue 6198. -/ +theorem bounds_13_6198 : exactInterval 13 6198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6198 : oddCount 6198 13 = 9 ∧ acceleratedOrbit 13 6198 = 14899 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6198) = 3 ^ 9 * m + 14899 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6198.1, data_13_6198.2] + +/-- Complete interval computation for depth 13, residue 6199. -/ +theorem bounds_13_6199 : exactInterval 13 6199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6199 : oddCount 6199 13 = 9 ∧ acceleratedOrbit 13 6199 = 14899 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6199) = 3 ^ 9 * m + 14899 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6199.1, data_13_6199.2] + +/-- Complete interval computation for depth 13, residue 6200. -/ +theorem bounds_13_6200 : exactInterval 13 6200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6200 : oddCount 6200 13 = 6 ∧ acceleratedOrbit 13 6200 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6200) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6200.1, data_13_6200.2] + +/-- Complete interval computation for depth 13, residue 6201. -/ +theorem bounds_13_6201 : exactInterval 13 6201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6201 : oddCount 6201 13 = 5 ∧ acceleratedOrbit 13 6201 = 184 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6201) = 3 ^ 5 * m + 184 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6201.1, data_13_6201.2] + +/-- Complete interval computation for depth 13, residue 6202. -/ +theorem bounds_13_6202 : exactInterval 13 6202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6202 : oddCount 6202 13 = 6 ∧ acceleratedOrbit 13 6202 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6202) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6202.1, data_13_6202.2] + +/-- Complete interval computation for depth 13, residue 6203. -/ +theorem bounds_13_6203 : exactInterval 13 6203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6203 : oddCount 6203 13 = 7 ∧ acceleratedOrbit 13 6203 = 1657 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6203) = 3 ^ 7 * m + 1657 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6203.1, data_13_6203.2] + +/-- Complete interval computation for depth 13, residue 6204. -/ +theorem bounds_13_6204 : exactInterval 13 6204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6204 : oddCount 6204 13 = 6 ∧ acceleratedOrbit 13 6204 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6204) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6204.1, data_13_6204.2] + +/-- Complete interval computation for depth 13, residue 6205. -/ +theorem bounds_13_6205 : exactInterval 13 6205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6205 : oddCount 6205 13 = 6 ∧ acceleratedOrbit 13 6205 = 553 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6205) = 3 ^ 6 * m + 553 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6205.1, data_13_6205.2] + +/-- Complete interval computation for depth 13, residue 6206. -/ +theorem bounds_13_6206 : exactInterval 13 6206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6206 : oddCount 6206 13 = 9 ∧ acceleratedOrbit 13 6206 = 14917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6206) = 3 ^ 9 * m + 14917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6206.1, data_13_6206.2] + +/-- Complete interval computation for depth 13, residue 6207. -/ +theorem bounds_13_6207 : exactInterval 13 6207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6207 : oddCount 6207 13 = 9 ∧ acceleratedOrbit 13 6207 = 14917 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6207) = 3 ^ 9 * m + 14917 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6207.1, data_13_6207.2] + +/-- Complete interval computation for depth 13, residue 6208. -/ +theorem bounds_13_6208 : exactInterval 13 6208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6208 : oddCount 6208 13 = 5 ∧ acceleratedOrbit 13 6208 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6208) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6208.1, data_13_6208.2] + +/-- Complete interval computation for depth 13, residue 6209. -/ +theorem bounds_13_6209 : exactInterval 13 6209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6209 : oddCount 6209 13 = 7 ∧ acceleratedOrbit 13 6209 = 1660 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6209) = 3 ^ 7 * m + 1660 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6209.1, data_13_6209.2] + +end Collatz.Research.StoppingAtlas.Batch0871 From df2a8628e987acf6cb1a0f48cab528bace86d824 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:13 +0530 Subject: [PATCH 0872/1001] proof: certify atlas Batch0872 (13:6210 to 13:6224) --- Collatz/Research/StoppingAtlas/Batch0872.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0872.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0872.lean b/Collatz/Research/StoppingAtlas/Batch0872.lean new file mode 100644 index 00000000..d3d266f1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0872.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0872 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6210. -/ +theorem bounds_13_6210 : exactInterval 13 6210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6210 : oddCount 6210 13 = 7 ∧ acceleratedOrbit 13 6210 = 1660 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6210) = 3 ^ 7 * m + 1660 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6210.1, data_13_6210.2] + +/-- Complete interval computation for depth 13, residue 6211. -/ +theorem bounds_13_6211 : exactInterval 13 6211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6211 : oddCount 6211 13 = 7 ∧ acceleratedOrbit 13 6211 = 1660 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6211) = 3 ^ 7 * m + 1660 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6211.1, data_13_6211.2] + +/-- Complete interval computation for depth 13, residue 6212. -/ +theorem bounds_13_6212 : exactInterval 13 6212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6212 : oddCount 6212 13 = 4 ∧ acceleratedOrbit 13 6212 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6212) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6212.1, data_13_6212.2] + +/-- Complete interval computation for depth 13, residue 6213. -/ +theorem bounds_13_6213 : exactInterval 13 6213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6213 : oddCount 6213 13 = 4 ∧ acceleratedOrbit 13 6213 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6213) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6213.1, data_13_6213.2] + +/-- Complete interval computation for depth 13, residue 6214. -/ +theorem bounds_13_6214 : exactInterval 13 6214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6214 : oddCount 6214 13 = 4 ∧ acceleratedOrbit 13 6214 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6214) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6214.1, data_13_6214.2] + +/-- Complete interval computation for depth 13, residue 6215. -/ +theorem bounds_13_6215 : exactInterval 13 6215 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6215) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6215 : oddCount 6215 13 = 8 ∧ acceleratedOrbit 13 6215 = 4979 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6215) = 3 ^ 8 * m + 4979 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6215.1, data_13_6215.2] + +/-- Complete interval computation for depth 13, residue 6216. -/ +theorem bounds_13_6216 : exactInterval 13 6216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6216 : oddCount 6216 13 = 7 ∧ acceleratedOrbit 13 6216 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6216) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6216.1, data_13_6216.2] + +/-- Complete interval computation for depth 13, residue 6217. -/ +theorem bounds_13_6217 : exactInterval 13 6217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6217 : oddCount 6217 13 = 9 ∧ acceleratedOrbit 13 6217 = 14944 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6217) = 3 ^ 9 * m + 14944 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6217.1, data_13_6217.2] + +/-- Complete interval computation for depth 13, residue 6218. -/ +theorem bounds_13_6218 : exactInterval 13 6218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6218 : oddCount 6218 13 = 7 ∧ acceleratedOrbit 13 6218 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6218) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6218.1, data_13_6218.2] + +/-- Complete interval computation for depth 13, residue 6219. -/ +theorem bounds_13_6219 : exactInterval 13 6219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6219 : oddCount 6219 13 = 4 ∧ acceleratedOrbit 13 6219 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6219) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6219.1, data_13_6219.2] + +/-- Complete interval computation for depth 13, residue 6220. -/ +theorem bounds_13_6220 : exactInterval 13 6220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6220 : oddCount 6220 13 = 7 ∧ acceleratedOrbit 13 6220 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6220) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6220.1, data_13_6220.2] + +/-- Complete interval computation for depth 13, residue 6221. -/ +theorem bounds_13_6221 : exactInterval 13 6221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6221 : oddCount 6221 13 = 7 ∧ acceleratedOrbit 13 6221 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6221) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6221.1, data_13_6221.2] + +/-- Complete interval computation for depth 13, residue 6222. -/ +theorem bounds_13_6222 : exactInterval 13 6222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6222 : oddCount 6222 13 = 6 ∧ acceleratedOrbit 13 6222 = 554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6222) = 3 ^ 6 * m + 554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6222.1, data_13_6222.2] + +/-- Complete interval computation for depth 13, residue 6223. -/ +theorem bounds_13_6223 : exactInterval 13 6223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6223 : oddCount 6223 13 = 6 ∧ acceleratedOrbit 13 6223 = 554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6223) = 3 ^ 6 * m + 554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6223.1, data_13_6223.2] + +/-- Complete interval computation for depth 13, residue 6224. -/ +theorem bounds_13_6224 : exactInterval 13 6224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6224 : oddCount 6224 13 = 5 ∧ acceleratedOrbit 13 6224 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6224) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6224.1, data_13_6224.2] + +end Collatz.Research.StoppingAtlas.Batch0872 From 638c5c2cb13500cdd96ced56918a2a9958aec3a9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:13 +0530 Subject: [PATCH 0873/1001] proof: certify atlas Batch0873 (13:6225 to 13:6240) --- Collatz/Research/StoppingAtlas/Batch0873.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0873.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0873.lean b/Collatz/Research/StoppingAtlas/Batch0873.lean new file mode 100644 index 00000000..a16be246 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0873.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0873 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6225. -/ +theorem bounds_13_6225 : exactInterval 13 6225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6225 : oddCount 6225 13 = 7 ∧ acceleratedOrbit 13 6225 = 1664 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6225) = 3 ^ 7 * m + 1664 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6225.1, data_13_6225.2] + +/-- Complete interval computation for depth 13, residue 6226. -/ +theorem bounds_13_6226 : exactInterval 13 6226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6226 : oddCount 6226 13 = 7 ∧ acceleratedOrbit 13 6226 = 1663 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6226) = 3 ^ 7 * m + 1663 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6226.1, data_13_6226.2] + +/-- Complete interval computation for depth 13, residue 6227. -/ +theorem bounds_13_6227 : exactInterval 13 6227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6227 : oddCount 6227 13 = 7 ∧ acceleratedOrbit 13 6227 = 1663 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6227) = 3 ^ 7 * m + 1663 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6227.1, data_13_6227.2] + +/-- Complete interval computation for depth 13, residue 6228. -/ +theorem bounds_13_6228 : exactInterval 13 6228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6228 : oddCount 6228 13 = 5 ∧ acceleratedOrbit 13 6228 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6228) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6228.1, data_13_6228.2] + +/-- Complete interval computation for depth 13, residue 6229. -/ +theorem bounds_13_6229 : exactInterval 13 6229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6229 : oddCount 6229 13 = 5 ∧ acceleratedOrbit 13 6229 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6229) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6229.1, data_13_6229.2] + +/-- Complete interval computation for depth 13, residue 6230. -/ +theorem bounds_13_6230 : exactInterval 13 6230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6230 : oddCount 6230 13 = 5 ∧ acceleratedOrbit 13 6230 = 185 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6230) = 3 ^ 5 * m + 185 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6230.1, data_13_6230.2] + +/-- Complete interval computation for depth 13, residue 6231. -/ +theorem bounds_13_6231 : exactInterval 13 6231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6231 : oddCount 6231 13 = 5 ∧ acceleratedOrbit 13 6231 = 185 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6231) = 3 ^ 5 * m + 185 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6231.1, data_13_6231.2] + +/-- Complete interval computation for depth 13, residue 6232. -/ +theorem bounds_13_6232 : exactInterval 13 6232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6232 : oddCount 6232 13 = 6 ∧ acceleratedOrbit 13 6232 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6232) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6232.1, data_13_6232.2] + +/-- Complete interval computation for depth 13, residue 6233. -/ +theorem bounds_13_6233 : exactInterval 13 6233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6233 : oddCount 6233 13 = 5 ∧ acceleratedOrbit 13 6233 = 185 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6233) = 3 ^ 5 * m + 185 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6233.1, data_13_6233.2] + +/-- Complete interval computation for depth 13, residue 6234. -/ +theorem bounds_13_6234 : exactInterval 13 6234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6234 : oddCount 6234 13 = 6 ∧ acceleratedOrbit 13 6234 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6234) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6234.1, data_13_6234.2] + +/-- Complete interval computation for depth 13, residue 6235. -/ +theorem bounds_13_6235 : exactInterval 13 6235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6235 : oddCount 6235 13 = 11 ∧ acceleratedOrbit 13 6235 = 134864 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6235) = 3 ^ 11 * m + 134864 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6235.1, data_13_6235.2] + +/-- Complete interval computation for depth 13, residue 6236. -/ +theorem bounds_13_6236 : exactInterval 13 6236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6236 : oddCount 6236 13 = 6 ∧ acceleratedOrbit 13 6236 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6236) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6236.1, data_13_6236.2] + +/-- Complete interval computation for depth 13, residue 6237. -/ +theorem bounds_13_6237 : exactInterval 13 6237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6237 : oddCount 6237 13 = 6 ∧ acceleratedOrbit 13 6237 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6237) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6237.1, data_13_6237.2] + +/-- Complete interval computation for depth 13, residue 6238. -/ +theorem bounds_13_6238 : exactInterval 13 6238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6238 : oddCount 6238 13 = 7 ∧ acceleratedOrbit 13 6238 = 1666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6238) = 3 ^ 7 * m + 1666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6238.1, data_13_6238.2] + +/-- Complete interval computation for depth 13, residue 6239. -/ +theorem bounds_13_6239 : exactInterval 13 6239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6239 : oddCount 6239 13 = 7 ∧ acceleratedOrbit 13 6239 = 1666 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6239) = 3 ^ 7 * m + 1666 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6239.1, data_13_6239.2] + +/-- Complete interval computation for depth 13, residue 6240. -/ +theorem bounds_13_6240 : exactInterval 13 6240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6240 : oddCount 6240 13 = 5 ∧ acceleratedOrbit 13 6240 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6240) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6240.1, data_13_6240.2] + +end Collatz.Research.StoppingAtlas.Batch0873 From 345b2ff040cd1d9ffb51f1b2b7ff5b9b4ff18af4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:14 +0530 Subject: [PATCH 0874/1001] proof: certify atlas Batch0874 (13:6241 to 13:6255) --- Collatz/Research/StoppingAtlas/Batch0874.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0874.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0874.lean b/Collatz/Research/StoppingAtlas/Batch0874.lean new file mode 100644 index 00000000..57743dbe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0874.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0874 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6241. -/ +theorem bounds_13_6241 : exactInterval 13 6241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6241 : oddCount 6241 13 = 7 ∧ acceleratedOrbit 13 6241 = 1667 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6241) = 3 ^ 7 * m + 1667 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6241.1, data_13_6241.2] + +/-- Complete interval computation for depth 13, residue 6242. -/ +theorem bounds_13_6242 : exactInterval 13 6242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6242 : oddCount 6242 13 = 6 ∧ acceleratedOrbit 13 6242 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6242) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6242.1, data_13_6242.2] + +/-- Complete interval computation for depth 13, residue 6243. -/ +theorem bounds_13_6243 : exactInterval 13 6243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6243 : oddCount 6243 13 = 6 ∧ acceleratedOrbit 13 6243 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6243) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6243.1, data_13_6243.2] + +/-- Complete interval computation for depth 13, residue 6244. -/ +theorem bounds_13_6244 : exactInterval 13 6244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6244 : oddCount 6244 13 = 6 ∧ acceleratedOrbit 13 6244 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6244) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6244.1, data_13_6244.2] + +/-- Complete interval computation for depth 13, residue 6245. -/ +theorem bounds_13_6245 : exactInterval 13 6245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6245 : oddCount 6245 13 = 6 ∧ acceleratedOrbit 13 6245 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6245) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6245.1, data_13_6245.2] + +/-- Complete interval computation for depth 13, residue 6246. -/ +theorem bounds_13_6246 : exactInterval 13 6246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6246 : oddCount 6246 13 = 6 ∧ acceleratedOrbit 13 6246 = 557 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6246) = 3 ^ 6 * m + 557 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6246.1, data_13_6246.2] + +/-- Complete interval computation for depth 13, residue 6247. -/ +theorem bounds_13_6247 : exactInterval 13 6247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6247 : oddCount 6247 13 = 9 ∧ acceleratedOrbit 13 6247 = 15013 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6247) = 3 ^ 9 * m + 15013 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6247.1, data_13_6247.2] + +/-- Complete interval computation for depth 13, residue 6248. -/ +theorem bounds_13_6248 : exactInterval 13 6248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6248 : oddCount 6248 13 = 5 ∧ acceleratedOrbit 13 6248 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6248) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6248.1, data_13_6248.2] + +/-- Complete interval computation for depth 13, residue 6249. -/ +theorem bounds_13_6249 : exactInterval 13 6249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6249 : oddCount 6249 13 = 7 ∧ acceleratedOrbit 13 6249 = 1669 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6249) = 3 ^ 7 * m + 1669 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6249.1, data_13_6249.2] + +/-- Complete interval computation for depth 13, residue 6250. -/ +theorem bounds_13_6250 : exactInterval 13 6250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6250 : oddCount 6250 13 = 5 ∧ acceleratedOrbit 13 6250 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6250) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6250.1, data_13_6250.2] + +/-- Complete interval computation for depth 13, residue 6251. -/ +theorem bounds_13_6251 : exactInterval 13 6251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6251 : oddCount 6251 13 = 9 ∧ acceleratedOrbit 13 6251 = 15025 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6251) = 3 ^ 9 * m + 15025 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6251.1, data_13_6251.2] + +/-- Complete interval computation for depth 13, residue 6252. -/ +theorem bounds_13_6252 : exactInterval 13 6252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6252 : oddCount 6252 13 = 8 ∧ acceleratedOrbit 13 6252 = 5012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6252) = 3 ^ 8 * m + 5012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6252.1, data_13_6252.2] + +/-- Complete interval computation for depth 13, residue 6253. -/ +theorem bounds_13_6253 : exactInterval 13 6253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6253 : oddCount 6253 13 = 8 ∧ acceleratedOrbit 13 6253 = 5012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6253) = 3 ^ 8 * m + 5012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6253.1, data_13_6253.2] + +/-- Complete interval computation for depth 13, residue 6254. -/ +theorem bounds_13_6254 : exactInterval 13 6254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6254 : oddCount 6254 13 = 8 ∧ acceleratedOrbit 13 6254 = 5012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6254) = 3 ^ 8 * m + 5012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6254.1, data_13_6254.2] + +/-- Complete interval computation for depth 13, residue 6255. -/ +theorem bounds_13_6255 : exactInterval 13 6255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6255 : oddCount 6255 13 = 9 ∧ acceleratedOrbit 13 6255 = 15032 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6255) = 3 ^ 9 * m + 15032 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6255.1, data_13_6255.2] + +end Collatz.Research.StoppingAtlas.Batch0874 From a4f273e2819311ef9eecaf00c4d366e4172e9294 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:14 +0530 Subject: [PATCH 0875/1001] proof: certify atlas Batch0875 (13:6256 to 13:6271) --- Collatz/Research/StoppingAtlas/Batch0875.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0875.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0875.lean b/Collatz/Research/StoppingAtlas/Batch0875.lean new file mode 100644 index 00000000..8c8d4be4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0875.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0875 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6256. -/ +theorem bounds_13_6256 : exactInterval 13 6256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6256 : oddCount 6256 13 = 4 ∧ acceleratedOrbit 13 6256 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6256) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6256.1, data_13_6256.2] + +/-- Complete interval computation for depth 13, residue 6257. -/ +theorem bounds_13_6257 : exactInterval 13 6257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6257 : oddCount 6257 13 = 5 ∧ acceleratedOrbit 13 6257 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6257) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6257.1, data_13_6257.2] + +/-- Complete interval computation for depth 13, residue 6258. -/ +theorem bounds_13_6258 : exactInterval 13 6258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6258 : oddCount 6258 13 = 7 ∧ acceleratedOrbit 13 6258 = 1673 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6258) = 3 ^ 7 * m + 1673 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6258.1, data_13_6258.2] + +/-- Complete interval computation for depth 13, residue 6259. -/ +theorem bounds_13_6259 : exactInterval 13 6259 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6259) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6259 : oddCount 6259 13 = 7 ∧ acceleratedOrbit 13 6259 = 1673 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6259) = 3 ^ 7 * m + 1673 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6259.1, data_13_6259.2] + +/-- Complete interval computation for depth 13, residue 6260. -/ +theorem bounds_13_6260 : exactInterval 13 6260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6260 : oddCount 6260 13 = 4 ∧ acceleratedOrbit 13 6260 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6260) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6260.1, data_13_6260.2] + +/-- Complete interval computation for depth 13, residue 6261. -/ +theorem bounds_13_6261 : exactInterval 13 6261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6261 : oddCount 6261 13 = 4 ∧ acceleratedOrbit 13 6261 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6261) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6261.1, data_13_6261.2] + +/-- Complete interval computation for depth 13, residue 6262. -/ +theorem bounds_13_6262 : exactInterval 13 6262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6262 : oddCount 6262 13 = 8 ∧ acceleratedOrbit 13 6262 = 5021 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6262) = 3 ^ 8 * m + 5021 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6262.1, data_13_6262.2] + +/-- Complete interval computation for depth 13, residue 6263. -/ +theorem bounds_13_6263 : exactInterval 13 6263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6263 : oddCount 6263 13 = 8 ∧ acceleratedOrbit 13 6263 = 5021 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6263) = 3 ^ 8 * m + 5021 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6263.1, data_13_6263.2] + +/-- Complete interval computation for depth 13, residue 6264. -/ +theorem bounds_13_6264 : exactInterval 13 6264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6264 : oddCount 6264 13 = 4 ∧ acceleratedOrbit 13 6264 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6264) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6264.1, data_13_6264.2] + +/-- Complete interval computation for depth 13, residue 6265. -/ +theorem bounds_13_6265 : exactInterval 13 6265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6265 : oddCount 6265 13 = 9 ∧ acceleratedOrbit 13 6265 = 15059 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6265) = 3 ^ 9 * m + 15059 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6265.1, data_13_6265.2] + +/-- Complete interval computation for depth 13, residue 6266. -/ +theorem bounds_13_6266 : exactInterval 13 6266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6266 : oddCount 6266 13 = 4 ∧ acceleratedOrbit 13 6266 = 62 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6266) = 3 ^ 4 * m + 62 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6266.1, data_13_6266.2] + +/-- Complete interval computation for depth 13, residue 6267. -/ +theorem bounds_13_6267 : exactInterval 13 6267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6267 : oddCount 6267 13 = 9 ∧ acceleratedOrbit 13 6267 = 15065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6267) = 3 ^ 9 * m + 15065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6267.1, data_13_6267.2] + +/-- Complete interval computation for depth 13, residue 6268. -/ +theorem bounds_13_6268 : exactInterval 13 6268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6268 : oddCount 6268 13 = 8 ∧ acceleratedOrbit 13 6268 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6268) = 3 ^ 8 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6268.1, data_13_6268.2] + +/-- Complete interval computation for depth 13, residue 6269. -/ +theorem bounds_13_6269 : exactInterval 13 6269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6269 : oddCount 6269 13 = 8 ∧ acceleratedOrbit 13 6269 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6269) = 3 ^ 8 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6269.1, data_13_6269.2] + +/-- Complete interval computation for depth 13, residue 6270. -/ +theorem bounds_13_6270 : exactInterval 13 6270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6270 : oddCount 6270 13 = 8 ∧ acceleratedOrbit 13 6270 = 5024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6270) = 3 ^ 8 * m + 5024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6270.1, data_13_6270.2] + +/-- Complete interval computation for depth 13, residue 6271. -/ +theorem bounds_13_6271 : exactInterval 13 6271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6271 : oddCount 6271 13 = 9 ∧ acceleratedOrbit 13 6271 = 15070 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6271) = 3 ^ 9 * m + 15070 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6271.1, data_13_6271.2] + +end Collatz.Research.StoppingAtlas.Batch0875 From d15c0610574b5521061b2a042df7e58ee1d76716 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:14 +0530 Subject: [PATCH 0876/1001] proof: certify atlas Batch0876 (13:6272 to 13:6286) --- Collatz/Research/StoppingAtlas/Batch0876.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0876.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0876.lean b/Collatz/Research/StoppingAtlas/Batch0876.lean new file mode 100644 index 00000000..88c1d247 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0876.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0876 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6272. -/ +theorem bounds_13_6272 : exactInterval 13 6272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6272 : oddCount 6272 13 = 2 ∧ acceleratedOrbit 13 6272 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6272) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6272.1, data_13_6272.2] + +/-- Complete interval computation for depth 13, residue 6273. -/ +theorem bounds_13_6273 : exactInterval 13 6273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6273 : oddCount 6273 13 = 7 ∧ acceleratedOrbit 13 6273 = 1676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6273) = 3 ^ 7 * m + 1676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6273.1, data_13_6273.2] + +/-- Complete interval computation for depth 13, residue 6274. -/ +theorem bounds_13_6274 : exactInterval 13 6274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6274 : oddCount 6274 13 = 6 ∧ acceleratedOrbit 13 6274 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6274) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6274.1, data_13_6274.2] + +/-- Complete interval computation for depth 13, residue 6275. -/ +theorem bounds_13_6275 : exactInterval 13 6275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6275 : oddCount 6275 13 = 6 ∧ acceleratedOrbit 13 6275 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6275) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6275.1, data_13_6275.2] + +/-- Complete interval computation for depth 13, residue 6276. -/ +theorem bounds_13_6276 : exactInterval 13 6276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6276 : oddCount 6276 13 = 6 ∧ acceleratedOrbit 13 6276 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6276) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6276.1, data_13_6276.2] + +/-- Complete interval computation for depth 13, residue 6277. -/ +theorem bounds_13_6277 : exactInterval 13 6277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6277 : oddCount 6277 13 = 6 ∧ acceleratedOrbit 13 6277 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6277) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6277.1, data_13_6277.2] + +/-- Complete interval computation for depth 13, residue 6278. -/ +theorem bounds_13_6278 : exactInterval 13 6278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6278 : oddCount 6278 13 = 6 ∧ acceleratedOrbit 13 6278 = 560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6278) = 3 ^ 6 * m + 560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6278.1, data_13_6278.2] + +/-- Complete interval computation for depth 13, residue 6279. -/ +theorem bounds_13_6279 : exactInterval 13 6279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6279 : oddCount 6279 13 = 6 ∧ acceleratedOrbit 13 6279 = 559 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6279) = 3 ^ 6 * m + 559 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6279.1, data_13_6279.2] + +/-- Complete interval computation for depth 13, residue 6280. -/ +theorem bounds_13_6280 : exactInterval 13 6280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6280 : oddCount 6280 13 = 5 ∧ acceleratedOrbit 13 6280 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6280) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6280.1, data_13_6280.2] + +/-- Complete interval computation for depth 13, residue 6281. -/ +theorem bounds_13_6281 : exactInterval 13 6281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6281 : oddCount 6281 13 = 8 ∧ acceleratedOrbit 13 6281 = 5032 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6281) = 3 ^ 8 * m + 5032 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6281.1, data_13_6281.2] + +/-- Complete interval computation for depth 13, residue 6282. -/ +theorem bounds_13_6282 : exactInterval 13 6282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6282 : oddCount 6282 13 = 5 ∧ acceleratedOrbit 13 6282 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6282) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6282.1, data_13_6282.2] + +/-- Complete interval computation for depth 13, residue 6283. -/ +theorem bounds_13_6283 : exactInterval 13 6283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6283 : oddCount 6283 13 = 8 ∧ acceleratedOrbit 13 6283 = 5035 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6283) = 3 ^ 8 * m + 5035 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6283.1, data_13_6283.2] + +/-- Complete interval computation for depth 13, residue 6284. -/ +theorem bounds_13_6284 : exactInterval 13 6284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6284 : oddCount 6284 13 = 5 ∧ acceleratedOrbit 13 6284 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6284) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6284.1, data_13_6284.2] + +/-- Complete interval computation for depth 13, residue 6285. -/ +theorem bounds_13_6285 : exactInterval 13 6285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6285 : oddCount 6285 13 = 5 ∧ acceleratedOrbit 13 6285 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6285) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6285.1, data_13_6285.2] + +/-- Complete interval computation for depth 13, residue 6286. -/ +theorem bounds_13_6286 : exactInterval 13 6286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6286 : oddCount 6286 13 = 7 ∧ acceleratedOrbit 13 6286 = 1679 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6286) = 3 ^ 7 * m + 1679 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6286.1, data_13_6286.2] + +end Collatz.Research.StoppingAtlas.Batch0876 From c360f3bb10c9d4780c03ea3ff3eaabb4d6e5d7de Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:14 +0530 Subject: [PATCH 0877/1001] proof: certify atlas Batch0877 (13:6287 to 13:6301) --- Collatz/Research/StoppingAtlas/Batch0877.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0877.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0877.lean b/Collatz/Research/StoppingAtlas/Batch0877.lean new file mode 100644 index 00000000..6ebbb681 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0877.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0877 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6287. -/ +theorem bounds_13_6287 : exactInterval 13 6287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6287 : oddCount 6287 13 = 7 ∧ acceleratedOrbit 13 6287 = 1679 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6287) = 3 ^ 7 * m + 1679 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6287.1, data_13_6287.2] + +/-- Complete interval computation for depth 13, residue 6288. -/ +theorem bounds_13_6288 : exactInterval 13 6288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6288 : oddCount 6288 13 = 6 ∧ acceleratedOrbit 13 6288 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6288) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6288.1, data_13_6288.2] + +/-- Complete interval computation for depth 13, residue 6289. -/ +theorem bounds_13_6289 : exactInterval 13 6289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6289 : oddCount 6289 13 = 8 ∧ acceleratedOrbit 13 6289 = 5042 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6289) = 3 ^ 8 * m + 5042 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6289.1, data_13_6289.2] + +/-- Complete interval computation for depth 13, residue 6290. -/ +theorem bounds_13_6290 : exactInterval 13 6290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6290 : oddCount 6290 13 = 8 ∧ acceleratedOrbit 13 6290 = 5042 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6290) = 3 ^ 8 * m + 5042 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6290.1, data_13_6290.2] + +/-- Complete interval computation for depth 13, residue 6291. -/ +theorem bounds_13_6291 : exactInterval 13 6291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6291 : oddCount 6291 13 = 8 ∧ acceleratedOrbit 13 6291 = 5042 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6291) = 3 ^ 8 * m + 5042 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6291.1, data_13_6291.2] + +/-- Complete interval computation for depth 13, residue 6292. -/ +theorem bounds_13_6292 : exactInterval 13 6292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6292 : oddCount 6292 13 = 6 ∧ acceleratedOrbit 13 6292 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6292) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6292.1, data_13_6292.2] + +/-- Complete interval computation for depth 13, residue 6293. -/ +theorem bounds_13_6293 : exactInterval 13 6293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6293 : oddCount 6293 13 = 6 ∧ acceleratedOrbit 13 6293 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6293) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6293.1, data_13_6293.2] + +/-- Complete interval computation for depth 13, residue 6294. -/ +theorem bounds_13_6294 : exactInterval 13 6294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6294 : oddCount 6294 13 = 5 ∧ acceleratedOrbit 13 6294 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6294) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6294.1, data_13_6294.2] + +/-- Complete interval computation for depth 13, residue 6295. -/ +theorem bounds_13_6295 : exactInterval 13 6295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6295 : oddCount 6295 13 = 5 ∧ acceleratedOrbit 13 6295 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6295) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6295.1, data_13_6295.2] + +/-- Complete interval computation for depth 13, residue 6296. -/ +theorem bounds_13_6296 : exactInterval 13 6296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6296 : oddCount 6296 13 = 6 ∧ acceleratedOrbit 13 6296 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6296) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6296.1, data_13_6296.2] + +/-- Complete interval computation for depth 13, residue 6297. -/ +theorem bounds_13_6297 : exactInterval 13 6297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6297 : oddCount 6297 13 = 8 ∧ acceleratedOrbit 13 6297 = 5048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6297) = 3 ^ 8 * m + 5048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6297.1, data_13_6297.2] + +/-- Complete interval computation for depth 13, residue 6298. -/ +theorem bounds_13_6298 : exactInterval 13 6298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6298 : oddCount 6298 13 = 6 ∧ acceleratedOrbit 13 6298 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6298) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6298.1, data_13_6298.2] + +/-- Complete interval computation for depth 13, residue 6299. -/ +theorem bounds_13_6299 : exactInterval 13 6299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6299 : oddCount 6299 13 = 7 ∧ acceleratedOrbit 13 6299 = 1682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6299) = 3 ^ 7 * m + 1682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6299.1, data_13_6299.2] + +/-- Complete interval computation for depth 13, residue 6300. -/ +theorem bounds_13_6300 : exactInterval 13 6300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6300 : oddCount 6300 13 = 5 ∧ acceleratedOrbit 13 6300 = 187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6300) = 3 ^ 5 * m + 187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6300.1, data_13_6300.2] + +/-- Complete interval computation for depth 13, residue 6301. -/ +theorem bounds_13_6301 : exactInterval 13 6301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6301 : oddCount 6301 13 = 5 ∧ acceleratedOrbit 13 6301 = 187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6301) = 3 ^ 5 * m + 187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6301.1, data_13_6301.2] + +end Collatz.Research.StoppingAtlas.Batch0877 From f8825e8dc62b74129b83a05bb0b6293c302a0b41 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:14 +0530 Subject: [PATCH 0878/1001] proof: certify atlas Batch0878 (13:6302 to 13:6317) --- Collatz/Research/StoppingAtlas/Batch0878.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0878.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0878.lean b/Collatz/Research/StoppingAtlas/Batch0878.lean new file mode 100644 index 00000000..cec24eb9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0878.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0878 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6302. -/ +theorem bounds_13_6302 : exactInterval 13 6302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6302 : oddCount 6302 13 = 5 ∧ acceleratedOrbit 13 6302 = 187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6302) = 3 ^ 5 * m + 187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6302.1, data_13_6302.2] + +/-- Complete interval computation for depth 13, residue 6303. -/ +theorem bounds_13_6303 : exactInterval 13 6303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6303 : oddCount 6303 13 = 12 ∧ acceleratedOrbit 13 6303 = 408968 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6303) = 3 ^ 12 * m + 408968 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6303.1, data_13_6303.2] + +/-- Complete interval computation for depth 13, residue 6304. -/ +theorem bounds_13_6304 : exactInterval 13 6304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6304 : oddCount 6304 13 = 2 ∧ acceleratedOrbit 13 6304 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6304) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6304.1, data_13_6304.2] + +/-- Complete interval computation for depth 13, residue 6305. -/ +theorem bounds_13_6305 : exactInterval 13 6305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6305 : oddCount 6305 13 = 7 ∧ acceleratedOrbit 13 6305 = 1684 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6305) = 3 ^ 7 * m + 1684 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6305.1, data_13_6305.2] + +/-- Complete interval computation for depth 13, residue 6306. -/ +theorem bounds_13_6306 : exactInterval 13 6306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6306 : oddCount 6306 13 = 6 ∧ acceleratedOrbit 13 6306 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6306) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6306.1, data_13_6306.2] + +/-- Complete interval computation for depth 13, residue 6307. -/ +theorem bounds_13_6307 : exactInterval 13 6307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6307 : oddCount 6307 13 = 6 ∧ acceleratedOrbit 13 6307 = 562 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6307) = 3 ^ 6 * m + 562 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6307.1, data_13_6307.2] + +/-- Complete interval computation for depth 13, residue 6308. -/ +theorem bounds_13_6308 : exactInterval 13 6308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6308 : oddCount 6308 13 = 9 ∧ acceleratedOrbit 13 6308 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6308) = 3 ^ 9 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6308.1, data_13_6308.2] + +/-- Complete interval computation for depth 13, residue 6309. -/ +theorem bounds_13_6309 : exactInterval 13 6309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6309 : oddCount 6309 13 = 9 ∧ acceleratedOrbit 13 6309 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6309) = 3 ^ 9 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6309.1, data_13_6309.2] + +/-- Complete interval computation for depth 13, residue 6310. -/ +theorem bounds_13_6310 : exactInterval 13 6310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6310 : oddCount 6310 13 = 9 ∧ acceleratedOrbit 13 6310 = 15173 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6310) = 3 ^ 9 * m + 15173 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6310.1, data_13_6310.2] + +/-- Complete interval computation for depth 13, residue 6311. -/ +theorem bounds_13_6311 : exactInterval 13 6311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6311 : oddCount 6311 13 = 9 ∧ acceleratedOrbit 13 6311 = 15167 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6311) = 3 ^ 9 * m + 15167 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6311.1, data_13_6311.2] + +/-- Complete interval computation for depth 13, residue 6312. -/ +theorem bounds_13_6312 : exactInterval 13 6312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6312 : oddCount 6312 13 = 2 ∧ acceleratedOrbit 13 6312 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6312) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6312.1, data_13_6312.2] + +/-- Complete interval computation for depth 13, residue 6313. -/ +theorem bounds_13_6313 : exactInterval 13 6313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6313 : oddCount 6313 13 = 10 ∧ acceleratedOrbit 13 6313 = 45517 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6313) = 3 ^ 10 * m + 45517 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6313.1, data_13_6313.2] + +/-- Complete interval computation for depth 13, residue 6314. -/ +theorem bounds_13_6314 : exactInterval 13 6314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6314 : oddCount 6314 13 = 2 ∧ acceleratedOrbit 13 6314 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6314) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6314.1, data_13_6314.2] + +/-- Complete interval computation for depth 13, residue 6315. -/ +theorem bounds_13_6315 : exactInterval 13 6315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6315 : oddCount 6315 13 = 7 ∧ acceleratedOrbit 13 6315 = 1687 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6315) = 3 ^ 7 * m + 1687 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6315.1, data_13_6315.2] + +/-- Complete interval computation for depth 13, residue 6316. -/ +theorem bounds_13_6316 : exactInterval 13 6316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6316 : oddCount 6316 13 = 5 ∧ acceleratedOrbit 13 6316 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6316) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6316.1, data_13_6316.2] + +/-- Complete interval computation for depth 13, residue 6317. -/ +theorem bounds_13_6317 : exactInterval 13 6317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6317 : oddCount 6317 13 = 5 ∧ acceleratedOrbit 13 6317 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6317) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6317.1, data_13_6317.2] + +end Collatz.Research.StoppingAtlas.Batch0878 From 90b10340df853c75eaed39d9e57a3f3d283ac297 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:15 +0530 Subject: [PATCH 0879/1001] proof: certify atlas Batch0879 (13:6318 to 13:6332) --- Collatz/Research/StoppingAtlas/Batch0879.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0879.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0879.lean b/Collatz/Research/StoppingAtlas/Batch0879.lean new file mode 100644 index 00000000..412678c5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0879.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0879 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6318. -/ +theorem bounds_13_6318 : exactInterval 13 6318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6318 : oddCount 6318 13 = 5 ∧ acceleratedOrbit 13 6318 = 188 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6318) = 3 ^ 5 * m + 188 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6318.1, data_13_6318.2] + +/-- Complete interval computation for depth 13, residue 6319. -/ +theorem bounds_13_6319 : exactInterval 13 6319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6319 : oddCount 6319 13 = 9 ∧ acceleratedOrbit 13 6319 = 15187 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6319) = 3 ^ 9 * m + 15187 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6319.1, data_13_6319.2] + +/-- Complete interval computation for depth 13, residue 6320. -/ +theorem bounds_13_6320 : exactInterval 13 6320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6320 : oddCount 6320 13 = 6 ∧ acceleratedOrbit 13 6320 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6320) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6320.1, data_13_6320.2] + +/-- Complete interval computation for depth 13, residue 6321. -/ +theorem bounds_13_6321 : exactInterval 13 6321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6321 : oddCount 6321 13 = 7 ∧ acceleratedOrbit 13 6321 = 1691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6321) = 3 ^ 7 * m + 1691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6321.1, data_13_6321.2] + +/-- Complete interval computation for depth 13, residue 6322. -/ +theorem bounds_13_6322 : exactInterval 13 6322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6322 : oddCount 6322 13 = 7 ∧ acceleratedOrbit 13 6322 = 1691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6322) = 3 ^ 7 * m + 1691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6322.1, data_13_6322.2] + +/-- Complete interval computation for depth 13, residue 6323. -/ +theorem bounds_13_6323 : exactInterval 13 6323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6323 : oddCount 6323 13 = 7 ∧ acceleratedOrbit 13 6323 = 1691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6323) = 3 ^ 7 * m + 1691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6323.1, data_13_6323.2] + +/-- Complete interval computation for depth 13, residue 6324. -/ +theorem bounds_13_6324 : exactInterval 13 6324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6324 : oddCount 6324 13 = 6 ∧ acceleratedOrbit 13 6324 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6324) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6324.1, data_13_6324.2] + +/-- Complete interval computation for depth 13, residue 6325. -/ +theorem bounds_13_6325 : exactInterval 13 6325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6325 : oddCount 6325 13 = 6 ∧ acceleratedOrbit 13 6325 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6325) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6325.1, data_13_6325.2] + +/-- Complete interval computation for depth 13, residue 6326. -/ +theorem bounds_13_6326 : exactInterval 13 6326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6326 : oddCount 6326 13 = 8 ∧ acceleratedOrbit 13 6326 = 5069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6326) = 3 ^ 8 * m + 5069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6326.1, data_13_6326.2] + +/-- Complete interval computation for depth 13, residue 6327. -/ +theorem bounds_13_6327 : exactInterval 13 6327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6327 : oddCount 6327 13 = 8 ∧ acceleratedOrbit 13 6327 = 5069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6327) = 3 ^ 8 * m + 5069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6327.1, data_13_6327.2] + +/-- Complete interval computation for depth 13, residue 6328. -/ +theorem bounds_13_6328 : exactInterval 13 6328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6328 : oddCount 6328 13 = 6 ∧ acceleratedOrbit 13 6328 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6328) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6328.1, data_13_6328.2] + +/-- Complete interval computation for depth 13, residue 6329. -/ +theorem bounds_13_6329 : exactInterval 13 6329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6329 : oddCount 6329 13 = 7 ∧ acceleratedOrbit 13 6329 = 1691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6329) = 3 ^ 7 * m + 1691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6329.1, data_13_6329.2] + +/-- Complete interval computation for depth 13, residue 6330. -/ +theorem bounds_13_6330 : exactInterval 13 6330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6330 : oddCount 6330 13 = 6 ∧ acceleratedOrbit 13 6330 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6330) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6330.1, data_13_6330.2] + +/-- Complete interval computation for depth 13, residue 6331. -/ +theorem bounds_13_6331 : exactInterval 13 6331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6331 : oddCount 6331 13 = 9 ∧ acceleratedOrbit 13 6331 = 15218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6331) = 3 ^ 9 * m + 15218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6331.1, data_13_6331.2] + +/-- Complete interval computation for depth 13, residue 6332. -/ +theorem bounds_13_6332 : exactInterval 13 6332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6332 : oddCount 6332 13 = 9 ∧ acceleratedOrbit 13 6332 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6332) = 3 ^ 9 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6332.1, data_13_6332.2] + +end Collatz.Research.StoppingAtlas.Batch0879 From 987fb6a66040282438dbcd7a95df268b0dc268f3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:15 +0530 Subject: [PATCH 0880/1001] proof: certify atlas Batch0880 (13:6333 to 13:6347) --- Collatz/Research/StoppingAtlas/Batch0880.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0880.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0880.lean b/Collatz/Research/StoppingAtlas/Batch0880.lean new file mode 100644 index 00000000..01080a5d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0880.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0880 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6333. -/ +theorem bounds_13_6333 : exactInterval 13 6333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6333 : oddCount 6333 13 = 9 ∧ acceleratedOrbit 13 6333 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6333) = 3 ^ 9 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6333.1, data_13_6333.2] + +/-- Complete interval computation for depth 13, residue 6334. -/ +theorem bounds_13_6334 : exactInterval 13 6334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6334 : oddCount 6334 13 = 9 ∧ acceleratedOrbit 13 6334 = 15227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6334) = 3 ^ 9 * m + 15227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6334.1, data_13_6334.2] + +/-- Complete interval computation for depth 13, residue 6335. -/ +theorem bounds_13_6335 : exactInterval 13 6335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6335 : oddCount 6335 13 = 8 ∧ acceleratedOrbit 13 6335 = 5075 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6335) = 3 ^ 8 * m + 5075 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6335.1, data_13_6335.2] + +/-- Complete interval computation for depth 13, residue 6336. -/ +theorem bounds_13_6336 : exactInterval 13 6336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6336 : oddCount 6336 13 = 2 ∧ acceleratedOrbit 13 6336 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6336) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6336.1, data_13_6336.2] + +/-- Complete interval computation for depth 13, residue 6337. -/ +theorem bounds_13_6337 : exactInterval 13 6337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6337 : oddCount 6337 13 = 7 ∧ acceleratedOrbit 13 6337 = 1694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6337) = 3 ^ 7 * m + 1694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6337.1, data_13_6337.2] + +/-- Complete interval computation for depth 13, residue 6338. -/ +theorem bounds_13_6338 : exactInterval 13 6338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6338 : oddCount 6338 13 = 7 ∧ acceleratedOrbit 13 6338 = 1694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6338) = 3 ^ 7 * m + 1694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6338.1, data_13_6338.2] + +/-- Complete interval computation for depth 13, residue 6339. -/ +theorem bounds_13_6339 : exactInterval 13 6339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6339 : oddCount 6339 13 = 7 ∧ acceleratedOrbit 13 6339 = 1694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6339) = 3 ^ 7 * m + 1694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6339.1, data_13_6339.2] + +/-- Complete interval computation for depth 13, residue 6340. -/ +theorem bounds_13_6340 : exactInterval 13 6340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6340 : oddCount 6340 13 = 7 ∧ acceleratedOrbit 13 6340 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6340) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6340.1, data_13_6340.2] + +/-- Complete interval computation for depth 13, residue 6341. -/ +theorem bounds_13_6341 : exactInterval 13 6341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6341 : oddCount 6341 13 = 7 ∧ acceleratedOrbit 13 6341 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6341) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6341.1, data_13_6341.2] + +/-- Complete interval computation for depth 13, residue 6342. -/ +theorem bounds_13_6342 : exactInterval 13 6342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6342 : oddCount 6342 13 = 7 ∧ acceleratedOrbit 13 6342 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6342) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6342.1, data_13_6342.2] + +/-- Complete interval computation for depth 13, residue 6343. -/ +theorem bounds_13_6343 : exactInterval 13 6343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6343 : oddCount 6343 13 = 7 ∧ acceleratedOrbit 13 6343 = 1694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6343) = 3 ^ 7 * m + 1694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6343.1, data_13_6343.2] + +/-- Complete interval computation for depth 13, residue 6344. -/ +theorem bounds_13_6344 : exactInterval 13 6344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6344 : oddCount 6344 13 = 7 ∧ acceleratedOrbit 13 6344 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6344) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6344.1, data_13_6344.2] + +/-- Complete interval computation for depth 13, residue 6345. -/ +theorem bounds_13_6345 : exactInterval 13 6345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6345 : oddCount 6345 13 = 6 ∧ acceleratedOrbit 13 6345 = 566 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6345) = 3 ^ 6 * m + 566 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6345.1, data_13_6345.2] + +/-- Complete interval computation for depth 13, residue 6346. -/ +theorem bounds_13_6346 : exactInterval 13 6346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6346 : oddCount 6346 13 = 7 ∧ acceleratedOrbit 13 6346 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6346) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6346.1, data_13_6346.2] + +/-- Complete interval computation for depth 13, residue 6347. -/ +theorem bounds_13_6347 : exactInterval 13 6347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6347 : oddCount 6347 13 = 7 ∧ acceleratedOrbit 13 6347 = 1696 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6347) = 3 ^ 7 * m + 1696 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6347.1, data_13_6347.2] + +end Collatz.Research.StoppingAtlas.Batch0880 From 01ff99afb5c785f4ba5f77a2d89172c20f099b32 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:15 +0530 Subject: [PATCH 0881/1001] proof: certify atlas Batch0881 (13:6348 to 13:6363) --- Collatz/Research/StoppingAtlas/Batch0881.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0881.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0881.lean b/Collatz/Research/StoppingAtlas/Batch0881.lean new file mode 100644 index 00000000..4431f4b2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0881.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0881 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6348. -/ +theorem bounds_13_6348 : exactInterval 13 6348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6348 : oddCount 6348 13 = 7 ∧ acceleratedOrbit 13 6348 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6348) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6348.1, data_13_6348.2] + +/-- Complete interval computation for depth 13, residue 6349. -/ +theorem bounds_13_6349 : exactInterval 13 6349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6349 : oddCount 6349 13 = 7 ∧ acceleratedOrbit 13 6349 = 1700 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6349) = 3 ^ 7 * m + 1700 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6349.1, data_13_6349.2] + +/-- Complete interval computation for depth 13, residue 6350. -/ +theorem bounds_13_6350 : exactInterval 13 6350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6350 : oddCount 6350 13 = 10 ∧ acceleratedOrbit 13 6350 = 45791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6350) = 3 ^ 10 * m + 45791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6350.1, data_13_6350.2] + +/-- Complete interval computation for depth 13, residue 6351. -/ +theorem bounds_13_6351 : exactInterval 13 6351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6351 : oddCount 6351 13 = 10 ∧ acceleratedOrbit 13 6351 = 45791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6351) = 3 ^ 10 * m + 45791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6351.1, data_13_6351.2] + +/-- Complete interval computation for depth 13, residue 6352. -/ +theorem bounds_13_6352 : exactInterval 13 6352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6352 : oddCount 6352 13 = 2 ∧ acceleratedOrbit 13 6352 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6352) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6352.1, data_13_6352.2] + +/-- Complete interval computation for depth 13, residue 6353. -/ +theorem bounds_13_6353 : exactInterval 13 6353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6353 : oddCount 6353 13 = 8 ∧ acceleratedOrbit 13 6353 = 5093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6353) = 3 ^ 8 * m + 5093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6353.1, data_13_6353.2] + +/-- Complete interval computation for depth 13, residue 6354. -/ +theorem bounds_13_6354 : exactInterval 13 6354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6354 : oddCount 6354 13 = 8 ∧ acceleratedOrbit 13 6354 = 5093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6354) = 3 ^ 8 * m + 5093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6354.1, data_13_6354.2] + +/-- Complete interval computation for depth 13, residue 6355. -/ +theorem bounds_13_6355 : exactInterval 13 6355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6355 : oddCount 6355 13 = 8 ∧ acceleratedOrbit 13 6355 = 5093 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6355) = 3 ^ 8 * m + 5093 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6355.1, data_13_6355.2] + +/-- Complete interval computation for depth 13, residue 6356. -/ +theorem bounds_13_6356 : exactInterval 13 6356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6356 : oddCount 6356 13 = 2 ∧ acceleratedOrbit 13 6356 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6356) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6356.1, data_13_6356.2] + +/-- Complete interval computation for depth 13, residue 6357. -/ +theorem bounds_13_6357 : exactInterval 13 6357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6357 : oddCount 6357 13 = 2 ∧ acceleratedOrbit 13 6357 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6357) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6357.1, data_13_6357.2] + +/-- Complete interval computation for depth 13, residue 6358. -/ +theorem bounds_13_6358 : exactInterval 13 6358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6358 : oddCount 6358 13 = 8 ∧ acceleratedOrbit 13 6358 = 5096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6358) = 3 ^ 8 * m + 5096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6358.1, data_13_6358.2] + +/-- Complete interval computation for depth 13, residue 6359. -/ +theorem bounds_13_6359 : exactInterval 13 6359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6359 : oddCount 6359 13 = 8 ∧ acceleratedOrbit 13 6359 = 5096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6359) = 3 ^ 8 * m + 5096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6359.1, data_13_6359.2] + +/-- Complete interval computation for depth 13, residue 6360. -/ +theorem bounds_13_6360 : exactInterval 13 6360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6360 : oddCount 6360 13 = 9 ∧ acceleratedOrbit 13 6360 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6360) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6360.1, data_13_6360.2] + +/-- Complete interval computation for depth 13, residue 6361. -/ +theorem bounds_13_6361 : exactInterval 13 6361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6361 : oddCount 6361 13 = 8 ∧ acceleratedOrbit 13 6361 = 5102 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6361) = 3 ^ 8 * m + 5102 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6361.1, data_13_6361.2] + +/-- Complete interval computation for depth 13, residue 6362. -/ +theorem bounds_13_6362 : exactInterval 13 6362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6362 : oddCount 6362 13 = 9 ∧ acceleratedOrbit 13 6362 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6362) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6362.1, data_13_6362.2] + +/-- Complete interval computation for depth 13, residue 6363. -/ +theorem bounds_13_6363 : exactInterval 13 6363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6363 : oddCount 6363 13 = 8 ∧ acceleratedOrbit 13 6363 = 5098 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6363) = 3 ^ 8 * m + 5098 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6363.1, data_13_6363.2] + +end Collatz.Research.StoppingAtlas.Batch0881 From 6617f01227ec8615408c88e0a21b4c311e132860 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:15 +0530 Subject: [PATCH 0882/1001] proof: certify atlas Batch0882 (13:6364 to 13:6378) --- Collatz/Research/StoppingAtlas/Batch0882.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0882.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0882.lean b/Collatz/Research/StoppingAtlas/Batch0882.lean new file mode 100644 index 00000000..2455f30f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0882.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0882 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6364. -/ +theorem bounds_13_6364 : exactInterval 13 6364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6364 : oddCount 6364 13 = 9 ∧ acceleratedOrbit 13 6364 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6364) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6364.1, data_13_6364.2] + +/-- Complete interval computation for depth 13, residue 6365. -/ +theorem bounds_13_6365 : exactInterval 13 6365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6365 : oddCount 6365 13 = 9 ∧ acceleratedOrbit 13 6365 = 15308 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6365) = 3 ^ 9 * m + 15308 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6365.1, data_13_6365.2] + +/-- Complete interval computation for depth 13, residue 6366. -/ +theorem bounds_13_6366 : exactInterval 13 6366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6366 : oddCount 6366 13 = 9 ∧ acceleratedOrbit 13 6366 = 15302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6366) = 3 ^ 9 * m + 15302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6366.1, data_13_6366.2] + +/-- Complete interval computation for depth 13, residue 6367. -/ +theorem bounds_13_6367 : exactInterval 13 6367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6367 : oddCount 6367 13 = 9 ∧ acceleratedOrbit 13 6367 = 15302 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6367) = 3 ^ 9 * m + 15302 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6367.1, data_13_6367.2] + +/-- Complete interval computation for depth 13, residue 6368. -/ +theorem bounds_13_6368 : exactInterval 13 6368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6368 : oddCount 6368 13 = 5 ∧ acceleratedOrbit 13 6368 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6368) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6368.1, data_13_6368.2] + +/-- Complete interval computation for depth 13, residue 6369. -/ +theorem bounds_13_6369 : exactInterval 13 6369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6369 : oddCount 6369 13 = 11 ∧ acceleratedOrbit 13 6369 = 137780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6369) = 3 ^ 11 * m + 137780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6369.1, data_13_6369.2] + +/-- Complete interval computation for depth 13, residue 6370. -/ +theorem bounds_13_6370 : exactInterval 13 6370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6370 : oddCount 6370 13 = 2 ∧ acceleratedOrbit 13 6370 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6370) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6370.1, data_13_6370.2] + +/-- Complete interval computation for depth 13, residue 6371. -/ +theorem bounds_13_6371 : exactInterval 13 6371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6371 : oddCount 6371 13 = 2 ∧ acceleratedOrbit 13 6371 = 7 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6371) = 3 ^ 2 * m + 7 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6371.1, data_13_6371.2] + +/-- Complete interval computation for depth 13, residue 6372. -/ +theorem bounds_13_6372 : exactInterval 13 6372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6372 : oddCount 6372 13 = 6 ∧ acceleratedOrbit 13 6372 = 568 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6372) = 3 ^ 6 * m + 568 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6372.1, data_13_6372.2] + +/-- Complete interval computation for depth 13, residue 6373. -/ +theorem bounds_13_6373 : exactInterval 13 6373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6373 : oddCount 6373 13 = 6 ∧ acceleratedOrbit 13 6373 = 568 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6373) = 3 ^ 6 * m + 568 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6373.1, data_13_6373.2] + +/-- Complete interval computation for depth 13, residue 6374. -/ +theorem bounds_13_6374 : exactInterval 13 6374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6374 : oddCount 6374 13 = 6 ∧ acceleratedOrbit 13 6374 = 568 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6374) = 3 ^ 6 * m + 568 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6374.1, data_13_6374.2] + +/-- Complete interval computation for depth 13, residue 6375. -/ +theorem bounds_13_6375 : exactInterval 13 6375 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6375) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6375 : oddCount 6375 13 = 8 ∧ acceleratedOrbit 13 6375 = 5107 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6375) = 3 ^ 8 * m + 5107 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6375.1, data_13_6375.2] + +/-- Complete interval computation for depth 13, residue 6376. -/ +theorem bounds_13_6376 : exactInterval 13 6376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6376 : oddCount 6376 13 = 5 ∧ acceleratedOrbit 13 6376 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6376) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6376.1, data_13_6376.2] + +/-- Complete interval computation for depth 13, residue 6377. -/ +theorem bounds_13_6377 : exactInterval 13 6377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6377 : oddCount 6377 13 = 7 ∧ acceleratedOrbit 13 6377 = 1703 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6377) = 3 ^ 7 * m + 1703 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6377.1, data_13_6377.2] + +/-- Complete interval computation for depth 13, residue 6378. -/ +theorem bounds_13_6378 : exactInterval 13 6378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6378 : oddCount 6378 13 = 5 ∧ acceleratedOrbit 13 6378 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6378) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6378.1, data_13_6378.2] + +end Collatz.Research.StoppingAtlas.Batch0882 From 3d022cdf4780a18bbbde96be0408f724ce901e99 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:15 +0530 Subject: [PATCH 0883/1001] proof: certify atlas Batch0883 (13:6379 to 13:6393) --- Collatz/Research/StoppingAtlas/Batch0883.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0883.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0883.lean b/Collatz/Research/StoppingAtlas/Batch0883.lean new file mode 100644 index 00000000..c199e123 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0883.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0883 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6379. -/ +theorem bounds_13_6379 : exactInterval 13 6379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6379 : oddCount 6379 13 = 8 ∧ acceleratedOrbit 13 6379 = 5111 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6379) = 3 ^ 8 * m + 5111 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6379.1, data_13_6379.2] + +/-- Complete interval computation for depth 13, residue 6380. -/ +theorem bounds_13_6380 : exactInterval 13 6380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6380 : oddCount 6380 13 = 6 ∧ acceleratedOrbit 13 6380 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6380) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6380.1, data_13_6380.2] + +/-- Complete interval computation for depth 13, residue 6381. -/ +theorem bounds_13_6381 : exactInterval 13 6381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6381 : oddCount 6381 13 = 6 ∧ acceleratedOrbit 13 6381 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6381) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6381.1, data_13_6381.2] + +/-- Complete interval computation for depth 13, residue 6382. -/ +theorem bounds_13_6382 : exactInterval 13 6382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6382 : oddCount 6382 13 = 6 ∧ acceleratedOrbit 13 6382 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6382) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6382.1, data_13_6382.2] + +/-- Complete interval computation for depth 13, residue 6383. -/ +theorem bounds_13_6383 : exactInterval 13 6383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6383 : oddCount 6383 13 = 10 ∧ acceleratedOrbit 13 6383 = 46018 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6383) = 3 ^ 10 * m + 46018 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6383.1, data_13_6383.2] + +/-- Complete interval computation for depth 13, residue 6384. -/ +theorem bounds_13_6384 : exactInterval 13 6384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6384 : oddCount 6384 13 = 5 ∧ acceleratedOrbit 13 6384 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6384) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6384.1, data_13_6384.2] + +/-- Complete interval computation for depth 13, residue 6385. -/ +theorem bounds_13_6385 : exactInterval 13 6385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6385 : oddCount 6385 13 = 5 ∧ acceleratedOrbit 13 6385 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6385) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6385.1, data_13_6385.2] + +/-- Complete interval computation for depth 13, residue 6386. -/ +theorem bounds_13_6386 : exactInterval 13 6386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6386 : oddCount 6386 13 = 7 ∧ acceleratedOrbit 13 6386 = 1706 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6386) = 3 ^ 7 * m + 1706 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6386.1, data_13_6386.2] + +/-- Complete interval computation for depth 13, residue 6387. -/ +theorem bounds_13_6387 : exactInterval 13 6387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6387 : oddCount 6387 13 = 7 ∧ acceleratedOrbit 13 6387 = 1706 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6387) = 3 ^ 7 * m + 1706 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6387.1, data_13_6387.2] + +/-- Complete interval computation for depth 13, residue 6388. -/ +theorem bounds_13_6388 : exactInterval 13 6388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6388 : oddCount 6388 13 = 5 ∧ acceleratedOrbit 13 6388 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6388) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6388.1, data_13_6388.2] + +/-- Complete interval computation for depth 13, residue 6389. -/ +theorem bounds_13_6389 : exactInterval 13 6389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6389 : oddCount 6389 13 = 5 ∧ acceleratedOrbit 13 6389 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6389) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6389.1, data_13_6389.2] + +/-- Complete interval computation for depth 13, residue 6390. -/ +theorem bounds_13_6390 : exactInterval 13 6390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6390 : oddCount 6390 13 = 6 ∧ acceleratedOrbit 13 6390 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6390) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6390.1, data_13_6390.2] + +/-- Complete interval computation for depth 13, residue 6391. -/ +theorem bounds_13_6391 : exactInterval 13 6391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6391 : oddCount 6391 13 = 6 ∧ acceleratedOrbit 13 6391 = 569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6391) = 3 ^ 6 * m + 569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6391.1, data_13_6391.2] + +/-- Complete interval computation for depth 13, residue 6392. -/ +theorem bounds_13_6392 : exactInterval 13 6392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6392 : oddCount 6392 13 = 7 ∧ acceleratedOrbit 13 6392 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6392) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6392.1, data_13_6392.2] + +/-- Complete interval computation for depth 13, residue 6393. -/ +theorem bounds_13_6393 : exactInterval 13 6393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6393 : oddCount 6393 13 = 8 ∧ acceleratedOrbit 13 6393 = 5123 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6393) = 3 ^ 8 * m + 5123 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6393.1, data_13_6393.2] + +end Collatz.Research.StoppingAtlas.Batch0883 From 1176ea541a3a401dbb08437c060e7f102e1123a7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:15 +0530 Subject: [PATCH 0884/1001] proof: certify atlas Batch0884 (13:6394 to 13:6409) --- Collatz/Research/StoppingAtlas/Batch0884.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0884.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0884.lean b/Collatz/Research/StoppingAtlas/Batch0884.lean new file mode 100644 index 00000000..bc9773e5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0884.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0884 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6394. -/ +theorem bounds_13_6394 : exactInterval 13 6394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6394 : oddCount 6394 13 = 7 ∧ acceleratedOrbit 13 6394 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6394) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6394.1, data_13_6394.2] + +/-- Complete interval computation for depth 13, residue 6395. -/ +theorem bounds_13_6395 : exactInterval 13 6395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6395 : oddCount 6395 13 = 10 ∧ acceleratedOrbit 13 6395 = 46109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6395) = 3 ^ 10 * m + 46109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6395.1, data_13_6395.2] + +/-- Complete interval computation for depth 13, residue 6396. -/ +theorem bounds_13_6396 : exactInterval 13 6396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6396 : oddCount 6396 13 = 7 ∧ acceleratedOrbit 13 6396 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6396) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6396.1, data_13_6396.2] + +/-- Complete interval computation for depth 13, residue 6397. -/ +theorem bounds_13_6397 : exactInterval 13 6397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6397 : oddCount 6397 13 = 7 ∧ acceleratedOrbit 13 6397 = 1709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6397) = 3 ^ 7 * m + 1709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6397.1, data_13_6397.2] + +/-- Complete interval computation for depth 13, residue 6398. -/ +theorem bounds_13_6398 : exactInterval 13 6398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6398 : oddCount 6398 13 = 10 ∧ acceleratedOrbit 13 6398 = 46133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6398) = 3 ^ 10 * m + 46133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6398.1, data_13_6398.2] + +/-- Complete interval computation for depth 13, residue 6399. -/ +theorem bounds_13_6399 : exactInterval 13 6399 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6399) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6399 : oddCount 6399 13 = 10 ∧ acceleratedOrbit 13 6399 = 46133 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6399) = 3 ^ 10 * m + 46133 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6399.1, data_13_6399.2] + +/-- Complete interval computation for depth 13, residue 6400. -/ +theorem bounds_13_6400 : exactInterval 13 6400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6400 : oddCount 6400 13 = 3 ∧ acceleratedOrbit 13 6400 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6400) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6400.1, data_13_6400.2] + +/-- Complete interval computation for depth 13, residue 6401. -/ +theorem bounds_13_6401 : exactInterval 13 6401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6401 : oddCount 6401 13 = 5 ∧ acceleratedOrbit 13 6401 = 190 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6401) = 3 ^ 5 * m + 190 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6401.1, data_13_6401.2] + +/-- Complete interval computation for depth 13, residue 6402. -/ +theorem bounds_13_6402 : exactInterval 13 6402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6402 : oddCount 6402 13 = 7 ∧ acceleratedOrbit 13 6402 = 1711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6402) = 3 ^ 7 * m + 1711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6402.1, data_13_6402.2] + +/-- Complete interval computation for depth 13, residue 6403. -/ +theorem bounds_13_6403 : exactInterval 13 6403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6403 : oddCount 6403 13 = 7 ∧ acceleratedOrbit 13 6403 = 1711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6403) = 3 ^ 7 * m + 1711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6403.1, data_13_6403.2] + +/-- Complete interval computation for depth 13, residue 6404. -/ +theorem bounds_13_6404 : exactInterval 13 6404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6404 : oddCount 6404 13 = 5 ∧ acceleratedOrbit 13 6404 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6404) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6404.1, data_13_6404.2] + +/-- Complete interval computation for depth 13, residue 6405. -/ +theorem bounds_13_6405 : exactInterval 13 6405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6405 : oddCount 6405 13 = 5 ∧ acceleratedOrbit 13 6405 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6405) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6405.1, data_13_6405.2] + +/-- Complete interval computation for depth 13, residue 6406. -/ +theorem bounds_13_6406 : exactInterval 13 6406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6406 : oddCount 6406 13 = 5 ∧ acceleratedOrbit 13 6406 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6406) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6406.1, data_13_6406.2] + +/-- Complete interval computation for depth 13, residue 6407. -/ +theorem bounds_13_6407 : exactInterval 13 6407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6407 : oddCount 6407 13 = 7 ∧ acceleratedOrbit 13 6407 = 1711 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6407) = 3 ^ 7 * m + 1711 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6407.1, data_13_6407.2] + +/-- Complete interval computation for depth 13, residue 6408. -/ +theorem bounds_13_6408 : exactInterval 13 6408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6408 : oddCount 6408 13 = 5 ∧ acceleratedOrbit 13 6408 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6408) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6408.1, data_13_6408.2] + +/-- Complete interval computation for depth 13, residue 6409. -/ +theorem bounds_13_6409 : exactInterval 13 6409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6409 : oddCount 6409 13 = 7 ∧ acceleratedOrbit 13 6409 = 1712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6409) = 3 ^ 7 * m + 1712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6409.1, data_13_6409.2] + +end Collatz.Research.StoppingAtlas.Batch0884 From 67a309ca7f02207d955be623696c5ada0224e6e2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:16 +0530 Subject: [PATCH 0885/1001] proof: certify atlas Batch0885 (13:6410 to 13:6424) --- Collatz/Research/StoppingAtlas/Batch0885.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0885.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0885.lean b/Collatz/Research/StoppingAtlas/Batch0885.lean new file mode 100644 index 00000000..372beb64 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0885.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0885 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6410. -/ +theorem bounds_13_6410 : exactInterval 13 6410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6410 : oddCount 6410 13 = 5 ∧ acceleratedOrbit 13 6410 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6410) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6410.1, data_13_6410.2] + +/-- Complete interval computation for depth 13, residue 6411. -/ +theorem bounds_13_6411 : exactInterval 13 6411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6411 : oddCount 6411 13 = 6 ∧ acceleratedOrbit 13 6411 = 571 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6411) = 3 ^ 6 * m + 571 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6411.1, data_13_6411.2] + +/-- Complete interval computation for depth 13, residue 6412. -/ +theorem bounds_13_6412 : exactInterval 13 6412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6412 : oddCount 6412 13 = 5 ∧ acceleratedOrbit 13 6412 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6412) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6412.1, data_13_6412.2] + +/-- Complete interval computation for depth 13, residue 6413. -/ +theorem bounds_13_6413 : exactInterval 13 6413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6413 : oddCount 6413 13 = 5 ∧ acceleratedOrbit 13 6413 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6413) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6413.1, data_13_6413.2] + +/-- Complete interval computation for depth 13, residue 6414. -/ +theorem bounds_13_6414 : exactInterval 13 6414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6414 : oddCount 6414 13 = 7 ∧ acceleratedOrbit 13 6414 = 1714 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6414) = 3 ^ 7 * m + 1714 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6414.1, data_13_6414.2] + +/-- Complete interval computation for depth 13, residue 6415. -/ +theorem bounds_13_6415 : exactInterval 13 6415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6415 : oddCount 6415 13 = 7 ∧ acceleratedOrbit 13 6415 = 1714 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6415) = 3 ^ 7 * m + 1714 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6415.1, data_13_6415.2] + +/-- Complete interval computation for depth 13, residue 6416. -/ +theorem bounds_13_6416 : exactInterval 13 6416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6416 : oddCount 6416 13 = 4 ∧ acceleratedOrbit 13 6416 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6416) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6416.1, data_13_6416.2] + +/-- Complete interval computation for depth 13, residue 6417. -/ +theorem bounds_13_6417 : exactInterval 13 6417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6417 : oddCount 6417 13 = 5 ∧ acceleratedOrbit 13 6417 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6417) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6417.1, data_13_6417.2] + +/-- Complete interval computation for depth 13, residue 6418. -/ +theorem bounds_13_6418 : exactInterval 13 6418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6418 : oddCount 6418 13 = 9 ∧ acceleratedOrbit 13 6418 = 15430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6418) = 3 ^ 9 * m + 15430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6418.1, data_13_6418.2] + +/-- Complete interval computation for depth 13, residue 6419. -/ +theorem bounds_13_6419 : exactInterval 13 6419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6419 : oddCount 6419 13 = 9 ∧ acceleratedOrbit 13 6419 = 15430 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6419) = 3 ^ 9 * m + 15430 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6419.1, data_13_6419.2] + +/-- Complete interval computation for depth 13, residue 6420. -/ +theorem bounds_13_6420 : exactInterval 13 6420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6420 : oddCount 6420 13 = 4 ∧ acceleratedOrbit 13 6420 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6420) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6420.1, data_13_6420.2] + +/-- Complete interval computation for depth 13, residue 6421. -/ +theorem bounds_13_6421 : exactInterval 13 6421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6421 : oddCount 6421 13 = 4 ∧ acceleratedOrbit 13 6421 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6421) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6421.1, data_13_6421.2] + +/-- Complete interval computation for depth 13, residue 6422. -/ +theorem bounds_13_6422 : exactInterval 13 6422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6422 : oddCount 6422 13 = 6 ∧ acceleratedOrbit 13 6422 = 572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6422) = 3 ^ 6 * m + 572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6422.1, data_13_6422.2] + +/-- Complete interval computation for depth 13, residue 6423. -/ +theorem bounds_13_6423 : exactInterval 13 6423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6423 : oddCount 6423 13 = 6 ∧ acceleratedOrbit 13 6423 = 572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6423) = 3 ^ 6 * m + 572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6423.1, data_13_6423.2] + +/-- Complete interval computation for depth 13, residue 6424. -/ +theorem bounds_13_6424 : exactInterval 13 6424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6424 : oddCount 6424 13 = 4 ∧ acceleratedOrbit 13 6424 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6424) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6424.1, data_13_6424.2] + +end Collatz.Research.StoppingAtlas.Batch0885 From af8efcec5a617317afb3d0ebbe3562c11164e20d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:16 +0530 Subject: [PATCH 0886/1001] proof: certify atlas Batch0886 (13:6425 to 13:6439) --- Collatz/Research/StoppingAtlas/Batch0886.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0886.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0886.lean b/Collatz/Research/StoppingAtlas/Batch0886.lean new file mode 100644 index 00000000..64143d56 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0886.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0886 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6425. -/ +theorem bounds_13_6425 : exactInterval 13 6425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6425 : oddCount 6425 13 = 6 ∧ acceleratedOrbit 13 6425 = 572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6425) = 3 ^ 6 * m + 572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6425.1, data_13_6425.2] + +/-- Complete interval computation for depth 13, residue 6426. -/ +theorem bounds_13_6426 : exactInterval 13 6426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6426 : oddCount 6426 13 = 4 ∧ acceleratedOrbit 13 6426 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6426) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6426.1, data_13_6426.2] + +/-- Complete interval computation for depth 13, residue 6427. -/ +theorem bounds_13_6427 : exactInterval 13 6427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6427 : oddCount 6427 13 = 9 ∧ acceleratedOrbit 13 6427 = 15446 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6427) = 3 ^ 9 * m + 15446 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6427.1, data_13_6427.2] + +/-- Complete interval computation for depth 13, residue 6428. -/ +theorem bounds_13_6428 : exactInterval 13 6428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6428 : oddCount 6428 13 = 7 ∧ acceleratedOrbit 13 6428 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6428) = 3 ^ 7 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6428.1, data_13_6428.2] + +/-- Complete interval computation for depth 13, residue 6429. -/ +theorem bounds_13_6429 : exactInterval 13 6429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6429 : oddCount 6429 13 = 7 ∧ acceleratedOrbit 13 6429 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6429) = 3 ^ 7 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6429.1, data_13_6429.2] + +/-- Complete interval computation for depth 13, residue 6430. -/ +theorem bounds_13_6430 : exactInterval 13 6430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6430 : oddCount 6430 13 = 7 ∧ acceleratedOrbit 13 6430 = 1718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6430) = 3 ^ 7 * m + 1718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6430.1, data_13_6430.2] + +/-- Complete interval computation for depth 13, residue 6431. -/ +theorem bounds_13_6431 : exactInterval 13 6431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6431 : oddCount 6431 13 = 8 ∧ acceleratedOrbit 13 6431 = 5152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6431) = 3 ^ 8 * m + 5152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6431.1, data_13_6431.2] + +/-- Complete interval computation for depth 13, residue 6432. -/ +theorem bounds_13_6432 : exactInterval 13 6432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6432 : oddCount 6432 13 = 4 ∧ acceleratedOrbit 13 6432 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6432) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6432.1, data_13_6432.2] + +/-- Complete interval computation for depth 13, residue 6433. -/ +theorem bounds_13_6433 : exactInterval 13 6433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6433 : oddCount 6433 13 = 5 ∧ acceleratedOrbit 13 6433 = 191 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6433) = 3 ^ 5 * m + 191 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6433.1, data_13_6433.2] + +/-- Complete interval computation for depth 13, residue 6434. -/ +theorem bounds_13_6434 : exactInterval 13 6434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6434 : oddCount 6434 13 = 7 ∧ acceleratedOrbit 13 6434 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6434) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6434.1, data_13_6434.2] + +/-- Complete interval computation for depth 13, residue 6435. -/ +theorem bounds_13_6435 : exactInterval 13 6435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6435 : oddCount 6435 13 = 7 ∧ acceleratedOrbit 13 6435 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6435) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6435.1, data_13_6435.2] + +/-- Complete interval computation for depth 13, residue 6436. -/ +theorem bounds_13_6436 : exactInterval 13 6436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6436 : oddCount 6436 13 = 7 ∧ acceleratedOrbit 13 6436 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6436) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6436.1, data_13_6436.2] + +/-- Complete interval computation for depth 13, residue 6437. -/ +theorem bounds_13_6437 : exactInterval 13 6437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6437 : oddCount 6437 13 = 7 ∧ acceleratedOrbit 13 6437 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6437) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6437.1, data_13_6437.2] + +/-- Complete interval computation for depth 13, residue 6438. -/ +theorem bounds_13_6438 : exactInterval 13 6438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6438 : oddCount 6438 13 = 7 ∧ acceleratedOrbit 13 6438 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6438) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6438.1, data_13_6438.2] + +/-- Complete interval computation for depth 13, residue 6439. -/ +theorem bounds_13_6439 : exactInterval 13 6439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6439 : oddCount 6439 13 = 8 ∧ acceleratedOrbit 13 6439 = 5159 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6439) = 3 ^ 8 * m + 5159 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6439.1, data_13_6439.2] + +end Collatz.Research.StoppingAtlas.Batch0886 From 62d9bdc8f44951a17b70907acebdf48a45e061fc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:16 +0530 Subject: [PATCH 0887/1001] proof: certify atlas Batch0887 (13:6440 to 13:6455) --- Collatz/Research/StoppingAtlas/Batch0887.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0887.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0887.lean b/Collatz/Research/StoppingAtlas/Batch0887.lean new file mode 100644 index 00000000..baaeb0fb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0887.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0887 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6440. -/ +theorem bounds_13_6440 : exactInterval 13 6440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6440 : oddCount 6440 13 = 4 ∧ acceleratedOrbit 13 6440 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6440) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6440.1, data_13_6440.2] + +/-- Complete interval computation for depth 13, residue 6441. -/ +theorem bounds_13_6441 : exactInterval 13 6441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6441 : oddCount 6441 13 = 7 ∧ acceleratedOrbit 13 6441 = 1720 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6441) = 3 ^ 7 * m + 1720 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6441.1, data_13_6441.2] + +/-- Complete interval computation for depth 13, residue 6442. -/ +theorem bounds_13_6442 : exactInterval 13 6442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6442 : oddCount 6442 13 = 4 ∧ acceleratedOrbit 13 6442 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6442) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6442.1, data_13_6442.2] + +/-- Complete interval computation for depth 13, residue 6443. -/ +theorem bounds_13_6443 : exactInterval 13 6443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6443 : oddCount 6443 13 = 7 ∧ acceleratedOrbit 13 6443 = 1721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6443) = 3 ^ 7 * m + 1721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6443.1, data_13_6443.2] + +/-- Complete interval computation for depth 13, residue 6444. -/ +theorem bounds_13_6444 : exactInterval 13 6444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6444 : oddCount 6444 13 = 4 ∧ acceleratedOrbit 13 6444 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6444) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6444.1, data_13_6444.2] + +/-- Complete interval computation for depth 13, residue 6445. -/ +theorem bounds_13_6445 : exactInterval 13 6445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6445 : oddCount 6445 13 = 4 ∧ acceleratedOrbit 13 6445 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6445) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6445.1, data_13_6445.2] + +/-- Complete interval computation for depth 13, residue 6446. -/ +theorem bounds_13_6446 : exactInterval 13 6446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6446 : oddCount 6446 13 = 4 ∧ acceleratedOrbit 13 6446 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6446) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6446.1, data_13_6446.2] + +/-- Complete interval computation for depth 13, residue 6447. -/ +theorem bounds_13_6447 : exactInterval 13 6447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6447 : oddCount 6447 13 = 8 ∧ acceleratedOrbit 13 6447 = 5165 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6447) = 3 ^ 8 * m + 5165 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6447.1, data_13_6447.2] + +/-- Complete interval computation for depth 13, residue 6448. -/ +theorem bounds_13_6448 : exactInterval 13 6448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6448 : oddCount 6448 13 = 4 ∧ acceleratedOrbit 13 6448 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6448) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6448.1, data_13_6448.2] + +/-- Complete interval computation for depth 13, residue 6449. -/ +theorem bounds_13_6449 : exactInterval 13 6449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6449 : oddCount 6449 13 = 6 ∧ acceleratedOrbit 13 6449 = 575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6449) = 3 ^ 6 * m + 575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6449.1, data_13_6449.2] + +/-- Complete interval computation for depth 13, residue 6450. -/ +theorem bounds_13_6450 : exactInterval 13 6450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6450 : oddCount 6450 13 = 6 ∧ acceleratedOrbit 13 6450 = 575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6450) = 3 ^ 6 * m + 575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6450.1, data_13_6450.2] + +/-- Complete interval computation for depth 13, residue 6451. -/ +theorem bounds_13_6451 : exactInterval 13 6451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6451 : oddCount 6451 13 = 6 ∧ acceleratedOrbit 13 6451 = 575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6451) = 3 ^ 6 * m + 575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6451.1, data_13_6451.2] + +/-- Complete interval computation for depth 13, residue 6452. -/ +theorem bounds_13_6452 : exactInterval 13 6452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6452 : oddCount 6452 13 = 4 ∧ acceleratedOrbit 13 6452 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6452) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6452.1, data_13_6452.2] + +/-- Complete interval computation for depth 13, residue 6453. -/ +theorem bounds_13_6453 : exactInterval 13 6453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6453 : oddCount 6453 13 = 4 ∧ acceleratedOrbit 13 6453 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6453) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6453.1, data_13_6453.2] + +/-- Complete interval computation for depth 13, residue 6454. -/ +theorem bounds_13_6454 : exactInterval 13 6454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6454 : oddCount 6454 13 = 9 ∧ acceleratedOrbit 13 6454 = 15515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6454) = 3 ^ 9 * m + 15515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6454.1, data_13_6454.2] + +/-- Complete interval computation for depth 13, residue 6455. -/ +theorem bounds_13_6455 : exactInterval 13 6455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6455) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6455 : oddCount 6455 13 = 9 ∧ acceleratedOrbit 13 6455 = 15515 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6455) = 3 ^ 9 * m + 15515 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6455.1, data_13_6455.2] + +end Collatz.Research.StoppingAtlas.Batch0887 From ab5d7036d0c2bb2dc944f84ae8b900825bd82cd4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:16 +0530 Subject: [PATCH 0888/1001] proof: certify atlas Batch0888 (13:6456 to 13:6470) --- Collatz/Research/StoppingAtlas/Batch0888.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0888.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0888.lean b/Collatz/Research/StoppingAtlas/Batch0888.lean new file mode 100644 index 00000000..dfbe972c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0888.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0888 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6456. -/ +theorem bounds_13_6456 : exactInterval 13 6456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6456 : oddCount 6456 13 = 7 ∧ acceleratedOrbit 13 6456 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6456) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6456.1, data_13_6456.2] + +/-- Complete interval computation for depth 13, residue 6457. -/ +theorem bounds_13_6457 : exactInterval 13 6457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6457 : oddCount 6457 13 = 8 ∧ acceleratedOrbit 13 6457 = 5174 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6457) = 3 ^ 8 * m + 5174 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6457.1, data_13_6457.2] + +/-- Complete interval computation for depth 13, residue 6458. -/ +theorem bounds_13_6458 : exactInterval 13 6458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6458 : oddCount 6458 13 = 7 ∧ acceleratedOrbit 13 6458 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6458) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6458.1, data_13_6458.2] + +/-- Complete interval computation for depth 13, residue 6459. -/ +theorem bounds_13_6459 : exactInterval 13 6459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6459 : oddCount 6459 13 = 7 ∧ acceleratedOrbit 13 6459 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6459) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6459.1, data_13_6459.2] + +/-- Complete interval computation for depth 13, residue 6460. -/ +theorem bounds_13_6460 : exactInterval 13 6460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6460 : oddCount 6460 13 = 7 ∧ acceleratedOrbit 13 6460 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6460) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6460.1, data_13_6460.2] + +/-- Complete interval computation for depth 13, residue 6461. -/ +theorem bounds_13_6461 : exactInterval 13 6461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6461 : oddCount 6461 13 = 7 ∧ acceleratedOrbit 13 6461 = 1727 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6461) = 3 ^ 7 * m + 1727 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6461.1, data_13_6461.2] + +/-- Complete interval computation for depth 13, residue 6462. -/ +theorem bounds_13_6462 : exactInterval 13 6462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6462 : oddCount 6462 13 = 10 ∧ acceleratedOrbit 13 6462 = 46595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6462) = 3 ^ 10 * m + 46595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6462.1, data_13_6462.2] + +/-- Complete interval computation for depth 13, residue 6463. -/ +theorem bounds_13_6463 : exactInterval 13 6463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6463 : oddCount 6463 13 = 10 ∧ acceleratedOrbit 13 6463 = 46595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6463) = 3 ^ 10 * m + 46595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6463.1, data_13_6463.2] + +/-- Complete interval computation for depth 13, residue 6464. -/ +theorem bounds_13_6464 : exactInterval 13 6464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6464 : oddCount 6464 13 = 3 ∧ acceleratedOrbit 13 6464 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6464) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6464.1, data_13_6464.2] + +/-- Complete interval computation for depth 13, residue 6465. -/ +theorem bounds_13_6465 : exactInterval 13 6465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6465 : oddCount 6465 13 = 4 ∧ acceleratedOrbit 13 6465 = 64 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6465) = 3 ^ 4 * m + 64 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6465.1, data_13_6465.2] + +/-- Complete interval computation for depth 13, residue 6466. -/ +theorem bounds_13_6466 : exactInterval 13 6466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6466 : oddCount 6466 13 = 9 ∧ acceleratedOrbit 13 6466 = 15551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6466) = 3 ^ 9 * m + 15551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6466.1, data_13_6466.2] + +/-- Complete interval computation for depth 13, residue 6467. -/ +theorem bounds_13_6467 : exactInterval 13 6467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6467 : oddCount 6467 13 = 9 ∧ acceleratedOrbit 13 6467 = 15551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6467) = 3 ^ 9 * m + 15551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6467.1, data_13_6467.2] + +/-- Complete interval computation for depth 13, residue 6468. -/ +theorem bounds_13_6468 : exactInterval 13 6468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6468 : oddCount 6468 13 = 6 ∧ acceleratedOrbit 13 6468 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6468) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6468.1, data_13_6468.2] + +/-- Complete interval computation for depth 13, residue 6469. -/ +theorem bounds_13_6469 : exactInterval 13 6469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6469 : oddCount 6469 13 = 6 ∧ acceleratedOrbit 13 6469 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6469) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6469.1, data_13_6469.2] + +/-- Complete interval computation for depth 13, residue 6470. -/ +theorem bounds_13_6470 : exactInterval 13 6470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6470 : oddCount 6470 13 = 6 ∧ acceleratedOrbit 13 6470 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6470) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6470.1, data_13_6470.2] + +end Collatz.Research.StoppingAtlas.Batch0888 From cd49366c8d09ba1ae9eeb1109771e6f0d8212911 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:16 +0530 Subject: [PATCH 0889/1001] proof: certify atlas Batch0889 (13:6471 to 13:6486) --- Collatz/Research/StoppingAtlas/Batch0889.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0889.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0889.lean b/Collatz/Research/StoppingAtlas/Batch0889.lean new file mode 100644 index 00000000..f83a9705 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0889.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0889 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6471. -/ +theorem bounds_13_6471 : exactInterval 13 6471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6471 : oddCount 6471 13 = 11 ∧ acceleratedOrbit 13 6471 = 139967 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6471) = 3 ^ 11 * m + 139967 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6471.1, data_13_6471.2] + +/-- Complete interval computation for depth 13, residue 6472. -/ +theorem bounds_13_6472 : exactInterval 13 6472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6472 : oddCount 6472 13 = 6 ∧ acceleratedOrbit 13 6472 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6472) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6472.1, data_13_6472.2] + +/-- Complete interval computation for depth 13, residue 6473. -/ +theorem bounds_13_6473 : exactInterval 13 6473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6473 : oddCount 6473 13 = 7 ∧ acceleratedOrbit 13 6473 = 1729 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6473) = 3 ^ 7 * m + 1729 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6473.1, data_13_6473.2] + +/-- Complete interval computation for depth 13, residue 6474. -/ +theorem bounds_13_6474 : exactInterval 13 6474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6474 : oddCount 6474 13 = 6 ∧ acceleratedOrbit 13 6474 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6474) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6474.1, data_13_6474.2] + +/-- Complete interval computation for depth 13, residue 6475. -/ +theorem bounds_13_6475 : exactInterval 13 6475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6475 : oddCount 6475 13 = 6 ∧ acceleratedOrbit 13 6475 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6475) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6475.1, data_13_6475.2] + +/-- Complete interval computation for depth 13, residue 6476. -/ +theorem bounds_13_6476 : exactInterval 13 6476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6476 : oddCount 6476 13 = 6 ∧ acceleratedOrbit 13 6476 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6476) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6476.1, data_13_6476.2] + +/-- Complete interval computation for depth 13, residue 6477. -/ +theorem bounds_13_6477 : exactInterval 13 6477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6477 : oddCount 6477 13 = 6 ∧ acceleratedOrbit 13 6477 = 577 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6477) = 3 ^ 6 * m + 577 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6477.1, data_13_6477.2] + +/-- Complete interval computation for depth 13, residue 6478. -/ +theorem bounds_13_6478 : exactInterval 13 6478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6478 : oddCount 6478 13 = 9 ∧ acceleratedOrbit 13 6478 = 15572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6478) = 3 ^ 9 * m + 15572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6478.1, data_13_6478.2] + +/-- Complete interval computation for depth 13, residue 6479. -/ +theorem bounds_13_6479 : exactInterval 13 6479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6479 : oddCount 6479 13 = 9 ∧ acceleratedOrbit 13 6479 = 15572 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6479) = 3 ^ 9 * m + 15572 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6479.1, data_13_6479.2] + +/-- Complete interval computation for depth 13, residue 6480. -/ +theorem bounds_13_6480 : exactInterval 13 6480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6480 : oddCount 6480 13 = 3 ∧ acceleratedOrbit 13 6480 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6480) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6480.1, data_13_6480.2] + +/-- Complete interval computation for depth 13, residue 6481. -/ +theorem bounds_13_6481 : exactInterval 13 6481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6481 : oddCount 6481 13 = 8 ∧ acceleratedOrbit 13 6481 = 5194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6481) = 3 ^ 8 * m + 5194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6481.1, data_13_6481.2] + +/-- Complete interval computation for depth 13, residue 6482. -/ +theorem bounds_13_6482 : exactInterval 13 6482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6482 : oddCount 6482 13 = 8 ∧ acceleratedOrbit 13 6482 = 5194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6482) = 3 ^ 8 * m + 5194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6482.1, data_13_6482.2] + +/-- Complete interval computation for depth 13, residue 6483. -/ +theorem bounds_13_6483 : exactInterval 13 6483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6483 : oddCount 6483 13 = 8 ∧ acceleratedOrbit 13 6483 = 5194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6483) = 3 ^ 8 * m + 5194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6483.1, data_13_6483.2] + +/-- Complete interval computation for depth 13, residue 6484. -/ +theorem bounds_13_6484 : exactInterval 13 6484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6484 : oddCount 6484 13 = 3 ∧ acceleratedOrbit 13 6484 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6484) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6484.1, data_13_6484.2] + +/-- Complete interval computation for depth 13, residue 6485. -/ +theorem bounds_13_6485 : exactInterval 13 6485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6485 : oddCount 6485 13 = 3 ∧ acceleratedOrbit 13 6485 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6485) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6485.1, data_13_6485.2] + +/-- Complete interval computation for depth 13, residue 6486. -/ +theorem bounds_13_6486 : exactInterval 13 6486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6486 : oddCount 6486 13 = 6 ∧ acceleratedOrbit 13 6486 = 578 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6486) = 3 ^ 6 * m + 578 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6486.1, data_13_6486.2] + +end Collatz.Research.StoppingAtlas.Batch0889 From 0b295f2629e7f2fc9a32f69e236e8a002d164ef3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:17 +0530 Subject: [PATCH 0890/1001] proof: certify atlas Batch0890 (13:6487 to 13:6501) --- Collatz/Research/StoppingAtlas/Batch0890.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0890.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0890.lean b/Collatz/Research/StoppingAtlas/Batch0890.lean new file mode 100644 index 00000000..17d71025 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0890.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0890 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6487. -/ +theorem bounds_13_6487 : exactInterval 13 6487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6487 : oddCount 6487 13 = 6 ∧ acceleratedOrbit 13 6487 = 578 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6487) = 3 ^ 6 * m + 578 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6487.1, data_13_6487.2] + +/-- Complete interval computation for depth 13, residue 6488. -/ +theorem bounds_13_6488 : exactInterval 13 6488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6488 : oddCount 6488 13 = 5 ∧ acceleratedOrbit 13 6488 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6488) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6488.1, data_13_6488.2] + +/-- Complete interval computation for depth 13, residue 6489. -/ +theorem bounds_13_6489 : exactInterval 13 6489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6489 : oddCount 6489 13 = 6 ∧ acceleratedOrbit 13 6489 = 578 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6489) = 3 ^ 6 * m + 578 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6489.1, data_13_6489.2] + +/-- Complete interval computation for depth 13, residue 6490. -/ +theorem bounds_13_6490 : exactInterval 13 6490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6490 : oddCount 6490 13 = 5 ∧ acceleratedOrbit 13 6490 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6490) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6490.1, data_13_6490.2] + +/-- Complete interval computation for depth 13, residue 6491. -/ +theorem bounds_13_6491 : exactInterval 13 6491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6491 : oddCount 6491 13 = 8 ∧ acceleratedOrbit 13 6491 = 5201 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6491) = 3 ^ 8 * m + 5201 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6491.1, data_13_6491.2] + +/-- Complete interval computation for depth 13, residue 6492. -/ +theorem bounds_13_6492 : exactInterval 13 6492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6492 : oddCount 6492 13 = 5 ∧ acceleratedOrbit 13 6492 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6492) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6492.1, data_13_6492.2] + +/-- Complete interval computation for depth 13, residue 6493. -/ +theorem bounds_13_6493 : exactInterval 13 6493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6493 : oddCount 6493 13 = 5 ∧ acceleratedOrbit 13 6493 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6493) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6493.1, data_13_6493.2] + +/-- Complete interval computation for depth 13, residue 6494. -/ +theorem bounds_13_6494 : exactInterval 13 6494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6494 : oddCount 6494 13 = 8 ∧ acceleratedOrbit 13 6494 = 5204 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6494) = 3 ^ 8 * m + 5204 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6494.1, data_13_6494.2] + +/-- Complete interval computation for depth 13, residue 6495. -/ +theorem bounds_13_6495 : exactInterval 13 6495 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6495) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6495 : oddCount 6495 13 = 8 ∧ acceleratedOrbit 13 6495 = 5204 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6495) = 3 ^ 8 * m + 5204 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6495.1, data_13_6495.2] + +/-- Complete interval computation for depth 13, residue 6496. -/ +theorem bounds_13_6496 : exactInterval 13 6496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6496 : oddCount 6496 13 = 4 ∧ acceleratedOrbit 13 6496 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6496) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6496.1, data_13_6496.2] + +/-- Complete interval computation for depth 13, residue 6497. -/ +theorem bounds_13_6497 : exactInterval 13 6497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6497 : oddCount 6497 13 = 8 ∧ acceleratedOrbit 13 6497 = 5206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6497) = 3 ^ 8 * m + 5206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6497.1, data_13_6497.2] + +/-- Complete interval computation for depth 13, residue 6498. -/ +theorem bounds_13_6498 : exactInterval 13 6498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6498 : oddCount 6498 13 = 6 ∧ acceleratedOrbit 13 6498 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6498) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6498.1, data_13_6498.2] + +/-- Complete interval computation for depth 13, residue 6499. -/ +theorem bounds_13_6499 : exactInterval 13 6499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6499 : oddCount 6499 13 = 6 ∧ acceleratedOrbit 13 6499 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6499) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6499.1, data_13_6499.2] + +/-- Complete interval computation for depth 13, residue 6500. -/ +theorem bounds_13_6500 : exactInterval 13 6500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6500 : oddCount 6500 13 = 6 ∧ acceleratedOrbit 13 6500 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6500) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6500.1, data_13_6500.2] + +/-- Complete interval computation for depth 13, residue 6501. -/ +theorem bounds_13_6501 : exactInterval 13 6501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6501 : oddCount 6501 13 = 6 ∧ acceleratedOrbit 13 6501 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6501) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6501.1, data_13_6501.2] + +end Collatz.Research.StoppingAtlas.Batch0890 From 99cf1ce0af7c88482eb148c95264b834b4603793 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:17 +0530 Subject: [PATCH 0891/1001] proof: certify atlas Batch0891 (13:6502 to 13:6516) --- Collatz/Research/StoppingAtlas/Batch0891.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0891.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0891.lean b/Collatz/Research/StoppingAtlas/Batch0891.lean new file mode 100644 index 00000000..0518ffc2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0891.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0891 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6502. -/ +theorem bounds_13_6502 : exactInterval 13 6502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6502 : oddCount 6502 13 = 6 ∧ acceleratedOrbit 13 6502 = 580 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6502) = 3 ^ 6 * m + 580 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6502.1, data_13_6502.2] + +/-- Complete interval computation for depth 13, residue 6503. -/ +theorem bounds_13_6503 : exactInterval 13 6503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6503 : oddCount 6503 13 = 9 ∧ acceleratedOrbit 13 6503 = 15628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6503) = 3 ^ 9 * m + 15628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6503.1, data_13_6503.2] + +/-- Complete interval computation for depth 13, residue 6504. -/ +theorem bounds_13_6504 : exactInterval 13 6504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6504 : oddCount 6504 13 = 4 ∧ acceleratedOrbit 13 6504 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6504) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6504.1, data_13_6504.2] + +/-- Complete interval computation for depth 13, residue 6505. -/ +theorem bounds_13_6505 : exactInterval 13 6505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6505 : oddCount 6505 13 = 5 ∧ acceleratedOrbit 13 6505 = 193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6505) = 3 ^ 5 * m + 193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6505.1, data_13_6505.2] + +/-- Complete interval computation for depth 13, residue 6506. -/ +theorem bounds_13_6506 : exactInterval 13 6506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6506 : oddCount 6506 13 = 4 ∧ acceleratedOrbit 13 6506 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6506) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6506.1, data_13_6506.2] + +/-- Complete interval computation for depth 13, residue 6507. -/ +theorem bounds_13_6507 : exactInterval 13 6507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6507 : oddCount 6507 13 = 7 ∧ acceleratedOrbit 13 6507 = 1738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6507) = 3 ^ 7 * m + 1738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6507.1, data_13_6507.2] + +/-- Complete interval computation for depth 13, residue 6508. -/ +theorem bounds_13_6508 : exactInterval 13 6508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6508 : oddCount 6508 13 = 7 ∧ acceleratedOrbit 13 6508 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6508) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6508.1, data_13_6508.2] + +/-- Complete interval computation for depth 13, residue 6509. -/ +theorem bounds_13_6509 : exactInterval 13 6509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6509 : oddCount 6509 13 = 7 ∧ acceleratedOrbit 13 6509 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6509) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6509.1, data_13_6509.2] + +/-- Complete interval computation for depth 13, residue 6510. -/ +theorem bounds_13_6510 : exactInterval 13 6510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6510 : oddCount 6510 13 = 7 ∧ acceleratedOrbit 13 6510 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6510) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6510.1, data_13_6510.2] + +/-- Complete interval computation for depth 13, residue 6511. -/ +theorem bounds_13_6511 : exactInterval 13 6511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6511 : oddCount 6511 13 = 7 ∧ acceleratedOrbit 13 6511 = 1739 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6511) = 3 ^ 7 * m + 1739 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6511.1, data_13_6511.2] + +/-- Complete interval computation for depth 13, residue 6512. -/ +theorem bounds_13_6512 : exactInterval 13 6512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6512 : oddCount 6512 13 = 4 ∧ acceleratedOrbit 13 6512 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6512) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6512.1, data_13_6512.2] + +/-- Complete interval computation for depth 13, residue 6513. -/ +theorem bounds_13_6513 : exactInterval 13 6513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6513 : oddCount 6513 13 = 4 ∧ acceleratedOrbit 13 6513 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6513) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6513.1, data_13_6513.2] + +/-- Complete interval computation for depth 13, residue 6514. -/ +theorem bounds_13_6514 : exactInterval 13 6514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6514 : oddCount 6514 13 = 7 ∧ acceleratedOrbit 13 6514 = 1741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6514) = 3 ^ 7 * m + 1741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6514.1, data_13_6514.2] + +/-- Complete interval computation for depth 13, residue 6515. -/ +theorem bounds_13_6515 : exactInterval 13 6515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6515 : oddCount 6515 13 = 7 ∧ acceleratedOrbit 13 6515 = 1741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6515) = 3 ^ 7 * m + 1741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6515.1, data_13_6515.2] + +/-- Complete interval computation for depth 13, residue 6516. -/ +theorem bounds_13_6516 : exactInterval 13 6516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6516 : oddCount 6516 13 = 4 ∧ acceleratedOrbit 13 6516 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6516) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6516.1, data_13_6516.2] + +end Collatz.Research.StoppingAtlas.Batch0891 From e90822ffbbbc2e4e044daf14e13f39df56679c72 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:17 +0530 Subject: [PATCH 0892/1001] proof: certify atlas Batch0892 (13:6517 to 13:6532) --- Collatz/Research/StoppingAtlas/Batch0892.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0892.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0892.lean b/Collatz/Research/StoppingAtlas/Batch0892.lean new file mode 100644 index 00000000..272e9257 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0892.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0892 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6517. -/ +theorem bounds_13_6517 : exactInterval 13 6517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6517 : oddCount 6517 13 = 4 ∧ acceleratedOrbit 13 6517 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6517) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6517.1, data_13_6517.2] + +/-- Complete interval computation for depth 13, residue 6518. -/ +theorem bounds_13_6518 : exactInterval 13 6518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6518 : oddCount 6518 13 = 8 ∧ acceleratedOrbit 13 6518 = 5224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6518) = 3 ^ 8 * m + 5224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6518.1, data_13_6518.2] + +/-- Complete interval computation for depth 13, residue 6519. -/ +theorem bounds_13_6519 : exactInterval 13 6519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6519 : oddCount 6519 13 = 8 ∧ acceleratedOrbit 13 6519 = 5224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6519) = 3 ^ 8 * m + 5224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6519.1, data_13_6519.2] + +/-- Complete interval computation for depth 13, residue 6520. -/ +theorem bounds_13_6520 : exactInterval 13 6520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6520 : oddCount 6520 13 = 6 ∧ acceleratedOrbit 13 6520 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6520) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6520.1, data_13_6520.2] + +/-- Complete interval computation for depth 13, residue 6521. -/ +theorem bounds_13_6521 : exactInterval 13 6521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6521 : oddCount 6521 13 = 10 ∧ acceleratedOrbit 13 6521 = 47020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6521) = 3 ^ 10 * m + 47020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6521.1, data_13_6521.2] + +/-- Complete interval computation for depth 13, residue 6522. -/ +theorem bounds_13_6522 : exactInterval 13 6522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6522 : oddCount 6522 13 = 6 ∧ acceleratedOrbit 13 6522 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6522) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6522.1, data_13_6522.2] + +/-- Complete interval computation for depth 13, residue 6523. -/ +theorem bounds_13_6523 : exactInterval 13 6523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6523 : oddCount 6523 13 = 7 ∧ acceleratedOrbit 13 6523 = 1742 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6523) = 3 ^ 7 * m + 1742 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6523.1, data_13_6523.2] + +/-- Complete interval computation for depth 13, residue 6524. -/ +theorem bounds_13_6524 : exactInterval 13 6524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6524 : oddCount 6524 13 = 6 ∧ acceleratedOrbit 13 6524 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6524) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6524.1, data_13_6524.2] + +/-- Complete interval computation for depth 13, residue 6525. -/ +theorem bounds_13_6525 : exactInterval 13 6525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6525 : oddCount 6525 13 = 6 ∧ acceleratedOrbit 13 6525 = 581 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6525) = 3 ^ 6 * m + 581 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6525.1, data_13_6525.2] + +/-- Complete interval computation for depth 13, residue 6526. -/ +theorem bounds_13_6526 : exactInterval 13 6526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6526 : oddCount 6526 13 = 9 ∧ acceleratedOrbit 13 6526 = 15686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6526) = 3 ^ 9 * m + 15686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6526.1, data_13_6526.2] + +/-- Complete interval computation for depth 13, residue 6527. -/ +theorem bounds_13_6527 : exactInterval 13 6527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6527 : oddCount 6527 13 = 9 ∧ acceleratedOrbit 13 6527 = 15686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6527) = 3 ^ 9 * m + 15686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6527.1, data_13_6527.2] + +/-- Complete interval computation for depth 13, residue 6528. -/ +theorem bounds_13_6528 : exactInterval 13 6528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6528 : oddCount 6528 13 = 3 ∧ acceleratedOrbit 13 6528 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6528) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6528.1, data_13_6528.2] + +/-- Complete interval computation for depth 13, residue 6529. -/ +theorem bounds_13_6529 : exactInterval 13 6529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6529 : oddCount 6529 13 = 7 ∧ acceleratedOrbit 13 6529 = 1745 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6529) = 3 ^ 7 * m + 1745 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6529.1, data_13_6529.2] + +/-- Complete interval computation for depth 13, residue 6530. -/ +theorem bounds_13_6530 : exactInterval 13 6530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6530 : oddCount 6530 13 = 5 ∧ acceleratedOrbit 13 6530 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6530) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6530.1, data_13_6530.2] + +/-- Complete interval computation for depth 13, residue 6531. -/ +theorem bounds_13_6531 : exactInterval 13 6531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6531 : oddCount 6531 13 = 5 ∧ acceleratedOrbit 13 6531 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6531) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6531.1, data_13_6531.2] + +/-- Complete interval computation for depth 13, residue 6532. -/ +theorem bounds_13_6532 : exactInterval 13 6532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6532 : oddCount 6532 13 = 5 ∧ acceleratedOrbit 13 6532 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6532) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6532.1, data_13_6532.2] + +end Collatz.Research.StoppingAtlas.Batch0892 From 1b75cf1ba225ade2e9d19f86818b16b859d3ea3e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:17 +0530 Subject: [PATCH 0893/1001] proof: certify atlas Batch0893 (13:6533 to 13:6547) --- Collatz/Research/StoppingAtlas/Batch0893.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0893.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0893.lean b/Collatz/Research/StoppingAtlas/Batch0893.lean new file mode 100644 index 00000000..965d7eab --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0893.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0893 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6533. -/ +theorem bounds_13_6533 : exactInterval 13 6533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6533 : oddCount 6533 13 = 5 ∧ acceleratedOrbit 13 6533 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6533) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6533.1, data_13_6533.2] + +/-- Complete interval computation for depth 13, residue 6534. -/ +theorem bounds_13_6534 : exactInterval 13 6534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6534 : oddCount 6534 13 = 5 ∧ acceleratedOrbit 13 6534 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6534) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6534.1, data_13_6534.2] + +/-- Complete interval computation for depth 13, residue 6535. -/ +theorem bounds_13_6535 : exactInterval 13 6535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6535 : oddCount 6535 13 = 5 ∧ acceleratedOrbit 13 6535 = 194 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6535) = 3 ^ 5 * m + 194 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6535.1, data_13_6535.2] + +/-- Complete interval computation for depth 13, residue 6536. -/ +theorem bounds_13_6536 : exactInterval 13 6536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6536 : oddCount 6536 13 = 4 ∧ acceleratedOrbit 13 6536 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6536) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6536.1, data_13_6536.2] + +/-- Complete interval computation for depth 13, residue 6537. -/ +theorem bounds_13_6537 : exactInterval 13 6537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6537 : oddCount 6537 13 = 9 ∧ acceleratedOrbit 13 6537 = 15713 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6537) = 3 ^ 9 * m + 15713 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6537.1, data_13_6537.2] + +/-- Complete interval computation for depth 13, residue 6538. -/ +theorem bounds_13_6538 : exactInterval 13 6538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6538 : oddCount 6538 13 = 4 ∧ acceleratedOrbit 13 6538 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6538) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6538.1, data_13_6538.2] + +/-- Complete interval computation for depth 13, residue 6539. -/ +theorem bounds_13_6539 : exactInterval 13 6539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6539 : oddCount 6539 13 = 8 ∧ acceleratedOrbit 13 6539 = 5240 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6539) = 3 ^ 8 * m + 5240 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6539.1, data_13_6539.2] + +/-- Complete interval computation for depth 13, residue 6540. -/ +theorem bounds_13_6540 : exactInterval 13 6540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6540 : oddCount 6540 13 = 4 ∧ acceleratedOrbit 13 6540 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6540) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6540.1, data_13_6540.2] + +/-- Complete interval computation for depth 13, residue 6541. -/ +theorem bounds_13_6541 : exactInterval 13 6541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6541 : oddCount 6541 13 = 4 ∧ acceleratedOrbit 13 6541 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6541) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6541.1, data_13_6541.2] + +/-- Complete interval computation for depth 13, residue 6542. -/ +theorem bounds_13_6542 : exactInterval 13 6542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6542 : oddCount 6542 13 = 7 ∧ acceleratedOrbit 13 6542 = 1748 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6542) = 3 ^ 7 * m + 1748 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6542.1, data_13_6542.2] + +/-- Complete interval computation for depth 13, residue 6543. -/ +theorem bounds_13_6543 : exactInterval 13 6543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6543 : oddCount 6543 13 = 7 ∧ acceleratedOrbit 13 6543 = 1748 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6543) = 3 ^ 7 * m + 1748 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6543.1, data_13_6543.2] + +/-- Complete interval computation for depth 13, residue 6544. -/ +theorem bounds_13_6544 : exactInterval 13 6544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6544 : oddCount 6544 13 = 4 ∧ acceleratedOrbit 13 6544 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6544) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6544.1, data_13_6544.2] + +/-- Complete interval computation for depth 13, residue 6545. -/ +theorem bounds_13_6545 : exactInterval 13 6545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6545 : oddCount 6545 13 = 6 ∧ acceleratedOrbit 13 6545 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6545) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6545.1, data_13_6545.2] + +/-- Complete interval computation for depth 13, residue 6546. -/ +theorem bounds_13_6546 : exactInterval 13 6546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6546 : oddCount 6546 13 = 6 ∧ acceleratedOrbit 13 6546 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6546) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6546.1, data_13_6546.2] + +/-- Complete interval computation for depth 13, residue 6547. -/ +theorem bounds_13_6547 : exactInterval 13 6547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6547 : oddCount 6547 13 = 6 ∧ acceleratedOrbit 13 6547 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6547) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6547.1, data_13_6547.2] + +end Collatz.Research.StoppingAtlas.Batch0893 From 3190155ec3ac8a812bbfa9388c76887bac6c7e00 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:18 +0530 Subject: [PATCH 0894/1001] proof: certify atlas Batch0894 (13:6548 to 13:6562) --- Collatz/Research/StoppingAtlas/Batch0894.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0894.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0894.lean b/Collatz/Research/StoppingAtlas/Batch0894.lean new file mode 100644 index 00000000..c2414234 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0894.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0894 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6548. -/ +theorem bounds_13_6548 : exactInterval 13 6548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6548 : oddCount 6548 13 = 4 ∧ acceleratedOrbit 13 6548 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6548) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6548.1, data_13_6548.2] + +/-- Complete interval computation for depth 13, residue 6549. -/ +theorem bounds_13_6549 : exactInterval 13 6549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6549 : oddCount 6549 13 = 4 ∧ acceleratedOrbit 13 6549 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6549) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6549.1, data_13_6549.2] + +/-- Complete interval computation for depth 13, residue 6550. -/ +theorem bounds_13_6550 : exactInterval 13 6550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6550 : oddCount 6550 13 = 6 ∧ acceleratedOrbit 13 6550 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6550) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6550.1, data_13_6550.2] + +/-- Complete interval computation for depth 13, residue 6551. -/ +theorem bounds_13_6551 : exactInterval 13 6551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6551 : oddCount 6551 13 = 6 ∧ acceleratedOrbit 13 6551 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6551) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6551.1, data_13_6551.2] + +/-- Complete interval computation for depth 13, residue 6552. -/ +theorem bounds_13_6552 : exactInterval 13 6552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6552 : oddCount 6552 13 = 4 ∧ acceleratedOrbit 13 6552 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6552) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6552.1, data_13_6552.2] + +/-- Complete interval computation for depth 13, residue 6553. -/ +theorem bounds_13_6553 : exactInterval 13 6553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6553 : oddCount 6553 13 = 6 ∧ acceleratedOrbit 13 6553 = 584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6553) = 3 ^ 6 * m + 584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6553.1, data_13_6553.2] + +/-- Complete interval computation for depth 13, residue 6554. -/ +theorem bounds_13_6554 : exactInterval 13 6554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6554 : oddCount 6554 13 = 4 ∧ acceleratedOrbit 13 6554 = 65 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6554) = 3 ^ 4 * m + 65 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6554.1, data_13_6554.2] + +/-- Complete interval computation for depth 13, residue 6555. -/ +theorem bounds_13_6555 : exactInterval 13 6555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6555 : oddCount 6555 13 = 9 ∧ acceleratedOrbit 13 6555 = 15754 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6555) = 3 ^ 9 * m + 15754 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6555.1, data_13_6555.2] + +/-- Complete interval computation for depth 13, residue 6556. -/ +theorem bounds_13_6556 : exactInterval 13 6556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6556 : oddCount 6556 13 = 8 ∧ acceleratedOrbit 13 6556 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6556) = 3 ^ 8 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6556.1, data_13_6556.2] + +/-- Complete interval computation for depth 13, residue 6557. -/ +theorem bounds_13_6557 : exactInterval 13 6557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6557 : oddCount 6557 13 = 8 ∧ acceleratedOrbit 13 6557 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6557) = 3 ^ 8 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6557.1, data_13_6557.2] + +/-- Complete interval computation for depth 13, residue 6558. -/ +theorem bounds_13_6558 : exactInterval 13 6558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6558 : oddCount 6558 13 = 8 ∧ acceleratedOrbit 13 6558 = 5255 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6558) = 3 ^ 8 * m + 5255 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6558.1, data_13_6558.2] + +/-- Complete interval computation for depth 13, residue 6559. -/ +theorem bounds_13_6559 : exactInterval 13 6559 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6559) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6559 : oddCount 6559 13 = 8 ∧ acceleratedOrbit 13 6559 = 5254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6559) = 3 ^ 8 * m + 5254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6559.1, data_13_6559.2] + +/-- Complete interval computation for depth 13, residue 6560. -/ +theorem bounds_13_6560 : exactInterval 13 6560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6560 : oddCount 6560 13 = 3 ∧ acceleratedOrbit 13 6560 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6560) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6560.1, data_13_6560.2] + +/-- Complete interval computation for depth 13, residue 6561. -/ +theorem bounds_13_6561 : exactInterval 13 6561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6561 : oddCount 6561 13 = 8 ∧ acceleratedOrbit 13 6561 = 5258 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6561) = 3 ^ 8 * m + 5258 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6561.1, data_13_6561.2] + +/-- Complete interval computation for depth 13, residue 6562. -/ +theorem bounds_13_6562 : exactInterval 13 6562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6562 : oddCount 6562 13 = 8 ∧ acceleratedOrbit 13 6562 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6562) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6562.1, data_13_6562.2] + +end Collatz.Research.StoppingAtlas.Batch0894 From b7c07b69053037ef1f64f909109b62de088d807d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:18 +0530 Subject: [PATCH 0895/1001] proof: certify atlas Batch0895 (13:6563 to 13:6578) --- Collatz/Research/StoppingAtlas/Batch0895.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0895.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0895.lean b/Collatz/Research/StoppingAtlas/Batch0895.lean new file mode 100644 index 00000000..3e813e6c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0895.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0895 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6563. -/ +theorem bounds_13_6563 : exactInterval 13 6563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6563 : oddCount 6563 13 = 8 ∧ acceleratedOrbit 13 6563 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6563) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6563.1, data_13_6563.2] + +/-- Complete interval computation for depth 13, residue 6564. -/ +theorem bounds_13_6564 : exactInterval 13 6564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6564 : oddCount 6564 13 = 8 ∧ acceleratedOrbit 13 6564 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6564) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6564.1, data_13_6564.2] + +/-- Complete interval computation for depth 13, residue 6565. -/ +theorem bounds_13_6565 : exactInterval 13 6565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6565 : oddCount 6565 13 = 8 ∧ acceleratedOrbit 13 6565 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6565) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6565.1, data_13_6565.2] + +/-- Complete interval computation for depth 13, residue 6566. -/ +theorem bounds_13_6566 : exactInterval 13 6566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6566 : oddCount 6566 13 = 8 ∧ acceleratedOrbit 13 6566 = 5264 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6566) = 3 ^ 8 * m + 5264 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6566.1, data_13_6566.2] + +/-- Complete interval computation for depth 13, residue 6567. -/ +theorem bounds_13_6567 : exactInterval 13 6567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6567 : oddCount 6567 13 = 7 ∧ acceleratedOrbit 13 6567 = 1754 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6567) = 3 ^ 7 * m + 1754 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6567.1, data_13_6567.2] + +/-- Complete interval computation for depth 13, residue 6568. -/ +theorem bounds_13_6568 : exactInterval 13 6568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6568 : oddCount 6568 13 = 3 ∧ acceleratedOrbit 13 6568 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6568) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6568.1, data_13_6568.2] + +/-- Complete interval computation for depth 13, residue 6569. -/ +theorem bounds_13_6569 : exactInterval 13 6569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6569 : oddCount 6569 13 = 9 ∧ acceleratedOrbit 13 6569 = 15788 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6569) = 3 ^ 9 * m + 15788 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6569.1, data_13_6569.2] + +/-- Complete interval computation for depth 13, residue 6570. -/ +theorem bounds_13_6570 : exactInterval 13 6570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6570 : oddCount 6570 13 = 3 ∧ acceleratedOrbit 13 6570 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6570) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6570.1, data_13_6570.2] + +/-- Complete interval computation for depth 13, residue 6571. -/ +theorem bounds_13_6571 : exactInterval 13 6571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6571 : oddCount 6571 13 = 10 ∧ acceleratedOrbit 13 6571 = 47384 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6571) = 3 ^ 10 * m + 47384 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6571.1, data_13_6571.2] + +/-- Complete interval computation for depth 13, residue 6572. -/ +theorem bounds_13_6572 : exactInterval 13 6572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6572 : oddCount 6572 13 = 7 ∧ acceleratedOrbit 13 6572 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6572) = 3 ^ 7 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6572.1, data_13_6572.2] + +/-- Complete interval computation for depth 13, residue 6573. -/ +theorem bounds_13_6573 : exactInterval 13 6573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6573 : oddCount 6573 13 = 7 ∧ acceleratedOrbit 13 6573 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6573) = 3 ^ 7 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6573.1, data_13_6573.2] + +/-- Complete interval computation for depth 13, residue 6574. -/ +theorem bounds_13_6574 : exactInterval 13 6574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6574 : oddCount 6574 13 = 7 ∧ acceleratedOrbit 13 6574 = 1757 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6574) = 3 ^ 7 * m + 1757 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6574.1, data_13_6574.2] + +/-- Complete interval computation for depth 13, residue 6575. -/ +theorem bounds_13_6575 : exactInterval 13 6575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6575 : oddCount 6575 13 = 7 ∧ acceleratedOrbit 13 6575 = 1756 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6575) = 3 ^ 7 * m + 1756 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6575.1, data_13_6575.2] + +/-- Complete interval computation for depth 13, residue 6576. -/ +theorem bounds_13_6576 : exactInterval 13 6576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6576 : oddCount 6576 13 = 6 ∧ acceleratedOrbit 13 6576 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6576) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6576.1, data_13_6576.2] + +/-- Complete interval computation for depth 13, residue 6577. -/ +theorem bounds_13_6577 : exactInterval 13 6577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6577 : oddCount 6577 13 = 6 ∧ acceleratedOrbit 13 6577 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6577) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6577.1, data_13_6577.2] + +/-- Complete interval computation for depth 13, residue 6578. -/ +theorem bounds_13_6578 : exactInterval 13 6578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6578 : oddCount 6578 13 = 6 ∧ acceleratedOrbit 13 6578 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6578) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6578.1, data_13_6578.2] + +end Collatz.Research.StoppingAtlas.Batch0895 From 1383809c11f8ea2f1483e270dbbdbf546f1f25db Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:18 +0530 Subject: [PATCH 0896/1001] proof: certify atlas Batch0896 (13:6579 to 13:6593) --- Collatz/Research/StoppingAtlas/Batch0896.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0896.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0896.lean b/Collatz/Research/StoppingAtlas/Batch0896.lean new file mode 100644 index 00000000..fdf4ce45 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0896.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0896 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6579. -/ +theorem bounds_13_6579 : exactInterval 13 6579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6579 : oddCount 6579 13 = 6 ∧ acceleratedOrbit 13 6579 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6579) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6579.1, data_13_6579.2] + +/-- Complete interval computation for depth 13, residue 6580. -/ +theorem bounds_13_6580 : exactInterval 13 6580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6580 : oddCount 6580 13 = 6 ∧ acceleratedOrbit 13 6580 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6580) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6580.1, data_13_6580.2] + +/-- Complete interval computation for depth 13, residue 6581. -/ +theorem bounds_13_6581 : exactInterval 13 6581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6581 : oddCount 6581 13 = 6 ∧ acceleratedOrbit 13 6581 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6581) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6581.1, data_13_6581.2] + +/-- Complete interval computation for depth 13, residue 6582. -/ +theorem bounds_13_6582 : exactInterval 13 6582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6582 : oddCount 6582 13 = 6 ∧ acceleratedOrbit 13 6582 = 586 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6582) = 3 ^ 6 * m + 586 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6582.1, data_13_6582.2] + +/-- Complete interval computation for depth 13, residue 6583. -/ +theorem bounds_13_6583 : exactInterval 13 6583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6583 : oddCount 6583 13 = 6 ∧ acceleratedOrbit 13 6583 = 586 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6583) = 3 ^ 6 * m + 586 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6583.1, data_13_6583.2] + +/-- Complete interval computation for depth 13, residue 6584. -/ +theorem bounds_13_6584 : exactInterval 13 6584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6584 : oddCount 6584 13 = 6 ∧ acceleratedOrbit 13 6584 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6584) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6584.1, data_13_6584.2] + +/-- Complete interval computation for depth 13, residue 6585. -/ +theorem bounds_13_6585 : exactInterval 13 6585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6585 : oddCount 6585 13 = 6 ∧ acceleratedOrbit 13 6585 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6585) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6585.1, data_13_6585.2] + +/-- Complete interval computation for depth 13, residue 6586. -/ +theorem bounds_13_6586 : exactInterval 13 6586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6586 : oddCount 6586 13 = 6 ∧ acceleratedOrbit 13 6586 = 587 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6586) = 3 ^ 6 * m + 587 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6586.1, data_13_6586.2] + +/-- Complete interval computation for depth 13, residue 6587. -/ +theorem bounds_13_6587 : exactInterval 13 6587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6587 : oddCount 6587 13 = 8 ∧ acceleratedOrbit 13 6587 = 5278 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6587) = 3 ^ 8 * m + 5278 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6587.1, data_13_6587.2] + +/-- Complete interval computation for depth 13, residue 6588. -/ +theorem bounds_13_6588 : exactInterval 13 6588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6588 : oddCount 6588 13 = 7 ∧ acceleratedOrbit 13 6588 = 1760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6588) = 3 ^ 7 * m + 1760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6588.1, data_13_6588.2] + +/-- Complete interval computation for depth 13, residue 6589. -/ +theorem bounds_13_6589 : exactInterval 13 6589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6589 : oddCount 6589 13 = 7 ∧ acceleratedOrbit 13 6589 = 1760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6589) = 3 ^ 7 * m + 1760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6589.1, data_13_6589.2] + +/-- Complete interval computation for depth 13, residue 6590. -/ +theorem bounds_13_6590 : exactInterval 13 6590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6590 : oddCount 6590 13 = 7 ∧ acceleratedOrbit 13 6590 = 1760 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6590) = 3 ^ 7 * m + 1760 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6590.1, data_13_6590.2] + +/-- Complete interval computation for depth 13, residue 6591. -/ +theorem bounds_13_6591 : exactInterval 13 6591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6591 : oddCount 6591 13 = 11 ∧ acceleratedOrbit 13 6591 = 142550 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6591) = 3 ^ 11 * m + 142550 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6591.1, data_13_6591.2] + +/-- Complete interval computation for depth 13, residue 6592. -/ +theorem bounds_13_6592 : exactInterval 13 6592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6592 : oddCount 6592 13 = 6 ∧ acceleratedOrbit 13 6592 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6592) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6592.1, data_13_6592.2] + +/-- Complete interval computation for depth 13, residue 6593. -/ +theorem bounds_13_6593 : exactInterval 13 6593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6593 : oddCount 6593 13 = 8 ∧ acceleratedOrbit 13 6593 = 5285 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6593) = 3 ^ 8 * m + 5285 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6593.1, data_13_6593.2] + +end Collatz.Research.StoppingAtlas.Batch0896 From 909cc3f378d0495df699122c2c677a23af3713c2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:18 +0530 Subject: [PATCH 0897/1001] proof: certify atlas Batch0897 (13:6594 to 13:6608) --- Collatz/Research/StoppingAtlas/Batch0897.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0897.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0897.lean b/Collatz/Research/StoppingAtlas/Batch0897.lean new file mode 100644 index 00000000..deda28b7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0897.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0897 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6594. -/ +theorem bounds_13_6594 : exactInterval 13 6594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6594 : oddCount 6594 13 = 8 ∧ acceleratedOrbit 13 6594 = 5285 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6594) = 3 ^ 8 * m + 5285 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6594.1, data_13_6594.2] + +/-- Complete interval computation for depth 13, residue 6595. -/ +theorem bounds_13_6595 : exactInterval 13 6595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6595 : oddCount 6595 13 = 8 ∧ acceleratedOrbit 13 6595 = 5285 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6595) = 3 ^ 8 * m + 5285 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6595.1, data_13_6595.2] + +/-- Complete interval computation for depth 13, residue 6596. -/ +theorem bounds_13_6596 : exactInterval 13 6596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6596 : oddCount 6596 13 = 3 ∧ acceleratedOrbit 13 6596 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6596) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6596.1, data_13_6596.2] + +/-- Complete interval computation for depth 13, residue 6597. -/ +theorem bounds_13_6597 : exactInterval 13 6597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6597 : oddCount 6597 13 = 3 ∧ acceleratedOrbit 13 6597 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6597) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6597.1, data_13_6597.2] + +/-- Complete interval computation for depth 13, residue 6598. -/ +theorem bounds_13_6598 : exactInterval 13 6598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6598 : oddCount 6598 13 = 3 ∧ acceleratedOrbit 13 6598 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6598) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6598.1, data_13_6598.2] + +/-- Complete interval computation for depth 13, residue 6599. -/ +theorem bounds_13_6599 : exactInterval 13 6599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6599 : oddCount 6599 13 = 8 ∧ acceleratedOrbit 13 6599 = 5287 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6599) = 3 ^ 8 * m + 5287 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6599.1, data_13_6599.2] + +/-- Complete interval computation for depth 13, residue 6600. -/ +theorem bounds_13_6600 : exactInterval 13 6600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6600 : oddCount 6600 13 = 6 ∧ acceleratedOrbit 13 6600 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6600) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6600.1, data_13_6600.2] + +/-- Complete interval computation for depth 13, residue 6601. -/ +theorem bounds_13_6601 : exactInterval 13 6601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6601 : oddCount 6601 13 = 8 ∧ acceleratedOrbit 13 6601 = 5291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6601) = 3 ^ 8 * m + 5291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6601.1, data_13_6601.2] + +/-- Complete interval computation for depth 13, residue 6602. -/ +theorem bounds_13_6602 : exactInterval 13 6602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6602 : oddCount 6602 13 = 6 ∧ acceleratedOrbit 13 6602 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6602) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6602.1, data_13_6602.2] + +/-- Complete interval computation for depth 13, residue 6603. -/ +theorem bounds_13_6603 : exactInterval 13 6603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6603 : oddCount 6603 13 = 5 ∧ acceleratedOrbit 13 6603 = 196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6603) = 3 ^ 5 * m + 196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6603.1, data_13_6603.2] + +/-- Complete interval computation for depth 13, residue 6604. -/ +theorem bounds_13_6604 : exactInterval 13 6604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6604 : oddCount 6604 13 = 6 ∧ acceleratedOrbit 13 6604 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6604) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6604.1, data_13_6604.2] + +/-- Complete interval computation for depth 13, residue 6605. -/ +theorem bounds_13_6605 : exactInterval 13 6605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6605 : oddCount 6605 13 = 6 ∧ acceleratedOrbit 13 6605 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6605) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6605.1, data_13_6605.2] + +/-- Complete interval computation for depth 13, residue 6606. -/ +theorem bounds_13_6606 : exactInterval 13 6606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6606 : oddCount 6606 13 = 8 ∧ acceleratedOrbit 13 6606 = 5293 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6606) = 3 ^ 8 * m + 5293 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6606.1, data_13_6606.2] + +/-- Complete interval computation for depth 13, residue 6607. -/ +theorem bounds_13_6607 : exactInterval 13 6607 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6607) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6607 : oddCount 6607 13 = 8 ∧ acceleratedOrbit 13 6607 = 5293 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6607) = 3 ^ 8 * m + 5293 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6607.1, data_13_6607.2] + +/-- Complete interval computation for depth 13, residue 6608. -/ +theorem bounds_13_6608 : exactInterval 13 6608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6608 : oddCount 6608 13 = 6 ∧ acceleratedOrbit 13 6608 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6608) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6608.1, data_13_6608.2] + +end Collatz.Research.StoppingAtlas.Batch0897 From edd2a0f32f71c4f2f429637d0b08130bfdd3d973 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:18 +0530 Subject: [PATCH 0898/1001] proof: certify atlas Batch0898 (13:6609 to 13:6624) --- Collatz/Research/StoppingAtlas/Batch0898.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0898.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0898.lean b/Collatz/Research/StoppingAtlas/Batch0898.lean new file mode 100644 index 00000000..59fdd0e9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0898.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0898 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6609. -/ +theorem bounds_13_6609 : exactInterval 13 6609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6609 : oddCount 6609 13 = 6 ∧ acceleratedOrbit 13 6609 = 589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6609) = 3 ^ 6 * m + 589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6609.1, data_13_6609.2] + +/-- Complete interval computation for depth 13, residue 6610. -/ +theorem bounds_13_6610 : exactInterval 13 6610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6610 : oddCount 6610 13 = 7 ∧ acceleratedOrbit 13 6610 = 1766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6610) = 3 ^ 7 * m + 1766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6610.1, data_13_6610.2] + +/-- Complete interval computation for depth 13, residue 6611. -/ +theorem bounds_13_6611 : exactInterval 13 6611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6611 : oddCount 6611 13 = 7 ∧ acceleratedOrbit 13 6611 = 1766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6611) = 3 ^ 7 * m + 1766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6611.1, data_13_6611.2] + +/-- Complete interval computation for depth 13, residue 6612. -/ +theorem bounds_13_6612 : exactInterval 13 6612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6612 : oddCount 6612 13 = 6 ∧ acceleratedOrbit 13 6612 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6612) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6612.1, data_13_6612.2] + +/-- Complete interval computation for depth 13, residue 6613. -/ +theorem bounds_13_6613 : exactInterval 13 6613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6613 : oddCount 6613 13 = 6 ∧ acceleratedOrbit 13 6613 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6613) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6613.1, data_13_6613.2] + +/-- Complete interval computation for depth 13, residue 6614. -/ +theorem bounds_13_6614 : exactInterval 13 6614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6614 : oddCount 6614 13 = 9 ∧ acceleratedOrbit 13 6614 = 15902 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6614) = 3 ^ 9 * m + 15902 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6614.1, data_13_6614.2] + +/-- Complete interval computation for depth 13, residue 6615. -/ +theorem bounds_13_6615 : exactInterval 13 6615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6615 : oddCount 6615 13 = 9 ∧ acceleratedOrbit 13 6615 = 15902 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6615) = 3 ^ 9 * m + 15902 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6615.1, data_13_6615.2] + +/-- Complete interval computation for depth 13, residue 6616. -/ +theorem bounds_13_6616 : exactInterval 13 6616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6616 : oddCount 6616 13 = 5 ∧ acceleratedOrbit 13 6616 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6616) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6616.1, data_13_6616.2] + +/-- Complete interval computation for depth 13, residue 6617. -/ +theorem bounds_13_6617 : exactInterval 13 6617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6617 : oddCount 6617 13 = 5 ∧ acceleratedOrbit 13 6617 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6617) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6617.1, data_13_6617.2] + +/-- Complete interval computation for depth 13, residue 6618. -/ +theorem bounds_13_6618 : exactInterval 13 6618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6618 : oddCount 6618 13 = 5 ∧ acceleratedOrbit 13 6618 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6618) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6618.1, data_13_6618.2] + +/-- Complete interval computation for depth 13, residue 6619. -/ +theorem bounds_13_6619 : exactInterval 13 6619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6619 : oddCount 6619 13 = 7 ∧ acceleratedOrbit 13 6619 = 1768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6619) = 3 ^ 7 * m + 1768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6619.1, data_13_6619.2] + +/-- Complete interval computation for depth 13, residue 6620. -/ +theorem bounds_13_6620 : exactInterval 13 6620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6620 : oddCount 6620 13 = 5 ∧ acceleratedOrbit 13 6620 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6620) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6620.1, data_13_6620.2] + +/-- Complete interval computation for depth 13, residue 6621. -/ +theorem bounds_13_6621 : exactInterval 13 6621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6621 : oddCount 6621 13 = 5 ∧ acceleratedOrbit 13 6621 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6621) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6621.1, data_13_6621.2] + +/-- Complete interval computation for depth 13, residue 6622. -/ +theorem bounds_13_6622 : exactInterval 13 6622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6622 : oddCount 6622 13 = 10 ∧ acceleratedOrbit 13 6622 = 47749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6622) = 3 ^ 10 * m + 47749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6622.1, data_13_6622.2] + +/-- Complete interval computation for depth 13, residue 6623. -/ +theorem bounds_13_6623 : exactInterval 13 6623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6623 : oddCount 6623 13 = 10 ∧ acceleratedOrbit 13 6623 = 47749 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6623) = 3 ^ 10 * m + 47749 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6623.1, data_13_6623.2] + +/-- Complete interval computation for depth 13, residue 6624. -/ +theorem bounds_13_6624 : exactInterval 13 6624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6624 : oddCount 6624 13 = 6 ∧ acceleratedOrbit 13 6624 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6624) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6624.1, data_13_6624.2] + +end Collatz.Research.StoppingAtlas.Batch0898 From 705350dafa2871756978ecc999b9df43436487e5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:18 +0530 Subject: [PATCH 0899/1001] proof: certify atlas Batch0899 (13:6625 to 13:6639) --- Collatz/Research/StoppingAtlas/Batch0899.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0899.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0899.lean b/Collatz/Research/StoppingAtlas/Batch0899.lean new file mode 100644 index 00000000..7db30f99 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0899.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0899 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6625. -/ +theorem bounds_13_6625 : exactInterval 13 6625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6625 : oddCount 6625 13 = 8 ∧ acceleratedOrbit 13 6625 = 5309 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6625) = 3 ^ 8 * m + 5309 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6625.1, data_13_6625.2] + +/-- Complete interval computation for depth 13, residue 6626. -/ +theorem bounds_13_6626 : exactInterval 13 6626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6626 : oddCount 6626 13 = 6 ∧ acceleratedOrbit 13 6626 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6626) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6626.1, data_13_6626.2] + +/-- Complete interval computation for depth 13, residue 6627. -/ +theorem bounds_13_6627 : exactInterval 13 6627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6627 : oddCount 6627 13 = 6 ∧ acceleratedOrbit 13 6627 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6627) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6627.1, data_13_6627.2] + +/-- Complete interval computation for depth 13, residue 6628. -/ +theorem bounds_13_6628 : exactInterval 13 6628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6628 : oddCount 6628 13 = 7 ∧ acceleratedOrbit 13 6628 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6628) = 3 ^ 7 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6628.1, data_13_6628.2] + +/-- Complete interval computation for depth 13, residue 6629. -/ +theorem bounds_13_6629 : exactInterval 13 6629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6629 : oddCount 6629 13 = 7 ∧ acceleratedOrbit 13 6629 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6629) = 3 ^ 7 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6629.1, data_13_6629.2] + +/-- Complete interval computation for depth 13, residue 6630. -/ +theorem bounds_13_6630 : exactInterval 13 6630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6630 : oddCount 6630 13 = 7 ∧ acceleratedOrbit 13 6630 = 1772 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6630) = 3 ^ 7 * m + 1772 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6630.1, data_13_6630.2] + +/-- Complete interval computation for depth 13, residue 6631. -/ +theorem bounds_13_6631 : exactInterval 13 6631 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6631) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6631 : oddCount 6631 13 = 8 ∧ acceleratedOrbit 13 6631 = 5312 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6631) = 3 ^ 8 * m + 5312 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6631.1, data_13_6631.2] + +/-- Complete interval computation for depth 13, residue 6632. -/ +theorem bounds_13_6632 : exactInterval 13 6632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6632 : oddCount 6632 13 = 6 ∧ acceleratedOrbit 13 6632 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6632) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6632.1, data_13_6632.2] + +/-- Complete interval computation for depth 13, residue 6633. -/ +theorem bounds_13_6633 : exactInterval 13 6633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6633 : oddCount 6633 13 = 8 ∧ acceleratedOrbit 13 6633 = 5314 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6633) = 3 ^ 8 * m + 5314 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6633.1, data_13_6633.2] + +/-- Complete interval computation for depth 13, residue 6634. -/ +theorem bounds_13_6634 : exactInterval 13 6634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6634 : oddCount 6634 13 = 6 ∧ acceleratedOrbit 13 6634 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6634) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6634.1, data_13_6634.2] + +/-- Complete interval computation for depth 13, residue 6635. -/ +theorem bounds_13_6635 : exactInterval 13 6635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6635 : oddCount 6635 13 = 9 ∧ acceleratedOrbit 13 6635 = 15947 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6635) = 3 ^ 9 * m + 15947 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6635.1, data_13_6635.2] + +/-- Complete interval computation for depth 13, residue 6636. -/ +theorem bounds_13_6636 : exactInterval 13 6636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6636 : oddCount 6636 13 = 5 ∧ acceleratedOrbit 13 6636 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6636) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6636.1, data_13_6636.2] + +/-- Complete interval computation for depth 13, residue 6637. -/ +theorem bounds_13_6637 : exactInterval 13 6637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6637 : oddCount 6637 13 = 5 ∧ acceleratedOrbit 13 6637 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6637) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6637.1, data_13_6637.2] + +/-- Complete interval computation for depth 13, residue 6638. -/ +theorem bounds_13_6638 : exactInterval 13 6638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6638 : oddCount 6638 13 = 5 ∧ acceleratedOrbit 13 6638 = 197 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6638) = 3 ^ 5 * m + 197 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6638.1, data_13_6638.2] + +/-- Complete interval computation for depth 13, residue 6639. -/ +theorem bounds_13_6639 : exactInterval 13 6639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6639 : oddCount 6639 13 = 10 ∧ acceleratedOrbit 13 6639 = 47864 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6639) = 3 ^ 10 * m + 47864 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6639.1, data_13_6639.2] + +end Collatz.Research.StoppingAtlas.Batch0899 From 9d49ad642e91db05e4774c16889bf797ffef9fe3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:19 +0530 Subject: [PATCH 0900/1001] proof: certify atlas Batch0900 (13:6640 to 13:6655) --- Collatz/Research/StoppingAtlas/Batch0900.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0900.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0900.lean b/Collatz/Research/StoppingAtlas/Batch0900.lean new file mode 100644 index 00000000..5b6ff288 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0900.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0900 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6640. -/ +theorem bounds_13_6640 : exactInterval 13 6640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6640 : oddCount 6640 13 = 7 ∧ acceleratedOrbit 13 6640 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6640) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6640.1, data_13_6640.2] + +/-- Complete interval computation for depth 13, residue 6641. -/ +theorem bounds_13_6641 : exactInterval 13 6641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6641 : oddCount 6641 13 = 6 ∧ acceleratedOrbit 13 6641 = 593 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6641) = 3 ^ 6 * m + 593 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6641.1, data_13_6641.2] + +/-- Complete interval computation for depth 13, residue 6642. -/ +theorem bounds_13_6642 : exactInterval 13 6642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6642 : oddCount 6642 13 = 7 ∧ acceleratedOrbit 13 6642 = 1775 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6642) = 3 ^ 7 * m + 1775 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6642.1, data_13_6642.2] + +/-- Complete interval computation for depth 13, residue 6643. -/ +theorem bounds_13_6643 : exactInterval 13 6643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6643 : oddCount 6643 13 = 7 ∧ acceleratedOrbit 13 6643 = 1775 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6643) = 3 ^ 7 * m + 1775 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6643.1, data_13_6643.2] + +/-- Complete interval computation for depth 13, residue 6644. -/ +theorem bounds_13_6644 : exactInterval 13 6644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6644 : oddCount 6644 13 = 7 ∧ acceleratedOrbit 13 6644 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6644) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6644.1, data_13_6644.2] + +/-- Complete interval computation for depth 13, residue 6645. -/ +theorem bounds_13_6645 : exactInterval 13 6645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6645 : oddCount 6645 13 = 7 ∧ acceleratedOrbit 13 6645 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6645) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6645.1, data_13_6645.2] + +/-- Complete interval computation for depth 13, residue 6646. -/ +theorem bounds_13_6646 : exactInterval 13 6646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6646 : oddCount 6646 13 = 9 ∧ acceleratedOrbit 13 6646 = 15977 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6646) = 3 ^ 9 * m + 15977 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6646.1, data_13_6646.2] + +/-- Complete interval computation for depth 13, residue 6647. -/ +theorem bounds_13_6647 : exactInterval 13 6647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6647 : oddCount 6647 13 = 9 ∧ acceleratedOrbit 13 6647 = 15977 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6647) = 3 ^ 9 * m + 15977 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6647.1, data_13_6647.2] + +/-- Complete interval computation for depth 13, residue 6648. -/ +theorem bounds_13_6648 : exactInterval 13 6648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6648 : oddCount 6648 13 = 7 ∧ acceleratedOrbit 13 6648 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6648) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6648.1, data_13_6648.2] + +/-- Complete interval computation for depth 13, residue 6649. -/ +theorem bounds_13_6649 : exactInterval 13 6649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6649 : oddCount 6649 13 = 9 ∧ acceleratedOrbit 13 6649 = 15983 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6649) = 3 ^ 9 * m + 15983 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6649.1, data_13_6649.2] + +/-- Complete interval computation for depth 13, residue 6650. -/ +theorem bounds_13_6650 : exactInterval 13 6650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6650 : oddCount 6650 13 = 7 ∧ acceleratedOrbit 13 6650 = 1777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6650) = 3 ^ 7 * m + 1777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6650.1, data_13_6650.2] + +/-- Complete interval computation for depth 13, residue 6651. -/ +theorem bounds_13_6651 : exactInterval 13 6651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6651 : oddCount 6651 13 = 6 ∧ acceleratedOrbit 13 6651 = 592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6651) = 3 ^ 6 * m + 592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6651.1, data_13_6651.2] + +/-- Complete interval computation for depth 13, residue 6652. -/ +theorem bounds_13_6652 : exactInterval 13 6652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6652 : oddCount 6652 13 = 10 ∧ acceleratedOrbit 13 6652 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6652) = 3 ^ 10 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6652.1, data_13_6652.2] + +/-- Complete interval computation for depth 13, residue 6653. -/ +theorem bounds_13_6653 : exactInterval 13 6653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6653 : oddCount 6653 13 = 10 ∧ acceleratedOrbit 13 6653 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6653) = 3 ^ 10 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6653.1, data_13_6653.2] + +/-- Complete interval computation for depth 13, residue 6654. -/ +theorem bounds_13_6654 : exactInterval 13 6654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6654 : oddCount 6654 13 = 10 ∧ acceleratedOrbit 13 6654 = 47978 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6654) = 3 ^ 10 * m + 47978 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6654.1, data_13_6654.2] + +/-- Complete interval computation for depth 13, residue 6655. -/ +theorem bounds_13_6655 : exactInterval 13 6655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6655 : oddCount 6655 13 = 11 ∧ acceleratedOrbit 13 6655 = 143932 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6655) = 3 ^ 11 * m + 143932 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6655.1, data_13_6655.2] + +end Collatz.Research.StoppingAtlas.Batch0900 From 341bbdada0d1c6680744c6b8c6138fe3796228cc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:19 +0530 Subject: [PATCH 0901/1001] proof: certify atlas Batch0901 (13:6656 to 13:6670) --- Collatz/Research/StoppingAtlas/Batch0901.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0901.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0901.lean b/Collatz/Research/StoppingAtlas/Batch0901.lean new file mode 100644 index 00000000..0fddfad9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0901.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0901 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6656. -/ +theorem bounds_13_6656 : exactInterval 13 6656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6656 : oddCount 6656 13 = 2 ∧ acceleratedOrbit 13 6656 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6656) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6656.1, data_13_6656.2] + +/-- Complete interval computation for depth 13, residue 6657. -/ +theorem bounds_13_6657 : exactInterval 13 6657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6657 : oddCount 6657 13 = 8 ∧ acceleratedOrbit 13 6657 = 5336 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6657) = 3 ^ 8 * m + 5336 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6657.1, data_13_6657.2] + +/-- Complete interval computation for depth 13, residue 6658. -/ +theorem bounds_13_6658 : exactInterval 13 6658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6658 : oddCount 6658 13 = 7 ∧ acceleratedOrbit 13 6658 = 1781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6658) = 3 ^ 7 * m + 1781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6658.1, data_13_6658.2] + +/-- Complete interval computation for depth 13, residue 6659. -/ +theorem bounds_13_6659 : exactInterval 13 6659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6659 : oddCount 6659 13 = 7 ∧ acceleratedOrbit 13 6659 = 1781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6659) = 3 ^ 7 * m + 1781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6659.1, data_13_6659.2] + +/-- Complete interval computation for depth 13, residue 6660. -/ +theorem bounds_13_6660 : exactInterval 13 6660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6660 : oddCount 6660 13 = 8 ∧ acceleratedOrbit 13 6660 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6660) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6660.1, data_13_6660.2] + +/-- Complete interval computation for depth 13, residue 6661. -/ +theorem bounds_13_6661 : exactInterval 13 6661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6661 : oddCount 6661 13 = 8 ∧ acceleratedOrbit 13 6661 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6661) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6661.1, data_13_6661.2] + +/-- Complete interval computation for depth 13, residue 6662. -/ +theorem bounds_13_6662 : exactInterval 13 6662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6662 : oddCount 6662 13 = 8 ∧ acceleratedOrbit 13 6662 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6662) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6662.1, data_13_6662.2] + +/-- Complete interval computation for depth 13, residue 6663. -/ +theorem bounds_13_6663 : exactInterval 13 6663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6663 : oddCount 6663 13 = 8 ∧ acceleratedOrbit 13 6663 = 5339 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6663) = 3 ^ 8 * m + 5339 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6663.1, data_13_6663.2] + +/-- Complete interval computation for depth 13, residue 6664. -/ +theorem bounds_13_6664 : exactInterval 13 6664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6664 : oddCount 6664 13 = 3 ∧ acceleratedOrbit 13 6664 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6664) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6664.1, data_13_6664.2] + +/-- Complete interval computation for depth 13, residue 6665. -/ +theorem bounds_13_6665 : exactInterval 13 6665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6665 : oddCount 6665 13 = 7 ∧ acceleratedOrbit 13 6665 = 1781 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6665) = 3 ^ 7 * m + 1781 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6665.1, data_13_6665.2] + +/-- Complete interval computation for depth 13, residue 6666. -/ +theorem bounds_13_6666 : exactInterval 13 6666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6666 : oddCount 6666 13 = 3 ∧ acceleratedOrbit 13 6666 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6666) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6666.1, data_13_6666.2] + +/-- Complete interval computation for depth 13, residue 6667. -/ +theorem bounds_13_6667 : exactInterval 13 6667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6667 : oddCount 6667 13 = 8 ∧ acceleratedOrbit 13 6667 = 5345 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6667) = 3 ^ 8 * m + 5345 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6667.1, data_13_6667.2] + +/-- Complete interval computation for depth 13, residue 6668. -/ +theorem bounds_13_6668 : exactInterval 13 6668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6668 : oddCount 6668 13 = 3 ∧ acceleratedOrbit 13 6668 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6668) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6668.1, data_13_6668.2] + +/-- Complete interval computation for depth 13, residue 6669. -/ +theorem bounds_13_6669 : exactInterval 13 6669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6669 : oddCount 6669 13 = 3 ∧ acceleratedOrbit 13 6669 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6669) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6669.1, data_13_6669.2] + +/-- Complete interval computation for depth 13, residue 6670. -/ +theorem bounds_13_6670 : exactInterval 13 6670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6670 : oddCount 6670 13 = 9 ∧ acceleratedOrbit 13 6670 = 16037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6670) = 3 ^ 9 * m + 16037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6670.1, data_13_6670.2] + +end Collatz.Research.StoppingAtlas.Batch0901 From ccacd2fe12cfc6d3ced9162f6677c5fe71fac0b9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:19 +0530 Subject: [PATCH 0902/1001] proof: certify atlas Batch0902 (13:6671 to 13:6685) --- Collatz/Research/StoppingAtlas/Batch0902.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0902.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0902.lean b/Collatz/Research/StoppingAtlas/Batch0902.lean new file mode 100644 index 00000000..8830e7d7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0902.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0902 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6671. -/ +theorem bounds_13_6671 : exactInterval 13 6671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6671 : oddCount 6671 13 = 9 ∧ acceleratedOrbit 13 6671 = 16037 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6671) = 3 ^ 9 * m + 16037 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6671.1, data_13_6671.2] + +/-- Complete interval computation for depth 13, residue 6672. -/ +theorem bounds_13_6672 : exactInterval 13 6672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6672 : oddCount 6672 13 = 5 ∧ acceleratedOrbit 13 6672 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6672) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6672.1, data_13_6672.2] + +/-- Complete interval computation for depth 13, residue 6673. -/ +theorem bounds_13_6673 : exactInterval 13 6673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6673 : oddCount 6673 13 = 3 ∧ acceleratedOrbit 13 6673 = 22 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6673) = 3 ^ 3 * m + 22 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6673.1, data_13_6673.2] + +/-- Complete interval computation for depth 13, residue 6674. -/ +theorem bounds_13_6674 : exactInterval 13 6674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6674 : oddCount 6674 13 = 7 ∧ acceleratedOrbit 13 6674 = 1783 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6674) = 3 ^ 7 * m + 1783 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6674.1, data_13_6674.2] + +/-- Complete interval computation for depth 13, residue 6675. -/ +theorem bounds_13_6675 : exactInterval 13 6675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6675 : oddCount 6675 13 = 7 ∧ acceleratedOrbit 13 6675 = 1783 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6675) = 3 ^ 7 * m + 1783 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6675.1, data_13_6675.2] + +/-- Complete interval computation for depth 13, residue 6676. -/ +theorem bounds_13_6676 : exactInterval 13 6676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6676 : oddCount 6676 13 = 5 ∧ acceleratedOrbit 13 6676 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6676) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6676.1, data_13_6676.2] + +/-- Complete interval computation for depth 13, residue 6677. -/ +theorem bounds_13_6677 : exactInterval 13 6677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6677 : oddCount 6677 13 = 5 ∧ acceleratedOrbit 13 6677 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6677) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6677.1, data_13_6677.2] + +/-- Complete interval computation for depth 13, residue 6678. -/ +theorem bounds_13_6678 : exactInterval 13 6678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6678 : oddCount 6678 13 = 6 ∧ acceleratedOrbit 13 6678 = 595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6678) = 3 ^ 6 * m + 595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6678.1, data_13_6678.2] + +/-- Complete interval computation for depth 13, residue 6679. -/ +theorem bounds_13_6679 : exactInterval 13 6679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6679 : oddCount 6679 13 = 6 ∧ acceleratedOrbit 13 6679 = 595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6679) = 3 ^ 6 * m + 595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6679.1, data_13_6679.2] + +/-- Complete interval computation for depth 13, residue 6680. -/ +theorem bounds_13_6680 : exactInterval 13 6680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6680 : oddCount 6680 13 = 5 ∧ acceleratedOrbit 13 6680 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6680) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6680.1, data_13_6680.2] + +/-- Complete interval computation for depth 13, residue 6681. -/ +theorem bounds_13_6681 : exactInterval 13 6681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6681 : oddCount 6681 13 = 6 ∧ acceleratedOrbit 13 6681 = 595 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6681) = 3 ^ 6 * m + 595 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6681.1, data_13_6681.2] + +/-- Complete interval computation for depth 13, residue 6682. -/ +theorem bounds_13_6682 : exactInterval 13 6682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6682 : oddCount 6682 13 = 5 ∧ acceleratedOrbit 13 6682 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6682) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6682.1, data_13_6682.2] + +/-- Complete interval computation for depth 13, residue 6683. -/ +theorem bounds_13_6683 : exactInterval 13 6683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6683 : oddCount 6683 13 = 8 ∧ acceleratedOrbit 13 6683 = 5354 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6683) = 3 ^ 8 * m + 5354 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6683.1, data_13_6683.2] + +/-- Complete interval computation for depth 13, residue 6684. -/ +theorem bounds_13_6684 : exactInterval 13 6684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6684 : oddCount 6684 13 = 6 ∧ acceleratedOrbit 13 6684 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6684) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6684.1, data_13_6684.2] + +/-- Complete interval computation for depth 13, residue 6685. -/ +theorem bounds_13_6685 : exactInterval 13 6685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6685 : oddCount 6685 13 = 6 ∧ acceleratedOrbit 13 6685 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6685) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6685.1, data_13_6685.2] + +end Collatz.Research.StoppingAtlas.Batch0902 From d5f2d84fd7f8bb58d659ed369fc02d053ac2cdf5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:19 +0530 Subject: [PATCH 0903/1001] proof: certify atlas Batch0903 (13:6686 to 13:6701) --- Collatz/Research/StoppingAtlas/Batch0903.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0903.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0903.lean b/Collatz/Research/StoppingAtlas/Batch0903.lean new file mode 100644 index 00000000..b1328965 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0903.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0903 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6686. -/ +theorem bounds_13_6686 : exactInterval 13 6686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6686 : oddCount 6686 13 = 6 ∧ acceleratedOrbit 13 6686 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6686) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6686.1, data_13_6686.2] + +/-- Complete interval computation for depth 13, residue 6687. -/ +theorem bounds_13_6687 : exactInterval 13 6687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6687 : oddCount 6687 13 = 8 ∧ acceleratedOrbit 13 6687 = 5357 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6687) = 3 ^ 8 * m + 5357 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6687.1, data_13_6687.2] + +/-- Complete interval computation for depth 13, residue 6688. -/ +theorem bounds_13_6688 : exactInterval 13 6688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6688 : oddCount 6688 13 = 4 ∧ acceleratedOrbit 13 6688 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6688) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6688.1, data_13_6688.2] + +/-- Complete interval computation for depth 13, residue 6689. -/ +theorem bounds_13_6689 : exactInterval 13 6689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6689 : oddCount 6689 13 = 6 ∧ acceleratedOrbit 13 6689 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6689) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6689.1, data_13_6689.2] + +/-- Complete interval computation for depth 13, residue 6690. -/ +theorem bounds_13_6690 : exactInterval 13 6690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6690 : oddCount 6690 13 = 5 ∧ acceleratedOrbit 13 6690 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6690) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6690.1, data_13_6690.2] + +/-- Complete interval computation for depth 13, residue 6691. -/ +theorem bounds_13_6691 : exactInterval 13 6691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6691 : oddCount 6691 13 = 5 ∧ acceleratedOrbit 13 6691 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6691) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6691.1, data_13_6691.2] + +/-- Complete interval computation for depth 13, residue 6692. -/ +theorem bounds_13_6692 : exactInterval 13 6692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6692 : oddCount 6692 13 = 8 ∧ acceleratedOrbit 13 6692 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6692) = 3 ^ 8 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6692.1, data_13_6692.2] + +/-- Complete interval computation for depth 13, residue 6693. -/ +theorem bounds_13_6693 : exactInterval 13 6693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6693 : oddCount 6693 13 = 8 ∧ acceleratedOrbit 13 6693 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6693) = 3 ^ 8 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6693.1, data_13_6693.2] + +/-- Complete interval computation for depth 13, residue 6694. -/ +theorem bounds_13_6694 : exactInterval 13 6694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6694 : oddCount 6694 13 = 8 ∧ acceleratedOrbit 13 6694 = 5366 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6694) = 3 ^ 8 * m + 5366 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6694.1, data_13_6694.2] + +/-- Complete interval computation for depth 13, residue 6695. -/ +theorem bounds_13_6695 : exactInterval 13 6695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6695 : oddCount 6695 13 = 6 ∧ acceleratedOrbit 13 6695 = 596 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6695) = 3 ^ 6 * m + 596 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6695.1, data_13_6695.2] + +/-- Complete interval computation for depth 13, residue 6696. -/ +theorem bounds_13_6696 : exactInterval 13 6696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6696 : oddCount 6696 13 = 4 ∧ acceleratedOrbit 13 6696 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6696) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6696.1, data_13_6696.2] + +/-- Complete interval computation for depth 13, residue 6697. -/ +theorem bounds_13_6697 : exactInterval 13 6697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6697 : oddCount 6697 13 = 8 ∧ acceleratedOrbit 13 6697 = 5365 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6697) = 3 ^ 8 * m + 5365 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6697.1, data_13_6697.2] + +/-- Complete interval computation for depth 13, residue 6698. -/ +theorem bounds_13_6698 : exactInterval 13 6698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6698 : oddCount 6698 13 = 4 ∧ acceleratedOrbit 13 6698 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6698) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6698.1, data_13_6698.2] + +/-- Complete interval computation for depth 13, residue 6699. -/ +theorem bounds_13_6699 : exactInterval 13 6699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6699 : oddCount 6699 13 = 5 ∧ acceleratedOrbit 13 6699 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6699) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6699.1, data_13_6699.2] + +/-- Complete interval computation for depth 13, residue 6700. -/ +theorem bounds_13_6700 : exactInterval 13 6700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6700 : oddCount 6700 13 = 5 ∧ acceleratedOrbit 13 6700 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6700) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6700.1, data_13_6700.2] + +/-- Complete interval computation for depth 13, residue 6701. -/ +theorem bounds_13_6701 : exactInterval 13 6701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6701 : oddCount 6701 13 = 5 ∧ acceleratedOrbit 13 6701 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6701) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6701.1, data_13_6701.2] + +end Collatz.Research.StoppingAtlas.Batch0903 From 4c2ed4d2617b7580bdab69d184c1fa64932c2293 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:19 +0530 Subject: [PATCH 0904/1001] proof: certify atlas Batch0904 (13:6702 to 13:6716) --- Collatz/Research/StoppingAtlas/Batch0904.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0904.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0904.lean b/Collatz/Research/StoppingAtlas/Batch0904.lean new file mode 100644 index 00000000..eaef9353 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0904.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0904 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6702. -/ +theorem bounds_13_6702 : exactInterval 13 6702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6702 : oddCount 6702 13 = 5 ∧ acceleratedOrbit 13 6702 = 199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6702) = 3 ^ 5 * m + 199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6702.1, data_13_6702.2] + +/-- Complete interval computation for depth 13, residue 6703. -/ +theorem bounds_13_6703 : exactInterval 13 6703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6703 : oddCount 6703 13 = 9 ∧ acceleratedOrbit 13 6703 = 16109 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6703) = 3 ^ 9 * m + 16109 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6703.1, data_13_6703.2] + +/-- Complete interval computation for depth 13, residue 6704. -/ +theorem bounds_13_6704 : exactInterval 13 6704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6704 : oddCount 6704 13 = 4 ∧ acceleratedOrbit 13 6704 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6704) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6704.1, data_13_6704.2] + +/-- Complete interval computation for depth 13, residue 6705. -/ +theorem bounds_13_6705 : exactInterval 13 6705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6705 : oddCount 6705 13 = 7 ∧ acceleratedOrbit 13 6705 = 1792 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6705) = 3 ^ 7 * m + 1792 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6705.1, data_13_6705.2] + +/-- Complete interval computation for depth 13, residue 6706. -/ +theorem bounds_13_6706 : exactInterval 13 6706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6706 : oddCount 6706 13 = 7 ∧ acceleratedOrbit 13 6706 = 1792 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6706) = 3 ^ 7 * m + 1792 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6706.1, data_13_6706.2] + +/-- Complete interval computation for depth 13, residue 6707. -/ +theorem bounds_13_6707 : exactInterval 13 6707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6707 : oddCount 6707 13 = 7 ∧ acceleratedOrbit 13 6707 = 1792 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6707) = 3 ^ 7 * m + 1792 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6707.1, data_13_6707.2] + +/-- Complete interval computation for depth 13, residue 6708. -/ +theorem bounds_13_6708 : exactInterval 13 6708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6708 : oddCount 6708 13 = 4 ∧ acceleratedOrbit 13 6708 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6708) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6708.1, data_13_6708.2] + +/-- Complete interval computation for depth 13, residue 6709. -/ +theorem bounds_13_6709 : exactInterval 13 6709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6709 : oddCount 6709 13 = 4 ∧ acceleratedOrbit 13 6709 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6709) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6709.1, data_13_6709.2] + +/-- Complete interval computation for depth 13, residue 6710. -/ +theorem bounds_13_6710 : exactInterval 13 6710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6710 : oddCount 6710 13 = 9 ∧ acceleratedOrbit 13 6710 = 16129 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6710) = 3 ^ 9 * m + 16129 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6710.1, data_13_6710.2] + +/-- Complete interval computation for depth 13, residue 6711. -/ +theorem bounds_13_6711 : exactInterval 13 6711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6711 : oddCount 6711 13 = 9 ∧ acceleratedOrbit 13 6711 = 16129 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6711) = 3 ^ 9 * m + 16129 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6711.1, data_13_6711.2] + +/-- Complete interval computation for depth 13, residue 6712. -/ +theorem bounds_13_6712 : exactInterval 13 6712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6712 : oddCount 6712 13 = 7 ∧ acceleratedOrbit 13 6712 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6712) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6712.1, data_13_6712.2] + +/-- Complete interval computation for depth 13, residue 6713. -/ +theorem bounds_13_6713 : exactInterval 13 6713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6713 : oddCount 6713 13 = 7 ∧ acceleratedOrbit 13 6713 = 1793 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6713) = 3 ^ 7 * m + 1793 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6713.1, data_13_6713.2] + +/-- Complete interval computation for depth 13, residue 6714. -/ +theorem bounds_13_6714 : exactInterval 13 6714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6714 : oddCount 6714 13 = 7 ∧ acceleratedOrbit 13 6714 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6714) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6714.1, data_13_6714.2] + +/-- Complete interval computation for depth 13, residue 6715. -/ +theorem bounds_13_6715 : exactInterval 13 6715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6715 : oddCount 6715 13 = 6 ∧ acceleratedOrbit 13 6715 = 598 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6715) = 3 ^ 6 * m + 598 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6715.1, data_13_6715.2] + +/-- Complete interval computation for depth 13, residue 6716. -/ +theorem bounds_13_6716 : exactInterval 13 6716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6716 : oddCount 6716 13 = 7 ∧ acceleratedOrbit 13 6716 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6716) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6716.1, data_13_6716.2] + +end Collatz.Research.StoppingAtlas.Batch0904 From 08646a0593a5e8f6df3067b24e35b21d13b1ba3e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:19 +0530 Subject: [PATCH 0905/1001] proof: certify atlas Batch0905 (13:6717 to 13:6731) --- Collatz/Research/StoppingAtlas/Batch0905.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0905.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0905.lean b/Collatz/Research/StoppingAtlas/Batch0905.lean new file mode 100644 index 00000000..e5947de0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0905.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0905 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6717. -/ +theorem bounds_13_6717 : exactInterval 13 6717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6717 : oddCount 6717 13 = 7 ∧ acceleratedOrbit 13 6717 = 1795 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6717) = 3 ^ 7 * m + 1795 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6717.1, data_13_6717.2] + +/-- Complete interval computation for depth 13, residue 6718. -/ +theorem bounds_13_6718 : exactInterval 13 6718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6718 : oddCount 6718 13 = 6 ∧ acceleratedOrbit 13 6718 = 598 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6718) = 3 ^ 6 * m + 598 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6718.1, data_13_6718.2] + +/-- Complete interval computation for depth 13, residue 6719. -/ +theorem bounds_13_6719 : exactInterval 13 6719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6719 : oddCount 6719 13 = 6 ∧ acceleratedOrbit 13 6719 = 598 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6719) = 3 ^ 6 * m + 598 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6719.1, data_13_6719.2] + +/-- Complete interval computation for depth 13, residue 6720. -/ +theorem bounds_13_6720 : exactInterval 13 6720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6720 : oddCount 6720 13 = 5 ∧ acceleratedOrbit 13 6720 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6720) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6720.1, data_13_6720.2] + +/-- Complete interval computation for depth 13, residue 6721. -/ +theorem bounds_13_6721 : exactInterval 13 6721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6721 : oddCount 6721 13 = 5 ∧ acceleratedOrbit 13 6721 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6721) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6721.1, data_13_6721.2] + +/-- Complete interval computation for depth 13, residue 6722. -/ +theorem bounds_13_6722 : exactInterval 13 6722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6722 : oddCount 6722 13 = 5 ∧ acceleratedOrbit 13 6722 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6722) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6722.1, data_13_6722.2] + +/-- Complete interval computation for depth 13, residue 6723. -/ +theorem bounds_13_6723 : exactInterval 13 6723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6723 : oddCount 6723 13 = 5 ∧ acceleratedOrbit 13 6723 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6723) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6723.1, data_13_6723.2] + +/-- Complete interval computation for depth 13, residue 6724. -/ +theorem bounds_13_6724 : exactInterval 13 6724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6724 : oddCount 6724 13 = 5 ∧ acceleratedOrbit 13 6724 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6724) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6724.1, data_13_6724.2] + +/-- Complete interval computation for depth 13, residue 6725. -/ +theorem bounds_13_6725 : exactInterval 13 6725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6725 : oddCount 6725 13 = 5 ∧ acceleratedOrbit 13 6725 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6725) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6725.1, data_13_6725.2] + +/-- Complete interval computation for depth 13, residue 6726. -/ +theorem bounds_13_6726 : exactInterval 13 6726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6726 : oddCount 6726 13 = 5 ∧ acceleratedOrbit 13 6726 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6726) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6726.1, data_13_6726.2] + +/-- Complete interval computation for depth 13, residue 6727. -/ +theorem bounds_13_6727 : exactInterval 13 6727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6727 : oddCount 6727 13 = 8 ∧ acceleratedOrbit 13 6727 = 5390 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6727) = 3 ^ 8 * m + 5390 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6727.1, data_13_6727.2] + +/-- Complete interval computation for depth 13, residue 6728. -/ +theorem bounds_13_6728 : exactInterval 13 6728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6728 : oddCount 6728 13 = 5 ∧ acceleratedOrbit 13 6728 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6728) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6728.1, data_13_6728.2] + +/-- Complete interval computation for depth 13, residue 6729. -/ +theorem bounds_13_6729 : exactInterval 13 6729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6729 : oddCount 6729 13 = 6 ∧ acceleratedOrbit 13 6729 = 599 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6729) = 3 ^ 6 * m + 599 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6729.1, data_13_6729.2] + +/-- Complete interval computation for depth 13, residue 6730. -/ +theorem bounds_13_6730 : exactInterval 13 6730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6730 : oddCount 6730 13 = 5 ∧ acceleratedOrbit 13 6730 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6730) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6730.1, data_13_6730.2] + +/-- Complete interval computation for depth 13, residue 6731. -/ +theorem bounds_13_6731 : exactInterval 13 6731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6731 : oddCount 6731 13 = 5 ∧ acceleratedOrbit 13 6731 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6731) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6731.1, data_13_6731.2] + +end Collatz.Research.StoppingAtlas.Batch0905 From 32b646ea212198ada75b49bc713e941b9eeef1d2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:20 +0530 Subject: [PATCH 0906/1001] proof: certify atlas Batch0906 (13:6732 to 13:6747) --- Collatz/Research/StoppingAtlas/Batch0906.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0906.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0906.lean b/Collatz/Research/StoppingAtlas/Batch0906.lean new file mode 100644 index 00000000..3b60610a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0906.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0906 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6732. -/ +theorem bounds_13_6732 : exactInterval 13 6732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6732 : oddCount 6732 13 = 5 ∧ acceleratedOrbit 13 6732 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6732) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6732.1, data_13_6732.2] + +/-- Complete interval computation for depth 13, residue 6733. -/ +theorem bounds_13_6733 : exactInterval 13 6733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6733 : oddCount 6733 13 = 5 ∧ acceleratedOrbit 13 6733 = 200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6733) = 3 ^ 5 * m + 200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6733.1, data_13_6733.2] + +/-- Complete interval computation for depth 13, residue 6734. -/ +theorem bounds_13_6734 : exactInterval 13 6734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6734 : oddCount 6734 13 = 7 ∧ acceleratedOrbit 13 6734 = 1799 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6734) = 3 ^ 7 * m + 1799 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6734.1, data_13_6734.2] + +/-- Complete interval computation for depth 13, residue 6735. -/ +theorem bounds_13_6735 : exactInterval 13 6735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6735 : oddCount 6735 13 = 7 ∧ acceleratedOrbit 13 6735 = 1799 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6735) = 3 ^ 7 * m + 1799 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6735.1, data_13_6735.2] + +/-- Complete interval computation for depth 13, residue 6736. -/ +theorem bounds_13_6736 : exactInterval 13 6736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6736 : oddCount 6736 13 = 5 ∧ acceleratedOrbit 13 6736 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6736) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6736.1, data_13_6736.2] + +/-- Complete interval computation for depth 13, residue 6737. -/ +theorem bounds_13_6737 : exactInterval 13 6737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6737 : oddCount 6737 13 = 9 ∧ acceleratedOrbit 13 6737 = 16199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6737) = 3 ^ 9 * m + 16199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6737.1, data_13_6737.2] + +/-- Complete interval computation for depth 13, residue 6738. -/ +theorem bounds_13_6738 : exactInterval 13 6738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6738 : oddCount 6738 13 = 9 ∧ acceleratedOrbit 13 6738 = 16199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6738) = 3 ^ 9 * m + 16199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6738.1, data_13_6738.2] + +/-- Complete interval computation for depth 13, residue 6739. -/ +theorem bounds_13_6739 : exactInterval 13 6739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6739 : oddCount 6739 13 = 9 ∧ acceleratedOrbit 13 6739 = 16199 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6739) = 3 ^ 9 * m + 16199 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6739.1, data_13_6739.2] + +/-- Complete interval computation for depth 13, residue 6740. -/ +theorem bounds_13_6740 : exactInterval 13 6740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6740 : oddCount 6740 13 = 5 ∧ acceleratedOrbit 13 6740 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6740) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6740.1, data_13_6740.2] + +/-- Complete interval computation for depth 13, residue 6741. -/ +theorem bounds_13_6741 : exactInterval 13 6741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6741 : oddCount 6741 13 = 5 ∧ acceleratedOrbit 13 6741 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6741) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6741.1, data_13_6741.2] + +/-- Complete interval computation for depth 13, residue 6742. -/ +theorem bounds_13_6742 : exactInterval 13 6742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6742 : oddCount 6742 13 = 7 ∧ acceleratedOrbit 13 6742 = 1802 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6742) = 3 ^ 7 * m + 1802 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6742.1, data_13_6742.2] + +/-- Complete interval computation for depth 13, residue 6743. -/ +theorem bounds_13_6743 : exactInterval 13 6743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6743 : oddCount 6743 13 = 7 ∧ acceleratedOrbit 13 6743 = 1802 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6743) = 3 ^ 7 * m + 1802 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6743.1, data_13_6743.2] + +/-- Complete interval computation for depth 13, residue 6744. -/ +theorem bounds_13_6744 : exactInterval 13 6744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6744 : oddCount 6744 13 = 4 ∧ acceleratedOrbit 13 6744 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6744) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6744.1, data_13_6744.2] + +/-- Complete interval computation for depth 13, residue 6745. -/ +theorem bounds_13_6745 : exactInterval 13 6745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6745 : oddCount 6745 13 = 7 ∧ acceleratedOrbit 13 6745 = 1802 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6745) = 3 ^ 7 * m + 1802 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6745.1, data_13_6745.2] + +/-- Complete interval computation for depth 13, residue 6746. -/ +theorem bounds_13_6746 : exactInterval 13 6746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6746 : oddCount 6746 13 = 4 ∧ acceleratedOrbit 13 6746 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6746) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6746.1, data_13_6746.2] + +/-- Complete interval computation for depth 13, residue 6747. -/ +theorem bounds_13_6747 : exactInterval 13 6747 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6747) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6747 : oddCount 6747 13 = 8 ∧ acceleratedOrbit 13 6747 = 5405 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6747) = 3 ^ 8 * m + 5405 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6747.1, data_13_6747.2] + +end Collatz.Research.StoppingAtlas.Batch0906 From a36f8ba817986a69e158cb4f8e1250da30875e5d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:20 +0530 Subject: [PATCH 0907/1001] proof: certify atlas Batch0907 (13:6748 to 13:6762) --- Collatz/Research/StoppingAtlas/Batch0907.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0907.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0907.lean b/Collatz/Research/StoppingAtlas/Batch0907.lean new file mode 100644 index 00000000..2820f94a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0907.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0907 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6748. -/ +theorem bounds_13_6748 : exactInterval 13 6748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6748 : oddCount 6748 13 = 4 ∧ acceleratedOrbit 13 6748 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6748) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6748.1, data_13_6748.2] + +/-- Complete interval computation for depth 13, residue 6749. -/ +theorem bounds_13_6749 : exactInterval 13 6749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6749 : oddCount 6749 13 = 4 ∧ acceleratedOrbit 13 6749 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6749) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6749.1, data_13_6749.2] + +/-- Complete interval computation for depth 13, residue 6750. -/ +theorem bounds_13_6750 : exactInterval 13 6750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6750 : oddCount 6750 13 = 9 ∧ acceleratedOrbit 13 6750 = 16226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6750) = 3 ^ 9 * m + 16226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6750.1, data_13_6750.2] + +/-- Complete interval computation for depth 13, residue 6751. -/ +theorem bounds_13_6751 : exactInterval 13 6751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6751 : oddCount 6751 13 = 9 ∧ acceleratedOrbit 13 6751 = 16226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6751) = 3 ^ 9 * m + 16226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6751.1, data_13_6751.2] + +/-- Complete interval computation for depth 13, residue 6752. -/ +theorem bounds_13_6752 : exactInterval 13 6752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6752 : oddCount 6752 13 = 5 ∧ acceleratedOrbit 13 6752 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6752) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6752.1, data_13_6752.2] + +/-- Complete interval computation for depth 13, residue 6753. -/ +theorem bounds_13_6753 : exactInterval 13 6753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6753 : oddCount 6753 13 = 7 ∧ acceleratedOrbit 13 6753 = 1804 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6753) = 3 ^ 7 * m + 1804 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6753.1, data_13_6753.2] + +/-- Complete interval computation for depth 13, residue 6754. -/ +theorem bounds_13_6754 : exactInterval 13 6754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6754 : oddCount 6754 13 = 7 ∧ acceleratedOrbit 13 6754 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6754) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6754.1, data_13_6754.2] + +/-- Complete interval computation for depth 13, residue 6755. -/ +theorem bounds_13_6755 : exactInterval 13 6755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6755 : oddCount 6755 13 = 7 ∧ acceleratedOrbit 13 6755 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6755) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6755.1, data_13_6755.2] + +/-- Complete interval computation for depth 13, residue 6756. -/ +theorem bounds_13_6756 : exactInterval 13 6756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6756 : oddCount 6756 13 = 7 ∧ acceleratedOrbit 13 6756 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6756) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6756.1, data_13_6756.2] + +/-- Complete interval computation for depth 13, residue 6757. -/ +theorem bounds_13_6757 : exactInterval 13 6757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6757 : oddCount 6757 13 = 7 ∧ acceleratedOrbit 13 6757 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6757) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6757.1, data_13_6757.2] + +/-- Complete interval computation for depth 13, residue 6758. -/ +theorem bounds_13_6758 : exactInterval 13 6758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6758 : oddCount 6758 13 = 7 ∧ acceleratedOrbit 13 6758 = 1808 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6758) = 3 ^ 7 * m + 1808 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6758.1, data_13_6758.2] + +/-- Complete interval computation for depth 13, residue 6759. -/ +theorem bounds_13_6759 : exactInterval 13 6759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6759 : oddCount 6759 13 = 9 ∧ acceleratedOrbit 13 6759 = 16244 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6759) = 3 ^ 9 * m + 16244 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6759.1, data_13_6759.2] + +/-- Complete interval computation for depth 13, residue 6760. -/ +theorem bounds_13_6760 : exactInterval 13 6760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6760 : oddCount 6760 13 = 5 ∧ acceleratedOrbit 13 6760 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6760) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6760.1, data_13_6760.2] + +/-- Complete interval computation for depth 13, residue 6761. -/ +theorem bounds_13_6761 : exactInterval 13 6761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6761 : oddCount 6761 13 = 8 ∧ acceleratedOrbit 13 6761 = 5417 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6761) = 3 ^ 8 * m + 5417 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6761.1, data_13_6761.2] + +/-- Complete interval computation for depth 13, residue 6762. -/ +theorem bounds_13_6762 : exactInterval 13 6762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6762 : oddCount 6762 13 = 5 ∧ acceleratedOrbit 13 6762 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6762) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6762.1, data_13_6762.2] + +end Collatz.Research.StoppingAtlas.Batch0907 From 2def37fc5dd7604ffe74dcfaf0cdc4d89d82067f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:20 +0530 Subject: [PATCH 0908/1001] proof: certify atlas Batch0908 (13:6763 to 13:6777) --- Collatz/Research/StoppingAtlas/Batch0908.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0908.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0908.lean b/Collatz/Research/StoppingAtlas/Batch0908.lean new file mode 100644 index 00000000..8ebb3c9e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0908.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0908 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6763. -/ +theorem bounds_13_6763 : exactInterval 13 6763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6763 : oddCount 6763 13 = 6 ∧ acceleratedOrbit 13 6763 = 602 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6763) = 3 ^ 6 * m + 602 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6763.1, data_13_6763.2] + +/-- Complete interval computation for depth 13, residue 6764. -/ +theorem bounds_13_6764 : exactInterval 13 6764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6764 : oddCount 6764 13 = 8 ∧ acceleratedOrbit 13 6764 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6764) = 3 ^ 8 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6764.1, data_13_6764.2] + +/-- Complete interval computation for depth 13, residue 6765. -/ +theorem bounds_13_6765 : exactInterval 13 6765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6765 : oddCount 6765 13 = 8 ∧ acceleratedOrbit 13 6765 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6765) = 3 ^ 8 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6765.1, data_13_6765.2] + +/-- Complete interval computation for depth 13, residue 6766. -/ +theorem bounds_13_6766 : exactInterval 13 6766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6766 : oddCount 6766 13 = 8 ∧ acceleratedOrbit 13 6766 = 5422 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6766) = 3 ^ 8 * m + 5422 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6766.1, data_13_6766.2] + +/-- Complete interval computation for depth 13, residue 6767. -/ +theorem bounds_13_6767 : exactInterval 13 6767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6767 : oddCount 6767 13 = 10 ∧ acceleratedOrbit 13 6767 = 48788 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6767) = 3 ^ 10 * m + 48788 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6767.1, data_13_6767.2] + +/-- Complete interval computation for depth 13, residue 6768. -/ +theorem bounds_13_6768 : exactInterval 13 6768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6768 : oddCount 6768 13 = 6 ∧ acceleratedOrbit 13 6768 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6768) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6768.1, data_13_6768.2] + +/-- Complete interval computation for depth 13, residue 6769. -/ +theorem bounds_13_6769 : exactInterval 13 6769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6769 : oddCount 6769 13 = 5 ∧ acceleratedOrbit 13 6769 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6769) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6769.1, data_13_6769.2] + +/-- Complete interval computation for depth 13, residue 6770. -/ +theorem bounds_13_6770 : exactInterval 13 6770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6770 : oddCount 6770 13 = 9 ∧ acceleratedOrbit 13 6770 = 16280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6770) = 3 ^ 9 * m + 16280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6770.1, data_13_6770.2] + +/-- Complete interval computation for depth 13, residue 6771. -/ +theorem bounds_13_6771 : exactInterval 13 6771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6771 : oddCount 6771 13 = 9 ∧ acceleratedOrbit 13 6771 = 16280 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6771) = 3 ^ 9 * m + 16280 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6771.1, data_13_6771.2] + +/-- Complete interval computation for depth 13, residue 6772. -/ +theorem bounds_13_6772 : exactInterval 13 6772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6772 : oddCount 6772 13 = 6 ∧ acceleratedOrbit 13 6772 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6772) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6772.1, data_13_6772.2] + +/-- Complete interval computation for depth 13, residue 6773. -/ +theorem bounds_13_6773 : exactInterval 13 6773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6773 : oddCount 6773 13 = 6 ∧ acceleratedOrbit 13 6773 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6773) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6773.1, data_13_6773.2] + +/-- Complete interval computation for depth 13, residue 6774. -/ +theorem bounds_13_6774 : exactInterval 13 6774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6774 : oddCount 6774 13 = 4 ∧ acceleratedOrbit 13 6774 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6774) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6774.1, data_13_6774.2] + +/-- Complete interval computation for depth 13, residue 6775. -/ +theorem bounds_13_6775 : exactInterval 13 6775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6775 : oddCount 6775 13 = 4 ∧ acceleratedOrbit 13 6775 = 67 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6775) = 3 ^ 4 * m + 67 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6775.1, data_13_6775.2] + +/-- Complete interval computation for depth 13, residue 6776. -/ +theorem bounds_13_6776 : exactInterval 13 6776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6776 : oddCount 6776 13 = 6 ∧ acceleratedOrbit 13 6776 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6776) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6776.1, data_13_6776.2] + +/-- Complete interval computation for depth 13, residue 6777. -/ +theorem bounds_13_6777 : exactInterval 13 6777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6777 : oddCount 6777 13 = 7 ∧ acceleratedOrbit 13 6777 = 1810 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6777) = 3 ^ 7 * m + 1810 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6777.1, data_13_6777.2] + +end Collatz.Research.StoppingAtlas.Batch0908 From c1244e9eee10f067ff14e3cd89eb121dfad3ac22 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:20 +0530 Subject: [PATCH 0909/1001] proof: certify atlas Batch0909 (13:6778 to 13:6793) --- Collatz/Research/StoppingAtlas/Batch0909.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0909.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0909.lean b/Collatz/Research/StoppingAtlas/Batch0909.lean new file mode 100644 index 00000000..0129a1b1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0909.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0909 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6778. -/ +theorem bounds_13_6778 : exactInterval 13 6778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6778 : oddCount 6778 13 = 6 ∧ acceleratedOrbit 13 6778 = 604 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6778) = 3 ^ 6 * m + 604 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6778.1, data_13_6778.2] + +/-- Complete interval computation for depth 13, residue 6779. -/ +theorem bounds_13_6779 : exactInterval 13 6779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6779 : oddCount 6779 13 = 7 ∧ acceleratedOrbit 13 6779 = 1811 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6779) = 3 ^ 7 * m + 1811 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6779.1, data_13_6779.2] + +/-- Complete interval computation for depth 13, residue 6780. -/ +theorem bounds_13_6780 : exactInterval 13 6780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6780 : oddCount 6780 13 = 9 ∧ acceleratedOrbit 13 6780 = 16301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6780) = 3 ^ 9 * m + 16301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6780.1, data_13_6780.2] + +/-- Complete interval computation for depth 13, residue 6781. -/ +theorem bounds_13_6781 : exactInterval 13 6781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6781 : oddCount 6781 13 = 9 ∧ acceleratedOrbit 13 6781 = 16301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6781) = 3 ^ 9 * m + 16301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6781.1, data_13_6781.2] + +/-- Complete interval computation for depth 13, residue 6782. -/ +theorem bounds_13_6782 : exactInterval 13 6782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6782 : oddCount 6782 13 = 9 ∧ acceleratedOrbit 13 6782 = 16301 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6782) = 3 ^ 9 * m + 16301 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6782.1, data_13_6782.2] + +/-- Complete interval computation for depth 13, residue 6783. -/ +theorem bounds_13_6783 : exactInterval 13 6783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6783 : oddCount 6783 13 = 9 ∧ acceleratedOrbit 13 6783 = 16300 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6783) = 3 ^ 9 * m + 16300 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6783.1, data_13_6783.2] + +/-- Complete interval computation for depth 13, residue 6784. -/ +theorem bounds_13_6784 : exactInterval 13 6784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6784 : oddCount 6784 13 = 2 ∧ acceleratedOrbit 13 6784 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6784) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6784.1, data_13_6784.2] + +/-- Complete interval computation for depth 13, residue 6785. -/ +theorem bounds_13_6785 : exactInterval 13 6785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6785 : oddCount 6785 13 = 8 ∧ acceleratedOrbit 13 6785 = 5437 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6785) = 3 ^ 8 * m + 5437 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6785.1, data_13_6785.2] + +/-- Complete interval computation for depth 13, residue 6786. -/ +theorem bounds_13_6786 : exactInterval 13 6786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6786 : oddCount 6786 13 = 5 ∧ acceleratedOrbit 13 6786 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6786) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6786.1, data_13_6786.2] + +/-- Complete interval computation for depth 13, residue 6787. -/ +theorem bounds_13_6787 : exactInterval 13 6787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6787 : oddCount 6787 13 = 5 ∧ acceleratedOrbit 13 6787 = 202 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6787) = 3 ^ 5 * m + 202 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6787.1, data_13_6787.2] + +/-- Complete interval computation for depth 13, residue 6788. -/ +theorem bounds_13_6788 : exactInterval 13 6788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6788 : oddCount 6788 13 = 6 ∧ acceleratedOrbit 13 6788 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6788) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6788.1, data_13_6788.2] + +/-- Complete interval computation for depth 13, residue 6789. -/ +theorem bounds_13_6789 : exactInterval 13 6789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6789 : oddCount 6789 13 = 6 ∧ acceleratedOrbit 13 6789 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6789) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6789.1, data_13_6789.2] + +/-- Complete interval computation for depth 13, residue 6790. -/ +theorem bounds_13_6790 : exactInterval 13 6790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6790 : oddCount 6790 13 = 6 ∧ acceleratedOrbit 13 6790 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6790) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6790.1, data_13_6790.2] + +/-- Complete interval computation for depth 13, residue 6791. -/ +theorem bounds_13_6791 : exactInterval 13 6791 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6791) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6791 : oddCount 6791 13 = 6 ∧ acceleratedOrbit 13 6791 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6791) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6791.1, data_13_6791.2] + +/-- Complete interval computation for depth 13, residue 6792. -/ +theorem bounds_13_6792 : exactInterval 13 6792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6792 : oddCount 6792 13 = 6 ∧ acceleratedOrbit 13 6792 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6792) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6792.1, data_13_6792.2] + +/-- Complete interval computation for depth 13, residue 6793. -/ +theorem bounds_13_6793 : exactInterval 13 6793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6793 : oddCount 6793 13 = 7 ∧ acceleratedOrbit 13 6793 = 1814 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6793) = 3 ^ 7 * m + 1814 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6793.1, data_13_6793.2] + +end Collatz.Research.StoppingAtlas.Batch0909 From 919b0d94c638fc225caf2a270c1493359241605a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:21 +0530 Subject: [PATCH 0910/1001] proof: certify atlas Batch0910 (13:6794 to 13:6808) --- Collatz/Research/StoppingAtlas/Batch0910.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0910.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0910.lean b/Collatz/Research/StoppingAtlas/Batch0910.lean new file mode 100644 index 00000000..312cb701 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0910.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0910 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6794. -/ +theorem bounds_13_6794 : exactInterval 13 6794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6794 : oddCount 6794 13 = 6 ∧ acceleratedOrbit 13 6794 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6794) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6794.1, data_13_6794.2] + +/-- Complete interval computation for depth 13, residue 6795. -/ +theorem bounds_13_6795 : exactInterval 13 6795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6795 : oddCount 6795 13 = 6 ∧ acceleratedOrbit 13 6795 = 605 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6795) = 3 ^ 6 * m + 605 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6795.1, data_13_6795.2] + +/-- Complete interval computation for depth 13, residue 6796. -/ +theorem bounds_13_6796 : exactInterval 13 6796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6796 : oddCount 6796 13 = 6 ∧ acceleratedOrbit 13 6796 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6796) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6796.1, data_13_6796.2] + +/-- Complete interval computation for depth 13, residue 6797. -/ +theorem bounds_13_6797 : exactInterval 13 6797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6797 : oddCount 6797 13 = 6 ∧ acceleratedOrbit 13 6797 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6797) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6797.1, data_13_6797.2] + +/-- Complete interval computation for depth 13, residue 6798. -/ +theorem bounds_13_6798 : exactInterval 13 6798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6798 : oddCount 6798 13 = 8 ∧ acceleratedOrbit 13 6798 = 5447 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6798) = 3 ^ 8 * m + 5447 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6798.1, data_13_6798.2] + +/-- Complete interval computation for depth 13, residue 6799. -/ +theorem bounds_13_6799 : exactInterval 13 6799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6799 : oddCount 6799 13 = 8 ∧ acceleratedOrbit 13 6799 = 5447 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6799) = 3 ^ 8 * m + 5447 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6799.1, data_13_6799.2] + +/-- Complete interval computation for depth 13, residue 6800. -/ +theorem bounds_13_6800 : exactInterval 13 6800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6800 : oddCount 6800 13 = 7 ∧ acceleratedOrbit 13 6800 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6800) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6800.1, data_13_6800.2] + +/-- Complete interval computation for depth 13, residue 6801. -/ +theorem bounds_13_6801 : exactInterval 13 6801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6801 : oddCount 6801 13 = 8 ∧ acceleratedOrbit 13 6801 = 5453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6801) = 3 ^ 8 * m + 5453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6801.1, data_13_6801.2] + +/-- Complete interval computation for depth 13, residue 6802. -/ +theorem bounds_13_6802 : exactInterval 13 6802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6802 : oddCount 6802 13 = 8 ∧ acceleratedOrbit 13 6802 = 5453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6802) = 3 ^ 8 * m + 5453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6802.1, data_13_6802.2] + +/-- Complete interval computation for depth 13, residue 6803. -/ +theorem bounds_13_6803 : exactInterval 13 6803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6803 : oddCount 6803 13 = 8 ∧ acceleratedOrbit 13 6803 = 5453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6803) = 3 ^ 8 * m + 5453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6803.1, data_13_6803.2] + +/-- Complete interval computation for depth 13, residue 6804. -/ +theorem bounds_13_6804 : exactInterval 13 6804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6804 : oddCount 6804 13 = 7 ∧ acceleratedOrbit 13 6804 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6804) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6804.1, data_13_6804.2] + +/-- Complete interval computation for depth 13, residue 6805. -/ +theorem bounds_13_6805 : exactInterval 13 6805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6805 : oddCount 6805 13 = 7 ∧ acceleratedOrbit 13 6805 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6805) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6805.1, data_13_6805.2] + +/-- Complete interval computation for depth 13, residue 6806. -/ +theorem bounds_13_6806 : exactInterval 13 6806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6806 : oddCount 6806 13 = 6 ∧ acceleratedOrbit 13 6806 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6806) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6806.1, data_13_6806.2] + +/-- Complete interval computation for depth 13, residue 6807. -/ +theorem bounds_13_6807 : exactInterval 13 6807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6807 : oddCount 6807 13 = 6 ∧ acceleratedOrbit 13 6807 = 607 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6807) = 3 ^ 6 * m + 607 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6807.1, data_13_6807.2] + +/-- Complete interval computation for depth 13, residue 6808. -/ +theorem bounds_13_6808 : exactInterval 13 6808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6808 : oddCount 6808 13 = 7 ∧ acceleratedOrbit 13 6808 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6808) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6808.1, data_13_6808.2] + +end Collatz.Research.StoppingAtlas.Batch0910 From 2116cfed51db5d651205e9e6932bacc4b648591e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:21 +0530 Subject: [PATCH 0911/1001] proof: certify atlas Batch0911 (13:6809 to 13:6823) --- Collatz/Research/StoppingAtlas/Batch0911.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0911.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0911.lean b/Collatz/Research/StoppingAtlas/Batch0911.lean new file mode 100644 index 00000000..9fa6ddb8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0911.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0911 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6809. -/ +theorem bounds_13_6809 : exactInterval 13 6809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6809 : oddCount 6809 13 = 7 ∧ acceleratedOrbit 13 6809 = 1819 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6809) = 3 ^ 7 * m + 1819 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6809.1, data_13_6809.2] + +/-- Complete interval computation for depth 13, residue 6810. -/ +theorem bounds_13_6810 : exactInterval 13 6810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6810 : oddCount 6810 13 = 7 ∧ acceleratedOrbit 13 6810 = 1822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6810) = 3 ^ 7 * m + 1822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6810.1, data_13_6810.2] + +/-- Complete interval computation for depth 13, residue 6811. -/ +theorem bounds_13_6811 : exactInterval 13 6811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6811 : oddCount 6811 13 = 10 ∧ acceleratedOrbit 13 6811 = 49106 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6811) = 3 ^ 10 * m + 49106 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6811.1, data_13_6811.2] + +/-- Complete interval computation for depth 13, residue 6812. -/ +theorem bounds_13_6812 : exactInterval 13 6812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6812 : oddCount 6812 13 = 7 ∧ acceleratedOrbit 13 6812 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6812) = 3 ^ 7 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6812.1, data_13_6812.2] + +/-- Complete interval computation for depth 13, residue 6813. -/ +theorem bounds_13_6813 : exactInterval 13 6813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6813 : oddCount 6813 13 = 7 ∧ acceleratedOrbit 13 6813 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6813) = 3 ^ 7 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6813.1, data_13_6813.2] + +/-- Complete interval computation for depth 13, residue 6814. -/ +theorem bounds_13_6814 : exactInterval 13 6814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6814 : oddCount 6814 13 = 7 ∧ acceleratedOrbit 13 6814 = 1820 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6814) = 3 ^ 7 * m + 1820 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6814.1, data_13_6814.2] + +/-- Complete interval computation for depth 13, residue 6815. -/ +theorem bounds_13_6815 : exactInterval 13 6815 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6815) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6815 : oddCount 6815 13 = 8 ∧ acceleratedOrbit 13 6815 = 5459 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6815) = 3 ^ 8 * m + 5459 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6815.1, data_13_6815.2] + +/-- Complete interval computation for depth 13, residue 6816. -/ +theorem bounds_13_6816 : exactInterval 13 6816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6816 : oddCount 6816 13 = 2 ∧ acceleratedOrbit 13 6816 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6816) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6816.1, data_13_6816.2] + +/-- Complete interval computation for depth 13, residue 6817. -/ +theorem bounds_13_6817 : exactInterval 13 6817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6817 : oddCount 6817 13 = 9 ∧ acceleratedOrbit 13 6817 = 16388 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6817) = 3 ^ 9 * m + 16388 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6817.1, data_13_6817.2] + +/-- Complete interval computation for depth 13, residue 6818. -/ +theorem bounds_13_6818 : exactInterval 13 6818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6818 : oddCount 6818 13 = 8 ∧ acceleratedOrbit 13 6818 = 5467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6818) = 3 ^ 8 * m + 5467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6818.1, data_13_6818.2] + +/-- Complete interval computation for depth 13, residue 6819. -/ +theorem bounds_13_6819 : exactInterval 13 6819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6819 : oddCount 6819 13 = 8 ∧ acceleratedOrbit 13 6819 = 5467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6819) = 3 ^ 8 * m + 5467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6819.1, data_13_6819.2] + +/-- Complete interval computation for depth 13, residue 6820. -/ +theorem bounds_13_6820 : exactInterval 13 6820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6820 : oddCount 6820 13 = 9 ∧ acceleratedOrbit 13 6820 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6820) = 3 ^ 9 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6820.1, data_13_6820.2] + +/-- Complete interval computation for depth 13, residue 6821. -/ +theorem bounds_13_6821 : exactInterval 13 6821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6821 : oddCount 6821 13 = 9 ∧ acceleratedOrbit 13 6821 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6821) = 3 ^ 9 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6821.1, data_13_6821.2] + +/-- Complete interval computation for depth 13, residue 6822. -/ +theorem bounds_13_6822 : exactInterval 13 6822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6822 : oddCount 6822 13 = 9 ∧ acceleratedOrbit 13 6822 = 16402 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6822) = 3 ^ 9 * m + 16402 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6822.1, data_13_6822.2] + +/-- Complete interval computation for depth 13, residue 6823. -/ +theorem bounds_13_6823 : exactInterval 13 6823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6823 : oddCount 6823 13 = 10 ∧ acceleratedOrbit 13 6823 = 49193 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6823) = 3 ^ 10 * m + 49193 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6823.1, data_13_6823.2] + +end Collatz.Research.StoppingAtlas.Batch0911 From 5542c47f76551396db01dd0620019d028318fd1d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:21 +0530 Subject: [PATCH 0912/1001] proof: certify atlas Batch0912 (13:6824 to 13:6839) --- Collatz/Research/StoppingAtlas/Batch0912.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0912.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0912.lean b/Collatz/Research/StoppingAtlas/Batch0912.lean new file mode 100644 index 00000000..45a48ea2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0912.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0912 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6824. -/ +theorem bounds_13_6824 : exactInterval 13 6824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6824 : oddCount 6824 13 = 2 ∧ acceleratedOrbit 13 6824 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6824) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6824.1, data_13_6824.2] + +/-- Complete interval computation for depth 13, residue 6825. -/ +theorem bounds_13_6825 : exactInterval 13 6825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6825 : oddCount 6825 13 = 11 ∧ acceleratedOrbit 13 6825 = 147622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6825) = 3 ^ 11 * m + 147622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6825.1, data_13_6825.2] + +/-- Complete interval computation for depth 13, residue 6826. -/ +theorem bounds_13_6826 : exactInterval 13 6826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6826 : oddCount 6826 13 = 2 ∧ acceleratedOrbit 13 6826 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6826) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6826.1, data_13_6826.2] + +/-- Complete interval computation for depth 13, residue 6827. -/ +theorem bounds_13_6827 : exactInterval 13 6827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6827 : oddCount 6827 13 = 8 ∧ acceleratedOrbit 13 6827 = 5471 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6827) = 3 ^ 8 * m + 5471 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6827.1, data_13_6827.2] + +/-- Complete interval computation for depth 13, residue 6828. -/ +theorem bounds_13_6828 : exactInterval 13 6828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6828 : oddCount 6828 13 = 7 ∧ acceleratedOrbit 13 6828 = 1826 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6828) = 3 ^ 7 * m + 1826 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6828.1, data_13_6828.2] + +/-- Complete interval computation for depth 13, residue 6829. -/ +theorem bounds_13_6829 : exactInterval 13 6829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6829 : oddCount 6829 13 = 7 ∧ acceleratedOrbit 13 6829 = 1826 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6829) = 3 ^ 7 * m + 1826 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6829.1, data_13_6829.2] + +/-- Complete interval computation for depth 13, residue 6830. -/ +theorem bounds_13_6830 : exactInterval 13 6830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6830 : oddCount 6830 13 = 7 ∧ acceleratedOrbit 13 6830 = 1826 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6830) = 3 ^ 7 * m + 1826 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6830.1, data_13_6830.2] + +/-- Complete interval computation for depth 13, residue 6831. -/ +theorem bounds_13_6831 : exactInterval 13 6831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6831 : oddCount 6831 13 = 6 ∧ acceleratedOrbit 13 6831 = 608 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6831) = 3 ^ 6 * m + 608 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6831.1, data_13_6831.2] + +/-- Complete interval computation for depth 13, residue 6832. -/ +theorem bounds_13_6832 : exactInterval 13 6832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6832 : oddCount 6832 13 = 6 ∧ acceleratedOrbit 13 6832 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6832) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6832.1, data_13_6832.2] + +/-- Complete interval computation for depth 13, residue 6833. -/ +theorem bounds_13_6833 : exactInterval 13 6833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6833 : oddCount 6833 13 = 5 ∧ acceleratedOrbit 13 6833 = 203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6833) = 3 ^ 5 * m + 203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6833.1, data_13_6833.2] + +/-- Complete interval computation for depth 13, residue 6834. -/ +theorem bounds_13_6834 : exactInterval 13 6834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6834 : oddCount 6834 13 = 5 ∧ acceleratedOrbit 13 6834 = 203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6834) = 3 ^ 5 * m + 203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6834.1, data_13_6834.2] + +/-- Complete interval computation for depth 13, residue 6835. -/ +theorem bounds_13_6835 : exactInterval 13 6835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6835 : oddCount 6835 13 = 5 ∧ acceleratedOrbit 13 6835 = 203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6835) = 3 ^ 5 * m + 203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6835.1, data_13_6835.2] + +/-- Complete interval computation for depth 13, residue 6836. -/ +theorem bounds_13_6836 : exactInterval 13 6836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6836 : oddCount 6836 13 = 6 ∧ acceleratedOrbit 13 6836 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6836) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6836.1, data_13_6836.2] + +/-- Complete interval computation for depth 13, residue 6837. -/ +theorem bounds_13_6837 : exactInterval 13 6837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6837 : oddCount 6837 13 = 6 ∧ acceleratedOrbit 13 6837 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6837) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6837.1, data_13_6837.2] + +/-- Complete interval computation for depth 13, residue 6838. -/ +theorem bounds_13_6838 : exactInterval 13 6838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6838 : oddCount 6838 13 = 8 ∧ acceleratedOrbit 13 6838 = 5480 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6838) = 3 ^ 8 * m + 5480 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6838.1, data_13_6838.2] + +/-- Complete interval computation for depth 13, residue 6839. -/ +theorem bounds_13_6839 : exactInterval 13 6839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6839 : oddCount 6839 13 = 8 ∧ acceleratedOrbit 13 6839 = 5480 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6839) = 3 ^ 8 * m + 5480 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6839.1, data_13_6839.2] + +end Collatz.Research.StoppingAtlas.Batch0912 From 4e49804bd23594b93b9da4fa93f2ce039485e405 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:21 +0530 Subject: [PATCH 0913/1001] proof: certify atlas Batch0913 (13:6840 to 13:6854) --- Collatz/Research/StoppingAtlas/Batch0913.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0913.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0913.lean b/Collatz/Research/StoppingAtlas/Batch0913.lean new file mode 100644 index 00000000..eda7fcfb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0913.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0913 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6840. -/ +theorem bounds_13_6840 : exactInterval 13 6840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6840 : oddCount 6840 13 = 6 ∧ acceleratedOrbit 13 6840 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6840) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6840.1, data_13_6840.2] + +/-- Complete interval computation for depth 13, residue 6841. -/ +theorem bounds_13_6841 : exactInterval 13 6841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6841 : oddCount 6841 13 = 5 ∧ acceleratedOrbit 13 6841 = 203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6841) = 3 ^ 5 * m + 203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6841.1, data_13_6841.2] + +/-- Complete interval computation for depth 13, residue 6842. -/ +theorem bounds_13_6842 : exactInterval 13 6842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6842 : oddCount 6842 13 = 6 ∧ acceleratedOrbit 13 6842 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6842) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6842.1, data_13_6842.2] + +/-- Complete interval computation for depth 13, residue 6843. -/ +theorem bounds_13_6843 : exactInterval 13 6843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6843 : oddCount 6843 13 = 8 ∧ acceleratedOrbit 13 6843 = 5483 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6843) = 3 ^ 8 * m + 5483 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6843.1, data_13_6843.2] + +/-- Complete interval computation for depth 13, residue 6844. -/ +theorem bounds_13_6844 : exactInterval 13 6844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6844 : oddCount 6844 13 = 7 ∧ acceleratedOrbit 13 6844 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6844) = 3 ^ 7 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6844.1, data_13_6844.2] + +/-- Complete interval computation for depth 13, residue 6845. -/ +theorem bounds_13_6845 : exactInterval 13 6845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6845 : oddCount 6845 13 = 7 ∧ acceleratedOrbit 13 6845 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6845) = 3 ^ 7 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6845.1, data_13_6845.2] + +/-- Complete interval computation for depth 13, residue 6846. -/ +theorem bounds_13_6846 : exactInterval 13 6846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6846 : oddCount 6846 13 = 7 ∧ acceleratedOrbit 13 6846 = 1829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6846) = 3 ^ 7 * m + 1829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6846.1, data_13_6846.2] + +/-- Complete interval computation for depth 13, residue 6847. -/ +theorem bounds_13_6847 : exactInterval 13 6847 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6847) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6847 : oddCount 6847 13 = 9 ∧ acceleratedOrbit 13 6847 = 16454 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6847) = 3 ^ 9 * m + 16454 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6847.1, data_13_6847.2] + +/-- Complete interval computation for depth 13, residue 6848. -/ +theorem bounds_13_6848 : exactInterval 13 6848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6848 : oddCount 6848 13 = 5 ∧ acceleratedOrbit 13 6848 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6848) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6848.1, data_13_6848.2] + +/-- Complete interval computation for depth 13, residue 6849. -/ +theorem bounds_13_6849 : exactInterval 13 6849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6849 : oddCount 6849 13 = 6 ∧ acceleratedOrbit 13 6849 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6849) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6849.1, data_13_6849.2] + +/-- Complete interval computation for depth 13, residue 6850. -/ +theorem bounds_13_6850 : exactInterval 13 6850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6850 : oddCount 6850 13 = 6 ∧ acceleratedOrbit 13 6850 = 610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6850) = 3 ^ 6 * m + 610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6850.1, data_13_6850.2] + +/-- Complete interval computation for depth 13, residue 6851. -/ +theorem bounds_13_6851 : exactInterval 13 6851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6851 : oddCount 6851 13 = 6 ∧ acceleratedOrbit 13 6851 = 610 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6851) = 3 ^ 6 * m + 610 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6851.1, data_13_6851.2] + +/-- Complete interval computation for depth 13, residue 6852. -/ +theorem bounds_13_6852 : exactInterval 13 6852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6852 : oddCount 6852 13 = 4 ∧ acceleratedOrbit 13 6852 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6852) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6852.1, data_13_6852.2] + +/-- Complete interval computation for depth 13, residue 6853. -/ +theorem bounds_13_6853 : exactInterval 13 6853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6853 : oddCount 6853 13 = 4 ∧ acceleratedOrbit 13 6853 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6853) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6853.1, data_13_6853.2] + +/-- Complete interval computation for depth 13, residue 6854. -/ +theorem bounds_13_6854 : exactInterval 13 6854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6854 : oddCount 6854 13 = 4 ∧ acceleratedOrbit 13 6854 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6854) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6854.1, data_13_6854.2] + +end Collatz.Research.StoppingAtlas.Batch0913 From 6fe6c996d337ebfda8d406347f1efe728f9ead10 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:22 +0530 Subject: [PATCH 0914/1001] proof: certify atlas Batch0914 (13:6855 to 13:6870) --- Collatz/Research/StoppingAtlas/Batch0914.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0914.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0914.lean b/Collatz/Research/StoppingAtlas/Batch0914.lean new file mode 100644 index 00000000..f7490fc2 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0914.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0914 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6855. -/ +theorem bounds_13_6855 : exactInterval 13 6855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6855 : oddCount 6855 13 = 7 ∧ acceleratedOrbit 13 6855 = 1831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6855) = 3 ^ 7 * m + 1831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6855.1, data_13_6855.2] + +/-- Complete interval computation for depth 13, residue 6856. -/ +theorem bounds_13_6856 : exactInterval 13 6856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6856 : oddCount 6856 13 = 4 ∧ acceleratedOrbit 13 6856 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6856) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6856.1, data_13_6856.2] + +/-- Complete interval computation for depth 13, residue 6857. -/ +theorem bounds_13_6857 : exactInterval 13 6857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6857 : oddCount 6857 13 = 6 ∧ acceleratedOrbit 13 6857 = 611 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6857) = 3 ^ 6 * m + 611 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6857.1, data_13_6857.2] + +/-- Complete interval computation for depth 13, residue 6858. -/ +theorem bounds_13_6858 : exactInterval 13 6858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6858 : oddCount 6858 13 = 4 ∧ acceleratedOrbit 13 6858 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6858) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6858.1, data_13_6858.2] + +/-- Complete interval computation for depth 13, residue 6859. -/ +theorem bounds_13_6859 : exactInterval 13 6859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6859 : oddCount 6859 13 = 8 ∧ acceleratedOrbit 13 6859 = 5498 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6859) = 3 ^ 8 * m + 5498 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6859.1, data_13_6859.2] + +/-- Complete interval computation for depth 13, residue 6860. -/ +theorem bounds_13_6860 : exactInterval 13 6860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6860 : oddCount 6860 13 = 4 ∧ acceleratedOrbit 13 6860 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6860) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6860.1, data_13_6860.2] + +/-- Complete interval computation for depth 13, residue 6861. -/ +theorem bounds_13_6861 : exactInterval 13 6861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6861 : oddCount 6861 13 = 4 ∧ acceleratedOrbit 13 6861 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6861) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6861.1, data_13_6861.2] + +/-- Complete interval computation for depth 13, residue 6862. -/ +theorem bounds_13_6862 : exactInterval 13 6862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6862 : oddCount 6862 13 = 10 ∧ acceleratedOrbit 13 6862 = 49481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6862) = 3 ^ 10 * m + 49481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6862.1, data_13_6862.2] + +/-- Complete interval computation for depth 13, residue 6863. -/ +theorem bounds_13_6863 : exactInterval 13 6863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6863 : oddCount 6863 13 = 10 ∧ acceleratedOrbit 13 6863 = 49481 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6863) = 3 ^ 10 * m + 49481 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6863.1, data_13_6863.2] + +/-- Complete interval computation for depth 13, residue 6864. -/ +theorem bounds_13_6864 : exactInterval 13 6864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6864 : oddCount 6864 13 = 5 ∧ acceleratedOrbit 13 6864 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6864) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6864.1, data_13_6864.2] + +/-- Complete interval computation for depth 13, residue 6865. -/ +theorem bounds_13_6865 : exactInterval 13 6865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6865 : oddCount 6865 13 = 7 ∧ acceleratedOrbit 13 6865 = 1835 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6865) = 3 ^ 7 * m + 1835 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6865.1, data_13_6865.2] + +/-- Complete interval computation for depth 13, residue 6866. -/ +theorem bounds_13_6866 : exactInterval 13 6866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6866 : oddCount 6866 13 = 7 ∧ acceleratedOrbit 13 6866 = 1835 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6866) = 3 ^ 7 * m + 1835 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6866.1, data_13_6866.2] + +/-- Complete interval computation for depth 13, residue 6867. -/ +theorem bounds_13_6867 : exactInterval 13 6867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6867 : oddCount 6867 13 = 7 ∧ acceleratedOrbit 13 6867 = 1835 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6867) = 3 ^ 7 * m + 1835 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6867.1, data_13_6867.2] + +/-- Complete interval computation for depth 13, residue 6868. -/ +theorem bounds_13_6868 : exactInterval 13 6868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6868 : oddCount 6868 13 = 5 ∧ acceleratedOrbit 13 6868 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6868) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6868.1, data_13_6868.2] + +/-- Complete interval computation for depth 13, residue 6869. -/ +theorem bounds_13_6869 : exactInterval 13 6869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6869 : oddCount 6869 13 = 5 ∧ acceleratedOrbit 13 6869 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6869) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6869.1, data_13_6869.2] + +/-- Complete interval computation for depth 13, residue 6870. -/ +theorem bounds_13_6870 : exactInterval 13 6870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6870 : oddCount 6870 13 = 8 ∧ acceleratedOrbit 13 6870 = 5507 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6870) = 3 ^ 8 * m + 5507 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6870.1, data_13_6870.2] + +end Collatz.Research.StoppingAtlas.Batch0914 From 8bc61ef106f7e3f827d92f1d7d0c7916ac656ea8 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:22 +0530 Subject: [PATCH 0915/1001] proof: certify atlas Batch0915 (13:6871 to 13:6885) --- Collatz/Research/StoppingAtlas/Batch0915.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0915.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0915.lean b/Collatz/Research/StoppingAtlas/Batch0915.lean new file mode 100644 index 00000000..b1d11d7f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0915.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0915 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6871. -/ +theorem bounds_13_6871 : exactInterval 13 6871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6871 : oddCount 6871 13 = 8 ∧ acceleratedOrbit 13 6871 = 5507 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6871) = 3 ^ 8 * m + 5507 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6871.1, data_13_6871.2] + +/-- Complete interval computation for depth 13, residue 6872. -/ +theorem bounds_13_6872 : exactInterval 13 6872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6872 : oddCount 6872 13 = 7 ∧ acceleratedOrbit 13 6872 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6872) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6872.1, data_13_6872.2] + +/-- Complete interval computation for depth 13, residue 6873. -/ +theorem bounds_13_6873 : exactInterval 13 6873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6873 : oddCount 6873 13 = 4 ∧ acceleratedOrbit 13 6873 = 68 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6873) = 3 ^ 4 * m + 68 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6873.1, data_13_6873.2] + +/-- Complete interval computation for depth 13, residue 6874. -/ +theorem bounds_13_6874 : exactInterval 13 6874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6874 : oddCount 6874 13 = 7 ∧ acceleratedOrbit 13 6874 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6874) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6874.1, data_13_6874.2] + +/-- Complete interval computation for depth 13, residue 6875. -/ +theorem bounds_13_6875 : exactInterval 13 6875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6875 : oddCount 6875 13 = 10 ∧ acceleratedOrbit 13 6875 = 49571 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6875) = 3 ^ 10 * m + 49571 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6875.1, data_13_6875.2] + +/-- Complete interval computation for depth 13, residue 6876. -/ +theorem bounds_13_6876 : exactInterval 13 6876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6876 : oddCount 6876 13 = 7 ∧ acceleratedOrbit 13 6876 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6876) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6876.1, data_13_6876.2] + +/-- Complete interval computation for depth 13, residue 6877. -/ +theorem bounds_13_6877 : exactInterval 13 6877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6877 : oddCount 6877 13 = 7 ∧ acceleratedOrbit 13 6877 = 1838 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6877) = 3 ^ 7 * m + 1838 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6877.1, data_13_6877.2] + +/-- Complete interval computation for depth 13, residue 6878. -/ +theorem bounds_13_6878 : exactInterval 13 6878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6878 : oddCount 6878 13 = 7 ∧ acceleratedOrbit 13 6878 = 1837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6878) = 3 ^ 7 * m + 1837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6878.1, data_13_6878.2] + +/-- Complete interval computation for depth 13, residue 6879. -/ +theorem bounds_13_6879 : exactInterval 13 6879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6879 : oddCount 6879 13 = 7 ∧ acceleratedOrbit 13 6879 = 1837 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6879) = 3 ^ 7 * m + 1837 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6879.1, data_13_6879.2] + +/-- Complete interval computation for depth 13, residue 6880. -/ +theorem bounds_13_6880 : exactInterval 13 6880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6880 : oddCount 6880 13 = 5 ∧ acceleratedOrbit 13 6880 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6880) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6880.1, data_13_6880.2] + +/-- Complete interval computation for depth 13, residue 6881. -/ +theorem bounds_13_6881 : exactInterval 13 6881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6881 : oddCount 6881 13 = 8 ∧ acceleratedOrbit 13 6881 = 5513 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6881) = 3 ^ 8 * m + 5513 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6881.1, data_13_6881.2] + +/-- Complete interval computation for depth 13, residue 6882. -/ +theorem bounds_13_6882 : exactInterval 13 6882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6882 : oddCount 6882 13 = 5 ∧ acceleratedOrbit 13 6882 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6882) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6882.1, data_13_6882.2] + +/-- Complete interval computation for depth 13, residue 6883. -/ +theorem bounds_13_6883 : exactInterval 13 6883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6883 : oddCount 6883 13 = 5 ∧ acceleratedOrbit 13 6883 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6883) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6883.1, data_13_6883.2] + +/-- Complete interval computation for depth 13, residue 6884. -/ +theorem bounds_13_6884 : exactInterval 13 6884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6884 : oddCount 6884 13 = 6 ∧ acceleratedOrbit 13 6884 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6884) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6884.1, data_13_6884.2] + +/-- Complete interval computation for depth 13, residue 6885. -/ +theorem bounds_13_6885 : exactInterval 13 6885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6885 : oddCount 6885 13 = 6 ∧ acceleratedOrbit 13 6885 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6885) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6885.1, data_13_6885.2] + +end Collatz.Research.StoppingAtlas.Batch0915 From 4173e471622631444134807bad193054fb0ac7f0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:22 +0530 Subject: [PATCH 0916/1001] proof: certify atlas Batch0916 (13:6886 to 13:6900) --- Collatz/Research/StoppingAtlas/Batch0916.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0916.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0916.lean b/Collatz/Research/StoppingAtlas/Batch0916.lean new file mode 100644 index 00000000..c2884b6a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0916.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0916 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6886. -/ +theorem bounds_13_6886 : exactInterval 13 6886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6886 : oddCount 6886 13 = 6 ∧ acceleratedOrbit 13 6886 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6886) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6886.1, data_13_6886.2] + +/-- Complete interval computation for depth 13, residue 6887. -/ +theorem bounds_13_6887 : exactInterval 13 6887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6887 : oddCount 6887 13 = 11 ∧ acceleratedOrbit 13 6887 = 148958 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6887) = 3 ^ 11 * m + 148958 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6887.1, data_13_6887.2] + +/-- Complete interval computation for depth 13, residue 6888. -/ +theorem bounds_13_6888 : exactInterval 13 6888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6888 : oddCount 6888 13 = 5 ∧ acceleratedOrbit 13 6888 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6888) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6888.1, data_13_6888.2] + +/-- Complete interval computation for depth 13, residue 6889. -/ +theorem bounds_13_6889 : exactInterval 13 6889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6889 : oddCount 6889 13 = 8 ∧ acceleratedOrbit 13 6889 = 5519 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6889) = 3 ^ 8 * m + 5519 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6889.1, data_13_6889.2] + +/-- Complete interval computation for depth 13, residue 6890. -/ +theorem bounds_13_6890 : exactInterval 13 6890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6890 : oddCount 6890 13 = 5 ∧ acceleratedOrbit 13 6890 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6890) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6890.1, data_13_6890.2] + +/-- Complete interval computation for depth 13, residue 6891. -/ +theorem bounds_13_6891 : exactInterval 13 6891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6891 : oddCount 6891 13 = 8 ∧ acceleratedOrbit 13 6891 = 5521 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6891) = 3 ^ 8 * m + 5521 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6891.1, data_13_6891.2] + +/-- Complete interval computation for depth 13, residue 6892. -/ +theorem bounds_13_6892 : exactInterval 13 6892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6892 : oddCount 6892 13 = 6 ∧ acceleratedOrbit 13 6892 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6892) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6892.1, data_13_6892.2] + +/-- Complete interval computation for depth 13, residue 6893. -/ +theorem bounds_13_6893 : exactInterval 13 6893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6893 : oddCount 6893 13 = 6 ∧ acceleratedOrbit 13 6893 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6893) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6893.1, data_13_6893.2] + +/-- Complete interval computation for depth 13, residue 6894. -/ +theorem bounds_13_6894 : exactInterval 13 6894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6894 : oddCount 6894 13 = 6 ∧ acceleratedOrbit 13 6894 = 614 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6894) = 3 ^ 6 * m + 614 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6894.1, data_13_6894.2] + +/-- Complete interval computation for depth 13, residue 6895. -/ +theorem bounds_13_6895 : exactInterval 13 6895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6895 : oddCount 6895 13 = 10 ∧ acceleratedOrbit 13 6895 = 49709 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6895) = 3 ^ 10 * m + 49709 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6895.1, data_13_6895.2] + +/-- Complete interval computation for depth 13, residue 6896. -/ +theorem bounds_13_6896 : exactInterval 13 6896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6896 : oddCount 6896 13 = 5 ∧ acceleratedOrbit 13 6896 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6896) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6896.1, data_13_6896.2] + +/-- Complete interval computation for depth 13, residue 6897. -/ +theorem bounds_13_6897 : exactInterval 13 6897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6897 : oddCount 6897 13 = 5 ∧ acceleratedOrbit 13 6897 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6897) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6897.1, data_13_6897.2] + +/-- Complete interval computation for depth 13, residue 6898. -/ +theorem bounds_13_6898 : exactInterval 13 6898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6898 : oddCount 6898 13 = 8 ∧ acceleratedOrbit 13 6898 = 5528 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6898) = 3 ^ 8 * m + 5528 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6898.1, data_13_6898.2] + +/-- Complete interval computation for depth 13, residue 6899. -/ +theorem bounds_13_6899 : exactInterval 13 6899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6899 : oddCount 6899 13 = 8 ∧ acceleratedOrbit 13 6899 = 5528 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6899) = 3 ^ 8 * m + 5528 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6899.1, data_13_6899.2] + +/-- Complete interval computation for depth 13, residue 6900. -/ +theorem bounds_13_6900 : exactInterval 13 6900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6900 : oddCount 6900 13 = 5 ∧ acceleratedOrbit 13 6900 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6900) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6900.1, data_13_6900.2] + +end Collatz.Research.StoppingAtlas.Batch0916 From 098d3141b3853f3535dd5009debcf3cef36deb3d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:22 +0530 Subject: [PATCH 0917/1001] proof: certify atlas Batch0917 (13:6901 to 13:6916) --- Collatz/Research/StoppingAtlas/Batch0917.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0917.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0917.lean b/Collatz/Research/StoppingAtlas/Batch0917.lean new file mode 100644 index 00000000..112cc528 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0917.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0917 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6901. -/ +theorem bounds_13_6901 : exactInterval 13 6901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6901 : oddCount 6901 13 = 5 ∧ acceleratedOrbit 13 6901 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6901) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6901.1, data_13_6901.2] + +/-- Complete interval computation for depth 13, residue 6902. -/ +theorem bounds_13_6902 : exactInterval 13 6902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6902 : oddCount 6902 13 = 7 ∧ acceleratedOrbit 13 6902 = 1844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6902) = 3 ^ 7 * m + 1844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6902.1, data_13_6902.2] + +/-- Complete interval computation for depth 13, residue 6903. -/ +theorem bounds_13_6903 : exactInterval 13 6903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6903 : oddCount 6903 13 = 7 ∧ acceleratedOrbit 13 6903 = 1844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6903) = 3 ^ 7 * m + 1844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6903.1, data_13_6903.2] + +/-- Complete interval computation for depth 13, residue 6904. -/ +theorem bounds_13_6904 : exactInterval 13 6904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6904 : oddCount 6904 13 = 5 ∧ acceleratedOrbit 13 6904 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6904) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6904.1, data_13_6904.2] + +/-- Complete interval computation for depth 13, residue 6905. -/ +theorem bounds_13_6905 : exactInterval 13 6905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6905 : oddCount 6905 13 = 8 ∧ acceleratedOrbit 13 6905 = 5534 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6905) = 3 ^ 8 * m + 5534 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6905.1, data_13_6905.2] + +/-- Complete interval computation for depth 13, residue 6906. -/ +theorem bounds_13_6906 : exactInterval 13 6906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6906 : oddCount 6906 13 = 5 ∧ acceleratedOrbit 13 6906 = 205 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6906) = 3 ^ 5 * m + 205 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6906.1, data_13_6906.2] + +/-- Complete interval computation for depth 13, residue 6907. -/ +theorem bounds_13_6907 : exactInterval 13 6907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6907 : oddCount 6907 13 = 9 ∧ acceleratedOrbit 13 6907 = 16600 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6907) = 3 ^ 9 * m + 16600 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6907.1, data_13_6907.2] + +/-- Complete interval computation for depth 13, residue 6908. -/ +theorem bounds_13_6908 : exactInterval 13 6908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6908 : oddCount 6908 13 = 8 ∧ acceleratedOrbit 13 6908 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6908) = 3 ^ 8 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6908.1, data_13_6908.2] + +/-- Complete interval computation for depth 13, residue 6909. -/ +theorem bounds_13_6909 : exactInterval 13 6909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6909 : oddCount 6909 13 = 8 ∧ acceleratedOrbit 13 6909 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6909) = 3 ^ 8 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6909.1, data_13_6909.2] + +/-- Complete interval computation for depth 13, residue 6910. -/ +theorem bounds_13_6910 : exactInterval 13 6910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6910 : oddCount 6910 13 = 8 ∧ acceleratedOrbit 13 6910 = 5536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6910) = 3 ^ 8 * m + 5536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6910.1, data_13_6910.2] + +/-- Complete interval computation for depth 13, residue 6911. -/ +theorem bounds_13_6911 : exactInterval 13 6911 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6911) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6911 : oddCount 6911 13 = 10 ∧ acceleratedOrbit 13 6911 = 49823 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6911) = 3 ^ 10 * m + 49823 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6911.1, data_13_6911.2] + +/-- Complete interval computation for depth 13, residue 6912. -/ +theorem bounds_13_6912 : exactInterval 13 6912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6912 : oddCount 6912 13 = 4 ∧ acceleratedOrbit 13 6912 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6912) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6912.1, data_13_6912.2] + +/-- Complete interval computation for depth 13, residue 6913. -/ +theorem bounds_13_6913 : exactInterval 13 6913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6913 : oddCount 6913 13 = 6 ∧ acceleratedOrbit 13 6913 = 616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6913) = 3 ^ 6 * m + 616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6913.1, data_13_6913.2] + +/-- Complete interval computation for depth 13, residue 6914. -/ +theorem bounds_13_6914 : exactInterval 13 6914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6914 : oddCount 6914 13 = 6 ∧ acceleratedOrbit 13 6914 = 616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6914) = 3 ^ 6 * m + 616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6914.1, data_13_6914.2] + +/-- Complete interval computation for depth 13, residue 6915. -/ +theorem bounds_13_6915 : exactInterval 13 6915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6915 : oddCount 6915 13 = 6 ∧ acceleratedOrbit 13 6915 = 616 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6915) = 3 ^ 6 * m + 616 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6915.1, data_13_6915.2] + +/-- Complete interval computation for depth 13, residue 6916. -/ +theorem bounds_13_6916 : exactInterval 13 6916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6916 : oddCount 6916 13 = 5 ∧ acceleratedOrbit 13 6916 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6916) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6916.1, data_13_6916.2] + +end Collatz.Research.StoppingAtlas.Batch0917 From 4bcfff9f9ade04cf9b13094f9422ba5ee63f489c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:23 +0530 Subject: [PATCH 0918/1001] proof: certify atlas Batch0918 (13:6917 to 13:6931) --- Collatz/Research/StoppingAtlas/Batch0918.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0918.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0918.lean b/Collatz/Research/StoppingAtlas/Batch0918.lean new file mode 100644 index 00000000..8c6f3aea --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0918.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0918 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6917. -/ +theorem bounds_13_6917 : exactInterval 13 6917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6917 : oddCount 6917 13 = 5 ∧ acceleratedOrbit 13 6917 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6917) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6917.1, data_13_6917.2] + +/-- Complete interval computation for depth 13, residue 6918. -/ +theorem bounds_13_6918 : exactInterval 13 6918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6918 : oddCount 6918 13 = 5 ∧ acceleratedOrbit 13 6918 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6918) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6918.1, data_13_6918.2] + +/-- Complete interval computation for depth 13, residue 6919. -/ +theorem bounds_13_6919 : exactInterval 13 6919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6919 : oddCount 6919 13 = 9 ∧ acceleratedOrbit 13 6919 = 16631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6919) = 3 ^ 9 * m + 16631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6919.1, data_13_6919.2] + +/-- Complete interval computation for depth 13, residue 6920. -/ +theorem bounds_13_6920 : exactInterval 13 6920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6920 : oddCount 6920 13 = 7 ∧ acceleratedOrbit 13 6920 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6920) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6920.1, data_13_6920.2] + +/-- Complete interval computation for depth 13, residue 6921. -/ +theorem bounds_13_6921 : exactInterval 13 6921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6921 : oddCount 6921 13 = 8 ∧ acceleratedOrbit 13 6921 = 5545 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6921) = 3 ^ 8 * m + 5545 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6921.1, data_13_6921.2] + +/-- Complete interval computation for depth 13, residue 6922. -/ +theorem bounds_13_6922 : exactInterval 13 6922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6922 : oddCount 6922 13 = 7 ∧ acceleratedOrbit 13 6922 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6922) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6922.1, data_13_6922.2] + +/-- Complete interval computation for depth 13, residue 6923. -/ +theorem bounds_13_6923 : exactInterval 13 6923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6923 : oddCount 6923 13 = 8 ∧ acceleratedOrbit 13 6923 = 5548 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6923) = 3 ^ 8 * m + 5548 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6923.1, data_13_6923.2] + +/-- Complete interval computation for depth 13, residue 6924. -/ +theorem bounds_13_6924 : exactInterval 13 6924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6924 : oddCount 6924 13 = 7 ∧ acceleratedOrbit 13 6924 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6924) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6924.1, data_13_6924.2] + +/-- Complete interval computation for depth 13, residue 6925. -/ +theorem bounds_13_6925 : exactInterval 13 6925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6925 : oddCount 6925 13 = 7 ∧ acceleratedOrbit 13 6925 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6925) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6925.1, data_13_6925.2] + +/-- Complete interval computation for depth 13, residue 6926. -/ +theorem bounds_13_6926 : exactInterval 13 6926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6926 : oddCount 6926 13 = 5 ∧ acceleratedOrbit 13 6926 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6926) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6926.1, data_13_6926.2] + +/-- Complete interval computation for depth 13, residue 6927. -/ +theorem bounds_13_6927 : exactInterval 13 6927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6927 : oddCount 6927 13 = 5 ∧ acceleratedOrbit 13 6927 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6927) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6927.1, data_13_6927.2] + +/-- Complete interval computation for depth 13, residue 6928. -/ +theorem bounds_13_6928 : exactInterval 13 6928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6928 : oddCount 6928 13 = 3 ∧ acceleratedOrbit 13 6928 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6928) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6928.1, data_13_6928.2] + +/-- Complete interval computation for depth 13, residue 6929. -/ +theorem bounds_13_6929 : exactInterval 13 6929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6929 : oddCount 6929 13 = 7 ∧ acceleratedOrbit 13 6929 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6929) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6929.1, data_13_6929.2] + +/-- Complete interval computation for depth 13, residue 6930. -/ +theorem bounds_13_6930 : exactInterval 13 6930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6930 : oddCount 6930 13 = 6 ∧ acceleratedOrbit 13 6930 = 617 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6930) = 3 ^ 6 * m + 617 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6930.1, data_13_6930.2] + +/-- Complete interval computation for depth 13, residue 6931. -/ +theorem bounds_13_6931 : exactInterval 13 6931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6931 : oddCount 6931 13 = 6 ∧ acceleratedOrbit 13 6931 = 617 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6931) = 3 ^ 6 * m + 617 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6931.1, data_13_6931.2] + +end Collatz.Research.StoppingAtlas.Batch0918 From 6434c8f6ca699b1a79d9f71b2166c5e8ec1fdd98 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:23 +0530 Subject: [PATCH 0919/1001] proof: certify atlas Batch0919 (13:6932 to 13:6946) --- Collatz/Research/StoppingAtlas/Batch0919.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0919.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0919.lean b/Collatz/Research/StoppingAtlas/Batch0919.lean new file mode 100644 index 00000000..f14cfd81 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0919.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0919 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6932. -/ +theorem bounds_13_6932 : exactInterval 13 6932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6932 : oddCount 6932 13 = 3 ∧ acceleratedOrbit 13 6932 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6932) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6932.1, data_13_6932.2] + +/-- Complete interval computation for depth 13, residue 6933. -/ +theorem bounds_13_6933 : exactInterval 13 6933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6933 : oddCount 6933 13 = 3 ∧ acceleratedOrbit 13 6933 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6933) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6933.1, data_13_6933.2] + +/-- Complete interval computation for depth 13, residue 6934. -/ +theorem bounds_13_6934 : exactInterval 13 6934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6934 : oddCount 6934 13 = 7 ∧ acceleratedOrbit 13 6934 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6934) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6934.1, data_13_6934.2] + +/-- Complete interval computation for depth 13, residue 6935. -/ +theorem bounds_13_6935 : exactInterval 13 6935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6935 : oddCount 6935 13 = 7 ∧ acceleratedOrbit 13 6935 = 1853 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6935) = 3 ^ 7 * m + 1853 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6935.1, data_13_6935.2] + +/-- Complete interval computation for depth 13, residue 6936. -/ +theorem bounds_13_6936 : exactInterval 13 6936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6936 : oddCount 6936 13 = 3 ∧ acceleratedOrbit 13 6936 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6936) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6936.1, data_13_6936.2] + +/-- Complete interval computation for depth 13, residue 6937. -/ +theorem bounds_13_6937 : exactInterval 13 6937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6937 : oddCount 6937 13 = 9 ∧ acceleratedOrbit 13 6937 = 16676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6937) = 3 ^ 9 * m + 16676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6937.1, data_13_6937.2] + +/-- Complete interval computation for depth 13, residue 6938. -/ +theorem bounds_13_6938 : exactInterval 13 6938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6938 : oddCount 6938 13 = 3 ∧ acceleratedOrbit 13 6938 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6938) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6938.1, data_13_6938.2] + +/-- Complete interval computation for depth 13, residue 6939. -/ +theorem bounds_13_6939 : exactInterval 13 6939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6939 : oddCount 6939 13 = 11 ∧ acceleratedOrbit 13 6939 = 150083 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6939) = 3 ^ 11 * m + 150083 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6939.1, data_13_6939.2] + +/-- Complete interval computation for depth 13, residue 6940. -/ +theorem bounds_13_6940 : exactInterval 13 6940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6940 : oddCount 6940 13 = 5 ∧ acceleratedOrbit 13 6940 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6940) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6940.1, data_13_6940.2] + +/-- Complete interval computation for depth 13, residue 6941. -/ +theorem bounds_13_6941 : exactInterval 13 6941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6941 : oddCount 6941 13 = 5 ∧ acceleratedOrbit 13 6941 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6941) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6941.1, data_13_6941.2] + +/-- Complete interval computation for depth 13, residue 6942. -/ +theorem bounds_13_6942 : exactInterval 13 6942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6942 : oddCount 6942 13 = 5 ∧ acceleratedOrbit 13 6942 = 206 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6942) = 3 ^ 5 * m + 206 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6942.1, data_13_6942.2] + +/-- Complete interval computation for depth 13, residue 6943. -/ +theorem bounds_13_6943 : exactInterval 13 6943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6943 : oddCount 6943 13 = 10 ∧ acceleratedOrbit 13 6943 = 50057 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6943) = 3 ^ 10 * m + 50057 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6943.1, data_13_6943.2] + +/-- Complete interval computation for depth 13, residue 6944. -/ +theorem bounds_13_6944 : exactInterval 13 6944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6944 : oddCount 6944 13 = 3 ∧ acceleratedOrbit 13 6944 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6944) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6944.1, data_13_6944.2] + +/-- Complete interval computation for depth 13, residue 6945. -/ +theorem bounds_13_6945 : exactInterval 13 6945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6945 : oddCount 6945 13 = 7 ∧ acceleratedOrbit 13 6945 = 1856 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6945) = 3 ^ 7 * m + 1856 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6945.1, data_13_6945.2] + +/-- Complete interval computation for depth 13, residue 6946. -/ +theorem bounds_13_6946 : exactInterval 13 6946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6946 : oddCount 6946 13 = 6 ∧ acceleratedOrbit 13 6946 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6946) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6946.1, data_13_6946.2] + +end Collatz.Research.StoppingAtlas.Batch0919 From 6e6d1841e597017df096c9875f2393d5ee7f800a Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:23 +0530 Subject: [PATCH 0920/1001] proof: certify atlas Batch0920 (13:6947 to 13:6962) --- Collatz/Research/StoppingAtlas/Batch0920.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0920.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0920.lean b/Collatz/Research/StoppingAtlas/Batch0920.lean new file mode 100644 index 00000000..42bf3fcf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0920.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0920 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6947. -/ +theorem bounds_13_6947 : exactInterval 13 6947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6947 : oddCount 6947 13 = 6 ∧ acceleratedOrbit 13 6947 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6947) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6947.1, data_13_6947.2] + +/-- Complete interval computation for depth 13, residue 6948. -/ +theorem bounds_13_6948 : exactInterval 13 6948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6948 : oddCount 6948 13 = 6 ∧ acceleratedOrbit 13 6948 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6948) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6948.1, data_13_6948.2] + +/-- Complete interval computation for depth 13, residue 6949. -/ +theorem bounds_13_6949 : exactInterval 13 6949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6949 : oddCount 6949 13 = 6 ∧ acceleratedOrbit 13 6949 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6949) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6949.1, data_13_6949.2] + +/-- Complete interval computation for depth 13, residue 6950. -/ +theorem bounds_13_6950 : exactInterval 13 6950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6950 : oddCount 6950 13 = 6 ∧ acceleratedOrbit 13 6950 = 620 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6950) = 3 ^ 6 * m + 620 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6950.1, data_13_6950.2] + +/-- Complete interval computation for depth 13, residue 6951. -/ +theorem bounds_13_6951 : exactInterval 13 6951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6951 : oddCount 6951 13 = 9 ∧ acceleratedOrbit 13 6951 = 16706 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6951) = 3 ^ 9 * m + 16706 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6951.1, data_13_6951.2] + +/-- Complete interval computation for depth 13, residue 6952. -/ +theorem bounds_13_6952 : exactInterval 13 6952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6952 : oddCount 6952 13 = 3 ∧ acceleratedOrbit 13 6952 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6952) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6952.1, data_13_6952.2] + +/-- Complete interval computation for depth 13, residue 6953. -/ +theorem bounds_13_6953 : exactInterval 13 6953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6953 : oddCount 6953 13 = 9 ∧ acceleratedOrbit 13 6953 = 16712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6953) = 3 ^ 9 * m + 16712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6953.1, data_13_6953.2] + +/-- Complete interval computation for depth 13, residue 6954. -/ +theorem bounds_13_6954 : exactInterval 13 6954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6954 : oddCount 6954 13 = 3 ∧ acceleratedOrbit 13 6954 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6954) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6954.1, data_13_6954.2] + +/-- Complete interval computation for depth 13, residue 6955. -/ +theorem bounds_13_6955 : exactInterval 13 6955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6955 : oddCount 6955 13 = 7 ∧ acceleratedOrbit 13 6955 = 1858 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6955) = 3 ^ 7 * m + 1858 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6955.1, data_13_6955.2] + +/-- Complete interval computation for depth 13, residue 6956. -/ +theorem bounds_13_6956 : exactInterval 13 6956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6956 : oddCount 6956 13 = 7 ∧ acceleratedOrbit 13 6956 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6956) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6956.1, data_13_6956.2] + +/-- Complete interval computation for depth 13, residue 6957. -/ +theorem bounds_13_6957 : exactInterval 13 6957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6957 : oddCount 6957 13 = 7 ∧ acceleratedOrbit 13 6957 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6957) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6957.1, data_13_6957.2] + +/-- Complete interval computation for depth 13, residue 6958. -/ +theorem bounds_13_6958 : exactInterval 13 6958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6958 : oddCount 6958 13 = 7 ∧ acceleratedOrbit 13 6958 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6958) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6958.1, data_13_6958.2] + +/-- Complete interval computation for depth 13, residue 6959. -/ +theorem bounds_13_6959 : exactInterval 13 6959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6959 : oddCount 6959 13 = 8 ∧ acceleratedOrbit 13 6959 = 5575 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6959) = 3 ^ 8 * m + 5575 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6959.1, data_13_6959.2] + +/-- Complete interval computation for depth 13, residue 6960. -/ +theorem bounds_13_6960 : exactInterval 13 6960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6960 : oddCount 6960 13 = 3 ∧ acceleratedOrbit 13 6960 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6960) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6960.1, data_13_6960.2] + +/-- Complete interval computation for depth 13, residue 6961. -/ +theorem bounds_13_6961 : exactInterval 13 6961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6961 : oddCount 6961 13 = 7 ∧ acceleratedOrbit 13 6961 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6961) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6961.1, data_13_6961.2] + +/-- Complete interval computation for depth 13, residue 6962. -/ +theorem bounds_13_6962 : exactInterval 13 6962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6962 : oddCount 6962 13 = 7 ∧ acceleratedOrbit 13 6962 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6962) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6962.1, data_13_6962.2] + +end Collatz.Research.StoppingAtlas.Batch0920 From f53cf776dfa96d1d96ae855e656876ff953bb2bd Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:23 +0530 Subject: [PATCH 0921/1001] proof: certify atlas Batch0921 (13:6963 to 13:6977) --- Collatz/Research/StoppingAtlas/Batch0921.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0921.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0921.lean b/Collatz/Research/StoppingAtlas/Batch0921.lean new file mode 100644 index 00000000..82d23b06 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0921.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0921 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6963. -/ +theorem bounds_13_6963 : exactInterval 13 6963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6963 : oddCount 6963 13 = 7 ∧ acceleratedOrbit 13 6963 = 1862 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6963) = 3 ^ 7 * m + 1862 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6963.1, data_13_6963.2] + +/-- Complete interval computation for depth 13, residue 6964. -/ +theorem bounds_13_6964 : exactInterval 13 6964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6964 : oddCount 6964 13 = 3 ∧ acceleratedOrbit 13 6964 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6964) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6964.1, data_13_6964.2] + +/-- Complete interval computation for depth 13, residue 6965. -/ +theorem bounds_13_6965 : exactInterval 13 6965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6965 : oddCount 6965 13 = 3 ∧ acceleratedOrbit 13 6965 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6965) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6965.1, data_13_6965.2] + +/-- Complete interval computation for depth 13, residue 6966. -/ +theorem bounds_13_6966 : exactInterval 13 6966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6966 : oddCount 6966 13 = 8 ∧ acceleratedOrbit 13 6966 = 5582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6966) = 3 ^ 8 * m + 5582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6966.1, data_13_6966.2] + +/-- Complete interval computation for depth 13, residue 6967. -/ +theorem bounds_13_6967 : exactInterval 13 6967 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6967) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6967 : oddCount 6967 13 = 8 ∧ acceleratedOrbit 13 6967 = 5582 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6967) = 3 ^ 8 * m + 5582 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6967.1, data_13_6967.2] + +/-- Complete interval computation for depth 13, residue 6968. -/ +theorem bounds_13_6968 : exactInterval 13 6968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6968 : oddCount 6968 13 = 9 ∧ acceleratedOrbit 13 6968 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6968) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6968.1, data_13_6968.2] + +/-- Complete interval computation for depth 13, residue 6969. -/ +theorem bounds_13_6969 : exactInterval 13 6969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6969 : oddCount 6969 13 = 8 ∧ acceleratedOrbit 13 6969 = 5584 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6969) = 3 ^ 8 * m + 5584 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6969.1, data_13_6969.2] + +/-- Complete interval computation for depth 13, residue 6970. -/ +theorem bounds_13_6970 : exactInterval 13 6970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6970 : oddCount 6970 13 = 9 ∧ acceleratedOrbit 13 6970 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6970) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6970.1, data_13_6970.2] + +/-- Complete interval computation for depth 13, residue 6971. -/ +theorem bounds_13_6971 : exactInterval 13 6971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6971 : oddCount 6971 13 = 8 ∧ acceleratedOrbit 13 6971 = 5588 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6971) = 3 ^ 8 * m + 5588 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6971.1, data_13_6971.2] + +/-- Complete interval computation for depth 13, residue 6972. -/ +theorem bounds_13_6972 : exactInterval 13 6972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6972 : oddCount 6972 13 = 9 ∧ acceleratedOrbit 13 6972 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6972) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6972.1, data_13_6972.2] + +/-- Complete interval computation for depth 13, residue 6973. -/ +theorem bounds_13_6973 : exactInterval 13 6973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6973 : oddCount 6973 13 = 9 ∧ acceleratedOrbit 13 6973 = 16766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6973) = 3 ^ 9 * m + 16766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6973.1, data_13_6973.2] + +/-- Complete interval computation for depth 13, residue 6974. -/ +theorem bounds_13_6974 : exactInterval 13 6974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6974 : oddCount 6974 13 = 9 ∧ acceleratedOrbit 13 6974 = 16762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6974) = 3 ^ 9 * m + 16762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6974.1, data_13_6974.2] + +/-- Complete interval computation for depth 13, residue 6975. -/ +theorem bounds_13_6975 : exactInterval 13 6975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6975 : oddCount 6975 13 = 9 ∧ acceleratedOrbit 13 6975 = 16762 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6975) = 3 ^ 9 * m + 16762 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6975.1, data_13_6975.2] + +/-- Complete interval computation for depth 13, residue 6976. -/ +theorem bounds_13_6976 : exactInterval 13 6976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6976 : oddCount 6976 13 = 4 ∧ acceleratedOrbit 13 6976 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6976) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6976.1, data_13_6976.2] + +/-- Complete interval computation for depth 13, residue 6977. -/ +theorem bounds_13_6977 : exactInterval 13 6977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6977 : oddCount 6977 13 = 3 ∧ acceleratedOrbit 13 6977 = 23 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6977) = 3 ^ 3 * m + 23 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6977.1, data_13_6977.2] + +end Collatz.Research.StoppingAtlas.Batch0921 From b87d3fbdccda509597812d57f70cb74d3d847737 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:23 +0530 Subject: [PATCH 0922/1001] proof: certify atlas Batch0922 (13:6978 to 13:6992) --- Collatz/Research/StoppingAtlas/Batch0922.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0922.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0922.lean b/Collatz/Research/StoppingAtlas/Batch0922.lean new file mode 100644 index 00000000..14a92539 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0922.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0922 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6978. -/ +theorem bounds_13_6978 : exactInterval 13 6978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6978 : oddCount 6978 13 = 7 ∧ acceleratedOrbit 13 6978 = 1865 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6978) = 3 ^ 7 * m + 1865 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6978.1, data_13_6978.2] + +/-- Complete interval computation for depth 13, residue 6979. -/ +theorem bounds_13_6979 : exactInterval 13 6979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6979 : oddCount 6979 13 = 7 ∧ acceleratedOrbit 13 6979 = 1865 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6979) = 3 ^ 7 * m + 1865 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6979.1, data_13_6979.2] + +/-- Complete interval computation for depth 13, residue 6980. -/ +theorem bounds_13_6980 : exactInterval 13 6980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6980 : oddCount 6980 13 = 6 ∧ acceleratedOrbit 13 6980 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6980) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6980.1, data_13_6980.2] + +/-- Complete interval computation for depth 13, residue 6981. -/ +theorem bounds_13_6981 : exactInterval 13 6981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6981 : oddCount 6981 13 = 6 ∧ acceleratedOrbit 13 6981 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6981) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6981.1, data_13_6981.2] + +/-- Complete interval computation for depth 13, residue 6982. -/ +theorem bounds_13_6982 : exactInterval 13 6982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6982 : oddCount 6982 13 = 6 ∧ acceleratedOrbit 13 6982 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6982) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6982.1, data_13_6982.2] + +/-- Complete interval computation for depth 13, residue 6983. -/ +theorem bounds_13_6983 : exactInterval 13 6983 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6983) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6983 : oddCount 6983 13 = 8 ∧ acceleratedOrbit 13 6983 = 5594 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6983) = 3 ^ 8 * m + 5594 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6983.1, data_13_6983.2] + +/-- Complete interval computation for depth 13, residue 6984. -/ +theorem bounds_13_6984 : exactInterval 13 6984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6984 : oddCount 6984 13 = 6 ∧ acceleratedOrbit 13 6984 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6984) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6984.1, data_13_6984.2] + +/-- Complete interval computation for depth 13, residue 6985. -/ +theorem bounds_13_6985 : exactInterval 13 6985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6985 : oddCount 6985 13 = 6 ∧ acceleratedOrbit 13 6985 = 622 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6985) = 3 ^ 6 * m + 622 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6985.1, data_13_6985.2] + +/-- Complete interval computation for depth 13, residue 6986. -/ +theorem bounds_13_6986 : exactInterval 13 6986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6986 : oddCount 6986 13 = 6 ∧ acceleratedOrbit 13 6986 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6986) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6986.1, data_13_6986.2] + +/-- Complete interval computation for depth 13, residue 6987. -/ +theorem bounds_13_6987 : exactInterval 13 6987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6987 : oddCount 6987 13 = 6 ∧ acceleratedOrbit 13 6987 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6987) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6987.1, data_13_6987.2] + +/-- Complete interval computation for depth 13, residue 6988. -/ +theorem bounds_13_6988 : exactInterval 13 6988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6988 : oddCount 6988 13 = 6 ∧ acceleratedOrbit 13 6988 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6988) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6988.1, data_13_6988.2] + +/-- Complete interval computation for depth 13, residue 6989. -/ +theorem bounds_13_6989 : exactInterval 13 6989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6989 : oddCount 6989 13 = 6 ∧ acceleratedOrbit 13 6989 = 623 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6989) = 3 ^ 6 * m + 623 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6989.1, data_13_6989.2] + +/-- Complete interval computation for depth 13, residue 6990. -/ +theorem bounds_13_6990 : exactInterval 13 6990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6990 : oddCount 6990 13 = 7 ∧ acceleratedOrbit 13 6990 = 1867 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6990) = 3 ^ 7 * m + 1867 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6990.1, data_13_6990.2] + +/-- Complete interval computation for depth 13, residue 6991. -/ +theorem bounds_13_6991 : exactInterval 13 6991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6991 : oddCount 6991 13 = 7 ∧ acceleratedOrbit 13 6991 = 1867 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6991) = 3 ^ 7 * m + 1867 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6991.1, data_13_6991.2] + +/-- Complete interval computation for depth 13, residue 6992. -/ +theorem bounds_13_6992 : exactInterval 13 6992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6992 : oddCount 6992 13 = 4 ∧ acceleratedOrbit 13 6992 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6992) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6992.1, data_13_6992.2] + +end Collatz.Research.StoppingAtlas.Batch0922 From bc21e701aeb27062fa7620658303e0e2a71e7693 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:24 +0530 Subject: [PATCH 0923/1001] proof: certify atlas Batch0923 (13:6993 to 13:7008) --- Collatz/Research/StoppingAtlas/Batch0923.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0923.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0923.lean b/Collatz/Research/StoppingAtlas/Batch0923.lean new file mode 100644 index 00000000..21264926 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0923.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0923 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 6993. -/ +theorem bounds_13_6993 : exactInterval 13 6993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6993 : oddCount 6993 13 = 7 ∧ acceleratedOrbit 13 6993 = 1868 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6993) = 3 ^ 7 * m + 1868 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6993.1, data_13_6993.2] + +/-- Complete interval computation for depth 13, residue 6994. -/ +theorem bounds_13_6994 : exactInterval 13 6994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6994 : oddCount 6994 13 = 7 ∧ acceleratedOrbit 13 6994 = 1868 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6994) = 3 ^ 7 * m + 1868 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6994.1, data_13_6994.2] + +/-- Complete interval computation for depth 13, residue 6995. -/ +theorem bounds_13_6995 : exactInterval 13 6995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6995 : oddCount 6995 13 = 7 ∧ acceleratedOrbit 13 6995 = 1868 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6995) = 3 ^ 7 * m + 1868 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6995.1, data_13_6995.2] + +/-- Complete interval computation for depth 13, residue 6996. -/ +theorem bounds_13_6996 : exactInterval 13 6996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6996 : oddCount 6996 13 = 4 ∧ acceleratedOrbit 13 6996 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6996) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6996.1, data_13_6996.2] + +/-- Complete interval computation for depth 13, residue 6997. -/ +theorem bounds_13_6997 : exactInterval 13 6997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6997 : oddCount 6997 13 = 4 ∧ acceleratedOrbit 13 6997 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6997) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6997.1, data_13_6997.2] + +/-- Complete interval computation for depth 13, residue 6998. -/ +theorem bounds_13_6998 : exactInterval 13 6998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6998 : oddCount 6998 13 = 8 ∧ acceleratedOrbit 13 6998 = 5609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6998) = 3 ^ 8 * m + 5609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6998.1, data_13_6998.2] + +/-- Complete interval computation for depth 13, residue 6999. -/ +theorem bounds_13_6999 : exactInterval 13 6999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_6999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 6999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_6999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_6999 : oddCount 6999 13 = 8 ∧ acceleratedOrbit 13 6999 = 5609 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_6999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 6999) = 3 ^ 8 * m + 5609 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_6999.1, data_13_6999.2] + +/-- Complete interval computation for depth 13, residue 7000. -/ +theorem bounds_13_7000 : exactInterval 13 7000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7000 : oddCount 7000 13 = 5 ∧ acceleratedOrbit 13 7000 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7000) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7000.1, data_13_7000.2] + +/-- Complete interval computation for depth 13, residue 7001. -/ +theorem bounds_13_7001 : exactInterval 13 7001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7001 : oddCount 7001 13 = 5 ∧ acceleratedOrbit 13 7001 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7001) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7001.1, data_13_7001.2] + +/-- Complete interval computation for depth 13, residue 7002. -/ +theorem bounds_13_7002 : exactInterval 13 7002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7002 : oddCount 7002 13 = 5 ∧ acceleratedOrbit 13 7002 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7002) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7002.1, data_13_7002.2] + +/-- Complete interval computation for depth 13, residue 7003. -/ +theorem bounds_13_7003 : exactInterval 13 7003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7003 : oddCount 7003 13 = 7 ∧ acceleratedOrbit 13 7003 = 1870 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7003) = 3 ^ 7 * m + 1870 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7003.1, data_13_7003.2] + +/-- Complete interval computation for depth 13, residue 7004. -/ +theorem bounds_13_7004 : exactInterval 13 7004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7004 : oddCount 7004 13 = 5 ∧ acceleratedOrbit 13 7004 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7004) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7004.1, data_13_7004.2] + +/-- Complete interval computation for depth 13, residue 7005. -/ +theorem bounds_13_7005 : exactInterval 13 7005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7005 : oddCount 7005 13 = 5 ∧ acceleratedOrbit 13 7005 = 208 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7005) = 3 ^ 5 * m + 208 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7005.1, data_13_7005.2] + +/-- Complete interval computation for depth 13, residue 7006. -/ +theorem bounds_13_7006 : exactInterval 13 7006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7006 : oddCount 7006 13 = 8 ∧ acceleratedOrbit 13 7006 = 5615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7006) = 3 ^ 8 * m + 5615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7006.1, data_13_7006.2] + +/-- Complete interval computation for depth 13, residue 7007. -/ +theorem bounds_13_7007 : exactInterval 13 7007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7007 : oddCount 7007 13 = 8 ∧ acceleratedOrbit 13 7007 = 5615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7007) = 3 ^ 8 * m + 5615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7007.1, data_13_7007.2] + +/-- Complete interval computation for depth 13, residue 7008. -/ +theorem bounds_13_7008 : exactInterval 13 7008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7008 : oddCount 7008 13 = 5 ∧ acceleratedOrbit 13 7008 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7008) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7008.1, data_13_7008.2] + +end Collatz.Research.StoppingAtlas.Batch0923 From a18d614967c436f00780a4f1d2cce1a5d3acff01 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:24 +0530 Subject: [PATCH 0924/1001] proof: certify atlas Batch0924 (13:7009 to 13:7023) --- Collatz/Research/StoppingAtlas/Batch0924.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0924.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0924.lean b/Collatz/Research/StoppingAtlas/Batch0924.lean new file mode 100644 index 00000000..a10a6543 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0924.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0924 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7009. -/ +theorem bounds_13_7009 : exactInterval 13 7009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7009 : oddCount 7009 13 = 10 ∧ acceleratedOrbit 13 7009 = 50543 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7009) = 3 ^ 10 * m + 50543 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7009.1, data_13_7009.2] + +/-- Complete interval computation for depth 13, residue 7010. -/ +theorem bounds_13_7010 : exactInterval 13 7010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7010 : oddCount 7010 13 = 5 ∧ acceleratedOrbit 13 7010 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7010) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7010.1, data_13_7010.2] + +/-- Complete interval computation for depth 13, residue 7011. -/ +theorem bounds_13_7011 : exactInterval 13 7011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7011 : oddCount 7011 13 = 5 ∧ acceleratedOrbit 13 7011 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7011) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7011.1, data_13_7011.2] + +/-- Complete interval computation for depth 13, residue 7012. -/ +theorem bounds_13_7012 : exactInterval 13 7012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7012 : oddCount 7012 13 = 5 ∧ acceleratedOrbit 13 7012 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7012) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7012.1, data_13_7012.2] + +/-- Complete interval computation for depth 13, residue 7013. -/ +theorem bounds_13_7013 : exactInterval 13 7013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7013 : oddCount 7013 13 = 5 ∧ acceleratedOrbit 13 7013 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7013) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7013.1, data_13_7013.2] + +/-- Complete interval computation for depth 13, residue 7014. -/ +theorem bounds_13_7014 : exactInterval 13 7014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7014 : oddCount 7014 13 = 5 ∧ acceleratedOrbit 13 7014 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7014) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7014.1, data_13_7014.2] + +/-- Complete interval computation for depth 13, residue 7015. -/ +theorem bounds_13_7015 : exactInterval 13 7015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7015 : oddCount 7015 13 = 9 ∧ acceleratedOrbit 13 7015 = 16858 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7015) = 3 ^ 9 * m + 16858 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7015.1, data_13_7015.2] + +/-- Complete interval computation for depth 13, residue 7016. -/ +theorem bounds_13_7016 : exactInterval 13 7016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7016 : oddCount 7016 13 = 5 ∧ acceleratedOrbit 13 7016 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7016) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7016.1, data_13_7016.2] + +/-- Complete interval computation for depth 13, residue 7017. -/ +theorem bounds_13_7017 : exactInterval 13 7017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7017 : oddCount 7017 13 = 7 ∧ acceleratedOrbit 13 7017 = 1874 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7017) = 3 ^ 7 * m + 1874 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7017.1, data_13_7017.2] + +/-- Complete interval computation for depth 13, residue 7018. -/ +theorem bounds_13_7018 : exactInterval 13 7018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7018 : oddCount 7018 13 = 5 ∧ acceleratedOrbit 13 7018 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7018) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7018.1, data_13_7018.2] + +/-- Complete interval computation for depth 13, residue 7019. -/ +theorem bounds_13_7019 : exactInterval 13 7019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7019 : oddCount 7019 13 = 6 ∧ acceleratedOrbit 13 7019 = 625 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7019) = 3 ^ 6 * m + 625 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7019.1, data_13_7019.2] + +/-- Complete interval computation for depth 13, residue 7020. -/ +theorem bounds_13_7020 : exactInterval 13 7020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7020 : oddCount 7020 13 = 7 ∧ acceleratedOrbit 13 7020 = 1876 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7020) = 3 ^ 7 * m + 1876 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7020.1, data_13_7020.2] + +/-- Complete interval computation for depth 13, residue 7021. -/ +theorem bounds_13_7021 : exactInterval 13 7021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7021 : oddCount 7021 13 = 7 ∧ acceleratedOrbit 13 7021 = 1876 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7021) = 3 ^ 7 * m + 1876 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7021.1, data_13_7021.2] + +/-- Complete interval computation for depth 13, residue 7022. -/ +theorem bounds_13_7022 : exactInterval 13 7022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7022 : oddCount 7022 13 = 7 ∧ acceleratedOrbit 13 7022 = 1876 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7022) = 3 ^ 7 * m + 1876 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7022.1, data_13_7022.2] + +/-- Complete interval computation for depth 13, residue 7023. -/ +theorem bounds_13_7023 : exactInterval 13 7023 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7023) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7023 : oddCount 7023 13 = 8 ∧ acceleratedOrbit 13 7023 = 5626 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7023) = 3 ^ 8 * m + 5626 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7023.1, data_13_7023.2] + +end Collatz.Research.StoppingAtlas.Batch0924 From 94f92bd6988b6f0d07462c0c8b3c2f312044b30e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:24 +0530 Subject: [PATCH 0925/1001] proof: certify atlas Batch0925 (13:7024 to 13:7039) --- Collatz/Research/StoppingAtlas/Batch0925.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0925.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0925.lean b/Collatz/Research/StoppingAtlas/Batch0925.lean new file mode 100644 index 00000000..6e7bd037 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0925.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0925 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7024. -/ +theorem bounds_13_7024 : exactInterval 13 7024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7024 : oddCount 7024 13 = 5 ∧ acceleratedOrbit 13 7024 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7024) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7024.1, data_13_7024.2] + +/-- Complete interval computation for depth 13, residue 7025. -/ +theorem bounds_13_7025 : exactInterval 13 7025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7025 : oddCount 7025 13 = 5 ∧ acceleratedOrbit 13 7025 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7025) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7025.1, data_13_7025.2] + +/-- Complete interval computation for depth 13, residue 7026. -/ +theorem bounds_13_7026 : exactInterval 13 7026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7026 : oddCount 7026 13 = 5 ∧ acceleratedOrbit 13 7026 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7026) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7026.1, data_13_7026.2] + +/-- Complete interval computation for depth 13, residue 7027. -/ +theorem bounds_13_7027 : exactInterval 13 7027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7027 : oddCount 7027 13 = 5 ∧ acceleratedOrbit 13 7027 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7027) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7027.1, data_13_7027.2] + +/-- Complete interval computation for depth 13, residue 7028. -/ +theorem bounds_13_7028 : exactInterval 13 7028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7028 : oddCount 7028 13 = 5 ∧ acceleratedOrbit 13 7028 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7028) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7028.1, data_13_7028.2] + +/-- Complete interval computation for depth 13, residue 7029. -/ +theorem bounds_13_7029 : exactInterval 13 7029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7029 : oddCount 7029 13 = 5 ∧ acceleratedOrbit 13 7029 = 209 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7029) = 3 ^ 5 * m + 209 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7029.1, data_13_7029.2] + +/-- Complete interval computation for depth 13, residue 7030. -/ +theorem bounds_13_7030 : exactInterval 13 7030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7030 : oddCount 7030 13 = 6 ∧ acceleratedOrbit 13 7030 = 626 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7030) = 3 ^ 6 * m + 626 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7030.1, data_13_7030.2] + +/-- Complete interval computation for depth 13, residue 7031. -/ +theorem bounds_13_7031 : exactInterval 13 7031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7031 : oddCount 7031 13 = 6 ∧ acceleratedOrbit 13 7031 = 626 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7031) = 3 ^ 6 * m + 626 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7031.1, data_13_7031.2] + +/-- Complete interval computation for depth 13, residue 7032. -/ +theorem bounds_13_7032 : exactInterval 13 7032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7032 : oddCount 7032 13 = 7 ∧ acceleratedOrbit 13 7032 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7032) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7032.1, data_13_7032.2] + +/-- Complete interval computation for depth 13, residue 7033. -/ +theorem bounds_13_7033 : exactInterval 13 7033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7033 : oddCount 7033 13 = 9 ∧ acceleratedOrbit 13 7033 = 16904 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7033) = 3 ^ 9 * m + 16904 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7033.1, data_13_7033.2] + +/-- Complete interval computation for depth 13, residue 7034. -/ +theorem bounds_13_7034 : exactInterval 13 7034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7034 : oddCount 7034 13 = 7 ∧ acceleratedOrbit 13 7034 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7034) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7034.1, data_13_7034.2] + +/-- Complete interval computation for depth 13, residue 7035. -/ +theorem bounds_13_7035 : exactInterval 13 7035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7035 : oddCount 7035 13 = 8 ∧ acceleratedOrbit 13 7035 = 5636 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7035) = 3 ^ 8 * m + 5636 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7035.1, data_13_7035.2] + +/-- Complete interval computation for depth 13, residue 7036. -/ +theorem bounds_13_7036 : exactInterval 13 7036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7036 : oddCount 7036 13 = 7 ∧ acceleratedOrbit 13 7036 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7036) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7036.1, data_13_7036.2] + +/-- Complete interval computation for depth 13, residue 7037. -/ +theorem bounds_13_7037 : exactInterval 13 7037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7037 : oddCount 7037 13 = 7 ∧ acceleratedOrbit 13 7037 = 1880 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7037) = 3 ^ 7 * m + 1880 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7037.1, data_13_7037.2] + +/-- Complete interval computation for depth 13, residue 7038. -/ +theorem bounds_13_7038 : exactInterval 13 7038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7038 : oddCount 7038 13 = 10 ∧ acceleratedOrbit 13 7038 = 50746 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7038) = 3 ^ 10 * m + 50746 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7038.1, data_13_7038.2] + +/-- Complete interval computation for depth 13, residue 7039. -/ +theorem bounds_13_7039 : exactInterval 13 7039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7039 : oddCount 7039 13 = 10 ∧ acceleratedOrbit 13 7039 = 50746 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7039) = 3 ^ 10 * m + 50746 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7039.1, data_13_7039.2] + +end Collatz.Research.StoppingAtlas.Batch0925 From ea1faab38cd83e7d091b1ca807535012666a8718 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:24 +0530 Subject: [PATCH 0926/1001] proof: certify atlas Batch0926 (13:7040 to 13:7054) --- Collatz/Research/StoppingAtlas/Batch0926.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0926.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0926.lean b/Collatz/Research/StoppingAtlas/Batch0926.lean new file mode 100644 index 00000000..1061025c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0926.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0926 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7040. -/ +theorem bounds_13_7040 : exactInterval 13 7040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7040 : oddCount 7040 13 = 4 ∧ acceleratedOrbit 13 7040 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7040) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7040.1, data_13_7040.2] + +/-- Complete interval computation for depth 13, residue 7041. -/ +theorem bounds_13_7041 : exactInterval 13 7041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7041 : oddCount 7041 13 = 9 ∧ acceleratedOrbit 13 7041 = 16928 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7041) = 3 ^ 9 * m + 16928 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7041.1, data_13_7041.2] + +/-- Complete interval computation for depth 13, residue 7042. -/ +theorem bounds_13_7042 : exactInterval 13 7042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7042 : oddCount 7042 13 = 7 ∧ acceleratedOrbit 13 7042 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7042) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7042.1, data_13_7042.2] + +/-- Complete interval computation for depth 13, residue 7043. -/ +theorem bounds_13_7043 : exactInterval 13 7043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7043 : oddCount 7043 13 = 7 ∧ acceleratedOrbit 13 7043 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7043) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7043.1, data_13_7043.2] + +/-- Complete interval computation for depth 13, residue 7044. -/ +theorem bounds_13_7044 : exactInterval 13 7044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7044 : oddCount 7044 13 = 7 ∧ acceleratedOrbit 13 7044 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7044) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7044.1, data_13_7044.2] + +/-- Complete interval computation for depth 13, residue 7045. -/ +theorem bounds_13_7045 : exactInterval 13 7045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7045 : oddCount 7045 13 = 7 ∧ acceleratedOrbit 13 7045 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7045) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7045.1, data_13_7045.2] + +/-- Complete interval computation for depth 13, residue 7046. -/ +theorem bounds_13_7046 : exactInterval 13 7046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7046 : oddCount 7046 13 = 7 ∧ acceleratedOrbit 13 7046 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7046) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7046.1, data_13_7046.2] + +/-- Complete interval computation for depth 13, residue 7047. -/ +theorem bounds_13_7047 : exactInterval 13 7047 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7047) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7047 : oddCount 7047 13 = 7 ∧ acceleratedOrbit 13 7047 = 1883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7047) = 3 ^ 7 * m + 1883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7047.1, data_13_7047.2] + +/-- Complete interval computation for depth 13, residue 7048. -/ +theorem bounds_13_7048 : exactInterval 13 7048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7048 : oddCount 7048 13 = 4 ∧ acceleratedOrbit 13 7048 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7048) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7048.1, data_13_7048.2] + +/-- Complete interval computation for depth 13, residue 7049. -/ +theorem bounds_13_7049 : exactInterval 13 7049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7049 : oddCount 7049 13 = 9 ∧ acceleratedOrbit 13 7049 = 16942 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7049) = 3 ^ 9 * m + 16942 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7049.1, data_13_7049.2] + +/-- Complete interval computation for depth 13, residue 7050. -/ +theorem bounds_13_7050 : exactInterval 13 7050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7050 : oddCount 7050 13 = 4 ∧ acceleratedOrbit 13 7050 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7050) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7050.1, data_13_7050.2] + +/-- Complete interval computation for depth 13, residue 7051. -/ +theorem bounds_13_7051 : exactInterval 13 7051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7051 : oddCount 7051 13 = 9 ∧ acceleratedOrbit 13 7051 = 16949 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7051) = 3 ^ 9 * m + 16949 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7051.1, data_13_7051.2] + +/-- Complete interval computation for depth 13, residue 7052. -/ +theorem bounds_13_7052 : exactInterval 13 7052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7052 : oddCount 7052 13 = 4 ∧ acceleratedOrbit 13 7052 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7052) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7052.1, data_13_7052.2] + +/-- Complete interval computation for depth 13, residue 7053. -/ +theorem bounds_13_7053 : exactInterval 13 7053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7053 : oddCount 7053 13 = 4 ∧ acceleratedOrbit 13 7053 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7053) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7053.1, data_13_7053.2] + +/-- Complete interval computation for depth 13, residue 7054. -/ +theorem bounds_13_7054 : exactInterval 13 7054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7054 : oddCount 7054 13 = 6 ∧ acceleratedOrbit 13 7054 = 628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7054) = 3 ^ 6 * m + 628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7054.1, data_13_7054.2] + +end Collatz.Research.StoppingAtlas.Batch0926 From 9279dc6637b81bce68231502ac046738fa395230 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:24 +0530 Subject: [PATCH 0927/1001] proof: certify atlas Batch0927 (13:7055 to 13:7069) --- Collatz/Research/StoppingAtlas/Batch0927.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0927.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0927.lean b/Collatz/Research/StoppingAtlas/Batch0927.lean new file mode 100644 index 00000000..d6b26821 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0927.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0927 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7055. -/ +theorem bounds_13_7055 : exactInterval 13 7055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7055 : oddCount 7055 13 = 6 ∧ acceleratedOrbit 13 7055 = 628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7055) = 3 ^ 6 * m + 628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7055.1, data_13_7055.2] + +/-- Complete interval computation for depth 13, residue 7056. -/ +theorem bounds_13_7056 : exactInterval 13 7056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7056 : oddCount 7056 13 = 4 ∧ acceleratedOrbit 13 7056 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7056) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7056.1, data_13_7056.2] + +/-- Complete interval computation for depth 13, residue 7057. -/ +theorem bounds_13_7057 : exactInterval 13 7057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7057 : oddCount 7057 13 = 6 ∧ acceleratedOrbit 13 7057 = 629 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7057) = 3 ^ 6 * m + 629 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7057.1, data_13_7057.2] + +/-- Complete interval computation for depth 13, residue 7058. -/ +theorem bounds_13_7058 : exactInterval 13 7058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7058 : oddCount 7058 13 = 6 ∧ acceleratedOrbit 13 7058 = 629 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7058) = 3 ^ 6 * m + 629 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7058.1, data_13_7058.2] + +/-- Complete interval computation for depth 13, residue 7059. -/ +theorem bounds_13_7059 : exactInterval 13 7059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7059 : oddCount 7059 13 = 6 ∧ acceleratedOrbit 13 7059 = 629 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7059) = 3 ^ 6 * m + 629 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7059.1, data_13_7059.2] + +/-- Complete interval computation for depth 13, residue 7060. -/ +theorem bounds_13_7060 : exactInterval 13 7060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7060 : oddCount 7060 13 = 4 ∧ acceleratedOrbit 13 7060 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7060) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7060.1, data_13_7060.2] + +/-- Complete interval computation for depth 13, residue 7061. -/ +theorem bounds_13_7061 : exactInterval 13 7061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7061 : oddCount 7061 13 = 4 ∧ acceleratedOrbit 13 7061 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7061) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7061.1, data_13_7061.2] + +/-- Complete interval computation for depth 13, residue 7062. -/ +theorem bounds_13_7062 : exactInterval 13 7062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7062 : oddCount 7062 13 = 7 ∧ acceleratedOrbit 13 7062 = 1889 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7062) = 3 ^ 7 * m + 1889 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7062.1, data_13_7062.2] + +/-- Complete interval computation for depth 13, residue 7063. -/ +theorem bounds_13_7063 : exactInterval 13 7063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7063 : oddCount 7063 13 = 7 ∧ acceleratedOrbit 13 7063 = 1889 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7063) = 3 ^ 7 * m + 1889 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7063.1, data_13_7063.2] + +/-- Complete interval computation for depth 13, residue 7064. -/ +theorem bounds_13_7064 : exactInterval 13 7064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7064 : oddCount 7064 13 = 4 ∧ acceleratedOrbit 13 7064 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7064) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7064.1, data_13_7064.2] + +/-- Complete interval computation for depth 13, residue 7065. -/ +theorem bounds_13_7065 : exactInterval 13 7065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7065 : oddCount 7065 13 = 7 ∧ acceleratedOrbit 13 7065 = 1889 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7065) = 3 ^ 7 * m + 1889 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7065.1, data_13_7065.2] + +/-- Complete interval computation for depth 13, residue 7066. -/ +theorem bounds_13_7066 : exactInterval 13 7066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7066 : oddCount 7066 13 = 4 ∧ acceleratedOrbit 13 7066 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7066) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7066.1, data_13_7066.2] + +/-- Complete interval computation for depth 13, residue 7067. -/ +theorem bounds_13_7067 : exactInterval 13 7067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7067 : oddCount 7067 13 = 6 ∧ acceleratedOrbit 13 7067 = 629 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7067) = 3 ^ 6 * m + 629 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7067.1, data_13_7067.2] + +/-- Complete interval computation for depth 13, residue 7068. -/ +theorem bounds_13_7068 : exactInterval 13 7068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7068 : oddCount 7068 13 = 8 ∧ acceleratedOrbit 13 7068 = 5665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7068) = 3 ^ 8 * m + 5665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7068.1, data_13_7068.2] + +/-- Complete interval computation for depth 13, residue 7069. -/ +theorem bounds_13_7069 : exactInterval 13 7069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7069 : oddCount 7069 13 = 8 ∧ acceleratedOrbit 13 7069 = 5665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7069) = 3 ^ 8 * m + 5665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7069.1, data_13_7069.2] + +end Collatz.Research.StoppingAtlas.Batch0927 From 4e8a62df4dd5d2e38731350b23c6709e45e96a88 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:24 +0530 Subject: [PATCH 0928/1001] proof: certify atlas Batch0928 (13:7070 to 13:7085) --- Collatz/Research/StoppingAtlas/Batch0928.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0928.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0928.lean b/Collatz/Research/StoppingAtlas/Batch0928.lean new file mode 100644 index 00000000..d5111530 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0928.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0928 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7070. -/ +theorem bounds_13_7070 : exactInterval 13 7070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7070 : oddCount 7070 13 = 8 ∧ acceleratedOrbit 13 7070 = 5665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7070) = 3 ^ 8 * m + 5665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7070.1, data_13_7070.2] + +/-- Complete interval computation for depth 13, residue 7071. -/ +theorem bounds_13_7071 : exactInterval 13 7071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7071 : oddCount 7071 13 = 7 ∧ acceleratedOrbit 13 7071 = 1888 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7071) = 3 ^ 7 * m + 1888 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7071.1, data_13_7071.2] + +/-- Complete interval computation for depth 13, residue 7072. -/ +theorem bounds_13_7072 : exactInterval 13 7072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7072 : oddCount 7072 13 = 4 ∧ acceleratedOrbit 13 7072 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7072) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7072.1, data_13_7072.2] + +/-- Complete interval computation for depth 13, residue 7073. -/ +theorem bounds_13_7073 : exactInterval 13 7073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7073 : oddCount 7073 13 = 8 ∧ acceleratedOrbit 13 7073 = 5669 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7073) = 3 ^ 8 * m + 5669 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7073.1, data_13_7073.2] + +/-- Complete interval computation for depth 13, residue 7074. -/ +theorem bounds_13_7074 : exactInterval 13 7074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7074 : oddCount 7074 13 = 4 ∧ acceleratedOrbit 13 7074 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7074) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7074.1, data_13_7074.2] + +/-- Complete interval computation for depth 13, residue 7075. -/ +theorem bounds_13_7075 : exactInterval 13 7075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7075 : oddCount 7075 13 = 4 ∧ acceleratedOrbit 13 7075 = 70 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7075) = 3 ^ 4 * m + 70 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7075.1, data_13_7075.2] + +/-- Complete interval computation for depth 13, residue 7076. -/ +theorem bounds_13_7076 : exactInterval 13 7076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7076 : oddCount 7076 13 = 7 ∧ acceleratedOrbit 13 7076 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7076) = 3 ^ 7 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7076.1, data_13_7076.2] + +/-- Complete interval computation for depth 13, residue 7077. -/ +theorem bounds_13_7077 : exactInterval 13 7077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7077 : oddCount 7077 13 = 7 ∧ acceleratedOrbit 13 7077 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7077) = 3 ^ 7 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7077.1, data_13_7077.2] + +/-- Complete interval computation for depth 13, residue 7078. -/ +theorem bounds_13_7078 : exactInterval 13 7078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7078 : oddCount 7078 13 = 7 ∧ acceleratedOrbit 13 7078 = 1891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7078) = 3 ^ 7 * m + 1891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7078.1, data_13_7078.2] + +/-- Complete interval computation for depth 13, residue 7079. -/ +theorem bounds_13_7079 : exactInterval 13 7079 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7079) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7079 : oddCount 7079 13 = 8 ∧ acceleratedOrbit 13 7079 = 5671 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7079) = 3 ^ 8 * m + 5671 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7079.1, data_13_7079.2] + +/-- Complete interval computation for depth 13, residue 7080. -/ +theorem bounds_13_7080 : exactInterval 13 7080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7080 : oddCount 7080 13 = 4 ∧ acceleratedOrbit 13 7080 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7080) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7080.1, data_13_7080.2] + +/-- Complete interval computation for depth 13, residue 7081. -/ +theorem bounds_13_7081 : exactInterval 13 7081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7081 : oddCount 7081 13 = 9 ∧ acceleratedOrbit 13 7081 = 17018 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7081) = 3 ^ 9 * m + 17018 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7081.1, data_13_7081.2] + +/-- Complete interval computation for depth 13, residue 7082. -/ +theorem bounds_13_7082 : exactInterval 13 7082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7082 : oddCount 7082 13 = 4 ∧ acceleratedOrbit 13 7082 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7082) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7082.1, data_13_7082.2] + +/-- Complete interval computation for depth 13, residue 7083. -/ +theorem bounds_13_7083 : exactInterval 13 7083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7083 : oddCount 7083 13 = 7 ∧ acceleratedOrbit 13 7083 = 1892 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7083) = 3 ^ 7 * m + 1892 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7083.1, data_13_7083.2] + +/-- Complete interval computation for depth 13, residue 7084. -/ +theorem bounds_13_7084 : exactInterval 13 7084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7084 : oddCount 7084 13 = 6 ∧ acceleratedOrbit 13 7084 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7084) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7084.1, data_13_7084.2] + +/-- Complete interval computation for depth 13, residue 7085. -/ +theorem bounds_13_7085 : exactInterval 13 7085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7085 : oddCount 7085 13 = 6 ∧ acceleratedOrbit 13 7085 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7085) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7085.1, data_13_7085.2] + +end Collatz.Research.StoppingAtlas.Batch0928 From a9f8163fcefe0ce950a8f1bd800262a772fc949b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:25 +0530 Subject: [PATCH 0929/1001] proof: certify atlas Batch0929 (13:7086 to 13:7100) --- Collatz/Research/StoppingAtlas/Batch0929.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0929.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0929.lean b/Collatz/Research/StoppingAtlas/Batch0929.lean new file mode 100644 index 00000000..8bf076be --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0929.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0929 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7086. -/ +theorem bounds_13_7086 : exactInterval 13 7086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7086 : oddCount 7086 13 = 6 ∧ acceleratedOrbit 13 7086 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7086) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7086.1, data_13_7086.2] + +/-- Complete interval computation for depth 13, residue 7087. -/ +theorem bounds_13_7087 : exactInterval 13 7087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7087 : oddCount 7087 13 = 6 ∧ acceleratedOrbit 13 7087 = 631 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7087) = 3 ^ 6 * m + 631 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7087.1, data_13_7087.2] + +/-- Complete interval computation for depth 13, residue 7088. -/ +theorem bounds_13_7088 : exactInterval 13 7088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7088 : oddCount 7088 13 = 5 ∧ acceleratedOrbit 13 7088 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7088) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7088.1, data_13_7088.2] + +/-- Complete interval computation for depth 13, residue 7089. -/ +theorem bounds_13_7089 : exactInterval 13 7089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7089 : oddCount 7089 13 = 5 ∧ acceleratedOrbit 13 7089 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7089) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7089.1, data_13_7089.2] + +/-- Complete interval computation for depth 13, residue 7090. -/ +theorem bounds_13_7090 : exactInterval 13 7090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7090 : oddCount 7090 13 = 5 ∧ acceleratedOrbit 13 7090 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7090) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7090.1, data_13_7090.2] + +/-- Complete interval computation for depth 13, residue 7091. -/ +theorem bounds_13_7091 : exactInterval 13 7091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7091 : oddCount 7091 13 = 5 ∧ acceleratedOrbit 13 7091 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7091) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7091.1, data_13_7091.2] + +/-- Complete interval computation for depth 13, residue 7092. -/ +theorem bounds_13_7092 : exactInterval 13 7092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7092 : oddCount 7092 13 = 5 ∧ acceleratedOrbit 13 7092 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7092) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7092.1, data_13_7092.2] + +/-- Complete interval computation for depth 13, residue 7093. -/ +theorem bounds_13_7093 : exactInterval 13 7093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7093 : oddCount 7093 13 = 5 ∧ acceleratedOrbit 13 7093 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7093) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7093.1, data_13_7093.2] + +/-- Complete interval computation for depth 13, residue 7094. -/ +theorem bounds_13_7094 : exactInterval 13 7094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7094 : oddCount 7094 13 = 6 ∧ acceleratedOrbit 13 7094 = 632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7094) = 3 ^ 6 * m + 632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7094.1, data_13_7094.2] + +/-- Complete interval computation for depth 13, residue 7095. -/ +theorem bounds_13_7095 : exactInterval 13 7095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7095 : oddCount 7095 13 = 6 ∧ acceleratedOrbit 13 7095 = 632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7095) = 3 ^ 6 * m + 632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7095.1, data_13_7095.2] + +/-- Complete interval computation for depth 13, residue 7096. -/ +theorem bounds_13_7096 : exactInterval 13 7096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7096 : oddCount 7096 13 = 5 ∧ acceleratedOrbit 13 7096 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7096) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7096.1, data_13_7096.2] + +/-- Complete interval computation for depth 13, residue 7097. -/ +theorem bounds_13_7097 : exactInterval 13 7097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7097 : oddCount 7097 13 = 6 ∧ acceleratedOrbit 13 7097 = 632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7097) = 3 ^ 6 * m + 632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7097.1, data_13_7097.2] + +/-- Complete interval computation for depth 13, residue 7098. -/ +theorem bounds_13_7098 : exactInterval 13 7098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7098 : oddCount 7098 13 = 5 ∧ acceleratedOrbit 13 7098 = 211 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7098) = 3 ^ 5 * m + 211 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7098.1, data_13_7098.2] + +/-- Complete interval computation for depth 13, residue 7099. -/ +theorem bounds_13_7099 : exactInterval 13 7099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7099 : oddCount 7099 13 = 6 ∧ acceleratedOrbit 13 7099 = 632 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7099) = 3 ^ 6 * m + 632 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7099.1, data_13_7099.2] + +/-- Complete interval computation for depth 13, residue 7100. -/ +theorem bounds_13_7100 : exactInterval 13 7100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7100 : oddCount 7100 13 = 8 ∧ acceleratedOrbit 13 7100 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7100) = 3 ^ 8 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7100.1, data_13_7100.2] + +end Collatz.Research.StoppingAtlas.Batch0929 From 471505b9b544da80a9b0fed64ccc4987c0f4a3b7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:25 +0530 Subject: [PATCH 0930/1001] proof: certify atlas Batch0930 (13:7101 to 13:7115) --- Collatz/Research/StoppingAtlas/Batch0930.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0930.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0930.lean b/Collatz/Research/StoppingAtlas/Batch0930.lean new file mode 100644 index 00000000..b753d985 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0930.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0930 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7101. -/ +theorem bounds_13_7101 : exactInterval 13 7101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7101 : oddCount 7101 13 = 8 ∧ acceleratedOrbit 13 7101 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7101) = 3 ^ 8 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7101.1, data_13_7101.2] + +/-- Complete interval computation for depth 13, residue 7102. -/ +theorem bounds_13_7102 : exactInterval 13 7102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7102 : oddCount 7102 13 = 8 ∧ acceleratedOrbit 13 7102 = 5690 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7102) = 3 ^ 8 * m + 5690 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7102.1, data_13_7102.2] + +/-- Complete interval computation for depth 13, residue 7103. -/ +theorem bounds_13_7103 : exactInterval 13 7103 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7103) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7103 : oddCount 7103 13 = 9 ∧ acceleratedOrbit 13 7103 = 17069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7103) = 3 ^ 9 * m + 17069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7103.1, data_13_7103.2] + +/-- Complete interval computation for depth 13, residue 7104. -/ +theorem bounds_13_7104 : exactInterval 13 7104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7104 : oddCount 7104 13 = 6 ∧ acceleratedOrbit 13 7104 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7104) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7104.1, data_13_7104.2] + +/-- Complete interval computation for depth 13, residue 7105. -/ +theorem bounds_13_7105 : exactInterval 13 7105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7105 : oddCount 7105 13 = 8 ∧ acceleratedOrbit 13 7105 = 5696 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7105) = 3 ^ 8 * m + 5696 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7105.1, data_13_7105.2] + +/-- Complete interval computation for depth 13, residue 7106. -/ +theorem bounds_13_7106 : exactInterval 13 7106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7106 : oddCount 7106 13 = 8 ∧ acceleratedOrbit 13 7106 = 5696 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7106) = 3 ^ 8 * m + 5696 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7106.1, data_13_7106.2] + +/-- Complete interval computation for depth 13, residue 7107. -/ +theorem bounds_13_7107 : exactInterval 13 7107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7107 : oddCount 7107 13 = 8 ∧ acceleratedOrbit 13 7107 = 5696 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7107) = 3 ^ 8 * m + 5696 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7107.1, data_13_7107.2] + +/-- Complete interval computation for depth 13, residue 7108. -/ +theorem bounds_13_7108 : exactInterval 13 7108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7108 : oddCount 7108 13 = 4 ∧ acceleratedOrbit 13 7108 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7108) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7108.1, data_13_7108.2] + +/-- Complete interval computation for depth 13, residue 7109. -/ +theorem bounds_13_7109 : exactInterval 13 7109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7109 : oddCount 7109 13 = 4 ∧ acceleratedOrbit 13 7109 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7109) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7109.1, data_13_7109.2] + +/-- Complete interval computation for depth 13, residue 7110. -/ +theorem bounds_13_7110 : exactInterval 13 7110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7110 : oddCount 7110 13 = 4 ∧ acceleratedOrbit 13 7110 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7110) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7110.1, data_13_7110.2] + +/-- Complete interval computation for depth 13, residue 7111. -/ +theorem bounds_13_7111 : exactInterval 13 7111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7111 : oddCount 7111 13 = 10 ∧ acceleratedOrbit 13 7111 = 51272 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7111) = 3 ^ 10 * m + 51272 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7111.1, data_13_7111.2] + +/-- Complete interval computation for depth 13, residue 7112. -/ +theorem bounds_13_7112 : exactInterval 13 7112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7112 : oddCount 7112 13 = 7 ∧ acceleratedOrbit 13 7112 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7112) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7112.1, data_13_7112.2] + +/-- Complete interval computation for depth 13, residue 7113. -/ +theorem bounds_13_7113 : exactInterval 13 7113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7113 : oddCount 7113 13 = 7 ∧ acceleratedOrbit 13 7113 = 1900 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7113) = 3 ^ 7 * m + 1900 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7113.1, data_13_7113.2] + +/-- Complete interval computation for depth 13, residue 7114. -/ +theorem bounds_13_7114 : exactInterval 13 7114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7114 : oddCount 7114 13 = 7 ∧ acceleratedOrbit 13 7114 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7114) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7114.1, data_13_7114.2] + +/-- Complete interval computation for depth 13, residue 7115. -/ +theorem bounds_13_7115 : exactInterval 13 7115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7115 : oddCount 7115 13 = 6 ∧ acceleratedOrbit 13 7115 = 634 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7115) = 3 ^ 6 * m + 634 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7115.1, data_13_7115.2] + +end Collatz.Research.StoppingAtlas.Batch0930 From 3e2e47048d9e06d505128d58f3a4df2bf5765245 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:25 +0530 Subject: [PATCH 0931/1001] proof: certify atlas Batch0931 (13:7116 to 13:7131) --- Collatz/Research/StoppingAtlas/Batch0931.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0931.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0931.lean b/Collatz/Research/StoppingAtlas/Batch0931.lean new file mode 100644 index 00000000..d40fa0a8 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0931.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0931 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7116. -/ +theorem bounds_13_7116 : exactInterval 13 7116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7116 : oddCount 7116 13 = 7 ∧ acceleratedOrbit 13 7116 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7116) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7116.1, data_13_7116.2] + +/-- Complete interval computation for depth 13, residue 7117. -/ +theorem bounds_13_7117 : exactInterval 13 7117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7117 : oddCount 7117 13 = 7 ∧ acceleratedOrbit 13 7117 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7117) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7117.1, data_13_7117.2] + +/-- Complete interval computation for depth 13, residue 7118. -/ +theorem bounds_13_7118 : exactInterval 13 7118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7118 : oddCount 7118 13 = 7 ∧ acceleratedOrbit 13 7118 = 1901 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7118) = 3 ^ 7 * m + 1901 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7118.1, data_13_7118.2] + +/-- Complete interval computation for depth 13, residue 7119. -/ +theorem bounds_13_7119 : exactInterval 13 7119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7119 : oddCount 7119 13 = 7 ∧ acceleratedOrbit 13 7119 = 1901 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7119) = 3 ^ 7 * m + 1901 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7119.1, data_13_7119.2] + +/-- Complete interval computation for depth 13, residue 7120. -/ +theorem bounds_13_7120 : exactInterval 13 7120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7120 : oddCount 7120 13 = 6 ∧ acceleratedOrbit 13 7120 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7120) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7120.1, data_13_7120.2] + +/-- Complete interval computation for depth 13, residue 7121. -/ +theorem bounds_13_7121 : exactInterval 13 7121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7121 : oddCount 7121 13 = 7 ∧ acceleratedOrbit 13 7121 = 1903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7121) = 3 ^ 7 * m + 1903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7121.1, data_13_7121.2] + +/-- Complete interval computation for depth 13, residue 7122. -/ +theorem bounds_13_7122 : exactInterval 13 7122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7122 : oddCount 7122 13 = 8 ∧ acceleratedOrbit 13 7122 = 5707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7122) = 3 ^ 8 * m + 5707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7122.1, data_13_7122.2] + +/-- Complete interval computation for depth 13, residue 7123. -/ +theorem bounds_13_7123 : exactInterval 13 7123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7123 : oddCount 7123 13 = 8 ∧ acceleratedOrbit 13 7123 = 5707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7123) = 3 ^ 8 * m + 5707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7123.1, data_13_7123.2] + +/-- Complete interval computation for depth 13, residue 7124. -/ +theorem bounds_13_7124 : exactInterval 13 7124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7124 : oddCount 7124 13 = 6 ∧ acceleratedOrbit 13 7124 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7124) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7124.1, data_13_7124.2] + +/-- Complete interval computation for depth 13, residue 7125. -/ +theorem bounds_13_7125 : exactInterval 13 7125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7125 : oddCount 7125 13 = 6 ∧ acceleratedOrbit 13 7125 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7125) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7125.1, data_13_7125.2] + +/-- Complete interval computation for depth 13, residue 7126. -/ +theorem bounds_13_7126 : exactInterval 13 7126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7126 : oddCount 7126 13 = 9 ∧ acceleratedOrbit 13 7126 = 17131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7126) = 3 ^ 9 * m + 17131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7126.1, data_13_7126.2] + +/-- Complete interval computation for depth 13, residue 7127. -/ +theorem bounds_13_7127 : exactInterval 13 7127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7127 : oddCount 7127 13 = 9 ∧ acceleratedOrbit 13 7127 = 17131 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7127) = 3 ^ 9 * m + 17131 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7127.1, data_13_7127.2] + +/-- Complete interval computation for depth 13, residue 7128. -/ +theorem bounds_13_7128 : exactInterval 13 7128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7128 : oddCount 7128 13 = 7 ∧ acceleratedOrbit 13 7128 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7128) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7128.1, data_13_7128.2] + +/-- Complete interval computation for depth 13, residue 7129. -/ +theorem bounds_13_7129 : exactInterval 13 7129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7129 : oddCount 7129 13 = 4 ∧ acceleratedOrbit 13 7129 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7129) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7129.1, data_13_7129.2] + +/-- Complete interval computation for depth 13, residue 7130. -/ +theorem bounds_13_7130 : exactInterval 13 7130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7130 : oddCount 7130 13 = 7 ∧ acceleratedOrbit 13 7130 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7130) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7130.1, data_13_7130.2] + +/-- Complete interval computation for depth 13, residue 7131. -/ +theorem bounds_13_7131 : exactInterval 13 7131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7131 : oddCount 7131 13 = 8 ∧ acceleratedOrbit 13 7131 = 5714 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7131) = 3 ^ 8 * m + 5714 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7131.1, data_13_7131.2] + +end Collatz.Research.StoppingAtlas.Batch0931 From b09bd60bf3b24048556183052e8b863eebad1da9 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:25 +0530 Subject: [PATCH 0932/1001] proof: certify atlas Batch0932 (13:7132 to 13:7146) --- Collatz/Research/StoppingAtlas/Batch0932.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0932.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0932.lean b/Collatz/Research/StoppingAtlas/Batch0932.lean new file mode 100644 index 00000000..7aed2a1b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0932.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0932 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7132. -/ +theorem bounds_13_7132 : exactInterval 13 7132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7132 : oddCount 7132 13 = 7 ∧ acceleratedOrbit 13 7132 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7132) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7132.1, data_13_7132.2] + +/-- Complete interval computation for depth 13, residue 7133. -/ +theorem bounds_13_7133 : exactInterval 13 7133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7133 : oddCount 7133 13 = 7 ∧ acceleratedOrbit 13 7133 = 1907 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7133) = 3 ^ 7 * m + 1907 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7133.1, data_13_7133.2] + +/-- Complete interval computation for depth 13, residue 7134. -/ +theorem bounds_13_7134 : exactInterval 13 7134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7134 : oddCount 7134 13 = 9 ∧ acceleratedOrbit 13 7134 = 17147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7134) = 3 ^ 9 * m + 17147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7134.1, data_13_7134.2] + +/-- Complete interval computation for depth 13, residue 7135. -/ +theorem bounds_13_7135 : exactInterval 13 7135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7135 : oddCount 7135 13 = 9 ∧ acceleratedOrbit 13 7135 = 17147 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7135) = 3 ^ 9 * m + 17147 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7135.1, data_13_7135.2] + +/-- Complete interval computation for depth 13, residue 7136. -/ +theorem bounds_13_7136 : exactInterval 13 7136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7136 : oddCount 7136 13 = 6 ∧ acceleratedOrbit 13 7136 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7136) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7136.1, data_13_7136.2] + +/-- Complete interval computation for depth 13, residue 7137. -/ +theorem bounds_13_7137 : exactInterval 13 7137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7137 : oddCount 7137 13 = 7 ∧ acceleratedOrbit 13 7137 = 1906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7137) = 3 ^ 7 * m + 1906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7137.1, data_13_7137.2] + +/-- Complete interval computation for depth 13, residue 7138. -/ +theorem bounds_13_7138 : exactInterval 13 7138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7138 : oddCount 7138 13 = 6 ∧ acceleratedOrbit 13 7138 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7138) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7138.1, data_13_7138.2] + +/-- Complete interval computation for depth 13, residue 7139. -/ +theorem bounds_13_7139 : exactInterval 13 7139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7139 : oddCount 7139 13 = 6 ∧ acceleratedOrbit 13 7139 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7139) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7139.1, data_13_7139.2] + +/-- Complete interval computation for depth 13, residue 7140. -/ +theorem bounds_13_7140 : exactInterval 13 7140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7140 : oddCount 7140 13 = 5 ∧ acceleratedOrbit 13 7140 = 212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7140) = 3 ^ 5 * m + 212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7140.1, data_13_7140.2] + +/-- Complete interval computation for depth 13, residue 7141. -/ +theorem bounds_13_7141 : exactInterval 13 7141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7141 : oddCount 7141 13 = 5 ∧ acceleratedOrbit 13 7141 = 212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7141) = 3 ^ 5 * m + 212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7141.1, data_13_7141.2] + +/-- Complete interval computation for depth 13, residue 7142. -/ +theorem bounds_13_7142 : exactInterval 13 7142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7142 : oddCount 7142 13 = 5 ∧ acceleratedOrbit 13 7142 = 212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7142) = 3 ^ 5 * m + 212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7142.1, data_13_7142.2] + +/-- Complete interval computation for depth 13, residue 7143. -/ +theorem bounds_13_7143 : exactInterval 13 7143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7143 : oddCount 7143 13 = 8 ∧ acceleratedOrbit 13 7143 = 5723 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7143) = 3 ^ 8 * m + 5723 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7143.1, data_13_7143.2] + +/-- Complete interval computation for depth 13, residue 7144. -/ +theorem bounds_13_7144 : exactInterval 13 7144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7144 : oddCount 7144 13 = 6 ∧ acceleratedOrbit 13 7144 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7144) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7144.1, data_13_7144.2] + +/-- Complete interval computation for depth 13, residue 7145. -/ +theorem bounds_13_7145 : exactInterval 13 7145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7145 : oddCount 7145 13 = 11 ∧ acceleratedOrbit 13 7145 = 154547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7145) = 3 ^ 11 * m + 154547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7145.1, data_13_7145.2] + +/-- Complete interval computation for depth 13, residue 7146. -/ +theorem bounds_13_7146 : exactInterval 13 7146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7146 : oddCount 7146 13 = 6 ∧ acceleratedOrbit 13 7146 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7146) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7146.1, data_13_7146.2] + +end Collatz.Research.StoppingAtlas.Batch0932 From dd02831a04ec4fd6a651e7b448aa4aa48a680984 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:25 +0530 Subject: [PATCH 0933/1001] proof: certify atlas Batch0933 (13:7147 to 13:7161) --- Collatz/Research/StoppingAtlas/Batch0933.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0933.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0933.lean b/Collatz/Research/StoppingAtlas/Batch0933.lean new file mode 100644 index 00000000..d4579c10 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0933.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0933 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7147. -/ +theorem bounds_13_7147 : exactInterval 13 7147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7147 : oddCount 7147 13 = 8 ∧ acceleratedOrbit 13 7147 = 5726 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7147) = 3 ^ 8 * m + 5726 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7147.1, data_13_7147.2] + +/-- Complete interval computation for depth 13, residue 7148. -/ +theorem bounds_13_7148 : exactInterval 13 7148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7148 : oddCount 7148 13 = 7 ∧ acceleratedOrbit 13 7148 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7148) = 3 ^ 7 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7148.1, data_13_7148.2] + +/-- Complete interval computation for depth 13, residue 7149. -/ +theorem bounds_13_7149 : exactInterval 13 7149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7149 : oddCount 7149 13 = 7 ∧ acceleratedOrbit 13 7149 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7149) = 3 ^ 7 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7149.1, data_13_7149.2] + +/-- Complete interval computation for depth 13, residue 7150. -/ +theorem bounds_13_7150 : exactInterval 13 7150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7150 : oddCount 7150 13 = 7 ∧ acceleratedOrbit 13 7150 = 1910 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7150) = 3 ^ 7 * m + 1910 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7150.1, data_13_7150.2] + +/-- Complete interval computation for depth 13, residue 7151. -/ +theorem bounds_13_7151 : exactInterval 13 7151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7151 : oddCount 7151 13 = 9 ∧ acceleratedOrbit 13 7151 = 17185 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7151) = 3 ^ 9 * m + 17185 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7151.1, data_13_7151.2] + +/-- Complete interval computation for depth 13, residue 7152. -/ +theorem bounds_13_7152 : exactInterval 13 7152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7152 : oddCount 7152 13 = 8 ∧ acceleratedOrbit 13 7152 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7152) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7152.1, data_13_7152.2] + +/-- Complete interval computation for depth 13, residue 7153. -/ +theorem bounds_13_7153 : exactInterval 13 7153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7153 : oddCount 7153 13 = 6 ∧ acceleratedOrbit 13 7153 = 638 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7153) = 3 ^ 6 * m + 638 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7153.1, data_13_7153.2] + +/-- Complete interval computation for depth 13, residue 7154. -/ +theorem bounds_13_7154 : exactInterval 13 7154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7154 : oddCount 7154 13 = 6 ∧ acceleratedOrbit 13 7154 = 637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7154) = 3 ^ 6 * m + 637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7154.1, data_13_7154.2] + +/-- Complete interval computation for depth 13, residue 7155. -/ +theorem bounds_13_7155 : exactInterval 13 7155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7155 : oddCount 7155 13 = 6 ∧ acceleratedOrbit 13 7155 = 637 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7155) = 3 ^ 6 * m + 637 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7155.1, data_13_7155.2] + +/-- Complete interval computation for depth 13, residue 7156. -/ +theorem bounds_13_7156 : exactInterval 13 7156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7156 : oddCount 7156 13 = 8 ∧ acceleratedOrbit 13 7156 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7156) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7156.1, data_13_7156.2] + +/-- Complete interval computation for depth 13, residue 7157. -/ +theorem bounds_13_7157 : exactInterval 13 7157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7157 : oddCount 7157 13 = 8 ∧ acceleratedOrbit 13 7157 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7157) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7157.1, data_13_7157.2] + +/-- Complete interval computation for depth 13, residue 7158. -/ +theorem bounds_13_7158 : exactInterval 13 7158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7158 : oddCount 7158 13 = 7 ∧ acceleratedOrbit 13 7158 = 1912 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7158) = 3 ^ 7 * m + 1912 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7158.1, data_13_7158.2] + +/-- Complete interval computation for depth 13, residue 7159. -/ +theorem bounds_13_7159 : exactInterval 13 7159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7159 : oddCount 7159 13 = 7 ∧ acceleratedOrbit 13 7159 = 1912 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7159) = 3 ^ 7 * m + 1912 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7159.1, data_13_7159.2] + +/-- Complete interval computation for depth 13, residue 7160. -/ +theorem bounds_13_7160 : exactInterval 13 7160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7160 : oddCount 7160 13 = 8 ∧ acceleratedOrbit 13 7160 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7160) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7160.1, data_13_7160.2] + +/-- Complete interval computation for depth 13, residue 7161. -/ +theorem bounds_13_7161 : exactInterval 13 7161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7161 : oddCount 7161 13 = 9 ∧ acceleratedOrbit 13 7161 = 17212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7161) = 3 ^ 9 * m + 17212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7161.1, data_13_7161.2] + +end Collatz.Research.StoppingAtlas.Batch0933 From 3e5603d3322a34e0ac76687fffbae90461ca1c3b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:26 +0530 Subject: [PATCH 0934/1001] proof: certify atlas Batch0934 (13:7162 to 13:7177) --- Collatz/Research/StoppingAtlas/Batch0934.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0934.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0934.lean b/Collatz/Research/StoppingAtlas/Batch0934.lean new file mode 100644 index 00000000..4b59c80d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0934.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0934 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7162. -/ +theorem bounds_13_7162 : exactInterval 13 7162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7162 : oddCount 7162 13 = 8 ∧ acceleratedOrbit 13 7162 = 5741 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7162) = 3 ^ 8 * m + 5741 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7162.1, data_13_7162.2] + +/-- Complete interval computation for depth 13, residue 7163. -/ +theorem bounds_13_7163 : exactInterval 13 7163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7163 : oddCount 7163 13 = 9 ∧ acceleratedOrbit 13 7163 = 17216 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7163) = 3 ^ 9 * m + 17216 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7163.1, data_13_7163.2] + +/-- Complete interval computation for depth 13, residue 7164. -/ +theorem bounds_13_7164 : exactInterval 13 7164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7164 : oddCount 7164 13 = 10 ∧ acceleratedOrbit 13 7164 = 51668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7164) = 3 ^ 10 * m + 51668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7164.1, data_13_7164.2] + +/-- Complete interval computation for depth 13, residue 7165. -/ +theorem bounds_13_7165 : exactInterval 13 7165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7165 : oddCount 7165 13 = 10 ∧ acceleratedOrbit 13 7165 = 51668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7165) = 3 ^ 10 * m + 51668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7165.1, data_13_7165.2] + +/-- Complete interval computation for depth 13, residue 7166. -/ +theorem bounds_13_7166 : exactInterval 13 7166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7166 : oddCount 7166 13 = 10 ∧ acceleratedOrbit 13 7166 = 51668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7166) = 3 ^ 10 * m + 51668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7166.1, data_13_7166.2] + +/-- Complete interval computation for depth 13, residue 7167. -/ +theorem bounds_13_7167 : exactInterval 13 7167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7167 : oddCount 7167 13 = 12 ∧ acceleratedOrbit 13 7167 = 465011 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7167) = 3 ^ 12 * m + 465011 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7167.1, data_13_7167.2] + +/-- Complete interval computation for depth 13, residue 7168. -/ +theorem bounds_13_7168 : exactInterval 13 7168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7168 : oddCount 7168 13 = 3 ∧ acceleratedOrbit 13 7168 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7168) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7168.1, data_13_7168.2] + +/-- Complete interval computation for depth 13, residue 7169. -/ +theorem bounds_13_7169 : exactInterval 13 7169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7169 : oddCount 7169 13 = 7 ∧ acceleratedOrbit 13 7169 = 1916 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7169) = 3 ^ 7 * m + 1916 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7169.1, data_13_7169.2] + +/-- Complete interval computation for depth 13, residue 7170. -/ +theorem bounds_13_7170 : exactInterval 13 7170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7170 : oddCount 7170 13 = 8 ∧ acceleratedOrbit 13 7170 = 5750 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7170) = 3 ^ 8 * m + 5750 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7170.1, data_13_7170.2] + +/-- Complete interval computation for depth 13, residue 7171. -/ +theorem bounds_13_7171 : exactInterval 13 7171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7171 : oddCount 7171 13 = 8 ∧ acceleratedOrbit 13 7171 = 5750 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7171) = 3 ^ 8 * m + 5750 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7171.1, data_13_7171.2] + +/-- Complete interval computation for depth 13, residue 7172. -/ +theorem bounds_13_7172 : exactInterval 13 7172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7172 : oddCount 7172 13 = 4 ∧ acceleratedOrbit 13 7172 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7172) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7172.1, data_13_7172.2] + +/-- Complete interval computation for depth 13, residue 7173. -/ +theorem bounds_13_7173 : exactInterval 13 7173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7173 : oddCount 7173 13 = 4 ∧ acceleratedOrbit 13 7173 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7173) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7173.1, data_13_7173.2] + +/-- Complete interval computation for depth 13, residue 7174. -/ +theorem bounds_13_7174 : exactInterval 13 7174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7174 : oddCount 7174 13 = 4 ∧ acceleratedOrbit 13 7174 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7174) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7174.1, data_13_7174.2] + +/-- Complete interval computation for depth 13, residue 7175. -/ +theorem bounds_13_7175 : exactInterval 13 7175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7175 : oddCount 7175 13 = 8 ∧ acceleratedOrbit 13 7175 = 5750 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7175) = 3 ^ 8 * m + 5750 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7175.1, data_13_7175.2] + +/-- Complete interval computation for depth 13, residue 7176. -/ +theorem bounds_13_7176 : exactInterval 13 7176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7176 : oddCount 7176 13 = 6 ∧ acceleratedOrbit 13 7176 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7176) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7176.1, data_13_7176.2] + +/-- Complete interval computation for depth 13, residue 7177. -/ +theorem bounds_13_7177 : exactInterval 13 7177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7177 : oddCount 7177 13 = 9 ∧ acceleratedOrbit 13 7177 = 17252 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7177) = 3 ^ 9 * m + 17252 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7177.1, data_13_7177.2] + +end Collatz.Research.StoppingAtlas.Batch0934 From 19caeb04d9c32fdb8032fe4a868615d30c004467 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:26 +0530 Subject: [PATCH 0935/1001] proof: certify atlas Batch0935 (13:7178 to 13:7192) --- Collatz/Research/StoppingAtlas/Batch0935.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0935.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0935.lean b/Collatz/Research/StoppingAtlas/Batch0935.lean new file mode 100644 index 00000000..100fe668 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0935.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0935 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7178. -/ +theorem bounds_13_7178 : exactInterval 13 7178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7178 : oddCount 7178 13 = 6 ∧ acceleratedOrbit 13 7178 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7178) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7178.1, data_13_7178.2] + +/-- Complete interval computation for depth 13, residue 7179. -/ +theorem bounds_13_7179 : exactInterval 13 7179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7179 : oddCount 7179 13 = 4 ∧ acceleratedOrbit 13 7179 = 71 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7179) = 3 ^ 4 * m + 71 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7179.1, data_13_7179.2] + +/-- Complete interval computation for depth 13, residue 7180. -/ +theorem bounds_13_7180 : exactInterval 13 7180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7180 : oddCount 7180 13 = 6 ∧ acceleratedOrbit 13 7180 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7180) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7180.1, data_13_7180.2] + +/-- Complete interval computation for depth 13, residue 7181. -/ +theorem bounds_13_7181 : exactInterval 13 7181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7181 : oddCount 7181 13 = 6 ∧ acceleratedOrbit 13 7181 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7181) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7181.1, data_13_7181.2] + +/-- Complete interval computation for depth 13, residue 7182. -/ +theorem bounds_13_7182 : exactInterval 13 7182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7182 : oddCount 7182 13 = 7 ∧ acceleratedOrbit 13 7182 = 1919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7182) = 3 ^ 7 * m + 1919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7182.1, data_13_7182.2] + +/-- Complete interval computation for depth 13, residue 7183. -/ +theorem bounds_13_7183 : exactInterval 13 7183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7183 : oddCount 7183 13 = 7 ∧ acceleratedOrbit 13 7183 = 1919 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7183) = 3 ^ 7 * m + 1919 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7183.1, data_13_7183.2] + +/-- Complete interval computation for depth 13, residue 7184. -/ +theorem bounds_13_7184 : exactInterval 13 7184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7184 : oddCount 7184 13 = 5 ∧ acceleratedOrbit 13 7184 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7184) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7184.1, data_13_7184.2] + +/-- Complete interval computation for depth 13, residue 7185. -/ +theorem bounds_13_7185 : exactInterval 13 7185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7185 : oddCount 7185 13 = 6 ∧ acceleratedOrbit 13 7185 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7185) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7185.1, data_13_7185.2] + +/-- Complete interval computation for depth 13, residue 7186. -/ +theorem bounds_13_7186 : exactInterval 13 7186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7186 : oddCount 7186 13 = 6 ∧ acceleratedOrbit 13 7186 = 640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7186) = 3 ^ 6 * m + 640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7186.1, data_13_7186.2] + +/-- Complete interval computation for depth 13, residue 7187. -/ +theorem bounds_13_7187 : exactInterval 13 7187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7187 : oddCount 7187 13 = 6 ∧ acceleratedOrbit 13 7187 = 640 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7187) = 3 ^ 6 * m + 640 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7187.1, data_13_7187.2] + +/-- Complete interval computation for depth 13, residue 7188. -/ +theorem bounds_13_7188 : exactInterval 13 7188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7188 : oddCount 7188 13 = 5 ∧ acceleratedOrbit 13 7188 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7188) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7188.1, data_13_7188.2] + +/-- Complete interval computation for depth 13, residue 7189. -/ +theorem bounds_13_7189 : exactInterval 13 7189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7189 : oddCount 7189 13 = 5 ∧ acceleratedOrbit 13 7189 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7189) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7189.1, data_13_7189.2] + +/-- Complete interval computation for depth 13, residue 7190. -/ +theorem bounds_13_7190 : exactInterval 13 7190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7190 : oddCount 7190 13 = 6 ∧ acceleratedOrbit 13 7190 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7190) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7190.1, data_13_7190.2] + +/-- Complete interval computation for depth 13, residue 7191. -/ +theorem bounds_13_7191 : exactInterval 13 7191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7191) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7191 : oddCount 7191 13 = 6 ∧ acceleratedOrbit 13 7191 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7191) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7191.1, data_13_7191.2] + +/-- Complete interval computation for depth 13, residue 7192. -/ +theorem bounds_13_7192 : exactInterval 13 7192 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7192 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7192) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7192 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7192 : oddCount 7192 13 = 5 ∧ acceleratedOrbit 13 7192 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7192 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7192) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7192.1, data_13_7192.2] + +end Collatz.Research.StoppingAtlas.Batch0935 From 21d7c8f6639a8094f5dd1d8ddedf0a4e50cd10fa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:26 +0530 Subject: [PATCH 0936/1001] proof: certify atlas Batch0936 (13:7193 to 13:7207) --- Collatz/Research/StoppingAtlas/Batch0936.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0936.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0936.lean b/Collatz/Research/StoppingAtlas/Batch0936.lean new file mode 100644 index 00000000..ebf8eeea --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0936.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0936 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7193. -/ +theorem bounds_13_7193 : exactInterval 13 7193 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7193 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7193) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7193 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7193 : oddCount 7193 13 = 8 ∧ acceleratedOrbit 13 7193 = 5764 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7193 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7193) = 3 ^ 8 * m + 5764 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7193.1, data_13_7193.2] + +/-- Complete interval computation for depth 13, residue 7194. -/ +theorem bounds_13_7194 : exactInterval 13 7194 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7194 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7194) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7194 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7194 : oddCount 7194 13 = 5 ∧ acceleratedOrbit 13 7194 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7194 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7194) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7194.1, data_13_7194.2] + +/-- Complete interval computation for depth 13, residue 7195. -/ +theorem bounds_13_7195 : exactInterval 13 7195 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7195 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7195) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7195 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7195 : oddCount 7195 13 = 9 ∧ acceleratedOrbit 13 7195 = 17291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7195 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7195) = 3 ^ 9 * m + 17291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7195.1, data_13_7195.2] + +/-- Complete interval computation for depth 13, residue 7196. -/ +theorem bounds_13_7196 : exactInterval 13 7196 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7196 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7196) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7196 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7196 : oddCount 7196 13 = 6 ∧ acceleratedOrbit 13 7196 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7196 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7196) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7196.1, data_13_7196.2] + +/-- Complete interval computation for depth 13, residue 7197. -/ +theorem bounds_13_7197 : exactInterval 13 7197 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7197 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7197) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7197 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7197 : oddCount 7197 13 = 6 ∧ acceleratedOrbit 13 7197 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7197 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7197) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7197.1, data_13_7197.2] + +/-- Complete interval computation for depth 13, residue 7198. -/ +theorem bounds_13_7198 : exactInterval 13 7198 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7198 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7198) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7198 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7198 : oddCount 7198 13 = 6 ∧ acceleratedOrbit 13 7198 = 641 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7198 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7198) = 3 ^ 6 * m + 641 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7198.1, data_13_7198.2] + +/-- Complete interval computation for depth 13, residue 7199. -/ +theorem bounds_13_7199 : exactInterval 13 7199 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7199 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7199) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7199 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7199 : oddCount 7199 13 = 9 ∧ acceleratedOrbit 13 7199 = 17300 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7199 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7199) = 3 ^ 9 * m + 17300 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7199.1, data_13_7199.2] + +/-- Complete interval computation for depth 13, residue 7200. -/ +theorem bounds_13_7200 : exactInterval 13 7200 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7200 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7200) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7200 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7200 : oddCount 7200 13 = 6 ∧ acceleratedOrbit 13 7200 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7200 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7200) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7200.1, data_13_7200.2] + +/-- Complete interval computation for depth 13, residue 7201. -/ +theorem bounds_13_7201 : exactInterval 13 7201 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7201 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7201) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7201 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7201 : oddCount 7201 13 = 8 ∧ acceleratedOrbit 13 7201 = 5771 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7201 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7201) = 3 ^ 8 * m + 5771 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7201.1, data_13_7201.2] + +/-- Complete interval computation for depth 13, residue 7202. -/ +theorem bounds_13_7202 : exactInterval 13 7202 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7202 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7202) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7202 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7202 : oddCount 7202 13 = 5 ∧ acceleratedOrbit 13 7202 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7202 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7202) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7202.1, data_13_7202.2] + +/-- Complete interval computation for depth 13, residue 7203. -/ +theorem bounds_13_7203 : exactInterval 13 7203 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7203 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7203) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7203 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7203 : oddCount 7203 13 = 5 ∧ acceleratedOrbit 13 7203 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7203 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7203) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7203.1, data_13_7203.2] + +/-- Complete interval computation for depth 13, residue 7204. -/ +theorem bounds_13_7204 : exactInterval 13 7204 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7204 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7204) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7204 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7204 : oddCount 7204 13 = 8 ∧ acceleratedOrbit 13 7204 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7204 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7204) = 3 ^ 8 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7204.1, data_13_7204.2] + +/-- Complete interval computation for depth 13, residue 7205. -/ +theorem bounds_13_7205 : exactInterval 13 7205 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7205 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7205) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7205 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7205 : oddCount 7205 13 = 8 ∧ acceleratedOrbit 13 7205 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7205 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7205) = 3 ^ 8 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7205.1, data_13_7205.2] + +/-- Complete interval computation for depth 13, residue 7206. -/ +theorem bounds_13_7206 : exactInterval 13 7206 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7206 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7206) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7206 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7206 : oddCount 7206 13 = 8 ∧ acceleratedOrbit 13 7206 = 5777 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7206 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7206) = 3 ^ 8 * m + 5777 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7206.1, data_13_7206.2] + +/-- Complete interval computation for depth 13, residue 7207. -/ +theorem bounds_13_7207 : exactInterval 13 7207 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7207 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7207) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7207 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7207 : oddCount 7207 13 = 7 ∧ acceleratedOrbit 13 7207 = 1925 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7207 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7207) = 3 ^ 7 * m + 1925 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7207.1, data_13_7207.2] + +end Collatz.Research.StoppingAtlas.Batch0936 From e6e1cee044a873da07a168ba9b98f38c1eedf6c6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:26 +0530 Subject: [PATCH 0937/1001] proof: certify atlas Batch0937 (13:7208 to 13:7223) --- Collatz/Research/StoppingAtlas/Batch0937.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0937.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0937.lean b/Collatz/Research/StoppingAtlas/Batch0937.lean new file mode 100644 index 00000000..08795af3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0937.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0937 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7208. -/ +theorem bounds_13_7208 : exactInterval 13 7208 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7208 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7208) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7208 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7208 : oddCount 7208 13 = 6 ∧ acceleratedOrbit 13 7208 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7208 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7208) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7208.1, data_13_7208.2] + +/-- Complete interval computation for depth 13, residue 7209. -/ +theorem bounds_13_7209 : exactInterval 13 7209 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7209 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7209) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7209 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7209 : oddCount 7209 13 = 7 ∧ acceleratedOrbit 13 7209 = 1925 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7209 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7209) = 3 ^ 7 * m + 1925 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7209.1, data_13_7209.2] + +/-- Complete interval computation for depth 13, residue 7210. -/ +theorem bounds_13_7210 : exactInterval 13 7210 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7210 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7210) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7210 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7210 : oddCount 7210 13 = 6 ∧ acceleratedOrbit 13 7210 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7210 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7210) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7210.1, data_13_7210.2] + +/-- Complete interval computation for depth 13, residue 7211. -/ +theorem bounds_13_7211 : exactInterval 13 7211 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7211 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7211) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7211 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7211 : oddCount 7211 13 = 5 ∧ acceleratedOrbit 13 7211 = 214 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7211 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7211) = 3 ^ 5 * m + 214 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7211.1, data_13_7211.2] + +/-- Complete interval computation for depth 13, residue 7212. -/ +theorem bounds_13_7212 : exactInterval 13 7212 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7212 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7212) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7212 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7212 : oddCount 7212 13 = 6 ∧ acceleratedOrbit 13 7212 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7212 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7212) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7212.1, data_13_7212.2] + +/-- Complete interval computation for depth 13, residue 7213. -/ +theorem bounds_13_7213 : exactInterval 13 7213 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7213 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7213) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7213 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7213 : oddCount 7213 13 = 6 ∧ acceleratedOrbit 13 7213 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7213 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7213) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7213.1, data_13_7213.2] + +/-- Complete interval computation for depth 13, residue 7214. -/ +theorem bounds_13_7214 : exactInterval 13 7214 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7214 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7214) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7214 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7214 : oddCount 7214 13 = 6 ∧ acceleratedOrbit 13 7214 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7214 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7214) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7214.1, data_13_7214.2] + +/-- Complete interval computation for depth 13, residue 7215. -/ +theorem bounds_13_7215 : exactInterval 13 7215 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7215 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7215) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7215 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7215 : oddCount 7215 13 = 8 ∧ acceleratedOrbit 13 7215 = 5780 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7215 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7215) = 3 ^ 8 * m + 5780 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7215.1, data_13_7215.2] + +/-- Complete interval computation for depth 13, residue 7216. -/ +theorem bounds_13_7216 : exactInterval 13 7216 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7216 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7216) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7216 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7216 : oddCount 7216 13 = 6 ∧ acceleratedOrbit 13 7216 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7216 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7216) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7216.1, data_13_7216.2] + +/-- Complete interval computation for depth 13, residue 7217. -/ +theorem bounds_13_7217 : exactInterval 13 7217 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7217 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7217) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7217 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7217 : oddCount 7217 13 = 6 ∧ acceleratedOrbit 13 7217 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7217 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7217) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7217.1, data_13_7217.2] + +/-- Complete interval computation for depth 13, residue 7218. -/ +theorem bounds_13_7218 : exactInterval 13 7218 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7218 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7218) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7218 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7218 : oddCount 7218 13 = 6 ∧ acceleratedOrbit 13 7218 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7218 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7218) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7218.1, data_13_7218.2] + +/-- Complete interval computation for depth 13, residue 7219. -/ +theorem bounds_13_7219 : exactInterval 13 7219 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7219 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7219) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7219 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7219 : oddCount 7219 13 = 6 ∧ acceleratedOrbit 13 7219 = 643 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7219 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7219) = 3 ^ 6 * m + 643 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7219.1, data_13_7219.2] + +/-- Complete interval computation for depth 13, residue 7220. -/ +theorem bounds_13_7220 : exactInterval 13 7220 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7220 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7220) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7220 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7220 : oddCount 7220 13 = 6 ∧ acceleratedOrbit 13 7220 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7220 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7220) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7220.1, data_13_7220.2] + +/-- Complete interval computation for depth 13, residue 7221. -/ +theorem bounds_13_7221 : exactInterval 13 7221 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7221 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7221) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7221 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7221 : oddCount 7221 13 = 6 ∧ acceleratedOrbit 13 7221 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7221 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7221) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7221.1, data_13_7221.2] + +/-- Complete interval computation for depth 13, residue 7222. -/ +theorem bounds_13_7222 : exactInterval 13 7222 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7222 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7222) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7222 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7222 : oddCount 7222 13 = 9 ∧ acceleratedOrbit 13 7222 = 17360 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7222 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7222) = 3 ^ 9 * m + 17360 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7222.1, data_13_7222.2] + +/-- Complete interval computation for depth 13, residue 7223. -/ +theorem bounds_13_7223 : exactInterval 13 7223 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7223 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7223) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7223 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7223 : oddCount 7223 13 = 9 ∧ acceleratedOrbit 13 7223 = 17360 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7223 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7223) = 3 ^ 9 * m + 17360 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7223.1, data_13_7223.2] + +end Collatz.Research.StoppingAtlas.Batch0937 From 9381db51c4b94e796a27e6a945043c5f8595c073 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:26 +0530 Subject: [PATCH 0938/1001] proof: certify atlas Batch0938 (13:7224 to 13:7238) --- Collatz/Research/StoppingAtlas/Batch0938.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0938.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0938.lean b/Collatz/Research/StoppingAtlas/Batch0938.lean new file mode 100644 index 00000000..e00a895a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0938.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0938 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7224. -/ +theorem bounds_13_7224 : exactInterval 13 7224 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7224 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7224) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7224 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7224 : oddCount 7224 13 = 5 ∧ acceleratedOrbit 13 7224 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7224 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7224) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7224.1, data_13_7224.2] + +/-- Complete interval computation for depth 13, residue 7225. -/ +theorem bounds_13_7225 : exactInterval 13 7225 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7225 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7225) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7225 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7225 : oddCount 7225 13 = 7 ∧ acceleratedOrbit 13 7225 = 1930 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7225 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7225) = 3 ^ 7 * m + 1930 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7225.1, data_13_7225.2] + +/-- Complete interval computation for depth 13, residue 7226. -/ +theorem bounds_13_7226 : exactInterval 13 7226 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7226 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7226) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7226 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7226 : oddCount 7226 13 = 5 ∧ acceleratedOrbit 13 7226 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7226 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7226) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7226.1, data_13_7226.2] + +/-- Complete interval computation for depth 13, residue 7227. -/ +theorem bounds_13_7227 : exactInterval 13 7227 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7227 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7227) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7227 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7227 : oddCount 7227 13 = 8 ∧ acceleratedOrbit 13 7227 = 5791 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7227 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7227) = 3 ^ 8 * m + 5791 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7227.1, data_13_7227.2] + +/-- Complete interval computation for depth 13, residue 7228. -/ +theorem bounds_13_7228 : exactInterval 13 7228 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7228 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7228) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7228 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7228 : oddCount 7228 13 = 5 ∧ acceleratedOrbit 13 7228 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7228 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7228) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7228.1, data_13_7228.2] + +/-- Complete interval computation for depth 13, residue 7229. -/ +theorem bounds_13_7229 : exactInterval 13 7229 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7229 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7229) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7229 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7229 : oddCount 7229 13 = 5 ∧ acceleratedOrbit 13 7229 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7229 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7229) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7229.1, data_13_7229.2] + +/-- Complete interval computation for depth 13, residue 7230. -/ +theorem bounds_13_7230 : exactInterval 13 7230 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7230 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7230) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7230 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7230 : oddCount 7230 13 = 9 ∧ acceleratedOrbit 13 7230 = 17378 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7230 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7230) = 3 ^ 9 * m + 17378 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7230.1, data_13_7230.2] + +/-- Complete interval computation for depth 13, residue 7231. -/ +theorem bounds_13_7231 : exactInterval 13 7231 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7231 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7231) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7231 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7231 : oddCount 7231 13 = 9 ∧ acceleratedOrbit 13 7231 = 17378 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7231 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7231) = 3 ^ 9 * m + 17378 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7231.1, data_13_7231.2] + +/-- Complete interval computation for depth 13, residue 7232. -/ +theorem bounds_13_7232 : exactInterval 13 7232 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7232 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7232) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7232 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7232 : oddCount 7232 13 = 2 ∧ acceleratedOrbit 13 7232 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7232 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7232) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7232.1, data_13_7232.2] + +/-- Complete interval computation for depth 13, residue 7233. -/ +theorem bounds_13_7233 : exactInterval 13 7233 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7233 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7233) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7233 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7233 : oddCount 7233 13 = 7 ∧ acceleratedOrbit 13 7233 = 1934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7233 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7233) = 3 ^ 7 * m + 1934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7233.1, data_13_7233.2] + +/-- Complete interval computation for depth 13, residue 7234. -/ +theorem bounds_13_7234 : exactInterval 13 7234 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7234 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7234) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7234 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7234 : oddCount 7234 13 = 7 ∧ acceleratedOrbit 13 7234 = 1934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7234 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7234) = 3 ^ 7 * m + 1934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7234.1, data_13_7234.2] + +/-- Complete interval computation for depth 13, residue 7235. -/ +theorem bounds_13_7235 : exactInterval 13 7235 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7235 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7235) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7235 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7235 : oddCount 7235 13 = 7 ∧ acceleratedOrbit 13 7235 = 1934 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7235 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7235) = 3 ^ 7 * m + 1934 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7235.1, data_13_7235.2] + +/-- Complete interval computation for depth 13, residue 7236. -/ +theorem bounds_13_7236 : exactInterval 13 7236 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7236 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7236) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7236 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7236 : oddCount 7236 13 = 6 ∧ acceleratedOrbit 13 7236 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7236 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7236) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7236.1, data_13_7236.2] + +/-- Complete interval computation for depth 13, residue 7237. -/ +theorem bounds_13_7237 : exactInterval 13 7237 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7237 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7237) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7237 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7237 : oddCount 7237 13 = 6 ∧ acceleratedOrbit 13 7237 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7237 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7237) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7237.1, data_13_7237.2] + +/-- Complete interval computation for depth 13, residue 7238. -/ +theorem bounds_13_7238 : exactInterval 13 7238 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7238 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7238) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7238 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7238 : oddCount 7238 13 = 6 ∧ acceleratedOrbit 13 7238 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7238 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7238) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7238.1, data_13_7238.2] + +end Collatz.Research.StoppingAtlas.Batch0938 From 652c554b0fae667124af7cffdd9fe0afdf54d868 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:27 +0530 Subject: [PATCH 0939/1001] proof: certify atlas Batch0939 (13:7239 to 13:7254) --- Collatz/Research/StoppingAtlas/Batch0939.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0939.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0939.lean b/Collatz/Research/StoppingAtlas/Batch0939.lean new file mode 100644 index 00000000..1253f542 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0939.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0939 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7239. -/ +theorem bounds_13_7239 : exactInterval 13 7239 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7239 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7239) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7239 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7239 : oddCount 7239 13 = 7 ∧ acceleratedOrbit 13 7239 = 1933 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7239 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7239) = 3 ^ 7 * m + 1933 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7239.1, data_13_7239.2] + +/-- Complete interval computation for depth 13, residue 7240. -/ +theorem bounds_13_7240 : exactInterval 13 7240 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7240 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7240) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7240 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7240 : oddCount 7240 13 = 7 ∧ acceleratedOrbit 13 7240 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7240 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7240) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7240.1, data_13_7240.2] + +/-- Complete interval computation for depth 13, residue 7241. -/ +theorem bounds_13_7241 : exactInterval 13 7241 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7241 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7241) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7241 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7241 : oddCount 7241 13 = 9 ∧ acceleratedOrbit 13 7241 = 17405 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7241 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7241) = 3 ^ 9 * m + 17405 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7241.1, data_13_7241.2] + +/-- Complete interval computation for depth 13, residue 7242. -/ +theorem bounds_13_7242 : exactInterval 13 7242 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7242 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7242) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7242 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7242 : oddCount 7242 13 = 7 ∧ acceleratedOrbit 13 7242 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7242 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7242) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7242.1, data_13_7242.2] + +/-- Complete interval computation for depth 13, residue 7243. -/ +theorem bounds_13_7243 : exactInterval 13 7243 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7243 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7243) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7243 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7243 : oddCount 7243 13 = 6 ∧ acceleratedOrbit 13 7243 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7243 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7243) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7243.1, data_13_7243.2] + +/-- Complete interval computation for depth 13, residue 7244. -/ +theorem bounds_13_7244 : exactInterval 13 7244 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7244 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7244) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7244 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7244 : oddCount 7244 13 = 7 ∧ acceleratedOrbit 13 7244 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7244 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7244) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7244.1, data_13_7244.2] + +/-- Complete interval computation for depth 13, residue 7245. -/ +theorem bounds_13_7245 : exactInterval 13 7245 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7245 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7245) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7245 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7245 : oddCount 7245 13 = 7 ∧ acceleratedOrbit 13 7245 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7245 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7245) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7245.1, data_13_7245.2] + +/-- Complete interval computation for depth 13, residue 7246. -/ +theorem bounds_13_7246 : exactInterval 13 7246 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7246 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7246) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7246 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7246 : oddCount 7246 13 = 5 ∧ acceleratedOrbit 13 7246 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7246 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7246) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7246.1, data_13_7246.2] + +/-- Complete interval computation for depth 13, residue 7247. -/ +theorem bounds_13_7247 : exactInterval 13 7247 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7247 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7247) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7247 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7247 : oddCount 7247 13 = 5 ∧ acceleratedOrbit 13 7247 = 215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7247 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7247) = 3 ^ 5 * m + 215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7247.1, data_13_7247.2] + +/-- Complete interval computation for depth 13, residue 7248. -/ +theorem bounds_13_7248 : exactInterval 13 7248 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7248 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7248) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7248 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7248 : oddCount 7248 13 = 2 ∧ acceleratedOrbit 13 7248 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7248 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7248) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7248.1, data_13_7248.2] + +/-- Complete interval computation for depth 13, residue 7249. -/ +theorem bounds_13_7249 : exactInterval 13 7249 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7249 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7249) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7249 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7249 : oddCount 7249 13 = 7 ∧ acceleratedOrbit 13 7249 = 1937 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7249 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7249) = 3 ^ 7 * m + 1937 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7249.1, data_13_7249.2] + +/-- Complete interval computation for depth 13, residue 7250. -/ +theorem bounds_13_7250 : exactInterval 13 7250 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7250 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7250) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7250 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7250 : oddCount 7250 13 = 9 ∧ acceleratedOrbit 13 7250 = 17428 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7250 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7250) = 3 ^ 9 * m + 17428 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7250.1, data_13_7250.2] + +/-- Complete interval computation for depth 13, residue 7251. -/ +theorem bounds_13_7251 : exactInterval 13 7251 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7251 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7251) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7251 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7251 : oddCount 7251 13 = 9 ∧ acceleratedOrbit 13 7251 = 17428 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7251 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7251) = 3 ^ 9 * m + 17428 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7251.1, data_13_7251.2] + +/-- Complete interval computation for depth 13, residue 7252. -/ +theorem bounds_13_7252 : exactInterval 13 7252 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7252 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7252) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7252 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7252 : oddCount 7252 13 = 2 ∧ acceleratedOrbit 13 7252 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7252 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7252) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7252.1, data_13_7252.2] + +/-- Complete interval computation for depth 13, residue 7253. -/ +theorem bounds_13_7253 : exactInterval 13 7253 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7253 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7253) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7253 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7253 : oddCount 7253 13 = 2 ∧ acceleratedOrbit 13 7253 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7253 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7253) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7253.1, data_13_7253.2] + +/-- Complete interval computation for depth 13, residue 7254. -/ +theorem bounds_13_7254 : exactInterval 13 7254 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7254 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7254) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7254 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7254 : oddCount 7254 13 = 6 ∧ acceleratedOrbit 13 7254 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7254 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7254) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7254.1, data_13_7254.2] + +end Collatz.Research.StoppingAtlas.Batch0939 From a51ff35c8a6e8a6c30cfefb26c75917eac591dc7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:27 +0530 Subject: [PATCH 0940/1001] proof: certify atlas Batch0940 (13:7255 to 13:7269) --- Collatz/Research/StoppingAtlas/Batch0940.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0940.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0940.lean b/Collatz/Research/StoppingAtlas/Batch0940.lean new file mode 100644 index 00000000..15a2b90c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0940.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0940 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7255. -/ +theorem bounds_13_7255 : exactInterval 13 7255 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7255 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7255) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7255 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7255 : oddCount 7255 13 = 6 ∧ acceleratedOrbit 13 7255 = 647 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7255 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7255) = 3 ^ 6 * m + 647 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7255.1, data_13_7255.2] + +/-- Complete interval computation for depth 13, residue 7256. -/ +theorem bounds_13_7256 : exactInterval 13 7256 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7256 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7256) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7256 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7256 : oddCount 7256 13 = 7 ∧ acceleratedOrbit 13 7256 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7256 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7256) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7256.1, data_13_7256.2] + +/-- Complete interval computation for depth 13, residue 7257. -/ +theorem bounds_13_7257 : exactInterval 13 7257 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7257 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7257) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7257 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7257 : oddCount 7257 13 = 7 ∧ acceleratedOrbit 13 7257 = 1939 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7257 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7257) = 3 ^ 7 * m + 1939 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7257.1, data_13_7257.2] + +/-- Complete interval computation for depth 13, residue 7258. -/ +theorem bounds_13_7258 : exactInterval 13 7258 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7258 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7258) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7258 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7258 : oddCount 7258 13 = 7 ∧ acceleratedOrbit 13 7258 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7258 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7258) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7258.1, data_13_7258.2] + +/-- Complete interval computation for depth 13, residue 7259. -/ +theorem bounds_13_7259 : exactInterval 13 7259 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7259 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7259) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7259 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7259 : oddCount 7259 13 = 8 ∧ acceleratedOrbit 13 7259 = 5815 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7259 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7259) = 3 ^ 8 * m + 5815 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7259.1, data_13_7259.2] + +/-- Complete interval computation for depth 13, residue 7260. -/ +theorem bounds_13_7260 : exactInterval 13 7260 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7260 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7260) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7260 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7260 : oddCount 7260 13 = 7 ∧ acceleratedOrbit 13 7260 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7260 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7260) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7260.1, data_13_7260.2] + +/-- Complete interval computation for depth 13, residue 7261. -/ +theorem bounds_13_7261 : exactInterval 13 7261 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7261 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7261) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7261 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7261 : oddCount 7261 13 = 7 ∧ acceleratedOrbit 13 7261 = 1943 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7261 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7261) = 3 ^ 7 * m + 1943 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7261.1, data_13_7261.2] + +/-- Complete interval computation for depth 13, residue 7262. -/ +theorem bounds_13_7262 : exactInterval 13 7262 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7262 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7262) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7262 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7262 : oddCount 7262 13 = 9 ∧ acceleratedOrbit 13 7262 = 17455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7262 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7262) = 3 ^ 9 * m + 17455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7262.1, data_13_7262.2] + +/-- Complete interval computation for depth 13, residue 7263. -/ +theorem bounds_13_7263 : exactInterval 13 7263 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7263 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7263) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7263 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7263 : oddCount 7263 13 = 9 ∧ acceleratedOrbit 13 7263 = 17455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7263 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7263) = 3 ^ 9 * m + 17455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7263.1, data_13_7263.2] + +/-- Complete interval computation for depth 13, residue 7264. -/ +theorem bounds_13_7264 : exactInterval 13 7264 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7264 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7264) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7264 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7264 : oddCount 7264 13 = 2 ∧ acceleratedOrbit 13 7264 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7264 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7264) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7264.1, data_13_7264.2] + +/-- Complete interval computation for depth 13, residue 7265. -/ +theorem bounds_13_7265 : exactInterval 13 7265 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7265 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7265) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7265 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7265 : oddCount 7265 13 = 8 ∧ acceleratedOrbit 13 7265 = 5822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7265 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7265) = 3 ^ 8 * m + 5822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7265.1, data_13_7265.2] + +/-- Complete interval computation for depth 13, residue 7266. -/ +theorem bounds_13_7266 : exactInterval 13 7266 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7266 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7266) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7266 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7266 : oddCount 7266 13 = 8 ∧ acceleratedOrbit 13 7266 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7266 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7266) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7266.1, data_13_7266.2] + +/-- Complete interval computation for depth 13, residue 7267. -/ +theorem bounds_13_7267 : exactInterval 13 7267 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7267 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7267) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7267 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7267 : oddCount 7267 13 = 8 ∧ acceleratedOrbit 13 7267 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7267 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7267) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7267.1, data_13_7267.2] + +/-- Complete interval computation for depth 13, residue 7268. -/ +theorem bounds_13_7268 : exactInterval 13 7268 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7268 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7268) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7268 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7268 : oddCount 7268 13 = 8 ∧ acceleratedOrbit 13 7268 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7268 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7268) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7268.1, data_13_7268.2] + +/-- Complete interval computation for depth 13, residue 7269. -/ +theorem bounds_13_7269 : exactInterval 13 7269 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7269 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7269) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7269 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7269 : oddCount 7269 13 = 8 ∧ acceleratedOrbit 13 7269 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7269 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7269) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7269.1, data_13_7269.2] + +end Collatz.Research.StoppingAtlas.Batch0940 From a59e39875b769400ed667c870fc7fee66d77324b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:27 +0530 Subject: [PATCH 0941/1001] proof: certify atlas Batch0941 (13:7270 to 13:7284) --- Collatz/Research/StoppingAtlas/Batch0941.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0941.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0941.lean b/Collatz/Research/StoppingAtlas/Batch0941.lean new file mode 100644 index 00000000..5e723aca --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0941.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0941 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7270. -/ +theorem bounds_13_7270 : exactInterval 13 7270 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7270 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7270) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7270 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7270 : oddCount 7270 13 = 8 ∧ acceleratedOrbit 13 7270 = 5831 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7270 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7270) = 3 ^ 8 * m + 5831 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7270.1, data_13_7270.2] + +/-- Complete interval computation for depth 13, residue 7271. -/ +theorem bounds_13_7271 : exactInterval 13 7271 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7271 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7271) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7271 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7271 : oddCount 7271 13 = 10 ∧ acceleratedOrbit 13 7271 = 52420 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7271 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7271) = 3 ^ 10 * m + 52420 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7271.1, data_13_7271.2] + +/-- Complete interval computation for depth 13, residue 7272. -/ +theorem bounds_13_7272 : exactInterval 13 7272 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7272 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7272) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7272 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7272 : oddCount 7272 13 = 2 ∧ acceleratedOrbit 13 7272 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7272 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7272) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7272.1, data_13_7272.2] + +/-- Complete interval computation for depth 13, residue 7273. -/ +theorem bounds_13_7273 : exactInterval 13 7273 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7273 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7273) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7273 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7273 : oddCount 7273 13 = 8 ∧ acceleratedOrbit 13 7273 = 5827 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7273 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7273) = 3 ^ 8 * m + 5827 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7273.1, data_13_7273.2] + +/-- Complete interval computation for depth 13, residue 7274. -/ +theorem bounds_13_7274 : exactInterval 13 7274 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7274 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7274) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7274 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7274 : oddCount 7274 13 = 2 ∧ acceleratedOrbit 13 7274 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7274 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7274) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7274.1, data_13_7274.2] + +/-- Complete interval computation for depth 13, residue 7275. -/ +theorem bounds_13_7275 : exactInterval 13 7275 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7275 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7275) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7275 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7275 : oddCount 7275 13 = 9 ∧ acceleratedOrbit 13 7275 = 17486 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7275 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7275) = 3 ^ 9 * m + 17486 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7275.1, data_13_7275.2] + +/-- Complete interval computation for depth 13, residue 7276. -/ +theorem bounds_13_7276 : exactInterval 13 7276 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7276 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7276) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7276 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7276 : oddCount 7276 13 = 10 ∧ acceleratedOrbit 13 7276 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7276 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7276) = 3 ^ 10 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7276.1, data_13_7276.2] + +/-- Complete interval computation for depth 13, residue 7277. -/ +theorem bounds_13_7277 : exactInterval 13 7277 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7277 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7277) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7277 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7277 : oddCount 7277 13 = 10 ∧ acceleratedOrbit 13 7277 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7277 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7277) = 3 ^ 10 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7277.1, data_13_7277.2] + +/-- Complete interval computation for depth 13, residue 7278. -/ +theorem bounds_13_7278 : exactInterval 13 7278 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7278 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7278) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7278 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7278 : oddCount 7278 13 = 10 ∧ acceleratedOrbit 13 7278 = 52487 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7278 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7278) = 3 ^ 10 * m + 52487 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7278.1, data_13_7278.2] + +/-- Complete interval computation for depth 13, residue 7279. -/ +theorem bounds_13_7279 : exactInterval 13 7279 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7279 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7279) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7279 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7279 : oddCount 7279 13 = 10 ∧ acceleratedOrbit 13 7279 = 52478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7279 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7279) = 3 ^ 10 * m + 52478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7279.1, data_13_7279.2] + +/-- Complete interval computation for depth 13, residue 7280. -/ +theorem bounds_13_7280 : exactInterval 13 7280 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7280 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7280) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7280 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7280 : oddCount 7280 13 = 6 ∧ acceleratedOrbit 13 7280 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7280 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7280) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7280.1, data_13_7280.2] + +/-- Complete interval computation for depth 13, residue 7281. -/ +theorem bounds_13_7281 : exactInterval 13 7281 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7281 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7281) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7281 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7281 : oddCount 7281 13 = 2 ∧ acceleratedOrbit 13 7281 = 8 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7281 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7281) = 3 ^ 2 * m + 8 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7281.1, data_13_7281.2] + +/-- Complete interval computation for depth 13, residue 7282. -/ +theorem bounds_13_7282 : exactInterval 13 7282 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7282 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7282) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7282 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7282 : oddCount 7282 13 = 7 ∧ acceleratedOrbit 13 7282 = 1946 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7282 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7282) = 3 ^ 7 * m + 1946 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7282.1, data_13_7282.2] + +/-- Complete interval computation for depth 13, residue 7283. -/ +theorem bounds_13_7283 : exactInterval 13 7283 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7283 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7283) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7283 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7283 : oddCount 7283 13 = 7 ∧ acceleratedOrbit 13 7283 = 1946 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7283 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7283) = 3 ^ 7 * m + 1946 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7283.1, data_13_7283.2] + +/-- Complete interval computation for depth 13, residue 7284. -/ +theorem bounds_13_7284 : exactInterval 13 7284 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7284 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7284) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7284 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7284 : oddCount 7284 13 = 6 ∧ acceleratedOrbit 13 7284 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7284 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7284) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7284.1, data_13_7284.2] + +end Collatz.Research.StoppingAtlas.Batch0941 From eeab1ea61c533799c7ec0f77a414b7282c366429 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:27 +0530 Subject: [PATCH 0942/1001] proof: certify atlas Batch0942 (13:7285 to 13:7300) --- Collatz/Research/StoppingAtlas/Batch0942.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0942.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0942.lean b/Collatz/Research/StoppingAtlas/Batch0942.lean new file mode 100644 index 00000000..404d4b89 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0942.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0942 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7285. -/ +theorem bounds_13_7285 : exactInterval 13 7285 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7285 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7285) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7285 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7285 : oddCount 7285 13 = 6 ∧ acceleratedOrbit 13 7285 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7285 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7285) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7285.1, data_13_7285.2] + +/-- Complete interval computation for depth 13, residue 7286. -/ +theorem bounds_13_7286 : exactInterval 13 7286 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7286 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7286) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7286 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7286 : oddCount 7286 13 = 6 ∧ acceleratedOrbit 13 7286 = 649 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7286 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7286) = 3 ^ 6 * m + 649 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7286.1, data_13_7286.2] + +/-- Complete interval computation for depth 13, residue 7287. -/ +theorem bounds_13_7287 : exactInterval 13 7287 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7287 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7287) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7287 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7287 : oddCount 7287 13 = 6 ∧ acceleratedOrbit 13 7287 = 649 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7287 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7287) = 3 ^ 6 * m + 649 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7287.1, data_13_7287.2] + +/-- Complete interval computation for depth 13, residue 7288. -/ +theorem bounds_13_7288 : exactInterval 13 7288 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7288 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7288) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7288 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7288 : oddCount 7288 13 = 6 ∧ acceleratedOrbit 13 7288 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7288 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7288) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7288.1, data_13_7288.2] + +/-- Complete interval computation for depth 13, residue 7289. -/ +theorem bounds_13_7289 : exactInterval 13 7289 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7289 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7289) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7289 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7289 : oddCount 7289 13 = 8 ∧ acceleratedOrbit 13 7289 = 5840 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7289 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7289) = 3 ^ 8 * m + 5840 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7289.1, data_13_7289.2] + +/-- Complete interval computation for depth 13, residue 7290. -/ +theorem bounds_13_7290 : exactInterval 13 7290 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7290 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7290) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7290 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7290 : oddCount 7290 13 = 6 ∧ acceleratedOrbit 13 7290 = 650 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7290 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7290) = 3 ^ 6 * m + 650 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7290.1, data_13_7290.2] + +/-- Complete interval computation for depth 13, residue 7291. -/ +theorem bounds_13_7291 : exactInterval 13 7291 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7291 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7291) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7291 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7291 : oddCount 7291 13 = 6 ∧ acceleratedOrbit 13 7291 = 649 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7291 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7291) = 3 ^ 6 * m + 649 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7291.1, data_13_7291.2] + +/-- Complete interval computation for depth 13, residue 7292. -/ +theorem bounds_13_7292 : exactInterval 13 7292 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7292 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7292) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7292 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7292 : oddCount 7292 13 = 7 ∧ acceleratedOrbit 13 7292 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7292 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7292) = 3 ^ 7 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7292.1, data_13_7292.2] + +/-- Complete interval computation for depth 13, residue 7293. -/ +theorem bounds_13_7293 : exactInterval 13 7293 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7293 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7293) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7293 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7293 : oddCount 7293 13 = 7 ∧ acceleratedOrbit 13 7293 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7293 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7293) = 3 ^ 7 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7293.1, data_13_7293.2] + +/-- Complete interval computation for depth 13, residue 7294. -/ +theorem bounds_13_7294 : exactInterval 13 7294 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7294 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7294) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7294 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7294 : oddCount 7294 13 = 7 ∧ acceleratedOrbit 13 7294 = 1948 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7294 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7294) = 3 ^ 7 * m + 1948 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7294.1, data_13_7294.2] + +/-- Complete interval computation for depth 13, residue 7295. -/ +theorem bounds_13_7295 : exactInterval 13 7295 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7295 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7295) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7295 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7295 : oddCount 7295 13 = 10 ∧ acceleratedOrbit 13 7295 = 52591 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7295 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7295) = 3 ^ 10 * m + 52591 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7295.1, data_13_7295.2] + +/-- Complete interval computation for depth 13, residue 7296. -/ +theorem bounds_13_7296 : exactInterval 13 7296 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7296 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7296) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7296 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7296 : oddCount 7296 13 = 4 ∧ acceleratedOrbit 13 7296 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7296 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7296) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7296.1, data_13_7296.2] + +/-- Complete interval computation for depth 13, residue 7297. -/ +theorem bounds_13_7297 : exactInterval 13 7297 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7297 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7297) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7297 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7297 : oddCount 7297 13 = 7 ∧ acceleratedOrbit 13 7297 = 1949 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7297 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7297) = 3 ^ 7 * m + 1949 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7297.1, data_13_7297.2] + +/-- Complete interval computation for depth 13, residue 7298. -/ +theorem bounds_13_7298 : exactInterval 13 7298 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7298 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7298) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7298 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7298 : oddCount 7298 13 = 5 ∧ acceleratedOrbit 13 7298 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7298 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7298) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7298.1, data_13_7298.2] + +/-- Complete interval computation for depth 13, residue 7299. -/ +theorem bounds_13_7299 : exactInterval 13 7299 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7299 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7299) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7299 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7299 : oddCount 7299 13 = 5 ∧ acceleratedOrbit 13 7299 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7299 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7299) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7299.1, data_13_7299.2] + +/-- Complete interval computation for depth 13, residue 7300. -/ +theorem bounds_13_7300 : exactInterval 13 7300 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7300 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7300) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7300 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7300 : oddCount 7300 13 = 5 ∧ acceleratedOrbit 13 7300 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7300 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7300) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7300.1, data_13_7300.2] + +end Collatz.Research.StoppingAtlas.Batch0942 From e0d1b73d53c803c26cd7e0e48214267c55acba9e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:27 +0530 Subject: [PATCH 0943/1001] proof: certify atlas Batch0943 (13:7301 to 13:7315) --- Collatz/Research/StoppingAtlas/Batch0943.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0943.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0943.lean b/Collatz/Research/StoppingAtlas/Batch0943.lean new file mode 100644 index 00000000..1efa7eb3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0943.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0943 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7301. -/ +theorem bounds_13_7301 : exactInterval 13 7301 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7301 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7301) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7301 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7301 : oddCount 7301 13 = 5 ∧ acceleratedOrbit 13 7301 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7301 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7301) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7301.1, data_13_7301.2] + +/-- Complete interval computation for depth 13, residue 7302. -/ +theorem bounds_13_7302 : exactInterval 13 7302 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7302 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7302) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7302 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7302 : oddCount 7302 13 = 5 ∧ acceleratedOrbit 13 7302 = 217 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7302 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7302) = 3 ^ 5 * m + 217 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7302.1, data_13_7302.2] + +/-- Complete interval computation for depth 13, residue 7303. -/ +theorem bounds_13_7303 : exactInterval 13 7303 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7303 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7303) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7303 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7303 : oddCount 7303 13 = 8 ∧ acceleratedOrbit 13 7303 = 5852 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7303 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7303) = 3 ^ 8 * m + 5852 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7303.1, data_13_7303.2] + +/-- Complete interval computation for depth 13, residue 7304. -/ +theorem bounds_13_7304 : exactInterval 13 7304 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7304 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7304) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7304 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7304 : oddCount 7304 13 = 5 ∧ acceleratedOrbit 13 7304 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7304 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7304) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7304.1, data_13_7304.2] + +/-- Complete interval computation for depth 13, residue 7305. -/ +theorem bounds_13_7305 : exactInterval 13 7305 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7305 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7305) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7305 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7305 : oddCount 7305 13 = 10 ∧ acceleratedOrbit 13 7305 = 52670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7305 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7305) = 3 ^ 10 * m + 52670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7305.1, data_13_7305.2] + +/-- Complete interval computation for depth 13, residue 7306. -/ +theorem bounds_13_7306 : exactInterval 13 7306 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7306 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7306) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7306 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7306 : oddCount 7306 13 = 5 ∧ acceleratedOrbit 13 7306 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7306 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7306) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7306.1, data_13_7306.2] + +/-- Complete interval computation for depth 13, residue 7307. -/ +theorem bounds_13_7307 : exactInterval 13 7307 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7307 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7307) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7307 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7307 : oddCount 7307 13 = 7 ∧ acceleratedOrbit 13 7307 = 1952 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7307 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7307) = 3 ^ 7 * m + 1952 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7307.1, data_13_7307.2] + +/-- Complete interval computation for depth 13, residue 7308. -/ +theorem bounds_13_7308 : exactInterval 13 7308 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7308 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7308) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7308 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7308 : oddCount 7308 13 = 5 ∧ acceleratedOrbit 13 7308 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7308 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7308) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7308.1, data_13_7308.2] + +/-- Complete interval computation for depth 13, residue 7309. -/ +theorem bounds_13_7309 : exactInterval 13 7309 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7309 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7309) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7309 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7309 : oddCount 7309 13 = 5 ∧ acceleratedOrbit 13 7309 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7309 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7309) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7309.1, data_13_7309.2] + +/-- Complete interval computation for depth 13, residue 7310. -/ +theorem bounds_13_7310 : exactInterval 13 7310 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7310 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7310) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7310 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7310 : oddCount 7310 13 = 8 ∧ acceleratedOrbit 13 7310 = 5858 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7310 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7310) = 3 ^ 8 * m + 5858 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7310.1, data_13_7310.2] + +/-- Complete interval computation for depth 13, residue 7311. -/ +theorem bounds_13_7311 : exactInterval 13 7311 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7311 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7311) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7311 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7311 : oddCount 7311 13 = 8 ∧ acceleratedOrbit 13 7311 = 5858 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7311 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7311) = 3 ^ 8 * m + 5858 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7311.1, data_13_7311.2] + +/-- Complete interval computation for depth 13, residue 7312. -/ +theorem bounds_13_7312 : exactInterval 13 7312 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7312 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7312) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7312 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7312 : oddCount 7312 13 = 5 ∧ acceleratedOrbit 13 7312 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7312 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7312) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7312.1, data_13_7312.2] + +/-- Complete interval computation for depth 13, residue 7313. -/ +theorem bounds_13_7313 : exactInterval 13 7313 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7313 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7313) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7313 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7313 : oddCount 7313 13 = 7 ∧ acceleratedOrbit 13 7313 = 1954 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7313 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7313) = 3 ^ 7 * m + 1954 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7313.1, data_13_7313.2] + +/-- Complete interval computation for depth 13, residue 7314. -/ +theorem bounds_13_7314 : exactInterval 13 7314 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7314 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7314) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7314 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7314 : oddCount 7314 13 = 7 ∧ acceleratedOrbit 13 7314 = 1954 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7314 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7314) = 3 ^ 7 * m + 1954 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7314.1, data_13_7314.2] + +/-- Complete interval computation for depth 13, residue 7315. -/ +theorem bounds_13_7315 : exactInterval 13 7315 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7315 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7315) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7315 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7315 : oddCount 7315 13 = 7 ∧ acceleratedOrbit 13 7315 = 1954 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7315 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7315) = 3 ^ 7 * m + 1954 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7315.1, data_13_7315.2] + +end Collatz.Research.StoppingAtlas.Batch0943 From 1bd823def2a784669dd1d01cdbac47e309c5cc9e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:28 +0530 Subject: [PATCH 0944/1001] proof: certify atlas Batch0944 (13:7316 to 13:7330) --- Collatz/Research/StoppingAtlas/Batch0944.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0944.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0944.lean b/Collatz/Research/StoppingAtlas/Batch0944.lean new file mode 100644 index 00000000..e37977e1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0944.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0944 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7316. -/ +theorem bounds_13_7316 : exactInterval 13 7316 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7316 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7316) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7316 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7316 : oddCount 7316 13 = 5 ∧ acceleratedOrbit 13 7316 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7316 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7316) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7316.1, data_13_7316.2] + +/-- Complete interval computation for depth 13, residue 7317. -/ +theorem bounds_13_7317 : exactInterval 13 7317 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7317 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7317) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7317 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7317 : oddCount 7317 13 = 5 ∧ acceleratedOrbit 13 7317 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7317 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7317) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7317.1, data_13_7317.2] + +/-- Complete interval computation for depth 13, residue 7318. -/ +theorem bounds_13_7318 : exactInterval 13 7318 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7318 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7318) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7318 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7318 : oddCount 7318 13 = 5 ∧ acceleratedOrbit 13 7318 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7318 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7318) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7318.1, data_13_7318.2] + +/-- Complete interval computation for depth 13, residue 7319. -/ +theorem bounds_13_7319 : exactInterval 13 7319 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7319 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7319) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7319 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7319 : oddCount 7319 13 = 5 ∧ acceleratedOrbit 13 7319 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7319 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7319) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7319.1, data_13_7319.2] + +/-- Complete interval computation for depth 13, residue 7320. -/ +theorem bounds_13_7320 : exactInterval 13 7320 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7320 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7320) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7320 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7320 : oddCount 7320 13 = 5 ∧ acceleratedOrbit 13 7320 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7320 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7320) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7320.1, data_13_7320.2] + +/-- Complete interval computation for depth 13, residue 7321. -/ +theorem bounds_13_7321 : exactInterval 13 7321 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7321 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7321) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7321 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7321 : oddCount 7321 13 = 6 ∧ acceleratedOrbit 13 7321 = 652 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7321 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7321) = 3 ^ 6 * m + 652 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7321.1, data_13_7321.2] + +/-- Complete interval computation for depth 13, residue 7322. -/ +theorem bounds_13_7322 : exactInterval 13 7322 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7322 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7322) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7322 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7322 : oddCount 7322 13 = 5 ∧ acceleratedOrbit 13 7322 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7322 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7322) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7322.1, data_13_7322.2] + +/-- Complete interval computation for depth 13, residue 7323. -/ +theorem bounds_13_7323 : exactInterval 13 7323 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7323 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7323) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7323 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7323 : oddCount 7323 13 = 9 ∧ acceleratedOrbit 13 7323 = 17599 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7323 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7323) = 3 ^ 9 * m + 17599 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7323.1, data_13_7323.2] + +/-- Complete interval computation for depth 13, residue 7324. -/ +theorem bounds_13_7324 : exactInterval 13 7324 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7324 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7324) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7324 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7324 : oddCount 7324 13 = 7 ∧ acceleratedOrbit 13 7324 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7324 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7324) = 3 ^ 7 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7324.1, data_13_7324.2] + +/-- Complete interval computation for depth 13, residue 7325. -/ +theorem bounds_13_7325 : exactInterval 13 7325 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7325 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7325) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7325 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7325 : oddCount 7325 13 = 7 ∧ acceleratedOrbit 13 7325 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7325 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7325) = 3 ^ 7 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7325.1, data_13_7325.2] + +/-- Complete interval computation for depth 13, residue 7326. -/ +theorem bounds_13_7326 : exactInterval 13 7326 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7326 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7326) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7326 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7326 : oddCount 7326 13 = 7 ∧ acceleratedOrbit 13 7326 = 1957 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7326 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7326) = 3 ^ 7 * m + 1957 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7326.1, data_13_7326.2] + +/-- Complete interval computation for depth 13, residue 7327. -/ +theorem bounds_13_7327 : exactInterval 13 7327 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7327 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7327) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7327 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7327 : oddCount 7327 13 = 10 ∧ acceleratedOrbit 13 7327 = 52822 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7327 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7327) = 3 ^ 10 * m + 52822 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7327.1, data_13_7327.2] + +/-- Complete interval computation for depth 13, residue 7328. -/ +theorem bounds_13_7328 : exactInterval 13 7328 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7328 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7328) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7328 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7328 : oddCount 7328 13 = 4 ∧ acceleratedOrbit 13 7328 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7328 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7328) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7328.1, data_13_7328.2] + +/-- Complete interval computation for depth 13, residue 7329. -/ +theorem bounds_13_7329 : exactInterval 13 7329 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7329 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7329) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7329 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7329 : oddCount 7329 13 = 9 ∧ acceleratedOrbit 13 7329 = 17617 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7329 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7329) = 3 ^ 9 * m + 17617 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7329.1, data_13_7329.2] + +/-- Complete interval computation for depth 13, residue 7330. -/ +theorem bounds_13_7330 : exactInterval 13 7330 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7330 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7330) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7330 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7330 : oddCount 7330 13 = 6 ∧ acceleratedOrbit 13 7330 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7330 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7330) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7330.1, data_13_7330.2] + +end Collatz.Research.StoppingAtlas.Batch0944 From b5a2e20d987ace504d285cabe61a33c089ec085e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:28 +0530 Subject: [PATCH 0945/1001] proof: certify atlas Batch0945 (13:7331 to 13:7346) --- Collatz/Research/StoppingAtlas/Batch0945.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0945.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0945.lean b/Collatz/Research/StoppingAtlas/Batch0945.lean new file mode 100644 index 00000000..063f5f25 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0945.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0945 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7331. -/ +theorem bounds_13_7331 : exactInterval 13 7331 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7331 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7331) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7331 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7331 : oddCount 7331 13 = 6 ∧ acceleratedOrbit 13 7331 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7331 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7331) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7331.1, data_13_7331.2] + +/-- Complete interval computation for depth 13, residue 7332. -/ +theorem bounds_13_7332 : exactInterval 13 7332 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7332 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7332) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7332 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7332 : oddCount 7332 13 = 6 ∧ acceleratedOrbit 13 7332 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7332 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7332) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7332.1, data_13_7332.2] + +/-- Complete interval computation for depth 13, residue 7333. -/ +theorem bounds_13_7333 : exactInterval 13 7333 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7333 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7333) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7333 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7333 : oddCount 7333 13 = 6 ∧ acceleratedOrbit 13 7333 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7333 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7333) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7333.1, data_13_7333.2] + +/-- Complete interval computation for depth 13, residue 7334. -/ +theorem bounds_13_7334 : exactInterval 13 7334 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7334 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7334) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7334 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7334 : oddCount 7334 13 = 6 ∧ acceleratedOrbit 13 7334 = 653 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7334 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7334) = 3 ^ 6 * m + 653 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7334.1, data_13_7334.2] + +/-- Complete interval computation for depth 13, residue 7335. -/ +theorem bounds_13_7335 : exactInterval 13 7335 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7335 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7335) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7335 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7335 : oddCount 7335 13 = 10 ∧ acceleratedOrbit 13 7335 = 52883 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7335 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7335) = 3 ^ 10 * m + 52883 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7335.1, data_13_7335.2] + +/-- Complete interval computation for depth 13, residue 7336. -/ +theorem bounds_13_7336 : exactInterval 13 7336 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7336 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7336) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7336 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7336 : oddCount 7336 13 = 4 ∧ acceleratedOrbit 13 7336 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7336 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7336) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7336.1, data_13_7336.2] + +/-- Complete interval computation for depth 13, residue 7337. -/ +theorem bounds_13_7337 : exactInterval 13 7337 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7337 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7337) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7337 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7337 : oddCount 7337 13 = 9 ∧ acceleratedOrbit 13 7337 = 17633 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7337 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7337) = 3 ^ 9 * m + 17633 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7337.1, data_13_7337.2] + +/-- Complete interval computation for depth 13, residue 7338. -/ +theorem bounds_13_7338 : exactInterval 13 7338 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7338 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7338) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7338 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7338 : oddCount 7338 13 = 4 ∧ acceleratedOrbit 13 7338 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7338 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7338) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7338.1, data_13_7338.2] + +/-- Complete interval computation for depth 13, residue 7339. -/ +theorem bounds_13_7339 : exactInterval 13 7339 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7339 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7339) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7339 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7339 : oddCount 7339 13 = 7 ∧ acceleratedOrbit 13 7339 = 1961 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7339 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7339) = 3 ^ 7 * m + 1961 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7339.1, data_13_7339.2] + +/-- Complete interval computation for depth 13, residue 7340. -/ +theorem bounds_13_7340 : exactInterval 13 7340 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7340 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7340) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7340 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7340 : oddCount 7340 13 = 5 ∧ acceleratedOrbit 13 7340 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7340 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7340) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7340.1, data_13_7340.2] + +/-- Complete interval computation for depth 13, residue 7341. -/ +theorem bounds_13_7341 : exactInterval 13 7341 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7341 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7341) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7341 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7341 : oddCount 7341 13 = 5 ∧ acceleratedOrbit 13 7341 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7341 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7341) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7341.1, data_13_7341.2] + +/-- Complete interval computation for depth 13, residue 7342. -/ +theorem bounds_13_7342 : exactInterval 13 7342 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7342 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7342) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7342 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7342 : oddCount 7342 13 = 5 ∧ acceleratedOrbit 13 7342 = 218 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7342 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7342) = 3 ^ 5 * m + 218 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7342.1, data_13_7342.2] + +/-- Complete interval computation for depth 13, residue 7343. -/ +theorem bounds_13_7343 : exactInterval 13 7343 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7343 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7343) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7343 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7343 : oddCount 7343 13 = 9 ∧ acceleratedOrbit 13 7343 = 17648 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7343 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7343) = 3 ^ 9 * m + 17648 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7343.1, data_13_7343.2] + +/-- Complete interval computation for depth 13, residue 7344. -/ +theorem bounds_13_7344 : exactInterval 13 7344 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7344 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7344) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7344 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7344 : oddCount 7344 13 = 4 ∧ acceleratedOrbit 13 7344 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7344 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7344) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7344.1, data_13_7344.2] + +/-- Complete interval computation for depth 13, residue 7345. -/ +theorem bounds_13_7345 : exactInterval 13 7345 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7345 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7345) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7345 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7345 : oddCount 7345 13 = 7 ∧ acceleratedOrbit 13 7345 = 1964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7345 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7345) = 3 ^ 7 * m + 1964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7345.1, data_13_7345.2] + +/-- Complete interval computation for depth 13, residue 7346. -/ +theorem bounds_13_7346 : exactInterval 13 7346 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7346 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7346) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7346 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7346 : oddCount 7346 13 = 7 ∧ acceleratedOrbit 13 7346 = 1964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7346 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7346) = 3 ^ 7 * m + 1964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7346.1, data_13_7346.2] + +end Collatz.Research.StoppingAtlas.Batch0945 From 86d2c0036bf05532cec35f38096a4f30981c609f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:28 +0530 Subject: [PATCH 0946/1001] proof: certify atlas Batch0946 (13:7347 to 13:7361) --- Collatz/Research/StoppingAtlas/Batch0946.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0946.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0946.lean b/Collatz/Research/StoppingAtlas/Batch0946.lean new file mode 100644 index 00000000..0dc5956a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0946.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0946 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7347. -/ +theorem bounds_13_7347 : exactInterval 13 7347 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7347 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7347) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7347 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7347 : oddCount 7347 13 = 7 ∧ acceleratedOrbit 13 7347 = 1964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7347 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7347) = 3 ^ 7 * m + 1964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7347.1, data_13_7347.2] + +/-- Complete interval computation for depth 13, residue 7348. -/ +theorem bounds_13_7348 : exactInterval 13 7348 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7348 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7348) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7348 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7348 : oddCount 7348 13 = 4 ∧ acceleratedOrbit 13 7348 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7348 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7348) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7348.1, data_13_7348.2] + +/-- Complete interval computation for depth 13, residue 7349. -/ +theorem bounds_13_7349 : exactInterval 13 7349 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7349 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7349) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7349 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7349 : oddCount 7349 13 = 4 ∧ acceleratedOrbit 13 7349 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7349 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7349) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7349.1, data_13_7349.2] + +/-- Complete interval computation for depth 13, residue 7350. -/ +theorem bounds_13_7350 : exactInterval 13 7350 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7350 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7350) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7350 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7350 : oddCount 7350 13 = 7 ∧ acceleratedOrbit 13 7350 = 1963 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7350 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7350) = 3 ^ 7 * m + 1963 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7350.1, data_13_7350.2] + +/-- Complete interval computation for depth 13, residue 7351. -/ +theorem bounds_13_7351 : exactInterval 13 7351 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7351 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7351) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7351 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7351 : oddCount 7351 13 = 7 ∧ acceleratedOrbit 13 7351 = 1963 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7351 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7351) = 3 ^ 7 * m + 1963 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7351.1, data_13_7351.2] + +/-- Complete interval computation for depth 13, residue 7352. -/ +theorem bounds_13_7352 : exactInterval 13 7352 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7352 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7352) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7352 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7352 : oddCount 7352 13 = 4 ∧ acceleratedOrbit 13 7352 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7352 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7352) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7352.1, data_13_7352.2] + +/-- Complete interval computation for depth 13, residue 7353. -/ +theorem bounds_13_7353 : exactInterval 13 7353 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7353 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7353) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7353 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7353 : oddCount 7353 13 = 7 ∧ acceleratedOrbit 13 7353 = 1964 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7353 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7353) = 3 ^ 7 * m + 1964 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7353.1, data_13_7353.2] + +/-- Complete interval computation for depth 13, residue 7354. -/ +theorem bounds_13_7354 : exactInterval 13 7354 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7354 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7354) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7354 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7354 : oddCount 7354 13 = 4 ∧ acceleratedOrbit 13 7354 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7354 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7354) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7354.1, data_13_7354.2] + +/-- Complete interval computation for depth 13, residue 7355. -/ +theorem bounds_13_7355 : exactInterval 13 7355 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7355 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7355) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7355 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7355 : oddCount 7355 13 = 9 ∧ acceleratedOrbit 13 7355 = 17678 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7355 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7355) = 3 ^ 9 * m + 17678 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7355.1, data_13_7355.2] + +/-- Complete interval computation for depth 13, residue 7356. -/ +theorem bounds_13_7356 : exactInterval 13 7356 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7356 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7356) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7356 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7356 : oddCount 7356 13 = 6 ∧ acceleratedOrbit 13 7356 = 655 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7356 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7356) = 3 ^ 6 * m + 655 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7356.1, data_13_7356.2] + +/-- Complete interval computation for depth 13, residue 7357. -/ +theorem bounds_13_7357 : exactInterval 13 7357 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7357 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7357) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7357 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7357 : oddCount 7357 13 = 6 ∧ acceleratedOrbit 13 7357 = 655 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7357 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7357) = 3 ^ 6 * m + 655 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7357.1, data_13_7357.2] + +/-- Complete interval computation for depth 13, residue 7358. -/ +theorem bounds_13_7358 : exactInterval 13 7358 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7358 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7358) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7358 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7358 : oddCount 7358 13 = 6 ∧ acceleratedOrbit 13 7358 = 655 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7358 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7358) = 3 ^ 6 * m + 655 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7358.1, data_13_7358.2] + +/-- Complete interval computation for depth 13, residue 7359. -/ +theorem bounds_13_7359 : exactInterval 13 7359 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7359 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7359) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7359 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7359 : oddCount 7359 13 = 10 ∧ acceleratedOrbit 13 7359 = 53054 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7359 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7359) = 3 ^ 10 * m + 53054 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7359.1, data_13_7359.2] + +/-- Complete interval computation for depth 13, residue 7360. -/ +theorem bounds_13_7360 : exactInterval 13 7360 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7360 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7360) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7360 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7360 : oddCount 7360 13 = 4 ∧ acceleratedOrbit 13 7360 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7360 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7360) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7360.1, data_13_7360.2] + +/-- Complete interval computation for depth 13, residue 7361. -/ +theorem bounds_13_7361 : exactInterval 13 7361 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7361 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7361) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7361 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7361 : oddCount 7361 13 = 6 ∧ acceleratedOrbit 13 7361 = 656 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7361 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7361) = 3 ^ 6 * m + 656 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7361.1, data_13_7361.2] + +end Collatz.Research.StoppingAtlas.Batch0946 From f4610520d3a2b4ab6115d65c9645083b6581614f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:28 +0530 Subject: [PATCH 0947/1001] proof: certify atlas Batch0947 (13:7362 to 13:7376) --- Collatz/Research/StoppingAtlas/Batch0947.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0947.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0947.lean b/Collatz/Research/StoppingAtlas/Batch0947.lean new file mode 100644 index 00000000..4a90dd23 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0947.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0947 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7362. -/ +theorem bounds_13_7362 : exactInterval 13 7362 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7362 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7362) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7362 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7362 : oddCount 7362 13 = 6 ∧ acceleratedOrbit 13 7362 = 656 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7362 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7362) = 3 ^ 6 * m + 656 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7362.1, data_13_7362.2] + +/-- Complete interval computation for depth 13, residue 7363. -/ +theorem bounds_13_7363 : exactInterval 13 7363 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7363 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7363) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7363 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7363 : oddCount 7363 13 = 6 ∧ acceleratedOrbit 13 7363 = 656 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7363 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7363) = 3 ^ 6 * m + 656 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7363.1, data_13_7363.2] + +/-- Complete interval computation for depth 13, residue 7364. -/ +theorem bounds_13_7364 : exactInterval 13 7364 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7364 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7364) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7364 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7364 : oddCount 7364 13 = 4 ∧ acceleratedOrbit 13 7364 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7364 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7364) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7364.1, data_13_7364.2] + +/-- Complete interval computation for depth 13, residue 7365. -/ +theorem bounds_13_7365 : exactInterval 13 7365 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7365 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7365) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7365 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7365 : oddCount 7365 13 = 4 ∧ acceleratedOrbit 13 7365 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7365 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7365) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7365.1, data_13_7365.2] + +/-- Complete interval computation for depth 13, residue 7366. -/ +theorem bounds_13_7366 : exactInterval 13 7366 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7366 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7366) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7366 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7366 : oddCount 7366 13 = 4 ∧ acceleratedOrbit 13 7366 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7366 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7366) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7366.1, data_13_7366.2] + +/-- Complete interval computation for depth 13, residue 7367. -/ +theorem bounds_13_7367 : exactInterval 13 7367 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7367 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7367) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7367 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7367 : oddCount 7367 13 = 8 ∧ acceleratedOrbit 13 7367 = 5903 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7367 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7367) = 3 ^ 8 * m + 5903 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7367.1, data_13_7367.2] + +/-- Complete interval computation for depth 13, residue 7368. -/ +theorem bounds_13_7368 : exactInterval 13 7368 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7368 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7368) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7368 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7368 : oddCount 7368 13 = 4 ∧ acceleratedOrbit 13 7368 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7368 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7368) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7368.1, data_13_7368.2] + +/-- Complete interval computation for depth 13, residue 7369. -/ +theorem bounds_13_7369 : exactInterval 13 7369 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7369 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7369) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7369 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7369 : oddCount 7369 13 = 7 ∧ acceleratedOrbit 13 7369 = 1970 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7369 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7369) = 3 ^ 7 * m + 1970 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7369.1, data_13_7369.2] + +/-- Complete interval computation for depth 13, residue 7370. -/ +theorem bounds_13_7370 : exactInterval 13 7370 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7370 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7370) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7370 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7370 : oddCount 7370 13 = 4 ∧ acceleratedOrbit 13 7370 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7370 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7370) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7370.1, data_13_7370.2] + +/-- Complete interval computation for depth 13, residue 7371. -/ +theorem bounds_13_7371 : exactInterval 13 7371 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7371 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7371) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7371 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7371 : oddCount 7371 13 = 7 ∧ acceleratedOrbit 13 7371 = 1970 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7371 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7371) = 3 ^ 7 * m + 1970 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7371.1, data_13_7371.2] + +/-- Complete interval computation for depth 13, residue 7372. -/ +theorem bounds_13_7372 : exactInterval 13 7372 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7372 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7372) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7372 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7372 : oddCount 7372 13 = 4 ∧ acceleratedOrbit 13 7372 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7372 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7372) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7372.1, data_13_7372.2] + +/-- Complete interval computation for depth 13, residue 7373. -/ +theorem bounds_13_7373 : exactInterval 13 7373 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7373 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7373) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7373 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7373 : oddCount 7373 13 = 4 ∧ acceleratedOrbit 13 7373 = 73 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7373 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7373) = 3 ^ 4 * m + 73 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7373.1, data_13_7373.2] + +/-- Complete interval computation for depth 13, residue 7374. -/ +theorem bounds_13_7374 : exactInterval 13 7374 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7374 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7374) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7374 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7374 : oddCount 7374 13 = 8 ∧ acceleratedOrbit 13 7374 = 5908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7374 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7374) = 3 ^ 8 * m + 5908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7374.1, data_13_7374.2] + +/-- Complete interval computation for depth 13, residue 7375. -/ +theorem bounds_13_7375 : exactInterval 13 7375 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7375 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7375) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7375 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7375 : oddCount 7375 13 = 8 ∧ acceleratedOrbit 13 7375 = 5908 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7375 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7375) = 3 ^ 8 * m + 5908 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7375.1, data_13_7375.2] + +/-- Complete interval computation for depth 13, residue 7376. -/ +theorem bounds_13_7376 : exactInterval 13 7376 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7376 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7376) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7376 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7376 : oddCount 7376 13 = 4 ∧ acceleratedOrbit 13 7376 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7376 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7376) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7376.1, data_13_7376.2] + +end Collatz.Research.StoppingAtlas.Batch0947 From 4ad39b81606436cc158f590de56753ecfdbfa6aa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:28 +0530 Subject: [PATCH 0948/1001] proof: certify atlas Batch0948 (13:7377 to 13:7392) --- Collatz/Research/StoppingAtlas/Batch0948.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0948.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0948.lean b/Collatz/Research/StoppingAtlas/Batch0948.lean new file mode 100644 index 00000000..1cad6ac5 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0948.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0948 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7377. -/ +theorem bounds_13_7377 : exactInterval 13 7377 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7377 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7377) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7377 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7377 : oddCount 7377 13 = 9 ∧ acceleratedOrbit 13 7377 = 17738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7377 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7377) = 3 ^ 9 * m + 17738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7377.1, data_13_7377.2] + +/-- Complete interval computation for depth 13, residue 7378. -/ +theorem bounds_13_7378 : exactInterval 13 7378 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7378 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7378) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7378 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7378 : oddCount 7378 13 = 9 ∧ acceleratedOrbit 13 7378 = 17738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7378 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7378) = 3 ^ 9 * m + 17738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7378.1, data_13_7378.2] + +/-- Complete interval computation for depth 13, residue 7379. -/ +theorem bounds_13_7379 : exactInterval 13 7379 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7379 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7379) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7379 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7379 : oddCount 7379 13 = 9 ∧ acceleratedOrbit 13 7379 = 17738 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7379 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7379) = 3 ^ 9 * m + 17738 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7379.1, data_13_7379.2] + +/-- Complete interval computation for depth 13, residue 7380. -/ +theorem bounds_13_7380 : exactInterval 13 7380 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7380 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7380) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7380 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7380 : oddCount 7380 13 = 4 ∧ acceleratedOrbit 13 7380 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7380 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7380) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7380.1, data_13_7380.2] + +/-- Complete interval computation for depth 13, residue 7381. -/ +theorem bounds_13_7381 : exactInterval 13 7381 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7381 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7381) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7381 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7381 : oddCount 7381 13 = 4 ∧ acceleratedOrbit 13 7381 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7381 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7381) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7381.1, data_13_7381.2] + +/-- Complete interval computation for depth 13, residue 7382. -/ +theorem bounds_13_7382 : exactInterval 13 7382 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7382 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7382) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7382 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7382 : oddCount 7382 13 = 7 ∧ acceleratedOrbit 13 7382 = 1972 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7382 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7382) = 3 ^ 7 * m + 1972 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7382.1, data_13_7382.2] + +/-- Complete interval computation for depth 13, residue 7383. -/ +theorem bounds_13_7383 : exactInterval 13 7383 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7383 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7383) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7383 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7383 : oddCount 7383 13 = 7 ∧ acceleratedOrbit 13 7383 = 1972 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7383 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7383) = 3 ^ 7 * m + 1972 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7383.1, data_13_7383.2] + +/-- Complete interval computation for depth 13, residue 7384. -/ +theorem bounds_13_7384 : exactInterval 13 7384 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7384 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7384) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7384 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7384 : oddCount 7384 13 = 6 ∧ acceleratedOrbit 13 7384 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7384 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7384) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7384.1, data_13_7384.2] + +/-- Complete interval computation for depth 13, residue 7385. -/ +theorem bounds_13_7385 : exactInterval 13 7385 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7385 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7385) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7385 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7385 : oddCount 7385 13 = 6 ∧ acceleratedOrbit 13 7385 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7385 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7385) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7385.1, data_13_7385.2] + +/-- Complete interval computation for depth 13, residue 7386. -/ +theorem bounds_13_7386 : exactInterval 13 7386 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7386 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7386) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7386 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7386 : oddCount 7386 13 = 6 ∧ acceleratedOrbit 13 7386 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7386 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7386) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7386.1, data_13_7386.2] + +/-- Complete interval computation for depth 13, residue 7387. -/ +theorem bounds_13_7387 : exactInterval 13 7387 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7387 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7387) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7387 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7387 : oddCount 7387 13 = 7 ∧ acceleratedOrbit 13 7387 = 1973 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7387 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7387) = 3 ^ 7 * m + 1973 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7387.1, data_13_7387.2] + +/-- Complete interval computation for depth 13, residue 7388. -/ +theorem bounds_13_7388 : exactInterval 13 7388 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7388 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7388) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7388 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7388 : oddCount 7388 13 = 6 ∧ acceleratedOrbit 13 7388 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7388 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7388) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7388.1, data_13_7388.2] + +/-- Complete interval computation for depth 13, residue 7389. -/ +theorem bounds_13_7389 : exactInterval 13 7389 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7389 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7389) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7389 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7389 : oddCount 7389 13 = 6 ∧ acceleratedOrbit 13 7389 = 658 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7389 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7389) = 3 ^ 6 * m + 658 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7389.1, data_13_7389.2] + +/-- Complete interval computation for depth 13, residue 7390. -/ +theorem bounds_13_7390 : exactInterval 13 7390 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7390 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7390) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7390 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7390 : oddCount 7390 13 = 8 ∧ acceleratedOrbit 13 7390 = 5921 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7390 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7390) = 3 ^ 8 * m + 5921 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7390.1, data_13_7390.2] + +/-- Complete interval computation for depth 13, residue 7391. -/ +theorem bounds_13_7391 : exactInterval 13 7391 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7391 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7391) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7391 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7391 : oddCount 7391 13 = 8 ∧ acceleratedOrbit 13 7391 = 5921 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7391 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7391) = 3 ^ 8 * m + 5921 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7391.1, data_13_7391.2] + +/-- Complete interval computation for depth 13, residue 7392. -/ +theorem bounds_13_7392 : exactInterval 13 7392 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7392 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7392) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7392 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7392 : oddCount 7392 13 = 6 ∧ acceleratedOrbit 13 7392 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7392 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7392) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7392.1, data_13_7392.2] + +end Collatz.Research.StoppingAtlas.Batch0948 From dd42694475912db29204ee1893e7f115c52c6b92 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:29 +0530 Subject: [PATCH 0949/1001] proof: certify atlas Batch0949 (13:7393 to 13:7407) --- Collatz/Research/StoppingAtlas/Batch0949.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0949.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0949.lean b/Collatz/Research/StoppingAtlas/Batch0949.lean new file mode 100644 index 00000000..e38a7f3b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0949.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0949 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7393. -/ +theorem bounds_13_7393 : exactInterval 13 7393 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7393 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7393) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7393 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7393 : oddCount 7393 13 = 8 ∧ acceleratedOrbit 13 7393 = 5923 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7393 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7393) = 3 ^ 8 * m + 5923 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7393.1, data_13_7393.2] + +/-- Complete interval computation for depth 13, residue 7394. -/ +theorem bounds_13_7394 : exactInterval 13 7394 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7394 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7394) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7394 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7394 : oddCount 7394 13 = 4 ∧ acceleratedOrbit 13 7394 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7394 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7394) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7394.1, data_13_7394.2] + +/-- Complete interval computation for depth 13, residue 7395. -/ +theorem bounds_13_7395 : exactInterval 13 7395 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7395 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7395) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7395 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7395 : oddCount 7395 13 = 4 ∧ acceleratedOrbit 13 7395 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7395 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7395) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7395.1, data_13_7395.2] + +/-- Complete interval computation for depth 13, residue 7396. -/ +theorem bounds_13_7396 : exactInterval 13 7396 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7396 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7396) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7396 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7396 : oddCount 7396 13 = 6 ∧ acceleratedOrbit 13 7396 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7396 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7396) = 3 ^ 6 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7396.1, data_13_7396.2] + +/-- Complete interval computation for depth 13, residue 7397. -/ +theorem bounds_13_7397 : exactInterval 13 7397 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7397 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7397) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7397 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7397 : oddCount 7397 13 = 6 ∧ acceleratedOrbit 13 7397 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7397 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7397) = 3 ^ 6 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7397.1, data_13_7397.2] + +/-- Complete interval computation for depth 13, residue 7398. -/ +theorem bounds_13_7398 : exactInterval 13 7398 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7398 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7398) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7398 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7398 : oddCount 7398 13 = 6 ∧ acceleratedOrbit 13 7398 = 659 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7398 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7398) = 3 ^ 6 * m + 659 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7398.1, data_13_7398.2] + +/-- Complete interval computation for depth 13, residue 7399. -/ +theorem bounds_13_7399 : exactInterval 13 7399 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7399 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7399) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7399 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7399 : oddCount 7399 13 = 8 ∧ acceleratedOrbit 13 7399 = 5927 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7399 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7399) = 3 ^ 8 * m + 5927 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7399.1, data_13_7399.2] + +/-- Complete interval computation for depth 13, residue 7400. -/ +theorem bounds_13_7400 : exactInterval 13 7400 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7400 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7400) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7400 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7400 : oddCount 7400 13 = 6 ∧ acceleratedOrbit 13 7400 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7400 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7400) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7400.1, data_13_7400.2] + +/-- Complete interval computation for depth 13, residue 7401. -/ +theorem bounds_13_7401 : exactInterval 13 7401 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7401 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7401) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7401 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7401 : oddCount 7401 13 = 8 ∧ acceleratedOrbit 13 7401 = 5930 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7401 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7401) = 3 ^ 8 * m + 5930 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7401.1, data_13_7401.2] + +/-- Complete interval computation for depth 13, residue 7402. -/ +theorem bounds_13_7402 : exactInterval 13 7402 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7402 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7402) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7402 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7402 : oddCount 7402 13 = 6 ∧ acceleratedOrbit 13 7402 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7402 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7402) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7402.1, data_13_7402.2] + +/-- Complete interval computation for depth 13, residue 7403. -/ +theorem bounds_13_7403 : exactInterval 13 7403 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7403 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7403) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7403 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7403 : oddCount 7403 13 = 10 ∧ acceleratedOrbit 13 7403 = 53378 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7403 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7403) = 3 ^ 10 * m + 53378 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7403.1, data_13_7403.2] + +/-- Complete interval computation for depth 13, residue 7404. -/ +theorem bounds_13_7404 : exactInterval 13 7404 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7404 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7404) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7404 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7404 : oddCount 7404 13 = 5 ∧ acceleratedOrbit 13 7404 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7404 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7404) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7404.1, data_13_7404.2] + +/-- Complete interval computation for depth 13, residue 7405. -/ +theorem bounds_13_7405 : exactInterval 13 7405 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7405 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7405) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7405 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7405 : oddCount 7405 13 = 5 ∧ acceleratedOrbit 13 7405 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7405 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7405) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7405.1, data_13_7405.2] + +/-- Complete interval computation for depth 13, residue 7406. -/ +theorem bounds_13_7406 : exactInterval 13 7406 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7406 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7406) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7406 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7406 : oddCount 7406 13 = 5 ∧ acceleratedOrbit 13 7406 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7406 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7406) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7406.1, data_13_7406.2] + +/-- Complete interval computation for depth 13, residue 7407. -/ +theorem bounds_13_7407 : exactInterval 13 7407 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7407 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7407) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7407 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7407 : oddCount 7407 13 = 10 ∧ acceleratedOrbit 13 7407 = 53399 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7407 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7407) = 3 ^ 10 * m + 53399 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7407.1, data_13_7407.2] + +end Collatz.Research.StoppingAtlas.Batch0949 From faccdefa67538e2d22fb9c71d5f08ded017597cc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:29 +0530 Subject: [PATCH 0950/1001] proof: certify atlas Batch0950 (13:7408 to 13:7423) --- Collatz/Research/StoppingAtlas/Batch0950.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0950.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0950.lean b/Collatz/Research/StoppingAtlas/Batch0950.lean new file mode 100644 index 00000000..3f67bf64 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0950.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0950 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7408. -/ +theorem bounds_13_7408 : exactInterval 13 7408 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7408 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7408) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7408 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7408 : oddCount 7408 13 = 6 ∧ acceleratedOrbit 13 7408 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7408 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7408) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7408.1, data_13_7408.2] + +/-- Complete interval computation for depth 13, residue 7409. -/ +theorem bounds_13_7409 : exactInterval 13 7409 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7409 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7409) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7409 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7409 : oddCount 7409 13 = 6 ∧ acceleratedOrbit 13 7409 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7409 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7409) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7409.1, data_13_7409.2] + +/-- Complete interval computation for depth 13, residue 7410. -/ +theorem bounds_13_7410 : exactInterval 13 7410 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7410 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7410) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7410 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7410 : oddCount 7410 13 = 8 ∧ acceleratedOrbit 13 7410 = 5939 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7410 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7410) = 3 ^ 8 * m + 5939 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7410.1, data_13_7410.2] + +/-- Complete interval computation for depth 13, residue 7411. -/ +theorem bounds_13_7411 : exactInterval 13 7411 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7411 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7411) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7411 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7411 : oddCount 7411 13 = 8 ∧ acceleratedOrbit 13 7411 = 5939 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7411 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7411) = 3 ^ 8 * m + 5939 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7411.1, data_13_7411.2] + +/-- Complete interval computation for depth 13, residue 7412. -/ +theorem bounds_13_7412 : exactInterval 13 7412 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7412 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7412) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7412 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7412 : oddCount 7412 13 = 6 ∧ acceleratedOrbit 13 7412 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7412 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7412) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7412.1, data_13_7412.2] + +/-- Complete interval computation for depth 13, residue 7413. -/ +theorem bounds_13_7413 : exactInterval 13 7413 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7413 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7413) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7413 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7413 : oddCount 7413 13 = 6 ∧ acceleratedOrbit 13 7413 = 661 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7413 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7413) = 3 ^ 6 * m + 661 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7413.1, data_13_7413.2] + +/-- Complete interval computation for depth 13, residue 7414. -/ +theorem bounds_13_7414 : exactInterval 13 7414 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7414 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7414) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7414 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7414 : oddCount 7414 13 = 5 ∧ acceleratedOrbit 13 7414 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7414 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7414) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7414.1, data_13_7414.2] + +/-- Complete interval computation for depth 13, residue 7415. -/ +theorem bounds_13_7415 : exactInterval 13 7415 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7415 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7415) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7415 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7415 : oddCount 7415 13 = 5 ∧ acceleratedOrbit 13 7415 = 220 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7415 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7415) = 3 ^ 5 * m + 220 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7415.1, data_13_7415.2] + +/-- Complete interval computation for depth 13, residue 7416. -/ +theorem bounds_13_7416 : exactInterval 13 7416 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7416 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7416) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7416 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7416 : oddCount 7416 13 = 7 ∧ acceleratedOrbit 13 7416 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7416 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7416) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7416.1, data_13_7416.2] + +/-- Complete interval computation for depth 13, residue 7417. -/ +theorem bounds_13_7417 : exactInterval 13 7417 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7417 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7417) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7417 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7417 : oddCount 7417 13 = 7 ∧ acceleratedOrbit 13 7417 = 1981 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7417 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7417) = 3 ^ 7 * m + 1981 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7417.1, data_13_7417.2] + +/-- Complete interval computation for depth 13, residue 7418. -/ +theorem bounds_13_7418 : exactInterval 13 7418 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7418 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7418) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7418 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7418 : oddCount 7418 13 = 7 ∧ acceleratedOrbit 13 7418 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7418 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7418) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7418.1, data_13_7418.2] + +/-- Complete interval computation for depth 13, residue 7419. -/ +theorem bounds_13_7419 : exactInterval 13 7419 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7419 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7419) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7419 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7419 : oddCount 7419 13 = 9 ∧ acceleratedOrbit 13 7419 = 17830 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7419 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7419) = 3 ^ 9 * m + 17830 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7419.1, data_13_7419.2] + +/-- Complete interval computation for depth 13, residue 7420. -/ +theorem bounds_13_7420 : exactInterval 13 7420 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7420 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7420) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7420 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7420 : oddCount 7420 13 = 7 ∧ acceleratedOrbit 13 7420 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7420 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7420) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7420.1, data_13_7420.2] + +/-- Complete interval computation for depth 13, residue 7421. -/ +theorem bounds_13_7421 : exactInterval 13 7421 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7421 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7421) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7421 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7421 : oddCount 7421 13 = 7 ∧ acceleratedOrbit 13 7421 = 1982 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7421 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7421) = 3 ^ 7 * m + 1982 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7421.1, data_13_7421.2] + +/-- Complete interval computation for depth 13, residue 7422. -/ +theorem bounds_13_7422 : exactInterval 13 7422 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7422 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7422) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7422 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7422 : oddCount 7422 13 = 11 ∧ acceleratedOrbit 13 7422 = 160541 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7422 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7422) = 3 ^ 11 * m + 160541 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7422.1, data_13_7422.2] + +/-- Complete interval computation for depth 13, residue 7423. -/ +theorem bounds_13_7423 : exactInterval 13 7423 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7423 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7423) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7423 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7423 : oddCount 7423 13 = 11 ∧ acceleratedOrbit 13 7423 = 160541 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7423 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7423) = 3 ^ 11 * m + 160541 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7423.1, data_13_7423.2] + +end Collatz.Research.StoppingAtlas.Batch0950 From f62feca62bb9058bd5869fe3224046079e63b888 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:29 +0530 Subject: [PATCH 0951/1001] proof: certify atlas Batch0951 (13:7424 to 13:7438) --- Collatz/Research/StoppingAtlas/Batch0951.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0951.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0951.lean b/Collatz/Research/StoppingAtlas/Batch0951.lean new file mode 100644 index 00000000..4077f064 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0951.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0951 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7424. -/ +theorem bounds_13_7424 : exactInterval 13 7424 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7424 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7424) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7424 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7424 : oddCount 7424 13 = 3 ∧ acceleratedOrbit 13 7424 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7424 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7424) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7424.1, data_13_7424.2] + +/-- Complete interval computation for depth 13, residue 7425. -/ +theorem bounds_13_7425 : exactInterval 13 7425 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7425 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7425) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7425 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7425 : oddCount 7425 13 = 7 ∧ acceleratedOrbit 13 7425 = 1984 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7425 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7425) = 3 ^ 7 * m + 1984 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7425.1, data_13_7425.2] + +/-- Complete interval computation for depth 13, residue 7426. -/ +theorem bounds_13_7426 : exactInterval 13 7426 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7426 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7426) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7426 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7426 : oddCount 7426 13 = 8 ∧ acceleratedOrbit 13 7426 = 5953 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7426 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7426) = 3 ^ 8 * m + 5953 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7426.1, data_13_7426.2] + +/-- Complete interval computation for depth 13, residue 7427. -/ +theorem bounds_13_7427 : exactInterval 13 7427 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7427 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7427) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7427 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7427 : oddCount 7427 13 = 8 ∧ acceleratedOrbit 13 7427 = 5953 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7427 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7427) = 3 ^ 8 * m + 5953 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7427.1, data_13_7427.2] + +/-- Complete interval computation for depth 13, residue 7428. -/ +theorem bounds_13_7428 : exactInterval 13 7428 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7428 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7428) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7428 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7428 : oddCount 7428 13 = 4 ∧ acceleratedOrbit 13 7428 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7428 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7428) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7428.1, data_13_7428.2] + +/-- Complete interval computation for depth 13, residue 7429. -/ +theorem bounds_13_7429 : exactInterval 13 7429 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7429 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7429) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7429 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7429 : oddCount 7429 13 = 4 ∧ acceleratedOrbit 13 7429 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7429 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7429) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7429.1, data_13_7429.2] + +/-- Complete interval computation for depth 13, residue 7430. -/ +theorem bounds_13_7430 : exactInterval 13 7430 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7430 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7430) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7430 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7430 : oddCount 7430 13 = 4 ∧ acceleratedOrbit 13 7430 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7430 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7430) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7430.1, data_13_7430.2] + +/-- Complete interval computation for depth 13, residue 7431. -/ +theorem bounds_13_7431 : exactInterval 13 7431 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7431 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7431) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7431 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7431 : oddCount 7431 13 = 9 ∧ acceleratedOrbit 13 7431 = 17860 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7431 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7431) = 3 ^ 9 * m + 17860 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7431.1, data_13_7431.2] + +/-- Complete interval computation for depth 13, residue 7432. -/ +theorem bounds_13_7432 : exactInterval 13 7432 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7432 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7432) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7432 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7432 : oddCount 7432 13 = 5 ∧ acceleratedOrbit 13 7432 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7432 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7432) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7432.1, data_13_7432.2] + +/-- Complete interval computation for depth 13, residue 7433. -/ +theorem bounds_13_7433 : exactInterval 13 7433 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7433 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7433) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7433 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7433 : oddCount 7433 13 = 7 ∧ acceleratedOrbit 13 7433 = 1985 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7433 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7433) = 3 ^ 7 * m + 1985 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7433.1, data_13_7433.2] + +/-- Complete interval computation for depth 13, residue 7434. -/ +theorem bounds_13_7434 : exactInterval 13 7434 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7434 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7434) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7434 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7434 : oddCount 7434 13 = 5 ∧ acceleratedOrbit 13 7434 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7434 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7434) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7434.1, data_13_7434.2] + +/-- Complete interval computation for depth 13, residue 7435. -/ +theorem bounds_13_7435 : exactInterval 13 7435 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7435 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7435) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7435 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7435 : oddCount 7435 13 = 6 ∧ acceleratedOrbit 13 7435 = 662 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7435 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7435) = 3 ^ 6 * m + 662 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7435.1, data_13_7435.2] + +/-- Complete interval computation for depth 13, residue 7436. -/ +theorem bounds_13_7436 : exactInterval 13 7436 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7436 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7436) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7436 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7436 : oddCount 7436 13 = 5 ∧ acceleratedOrbit 13 7436 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7436 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7436) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7436.1, data_13_7436.2] + +/-- Complete interval computation for depth 13, residue 7437. -/ +theorem bounds_13_7437 : exactInterval 13 7437 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7437 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7437) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7437 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7437 : oddCount 7437 13 = 5 ∧ acceleratedOrbit 13 7437 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7437 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7437) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7437.1, data_13_7437.2] + +/-- Complete interval computation for depth 13, residue 7438. -/ +theorem bounds_13_7438 : exactInterval 13 7438 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7438 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7438) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7438 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7438 : oddCount 7438 13 = 7 ∧ acceleratedOrbit 13 7438 = 1988 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7438 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7438) = 3 ^ 7 * m + 1988 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7438.1, data_13_7438.2] + +end Collatz.Research.StoppingAtlas.Batch0951 From 057a27b63742afdafd8cd0acbe948c9ecc5436c2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:29 +0530 Subject: [PATCH 0952/1001] proof: certify atlas Batch0952 (13:7439 to 13:7453) --- Collatz/Research/StoppingAtlas/Batch0952.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0952.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0952.lean b/Collatz/Research/StoppingAtlas/Batch0952.lean new file mode 100644 index 00000000..5809923e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0952.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0952 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7439. -/ +theorem bounds_13_7439 : exactInterval 13 7439 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7439 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7439) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7439 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7439 : oddCount 7439 13 = 7 ∧ acceleratedOrbit 13 7439 = 1988 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7439 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7439) = 3 ^ 7 * m + 1988 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7439.1, data_13_7439.2] + +/-- Complete interval computation for depth 13, residue 7440. -/ +theorem bounds_13_7440 : exactInterval 13 7440 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7440 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7440) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7440 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7440 : oddCount 7440 13 = 4 ∧ acceleratedOrbit 13 7440 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7440 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7440) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7440.1, data_13_7440.2] + +/-- Complete interval computation for depth 13, residue 7441. -/ +theorem bounds_13_7441 : exactInterval 13 7441 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7441 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7441) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7441 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7441 : oddCount 7441 13 = 5 ∧ acceleratedOrbit 13 7441 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7441 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7441) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7441.1, data_13_7441.2] + +/-- Complete interval computation for depth 13, residue 7442. -/ +theorem bounds_13_7442 : exactInterval 13 7442 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7442 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7442) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7442 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7442 : oddCount 7442 13 = 9 ∧ acceleratedOrbit 13 7442 = 17891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7442 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7442) = 3 ^ 9 * m + 17891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7442.1, data_13_7442.2] + +/-- Complete interval computation for depth 13, residue 7443. -/ +theorem bounds_13_7443 : exactInterval 13 7443 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7443 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7443) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7443 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7443 : oddCount 7443 13 = 9 ∧ acceleratedOrbit 13 7443 = 17891 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7443 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7443) = 3 ^ 9 * m + 17891 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7443.1, data_13_7443.2] + +/-- Complete interval computation for depth 13, residue 7444. -/ +theorem bounds_13_7444 : exactInterval 13 7444 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7444 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7444) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7444 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7444 : oddCount 7444 13 = 4 ∧ acceleratedOrbit 13 7444 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7444 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7444) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7444.1, data_13_7444.2] + +/-- Complete interval computation for depth 13, residue 7445. -/ +theorem bounds_13_7445 : exactInterval 13 7445 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7445 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7445) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7445 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7445 : oddCount 7445 13 = 4 ∧ acceleratedOrbit 13 7445 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7445 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7445) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7445.1, data_13_7445.2] + +/-- Complete interval computation for depth 13, residue 7446. -/ +theorem bounds_13_7446 : exactInterval 13 7446 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7446 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7446) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7446 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7446 : oddCount 7446 13 = 5 ∧ acceleratedOrbit 13 7446 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7446 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7446) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7446.1, data_13_7446.2] + +/-- Complete interval computation for depth 13, residue 7447. -/ +theorem bounds_13_7447 : exactInterval 13 7447 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7447 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7447) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7447 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7447 : oddCount 7447 13 = 5 ∧ acceleratedOrbit 13 7447 = 221 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7447 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7447) = 3 ^ 5 * m + 221 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7447.1, data_13_7447.2] + +/-- Complete interval computation for depth 13, residue 7448. -/ +theorem bounds_13_7448 : exactInterval 13 7448 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7448 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7448) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7448 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7448 : oddCount 7448 13 = 4 ∧ acceleratedOrbit 13 7448 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7448 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7448) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7448.1, data_13_7448.2] + +/-- Complete interval computation for depth 13, residue 7449. -/ +theorem bounds_13_7449 : exactInterval 13 7449 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7449 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7449) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7449 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7449 : oddCount 7449 13 = 8 ∧ acceleratedOrbit 13 7449 = 5969 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7449 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7449) = 3 ^ 8 * m + 5969 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7449.1, data_13_7449.2] + +/-- Complete interval computation for depth 13, residue 7450. -/ +theorem bounds_13_7450 : exactInterval 13 7450 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7450 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7450) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7450 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7450 : oddCount 7450 13 = 4 ∧ acceleratedOrbit 13 7450 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7450 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7450) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7450.1, data_13_7450.2] + +/-- Complete interval computation for depth 13, residue 7451. -/ +theorem bounds_13_7451 : exactInterval 13 7451 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7451 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7451) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7451 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7451 : oddCount 7451 13 = 9 ∧ acceleratedOrbit 13 7451 = 17906 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7451 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7451) = 3 ^ 9 * m + 17906 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7451.1, data_13_7451.2] + +/-- Complete interval computation for depth 13, residue 7452. -/ +theorem bounds_13_7452 : exactInterval 13 7452 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7452 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7452) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7452 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7452 : oddCount 7452 13 = 7 ∧ acceleratedOrbit 13 7452 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7452 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7452) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7452.1, data_13_7452.2] + +/-- Complete interval computation for depth 13, residue 7453. -/ +theorem bounds_13_7453 : exactInterval 13 7453 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7453 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7453) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7453 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7453 : oddCount 7453 13 = 7 ∧ acceleratedOrbit 13 7453 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7453 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7453) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7453.1, data_13_7453.2] + +end Collatz.Research.StoppingAtlas.Batch0952 From 2c7a292869bcd3b28eab0fcf4af1046b3f2f164b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:29 +0530 Subject: [PATCH 0953/1001] proof: certify atlas Batch0953 (13:7454 to 13:7469) --- Collatz/Research/StoppingAtlas/Batch0953.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0953.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0953.lean b/Collatz/Research/StoppingAtlas/Batch0953.lean new file mode 100644 index 00000000..6219544b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0953.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0953 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7454. -/ +theorem bounds_13_7454 : exactInterval 13 7454 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7454 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7454) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7454 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7454 : oddCount 7454 13 = 7 ∧ acceleratedOrbit 13 7454 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7454 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7454) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7454.1, data_13_7454.2] + +/-- Complete interval computation for depth 13, residue 7455. -/ +theorem bounds_13_7455 : exactInterval 13 7455 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7455 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7455) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7455 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7455 : oddCount 7455 13 = 7 ∧ acceleratedOrbit 13 7455 = 1991 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7455 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7455) = 3 ^ 7 * m + 1991 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7455.1, data_13_7455.2] + +/-- Complete interval computation for depth 13, residue 7456. -/ +theorem bounds_13_7456 : exactInterval 13 7456 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7456 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7456) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7456 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7456 : oddCount 7456 13 = 6 ∧ acceleratedOrbit 13 7456 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7456 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7456) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7456.1, data_13_7456.2] + +/-- Complete interval computation for depth 13, residue 7457. -/ +theorem bounds_13_7457 : exactInterval 13 7457 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7457 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7457) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7457 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7457 : oddCount 7457 13 = 6 ∧ acceleratedOrbit 13 7457 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7457 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7457) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7457.1, data_13_7457.2] + +/-- Complete interval computation for depth 13, residue 7458. -/ +theorem bounds_13_7458 : exactInterval 13 7458 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7458 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7458) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7458 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7458 : oddCount 7458 13 = 6 ∧ acceleratedOrbit 13 7458 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7458 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7458) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7458.1, data_13_7458.2] + +/-- Complete interval computation for depth 13, residue 7459. -/ +theorem bounds_13_7459 : exactInterval 13 7459 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7459 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7459) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7459 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7459 : oddCount 7459 13 = 6 ∧ acceleratedOrbit 13 7459 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7459 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7459) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7459.1, data_13_7459.2] + +/-- Complete interval computation for depth 13, residue 7460. -/ +theorem bounds_13_7460 : exactInterval 13 7460 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7460 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7460) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7460 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7460 : oddCount 7460 13 = 6 ∧ acceleratedOrbit 13 7460 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7460 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7460) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7460.1, data_13_7460.2] + +/-- Complete interval computation for depth 13, residue 7461. -/ +theorem bounds_13_7461 : exactInterval 13 7461 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7461 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7461) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7461 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7461 : oddCount 7461 13 = 6 ∧ acceleratedOrbit 13 7461 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7461 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7461) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7461.1, data_13_7461.2] + +/-- Complete interval computation for depth 13, residue 7462. -/ +theorem bounds_13_7462 : exactInterval 13 7462 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7462 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7462) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7462 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7462 : oddCount 7462 13 = 6 ∧ acceleratedOrbit 13 7462 = 665 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7462 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7462) = 3 ^ 6 * m + 665 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7462.1, data_13_7462.2] + +/-- Complete interval computation for depth 13, residue 7463. -/ +theorem bounds_13_7463 : exactInterval 13 7463 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7463 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7463) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7463 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7463 : oddCount 7463 13 = 7 ∧ acceleratedOrbit 13 7463 = 1993 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7463 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7463) = 3 ^ 7 * m + 1993 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7463.1, data_13_7463.2] + +/-- Complete interval computation for depth 13, residue 7464. -/ +theorem bounds_13_7464 : exactInterval 13 7464 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7464 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7464) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7464 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7464 : oddCount 7464 13 = 6 ∧ acceleratedOrbit 13 7464 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7464 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7464) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7464.1, data_13_7464.2] + +/-- Complete interval computation for depth 13, residue 7465. -/ +theorem bounds_13_7465 : exactInterval 13 7465 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7465 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7465) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7465 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7465 : oddCount 7465 13 = 9 ∧ acceleratedOrbit 13 7465 = 17941 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7465 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7465) = 3 ^ 9 * m + 17941 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7465.1, data_13_7465.2] + +/-- Complete interval computation for depth 13, residue 7466. -/ +theorem bounds_13_7466 : exactInterval 13 7466 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7466 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7466) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7466 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7466 : oddCount 7466 13 = 6 ∧ acceleratedOrbit 13 7466 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7466 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7466) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7466.1, data_13_7466.2] + +/-- Complete interval computation for depth 13, residue 7467. -/ +theorem bounds_13_7467 : exactInterval 13 7467 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7467 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7467) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7467 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7467 : oddCount 7467 13 = 8 ∧ acceleratedOrbit 13 7467 = 5984 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7467 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7467) = 3 ^ 8 * m + 5984 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7467.1, data_13_7467.2] + +/-- Complete interval computation for depth 13, residue 7468. -/ +theorem bounds_13_7468 : exactInterval 13 7468 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7468 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7468) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7468 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7468 : oddCount 7468 13 = 4 ∧ acceleratedOrbit 13 7468 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7468 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7468) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7468.1, data_13_7468.2] + +/-- Complete interval computation for depth 13, residue 7469. -/ +theorem bounds_13_7469 : exactInterval 13 7469 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7469 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7469) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7469 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7469 : oddCount 7469 13 = 4 ∧ acceleratedOrbit 13 7469 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7469 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7469) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7469.1, data_13_7469.2] + +end Collatz.Research.StoppingAtlas.Batch0953 From ab8b9f815351753ed513ffd6aef6d33a819e292e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:30 +0530 Subject: [PATCH 0954/1001] proof: certify atlas Batch0954 (13:7470 to 13:7484) --- Collatz/Research/StoppingAtlas/Batch0954.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0954.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0954.lean b/Collatz/Research/StoppingAtlas/Batch0954.lean new file mode 100644 index 00000000..2941a527 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0954.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0954 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7470. -/ +theorem bounds_13_7470 : exactInterval 13 7470 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7470 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7470) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7470 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7470 : oddCount 7470 13 = 4 ∧ acceleratedOrbit 13 7470 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7470 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7470) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7470.1, data_13_7470.2] + +/-- Complete interval computation for depth 13, residue 7471. -/ +theorem bounds_13_7471 : exactInterval 13 7471 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7471 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7471) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7471 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7471 : oddCount 7471 13 = 10 ∧ acceleratedOrbit 13 7471 = 53864 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7471 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7471) = 3 ^ 10 * m + 53864 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7471.1, data_13_7471.2] + +/-- Complete interval computation for depth 13, residue 7472. -/ +theorem bounds_13_7472 : exactInterval 13 7472 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7472 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7472) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7472 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7472 : oddCount 7472 13 = 6 ∧ acceleratedOrbit 13 7472 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7472 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7472) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7472.1, data_13_7472.2] + +/-- Complete interval computation for depth 13, residue 7473. -/ +theorem bounds_13_7473 : exactInterval 13 7473 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7473 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7473) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7473 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7473 : oddCount 7473 13 = 8 ∧ acceleratedOrbit 13 7473 = 5993 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7473 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7473) = 3 ^ 8 * m + 5993 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7473.1, data_13_7473.2] + +/-- Complete interval computation for depth 13, residue 7474. -/ +theorem bounds_13_7474 : exactInterval 13 7474 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7474 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7474) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7474 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7474 : oddCount 7474 13 = 8 ∧ acceleratedOrbit 13 7474 = 5993 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7474 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7474) = 3 ^ 8 * m + 5993 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7474.1, data_13_7474.2] + +/-- Complete interval computation for depth 13, residue 7475. -/ +theorem bounds_13_7475 : exactInterval 13 7475 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7475 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7475) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7475 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7475 : oddCount 7475 13 = 8 ∧ acceleratedOrbit 13 7475 = 5993 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7475 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7475) = 3 ^ 8 * m + 5993 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7475.1, data_13_7475.2] + +/-- Complete interval computation for depth 13, residue 7476. -/ +theorem bounds_13_7476 : exactInterval 13 7476 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7476 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7476) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7476 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7476 : oddCount 7476 13 = 6 ∧ acceleratedOrbit 13 7476 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7476 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7476) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7476.1, data_13_7476.2] + +/-- Complete interval computation for depth 13, residue 7477. -/ +theorem bounds_13_7477 : exactInterval 13 7477 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7477 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7477) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7477 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7477 : oddCount 7477 13 = 6 ∧ acceleratedOrbit 13 7477 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7477 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7477) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7477.1, data_13_7477.2] + +/-- Complete interval computation for depth 13, residue 7478. -/ +theorem bounds_13_7478 : exactInterval 13 7478 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7478 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7478) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7478 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7478 : oddCount 7478 13 = 9 ∧ acceleratedOrbit 13 7478 = 17975 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7478 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7478) = 3 ^ 9 * m + 17975 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7478.1, data_13_7478.2] + +/-- Complete interval computation for depth 13, residue 7479. -/ +theorem bounds_13_7479 : exactInterval 13 7479 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7479 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7479) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7479 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7479 : oddCount 7479 13 = 9 ∧ acceleratedOrbit 13 7479 = 17975 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7479 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7479) = 3 ^ 9 * m + 17975 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7479.1, data_13_7479.2] + +/-- Complete interval computation for depth 13, residue 7480. -/ +theorem bounds_13_7480 : exactInterval 13 7480 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7480 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7480) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7480 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7480 : oddCount 7480 13 = 7 ∧ acceleratedOrbit 13 7480 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7480 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7480) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7480.1, data_13_7480.2] + +/-- Complete interval computation for depth 13, residue 7481. -/ +theorem bounds_13_7481 : exactInterval 13 7481 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7481 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7481) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7481 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7481 : oddCount 7481 13 = 10 ∧ acceleratedOrbit 13 7481 = 53945 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7481 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7481) = 3 ^ 10 * m + 53945 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7481.1, data_13_7481.2] + +/-- Complete interval computation for depth 13, residue 7482. -/ +theorem bounds_13_7482 : exactInterval 13 7482 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7482 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7482) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7482 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7482 : oddCount 7482 13 = 7 ∧ acceleratedOrbit 13 7482 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7482 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7482) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7482.1, data_13_7482.2] + +/-- Complete interval computation for depth 13, residue 7483. -/ +theorem bounds_13_7483 : exactInterval 13 7483 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7483 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7483) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7483 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7483 : oddCount 7483 13 = 4 ∧ acceleratedOrbit 13 7483 = 74 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7483 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7483) = 3 ^ 4 * m + 74 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7483.1, data_13_7483.2] + +/-- Complete interval computation for depth 13, residue 7484. -/ +theorem bounds_13_7484 : exactInterval 13 7484 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7484 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7484) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7484 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7484 : oddCount 7484 13 = 7 ∧ acceleratedOrbit 13 7484 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7484 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7484) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7484.1, data_13_7484.2] + +end Collatz.Research.StoppingAtlas.Batch0954 From e1026608055e522988197a6afd51b031a2f0c8c5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:30 +0530 Subject: [PATCH 0955/1001] proof: certify atlas Batch0955 (13:7485 to 13:7499) --- Collatz/Research/StoppingAtlas/Batch0955.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0955.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0955.lean b/Collatz/Research/StoppingAtlas/Batch0955.lean new file mode 100644 index 00000000..e0f2ec13 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0955.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0955 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7485. -/ +theorem bounds_13_7485 : exactInterval 13 7485 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7485 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7485) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7485 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7485 : oddCount 7485 13 = 7 ∧ acceleratedOrbit 13 7485 = 2000 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7485 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7485) = 3 ^ 7 * m + 2000 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7485.1, data_13_7485.2] + +/-- Complete interval computation for depth 13, residue 7486. -/ +theorem bounds_13_7486 : exactInterval 13 7486 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7486 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7486) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7486 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7486 : oddCount 7486 13 = 9 ∧ acceleratedOrbit 13 7486 = 17992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7486 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7486) = 3 ^ 9 * m + 17992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7486.1, data_13_7486.2] + +/-- Complete interval computation for depth 13, residue 7487. -/ +theorem bounds_13_7487 : exactInterval 13 7487 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7487 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7487) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7487 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7487 : oddCount 7487 13 = 9 ∧ acceleratedOrbit 13 7487 = 17992 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7487 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7487) = 3 ^ 9 * m + 17992 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7487.1, data_13_7487.2] + +/-- Complete interval computation for depth 13, residue 7488. -/ +theorem bounds_13_7488 : exactInterval 13 7488 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7488 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7488) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7488 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7488 : oddCount 7488 13 = 3 ∧ acceleratedOrbit 13 7488 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7488 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7488) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7488.1, data_13_7488.2] + +/-- Complete interval computation for depth 13, residue 7489. -/ +theorem bounds_13_7489 : exactInterval 13 7489 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7489 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7489) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7489 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7489 : oddCount 7489 13 = 6 ∧ acceleratedOrbit 13 7489 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7489 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7489) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7489.1, data_13_7489.2] + +/-- Complete interval computation for depth 13, residue 7490. -/ +theorem bounds_13_7490 : exactInterval 13 7490 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7490 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7490) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7490 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7490 : oddCount 7490 13 = 6 ∧ acceleratedOrbit 13 7490 = 667 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7490 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7490) = 3 ^ 6 * m + 667 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7490.1, data_13_7490.2] + +/-- Complete interval computation for depth 13, residue 7491. -/ +theorem bounds_13_7491 : exactInterval 13 7491 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7491 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7491) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7491 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7491 : oddCount 7491 13 = 6 ∧ acceleratedOrbit 13 7491 = 667 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7491 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7491) = 3 ^ 6 * m + 667 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7491.1, data_13_7491.2] + +/-- Complete interval computation for depth 13, residue 7492. -/ +theorem bounds_13_7492 : exactInterval 13 7492 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7492 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7492) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7492 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7492 : oddCount 7492 13 = 6 ∧ acceleratedOrbit 13 7492 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7492 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7492) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7492.1, data_13_7492.2] + +/-- Complete interval computation for depth 13, residue 7493. -/ +theorem bounds_13_7493 : exactInterval 13 7493 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7493 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7493) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7493 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7493 : oddCount 7493 13 = 6 ∧ acceleratedOrbit 13 7493 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7493 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7493) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7493.1, data_13_7493.2] + +/-- Complete interval computation for depth 13, residue 7494. -/ +theorem bounds_13_7494 : exactInterval 13 7494 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7494 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7494) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7494 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7494 : oddCount 7494 13 = 6 ∧ acceleratedOrbit 13 7494 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7494 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7494) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7494.1, data_13_7494.2] + +/-- Complete interval computation for depth 13, residue 7495. -/ +theorem bounds_13_7495 : exactInterval 13 7495 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7495 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7495) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7495 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7495 : oddCount 7495 13 = 8 ∧ acceleratedOrbit 13 7495 = 6004 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7495 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7495) = 3 ^ 8 * m + 6004 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7495.1, data_13_7495.2] + +/-- Complete interval computation for depth 13, residue 7496. -/ +theorem bounds_13_7496 : exactInterval 13 7496 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7496 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7496) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7496 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7496 : oddCount 7496 13 = 8 ∧ acceleratedOrbit 13 7496 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7496 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7496) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7496.1, data_13_7496.2] + +/-- Complete interval computation for depth 13, residue 7497. -/ +theorem bounds_13_7497 : exactInterval 13 7497 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7497 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7497) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7497 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7497 : oddCount 7497 13 = 8 ∧ acceleratedOrbit 13 7497 = 6007 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7497 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7497) = 3 ^ 8 * m + 6007 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7497.1, data_13_7497.2] + +/-- Complete interval computation for depth 13, residue 7498. -/ +theorem bounds_13_7498 : exactInterval 13 7498 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7498 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7498) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7498 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7498 : oddCount 7498 13 = 8 ∧ acceleratedOrbit 13 7498 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7498 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7498) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7498.1, data_13_7498.2] + +/-- Complete interval computation for depth 13, residue 7499. -/ +theorem bounds_13_7499 : exactInterval 13 7499 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7499 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7499) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7499 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7499 : oddCount 7499 13 = 6 ∧ acceleratedOrbit 13 7499 = 668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7499 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7499) = 3 ^ 6 * m + 668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7499.1, data_13_7499.2] + +end Collatz.Research.StoppingAtlas.Batch0955 From 31139554a6f408e09c1b9d90b21c0751cdcfc85d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:30 +0530 Subject: [PATCH 0956/1001] proof: certify atlas Batch0956 (13:7500 to 13:7515) --- Collatz/Research/StoppingAtlas/Batch0956.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0956.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0956.lean b/Collatz/Research/StoppingAtlas/Batch0956.lean new file mode 100644 index 00000000..865dc549 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0956.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0956 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7500. -/ +theorem bounds_13_7500 : exactInterval 13 7500 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7500 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7500) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7500 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7500 : oddCount 7500 13 = 8 ∧ acceleratedOrbit 13 7500 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7500 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7500) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7500.1, data_13_7500.2] + +/-- Complete interval computation for depth 13, residue 7501. -/ +theorem bounds_13_7501 : exactInterval 13 7501 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7501 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7501) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7501 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7501 : oddCount 7501 13 = 8 ∧ acceleratedOrbit 13 7501 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7501 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7501) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7501.1, data_13_7501.2] + +/-- Complete interval computation for depth 13, residue 7502. -/ +theorem bounds_13_7502 : exactInterval 13 7502 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7502 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7502) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7502 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7502 : oddCount 7502 13 = 8 ∧ acceleratedOrbit 13 7502 = 6011 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7502 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7502) = 3 ^ 8 * m + 6011 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7502.1, data_13_7502.2] + +/-- Complete interval computation for depth 13, residue 7503. -/ +theorem bounds_13_7503 : exactInterval 13 7503 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7503 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7503) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7503 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7503 : oddCount 7503 13 = 8 ∧ acceleratedOrbit 13 7503 = 6011 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7503 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7503) = 3 ^ 8 * m + 6011 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7503.1, data_13_7503.2] + +/-- Complete interval computation for depth 13, residue 7504. -/ +theorem bounds_13_7504 : exactInterval 13 7504 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7504 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7504) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7504 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7504 : oddCount 7504 13 = 3 ∧ acceleratedOrbit 13 7504 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7504 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7504) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7504.1, data_13_7504.2] + +/-- Complete interval computation for depth 13, residue 7505. -/ +theorem bounds_13_7505 : exactInterval 13 7505 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7505 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7505) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7505 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7505 : oddCount 7505 13 = 8 ∧ acceleratedOrbit 13 7505 = 6014 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7505 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7505) = 3 ^ 8 * m + 6014 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7505.1, data_13_7505.2] + +/-- Complete interval computation for depth 13, residue 7506. -/ +theorem bounds_13_7506 : exactInterval 13 7506 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7506 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7506) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7506 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7506 : oddCount 7506 13 = 10 ∧ acceleratedOrbit 13 7506 = 54128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7506 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7506) = 3 ^ 10 * m + 54128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7506.1, data_13_7506.2] + +/-- Complete interval computation for depth 13, residue 7507. -/ +theorem bounds_13_7507 : exactInterval 13 7507 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7507 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7507) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7507 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7507 : oddCount 7507 13 = 10 ∧ acceleratedOrbit 13 7507 = 54128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7507 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7507) = 3 ^ 10 * m + 54128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7507.1, data_13_7507.2] + +/-- Complete interval computation for depth 13, residue 7508. -/ +theorem bounds_13_7508 : exactInterval 13 7508 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7508 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7508) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7508 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7508 : oddCount 7508 13 = 3 ∧ acceleratedOrbit 13 7508 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7508 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7508) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7508.1, data_13_7508.2] + +/-- Complete interval computation for depth 13, residue 7509. -/ +theorem bounds_13_7509 : exactInterval 13 7509 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7509 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7509) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7509 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7509 : oddCount 7509 13 = 3 ∧ acceleratedOrbit 13 7509 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7509 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7509) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7509.1, data_13_7509.2] + +/-- Complete interval computation for depth 13, residue 7510. -/ +theorem bounds_13_7510 : exactInterval 13 7510 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7510 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7510) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7510 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7510 : oddCount 7510 13 = 8 ∧ acceleratedOrbit 13 7510 = 6020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7510 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7510) = 3 ^ 8 * m + 6020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7510.1, data_13_7510.2] + +/-- Complete interval computation for depth 13, residue 7511. -/ +theorem bounds_13_7511 : exactInterval 13 7511 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7511 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7511) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7511 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7511 : oddCount 7511 13 = 8 ∧ acceleratedOrbit 13 7511 = 6020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7511 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7511) = 3 ^ 8 * m + 6020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7511.1, data_13_7511.2] + +/-- Complete interval computation for depth 13, residue 7512. -/ +theorem bounds_13_7512 : exactInterval 13 7512 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7512 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7512) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7512 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7512 : oddCount 7512 13 = 6 ∧ acceleratedOrbit 13 7512 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7512 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7512) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7512.1, data_13_7512.2] + +/-- Complete interval computation for depth 13, residue 7513. -/ +theorem bounds_13_7513 : exactInterval 13 7513 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7513 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7513) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7513 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7513 : oddCount 7513 13 = 5 ∧ acceleratedOrbit 13 7513 = 223 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7513 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7513) = 3 ^ 5 * m + 223 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7513.1, data_13_7513.2] + +/-- Complete interval computation for depth 13, residue 7514. -/ +theorem bounds_13_7514 : exactInterval 13 7514 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7514 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7514) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7514 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7514 : oddCount 7514 13 = 6 ∧ acceleratedOrbit 13 7514 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7514 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7514) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7514.1, data_13_7514.2] + +/-- Complete interval computation for depth 13, residue 7515. -/ +theorem bounds_13_7515 : exactInterval 13 7515 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7515 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7515) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7515 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7515 : oddCount 7515 13 = 9 ∧ acceleratedOrbit 13 7515 = 18062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7515 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7515) = 3 ^ 9 * m + 18062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7515.1, data_13_7515.2] + +end Collatz.Research.StoppingAtlas.Batch0956 From 5d1fd35343f86ff29341822c443a000b59dfaf31 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:30 +0530 Subject: [PATCH 0957/1001] proof: certify atlas Batch0957 (13:7516 to 13:7530) --- Collatz/Research/StoppingAtlas/Batch0957.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0957.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0957.lean b/Collatz/Research/StoppingAtlas/Batch0957.lean new file mode 100644 index 00000000..8d8de6cb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0957.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0957 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7516. -/ +theorem bounds_13_7516 : exactInterval 13 7516 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7516 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7516) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7516 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7516 : oddCount 7516 13 = 6 ∧ acceleratedOrbit 13 7516 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7516 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7516) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7516.1, data_13_7516.2] + +/-- Complete interval computation for depth 13, residue 7517. -/ +theorem bounds_13_7517 : exactInterval 13 7517 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7517 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7517) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7517 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7517 : oddCount 7517 13 = 6 ∧ acceleratedOrbit 13 7517 = 670 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7517 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7517) = 3 ^ 6 * m + 670 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7517.1, data_13_7517.2] + +/-- Complete interval computation for depth 13, residue 7518. -/ +theorem bounds_13_7518 : exactInterval 13 7518 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7518 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7518) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7518 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7518 : oddCount 7518 13 = 7 ∧ acceleratedOrbit 13 7518 = 2008 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7518 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7518) = 3 ^ 7 * m + 2008 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7518.1, data_13_7518.2] + +/-- Complete interval computation for depth 13, residue 7519. -/ +theorem bounds_13_7519 : exactInterval 13 7519 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7519 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7519) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7519 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7519 : oddCount 7519 13 = 7 ∧ acceleratedOrbit 13 7519 = 2008 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7519 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7519) = 3 ^ 7 * m + 2008 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7519.1, data_13_7519.2] + +/-- Complete interval computation for depth 13, residue 7520. -/ +theorem bounds_13_7520 : exactInterval 13 7520 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7520 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7520) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7520 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7520 : oddCount 7520 13 = 6 ∧ acceleratedOrbit 13 7520 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7520 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7520) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7520.1, data_13_7520.2] + +/-- Complete interval computation for depth 13, residue 7521. -/ +theorem bounds_13_7521 : exactInterval 13 7521 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7521 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7521) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7521 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7521 : oddCount 7521 13 = 7 ∧ acceleratedOrbit 13 7521 = 2009 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7521 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7521) = 3 ^ 7 * m + 2009 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7521.1, data_13_7521.2] + +/-- Complete interval computation for depth 13, residue 7522. -/ +theorem bounds_13_7522 : exactInterval 13 7522 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7522 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7522) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7522 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7522 : oddCount 7522 13 = 5 ∧ acceleratedOrbit 13 7522 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7522 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7522) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7522.1, data_13_7522.2] + +/-- Complete interval computation for depth 13, residue 7523. -/ +theorem bounds_13_7523 : exactInterval 13 7523 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7523 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7523) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7523 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7523 : oddCount 7523 13 = 5 ∧ acceleratedOrbit 13 7523 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7523 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7523) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7523.1, data_13_7523.2] + +/-- Complete interval computation for depth 13, residue 7524. -/ +theorem bounds_13_7524 : exactInterval 13 7524 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7524 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7524) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7524 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7524 : oddCount 7524 13 = 5 ∧ acceleratedOrbit 13 7524 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7524 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7524) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7524.1, data_13_7524.2] + +/-- Complete interval computation for depth 13, residue 7525. -/ +theorem bounds_13_7525 : exactInterval 13 7525 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7525 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7525) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7525 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7525 : oddCount 7525 13 = 5 ∧ acceleratedOrbit 13 7525 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7525 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7525) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7525.1, data_13_7525.2] + +/-- Complete interval computation for depth 13, residue 7526. -/ +theorem bounds_13_7526 : exactInterval 13 7526 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7526 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7526) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7526 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7526 : oddCount 7526 13 = 5 ∧ acceleratedOrbit 13 7526 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7526 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7526) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7526.1, data_13_7526.2] + +/-- Complete interval computation for depth 13, residue 7527. -/ +theorem bounds_13_7527 : exactInterval 13 7527 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7527 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7527) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7527 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7527 : oddCount 7527 13 = 10 ∧ acceleratedOrbit 13 7527 = 54265 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7527 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7527) = 3 ^ 10 * m + 54265 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7527.1, data_13_7527.2] + +/-- Complete interval computation for depth 13, residue 7528. -/ +theorem bounds_13_7528 : exactInterval 13 7528 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7528 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7528) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7528 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7528 : oddCount 7528 13 = 6 ∧ acceleratedOrbit 13 7528 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7528 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7528) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7528.1, data_13_7528.2] + +/-- Complete interval computation for depth 13, residue 7529. -/ +theorem bounds_13_7529 : exactInterval 13 7529 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7529 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7529) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7529 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7529 : oddCount 7529 13 = 7 ∧ acceleratedOrbit 13 7529 = 2011 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7529 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7529) = 3 ^ 7 * m + 2011 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7529.1, data_13_7529.2] + +/-- Complete interval computation for depth 13, residue 7530. -/ +theorem bounds_13_7530 : exactInterval 13 7530 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7530 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7530) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7530 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7530 : oddCount 7530 13 = 6 ∧ acceleratedOrbit 13 7530 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7530 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7530) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7530.1, data_13_7530.2] + +end Collatz.Research.StoppingAtlas.Batch0957 From 9fe74488825baafd26dc8f63262069033c4b5d21 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:30 +0530 Subject: [PATCH 0958/1001] proof: certify atlas Batch0958 (13:7531 to 13:7545) --- Collatz/Research/StoppingAtlas/Batch0958.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0958.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0958.lean b/Collatz/Research/StoppingAtlas/Batch0958.lean new file mode 100644 index 00000000..35c6e1fe --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0958.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0958 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7531. -/ +theorem bounds_13_7531 : exactInterval 13 7531 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7531 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7531) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7531 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7531 : oddCount 7531 13 = 8 ∧ acceleratedOrbit 13 7531 = 6034 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7531 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7531) = 3 ^ 8 * m + 6034 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7531.1, data_13_7531.2] + +/-- Complete interval computation for depth 13, residue 7532. -/ +theorem bounds_13_7532 : exactInterval 13 7532 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7532 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7532) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7532 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7532 : oddCount 7532 13 = 8 ∧ acceleratedOrbit 13 7532 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7532 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7532) = 3 ^ 8 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7532.1, data_13_7532.2] + +/-- Complete interval computation for depth 13, residue 7533. -/ +theorem bounds_13_7533 : exactInterval 13 7533 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7533 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7533) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7533 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7533 : oddCount 7533 13 = 8 ∧ acceleratedOrbit 13 7533 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7533 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7533) = 3 ^ 8 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7533.1, data_13_7533.2] + +/-- Complete interval computation for depth 13, residue 7534. -/ +theorem bounds_13_7534 : exactInterval 13 7534 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7534 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7534) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7534 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7534 : oddCount 7534 13 = 8 ∧ acceleratedOrbit 13 7534 = 6038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7534 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7534) = 3 ^ 8 * m + 6038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7534.1, data_13_7534.2] + +/-- Complete interval computation for depth 13, residue 7535. -/ +theorem bounds_13_7535 : exactInterval 13 7535 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7535 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7535) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7535 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7535 : oddCount 7535 13 = 7 ∧ acceleratedOrbit 13 7535 = 2012 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7535 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7535) = 3 ^ 7 * m + 2012 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7535.1, data_13_7535.2] + +/-- Complete interval computation for depth 13, residue 7536. -/ +theorem bounds_13_7536 : exactInterval 13 7536 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7536 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7536) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7536 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7536 : oddCount 7536 13 = 6 ∧ acceleratedOrbit 13 7536 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7536 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7536) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7536.1, data_13_7536.2] + +/-- Complete interval computation for depth 13, residue 7537. -/ +theorem bounds_13_7537 : exactInterval 13 7537 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7537 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7537) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7537 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7537 : oddCount 7537 13 = 6 ∧ acceleratedOrbit 13 7537 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7537 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7537) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7537.1, data_13_7537.2] + +/-- Complete interval computation for depth 13, residue 7538. -/ +theorem bounds_13_7538 : exactInterval 13 7538 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7538 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7538) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7538 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7538 : oddCount 7538 13 = 7 ∧ acceleratedOrbit 13 7538 = 2015 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7538 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7538) = 3 ^ 7 * m + 2015 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7538.1, data_13_7538.2] + +/-- Complete interval computation for depth 13, residue 7539. -/ +theorem bounds_13_7539 : exactInterval 13 7539 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7539 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7539) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7539 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7539 : oddCount 7539 13 = 7 ∧ acceleratedOrbit 13 7539 = 2015 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7539 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7539) = 3 ^ 7 * m + 2015 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7539.1, data_13_7539.2] + +/-- Complete interval computation for depth 13, residue 7540. -/ +theorem bounds_13_7540 : exactInterval 13 7540 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7540 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7540) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7540 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7540 : oddCount 7540 13 = 6 ∧ acceleratedOrbit 13 7540 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7540 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7540) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7540.1, data_13_7540.2] + +/-- Complete interval computation for depth 13, residue 7541. -/ +theorem bounds_13_7541 : exactInterval 13 7541 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7541 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7541) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7541 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7541 : oddCount 7541 13 = 6 ∧ acceleratedOrbit 13 7541 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7541 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7541) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7541.1, data_13_7541.2] + +/-- Complete interval computation for depth 13, residue 7542. -/ +theorem bounds_13_7542 : exactInterval 13 7542 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7542 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7542) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7542 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7542 : oddCount 7542 13 = 7 ∧ acceleratedOrbit 13 7542 = 2015 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7542 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7542) = 3 ^ 7 * m + 2015 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7542.1, data_13_7542.2] + +/-- Complete interval computation for depth 13, residue 7543. -/ +theorem bounds_13_7543 : exactInterval 13 7543 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7543 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7543) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7543 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7543 : oddCount 7543 13 = 7 ∧ acceleratedOrbit 13 7543 = 2015 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7543 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7543) = 3 ^ 7 * m + 2015 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7543.1, data_13_7543.2] + +/-- Complete interval computation for depth 13, residue 7544. -/ +theorem bounds_13_7544 : exactInterval 13 7544 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7544 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7544) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7544 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7544 : oddCount 7544 13 = 5 ∧ acceleratedOrbit 13 7544 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7544 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7544) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7544.1, data_13_7544.2] + +/-- Complete interval computation for depth 13, residue 7545. -/ +theorem bounds_13_7545 : exactInterval 13 7545 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7545 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7545) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7545 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7545 : oddCount 7545 13 = 9 ∧ acceleratedOrbit 13 7545 = 18134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7545 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7545) = 3 ^ 9 * m + 18134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7545.1, data_13_7545.2] + +end Collatz.Research.StoppingAtlas.Batch0958 From 2e0d52c074cf83667b1835e7734441cccba49932 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:30 +0530 Subject: [PATCH 0959/1001] proof: certify atlas Batch0959 (13:7546 to 13:7561) --- Collatz/Research/StoppingAtlas/Batch0959.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0959.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0959.lean b/Collatz/Research/StoppingAtlas/Batch0959.lean new file mode 100644 index 00000000..6870113c --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0959.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0959 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7546. -/ +theorem bounds_13_7546 : exactInterval 13 7546 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7546 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7546) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7546 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7546 : oddCount 7546 13 = 5 ∧ acceleratedOrbit 13 7546 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7546 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7546) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7546.1, data_13_7546.2] + +/-- Complete interval computation for depth 13, residue 7547. -/ +theorem bounds_13_7547 : exactInterval 13 7547 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7547 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7547) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7547 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7547 : oddCount 7547 13 = 8 ∧ acceleratedOrbit 13 7547 = 6047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7547 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7547) = 3 ^ 8 * m + 6047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7547.1, data_13_7547.2] + +/-- Complete interval computation for depth 13, residue 7548. -/ +theorem bounds_13_7548 : exactInterval 13 7548 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7548 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7548) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7548 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7548 : oddCount 7548 13 = 5 ∧ acceleratedOrbit 13 7548 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7548 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7548) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7548.1, data_13_7548.2] + +/-- Complete interval computation for depth 13, residue 7549. -/ +theorem bounds_13_7549 : exactInterval 13 7549 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7549 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7549) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7549 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7549 : oddCount 7549 13 = 5 ∧ acceleratedOrbit 13 7549 = 224 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7549 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7549) = 3 ^ 5 * m + 224 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7549.1, data_13_7549.2] + +/-- Complete interval computation for depth 13, residue 7550. -/ +theorem bounds_13_7550 : exactInterval 13 7550 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7550 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7550) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7550 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7550 : oddCount 7550 13 = 9 ∧ acceleratedOrbit 13 7550 = 18146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7550 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7550) = 3 ^ 9 * m + 18146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7550.1, data_13_7550.2] + +/-- Complete interval computation for depth 13, residue 7551. -/ +theorem bounds_13_7551 : exactInterval 13 7551 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7551 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7551) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7551 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7551 : oddCount 7551 13 = 9 ∧ acceleratedOrbit 13 7551 = 18146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7551 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7551) = 3 ^ 9 * m + 18146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7551.1, data_13_7551.2] + +/-- Complete interval computation for depth 13, residue 7552. -/ +theorem bounds_13_7552 : exactInterval 13 7552 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7552 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7552) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7552 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7552 : oddCount 7552 13 = 4 ∧ acceleratedOrbit 13 7552 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7552 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7552) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7552.1, data_13_7552.2] + +/-- Complete interval computation for depth 13, residue 7553. -/ +theorem bounds_13_7553 : exactInterval 13 7553 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7553 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7553) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7553 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7553 : oddCount 7553 13 = 7 ∧ acceleratedOrbit 13 7553 = 2018 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7553 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7553) = 3 ^ 7 * m + 2018 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7553.1, data_13_7553.2] + +/-- Complete interval computation for depth 13, residue 7554. -/ +theorem bounds_13_7554 : exactInterval 13 7554 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7554 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7554) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7554 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7554 : oddCount 7554 13 = 6 ∧ acceleratedOrbit 13 7554 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7554 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7554) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7554.1, data_13_7554.2] + +/-- Complete interval computation for depth 13, residue 7555. -/ +theorem bounds_13_7555 : exactInterval 13 7555 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7555 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7555) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7555 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7555 : oddCount 7555 13 = 6 ∧ acceleratedOrbit 13 7555 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7555 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7555) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7555.1, data_13_7555.2] + +/-- Complete interval computation for depth 13, residue 7556. -/ +theorem bounds_13_7556 : exactInterval 13 7556 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7556 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7556) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7556 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7556 : oddCount 7556 13 = 7 ∧ acceleratedOrbit 13 7556 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7556 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7556) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7556.1, data_13_7556.2] + +/-- Complete interval computation for depth 13, residue 7557. -/ +theorem bounds_13_7557 : exactInterval 13 7557 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7557 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7557) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7557 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7557 : oddCount 7557 13 = 7 ∧ acceleratedOrbit 13 7557 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7557 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7557) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7557.1, data_13_7557.2] + +/-- Complete interval computation for depth 13, residue 7558. -/ +theorem bounds_13_7558 : exactInterval 13 7558 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7558 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7558) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7558 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7558 : oddCount 7558 13 = 7 ∧ acceleratedOrbit 13 7558 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7558 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7558) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7558.1, data_13_7558.2] + +/-- Complete interval computation for depth 13, residue 7559. -/ +theorem bounds_13_7559 : exactInterval 13 7559 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7559 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7559) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7559 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7559 : oddCount 7559 13 = 6 ∧ acceleratedOrbit 13 7559 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7559 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7559) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7559.1, data_13_7559.2] + +/-- Complete interval computation for depth 13, residue 7560. -/ +theorem bounds_13_7560 : exactInterval 13 7560 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7560 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7560) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7560 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7560 : oddCount 7560 13 = 3 ∧ acceleratedOrbit 13 7560 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7560 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7560) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7560.1, data_13_7560.2] + +/-- Complete interval computation for depth 13, residue 7561. -/ +theorem bounds_13_7561 : exactInterval 13 7561 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7561 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7561) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7561 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7561 : oddCount 7561 13 = 6 ∧ acceleratedOrbit 13 7561 = 673 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7561 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7561) = 3 ^ 6 * m + 673 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7561.1, data_13_7561.2] + +end Collatz.Research.StoppingAtlas.Batch0959 From f824c80a57d1f5b7dfbcc9829ba0516900bf65a1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:31 +0530 Subject: [PATCH 0960/1001] proof: certify atlas Batch0960 (13:7562 to 13:7576) --- Collatz/Research/StoppingAtlas/Batch0960.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0960.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0960.lean b/Collatz/Research/StoppingAtlas/Batch0960.lean new file mode 100644 index 00000000..0f0335ea --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0960.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0960 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7562. -/ +theorem bounds_13_7562 : exactInterval 13 7562 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7562 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7562) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7562 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7562 : oddCount 7562 13 = 3 ∧ acceleratedOrbit 13 7562 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7562 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7562) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7562.1, data_13_7562.2] + +/-- Complete interval computation for depth 13, residue 7563. -/ +theorem bounds_13_7563 : exactInterval 13 7563 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7563 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7563) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7563 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7563 : oddCount 7563 13 = 7 ∧ acceleratedOrbit 13 7563 = 2020 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7563 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7563) = 3 ^ 7 * m + 2020 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7563.1, data_13_7563.2] + +/-- Complete interval computation for depth 13, residue 7564. -/ +theorem bounds_13_7564 : exactInterval 13 7564 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7564 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7564) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7564 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7564 : oddCount 7564 13 = 3 ∧ acceleratedOrbit 13 7564 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7564 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7564) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7564.1, data_13_7564.2] + +/-- Complete interval computation for depth 13, residue 7565. -/ +theorem bounds_13_7565 : exactInterval 13 7565 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7565 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7565) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7565 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7565 : oddCount 7565 13 = 3 ∧ acceleratedOrbit 13 7565 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7565 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7565) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7565.1, data_13_7565.2] + +/-- Complete interval computation for depth 13, residue 7566. -/ +theorem bounds_13_7566 : exactInterval 13 7566 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7566 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7566) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7566 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7566 : oddCount 7566 13 = 6 ∧ acceleratedOrbit 13 7566 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7566 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7566) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7566.1, data_13_7566.2] + +/-- Complete interval computation for depth 13, residue 7567. -/ +theorem bounds_13_7567 : exactInterval 13 7567 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7567 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7567) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7567 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7567 : oddCount 7567 13 = 6 ∧ acceleratedOrbit 13 7567 = 674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7567 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7567) = 3 ^ 6 * m + 674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7567.1, data_13_7567.2] + +/-- Complete interval computation for depth 13, residue 7568. -/ +theorem bounds_13_7568 : exactInterval 13 7568 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7568 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7568) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7568 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7568 : oddCount 7568 13 = 3 ∧ acceleratedOrbit 13 7568 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7568 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7568) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7568.1, data_13_7568.2] + +/-- Complete interval computation for depth 13, residue 7569. -/ +theorem bounds_13_7569 : exactInterval 13 7569 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7569 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7569) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7569 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7569 : oddCount 7569 13 = 7 ∧ acceleratedOrbit 13 7569 = 2024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7569 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7569) = 3 ^ 7 * m + 2024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7569.1, data_13_7569.2] + +/-- Complete interval computation for depth 13, residue 7570. -/ +theorem bounds_13_7570 : exactInterval 13 7570 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7570 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7570) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7570 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7570 : oddCount 7570 13 = 7 ∧ acceleratedOrbit 13 7570 = 2024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7570 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7570) = 3 ^ 7 * m + 2024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7570.1, data_13_7570.2] + +/-- Complete interval computation for depth 13, residue 7571. -/ +theorem bounds_13_7571 : exactInterval 13 7571 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7571 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7571) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7571 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7571 : oddCount 7571 13 = 7 ∧ acceleratedOrbit 13 7571 = 2024 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7571 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7571) = 3 ^ 7 * m + 2024 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7571.1, data_13_7571.2] + +/-- Complete interval computation for depth 13, residue 7572. -/ +theorem bounds_13_7572 : exactInterval 13 7572 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7572 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7572) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7572 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7572 : oddCount 7572 13 = 3 ∧ acceleratedOrbit 13 7572 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7572 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7572) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7572.1, data_13_7572.2] + +/-- Complete interval computation for depth 13, residue 7573. -/ +theorem bounds_13_7573 : exactInterval 13 7573 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7573 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7573) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7573 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7573 : oddCount 7573 13 = 3 ∧ acceleratedOrbit 13 7573 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7573 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7573) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7573.1, data_13_7573.2] + +/-- Complete interval computation for depth 13, residue 7574. -/ +theorem bounds_13_7574 : exactInterval 13 7574 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7574 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7574) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7574 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7574 : oddCount 7574 13 = 8 ∧ acceleratedOrbit 13 7574 = 6074 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7574 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7574) = 3 ^ 8 * m + 6074 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7574.1, data_13_7574.2] + +/-- Complete interval computation for depth 13, residue 7575. -/ +theorem bounds_13_7575 : exactInterval 13 7575 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7575 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7575) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7575 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7575 : oddCount 7575 13 = 8 ∧ acceleratedOrbit 13 7575 = 6074 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7575 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7575) = 3 ^ 8 * m + 6074 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7575.1, data_13_7575.2] + +/-- Complete interval computation for depth 13, residue 7576. -/ +theorem bounds_13_7576 : exactInterval 13 7576 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7576 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7576) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7576 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7576 : oddCount 7576 13 = 3 ∧ acceleratedOrbit 13 7576 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7576 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7576) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7576.1, data_13_7576.2] + +end Collatz.Research.StoppingAtlas.Batch0960 From 71f9a50a79a2ff1e3c2569957f2efb70d294cb3c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:31 +0530 Subject: [PATCH 0961/1001] proof: certify atlas Batch0961 (13:7577 to 13:7591) --- Collatz/Research/StoppingAtlas/Batch0961.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0961.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0961.lean b/Collatz/Research/StoppingAtlas/Batch0961.lean new file mode 100644 index 00000000..902c0a46 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0961.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0961 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7577. -/ +theorem bounds_13_7577 : exactInterval 13 7577 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7577 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7577) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7577 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7577 : oddCount 7577 13 = 8 ∧ acceleratedOrbit 13 7577 = 6074 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7577 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7577) = 3 ^ 8 * m + 6074 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7577.1, data_13_7577.2] + +/-- Complete interval computation for depth 13, residue 7578. -/ +theorem bounds_13_7578 : exactInterval 13 7578 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7578 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7578) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7578 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7578 : oddCount 7578 13 = 3 ∧ acceleratedOrbit 13 7578 = 25 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7578 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7578) = 3 ^ 3 * m + 25 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7578.1, data_13_7578.2] + +/-- Complete interval computation for depth 13, residue 7579. -/ +theorem bounds_13_7579 : exactInterval 13 7579 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7579 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7579) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7579 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7579 : oddCount 7579 13 = 9 ∧ acceleratedOrbit 13 7579 = 18215 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7579 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7579) = 3 ^ 9 * m + 18215 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7579.1, data_13_7579.2] + +/-- Complete interval computation for depth 13, residue 7580. -/ +theorem bounds_13_7580 : exactInterval 13 7580 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7580 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7580) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7580 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7580 : oddCount 7580 13 = 10 ∧ acceleratedOrbit 13 7580 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7580 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7580) = 3 ^ 10 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7580.1, data_13_7580.2] + +/-- Complete interval computation for depth 13, residue 7581. -/ +theorem bounds_13_7581 : exactInterval 13 7581 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7581 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7581) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7581 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7581 : oddCount 7581 13 = 10 ∧ acceleratedOrbit 13 7581 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7581 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7581) = 3 ^ 10 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7581.1, data_13_7581.2] + +/-- Complete interval computation for depth 13, residue 7582. -/ +theorem bounds_13_7582 : exactInterval 13 7582 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7582 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7582) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7582 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7582 : oddCount 7582 13 = 10 ∧ acceleratedOrbit 13 7582 = 54674 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7582 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7582) = 3 ^ 10 * m + 54674 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7582.1, data_13_7582.2] + +/-- Complete interval computation for depth 13, residue 7583. -/ +theorem bounds_13_7583 : exactInterval 13 7583 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7583 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7583) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7583 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7583 : oddCount 7583 13 = 10 ∧ acceleratedOrbit 13 7583 = 54668 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7583 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7583) = 3 ^ 10 * m + 54668 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7583.1, data_13_7583.2] + +/-- Complete interval computation for depth 13, residue 7584. -/ +theorem bounds_13_7584 : exactInterval 13 7584 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7584 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7584) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7584 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7584 : oddCount 7584 13 = 4 ∧ acceleratedOrbit 13 7584 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7584 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7584) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7584.1, data_13_7584.2] + +/-- Complete interval computation for depth 13, residue 7585. -/ +theorem bounds_13_7585 : exactInterval 13 7585 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7585 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7585) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7585 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7585 : oddCount 7585 13 = 7 ∧ acceleratedOrbit 13 7585 = 2026 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7585 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7585) = 3 ^ 7 * m + 2026 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7585.1, data_13_7585.2] + +/-- Complete interval computation for depth 13, residue 7586. -/ +theorem bounds_13_7586 : exactInterval 13 7586 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7586 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7586) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7586 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7586 : oddCount 7586 13 = 6 ∧ acceleratedOrbit 13 7586 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7586 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7586) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7586.1, data_13_7586.2] + +/-- Complete interval computation for depth 13, residue 7587. -/ +theorem bounds_13_7587 : exactInterval 13 7587 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7587 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7587) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7587 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7587 : oddCount 7587 13 = 6 ∧ acceleratedOrbit 13 7587 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7587 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7587) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7587.1, data_13_7587.2] + +/-- Complete interval computation for depth 13, residue 7588. -/ +theorem bounds_13_7588 : exactInterval 13 7588 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7588 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7588) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7588 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7588 : oddCount 7588 13 = 6 ∧ acceleratedOrbit 13 7588 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7588 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7588) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7588.1, data_13_7588.2] + +/-- Complete interval computation for depth 13, residue 7589. -/ +theorem bounds_13_7589 : exactInterval 13 7589 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7589 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7589) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7589 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7589 : oddCount 7589 13 = 6 ∧ acceleratedOrbit 13 7589 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7589 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7589) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7589.1, data_13_7589.2] + +/-- Complete interval computation for depth 13, residue 7590. -/ +theorem bounds_13_7590 : exactInterval 13 7590 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7590 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7590) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7590 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7590 : oddCount 7590 13 = 6 ∧ acceleratedOrbit 13 7590 = 676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7590 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7590) = 3 ^ 6 * m + 676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7590.1, data_13_7590.2] + +/-- Complete interval computation for depth 13, residue 7591. -/ +theorem bounds_13_7591 : exactInterval 13 7591 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7591 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7591) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7591 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7591 : oddCount 7591 13 = 7 ∧ acceleratedOrbit 13 7591 = 2027 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7591 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7591) = 3 ^ 7 * m + 2027 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7591.1, data_13_7591.2] + +end Collatz.Research.StoppingAtlas.Batch0961 From 510dc0065d82e2154a6e742111d093703d36b1de Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:31 +0530 Subject: [PATCH 0962/1001] proof: certify atlas Batch0962 (13:7592 to 13:7607) --- Collatz/Research/StoppingAtlas/Batch0962.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0962.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0962.lean b/Collatz/Research/StoppingAtlas/Batch0962.lean new file mode 100644 index 00000000..1d9ae247 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0962.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0962 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7592. -/ +theorem bounds_13_7592 : exactInterval 13 7592 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7592 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7592) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7592 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7592 : oddCount 7592 13 = 4 ∧ acceleratedOrbit 13 7592 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7592 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7592) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7592.1, data_13_7592.2] + +/-- Complete interval computation for depth 13, residue 7593. -/ +theorem bounds_13_7593 : exactInterval 13 7593 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7593 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7593) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7593 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7593 : oddCount 7593 13 = 8 ∧ acceleratedOrbit 13 7593 = 6083 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7593 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7593) = 3 ^ 8 * m + 6083 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7593.1, data_13_7593.2] + +/-- Complete interval computation for depth 13, residue 7594. -/ +theorem bounds_13_7594 : exactInterval 13 7594 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7594 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7594) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7594 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7594 : oddCount 7594 13 = 4 ∧ acceleratedOrbit 13 7594 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7594 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7594) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7594.1, data_13_7594.2] + +/-- Complete interval computation for depth 13, residue 7595. -/ +theorem bounds_13_7595 : exactInterval 13 7595 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7595 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7595) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7595 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7595 : oddCount 7595 13 = 8 ∧ acceleratedOrbit 13 7595 = 6085 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7595 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7595) = 3 ^ 8 * m + 6085 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7595.1, data_13_7595.2] + +/-- Complete interval computation for depth 13, residue 7596. -/ +theorem bounds_13_7596 : exactInterval 13 7596 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7596 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7596) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7596 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7596 : oddCount 7596 13 = 6 ∧ acceleratedOrbit 13 7596 = 677 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7596 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7596) = 3 ^ 6 * m + 677 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7596.1, data_13_7596.2] + +/-- Complete interval computation for depth 13, residue 7597. -/ +theorem bounds_13_7597 : exactInterval 13 7597 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7597 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7597) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7597 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7597 : oddCount 7597 13 = 6 ∧ acceleratedOrbit 13 7597 = 677 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7597 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7597) = 3 ^ 6 * m + 677 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7597.1, data_13_7597.2] + +/-- Complete interval computation for depth 13, residue 7598. -/ +theorem bounds_13_7598 : exactInterval 13 7598 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7598 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7598) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7598 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7598 : oddCount 7598 13 = 6 ∧ acceleratedOrbit 13 7598 = 677 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7598 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7598) = 3 ^ 6 * m + 677 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7598.1, data_13_7598.2] + +/-- Complete interval computation for depth 13, residue 7599. -/ +theorem bounds_13_7599 : exactInterval 13 7599 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7599 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7599) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7599 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7599 : oddCount 7599 13 = 8 ∧ acceleratedOrbit 13 7599 = 6088 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7599 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7599) = 3 ^ 8 * m + 6088 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7599.1, data_13_7599.2] + +/-- Complete interval computation for depth 13, residue 7600. -/ +theorem bounds_13_7600 : exactInterval 13 7600 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7600 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7600) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7600 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7600 : oddCount 7600 13 = 5 ∧ acceleratedOrbit 13 7600 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7600 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7600) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7600.1, data_13_7600.2] + +/-- Complete interval computation for depth 13, residue 7601. -/ +theorem bounds_13_7601 : exactInterval 13 7601 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7601 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7601) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7601 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7601 : oddCount 7601 13 = 5 ∧ acceleratedOrbit 13 7601 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7601 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7601) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7601.1, data_13_7601.2] + +/-- Complete interval computation for depth 13, residue 7602. -/ +theorem bounds_13_7602 : exactInterval 13 7602 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7602 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7602) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7602 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7602 : oddCount 7602 13 = 5 ∧ acceleratedOrbit 13 7602 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7602 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7602) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7602.1, data_13_7602.2] + +/-- Complete interval computation for depth 13, residue 7603. -/ +theorem bounds_13_7603 : exactInterval 13 7603 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7603 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7603) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7603 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7603 : oddCount 7603 13 = 5 ∧ acceleratedOrbit 13 7603 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7603 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7603) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7603.1, data_13_7603.2] + +/-- Complete interval computation for depth 13, residue 7604. -/ +theorem bounds_13_7604 : exactInterval 13 7604 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7604 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7604) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7604 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7604 : oddCount 7604 13 = 5 ∧ acceleratedOrbit 13 7604 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7604 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7604) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7604.1, data_13_7604.2] + +/-- Complete interval computation for depth 13, residue 7605. -/ +theorem bounds_13_7605 : exactInterval 13 7605 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7605 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7605) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7605 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7605 : oddCount 7605 13 = 5 ∧ acceleratedOrbit 13 7605 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7605 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7605) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7605.1, data_13_7605.2] + +/-- Complete interval computation for depth 13, residue 7606. -/ +theorem bounds_13_7606 : exactInterval 13 7606 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7606 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7606) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7606 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7606 : oddCount 7606 13 = 8 ∧ acceleratedOrbit 13 7606 = 6095 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7606 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7606) = 3 ^ 8 * m + 6095 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7606.1, data_13_7606.2] + +/-- Complete interval computation for depth 13, residue 7607. -/ +theorem bounds_13_7607 : exactInterval 13 7607 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7607 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7607) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7607 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7607 : oddCount 7607 13 = 8 ∧ acceleratedOrbit 13 7607 = 6095 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7607 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7607) = 3 ^ 8 * m + 6095 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7607.1, data_13_7607.2] + +end Collatz.Research.StoppingAtlas.Batch0962 From 08f0ac662c6cdbcd49f3813f53d0163f82636987 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:31 +0530 Subject: [PATCH 0963/1001] proof: certify atlas Batch0963 (13:7608 to 13:7622) --- Collatz/Research/StoppingAtlas/Batch0963.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0963.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0963.lean b/Collatz/Research/StoppingAtlas/Batch0963.lean new file mode 100644 index 00000000..7116f5c4 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0963.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0963 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7608. -/ +theorem bounds_13_7608 : exactInterval 13 7608 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7608 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7608) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7608 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7608 : oddCount 7608 13 = 5 ∧ acceleratedOrbit 13 7608 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7608 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7608) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7608.1, data_13_7608.2] + +/-- Complete interval computation for depth 13, residue 7609. -/ +theorem bounds_13_7609 : exactInterval 13 7609 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7609 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7609) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7609 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7609 : oddCount 7609 13 = 5 ∧ acceleratedOrbit 13 7609 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7609 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7609) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7609.1, data_13_7609.2] + +/-- Complete interval computation for depth 13, residue 7610. -/ +theorem bounds_13_7610 : exactInterval 13 7610 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7610 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7610) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7610 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7610 : oddCount 7610 13 = 5 ∧ acceleratedOrbit 13 7610 = 226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7610 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7610) = 3 ^ 5 * m + 226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7610.1, data_13_7610.2] + +/-- Complete interval computation for depth 13, residue 7611. -/ +theorem bounds_13_7611 : exactInterval 13 7611 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7611 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7611) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7611 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7611 : oddCount 7611 13 = 7 ∧ acceleratedOrbit 13 7611 = 2033 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7611 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7611) = 3 ^ 7 * m + 2033 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7611.1, data_13_7611.2] + +/-- Complete interval computation for depth 13, residue 7612. -/ +theorem bounds_13_7612 : exactInterval 13 7612 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7612 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7612) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7612 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7612 : oddCount 7612 13 = 8 ∧ acceleratedOrbit 13 7612 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7612 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7612) = 3 ^ 8 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7612.1, data_13_7612.2] + +/-- Complete interval computation for depth 13, residue 7613. -/ +theorem bounds_13_7613 : exactInterval 13 7613 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7613 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7613) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7613 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7613 : oddCount 7613 13 = 8 ∧ acceleratedOrbit 13 7613 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7613 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7613) = 3 ^ 8 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7613.1, data_13_7613.2] + +/-- Complete interval computation for depth 13, residue 7614. -/ +theorem bounds_13_7614 : exactInterval 13 7614 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7614 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7614) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7614 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7614 : oddCount 7614 13 = 8 ∧ acceleratedOrbit 13 7614 = 6101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7614 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7614) = 3 ^ 8 * m + 6101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7614.1, data_13_7614.2] + +/-- Complete interval computation for depth 13, residue 7615. -/ +theorem bounds_13_7615 : exactInterval 13 7615 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7615 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7615) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7615 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7615 : oddCount 7615 13 = 11 ∧ acceleratedOrbit 13 7615 = 164693 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7615 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7615) = 3 ^ 11 * m + 164693 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7615.1, data_13_7615.2] + +/-- Complete interval computation for depth 13, residue 7616. -/ +theorem bounds_13_7616 : exactInterval 13 7616 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7616 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7616) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7616 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7616 : oddCount 7616 13 = 4 ∧ acceleratedOrbit 13 7616 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7616 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7616) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7616.1, data_13_7616.2] + +/-- Complete interval computation for depth 13, residue 7617. -/ +theorem bounds_13_7617 : exactInterval 13 7617 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7617 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7617) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7617 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7617 : oddCount 7617 13 = 7 ∧ acceleratedOrbit 13 7617 = 2035 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7617 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7617) = 3 ^ 7 * m + 2035 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7617.1, data_13_7617.2] + +/-- Complete interval computation for depth 13, residue 7618. -/ +theorem bounds_13_7618 : exactInterval 13 7618 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7618 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7618) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7618 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7618 : oddCount 7618 13 = 7 ∧ acceleratedOrbit 13 7618 = 2035 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7618 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7618) = 3 ^ 7 * m + 2035 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7618.1, data_13_7618.2] + +/-- Complete interval computation for depth 13, residue 7619. -/ +theorem bounds_13_7619 : exactInterval 13 7619 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7619 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7619) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7619 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7619 : oddCount 7619 13 = 7 ∧ acceleratedOrbit 13 7619 = 2035 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7619 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7619) = 3 ^ 7 * m + 2035 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7619.1, data_13_7619.2] + +/-- Complete interval computation for depth 13, residue 7620. -/ +theorem bounds_13_7620 : exactInterval 13 7620 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7620 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7620) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7620 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7620 : oddCount 7620 13 = 4 ∧ acceleratedOrbit 13 7620 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7620 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7620) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7620.1, data_13_7620.2] + +/-- Complete interval computation for depth 13, residue 7621. -/ +theorem bounds_13_7621 : exactInterval 13 7621 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7621 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7621) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7621 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7621 : oddCount 7621 13 = 4 ∧ acceleratedOrbit 13 7621 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7621 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7621) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7621.1, data_13_7621.2] + +/-- Complete interval computation for depth 13, residue 7622. -/ +theorem bounds_13_7622 : exactInterval 13 7622 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7622 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7622) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7622 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7622 : oddCount 7622 13 = 4 ∧ acceleratedOrbit 13 7622 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7622 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7622) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7622.1, data_13_7622.2] + +end Collatz.Research.StoppingAtlas.Batch0963 From 460226e5d6220614a3ce5c1e024246711363fef0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:31 +0530 Subject: [PATCH 0964/1001] proof: certify atlas Batch0964 (13:7623 to 13:7638) --- Collatz/Research/StoppingAtlas/Batch0964.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0964.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0964.lean b/Collatz/Research/StoppingAtlas/Batch0964.lean new file mode 100644 index 00000000..46d50421 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0964.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0964 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7623. -/ +theorem bounds_13_7623 : exactInterval 13 7623 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7623 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7623) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7623 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7623 : oddCount 7623 13 = 7 ∧ acceleratedOrbit 13 7623 = 2036 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7623 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7623) = 3 ^ 7 * m + 2036 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7623.1, data_13_7623.2] + +/-- Complete interval computation for depth 13, residue 7624. -/ +theorem bounds_13_7624 : exactInterval 13 7624 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7624 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7624) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7624 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7624 : oddCount 7624 13 = 5 ∧ acceleratedOrbit 13 7624 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7624 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7624) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7624.1, data_13_7624.2] + +/-- Complete interval computation for depth 13, residue 7625. -/ +theorem bounds_13_7625 : exactInterval 13 7625 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7625 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7625) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7625 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7625 : oddCount 7625 13 = 6 ∧ acceleratedOrbit 13 7625 = 679 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7625 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7625) = 3 ^ 6 * m + 679 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7625.1, data_13_7625.2] + +/-- Complete interval computation for depth 13, residue 7626. -/ +theorem bounds_13_7626 : exactInterval 13 7626 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7626 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7626) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7626 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7626 : oddCount 7626 13 = 5 ∧ acceleratedOrbit 13 7626 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7626 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7626) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7626.1, data_13_7626.2] + +/-- Complete interval computation for depth 13, residue 7627. -/ +theorem bounds_13_7627 : exactInterval 13 7627 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7627 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7627) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7627 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7627 : oddCount 7627 13 = 7 ∧ acceleratedOrbit 13 7627 = 2038 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7627 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7627) = 3 ^ 7 * m + 2038 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7627.1, data_13_7627.2] + +/-- Complete interval computation for depth 13, residue 7628. -/ +theorem bounds_13_7628 : exactInterval 13 7628 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7628 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7628) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7628 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7628 : oddCount 7628 13 = 5 ∧ acceleratedOrbit 13 7628 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7628 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7628) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7628.1, data_13_7628.2] + +/-- Complete interval computation for depth 13, residue 7629. -/ +theorem bounds_13_7629 : exactInterval 13 7629 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7629 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7629) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7629 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7629 : oddCount 7629 13 = 5 ∧ acceleratedOrbit 13 7629 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7629 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7629) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7629.1, data_13_7629.2] + +/-- Complete interval computation for depth 13, residue 7630. -/ +theorem bounds_13_7630 : exactInterval 13 7630 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7630 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7630) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7630 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7630 : oddCount 7630 13 = 8 ∧ acceleratedOrbit 13 7630 = 6113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7630 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7630) = 3 ^ 8 * m + 6113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7630.1, data_13_7630.2] + +/-- Complete interval computation for depth 13, residue 7631. -/ +theorem bounds_13_7631 : exactInterval 13 7631 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7631 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7631) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7631 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7631 : oddCount 7631 13 = 8 ∧ acceleratedOrbit 13 7631 = 6113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7631 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7631) = 3 ^ 8 * m + 6113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7631.1, data_13_7631.2] + +/-- Complete interval computation for depth 13, residue 7632. -/ +theorem bounds_13_7632 : exactInterval 13 7632 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7632 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7632) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7632 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7632 : oddCount 7632 13 = 4 ∧ acceleratedOrbit 13 7632 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7632 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7632) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7632.1, data_13_7632.2] + +/-- Complete interval computation for depth 13, residue 7633. -/ +theorem bounds_13_7633 : exactInterval 13 7633 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7633 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7633) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7633 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7633 : oddCount 7633 13 = 5 ∧ acceleratedOrbit 13 7633 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7633 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7633) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7633.1, data_13_7633.2] + +/-- Complete interval computation for depth 13, residue 7634. -/ +theorem bounds_13_7634 : exactInterval 13 7634 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7634 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7634) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7634 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7634 : oddCount 7634 13 = 7 ∧ acceleratedOrbit 13 7634 = 2039 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7634 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7634) = 3 ^ 7 * m + 2039 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7634.1, data_13_7634.2] + +/-- Complete interval computation for depth 13, residue 7635. -/ +theorem bounds_13_7635 : exactInterval 13 7635 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7635 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7635) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7635 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7635 : oddCount 7635 13 = 7 ∧ acceleratedOrbit 13 7635 = 2039 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7635 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7635) = 3 ^ 7 * m + 2039 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7635.1, data_13_7635.2] + +/-- Complete interval computation for depth 13, residue 7636. -/ +theorem bounds_13_7636 : exactInterval 13 7636 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7636 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7636) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7636 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7636 : oddCount 7636 13 = 4 ∧ acceleratedOrbit 13 7636 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7636 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7636) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7636.1, data_13_7636.2] + +/-- Complete interval computation for depth 13, residue 7637. -/ +theorem bounds_13_7637 : exactInterval 13 7637 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7637 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7637) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7637 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7637 : oddCount 7637 13 = 4 ∧ acceleratedOrbit 13 7637 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7637 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7637) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7637.1, data_13_7637.2] + +/-- Complete interval computation for depth 13, residue 7638. -/ +theorem bounds_13_7638 : exactInterval 13 7638 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7638 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7638) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7638 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7638 : oddCount 7638 13 = 6 ∧ acceleratedOrbit 13 7638 = 680 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7638 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7638) = 3 ^ 6 * m + 680 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7638.1, data_13_7638.2] + +end Collatz.Research.StoppingAtlas.Batch0964 From 2e658e48004297240f759afeda825eeae8479aff Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:32 +0530 Subject: [PATCH 0965/1001] proof: certify atlas Batch0965 (13:7639 to 13:7653) --- Collatz/Research/StoppingAtlas/Batch0965.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0965.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0965.lean b/Collatz/Research/StoppingAtlas/Batch0965.lean new file mode 100644 index 00000000..ee12ac00 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0965.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0965 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7639. -/ +theorem bounds_13_7639 : exactInterval 13 7639 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7639 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7639) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7639 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7639 : oddCount 7639 13 = 6 ∧ acceleratedOrbit 13 7639 = 680 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7639 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7639) = 3 ^ 6 * m + 680 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7639.1, data_13_7639.2] + +/-- Complete interval computation for depth 13, residue 7640. -/ +theorem bounds_13_7640 : exactInterval 13 7640 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7640 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7640) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7640 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7640 : oddCount 7640 13 = 5 ∧ acceleratedOrbit 13 7640 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7640 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7640) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7640.1, data_13_7640.2] + +/-- Complete interval computation for depth 13, residue 7641. -/ +theorem bounds_13_7641 : exactInterval 13 7641 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7641 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7641) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7641 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7641 : oddCount 7641 13 = 5 ∧ acceleratedOrbit 13 7641 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7641 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7641) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7641.1, data_13_7641.2] + +/-- Complete interval computation for depth 13, residue 7642. -/ +theorem bounds_13_7642 : exactInterval 13 7642 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7642 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7642) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7642 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7642 : oddCount 7642 13 = 5 ∧ acceleratedOrbit 13 7642 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7642 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7642) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7642.1, data_13_7642.2] + +/-- Complete interval computation for depth 13, residue 7643. -/ +theorem bounds_13_7643 : exactInterval 13 7643 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7643 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7643) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7643 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7643 : oddCount 7643 13 = 7 ∧ acceleratedOrbit 13 7643 = 2042 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7643 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7643) = 3 ^ 7 * m + 2042 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7643.1, data_13_7643.2] + +/-- Complete interval computation for depth 13, residue 7644. -/ +theorem bounds_13_7644 : exactInterval 13 7644 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7644 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7644) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7644 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7644 : oddCount 7644 13 = 5 ∧ acceleratedOrbit 13 7644 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7644 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7644) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7644.1, data_13_7644.2] + +/-- Complete interval computation for depth 13, residue 7645. -/ +theorem bounds_13_7645 : exactInterval 13 7645 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7645 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7645) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7645 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7645 : oddCount 7645 13 = 5 ∧ acceleratedOrbit 13 7645 = 227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7645 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7645) = 3 ^ 5 * m + 227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7645.1, data_13_7645.2] + +/-- Complete interval computation for depth 13, residue 7646. -/ +theorem bounds_13_7646 : exactInterval 13 7646 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7646 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7646) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7646 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7646 : oddCount 7646 13 = 9 ∧ acceleratedOrbit 13 7646 = 18377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7646 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7646) = 3 ^ 9 * m + 18377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7646.1, data_13_7646.2] + +/-- Complete interval computation for depth 13, residue 7647. -/ +theorem bounds_13_7647 : exactInterval 13 7647 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7647 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7647) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7647 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7647 : oddCount 7647 13 = 9 ∧ acceleratedOrbit 13 7647 = 18377 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7647 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7647) = 3 ^ 9 * m + 18377 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7647.1, data_13_7647.2] + +/-- Complete interval computation for depth 13, residue 7648. -/ +theorem bounds_13_7648 : exactInterval 13 7648 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7648 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7648) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7648 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7648 : oddCount 7648 13 = 7 ∧ acceleratedOrbit 13 7648 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7648 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7648) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7648.1, data_13_7648.2] + +/-- Complete interval computation for depth 13, residue 7649. -/ +theorem bounds_13_7649 : exactInterval 13 7649 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7649 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7649) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7649 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7649 : oddCount 7649 13 = 9 ∧ acceleratedOrbit 13 7649 = 18386 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7649 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7649) = 3 ^ 9 * m + 18386 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7649.1, data_13_7649.2] + +/-- Complete interval computation for depth 13, residue 7650. -/ +theorem bounds_13_7650 : exactInterval 13 7650 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7650 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7650) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7650 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7650 : oddCount 7650 13 = 4 ∧ acceleratedOrbit 13 7650 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7650 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7650) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7650.1, data_13_7650.2] + +/-- Complete interval computation for depth 13, residue 7651. -/ +theorem bounds_13_7651 : exactInterval 13 7651 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7651 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7651) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7651 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7651 : oddCount 7651 13 = 4 ∧ acceleratedOrbit 13 7651 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7651 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7651) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7651.1, data_13_7651.2] + +/-- Complete interval computation for depth 13, residue 7652. -/ +theorem bounds_13_7652 : exactInterval 13 7652 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7652 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7652) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7652 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7652 : oddCount 7652 13 = 7 ∧ acceleratedOrbit 13 7652 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7652 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7652) = 3 ^ 7 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7652.1, data_13_7652.2] + +/-- Complete interval computation for depth 13, residue 7653. -/ +theorem bounds_13_7653 : exactInterval 13 7653 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7653 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7653) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7653 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7653 : oddCount 7653 13 = 7 ∧ acceleratedOrbit 13 7653 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7653 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7653) = 3 ^ 7 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7653.1, data_13_7653.2] + +end Collatz.Research.StoppingAtlas.Batch0965 From a8b26a4a58b5cb0ce6e7c7942b17504dc9381e1e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:32 +0530 Subject: [PATCH 0966/1001] proof: certify atlas Batch0966 (13:7654 to 13:7668) --- Collatz/Research/StoppingAtlas/Batch0966.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0966.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0966.lean b/Collatz/Research/StoppingAtlas/Batch0966.lean new file mode 100644 index 00000000..23426ed1 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0966.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0966 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7654. -/ +theorem bounds_13_7654 : exactInterval 13 7654 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7654 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7654) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7654 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7654 : oddCount 7654 13 = 7 ∧ acceleratedOrbit 13 7654 = 2045 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7654 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7654) = 3 ^ 7 * m + 2045 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7654.1, data_13_7654.2] + +/-- Complete interval computation for depth 13, residue 7655. -/ +theorem bounds_13_7655 : exactInterval 13 7655 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7655 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7655) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7655 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7655 : oddCount 7655 13 = 7 ∧ acceleratedOrbit 13 7655 = 2044 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7655 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7655) = 3 ^ 7 * m + 2044 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7655.1, data_13_7655.2] + +/-- Complete interval computation for depth 13, residue 7656. -/ +theorem bounds_13_7656 : exactInterval 13 7656 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7656 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7656) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7656 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7656 : oddCount 7656 13 = 7 ∧ acceleratedOrbit 13 7656 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7656 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7656) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7656.1, data_13_7656.2] + +/-- Complete interval computation for depth 13, residue 7657. -/ +theorem bounds_13_7657 : exactInterval 13 7657 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7657 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7657) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7657 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7657 : oddCount 7657 13 = 8 ∧ acceleratedOrbit 13 7657 = 6134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7657 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7657) = 3 ^ 8 * m + 6134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7657.1, data_13_7657.2] + +/-- Complete interval computation for depth 13, residue 7658. -/ +theorem bounds_13_7658 : exactInterval 13 7658 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7658 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7658) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7658 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7658 : oddCount 7658 13 = 7 ∧ acceleratedOrbit 13 7658 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7658 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7658) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7658.1, data_13_7658.2] + +/-- Complete interval computation for depth 13, residue 7659. -/ +theorem bounds_13_7659 : exactInterval 13 7659 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7659 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7659) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7659 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7659 : oddCount 7659 13 = 9 ∧ acceleratedOrbit 13 7659 = 18407 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7659 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7659) = 3 ^ 9 * m + 18407 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7659.1, data_13_7659.2] + +/-- Complete interval computation for depth 13, residue 7660. -/ +theorem bounds_13_7660 : exactInterval 13 7660 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7660 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7660) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7660 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7660 : oddCount 7660 13 = 7 ∧ acceleratedOrbit 13 7660 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7660 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7660) = 3 ^ 7 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7660.1, data_13_7660.2] + +/-- Complete interval computation for depth 13, residue 7661. -/ +theorem bounds_13_7661 : exactInterval 13 7661 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7661 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7661) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7661 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7661 : oddCount 7661 13 = 7 ∧ acceleratedOrbit 13 7661 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7661 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7661) = 3 ^ 7 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7661.1, data_13_7661.2] + +/-- Complete interval computation for depth 13, residue 7662. -/ +theorem bounds_13_7662 : exactInterval 13 7662 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7662 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7662) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7662 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7662 : oddCount 7662 13 = 7 ∧ acceleratedOrbit 13 7662 = 2047 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7662 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7662) = 3 ^ 7 * m + 2047 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7662.1, data_13_7662.2] + +/-- Complete interval computation for depth 13, residue 7663. -/ +theorem bounds_13_7663 : exactInterval 13 7663 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7663 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7663) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7663 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7663 : oddCount 7663 13 = 9 ∧ acceleratedOrbit 13 7663 = 18415 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7663 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7663) = 3 ^ 9 * m + 18415 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7663.1, data_13_7663.2] + +/-- Complete interval computation for depth 13, residue 7664. -/ +theorem bounds_13_7664 : exactInterval 13 7664 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7664 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7664) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7664 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7664 : oddCount 7664 13 = 7 ∧ acceleratedOrbit 13 7664 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7664 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7664) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7664.1, data_13_7664.2] + +/-- Complete interval computation for depth 13, residue 7665. -/ +theorem bounds_13_7665 : exactInterval 13 7665 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7665 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7665) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7665 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7665 : oddCount 7665 13 = 7 ∧ acceleratedOrbit 13 7665 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7665 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7665) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7665.1, data_13_7665.2] + +/-- Complete interval computation for depth 13, residue 7666. -/ +theorem bounds_13_7666 : exactInterval 13 7666 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7666 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7666) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7666 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7666 : oddCount 7666 13 = 6 ∧ acceleratedOrbit 13 7666 = 683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7666 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7666) = 3 ^ 6 * m + 683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7666.1, data_13_7666.2] + +/-- Complete interval computation for depth 13, residue 7667. -/ +theorem bounds_13_7667 : exactInterval 13 7667 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7667 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7667) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7667 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7667 : oddCount 7667 13 = 6 ∧ acceleratedOrbit 13 7667 = 683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7667 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7667) = 3 ^ 6 * m + 683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7667.1, data_13_7667.2] + +/-- Complete interval computation for depth 13, residue 7668. -/ +theorem bounds_13_7668 : exactInterval 13 7668 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7668 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7668) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7668 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7668 : oddCount 7668 13 = 7 ∧ acceleratedOrbit 13 7668 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7668 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7668) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7668.1, data_13_7668.2] + +end Collatz.Research.StoppingAtlas.Batch0966 From 66ae081ca45b41da6a3ec49f6cd01d8a73fb29f6 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:32 +0530 Subject: [PATCH 0967/1001] proof: certify atlas Batch0967 (13:7669 to 13:7684) --- Collatz/Research/StoppingAtlas/Batch0967.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0967.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0967.lean b/Collatz/Research/StoppingAtlas/Batch0967.lean new file mode 100644 index 00000000..7bc610c0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0967.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0967 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7669. -/ +theorem bounds_13_7669 : exactInterval 13 7669 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7669 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7669) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7669 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7669 : oddCount 7669 13 = 7 ∧ acceleratedOrbit 13 7669 = 2051 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7669 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7669) = 3 ^ 7 * m + 2051 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7669.1, data_13_7669.2] + +/-- Complete interval computation for depth 13, residue 7670. -/ +theorem bounds_13_7670 : exactInterval 13 7670 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7670 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7670) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7670 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7670 : oddCount 7670 13 = 8 ∧ acceleratedOrbit 13 7670 = 6146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7670 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7670) = 3 ^ 8 * m + 6146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7670.1, data_13_7670.2] + +/-- Complete interval computation for depth 13, residue 7671. -/ +theorem bounds_13_7671 : exactInterval 13 7671 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7671 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7671) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7671 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7671 : oddCount 7671 13 = 8 ∧ acceleratedOrbit 13 7671 = 6146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7671 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7671) = 3 ^ 8 * m + 6146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7671.1, data_13_7671.2] + +/-- Complete interval computation for depth 13, residue 7672. -/ +theorem bounds_13_7672 : exactInterval 13 7672 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7672 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7672) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7672 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7672 : oddCount 7672 13 = 8 ∧ acceleratedOrbit 13 7672 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7672 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7672) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7672.1, data_13_7672.2] + +/-- Complete interval computation for depth 13, residue 7673. -/ +theorem bounds_13_7673 : exactInterval 13 7673 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7673 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7673) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7673 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7673 : oddCount 7673 13 = 6 ∧ acceleratedOrbit 13 7673 = 683 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7673 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7673) = 3 ^ 6 * m + 683 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7673.1, data_13_7673.2] + +/-- Complete interval computation for depth 13, residue 7674. -/ +theorem bounds_13_7674 : exactInterval 13 7674 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7674 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7674) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7674 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7674 : oddCount 7674 13 = 8 ∧ acceleratedOrbit 13 7674 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7674 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7674) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7674.1, data_13_7674.2] + +/-- Complete interval computation for depth 13, residue 7675. -/ +theorem bounds_13_7675 : exactInterval 13 7675 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7675 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7675) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7675 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7675 : oddCount 7675 13 = 8 ∧ acceleratedOrbit 13 7675 = 6149 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7675 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7675) = 3 ^ 8 * m + 6149 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7675.1, data_13_7675.2] + +/-- Complete interval computation for depth 13, residue 7676. -/ +theorem bounds_13_7676 : exactInterval 13 7676 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7676 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7676) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7676 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7676 : oddCount 7676 13 = 8 ∧ acceleratedOrbit 13 7676 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7676 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7676) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7676.1, data_13_7676.2] + +/-- Complete interval computation for depth 13, residue 7677. -/ +theorem bounds_13_7677 : exactInterval 13 7677 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7677 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7677) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7677 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7677 : oddCount 7677 13 = 8 ∧ acceleratedOrbit 13 7677 = 6151 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7677 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7677) = 3 ^ 8 * m + 6151 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7677.1, data_13_7677.2] + +/-- Complete interval computation for depth 13, residue 7678. -/ +theorem bounds_13_7678 : exactInterval 13 7678 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7678 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7678) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7678 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7678 : oddCount 7678 13 = 11 ∧ acceleratedOrbit 13 7678 = 166076 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7678 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7678) = 3 ^ 11 * m + 166076 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7678.1, data_13_7678.2] + +/-- Complete interval computation for depth 13, residue 7679. -/ +theorem bounds_13_7679 : exactInterval 13 7679 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7679 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7679) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7679 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7679 : oddCount 7679 13 = 11 ∧ acceleratedOrbit 13 7679 = 166076 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7679 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7679) = 3 ^ 11 * m + 166076 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7679.1, data_13_7679.2] + +/-- Complete interval computation for depth 13, residue 7680. -/ +theorem bounds_13_7680 : exactInterval 13 7680 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7680 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7680) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7680 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7680 : oddCount 7680 13 = 4 ∧ acceleratedOrbit 13 7680 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7680 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7680) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7680.1, data_13_7680.2] + +/-- Complete interval computation for depth 13, residue 7681. -/ +theorem bounds_13_7681 : exactInterval 13 7681 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7681 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7681) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7681 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7681 : oddCount 7681 13 = 9 ∧ acceleratedOrbit 13 7681 = 18467 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7681 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7681) = 3 ^ 9 * m + 18467 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7681.1, data_13_7681.2] + +/-- Complete interval computation for depth 13, residue 7682. -/ +theorem bounds_13_7682 : exactInterval 13 7682 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7682 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7682) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7682 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7682 : oddCount 7682 13 = 4 ∧ acceleratedOrbit 13 7682 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7682 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7682) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7682.1, data_13_7682.2] + +/-- Complete interval computation for depth 13, residue 7683. -/ +theorem bounds_13_7683 : exactInterval 13 7683 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7683 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7683) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7683 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7683 : oddCount 7683 13 = 4 ∧ acceleratedOrbit 13 7683 = 76 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7683 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7683) = 3 ^ 4 * m + 76 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7683.1, data_13_7683.2] + +/-- Complete interval computation for depth 13, residue 7684. -/ +theorem bounds_13_7684 : exactInterval 13 7684 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7684 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7684) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7684 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7684 : oddCount 7684 13 = 6 ∧ acceleratedOrbit 13 7684 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7684 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7684) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7684.1, data_13_7684.2] + +end Collatz.Research.StoppingAtlas.Batch0967 From 85ec6992a31220463ab9b46d73206ae62a6ce0cc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:32 +0530 Subject: [PATCH 0968/1001] proof: certify atlas Batch0968 (13:7685 to 13:7699) --- Collatz/Research/StoppingAtlas/Batch0968.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0968.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0968.lean b/Collatz/Research/StoppingAtlas/Batch0968.lean new file mode 100644 index 00000000..7e5e2521 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0968.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0968 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7685. -/ +theorem bounds_13_7685 : exactInterval 13 7685 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7685 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7685) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7685 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7685 : oddCount 7685 13 = 6 ∧ acceleratedOrbit 13 7685 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7685 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7685) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7685.1, data_13_7685.2] + +/-- Complete interval computation for depth 13, residue 7686. -/ +theorem bounds_13_7686 : exactInterval 13 7686 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7686 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7686) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7686 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7686 : oddCount 7686 13 = 6 ∧ acceleratedOrbit 13 7686 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7686 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7686) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7686.1, data_13_7686.2] + +/-- Complete interval computation for depth 13, residue 7687. -/ +theorem bounds_13_7687 : exactInterval 13 7687 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7687 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7687) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7687 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7687 : oddCount 7687 13 = 7 ∧ acceleratedOrbit 13 7687 = 2053 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7687 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7687) = 3 ^ 7 * m + 2053 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7687.1, data_13_7687.2] + +/-- Complete interval computation for depth 13, residue 7688. -/ +theorem bounds_13_7688 : exactInterval 13 7688 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7688 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7688) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7688 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7688 : oddCount 7688 13 = 5 ∧ acceleratedOrbit 13 7688 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7688 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7688) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7688.1, data_13_7688.2] + +/-- Complete interval computation for depth 13, residue 7689. -/ +theorem bounds_13_7689 : exactInterval 13 7689 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7689 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7689) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7689 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7689 : oddCount 7689 13 = 7 ∧ acceleratedOrbit 13 7689 = 2054 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7689 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7689) = 3 ^ 7 * m + 2054 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7689.1, data_13_7689.2] + +/-- Complete interval computation for depth 13, residue 7690. -/ +theorem bounds_13_7690 : exactInterval 13 7690 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7690 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7690) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7690 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7690 : oddCount 7690 13 = 5 ∧ acceleratedOrbit 13 7690 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7690 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7690) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7690.1, data_13_7690.2] + +/-- Complete interval computation for depth 13, residue 7691. -/ +theorem bounds_13_7691 : exactInterval 13 7691 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7691 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7691) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7691 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7691 : oddCount 7691 13 = 6 ∧ acceleratedOrbit 13 7691 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7691 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7691) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7691.1, data_13_7691.2] + +/-- Complete interval computation for depth 13, residue 7692. -/ +theorem bounds_13_7692 : exactInterval 13 7692 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7692 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7692) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7692 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7692 : oddCount 7692 13 = 5 ∧ acceleratedOrbit 13 7692 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7692 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7692) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7692.1, data_13_7692.2] + +/-- Complete interval computation for depth 13, residue 7693. -/ +theorem bounds_13_7693 : exactInterval 13 7693 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7693 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7693) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7693 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7693 : oddCount 7693 13 = 5 ∧ acceleratedOrbit 13 7693 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7693 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7693) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7693.1, data_13_7693.2] + +/-- Complete interval computation for depth 13, residue 7694. -/ +theorem bounds_13_7694 : exactInterval 13 7694 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7694 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7694) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7694 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7694 : oddCount 7694 13 = 6 ∧ acceleratedOrbit 13 7694 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7694 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7694) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7694.1, data_13_7694.2] + +/-- Complete interval computation for depth 13, residue 7695. -/ +theorem bounds_13_7695 : exactInterval 13 7695 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7695 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7695) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7695 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7695 : oddCount 7695 13 = 6 ∧ acceleratedOrbit 13 7695 = 685 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7695 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7695) = 3 ^ 6 * m + 685 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7695.1, data_13_7695.2] + +/-- Complete interval computation for depth 13, residue 7696. -/ +theorem bounds_13_7696 : exactInterval 13 7696 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7696 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7696) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7696 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7696 : oddCount 7696 13 = 6 ∧ acceleratedOrbit 13 7696 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7696 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7696) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7696.1, data_13_7696.2] + +/-- Complete interval computation for depth 13, residue 7697. -/ +theorem bounds_13_7697 : exactInterval 13 7697 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7697 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7697) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7697 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7697 : oddCount 7697 13 = 5 ∧ acceleratedOrbit 13 7697 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7697 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7697) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7697.1, data_13_7697.2] + +/-- Complete interval computation for depth 13, residue 7698. -/ +theorem bounds_13_7698 : exactInterval 13 7698 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7698 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7698) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7698 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7698 : oddCount 7698 13 = 8 ∧ acceleratedOrbit 13 7698 = 6169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7698 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7698) = 3 ^ 8 * m + 6169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7698.1, data_13_7698.2] + +/-- Complete interval computation for depth 13, residue 7699. -/ +theorem bounds_13_7699 : exactInterval 13 7699 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7699 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7699) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7699 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7699 : oddCount 7699 13 = 8 ∧ acceleratedOrbit 13 7699 = 6169 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7699 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7699) = 3 ^ 8 * m + 6169 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7699.1, data_13_7699.2] + +end Collatz.Research.StoppingAtlas.Batch0968 From e383c930b3d9bc0bf77f765fcd7eacf671625742 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:32 +0530 Subject: [PATCH 0969/1001] proof: certify atlas Batch0969 (13:7700 to 13:7714) --- Collatz/Research/StoppingAtlas/Batch0969.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0969.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0969.lean b/Collatz/Research/StoppingAtlas/Batch0969.lean new file mode 100644 index 00000000..856ccac0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0969.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0969 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7700. -/ +theorem bounds_13_7700 : exactInterval 13 7700 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7700 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7700) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7700 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7700 : oddCount 7700 13 = 6 ∧ acceleratedOrbit 13 7700 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7700 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7700) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7700.1, data_13_7700.2] + +/-- Complete interval computation for depth 13, residue 7701. -/ +theorem bounds_13_7701 : exactInterval 13 7701 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7701 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7701) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7701 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7701 : oddCount 7701 13 = 6 ∧ acceleratedOrbit 13 7701 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7701 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7701) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7701.1, data_13_7701.2] + +/-- Complete interval computation for depth 13, residue 7702. -/ +theorem bounds_13_7702 : exactInterval 13 7702 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7702 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7702) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7702 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7702 : oddCount 7702 13 = 6 ∧ acceleratedOrbit 13 7702 = 686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7702 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7702) = 3 ^ 6 * m + 686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7702.1, data_13_7702.2] + +/-- Complete interval computation for depth 13, residue 7703. -/ +theorem bounds_13_7703 : exactInterval 13 7703 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7703 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7703) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7703 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7703 : oddCount 7703 13 = 6 ∧ acceleratedOrbit 13 7703 = 686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7703 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7703) = 3 ^ 6 * m + 686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7703.1, data_13_7703.2] + +/-- Complete interval computation for depth 13, residue 7704. -/ +theorem bounds_13_7704 : exactInterval 13 7704 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7704 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7704) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7704 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7704 : oddCount 7704 13 = 6 ∧ acceleratedOrbit 13 7704 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7704 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7704) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7704.1, data_13_7704.2] + +/-- Complete interval computation for depth 13, residue 7705. -/ +theorem bounds_13_7705 : exactInterval 13 7705 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7705 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7705) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7705 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7705 : oddCount 7705 13 = 6 ∧ acceleratedOrbit 13 7705 = 686 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7705 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7705) = 3 ^ 6 * m + 686 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7705.1, data_13_7705.2] + +/-- Complete interval computation for depth 13, residue 7706. -/ +theorem bounds_13_7706 : exactInterval 13 7706 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7706 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7706) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7706 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7706 : oddCount 7706 13 = 6 ∧ acceleratedOrbit 13 7706 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7706 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7706) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7706.1, data_13_7706.2] + +/-- Complete interval computation for depth 13, residue 7707. -/ +theorem bounds_13_7707 : exactInterval 13 7707 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7707 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7707) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7707 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7707 : oddCount 7707 13 = 10 ∧ acceleratedOrbit 13 7707 = 55565 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7707 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7707) = 3 ^ 10 * m + 55565 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7707.1, data_13_7707.2] + +/-- Complete interval computation for depth 13, residue 7708. -/ +theorem bounds_13_7708 : exactInterval 13 7708 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7708 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7708) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7708 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7708 : oddCount 7708 13 = 5 ∧ acceleratedOrbit 13 7708 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7708 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7708) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7708.1, data_13_7708.2] + +/-- Complete interval computation for depth 13, residue 7709. -/ +theorem bounds_13_7709 : exactInterval 13 7709 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7709 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7709) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7709 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7709 : oddCount 7709 13 = 5 ∧ acceleratedOrbit 13 7709 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7709 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7709) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7709.1, data_13_7709.2] + +/-- Complete interval computation for depth 13, residue 7710. -/ +theorem bounds_13_7710 : exactInterval 13 7710 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7710 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7710) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7710 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7710 : oddCount 7710 13 = 5 ∧ acceleratedOrbit 13 7710 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7710 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7710) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7710.1, data_13_7710.2] + +/-- Complete interval computation for depth 13, residue 7711. -/ +theorem bounds_13_7711 : exactInterval 13 7711 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7711 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7711) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7711 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7711 : oddCount 7711 13 = 10 ∧ acceleratedOrbit 13 7711 = 55592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7711 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7711) = 3 ^ 10 * m + 55592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7711.1, data_13_7711.2] + +/-- Complete interval computation for depth 13, residue 7712. -/ +theorem bounds_13_7712 : exactInterval 13 7712 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7712 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7712) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7712 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7712 : oddCount 7712 13 = 3 ∧ acceleratedOrbit 13 7712 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7712 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7712) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7712.1, data_13_7712.2] + +/-- Complete interval computation for depth 13, residue 7713. -/ +theorem bounds_13_7713 : exactInterval 13 7713 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7713 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7713) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7713 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7713 : oddCount 7713 13 = 8 ∧ acceleratedOrbit 13 7713 = 6182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7713 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7713) = 3 ^ 8 * m + 6182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7713.1, data_13_7713.2] + +/-- Complete interval computation for depth 13, residue 7714. -/ +theorem bounds_13_7714 : exactInterval 13 7714 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7714 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7714) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7714 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7714 : oddCount 7714 13 = 6 ∧ acceleratedOrbit 13 7714 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7714 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7714) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7714.1, data_13_7714.2] + +end Collatz.Research.StoppingAtlas.Batch0969 From 38861164e7cd8823794359735a7360229b20975d Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:32 +0530 Subject: [PATCH 0970/1001] proof: certify atlas Batch0970 (13:7715 to 13:7730) --- Collatz/Research/StoppingAtlas/Batch0970.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0970.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0970.lean b/Collatz/Research/StoppingAtlas/Batch0970.lean new file mode 100644 index 00000000..7593ff4d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0970.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0970 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7715. -/ +theorem bounds_13_7715 : exactInterval 13 7715 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7715 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7715) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7715 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7715 : oddCount 7715 13 = 6 ∧ acceleratedOrbit 13 7715 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7715 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7715) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7715.1, data_13_7715.2] + +/-- Complete interval computation for depth 13, residue 7716. -/ +theorem bounds_13_7716 : exactInterval 13 7716 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7716 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7716) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7716 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7716 : oddCount 7716 13 = 7 ∧ acceleratedOrbit 13 7716 = 2062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7716 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7716) = 3 ^ 7 * m + 2062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7716.1, data_13_7716.2] + +/-- Complete interval computation for depth 13, residue 7717. -/ +theorem bounds_13_7717 : exactInterval 13 7717 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7717 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7717) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7717 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7717 : oddCount 7717 13 = 7 ∧ acceleratedOrbit 13 7717 = 2062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7717 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7717) = 3 ^ 7 * m + 2062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7717.1, data_13_7717.2] + +/-- Complete interval computation for depth 13, residue 7718. -/ +theorem bounds_13_7718 : exactInterval 13 7718 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7718 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7718) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7718 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7718 : oddCount 7718 13 = 7 ∧ acceleratedOrbit 13 7718 = 2062 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7718 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7718) = 3 ^ 7 * m + 2062 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7718.1, data_13_7718.2] + +/-- Complete interval computation for depth 13, residue 7719. -/ +theorem bounds_13_7719 : exactInterval 13 7719 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7719 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7719) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7719 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7719 : oddCount 7719 13 = 5 ∧ acceleratedOrbit 13 7719 = 229 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7719 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7719) = 3 ^ 5 * m + 229 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7719.1, data_13_7719.2] + +/-- Complete interval computation for depth 13, residue 7720. -/ +theorem bounds_13_7720 : exactInterval 13 7720 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7720 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7720) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7720 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7720 : oddCount 7720 13 = 3 ∧ acceleratedOrbit 13 7720 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7720 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7720) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7720.1, data_13_7720.2] + +/-- Complete interval computation for depth 13, residue 7721. -/ +theorem bounds_13_7721 : exactInterval 13 7721 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7721 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7721) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7721 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7721 : oddCount 7721 13 = 10 ∧ acceleratedOrbit 13 7721 = 55667 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7721 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7721) = 3 ^ 10 * m + 55667 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7721.1, data_13_7721.2] + +/-- Complete interval computation for depth 13, residue 7722. -/ +theorem bounds_13_7722 : exactInterval 13 7722 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7722 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7722) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7722 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7722 : oddCount 7722 13 = 3 ∧ acceleratedOrbit 13 7722 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7722 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7722) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7722.1, data_13_7722.2] + +/-- Complete interval computation for depth 13, residue 7723. -/ +theorem bounds_13_7723 : exactInterval 13 7723 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7723 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7723) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7723 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7723 : oddCount 7723 13 = 6 ∧ acceleratedOrbit 13 7723 = 688 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7723 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7723) = 3 ^ 6 * m + 688 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7723.1, data_13_7723.2] + +/-- Complete interval computation for depth 13, residue 7724. -/ +theorem bounds_13_7724 : exactInterval 13 7724 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7724 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7724) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7724 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7724 : oddCount 7724 13 = 7 ∧ acceleratedOrbit 13 7724 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7724 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7724) = 3 ^ 7 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7724.1, data_13_7724.2] + +/-- Complete interval computation for depth 13, residue 7725. -/ +theorem bounds_13_7725 : exactInterval 13 7725 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7725 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7725) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7725 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7725 : oddCount 7725 13 = 7 ∧ acceleratedOrbit 13 7725 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7725 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7725) = 3 ^ 7 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7725.1, data_13_7725.2] + +/-- Complete interval computation for depth 13, residue 7726. -/ +theorem bounds_13_7726 : exactInterval 13 7726 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7726 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7726) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7726 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7726 : oddCount 7726 13 = 7 ∧ acceleratedOrbit 13 7726 = 2065 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7726 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7726) = 3 ^ 7 * m + 2065 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7726.1, data_13_7726.2] + +/-- Complete interval computation for depth 13, residue 7727. -/ +theorem bounds_13_7727 : exactInterval 13 7727 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7727 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7727) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7727 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7727 : oddCount 7727 13 = 9 ∧ acceleratedOrbit 13 7727 = 18569 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7727 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7727) = 3 ^ 9 * m + 18569 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7727.1, data_13_7727.2] + +/-- Complete interval computation for depth 13, residue 7728. -/ +theorem bounds_13_7728 : exactInterval 13 7728 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7728 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7728) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7728 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7728 : oddCount 7728 13 = 3 ∧ acceleratedOrbit 13 7728 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7728 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7728) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7728.1, data_13_7728.2] + +/-- Complete interval computation for depth 13, residue 7729. -/ +theorem bounds_13_7729 : exactInterval 13 7729 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7729 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7729) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7729 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7729 : oddCount 7729 13 = 8 ∧ acceleratedOrbit 13 7729 = 6196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7729 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7729) = 3 ^ 8 * m + 6196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7729.1, data_13_7729.2] + +/-- Complete interval computation for depth 13, residue 7730. -/ +theorem bounds_13_7730 : exactInterval 13 7730 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7730 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7730) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7730 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7730 : oddCount 7730 13 = 8 ∧ acceleratedOrbit 13 7730 = 6196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7730 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7730) = 3 ^ 8 * m + 6196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7730.1, data_13_7730.2] + +end Collatz.Research.StoppingAtlas.Batch0970 From 2a1efe0d8e710f57876d9d9aff3905e67cf98571 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:33 +0530 Subject: [PATCH 0971/1001] proof: certify atlas Batch0971 (13:7731 to 13:7745) --- Collatz/Research/StoppingAtlas/Batch0971.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0971.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0971.lean b/Collatz/Research/StoppingAtlas/Batch0971.lean new file mode 100644 index 00000000..639c978a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0971.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0971 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7731. -/ +theorem bounds_13_7731 : exactInterval 13 7731 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7731 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7731) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7731 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7731 : oddCount 7731 13 = 8 ∧ acceleratedOrbit 13 7731 = 6196 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7731 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7731) = 3 ^ 8 * m + 6196 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7731.1, data_13_7731.2] + +/-- Complete interval computation for depth 13, residue 7732. -/ +theorem bounds_13_7732 : exactInterval 13 7732 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7732 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7732) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7732 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7732 : oddCount 7732 13 = 3 ∧ acceleratedOrbit 13 7732 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7732 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7732) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7732.1, data_13_7732.2] + +/-- Complete interval computation for depth 13, residue 7733. -/ +theorem bounds_13_7733 : exactInterval 13 7733 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7733 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7733) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7733 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7733 : oddCount 7733 13 = 3 ∧ acceleratedOrbit 13 7733 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7733 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7733) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7733.1, data_13_7733.2] + +/-- Complete interval computation for depth 13, residue 7734. -/ +theorem bounds_13_7734 : exactInterval 13 7734 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7734 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7734) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7734 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7734 : oddCount 7734 13 = 10 ∧ acceleratedOrbit 13 7734 = 55768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7734 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7734) = 3 ^ 10 * m + 55768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7734.1, data_13_7734.2] + +/-- Complete interval computation for depth 13, residue 7735. -/ +theorem bounds_13_7735 : exactInterval 13 7735 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7735 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7735) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7735 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7735 : oddCount 7735 13 = 10 ∧ acceleratedOrbit 13 7735 = 55768 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7735 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7735) = 3 ^ 10 * m + 55768 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7735.1, data_13_7735.2] + +/-- Complete interval computation for depth 13, residue 7736. -/ +theorem bounds_13_7736 : exactInterval 13 7736 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7736 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7736) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7736 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7736 : oddCount 7736 13 = 7 ∧ acceleratedOrbit 13 7736 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7736 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7736) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7736.1, data_13_7736.2] + +/-- Complete interval computation for depth 13, residue 7737. -/ +theorem bounds_13_7737 : exactInterval 13 7737 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7737 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7737) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7737 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7737 : oddCount 7737 13 = 8 ∧ acceleratedOrbit 13 7737 = 6200 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7737 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7737) = 3 ^ 8 * m + 6200 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7737.1, data_13_7737.2] + +/-- Complete interval computation for depth 13, residue 7738. -/ +theorem bounds_13_7738 : exactInterval 13 7738 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7738 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7738) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7738 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7738 : oddCount 7738 13 = 7 ∧ acceleratedOrbit 13 7738 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7738 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7738) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7738.1, data_13_7738.2] + +/-- Complete interval computation for depth 13, residue 7739. -/ +theorem bounds_13_7739 : exactInterval 13 7739 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7739 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7739) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7739 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7739 : oddCount 7739 13 = 6 ∧ acceleratedOrbit 13 7739 = 689 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7739 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7739) = 3 ^ 6 * m + 689 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7739.1, data_13_7739.2] + +/-- Complete interval computation for depth 13, residue 7740. -/ +theorem bounds_13_7740 : exactInterval 13 7740 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7740 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7740) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7740 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7740 : oddCount 7740 13 = 7 ∧ acceleratedOrbit 13 7740 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7740 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7740) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7740.1, data_13_7740.2] + +/-- Complete interval computation for depth 13, residue 7741. -/ +theorem bounds_13_7741 : exactInterval 13 7741 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7741 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7741) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7741 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7741 : oddCount 7741 13 = 7 ∧ acceleratedOrbit 13 7741 = 2069 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7741 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7741) = 3 ^ 7 * m + 2069 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7741.1, data_13_7741.2] + +/-- Complete interval computation for depth 13, residue 7742. -/ +theorem bounds_13_7742 : exactInterval 13 7742 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7742 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7742) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7742 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7742 : oddCount 7742 13 = 8 ∧ acceleratedOrbit 13 7742 = 6203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7742 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7742) = 3 ^ 8 * m + 6203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7742.1, data_13_7742.2] + +/-- Complete interval computation for depth 13, residue 7743. -/ +theorem bounds_13_7743 : exactInterval 13 7743 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7743 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7743) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7743 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7743 : oddCount 7743 13 = 8 ∧ acceleratedOrbit 13 7743 = 6203 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7743 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7743) = 3 ^ 8 * m + 6203 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7743.1, data_13_7743.2] + +/-- Complete interval computation for depth 13, residue 7744. -/ +theorem bounds_13_7744 : exactInterval 13 7744 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7744 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7744) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7744 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7744 : oddCount 7744 13 = 5 ∧ acceleratedOrbit 13 7744 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7744 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7744) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7744.1, data_13_7744.2] + +/-- Complete interval computation for depth 13, residue 7745. -/ +theorem bounds_13_7745 : exactInterval 13 7745 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7745 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7745) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7745 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7745 : oddCount 7745 13 = 5 ∧ acceleratedOrbit 13 7745 = 230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7745 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7745) = 3 ^ 5 * m + 230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7745.1, data_13_7745.2] + +end Collatz.Research.StoppingAtlas.Batch0971 From 3a76b16496fb6dfd8e8a239fcc98391a4e655a5b Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:33 +0530 Subject: [PATCH 0972/1001] proof: certify atlas Batch0972 (13:7746 to 13:7760) --- Collatz/Research/StoppingAtlas/Batch0972.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0972.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0972.lean b/Collatz/Research/StoppingAtlas/Batch0972.lean new file mode 100644 index 00000000..cb4c5ffc --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0972.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0972 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7746. -/ +theorem bounds_13_7746 : exactInterval 13 7746 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7746 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7746) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7746 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7746 : oddCount 7746 13 = 5 ∧ acceleratedOrbit 13 7746 = 230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7746 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7746) = 3 ^ 5 * m + 230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7746.1, data_13_7746.2] + +/-- Complete interval computation for depth 13, residue 7747. -/ +theorem bounds_13_7747 : exactInterval 13 7747 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7747 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7747) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7747 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7747 : oddCount 7747 13 = 5 ∧ acceleratedOrbit 13 7747 = 230 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7747 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7747) = 3 ^ 5 * m + 230 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7747.1, data_13_7747.2] + +/-- Complete interval computation for depth 13, residue 7748. -/ +theorem bounds_13_7748 : exactInterval 13 7748 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7748 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7748) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7748 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7748 : oddCount 7748 13 = 6 ∧ acceleratedOrbit 13 7748 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7748 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7748) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7748.1, data_13_7748.2] + +/-- Complete interval computation for depth 13, residue 7749. -/ +theorem bounds_13_7749 : exactInterval 13 7749 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7749 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7749) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7749 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7749 : oddCount 7749 13 = 6 ∧ acceleratedOrbit 13 7749 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7749 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7749) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7749.1, data_13_7749.2] + +/-- Complete interval computation for depth 13, residue 7750. -/ +theorem bounds_13_7750 : exactInterval 13 7750 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7750 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7750) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7750 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7750 : oddCount 7750 13 = 6 ∧ acceleratedOrbit 13 7750 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7750 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7750) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7750.1, data_13_7750.2] + +/-- Complete interval computation for depth 13, residue 7751. -/ +theorem bounds_13_7751 : exactInterval 13 7751 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7751 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7751) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7751 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7751 : oddCount 7751 13 = 9 ∧ acceleratedOrbit 13 7751 = 18629 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7751 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7751) = 3 ^ 9 * m + 18629 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7751.1, data_13_7751.2] + +/-- Complete interval computation for depth 13, residue 7752. -/ +theorem bounds_13_7752 : exactInterval 13 7752 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7752 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7752) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7752 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7752 : oddCount 7752 13 = 6 ∧ acceleratedOrbit 13 7752 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7752 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7752) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7752.1, data_13_7752.2] + +/-- Complete interval computation for depth 13, residue 7753. -/ +theorem bounds_13_7753 : exactInterval 13 7753 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7753 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7753) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7753 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7753 : oddCount 7753 13 = 8 ∧ acceleratedOrbit 13 7753 = 6212 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7753 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7753) = 3 ^ 8 * m + 6212 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7753.1, data_13_7753.2] + +/-- Complete interval computation for depth 13, residue 7754. -/ +theorem bounds_13_7754 : exactInterval 13 7754 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7754 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7754) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7754 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7754 : oddCount 7754 13 = 6 ∧ acceleratedOrbit 13 7754 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7754 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7754) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7754.1, data_13_7754.2] + +/-- Complete interval computation for depth 13, residue 7755. -/ +theorem bounds_13_7755 : exactInterval 13 7755 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7755 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7755) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7755 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7755 : oddCount 7755 13 = 6 ∧ acceleratedOrbit 13 7755 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7755 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7755) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7755.1, data_13_7755.2] + +/-- Complete interval computation for depth 13, residue 7756. -/ +theorem bounds_13_7756 : exactInterval 13 7756 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7756 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7756) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7756 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7756 : oddCount 7756 13 = 6 ∧ acceleratedOrbit 13 7756 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7756 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7756) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7756.1, data_13_7756.2] + +/-- Complete interval computation for depth 13, residue 7757. -/ +theorem bounds_13_7757 : exactInterval 13 7757 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7757 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7757) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7757 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7757 : oddCount 7757 13 = 6 ∧ acceleratedOrbit 13 7757 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7757 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7757) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7757.1, data_13_7757.2] + +/-- Complete interval computation for depth 13, residue 7758. -/ +theorem bounds_13_7758 : exactInterval 13 7758 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7758 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7758) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7758 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7758 : oddCount 7758 13 = 7 ∧ acceleratedOrbit 13 7758 = 2072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7758 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7758) = 3 ^ 7 * m + 2072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7758.1, data_13_7758.2] + +/-- Complete interval computation for depth 13, residue 7759. -/ +theorem bounds_13_7759 : exactInterval 13 7759 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7759 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7759) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7759 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7759 : oddCount 7759 13 = 7 ∧ acceleratedOrbit 13 7759 = 2072 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7759 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7759) = 3 ^ 7 * m + 2072 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7759.1, data_13_7759.2] + +/-- Complete interval computation for depth 13, residue 7760. -/ +theorem bounds_13_7760 : exactInterval 13 7760 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7760 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7760) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7760 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7760 : oddCount 7760 13 = 5 ∧ acceleratedOrbit 13 7760 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7760 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7760) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7760.1, data_13_7760.2] + +end Collatz.Research.StoppingAtlas.Batch0972 From 5fdb2fb26fc2d32b301ca17984cfe8e1a5b51181 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:33 +0530 Subject: [PATCH 0973/1001] proof: certify atlas Batch0973 (13:7761 to 13:7776) --- Collatz/Research/StoppingAtlas/Batch0973.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0973.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0973.lean b/Collatz/Research/StoppingAtlas/Batch0973.lean new file mode 100644 index 00000000..1721de15 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0973.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0973 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7761. -/ +theorem bounds_13_7761 : exactInterval 13 7761 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7761 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7761) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7761 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7761 : oddCount 7761 13 = 6 ∧ acceleratedOrbit 13 7761 = 691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7761 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7761) = 3 ^ 6 * m + 691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7761.1, data_13_7761.2] + +/-- Complete interval computation for depth 13, residue 7762. -/ +theorem bounds_13_7762 : exactInterval 13 7762 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7762 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7762) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7762 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7762 : oddCount 7762 13 = 6 ∧ acceleratedOrbit 13 7762 = 691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7762 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7762) = 3 ^ 6 * m + 691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7762.1, data_13_7762.2] + +/-- Complete interval computation for depth 13, residue 7763. -/ +theorem bounds_13_7763 : exactInterval 13 7763 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7763 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7763) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7763 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7763 : oddCount 7763 13 = 6 ∧ acceleratedOrbit 13 7763 = 691 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7763 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7763) = 3 ^ 6 * m + 691 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7763.1, data_13_7763.2] + +/-- Complete interval computation for depth 13, residue 7764. -/ +theorem bounds_13_7764 : exactInterval 13 7764 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7764 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7764) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7764 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7764 : oddCount 7764 13 = 5 ∧ acceleratedOrbit 13 7764 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7764 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7764) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7764.1, data_13_7764.2] + +/-- Complete interval computation for depth 13, residue 7765. -/ +theorem bounds_13_7765 : exactInterval 13 7765 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7765 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7765) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7765 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7765 : oddCount 7765 13 = 5 ∧ acceleratedOrbit 13 7765 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7765 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7765) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7765.1, data_13_7765.2] + +/-- Complete interval computation for depth 13, residue 7766. -/ +theorem bounds_13_7766 : exactInterval 13 7766 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7766 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7766) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7766 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7766 : oddCount 7766 13 = 6 ∧ acceleratedOrbit 13 7766 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7766 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7766) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7766.1, data_13_7766.2] + +/-- Complete interval computation for depth 13, residue 7767. -/ +theorem bounds_13_7767 : exactInterval 13 7767 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7767 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7767) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7767 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7767 : oddCount 7767 13 = 6 ∧ acceleratedOrbit 13 7767 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7767 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7767) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7767.1, data_13_7767.2] + +/-- Complete interval computation for depth 13, residue 7768. -/ +theorem bounds_13_7768 : exactInterval 13 7768 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7768 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7768) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7768 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7768 : oddCount 7768 13 = 4 ∧ acceleratedOrbit 13 7768 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7768 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7768) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7768.1, data_13_7768.2] + +/-- Complete interval computation for depth 13, residue 7769. -/ +theorem bounds_13_7769 : exactInterval 13 7769 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7769 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7769) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7769 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7769 : oddCount 7769 13 = 8 ∧ acceleratedOrbit 13 7769 = 6227 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7769 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7769) = 3 ^ 8 * m + 6227 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7769.1, data_13_7769.2] + +/-- Complete interval computation for depth 13, residue 7770. -/ +theorem bounds_13_7770 : exactInterval 13 7770 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7770 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7770) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7770 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7770 : oddCount 7770 13 = 4 ∧ acceleratedOrbit 13 7770 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7770 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7770) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7770.1, data_13_7770.2] + +/-- Complete interval computation for depth 13, residue 7771. -/ +theorem bounds_13_7771 : exactInterval 13 7771 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7771 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7771) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7771 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7771 : oddCount 7771 13 = 7 ∧ acceleratedOrbit 13 7771 = 2075 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7771 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7771) = 3 ^ 7 * m + 2075 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7771.1, data_13_7771.2] + +/-- Complete interval computation for depth 13, residue 7772. -/ +theorem bounds_13_7772 : exactInterval 13 7772 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7772 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7772) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7772 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7772 : oddCount 7772 13 = 4 ∧ acceleratedOrbit 13 7772 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7772 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7772) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7772.1, data_13_7772.2] + +/-- Complete interval computation for depth 13, residue 7773. -/ +theorem bounds_13_7773 : exactInterval 13 7773 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7773 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7773) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7773 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7773 : oddCount 7773 13 = 4 ∧ acceleratedOrbit 13 7773 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7773 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7773) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7773.1, data_13_7773.2] + +/-- Complete interval computation for depth 13, residue 7774. -/ +theorem bounds_13_7774 : exactInterval 13 7774 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7774 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7774) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7774 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7774 : oddCount 7774 13 = 6 ∧ acceleratedOrbit 13 7774 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7774 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7774) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7774.1, data_13_7774.2] + +/-- Complete interval computation for depth 13, residue 7775. -/ +theorem bounds_13_7775 : exactInterval 13 7775 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7775 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7775) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7775 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7775 : oddCount 7775 13 = 6 ∧ acceleratedOrbit 13 7775 = 692 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7775 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7775) = 3 ^ 6 * m + 692 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7775.1, data_13_7775.2] + +/-- Complete interval computation for depth 13, residue 7776. -/ +theorem bounds_13_7776 : exactInterval 13 7776 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7776 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7776) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7776 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7776 : oddCount 7776 13 = 5 ∧ acceleratedOrbit 13 7776 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7776 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7776) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7776.1, data_13_7776.2] + +end Collatz.Research.StoppingAtlas.Batch0973 From 8dd975a97cc46b5e22be917032fb2499eab13868 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:33 +0530 Subject: [PATCH 0974/1001] proof: certify atlas Batch0974 (13:7777 to 13:7791) --- Collatz/Research/StoppingAtlas/Batch0974.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0974.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0974.lean b/Collatz/Research/StoppingAtlas/Batch0974.lean new file mode 100644 index 00000000..9df05b92 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0974.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0974 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7777. -/ +theorem bounds_13_7777 : exactInterval 13 7777 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7777 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7777) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7777 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7777 : oddCount 7777 13 = 7 ∧ acceleratedOrbit 13 7777 = 2078 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7777 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7777) = 3 ^ 7 * m + 2078 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7777.1, data_13_7777.2] + +/-- Complete interval computation for depth 13, residue 7778. -/ +theorem bounds_13_7778 : exactInterval 13 7778 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7778 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7778) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7778 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7778 : oddCount 7778 13 = 4 ∧ acceleratedOrbit 13 7778 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7778 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7778) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7778.1, data_13_7778.2] + +/-- Complete interval computation for depth 13, residue 7779. -/ +theorem bounds_13_7779 : exactInterval 13 7779 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7779 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7779) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7779 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7779 : oddCount 7779 13 = 4 ∧ acceleratedOrbit 13 7779 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7779 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7779) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7779.1, data_13_7779.2] + +/-- Complete interval computation for depth 13, residue 7780. -/ +theorem bounds_13_7780 : exactInterval 13 7780 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7780 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7780) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7780 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7780 : oddCount 7780 13 = 4 ∧ acceleratedOrbit 13 7780 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7780 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7780) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7780.1, data_13_7780.2] + +/-- Complete interval computation for depth 13, residue 7781. -/ +theorem bounds_13_7781 : exactInterval 13 7781 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7781 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7781) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7781 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7781 : oddCount 7781 13 = 4 ∧ acceleratedOrbit 13 7781 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7781 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7781) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7781.1, data_13_7781.2] + +/-- Complete interval computation for depth 13, residue 7782. -/ +theorem bounds_13_7782 : exactInterval 13 7782 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7782 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7782) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7782 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7782 : oddCount 7782 13 = 4 ∧ acceleratedOrbit 13 7782 = 77 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7782 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7782) = 3 ^ 4 * m + 77 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7782.1, data_13_7782.2] + +/-- Complete interval computation for depth 13, residue 7783. -/ +theorem bounds_13_7783 : exactInterval 13 7783 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7783 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7783) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7783 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7783 : oddCount 7783 13 = 9 ∧ acceleratedOrbit 13 7783 = 18704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7783 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7783) = 3 ^ 9 * m + 18704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7783.1, data_13_7783.2] + +/-- Complete interval computation for depth 13, residue 7784. -/ +theorem bounds_13_7784 : exactInterval 13 7784 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7784 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7784) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7784 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7784 : oddCount 7784 13 = 5 ∧ acceleratedOrbit 13 7784 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7784 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7784) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7784.1, data_13_7784.2] + +/-- Complete interval computation for depth 13, residue 7785. -/ +theorem bounds_13_7785 : exactInterval 13 7785 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7785 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7785) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7785 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7785 : oddCount 7785 13 = 10 ∧ acceleratedOrbit 13 7785 = 56132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7785 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7785) = 3 ^ 10 * m + 56132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7785.1, data_13_7785.2] + +/-- Complete interval computation for depth 13, residue 7786. -/ +theorem bounds_13_7786 : exactInterval 13 7786 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7786 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7786) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7786 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7786 : oddCount 7786 13 = 5 ∧ acceleratedOrbit 13 7786 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7786 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7786) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7786.1, data_13_7786.2] + +/-- Complete interval computation for depth 13, residue 7787. -/ +theorem bounds_13_7787 : exactInterval 13 7787 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7787 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7787) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7787 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7787 : oddCount 7787 13 = 8 ∧ acceleratedOrbit 13 7787 = 6239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7787 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7787) = 3 ^ 8 * m + 6239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7787.1, data_13_7787.2] + +/-- Complete interval computation for depth 13, residue 7788. -/ +theorem bounds_13_7788 : exactInterval 13 7788 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7788 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7788) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7788 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7788 : oddCount 7788 13 = 7 ∧ acceleratedOrbit 13 7788 = 2081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7788 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7788) = 3 ^ 7 * m + 2081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7788.1, data_13_7788.2] + +/-- Complete interval computation for depth 13, residue 7789. -/ +theorem bounds_13_7789 : exactInterval 13 7789 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7789 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7789) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7789 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7789 : oddCount 7789 13 = 7 ∧ acceleratedOrbit 13 7789 = 2081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7789 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7789) = 3 ^ 7 * m + 2081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7789.1, data_13_7789.2] + +/-- Complete interval computation for depth 13, residue 7790. -/ +theorem bounds_13_7790 : exactInterval 13 7790 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7790 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7790) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7790 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7790 : oddCount 7790 13 = 7 ∧ acceleratedOrbit 13 7790 = 2081 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7790 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7790) = 3 ^ 7 * m + 2081 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7790.1, data_13_7790.2] + +/-- Complete interval computation for depth 13, residue 7791. -/ +theorem bounds_13_7791 : exactInterval 13 7791 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7791 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7791) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7791 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7791 : oddCount 7791 13 = 8 ∧ acceleratedOrbit 13 7791 = 6241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7791 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7791) = 3 ^ 8 * m + 6241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7791.1, data_13_7791.2] + +end Collatz.Research.StoppingAtlas.Batch0974 From 26fd517e923bb92b260af73ece54dbee9ced78c5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:33 +0530 Subject: [PATCH 0975/1001] proof: certify atlas Batch0975 (13:7792 to 13:7807) --- Collatz/Research/StoppingAtlas/Batch0975.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0975.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0975.lean b/Collatz/Research/StoppingAtlas/Batch0975.lean new file mode 100644 index 00000000..51e1758a --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0975.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0975 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7792. -/ +theorem bounds_13_7792 : exactInterval 13 7792 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7792 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7792) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7792 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7792 : oddCount 7792 13 = 6 ∧ acceleratedOrbit 13 7792 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7792 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7792) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7792.1, data_13_7792.2] + +/-- Complete interval computation for depth 13, residue 7793. -/ +theorem bounds_13_7793 : exactInterval 13 7793 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7793 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7793) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7793 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7793 : oddCount 7793 13 = 5 ∧ acceleratedOrbit 13 7793 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7793 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7793) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7793.1, data_13_7793.2] + +/-- Complete interval computation for depth 13, residue 7794. -/ +theorem bounds_13_7794 : exactInterval 13 7794 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7794 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7794) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7794 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7794 : oddCount 7794 13 = 6 ∧ acceleratedOrbit 13 7794 = 694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7794 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7794) = 3 ^ 6 * m + 694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7794.1, data_13_7794.2] + +/-- Complete interval computation for depth 13, residue 7795. -/ +theorem bounds_13_7795 : exactInterval 13 7795 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7795 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7795) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7795 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7795 : oddCount 7795 13 = 6 ∧ acceleratedOrbit 13 7795 = 694 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7795 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7795) = 3 ^ 6 * m + 694 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7795.1, data_13_7795.2] + +/-- Complete interval computation for depth 13, residue 7796. -/ +theorem bounds_13_7796 : exactInterval 13 7796 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7796 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7796) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7796 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7796 : oddCount 7796 13 = 6 ∧ acceleratedOrbit 13 7796 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7796 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7796) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7796.1, data_13_7796.2] + +/-- Complete interval computation for depth 13, residue 7797. -/ +theorem bounds_13_7797 : exactInterval 13 7797 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7797 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7797) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7797 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7797 : oddCount 7797 13 = 6 ∧ acceleratedOrbit 13 7797 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7797 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7797) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7797.1, data_13_7797.2] + +/-- Complete interval computation for depth 13, residue 7798. -/ +theorem bounds_13_7798 : exactInterval 13 7798 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7798 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7798) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7798 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7798 : oddCount 7798 13 = 6 ∧ acceleratedOrbit 13 7798 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7798 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7798) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7798.1, data_13_7798.2] + +/-- Complete interval computation for depth 13, residue 7799. -/ +theorem bounds_13_7799 : exactInterval 13 7799 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7799 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7799) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7799 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7799 : oddCount 7799 13 = 6 ∧ acceleratedOrbit 13 7799 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7799 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7799) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7799.1, data_13_7799.2] + +/-- Complete interval computation for depth 13, residue 7800. -/ +theorem bounds_13_7800 : exactInterval 13 7800 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7800 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7800) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7800 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7800 : oddCount 7800 13 = 6 ∧ acceleratedOrbit 13 7800 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7800 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7800) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7800.1, data_13_7800.2] + +/-- Complete interval computation for depth 13, residue 7801. -/ +theorem bounds_13_7801 : exactInterval 13 7801 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7801 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7801) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7801 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7801 : oddCount 7801 13 = 8 ∧ acceleratedOrbit 13 7801 = 6250 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7801 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7801) = 3 ^ 8 * m + 6250 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7801.1, data_13_7801.2] + +/-- Complete interval computation for depth 13, residue 7802. -/ +theorem bounds_13_7802 : exactInterval 13 7802 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7802 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7802) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7802 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7802 : oddCount 7802 13 = 6 ∧ acceleratedOrbit 13 7802 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7802 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7802) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7802.1, data_13_7802.2] + +/-- Complete interval computation for depth 13, residue 7803. -/ +theorem bounds_13_7803 : exactInterval 13 7803 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7803 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7803) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7803 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7803 : oddCount 7803 13 = 6 ∧ acceleratedOrbit 13 7803 = 695 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7803 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7803) = 3 ^ 6 * m + 695 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7803.1, data_13_7803.2] + +/-- Complete interval computation for depth 13, residue 7804. -/ +theorem bounds_13_7804 : exactInterval 13 7804 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7804 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7804) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7804 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7804 : oddCount 7804 13 = 8 ∧ acceleratedOrbit 13 7804 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7804 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7804) = 3 ^ 8 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7804.1, data_13_7804.2] + +/-- Complete interval computation for depth 13, residue 7805. -/ +theorem bounds_13_7805 : exactInterval 13 7805 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7805 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7805) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7805 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7805 : oddCount 7805 13 = 8 ∧ acceleratedOrbit 13 7805 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7805 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7805) = 3 ^ 8 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7805.1, data_13_7805.2] + +/-- Complete interval computation for depth 13, residue 7806. -/ +theorem bounds_13_7806 : exactInterval 13 7806 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7806 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7806) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7806 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7806 : oddCount 7806 13 = 8 ∧ acceleratedOrbit 13 7806 = 6254 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7806 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7806) = 3 ^ 8 * m + 6254 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7806.1, data_13_7806.2] + +/-- Complete interval computation for depth 13, residue 7807. -/ +theorem bounds_13_7807 : exactInterval 13 7807 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7807 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7807) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7807 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7807 : oddCount 7807 13 = 11 ∧ acceleratedOrbit 13 7807 = 168844 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7807 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7807) = 3 ^ 11 * m + 168844 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7807.1, data_13_7807.2] + +end Collatz.Research.StoppingAtlas.Batch0975 From 7adf077e4c9d381fd1be9b7916bdfbb8b3d2aa14 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:33 +0530 Subject: [PATCH 0976/1001] proof: certify atlas Batch0976 (13:7808 to 13:7822) --- Collatz/Research/StoppingAtlas/Batch0976.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0976.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0976.lean b/Collatz/Research/StoppingAtlas/Batch0976.lean new file mode 100644 index 00000000..69f266f0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0976.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0976 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7808. -/ +theorem bounds_13_7808 : exactInterval 13 7808 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7808 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7808) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7808 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7808 : oddCount 7808 13 = 4 ∧ acceleratedOrbit 13 7808 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7808 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7808) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7808.1, data_13_7808.2] + +/-- Complete interval computation for depth 13, residue 7809. -/ +theorem bounds_13_7809 : exactInterval 13 7809 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7809 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7809) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7809 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7809 : oddCount 7809 13 = 8 ∧ acceleratedOrbit 13 7809 = 6257 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7809 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7809) = 3 ^ 8 * m + 6257 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7809.1, data_13_7809.2] + +/-- Complete interval computation for depth 13, residue 7810. -/ +theorem bounds_13_7810 : exactInterval 13 7810 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7810 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7810) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7810 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7810 : oddCount 7810 13 = 5 ∧ acceleratedOrbit 13 7810 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7810 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7810) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7810.1, data_13_7810.2] + +/-- Complete interval computation for depth 13, residue 7811. -/ +theorem bounds_13_7811 : exactInterval 13 7811 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7811 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7811) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7811 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7811 : oddCount 7811 13 = 5 ∧ acceleratedOrbit 13 7811 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7811 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7811) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7811.1, data_13_7811.2] + +/-- Complete interval computation for depth 13, residue 7812. -/ +theorem bounds_13_7812 : exactInterval 13 7812 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7812 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7812) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7812 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7812 : oddCount 7812 13 = 5 ∧ acceleratedOrbit 13 7812 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7812 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7812) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7812.1, data_13_7812.2] + +/-- Complete interval computation for depth 13, residue 7813. -/ +theorem bounds_13_7813 : exactInterval 13 7813 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7813 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7813) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7813 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7813 : oddCount 7813 13 = 5 ∧ acceleratedOrbit 13 7813 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7813 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7813) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7813.1, data_13_7813.2] + +/-- Complete interval computation for depth 13, residue 7814. -/ +theorem bounds_13_7814 : exactInterval 13 7814 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7814 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7814) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7814 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7814 : oddCount 7814 13 = 5 ∧ acceleratedOrbit 13 7814 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7814 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7814) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7814.1, data_13_7814.2] + +/-- Complete interval computation for depth 13, residue 7815. -/ +theorem bounds_13_7815 : exactInterval 13 7815 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7815 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7815) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7815 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7815 : oddCount 7815 13 = 8 ∧ acceleratedOrbit 13 7815 = 6263 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7815 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7815) = 3 ^ 8 * m + 6263 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7815.1, data_13_7815.2] + +/-- Complete interval computation for depth 13, residue 7816. -/ +theorem bounds_13_7816 : exactInterval 13 7816 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7816 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7816) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7816 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7816 : oddCount 7816 13 = 5 ∧ acceleratedOrbit 13 7816 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7816 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7816) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7816.1, data_13_7816.2] + +/-- Complete interval computation for depth 13, residue 7817. -/ +theorem bounds_13_7817 : exactInterval 13 7817 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7817 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7817) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7817 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7817 : oddCount 7817 13 = 9 ∧ acceleratedOrbit 13 7817 = 18787 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7817 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7817) = 3 ^ 9 * m + 18787 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7817.1, data_13_7817.2] + +/-- Complete interval computation for depth 13, residue 7818. -/ +theorem bounds_13_7818 : exactInterval 13 7818 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7818 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7818) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7818 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7818 : oddCount 7818 13 = 5 ∧ acceleratedOrbit 13 7818 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7818 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7818) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7818.1, data_13_7818.2] + +/-- Complete interval computation for depth 13, residue 7819. -/ +theorem bounds_13_7819 : exactInterval 13 7819 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7819 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7819) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7819 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7819 : oddCount 7819 13 = 5 ∧ acceleratedOrbit 13 7819 = 232 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7819 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7819) = 3 ^ 5 * m + 232 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7819.1, data_13_7819.2] + +/-- Complete interval computation for depth 13, residue 7820. -/ +theorem bounds_13_7820 : exactInterval 13 7820 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7820 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7820) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7820 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7820 : oddCount 7820 13 = 5 ∧ acceleratedOrbit 13 7820 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7820 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7820) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7820.1, data_13_7820.2] + +/-- Complete interval computation for depth 13, residue 7821. -/ +theorem bounds_13_7821 : exactInterval 13 7821 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7821 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7821) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7821 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7821 : oddCount 7821 13 = 5 ∧ acceleratedOrbit 13 7821 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7821 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7821) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7821.1, data_13_7821.2] + +/-- Complete interval computation for depth 13, residue 7822. -/ +theorem bounds_13_7822 : exactInterval 13 7822 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7822 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7822) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7822 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7822 : oddCount 7822 13 = 7 ∧ acceleratedOrbit 13 7822 = 2089 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7822 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7822) = 3 ^ 7 * m + 2089 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7822.1, data_13_7822.2] + +end Collatz.Research.StoppingAtlas.Batch0976 From 93b0360438a622dc4c69079d9d41ce99ae4ae0ed Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:34 +0530 Subject: [PATCH 0977/1001] proof: certify atlas Batch0977 (13:7823 to 13:7837) --- Collatz/Research/StoppingAtlas/Batch0977.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0977.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0977.lean b/Collatz/Research/StoppingAtlas/Batch0977.lean new file mode 100644 index 00000000..0ad3952f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0977.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0977 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7823. -/ +theorem bounds_13_7823 : exactInterval 13 7823 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7823 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7823) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7823 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7823 : oddCount 7823 13 = 7 ∧ acceleratedOrbit 13 7823 = 2089 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7823 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7823) = 3 ^ 7 * m + 2089 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7823.1, data_13_7823.2] + +/-- Complete interval computation for depth 13, residue 7824. -/ +theorem bounds_13_7824 : exactInterval 13 7824 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7824 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7824) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7824 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7824 : oddCount 7824 13 = 7 ∧ acceleratedOrbit 13 7824 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7824 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7824) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7824.1, data_13_7824.2] + +/-- Complete interval computation for depth 13, residue 7825. -/ +theorem bounds_13_7825 : exactInterval 13 7825 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7825 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7825) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7825 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7825 : oddCount 7825 13 = 6 ∧ acceleratedOrbit 13 7825 = 697 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7825 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7825) = 3 ^ 6 * m + 697 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7825.1, data_13_7825.2] + +/-- Complete interval computation for depth 13, residue 7826. -/ +theorem bounds_13_7826 : exactInterval 13 7826 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7826 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7826) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7826 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7826 : oddCount 7826 13 = 6 ∧ acceleratedOrbit 13 7826 = 697 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7826 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7826) = 3 ^ 6 * m + 697 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7826.1, data_13_7826.2] + +/-- Complete interval computation for depth 13, residue 7827. -/ +theorem bounds_13_7827 : exactInterval 13 7827 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7827 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7827) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7827 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7827 : oddCount 7827 13 = 6 ∧ acceleratedOrbit 13 7827 = 697 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7827 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7827) = 3 ^ 6 * m + 697 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7827.1, data_13_7827.2] + +/-- Complete interval computation for depth 13, residue 7828. -/ +theorem bounds_13_7828 : exactInterval 13 7828 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7828 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7828) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7828 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7828 : oddCount 7828 13 = 7 ∧ acceleratedOrbit 13 7828 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7828 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7828) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7828.1, data_13_7828.2] + +/-- Complete interval computation for depth 13, residue 7829. -/ +theorem bounds_13_7829 : exactInterval 13 7829 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7829 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7829) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7829 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7829 : oddCount 7829 13 = 7 ∧ acceleratedOrbit 13 7829 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7829 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7829) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7829.1, data_13_7829.2] + +/-- Complete interval computation for depth 13, residue 7830. -/ +theorem bounds_13_7830 : exactInterval 13 7830 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7830 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7830) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7830 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7830 : oddCount 7830 13 = 5 ∧ acceleratedOrbit 13 7830 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7830 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7830) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7830.1, data_13_7830.2] + +/-- Complete interval computation for depth 13, residue 7831. -/ +theorem bounds_13_7831 : exactInterval 13 7831 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7831 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7831) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7831 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7831 : oddCount 7831 13 = 5 ∧ acceleratedOrbit 13 7831 = 233 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7831 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7831) = 3 ^ 5 * m + 233 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7831.1, data_13_7831.2] + +/-- Complete interval computation for depth 13, residue 7832. -/ +theorem bounds_13_7832 : exactInterval 13 7832 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7832 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7832) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7832 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7832 : oddCount 7832 13 = 7 ∧ acceleratedOrbit 13 7832 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7832 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7832) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7832.1, data_13_7832.2] + +/-- Complete interval computation for depth 13, residue 7833. -/ +theorem bounds_13_7833 : exactInterval 13 7833 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7833 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7833) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7833 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7833 : oddCount 7833 13 = 8 ∧ acceleratedOrbit 13 7833 = 6277 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7833 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7833) = 3 ^ 8 * m + 6277 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7833.1, data_13_7833.2] + +/-- Complete interval computation for depth 13, residue 7834. -/ +theorem bounds_13_7834 : exactInterval 13 7834 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7834 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7834) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7834 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7834 : oddCount 7834 13 = 7 ∧ acceleratedOrbit 13 7834 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7834 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7834) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7834.1, data_13_7834.2] + +/-- Complete interval computation for depth 13, residue 7835. -/ +theorem bounds_13_7835 : exactInterval 13 7835 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7835 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7835) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7835 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7835 : oddCount 7835 13 = 9 ∧ acceleratedOrbit 13 7835 = 18829 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7835 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7835) = 3 ^ 9 * m + 18829 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7835.1, data_13_7835.2] + +/-- Complete interval computation for depth 13, residue 7836. -/ +theorem bounds_13_7836 : exactInterval 13 7836 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7836 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7836) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7836 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7836 : oddCount 7836 13 = 8 ∧ acceleratedOrbit 13 7836 = 6281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7836 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7836) = 3 ^ 8 * m + 6281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7836.1, data_13_7836.2] + +/-- Complete interval computation for depth 13, residue 7837. -/ +theorem bounds_13_7837 : exactInterval 13 7837 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7837 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7837) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7837 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7837 : oddCount 7837 13 = 8 ∧ acceleratedOrbit 13 7837 = 6281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7837 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7837) = 3 ^ 8 * m + 6281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7837.1, data_13_7837.2] + +end Collatz.Research.StoppingAtlas.Batch0977 From c163822e87954760be7c09c59b15590e21b04b4c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:34 +0530 Subject: [PATCH 0978/1001] proof: certify atlas Batch0978 (13:7838 to 13:7853) --- Collatz/Research/StoppingAtlas/Batch0978.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0978.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0978.lean b/Collatz/Research/StoppingAtlas/Batch0978.lean new file mode 100644 index 00000000..2c5d0e41 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0978.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0978 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7838. -/ +theorem bounds_13_7838 : exactInterval 13 7838 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7838 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7838) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7838 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7838 : oddCount 7838 13 = 8 ∧ acceleratedOrbit 13 7838 = 6281 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7838 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7838) = 3 ^ 8 * m + 6281 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7838.1, data_13_7838.2] + +/-- Complete interval computation for depth 13, residue 7839. -/ +theorem bounds_13_7839 : exactInterval 13 7839 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7839 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7839) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7839 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7839 : oddCount 7839 13 = 10 ∧ acceleratedOrbit 13 7839 = 56513 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7839 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7839) = 3 ^ 10 * m + 56513 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7839.1, data_13_7839.2] + +/-- Complete interval computation for depth 13, residue 7840. -/ +theorem bounds_13_7840 : exactInterval 13 7840 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7840 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7840) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7840 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7840 : oddCount 7840 13 = 4 ∧ acceleratedOrbit 13 7840 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7840 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7840) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7840.1, data_13_7840.2] + +/-- Complete interval computation for depth 13, residue 7841. -/ +theorem bounds_13_7841 : exactInterval 13 7841 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7841 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7841) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7841 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7841 : oddCount 7841 13 = 6 ∧ acceleratedOrbit 13 7841 = 698 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7841 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7841) = 3 ^ 6 * m + 698 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7841.1, data_13_7841.2] + +/-- Complete interval computation for depth 13, residue 7842. -/ +theorem bounds_13_7842 : exactInterval 13 7842 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7842 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7842) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7842 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7842 : oddCount 7842 13 = 7 ∧ acceleratedOrbit 13 7842 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7842 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7842) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7842.1, data_13_7842.2] + +/-- Complete interval computation for depth 13, residue 7843. -/ +theorem bounds_13_7843 : exactInterval 13 7843 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7843 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7843) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7843 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7843 : oddCount 7843 13 = 7 ∧ acceleratedOrbit 13 7843 = 2096 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7843 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7843) = 3 ^ 7 * m + 2096 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7843.1, data_13_7843.2] + +/-- Complete interval computation for depth 13, residue 7844. -/ +theorem bounds_13_7844 : exactInterval 13 7844 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7844 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7844) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7844 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7844 : oddCount 7844 13 = 9 ∧ acceleratedOrbit 13 7844 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7844 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7844) = 3 ^ 9 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7844.1, data_13_7844.2] + +/-- Complete interval computation for depth 13, residue 7845. -/ +theorem bounds_13_7845 : exactInterval 13 7845 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7845 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7845) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7845 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7845 : oddCount 7845 13 = 9 ∧ acceleratedOrbit 13 7845 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7845 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7845) = 3 ^ 9 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7845.1, data_13_7845.2] + +/-- Complete interval computation for depth 13, residue 7846. -/ +theorem bounds_13_7846 : exactInterval 13 7846 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7846 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7846) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7846 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7846 : oddCount 7846 13 = 9 ∧ acceleratedOrbit 13 7846 = 18863 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7846 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7846) = 3 ^ 9 * m + 18863 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7846.1, data_13_7846.2] + +/-- Complete interval computation for depth 13, residue 7847. -/ +theorem bounds_13_7847 : exactInterval 13 7847 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7847 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7847) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7847 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7847 : oddCount 7847 13 = 8 ∧ acceleratedOrbit 13 7847 = 6286 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7847 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7847) = 3 ^ 8 * m + 6286 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7847.1, data_13_7847.2] + +/-- Complete interval computation for depth 13, residue 7848. -/ +theorem bounds_13_7848 : exactInterval 13 7848 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7848 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7848) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7848 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7848 : oddCount 7848 13 = 4 ∧ acceleratedOrbit 13 7848 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7848 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7848) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7848.1, data_13_7848.2] + +/-- Complete interval computation for depth 13, residue 7849. -/ +theorem bounds_13_7849 : exactInterval 13 7849 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7849 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7849) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7849 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7849 : oddCount 7849 13 = 11 ∧ acceleratedOrbit 13 7849 = 169766 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7849 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7849) = 3 ^ 11 * m + 169766 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7849.1, data_13_7849.2] + +/-- Complete interval computation for depth 13, residue 7850. -/ +theorem bounds_13_7850 : exactInterval 13 7850 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7850 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7850) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7850 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7850 : oddCount 7850 13 = 4 ∧ acceleratedOrbit 13 7850 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7850 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7850) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7850.1, data_13_7850.2] + +/-- Complete interval computation for depth 13, residue 7851. -/ +theorem bounds_13_7851 : exactInterval 13 7851 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7851 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7851) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7851 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7851 : oddCount 7851 13 = 9 ∧ acceleratedOrbit 13 7851 = 18872 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7851 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7851) = 3 ^ 9 * m + 18872 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7851.1, data_13_7851.2] + +/-- Complete interval computation for depth 13, residue 7852. -/ +theorem bounds_13_7852 : exactInterval 13 7852 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7852 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7852) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7852 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7852 : oddCount 7852 13 = 7 ∧ acceleratedOrbit 13 7852 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7852 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7852) = 3 ^ 7 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7852.1, data_13_7852.2] + +/-- Complete interval computation for depth 13, residue 7853. -/ +theorem bounds_13_7853 : exactInterval 13 7853 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7853 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7853) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7853 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7853 : oddCount 7853 13 = 7 ∧ acceleratedOrbit 13 7853 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7853 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7853) = 3 ^ 7 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7853.1, data_13_7853.2] + +end Collatz.Research.StoppingAtlas.Batch0978 From 33a78e5a7d219efc6ac6f81e2d71a7a706a30c1e Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:34 +0530 Subject: [PATCH 0979/1001] proof: certify atlas Batch0979 (13:7854 to 13:7868) --- Collatz/Research/StoppingAtlas/Batch0979.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0979.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0979.lean b/Collatz/Research/StoppingAtlas/Batch0979.lean new file mode 100644 index 00000000..a53b3788 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0979.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0979 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7854. -/ +theorem bounds_13_7854 : exactInterval 13 7854 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7854 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7854) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7854 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7854 : oddCount 7854 13 = 7 ∧ acceleratedOrbit 13 7854 = 2099 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7854 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7854) = 3 ^ 7 * m + 2099 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7854.1, data_13_7854.2] + +/-- Complete interval computation for depth 13, residue 7855. -/ +theorem bounds_13_7855 : exactInterval 13 7855 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7855 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7855) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7855 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7855 : oddCount 7855 13 = 8 ∧ acceleratedOrbit 13 7855 = 6293 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7855 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7855) = 3 ^ 8 * m + 6293 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7855.1, data_13_7855.2] + +/-- Complete interval computation for depth 13, residue 7856. -/ +theorem bounds_13_7856 : exactInterval 13 7856 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7856 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7856) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7856 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7856 : oddCount 7856 13 = 7 ∧ acceleratedOrbit 13 7856 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7856 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7856) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7856.1, data_13_7856.2] + +/-- Complete interval computation for depth 13, residue 7857. -/ +theorem bounds_13_7857 : exactInterval 13 7857 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7857 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7857) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7857 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7857 : oddCount 7857 13 = 6 ∧ acceleratedOrbit 13 7857 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7857 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7857) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7857.1, data_13_7857.2] + +/-- Complete interval computation for depth 13, residue 7858. -/ +theorem bounds_13_7858 : exactInterval 13 7858 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7858 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7858) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7858 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7858 : oddCount 7858 13 = 6 ∧ acceleratedOrbit 13 7858 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7858 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7858) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7858.1, data_13_7858.2] + +/-- Complete interval computation for depth 13, residue 7859. -/ +theorem bounds_13_7859 : exactInterval 13 7859 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7859 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7859) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7859 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7859 : oddCount 7859 13 = 6 ∧ acceleratedOrbit 13 7859 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7859 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7859) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7859.1, data_13_7859.2] + +/-- Complete interval computation for depth 13, residue 7860. -/ +theorem bounds_13_7860 : exactInterval 13 7860 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7860 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7860) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7860 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7860 : oddCount 7860 13 = 7 ∧ acceleratedOrbit 13 7860 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7860 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7860) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7860.1, data_13_7860.2] + +/-- Complete interval computation for depth 13, residue 7861. -/ +theorem bounds_13_7861 : exactInterval 13 7861 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7861 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7861) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7861 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7861 : oddCount 7861 13 = 7 ∧ acceleratedOrbit 13 7861 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7861 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7861) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7861.1, data_13_7861.2] + +/-- Complete interval computation for depth 13, residue 7862. -/ +theorem bounds_13_7862 : exactInterval 13 7862 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7862 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7862) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7862 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7862 : oddCount 7862 13 = 9 ∧ acceleratedOrbit 13 7862 = 18899 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7862 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7862) = 3 ^ 9 * m + 18899 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7862.1, data_13_7862.2] + +/-- Complete interval computation for depth 13, residue 7863. -/ +theorem bounds_13_7863 : exactInterval 13 7863 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7863 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7863) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7863 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7863 : oddCount 7863 13 = 9 ∧ acceleratedOrbit 13 7863 = 18899 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7863 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7863) = 3 ^ 9 * m + 18899 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7863.1, data_13_7863.2] + +/-- Complete interval computation for depth 13, residue 7864. -/ +theorem bounds_13_7864 : exactInterval 13 7864 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7864 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7864) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7864 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7864 : oddCount 7864 13 = 7 ∧ acceleratedOrbit 13 7864 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7864 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7864) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7864.1, data_13_7864.2] + +/-- Complete interval computation for depth 13, residue 7865. -/ +theorem bounds_13_7865 : exactInterval 13 7865 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7865 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7865) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7865 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7865 : oddCount 7865 13 = 7 ∧ acceleratedOrbit 13 7865 = 2101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7865 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7865) = 3 ^ 7 * m + 2101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7865.1, data_13_7865.2] + +/-- Complete interval computation for depth 13, residue 7866. -/ +theorem bounds_13_7866 : exactInterval 13 7866 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7866 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7866) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7866 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7866 : oddCount 7866 13 = 7 ∧ acceleratedOrbit 13 7866 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7866 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7866) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7866.1, data_13_7866.2] + +/-- Complete interval computation for depth 13, residue 7867. -/ +theorem bounds_13_7867 : exactInterval 13 7867 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7867 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7867) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7867 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7867 : oddCount 7867 13 = 7 ∧ acceleratedOrbit 13 7867 = 2101 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7867 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7867) = 3 ^ 7 * m + 2101 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7867.1, data_13_7867.2] + +/-- Complete interval computation for depth 13, residue 7868. -/ +theorem bounds_13_7868 : exactInterval 13 7868 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7868 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7868) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7868 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7868 : oddCount 7868 13 = 6 ∧ acceleratedOrbit 13 7868 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7868 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7868) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7868.1, data_13_7868.2] + +end Collatz.Research.StoppingAtlas.Batch0979 From 0ab909fde0e6bb57ca24c1e7874e6f0353a819b7 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:34 +0530 Subject: [PATCH 0980/1001] proof: certify atlas Batch0980 (13:7869 to 13:7883) --- Collatz/Research/StoppingAtlas/Batch0980.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0980.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0980.lean b/Collatz/Research/StoppingAtlas/Batch0980.lean new file mode 100644 index 00000000..d71d990f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0980.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0980 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7869. -/ +theorem bounds_13_7869 : exactInterval 13 7869 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7869 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7869) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7869 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7869 : oddCount 7869 13 = 6 ∧ acceleratedOrbit 13 7869 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7869 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7869) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7869.1, data_13_7869.2] + +/-- Complete interval computation for depth 13, residue 7870. -/ +theorem bounds_13_7870 : exactInterval 13 7870 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7870 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7870) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7870 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7870 : oddCount 7870 13 = 6 ∧ acceleratedOrbit 13 7870 = 701 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7870 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7870) = 3 ^ 6 * m + 701 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7870.1, data_13_7870.2] + +/-- Complete interval computation for depth 13, residue 7871. -/ +theorem bounds_13_7871 : exactInterval 13 7871 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7871 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7871) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7871 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7871 : oddCount 7871 13 = 10 ∧ acceleratedOrbit 13 7871 = 56744 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7871 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7871) = 3 ^ 10 * m + 56744 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7871.1, data_13_7871.2] + +/-- Complete interval computation for depth 13, residue 7872. -/ +theorem bounds_13_7872 : exactInterval 13 7872 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7872 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7872) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7872 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7872 : oddCount 7872 13 = 5 ∧ acceleratedOrbit 13 7872 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7872 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7872) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7872.1, data_13_7872.2] + +/-- Complete interval computation for depth 13, residue 7873. -/ +theorem bounds_13_7873 : exactInterval 13 7873 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7873 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7873) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7873 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7873 : oddCount 7873 13 = 7 ∧ acceleratedOrbit 13 7873 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7873 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7873) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7873.1, data_13_7873.2] + +/-- Complete interval computation for depth 13, residue 7874. -/ +theorem bounds_13_7874 : exactInterval 13 7874 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7874 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7874) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7874 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7874 : oddCount 7874 13 = 8 ∧ acceleratedOrbit 13 7874 = 6311 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7874 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7874) = 3 ^ 8 * m + 6311 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7874.1, data_13_7874.2] + +/-- Complete interval computation for depth 13, residue 7875. -/ +theorem bounds_13_7875 : exactInterval 13 7875 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7875 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7875) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7875 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7875 : oddCount 7875 13 = 8 ∧ acceleratedOrbit 13 7875 = 6311 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7875 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7875) = 3 ^ 8 * m + 6311 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7875.1, data_13_7875.2] + +/-- Complete interval computation for depth 13, residue 7876. -/ +theorem bounds_13_7876 : exactInterval 13 7876 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7876 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7876) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7876 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7876 : oddCount 7876 13 = 3 ∧ acceleratedOrbit 13 7876 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7876 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7876) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7876.1, data_13_7876.2] + +/-- Complete interval computation for depth 13, residue 7877. -/ +theorem bounds_13_7877 : exactInterval 13 7877 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7877 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7877) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7877 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7877 : oddCount 7877 13 = 3 ∧ acceleratedOrbit 13 7877 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7877 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7877) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7877.1, data_13_7877.2] + +/-- Complete interval computation for depth 13, residue 7878. -/ +theorem bounds_13_7878 : exactInterval 13 7878 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7878 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7878) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7878 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7878 : oddCount 7878 13 = 3 ∧ acceleratedOrbit 13 7878 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7878 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7878) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7878.1, data_13_7878.2] + +/-- Complete interval computation for depth 13, residue 7879. -/ +theorem bounds_13_7879 : exactInterval 13 7879 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7879 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7879) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7879 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7879 : oddCount 7879 13 = 7 ∧ acceleratedOrbit 13 7879 = 2105 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7879 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7879) = 3 ^ 7 * m + 2105 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7879.1, data_13_7879.2] + +/-- Complete interval computation for depth 13, residue 7880. -/ +theorem bounds_13_7880 : exactInterval 13 7880 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7880 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7880) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7880 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7880 : oddCount 7880 13 = 3 ∧ acceleratedOrbit 13 7880 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7880 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7880) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7880.1, data_13_7880.2] + +/-- Complete interval computation for depth 13, residue 7881. -/ +theorem bounds_13_7881 : exactInterval 13 7881 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7881 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7881) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7881 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7881 : oddCount 7881 13 = 8 ∧ acceleratedOrbit 13 7881 = 6317 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7881 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7881) = 3 ^ 8 * m + 6317 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7881.1, data_13_7881.2] + +/-- Complete interval computation for depth 13, residue 7882. -/ +theorem bounds_13_7882 : exactInterval 13 7882 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7882 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7882) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7882 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7882 : oddCount 7882 13 = 3 ∧ acceleratedOrbit 13 7882 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7882 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7882) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7882.1, data_13_7882.2] + +/-- Complete interval computation for depth 13, residue 7883. -/ +theorem bounds_13_7883 : exactInterval 13 7883 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7883 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7883) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7883 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7883 : oddCount 7883 13 = 9 ∧ acceleratedOrbit 13 7883 = 18953 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7883 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7883) = 3 ^ 9 * m + 18953 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7883.1, data_13_7883.2] + +end Collatz.Research.StoppingAtlas.Batch0980 From 726c34bcc5be8f787bd9b832f6b9de1d8cc23152 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:34 +0530 Subject: [PATCH 0981/1001] proof: certify atlas Batch0981 (13:7884 to 13:7899) --- Collatz/Research/StoppingAtlas/Batch0981.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0981.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0981.lean b/Collatz/Research/StoppingAtlas/Batch0981.lean new file mode 100644 index 00000000..eb1c98bf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0981.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0981 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7884. -/ +theorem bounds_13_7884 : exactInterval 13 7884 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7884 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7884) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7884 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7884 : oddCount 7884 13 = 3 ∧ acceleratedOrbit 13 7884 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7884 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7884) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7884.1, data_13_7884.2] + +/-- Complete interval computation for depth 13, residue 7885. -/ +theorem bounds_13_7885 : exactInterval 13 7885 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7885 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7885) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7885 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7885 : oddCount 7885 13 = 3 ∧ acceleratedOrbit 13 7885 = 26 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7885 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7885) = 3 ^ 3 * m + 26 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7885.1, data_13_7885.2] + +/-- Complete interval computation for depth 13, residue 7886. -/ +theorem bounds_13_7886 : exactInterval 13 7886 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7886 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7886) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7886 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7886 : oddCount 7886 13 = 11 ∧ acceleratedOrbit 13 7886 = 170585 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7886 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7886) = 3 ^ 11 * m + 170585 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7886.1, data_13_7886.2] + +/-- Complete interval computation for depth 13, residue 7887. -/ +theorem bounds_13_7887 : exactInterval 13 7887 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7887 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7887) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7887 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7887 : oddCount 7887 13 = 11 ∧ acceleratedOrbit 13 7887 = 170585 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7887 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7887) = 3 ^ 11 * m + 170585 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7887.1, data_13_7887.2] + +/-- Complete interval computation for depth 13, residue 7888. -/ +theorem bounds_13_7888 : exactInterval 13 7888 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7888 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7888) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7888 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7888 : oddCount 7888 13 = 5 ∧ acceleratedOrbit 13 7888 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7888 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7888) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7888.1, data_13_7888.2] + +/-- Complete interval computation for depth 13, residue 7889. -/ +theorem bounds_13_7889 : exactInterval 13 7889 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7889 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7889) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7889 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7889 : oddCount 7889 13 = 7 ∧ acceleratedOrbit 13 7889 = 2108 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7889 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7889) = 3 ^ 7 * m + 2108 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7889.1, data_13_7889.2] + +/-- Complete interval computation for depth 13, residue 7890. -/ +theorem bounds_13_7890 : exactInterval 13 7890 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7890 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7890) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7890 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7890 : oddCount 7890 13 = 7 ∧ acceleratedOrbit 13 7890 = 2108 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7890 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7890) = 3 ^ 7 * m + 2108 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7890.1, data_13_7890.2] + +/-- Complete interval computation for depth 13, residue 7891. -/ +theorem bounds_13_7891 : exactInterval 13 7891 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7891 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7891) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7891 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7891 : oddCount 7891 13 = 7 ∧ acceleratedOrbit 13 7891 = 2108 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7891 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7891) = 3 ^ 7 * m + 2108 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7891.1, data_13_7891.2] + +/-- Complete interval computation for depth 13, residue 7892. -/ +theorem bounds_13_7892 : exactInterval 13 7892 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7892 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7892) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7892 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7892 : oddCount 7892 13 = 5 ∧ acceleratedOrbit 13 7892 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7892 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7892) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7892.1, data_13_7892.2] + +/-- Complete interval computation for depth 13, residue 7893. -/ +theorem bounds_13_7893 : exactInterval 13 7893 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7893 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7893) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7893 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7893 : oddCount 7893 13 = 5 ∧ acceleratedOrbit 13 7893 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7893 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7893) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7893.1, data_13_7893.2] + +/-- Complete interval computation for depth 13, residue 7894. -/ +theorem bounds_13_7894 : exactInterval 13 7894 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7894 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7894) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7894 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7894 : oddCount 7894 13 = 6 ∧ acceleratedOrbit 13 7894 = 703 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7894 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7894) = 3 ^ 6 * m + 703 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7894.1, data_13_7894.2] + +/-- Complete interval computation for depth 13, residue 7895. -/ +theorem bounds_13_7895 : exactInterval 13 7895 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7895 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7895) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7895 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7895 : oddCount 7895 13 = 6 ∧ acceleratedOrbit 13 7895 = 703 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7895 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7895) = 3 ^ 6 * m + 703 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7895.1, data_13_7895.2] + +/-- Complete interval computation for depth 13, residue 7896. -/ +theorem bounds_13_7896 : exactInterval 13 7896 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7896 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7896) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7896 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7896 : oddCount 7896 13 = 6 ∧ acceleratedOrbit 13 7896 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7896 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7896) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7896.1, data_13_7896.2] + +/-- Complete interval computation for depth 13, residue 7897. -/ +theorem bounds_13_7897 : exactInterval 13 7897 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7897 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7897) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7897 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7897 : oddCount 7897 13 = 6 ∧ acceleratedOrbit 13 7897 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7897 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7897) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7897.1, data_13_7897.2] + +/-- Complete interval computation for depth 13, residue 7898. -/ +theorem bounds_13_7898 : exactInterval 13 7898 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7898 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7898) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7898 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7898 : oddCount 7898 13 = 6 ∧ acceleratedOrbit 13 7898 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7898 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7898) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7898.1, data_13_7898.2] + +/-- Complete interval computation for depth 13, residue 7899. -/ +theorem bounds_13_7899 : exactInterval 13 7899 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7899 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7899) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7899 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7899 : oddCount 7899 13 = 8 ∧ acceleratedOrbit 13 7899 = 6328 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7899 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7899) = 3 ^ 8 * m + 6328 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7899.1, data_13_7899.2] + +end Collatz.Research.StoppingAtlas.Batch0981 From c0721d88962fd09e405fdf49417981ed435c41aa Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:35 +0530 Subject: [PATCH 0982/1001] proof: certify atlas Batch0982 (13:7900 to 13:7914) --- Collatz/Research/StoppingAtlas/Batch0982.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0982.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0982.lean b/Collatz/Research/StoppingAtlas/Batch0982.lean new file mode 100644 index 00000000..996e4dc0 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0982.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0982 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7900. -/ +theorem bounds_13_7900 : exactInterval 13 7900 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7900 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7900) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7900 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7900 : oddCount 7900 13 = 6 ∧ acceleratedOrbit 13 7900 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7900 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7900) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7900.1, data_13_7900.2] + +/-- Complete interval computation for depth 13, residue 7901. -/ +theorem bounds_13_7901 : exactInterval 13 7901 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7901 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7901) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7901 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7901 : oddCount 7901 13 = 6 ∧ acceleratedOrbit 13 7901 = 704 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7901 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7901) = 3 ^ 6 * m + 704 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7901.1, data_13_7901.2] + +/-- Complete interval computation for depth 13, residue 7902. -/ +theorem bounds_13_7902 : exactInterval 13 7902 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7902 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7902) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7902 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7902 : oddCount 7902 13 = 8 ∧ acceleratedOrbit 13 7902 = 6331 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7902 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7902) = 3 ^ 8 * m + 6331 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7902.1, data_13_7902.2] + +/-- Complete interval computation for depth 13, residue 7903. -/ +theorem bounds_13_7903 : exactInterval 13 7903 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7903 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7903) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7903 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7903 : oddCount 7903 13 = 8 ∧ acceleratedOrbit 13 7903 = 6331 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7903 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7903) = 3 ^ 8 * m + 6331 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7903.1, data_13_7903.2] + +/-- Complete interval computation for depth 13, residue 7904. -/ +theorem bounds_13_7904 : exactInterval 13 7904 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7904 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7904) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7904 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7904 : oddCount 7904 13 = 5 ∧ acceleratedOrbit 13 7904 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7904 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7904) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7904.1, data_13_7904.2] + +/-- Complete interval computation for depth 13, residue 7905. -/ +theorem bounds_13_7905 : exactInterval 13 7905 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7905 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7905) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7905 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7905 : oddCount 7905 13 = 7 ∧ acceleratedOrbit 13 7905 = 2111 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7905 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7905) = 3 ^ 7 * m + 2111 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7905.1, data_13_7905.2] + +/-- Complete interval computation for depth 13, residue 7906. -/ +theorem bounds_13_7906 : exactInterval 13 7906 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7906 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7906) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7906 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7906 : oddCount 7906 13 = 5 ∧ acceleratedOrbit 13 7906 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7906 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7906) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7906.1, data_13_7906.2] + +/-- Complete interval computation for depth 13, residue 7907. -/ +theorem bounds_13_7907 : exactInterval 13 7907 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7907 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7907) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7907 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7907 : oddCount 7907 13 = 5 ∧ acceleratedOrbit 13 7907 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7907 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7907) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7907.1, data_13_7907.2] + +/-- Complete interval computation for depth 13, residue 7908. -/ +theorem bounds_13_7908 : exactInterval 13 7908 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7908 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7908) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7908 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7908 : oddCount 7908 13 = 5 ∧ acceleratedOrbit 13 7908 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7908 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7908) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7908.1, data_13_7908.2] + +/-- Complete interval computation for depth 13, residue 7909. -/ +theorem bounds_13_7909 : exactInterval 13 7909 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7909 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7909) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7909 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7909 : oddCount 7909 13 = 5 ∧ acceleratedOrbit 13 7909 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7909 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7909) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7909.1, data_13_7909.2] + +/-- Complete interval computation for depth 13, residue 7910. -/ +theorem bounds_13_7910 : exactInterval 13 7910 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7910 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7910) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7910 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7910 : oddCount 7910 13 = 5 ∧ acceleratedOrbit 13 7910 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7910 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7910) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7910.1, data_13_7910.2] + +/-- Complete interval computation for depth 13, residue 7911. -/ +theorem bounds_13_7911 : exactInterval 13 7911 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7911 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7911) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7911 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7911 : oddCount 7911 13 = 8 ∧ acceleratedOrbit 13 7911 = 6337 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7911 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7911) = 3 ^ 8 * m + 6337 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7911.1, data_13_7911.2] + +/-- Complete interval computation for depth 13, residue 7912. -/ +theorem bounds_13_7912 : exactInterval 13 7912 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7912 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7912) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7912 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7912 : oddCount 7912 13 = 5 ∧ acceleratedOrbit 13 7912 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7912 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7912) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7912.1, data_13_7912.2] + +/-- Complete interval computation for depth 13, residue 7913. -/ +theorem bounds_13_7913 : exactInterval 13 7913 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7913 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7913) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7913 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7913 : oddCount 7913 13 = 7 ∧ acceleratedOrbit 13 7913 = 2113 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7913 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7913) = 3 ^ 7 * m + 2113 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7913.1, data_13_7913.2] + +/-- Complete interval computation for depth 13, residue 7914. -/ +theorem bounds_13_7914 : exactInterval 13 7914 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7914 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7914) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7914 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7914 : oddCount 7914 13 = 5 ∧ acceleratedOrbit 13 7914 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7914 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7914) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7914.1, data_13_7914.2] + +end Collatz.Research.StoppingAtlas.Batch0982 From 3ec69dc6789523c0143f322f430cd315998223c4 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:35 +0530 Subject: [PATCH 0983/1001] proof: certify atlas Batch0983 (13:7915 to 13:7929) --- Collatz/Research/StoppingAtlas/Batch0983.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0983.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0983.lean b/Collatz/Research/StoppingAtlas/Batch0983.lean new file mode 100644 index 00000000..32241f8e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0983.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0983 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7915. -/ +theorem bounds_13_7915 : exactInterval 13 7915 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7915 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7915) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7915 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7915 : oddCount 7915 13 = 7 ∧ acceleratedOrbit 13 7915 = 2114 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7915 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7915) = 3 ^ 7 * m + 2114 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7915.1, data_13_7915.2] + +/-- Complete interval computation for depth 13, residue 7916. -/ +theorem bounds_13_7916 : exactInterval 13 7916 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7916 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7916) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7916 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7916 : oddCount 7916 13 = 5 ∧ acceleratedOrbit 13 7916 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7916 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7916) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7916.1, data_13_7916.2] + +/-- Complete interval computation for depth 13, residue 7917. -/ +theorem bounds_13_7917 : exactInterval 13 7917 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7917 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7917) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7917 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7917 : oddCount 7917 13 = 5 ∧ acceleratedOrbit 13 7917 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7917 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7917) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7917.1, data_13_7917.2] + +/-- Complete interval computation for depth 13, residue 7918. -/ +theorem bounds_13_7918 : exactInterval 13 7918 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7918 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7918) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7918 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7918 : oddCount 7918 13 = 5 ∧ acceleratedOrbit 13 7918 = 235 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7918 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7918) = 3 ^ 5 * m + 235 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7918.1, data_13_7918.2] + +/-- Complete interval computation for depth 13, residue 7919. -/ +theorem bounds_13_7919 : exactInterval 13 7919 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7919 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7919) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7919 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7919 : oddCount 7919 13 = 9 ∧ acceleratedOrbit 13 7919 = 19030 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7919 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7919) = 3 ^ 9 * m + 19030 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7919.1, data_13_7919.2] + +/-- Complete interval computation for depth 13, residue 7920. -/ +theorem bounds_13_7920 : exactInterval 13 7920 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7920 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7920) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7920 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7920 : oddCount 7920 13 = 7 ∧ acceleratedOrbit 13 7920 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7920 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7920) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7920.1, data_13_7920.2] + +/-- Complete interval computation for depth 13, residue 7921. -/ +theorem bounds_13_7921 : exactInterval 13 7921 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7921 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7921) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7921 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7921 : oddCount 7921 13 = 5 ∧ acceleratedOrbit 13 7921 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7921 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7921) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7921.1, data_13_7921.2] + +/-- Complete interval computation for depth 13, residue 7922. -/ +theorem bounds_13_7922 : exactInterval 13 7922 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7922 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7922) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7922 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7922 : oddCount 7922 13 = 7 ∧ acceleratedOrbit 13 7922 = 2116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7922 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7922) = 3 ^ 7 * m + 2116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7922.1, data_13_7922.2] + +/-- Complete interval computation for depth 13, residue 7923. -/ +theorem bounds_13_7923 : exactInterval 13 7923 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7923 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7923) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7923 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7923 : oddCount 7923 13 = 7 ∧ acceleratedOrbit 13 7923 = 2116 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7923 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7923) = 3 ^ 7 * m + 2116 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7923.1, data_13_7923.2] + +/-- Complete interval computation for depth 13, residue 7924. -/ +theorem bounds_13_7924 : exactInterval 13 7924 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7924 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7924) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7924 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7924 : oddCount 7924 13 = 7 ∧ acceleratedOrbit 13 7924 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7924 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7924) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7924.1, data_13_7924.2] + +/-- Complete interval computation for depth 13, residue 7925. -/ +theorem bounds_13_7925 : exactInterval 13 7925 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7925 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7925) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7925 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7925 : oddCount 7925 13 = 7 ∧ acceleratedOrbit 13 7925 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7925 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7925) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7925.1, data_13_7925.2] + +/-- Complete interval computation for depth 13, residue 7926. -/ +theorem bounds_13_7926 : exactInterval 13 7926 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7926 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7926) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7926 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7926 : oddCount 7926 13 = 7 ∧ acceleratedOrbit 13 7926 = 2117 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7926 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7926) = 3 ^ 7 * m + 2117 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7926.1, data_13_7926.2] + +/-- Complete interval computation for depth 13, residue 7927. -/ +theorem bounds_13_7927 : exactInterval 13 7927 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7927 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7927) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7927 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7927 : oddCount 7927 13 = 7 ∧ acceleratedOrbit 13 7927 = 2117 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7927 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7927) = 3 ^ 7 * m + 2117 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7927.1, data_13_7927.2] + +/-- Complete interval computation for depth 13, residue 7928. -/ +theorem bounds_13_7928 : exactInterval 13 7928 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7928 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7928) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7928 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7928 : oddCount 7928 13 = 7 ∧ acceleratedOrbit 13 7928 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7928 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7928) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7928.1, data_13_7928.2] + +/-- Complete interval computation for depth 13, residue 7929. -/ +theorem bounds_13_7929 : exactInterval 13 7929 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7929 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7929) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7929 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7929 : oddCount 7929 13 = 6 ∧ acceleratedOrbit 13 7929 = 706 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7929 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7929) = 3 ^ 6 * m + 706 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7929.1, data_13_7929.2] + +end Collatz.Research.StoppingAtlas.Batch0983 From b5f3a2e3369ce6789f03d60f5b52a1b85d429ff2 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:35 +0530 Subject: [PATCH 0984/1001] proof: certify atlas Batch0984 (13:7930 to 13:7945) --- Collatz/Research/StoppingAtlas/Batch0984.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0984.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0984.lean b/Collatz/Research/StoppingAtlas/Batch0984.lean new file mode 100644 index 00000000..b116d74b --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0984.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0984 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7930. -/ +theorem bounds_13_7930 : exactInterval 13 7930 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7930 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7930) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7930 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7930 : oddCount 7930 13 = 7 ∧ acceleratedOrbit 13 7930 = 2119 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7930 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7930) = 3 ^ 7 * m + 2119 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7930.1, data_13_7930.2] + +/-- Complete interval computation for depth 13, residue 7931. -/ +theorem bounds_13_7931 : exactInterval 13 7931 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7931 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7931) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7931 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7931 : oddCount 7931 13 = 9 ∧ acceleratedOrbit 13 7931 = 19061 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7931 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7931) = 3 ^ 9 * m + 19061 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7931.1, data_13_7931.2] + +/-- Complete interval computation for depth 13, residue 7932. -/ +theorem bounds_13_7932 : exactInterval 13 7932 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7932 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7932) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7932 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7932 : oddCount 7932 13 = 8 ∧ acceleratedOrbit 13 7932 = 6356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7932 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7932) = 3 ^ 8 * m + 6356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7932.1, data_13_7932.2] + +/-- Complete interval computation for depth 13, residue 7933. -/ +theorem bounds_13_7933 : exactInterval 13 7933 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7933 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7933) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7933 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7933 : oddCount 7933 13 = 8 ∧ acceleratedOrbit 13 7933 = 6356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7933 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7933) = 3 ^ 8 * m + 6356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7933.1, data_13_7933.2] + +/-- Complete interval computation for depth 13, residue 7934. -/ +theorem bounds_13_7934 : exactInterval 13 7934 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7934 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7934) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7934 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7934 : oddCount 7934 13 = 8 ∧ acceleratedOrbit 13 7934 = 6356 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7934 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7934) = 3 ^ 8 * m + 6356 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7934.1, data_13_7934.2] + +/-- Complete interval computation for depth 13, residue 7935. -/ +theorem bounds_13_7935 : exactInterval 13 7935 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7935 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7935) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7935 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7935 : oddCount 7935 13 = 12 ∧ acceleratedOrbit 13 7935 = 514835 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7935 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7935) = 3 ^ 12 * m + 514835 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7935.1, data_13_7935.2] + +/-- Complete interval computation for depth 13, residue 7936. -/ +theorem bounds_13_7936 : exactInterval 13 7936 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7936 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7936) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7936 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7936 : oddCount 7936 13 = 5 ∧ acceleratedOrbit 13 7936 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7936 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7936) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7936.1, data_13_7936.2] + +/-- Complete interval computation for depth 13, residue 7937. -/ +theorem bounds_13_7937 : exactInterval 13 7937 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7937 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7937) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7937 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7937 : oddCount 7937 13 = 5 ∧ acceleratedOrbit 13 7937 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7937 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7937) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7937.1, data_13_7937.2] + +/-- Complete interval computation for depth 13, residue 7938. -/ +theorem bounds_13_7938 : exactInterval 13 7938 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7938 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7938) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7938 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7938 : oddCount 7938 13 = 6 ∧ acceleratedOrbit 13 7938 = 707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7938 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7938) = 3 ^ 6 * m + 707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7938.1, data_13_7938.2] + +/-- Complete interval computation for depth 13, residue 7939. -/ +theorem bounds_13_7939 : exactInterval 13 7939 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7939 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7939) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7939 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7939 : oddCount 7939 13 = 6 ∧ acceleratedOrbit 13 7939 = 707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7939 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7939) = 3 ^ 6 * m + 707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7939.1, data_13_7939.2] + +/-- Complete interval computation for depth 13, residue 7940. -/ +theorem bounds_13_7940 : exactInterval 13 7940 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7940 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7940) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7940 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7940 : oddCount 7940 13 = 5 ∧ acceleratedOrbit 13 7940 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7940 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7940) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7940.1, data_13_7940.2] + +/-- Complete interval computation for depth 13, residue 7941. -/ +theorem bounds_13_7941 : exactInterval 13 7941 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7941 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7941) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7941 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7941 : oddCount 7941 13 = 5 ∧ acceleratedOrbit 13 7941 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7941 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7941) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7941.1, data_13_7941.2] + +/-- Complete interval computation for depth 13, residue 7942. -/ +theorem bounds_13_7942 : exactInterval 13 7942 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7942 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7942) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7942 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7942 : oddCount 7942 13 = 5 ∧ acceleratedOrbit 13 7942 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7942 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7942) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7942.1, data_13_7942.2] + +/-- Complete interval computation for depth 13, residue 7943. -/ +theorem bounds_13_7943 : exactInterval 13 7943 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7943 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7943) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7943 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7943 : oddCount 7943 13 = 6 ∧ acceleratedOrbit 13 7943 = 707 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7943 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7943) = 3 ^ 6 * m + 707 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7943.1, data_13_7943.2] + +/-- Complete interval computation for depth 13, residue 7944. -/ +theorem bounds_13_7944 : exactInterval 13 7944 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7944 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7944) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7944 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7944 : oddCount 7944 13 = 7 ∧ acceleratedOrbit 13 7944 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7944 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7944) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7944.1, data_13_7944.2] + +/-- Complete interval computation for depth 13, residue 7945. -/ +theorem bounds_13_7945 : exactInterval 13 7945 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7945 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7945) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7945 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7945 : oddCount 7945 13 = 8 ∧ acceleratedOrbit 13 7945 = 6365 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7945 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7945) = 3 ^ 8 * m + 6365 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7945.1, data_13_7945.2] + +end Collatz.Research.StoppingAtlas.Batch0984 From 8ab0c5802acf33e5b0101694c26831a0a00e8515 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:35 +0530 Subject: [PATCH 0985/1001] proof: certify atlas Batch0985 (13:7946 to 13:7960) --- Collatz/Research/StoppingAtlas/Batch0985.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0985.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0985.lean b/Collatz/Research/StoppingAtlas/Batch0985.lean new file mode 100644 index 00000000..cb4a603e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0985.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0985 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7946. -/ +theorem bounds_13_7946 : exactInterval 13 7946 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7946 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7946) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7946 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7946 : oddCount 7946 13 = 7 ∧ acceleratedOrbit 13 7946 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7946 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7946) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7946.1, data_13_7946.2] + +/-- Complete interval computation for depth 13, residue 7947. -/ +theorem bounds_13_7947 : exactInterval 13 7947 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7947 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7947) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7947 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7947 : oddCount 7947 13 = 7 ∧ acceleratedOrbit 13 7947 = 2123 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7947 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7947) = 3 ^ 7 * m + 2123 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7947.1, data_13_7947.2] + +/-- Complete interval computation for depth 13, residue 7948. -/ +theorem bounds_13_7948 : exactInterval 13 7948 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7948 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7948) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7948 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7948 : oddCount 7948 13 = 7 ∧ acceleratedOrbit 13 7948 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7948 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7948) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7948.1, data_13_7948.2] + +/-- Complete interval computation for depth 13, residue 7949. -/ +theorem bounds_13_7949 : exactInterval 13 7949 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7949 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7949) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7949 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7949 : oddCount 7949 13 = 7 ∧ acceleratedOrbit 13 7949 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7949 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7949) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7949.1, data_13_7949.2] + +/-- Complete interval computation for depth 13, residue 7950. -/ +theorem bounds_13_7950 : exactInterval 13 7950 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7950 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7950) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7950 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7950 : oddCount 7950 13 = 5 ∧ acceleratedOrbit 13 7950 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7950 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7950) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7950.1, data_13_7950.2] + +/-- Complete interval computation for depth 13, residue 7951. -/ +theorem bounds_13_7951 : exactInterval 13 7951 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7951 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7951) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7951 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7951 : oddCount 7951 13 = 5 ∧ acceleratedOrbit 13 7951 = 236 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7951 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7951) = 3 ^ 5 * m + 236 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7951.1, data_13_7951.2] + +/-- Complete interval computation for depth 13, residue 7952. -/ +theorem bounds_13_7952 : exactInterval 13 7952 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7952 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7952) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7952 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7952 : oddCount 7952 13 = 4 ∧ acceleratedOrbit 13 7952 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7952 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7952) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7952.1, data_13_7952.2] + +/-- Complete interval computation for depth 13, residue 7953. -/ +theorem bounds_13_7953 : exactInterval 13 7953 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7953 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7953) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7953 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7953 : oddCount 7953 13 = 7 ∧ acceleratedOrbit 13 7953 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7953 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7953) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7953.1, data_13_7953.2] + +/-- Complete interval computation for depth 13, residue 7954. -/ +theorem bounds_13_7954 : exactInterval 13 7954 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7954 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7954) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7954 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7954 : oddCount 7954 13 = 8 ∧ acceleratedOrbit 13 7954 = 6374 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7954 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7954) = 3 ^ 8 * m + 6374 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7954.1, data_13_7954.2] + +/-- Complete interval computation for depth 13, residue 7955. -/ +theorem bounds_13_7955 : exactInterval 13 7955 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7955 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7955) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7955 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7955 : oddCount 7955 13 = 8 ∧ acceleratedOrbit 13 7955 = 6374 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7955 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7955) = 3 ^ 8 * m + 6374 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7955.1, data_13_7955.2] + +/-- Complete interval computation for depth 13, residue 7956. -/ +theorem bounds_13_7956 : exactInterval 13 7956 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7956 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7956) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7956 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7956 : oddCount 7956 13 = 4 ∧ acceleratedOrbit 13 7956 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7956 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7956) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7956.1, data_13_7956.2] + +/-- Complete interval computation for depth 13, residue 7957. -/ +theorem bounds_13_7957 : exactInterval 13 7957 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7957 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7957) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7957 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7957 : oddCount 7957 13 = 4 ∧ acceleratedOrbit 13 7957 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7957 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7957) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7957.1, data_13_7957.2] + +/-- Complete interval computation for depth 13, residue 7958. -/ +theorem bounds_13_7958 : exactInterval 13 7958 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7958 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7958) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7958 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7958 : oddCount 7958 13 = 7 ∧ acceleratedOrbit 13 7958 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7958 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7958) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7958.1, data_13_7958.2] + +/-- Complete interval computation for depth 13, residue 7959. -/ +theorem bounds_13_7959 : exactInterval 13 7959 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7959 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7959) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7959 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7959 : oddCount 7959 13 = 7 ∧ acceleratedOrbit 13 7959 = 2126 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7959 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7959) = 3 ^ 7 * m + 2126 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7959.1, data_13_7959.2] + +/-- Complete interval computation for depth 13, residue 7960. -/ +theorem bounds_13_7960 : exactInterval 13 7960 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7960 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7960) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7960 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7960 : oddCount 7960 13 = 4 ∧ acceleratedOrbit 13 7960 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7960 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7960) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7960.1, data_13_7960.2] + +end Collatz.Research.StoppingAtlas.Batch0985 From 9f78ee40cbe17ee9a10ec8484c15ad46251c04d1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:35 +0530 Subject: [PATCH 0986/1001] proof: certify atlas Batch0986 (13:7961 to 13:7975) --- Collatz/Research/StoppingAtlas/Batch0986.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0986.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0986.lean b/Collatz/Research/StoppingAtlas/Batch0986.lean new file mode 100644 index 00000000..0360f88d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0986.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0986 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7961. -/ +theorem bounds_13_7961 : exactInterval 13 7961 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7961 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7961) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7961 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7961 : oddCount 7961 13 = 9 ∧ acceleratedOrbit 13 7961 = 19136 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7961 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7961) = 3 ^ 9 * m + 19136 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7961.1, data_13_7961.2] + +/-- Complete interval computation for depth 13, residue 7962. -/ +theorem bounds_13_7962 : exactInterval 13 7962 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7962 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7962) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7962 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7962 : oddCount 7962 13 = 4 ∧ acceleratedOrbit 13 7962 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7962 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7962) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7962.1, data_13_7962.2] + +/-- Complete interval computation for depth 13, residue 7963. -/ +theorem bounds_13_7963 : exactInterval 13 7963 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7963 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7963) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7963 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7963 : oddCount 7963 13 = 11 ∧ acceleratedOrbit 13 7963 = 172226 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7963 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7963) = 3 ^ 11 * m + 172226 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7963.1, data_13_7963.2] + +/-- Complete interval computation for depth 13, residue 7964. -/ +theorem bounds_13_7964 : exactInterval 13 7964 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7964 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7964) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7964 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7964 : oddCount 7964 13 = 7 ∧ acceleratedOrbit 13 7964 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7964 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7964) = 3 ^ 7 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7964.1, data_13_7964.2] + +/-- Complete interval computation for depth 13, residue 7965. -/ +theorem bounds_13_7965 : exactInterval 13 7965 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7965 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7965) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7965 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7965 : oddCount 7965 13 = 7 ∧ acceleratedOrbit 13 7965 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7965 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7965) = 3 ^ 7 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7965.1, data_13_7965.2] + +/-- Complete interval computation for depth 13, residue 7966. -/ +theorem bounds_13_7966 : exactInterval 13 7966 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7966 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7966) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7966 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7966 : oddCount 7966 13 = 7 ∧ acceleratedOrbit 13 7966 = 2128 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7966 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7966) = 3 ^ 7 * m + 2128 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7966.1, data_13_7966.2] + +/-- Complete interval computation for depth 13, residue 7967. -/ +theorem bounds_13_7967 : exactInterval 13 7967 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7967 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7967) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7967 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7967 : oddCount 7967 13 = 8 ∧ acceleratedOrbit 13 7967 = 6382 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7967 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7967) = 3 ^ 8 * m + 6382 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7967.1, data_13_7967.2] + +/-- Complete interval computation for depth 13, residue 7968. -/ +theorem bounds_13_7968 : exactInterval 13 7968 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7968 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7968) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7968 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7968 : oddCount 7968 13 = 5 ∧ acceleratedOrbit 13 7968 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7968 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7968) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7968.1, data_13_7968.2] + +/-- Complete interval computation for depth 13, residue 7969. -/ +theorem bounds_13_7969 : exactInterval 13 7969 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7969 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7969) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7969 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7969 : oddCount 7969 13 = 6 ∧ acceleratedOrbit 13 7969 = 710 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7969 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7969) = 3 ^ 6 * m + 710 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7969.1, data_13_7969.2] + +/-- Complete interval computation for depth 13, residue 7970. -/ +theorem bounds_13_7970 : exactInterval 13 7970 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7970 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7970) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7970 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7970 : oddCount 7970 13 = 7 ∧ acceleratedOrbit 13 7970 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7970 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7970) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7970.1, data_13_7970.2] + +/-- Complete interval computation for depth 13, residue 7971. -/ +theorem bounds_13_7971 : exactInterval 13 7971 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7971 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7971) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7971 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7971 : oddCount 7971 13 = 7 ∧ acceleratedOrbit 13 7971 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7971 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7971) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7971.1, data_13_7971.2] + +/-- Complete interval computation for depth 13, residue 7972. -/ +theorem bounds_13_7972 : exactInterval 13 7972 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7972 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7972) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7972 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7972 : oddCount 7972 13 = 7 ∧ acceleratedOrbit 13 7972 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7972 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7972) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7972.1, data_13_7972.2] + +/-- Complete interval computation for depth 13, residue 7973. -/ +theorem bounds_13_7973 : exactInterval 13 7973 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7973 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7973) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7973 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7973 : oddCount 7973 13 = 7 ∧ acceleratedOrbit 13 7973 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7973 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7973) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7973.1, data_13_7973.2] + +/-- Complete interval computation for depth 13, residue 7974. -/ +theorem bounds_13_7974 : exactInterval 13 7974 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7974 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7974) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7974 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7974 : oddCount 7974 13 = 7 ∧ acceleratedOrbit 13 7974 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7974 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7974) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7974.1, data_13_7974.2] + +/-- Complete interval computation for depth 13, residue 7975. -/ +theorem bounds_13_7975 : exactInterval 13 7975 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7975 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7975) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7975 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7975 : oddCount 7975 13 = 8 ∧ acceleratedOrbit 13 7975 = 6389 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7975 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7975) = 3 ^ 8 * m + 6389 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7975.1, data_13_7975.2] + +end Collatz.Research.StoppingAtlas.Batch0986 From 11446b4d5a854ccca97bfee5843d2df73759ae34 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:35 +0530 Subject: [PATCH 0987/1001] proof: certify atlas Batch0987 (13:7976 to 13:7991) --- Collatz/Research/StoppingAtlas/Batch0987.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0987.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0987.lean b/Collatz/Research/StoppingAtlas/Batch0987.lean new file mode 100644 index 00000000..ebf3d87e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0987.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0987 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7976. -/ +theorem bounds_13_7976 : exactInterval 13 7976 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7976 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7976) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7976 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7976 : oddCount 7976 13 = 5 ∧ acceleratedOrbit 13 7976 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7976 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7976) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7976.1, data_13_7976.2] + +/-- Complete interval computation for depth 13, residue 7977. -/ +theorem bounds_13_7977 : exactInterval 13 7977 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7977 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7977) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7977 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7977 : oddCount 7977 13 = 6 ∧ acceleratedOrbit 13 7977 = 710 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7977 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7977) = 3 ^ 6 * m + 710 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7977.1, data_13_7977.2] + +/-- Complete interval computation for depth 13, residue 7978. -/ +theorem bounds_13_7978 : exactInterval 13 7978 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7978 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7978) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7978 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7978 : oddCount 7978 13 = 5 ∧ acceleratedOrbit 13 7978 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7978 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7978) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7978.1, data_13_7978.2] + +/-- Complete interval computation for depth 13, residue 7979. -/ +theorem bounds_13_7979 : exactInterval 13 7979 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7979 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7979) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7979 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7979 : oddCount 7979 13 = 7 ∧ acceleratedOrbit 13 7979 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7979 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7979) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7979.1, data_13_7979.2] + +/-- Complete interval computation for depth 13, residue 7980. -/ +theorem bounds_13_7980 : exactInterval 13 7980 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7980 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7980) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7980 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7980 : oddCount 7980 13 = 4 ∧ acceleratedOrbit 13 7980 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7980 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7980) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7980.1, data_13_7980.2] + +/-- Complete interval computation for depth 13, residue 7981. -/ +theorem bounds_13_7981 : exactInterval 13 7981 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7981 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7981) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7981 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7981 : oddCount 7981 13 = 4 ∧ acceleratedOrbit 13 7981 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7981 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7981) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7981.1, data_13_7981.2] + +/-- Complete interval computation for depth 13, residue 7982. -/ +theorem bounds_13_7982 : exactInterval 13 7982 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7982 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7982) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7982 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7982 : oddCount 7982 13 = 4 ∧ acceleratedOrbit 13 7982 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7982 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7982) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7982.1, data_13_7982.2] + +/-- Complete interval computation for depth 13, residue 7983. -/ +theorem bounds_13_7983 : exactInterval 13 7983 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7983 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7983) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7983 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7983 : oddCount 7983 13 = 7 ∧ acceleratedOrbit 13 7983 = 2132 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7983 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7983) = 3 ^ 7 * m + 2132 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7983.1, data_13_7983.2] + +/-- Complete interval computation for depth 13, residue 7984. -/ +theorem bounds_13_7984 : exactInterval 13 7984 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7984 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7984) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7984 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7984 : oddCount 7984 13 = 5 ∧ acceleratedOrbit 13 7984 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7984 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7984) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7984.1, data_13_7984.2] + +/-- Complete interval computation for depth 13, residue 7985. -/ +theorem bounds_13_7985 : exactInterval 13 7985 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7985 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7985) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7985 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7985 : oddCount 7985 13 = 4 ∧ acceleratedOrbit 13 7985 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7985 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7985) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7985.1, data_13_7985.2] + +/-- Complete interval computation for depth 13, residue 7986. -/ +theorem bounds_13_7986 : exactInterval 13 7986 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7986 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7986) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7986 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7986 : oddCount 7986 13 = 4 ∧ acceleratedOrbit 13 7986 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7986 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7986) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7986.1, data_13_7986.2] + +/-- Complete interval computation for depth 13, residue 7987. -/ +theorem bounds_13_7987 : exactInterval 13 7987 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7987 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7987) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7987 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7987 : oddCount 7987 13 = 4 ∧ acceleratedOrbit 13 7987 = 79 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7987 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7987) = 3 ^ 4 * m + 79 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7987.1, data_13_7987.2] + +/-- Complete interval computation for depth 13, residue 7988. -/ +theorem bounds_13_7988 : exactInterval 13 7988 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7988 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7988) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7988 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7988 : oddCount 7988 13 = 5 ∧ acceleratedOrbit 13 7988 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7988 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7988) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7988.1, data_13_7988.2] + +/-- Complete interval computation for depth 13, residue 7989. -/ +theorem bounds_13_7989 : exactInterval 13 7989 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7989 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7989) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7989 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7989 : oddCount 7989 13 = 5 ∧ acceleratedOrbit 13 7989 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7989 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7989) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7989.1, data_13_7989.2] + +/-- Complete interval computation for depth 13, residue 7990. -/ +theorem bounds_13_7990 : exactInterval 13 7990 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7990 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7990) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7990 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7990 : oddCount 7990 13 = 7 ∧ acceleratedOrbit 13 7990 = 2134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7990 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7990) = 3 ^ 7 * m + 2134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7990.1, data_13_7990.2] + +/-- Complete interval computation for depth 13, residue 7991. -/ +theorem bounds_13_7991 : exactInterval 13 7991 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7991 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7991) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7991 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7991 : oddCount 7991 13 = 7 ∧ acceleratedOrbit 13 7991 = 2134 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7991 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7991) = 3 ^ 7 * m + 2134 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7991.1, data_13_7991.2] + +end Collatz.Research.StoppingAtlas.Batch0987 From 98c327ba379edc302116c7adb1b7a262436da67c Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:36 +0530 Subject: [PATCH 0988/1001] proof: certify atlas Batch0988 (13:7992 to 13:8006) --- Collatz/Research/StoppingAtlas/Batch0988.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0988.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0988.lean b/Collatz/Research/StoppingAtlas/Batch0988.lean new file mode 100644 index 00000000..9502e05d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0988.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0988 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 7992. -/ +theorem bounds_13_7992 : exactInterval 13 7992 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7992 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7992) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7992 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7992 : oddCount 7992 13 = 6 ∧ acceleratedOrbit 13 7992 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7992 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7992) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7992.1, data_13_7992.2] + +/-- Complete interval computation for depth 13, residue 7993. -/ +theorem bounds_13_7993 : exactInterval 13 7993 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7993 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7993) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7993 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7993 : oddCount 7993 13 = 7 ∧ acceleratedOrbit 13 7993 = 2135 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7993 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7993) = 3 ^ 7 * m + 2135 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7993.1, data_13_7993.2] + +/-- Complete interval computation for depth 13, residue 7994. -/ +theorem bounds_13_7994 : exactInterval 13 7994 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7994 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7994) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7994 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7994 : oddCount 7994 13 = 6 ∧ acceleratedOrbit 13 7994 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7994 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7994) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7994.1, data_13_7994.2] + +/-- Complete interval computation for depth 13, residue 7995. -/ +theorem bounds_13_7995 : exactInterval 13 7995 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7995 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7995) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7995 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7995 : oddCount 7995 13 = 6 ∧ acceleratedOrbit 13 7995 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7995 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7995) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7995.1, data_13_7995.2] + +/-- Complete interval computation for depth 13, residue 7996. -/ +theorem bounds_13_7996 : exactInterval 13 7996 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7996 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7996) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7996 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7996 : oddCount 7996 13 = 6 ∧ acceleratedOrbit 13 7996 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7996 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7996) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7996.1, data_13_7996.2] + +/-- Complete interval computation for depth 13, residue 7997. -/ +theorem bounds_13_7997 : exactInterval 13 7997 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7997 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7997) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7997 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7997 : oddCount 7997 13 = 6 ∧ acceleratedOrbit 13 7997 = 712 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7997 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7997) = 3 ^ 6 * m + 712 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7997.1, data_13_7997.2] + +/-- Complete interval computation for depth 13, residue 7998. -/ +theorem bounds_13_7998 : exactInterval 13 7998 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7998 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7998) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7998 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7998 : oddCount 7998 13 = 9 ∧ acceleratedOrbit 13 7998 = 19223 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7998 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7998) = 3 ^ 9 * m + 19223 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7998.1, data_13_7998.2] + +/-- Complete interval computation for depth 13, residue 7999. -/ +theorem bounds_13_7999 : exactInterval 13 7999 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_7999 (m : Nat) : + stoppingTime (2 ^ 13 * m + 7999) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_7999 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_7999 : oddCount 7999 13 = 9 ∧ acceleratedOrbit 13 7999 = 19223 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_7999 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 7999) = 3 ^ 9 * m + 19223 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_7999.1, data_13_7999.2] + +/-- Complete interval computation for depth 13, residue 8000. -/ +theorem bounds_13_8000 : exactInterval 13 8000 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8000 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8000) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8000 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8000 : oddCount 8000 13 = 5 ∧ acceleratedOrbit 13 8000 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8000 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8000) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8000.1, data_13_8000.2] + +/-- Complete interval computation for depth 13, residue 8001. -/ +theorem bounds_13_8001 : exactInterval 13 8001 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8001 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8001) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8001 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8001 : oddCount 8001 13 = 5 ∧ acceleratedOrbit 13 8001 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8001 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8001) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8001.1, data_13_8001.2] + +/-- Complete interval computation for depth 13, residue 8002. -/ +theorem bounds_13_8002 : exactInterval 13 8002 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8002 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8002) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8002 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8002 : oddCount 8002 13 = 6 ∧ acceleratedOrbit 13 8002 = 713 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8002 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8002) = 3 ^ 6 * m + 713 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8002.1, data_13_8002.2] + +/-- Complete interval computation for depth 13, residue 8003. -/ +theorem bounds_13_8003 : exactInterval 13 8003 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8003 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8003) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8003 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8003 : oddCount 8003 13 = 6 ∧ acceleratedOrbit 13 8003 = 713 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8003 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8003) = 3 ^ 6 * m + 713 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8003.1, data_13_8003.2] + +/-- Complete interval computation for depth 13, residue 8004. -/ +theorem bounds_13_8004 : exactInterval 13 8004 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8004 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8004) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8004 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8004 : oddCount 8004 13 = 5 ∧ acceleratedOrbit 13 8004 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8004 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8004) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8004.1, data_13_8004.2] + +/-- Complete interval computation for depth 13, residue 8005. -/ +theorem bounds_13_8005 : exactInterval 13 8005 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8005 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8005) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8005 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8005 : oddCount 8005 13 = 5 ∧ acceleratedOrbit 13 8005 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8005 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8005) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8005.1, data_13_8005.2] + +/-- Complete interval computation for depth 13, residue 8006. -/ +theorem bounds_13_8006 : exactInterval 13 8006 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8006 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8006) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8006 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8006 : oddCount 8006 13 = 5 ∧ acceleratedOrbit 13 8006 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8006 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8006) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8006.1, data_13_8006.2] + +end Collatz.Research.StoppingAtlas.Batch0988 From 77e4c09e124d2e74f087afa0fc6cbfe9ef2b6fbc Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:36 +0530 Subject: [PATCH 0989/1001] proof: certify atlas Batch0989 (13:8007 to 13:8022) --- Collatz/Research/StoppingAtlas/Batch0989.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0989.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0989.lean b/Collatz/Research/StoppingAtlas/Batch0989.lean new file mode 100644 index 00000000..d9f9d8d7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0989.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0989 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8007. -/ +theorem bounds_13_8007 : exactInterval 13 8007 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8007 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8007) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8007 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8007 : oddCount 8007 13 = 7 ∧ acceleratedOrbit 13 8007 = 2138 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8007 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8007) = 3 ^ 7 * m + 2138 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8007.1, data_13_8007.2] + +/-- Complete interval computation for depth 13, residue 8008. -/ +theorem bounds_13_8008 : exactInterval 13 8008 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8008 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8008) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8008 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8008 : oddCount 8008 13 = 8 ∧ acceleratedOrbit 13 8008 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8008 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8008) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8008.1, data_13_8008.2] + +/-- Complete interval computation for depth 13, residue 8009. -/ +theorem bounds_13_8009 : exactInterval 13 8009 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8009 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8009) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8009 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8009 : oddCount 8009 13 = 6 ∧ acceleratedOrbit 13 8009 = 713 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8009 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8009) = 3 ^ 6 * m + 713 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8009.1, data_13_8009.2] + +/-- Complete interval computation for depth 13, residue 8010. -/ +theorem bounds_13_8010 : exactInterval 13 8010 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8010 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8010) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8010 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8010 : oddCount 8010 13 = 8 ∧ acceleratedOrbit 13 8010 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8010 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8010) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8010.1, data_13_8010.2] + +/-- Complete interval computation for depth 13, residue 8011. -/ +theorem bounds_13_8011 : exactInterval 13 8011 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8011 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8011) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8011 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8011 : oddCount 8011 13 = 5 ∧ acceleratedOrbit 13 8011 = 238 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8011 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8011) = 3 ^ 5 * m + 238 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8011.1, data_13_8011.2] + +/-- Complete interval computation for depth 13, residue 8012. -/ +theorem bounds_13_8012 : exactInterval 13 8012 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8012 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8012) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8012 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8012 : oddCount 8012 13 = 8 ∧ acceleratedOrbit 13 8012 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8012 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8012) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8012.1, data_13_8012.2] + +/-- Complete interval computation for depth 13, residue 8013. -/ +theorem bounds_13_8013 : exactInterval 13 8013 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8013 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8013) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8013 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8013 : oddCount 8013 13 = 8 ∧ acceleratedOrbit 13 8013 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8013 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8013) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8013.1, data_13_8013.2] + +/-- Complete interval computation for depth 13, residue 8014. -/ +theorem bounds_13_8014 : exactInterval 13 8014 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8014 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8014) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8014 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8014 : oddCount 8014 13 = 8 ∧ acceleratedOrbit 13 8014 = 6421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8014 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8014) = 3 ^ 8 * m + 6421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8014.1, data_13_8014.2] + +/-- Complete interval computation for depth 13, residue 8015. -/ +theorem bounds_13_8015 : exactInterval 13 8015 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8015 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8015) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8015 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8015 : oddCount 8015 13 = 8 ∧ acceleratedOrbit 13 8015 = 6421 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8015 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8015) = 3 ^ 8 * m + 6421 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8015.1, data_13_8015.2] + +/-- Complete interval computation for depth 13, residue 8016. -/ +theorem bounds_13_8016 : exactInterval 13 8016 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8016 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8016) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8016 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8016 : oddCount 8016 13 = 5 ∧ acceleratedOrbit 13 8016 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8016 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8016) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8016.1, data_13_8016.2] + +/-- Complete interval computation for depth 13, residue 8017. -/ +theorem bounds_13_8017 : exactInterval 13 8017 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8017 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8017) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8017 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8017 : oddCount 8017 13 = 8 ∧ acceleratedOrbit 13 8017 = 6425 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8017 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8017) = 3 ^ 8 * m + 6425 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8017.1, data_13_8017.2] + +/-- Complete interval computation for depth 13, residue 8018. -/ +theorem bounds_13_8018 : exactInterval 13 8018 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8018 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8018) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8018 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8018 : oddCount 8018 13 = 9 ∧ acceleratedOrbit 13 8018 = 19273 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8018 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8018) = 3 ^ 9 * m + 19273 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8018.1, data_13_8018.2] + +/-- Complete interval computation for depth 13, residue 8019. -/ +theorem bounds_13_8019 : exactInterval 13 8019 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8019 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8019) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8019 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8019 : oddCount 8019 13 = 9 ∧ acceleratedOrbit 13 8019 = 19273 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8019 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8019) = 3 ^ 9 * m + 19273 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8019.1, data_13_8019.2] + +/-- Complete interval computation for depth 13, residue 8020. -/ +theorem bounds_13_8020 : exactInterval 13 8020 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8020 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8020) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8020 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8020 : oddCount 8020 13 = 5 ∧ acceleratedOrbit 13 8020 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8020 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8020) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8020.1, data_13_8020.2] + +/-- Complete interval computation for depth 13, residue 8021. -/ +theorem bounds_13_8021 : exactInterval 13 8021 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8021 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8021) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8021 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8021 : oddCount 8021 13 = 5 ∧ acceleratedOrbit 13 8021 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8021 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8021) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8021.1, data_13_8021.2] + +/-- Complete interval computation for depth 13, residue 8022. -/ +theorem bounds_13_8022 : exactInterval 13 8022 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8022 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8022) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8022 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8022 : oddCount 8022 13 = 7 ∧ acceleratedOrbit 13 8022 = 2143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8022 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8022) = 3 ^ 7 * m + 2143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8022.1, data_13_8022.2] + +end Collatz.Research.StoppingAtlas.Batch0989 From 880fd5f3188233130f8a2c5c779c53ce53b8dd06 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:36 +0530 Subject: [PATCH 0990/1001] proof: certify atlas Batch0990 (13:8023 to 13:8037) --- Collatz/Research/StoppingAtlas/Batch0990.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0990.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0990.lean b/Collatz/Research/StoppingAtlas/Batch0990.lean new file mode 100644 index 00000000..548a30e3 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0990.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0990 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8023. -/ +theorem bounds_13_8023 : exactInterval 13 8023 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8023 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8023) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8023 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8023 : oddCount 8023 13 = 7 ∧ acceleratedOrbit 13 8023 = 2143 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8023 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8023) = 3 ^ 7 * m + 2143 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8023.1, data_13_8023.2] + +/-- Complete interval computation for depth 13, residue 8024. -/ +theorem bounds_13_8024 : exactInterval 13 8024 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8024 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8024) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8024 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8024 : oddCount 8024 13 = 7 ∧ acceleratedOrbit 13 8024 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8024 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8024) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8024.1, data_13_8024.2] + +/-- Complete interval computation for depth 13, residue 8025. -/ +theorem bounds_13_8025 : exactInterval 13 8025 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8025 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8025) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8025 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8025 : oddCount 8025 13 = 6 ∧ acceleratedOrbit 13 8025 = 715 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8025 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8025) = 3 ^ 6 * m + 715 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8025.1, data_13_8025.2] + +/-- Complete interval computation for depth 13, residue 8026. -/ +theorem bounds_13_8026 : exactInterval 13 8026 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8026 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8026) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8026 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8026 : oddCount 8026 13 = 7 ∧ acceleratedOrbit 13 8026 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8026 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8026) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8026.1, data_13_8026.2] + +/-- Complete interval computation for depth 13, residue 8027. -/ +theorem bounds_13_8027 : exactInterval 13 8027 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8027 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8027) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8027 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8027 : oddCount 8027 13 = 9 ∧ acceleratedOrbit 13 8027 = 19291 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8027 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8027) = 3 ^ 9 * m + 19291 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8027.1, data_13_8027.2] + +/-- Complete interval computation for depth 13, residue 8028. -/ +theorem bounds_13_8028 : exactInterval 13 8028 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8028 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8028) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8028 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8028 : oddCount 8028 13 = 7 ∧ acceleratedOrbit 13 8028 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8028 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8028) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8028.1, data_13_8028.2] + +/-- Complete interval computation for depth 13, residue 8029. -/ +theorem bounds_13_8029 : exactInterval 13 8029 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8029 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8029) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8029 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8029 : oddCount 8029 13 = 7 ∧ acceleratedOrbit 13 8029 = 2146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8029 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8029) = 3 ^ 7 * m + 2146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8029.1, data_13_8029.2] + +/-- Complete interval computation for depth 13, residue 8030. -/ +theorem bounds_13_8030 : exactInterval 13 8030 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8030 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8030) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8030 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8030 : oddCount 8030 13 = 6 ∧ acceleratedOrbit 13 8030 = 715 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8030 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8030) = 3 ^ 6 * m + 715 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8030.1, data_13_8030.2] + +/-- Complete interval computation for depth 13, residue 8031. -/ +theorem bounds_13_8031 : exactInterval 13 8031 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8031 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8031) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8031 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8031 : oddCount 8031 13 = 6 ∧ acceleratedOrbit 13 8031 = 715 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8031 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8031) = 3 ^ 6 * m + 715 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8031.1, data_13_8031.2] + +/-- Complete interval computation for depth 13, residue 8032. -/ +theorem bounds_13_8032 : exactInterval 13 8032 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8032 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8032) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8032 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8032 : oddCount 8032 13 = 6 ∧ acceleratedOrbit 13 8032 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8032 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8032) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8032.1, data_13_8032.2] + +/-- Complete interval computation for depth 13, residue 8033. -/ +theorem bounds_13_8033 : exactInterval 13 8033 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8033 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8033) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8033 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8033 : oddCount 8033 13 = 8 ∧ acceleratedOrbit 13 8033 = 6436 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8033 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8033) = 3 ^ 8 * m + 6436 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8033.1, data_13_8033.2] + +/-- Complete interval computation for depth 13, residue 8034. -/ +theorem bounds_13_8034 : exactInterval 13 8034 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8034 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8034) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8034 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8034 : oddCount 8034 13 = 4 ∧ acceleratedOrbit 13 8034 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8034 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8034) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8034.1, data_13_8034.2] + +/-- Complete interval computation for depth 13, residue 8035. -/ +theorem bounds_13_8035 : exactInterval 13 8035 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8035 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8035) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8035 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8035 : oddCount 8035 13 = 4 ∧ acceleratedOrbit 13 8035 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8035 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8035) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8035.1, data_13_8035.2] + +/-- Complete interval computation for depth 13, residue 8036. -/ +theorem bounds_13_8036 : exactInterval 13 8036 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8036 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8036) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8036 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8036 : oddCount 8036 13 = 4 ∧ acceleratedOrbit 13 8036 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8036 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8036) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8036.1, data_13_8036.2] + +/-- Complete interval computation for depth 13, residue 8037. -/ +theorem bounds_13_8037 : exactInterval 13 8037 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8037 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8037) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8037 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8037 : oddCount 8037 13 = 4 ∧ acceleratedOrbit 13 8037 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8037 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8037) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8037.1, data_13_8037.2] + +end Collatz.Research.StoppingAtlas.Batch0990 From 54a1bec3c6e20918e9c3ad863170cf8945017e97 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:36 +0530 Subject: [PATCH 0991/1001] proof: certify atlas Batch0991 (13:8038 to 13:8052) --- Collatz/Research/StoppingAtlas/Batch0991.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0991.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0991.lean b/Collatz/Research/StoppingAtlas/Batch0991.lean new file mode 100644 index 00000000..9575c6a9 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0991.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0991 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8038. -/ +theorem bounds_13_8038 : exactInterval 13 8038 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8038 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8038) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8038 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8038 : oddCount 8038 13 = 4 ∧ acceleratedOrbit 13 8038 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8038 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8038) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8038.1, data_13_8038.2] + +/-- Complete interval computation for depth 13, residue 8039. -/ +theorem bounds_13_8039 : exactInterval 13 8039 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8039 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8039) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8039 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8039 : oddCount 8039 13 = 11 ∧ acceleratedOrbit 13 8039 = 173866 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8039 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8039) = 3 ^ 11 * m + 173866 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8039.1, data_13_8039.2] + +/-- Complete interval computation for depth 13, residue 8040. -/ +theorem bounds_13_8040 : exactInterval 13 8040 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8040 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8040) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8040 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8040 : oddCount 8040 13 = 6 ∧ acceleratedOrbit 13 8040 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8040 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8040) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8040.1, data_13_8040.2] + +/-- Complete interval computation for depth 13, residue 8041. -/ +theorem bounds_13_8041 : exactInterval 13 8041 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8041 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8041) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8041 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8041 : oddCount 8041 13 = 8 ∧ acceleratedOrbit 13 8041 = 6443 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8041 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8041) = 3 ^ 8 * m + 6443 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8041.1, data_13_8041.2] + +/-- Complete interval computation for depth 13, residue 8042. -/ +theorem bounds_13_8042 : exactInterval 13 8042 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8042 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8042) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8042 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8042 : oddCount 8042 13 = 6 ∧ acceleratedOrbit 13 8042 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8042 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8042) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8042.1, data_13_8042.2] + +/-- Complete interval computation for depth 13, residue 8043. -/ +theorem bounds_13_8043 : exactInterval 13 8043 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8043 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8043) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8043 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8043 : oddCount 8043 13 = 6 ∧ acceleratedOrbit 13 8043 = 716 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8043 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8043) = 3 ^ 6 * m + 716 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8043.1, data_13_8043.2] + +/-- Complete interval computation for depth 13, residue 8044. -/ +theorem bounds_13_8044 : exactInterval 13 8044 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8044 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8044) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8044 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8044 : oddCount 8044 13 = 7 ∧ acceleratedOrbit 13 8044 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8044 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8044) = 3 ^ 7 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8044.1, data_13_8044.2] + +/-- Complete interval computation for depth 13, residue 8045. -/ +theorem bounds_13_8045 : exactInterval 13 8045 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8045 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8045) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8045 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8045 : oddCount 8045 13 = 7 ∧ acceleratedOrbit 13 8045 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8045 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8045) = 3 ^ 7 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8045.1, data_13_8045.2] + +/-- Complete interval computation for depth 13, residue 8046. -/ +theorem bounds_13_8046 : exactInterval 13 8046 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8046 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8046) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8046 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8046 : oddCount 8046 13 = 7 ∧ acceleratedOrbit 13 8046 = 2150 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8046 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8046) = 3 ^ 7 * m + 2150 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8046.1, data_13_8046.2] + +/-- Complete interval computation for depth 13, residue 8047. -/ +theorem bounds_13_8047 : exactInterval 13 8047 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8047 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8047) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8047 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8047 : oddCount 8047 13 = 8 ∧ acceleratedOrbit 13 8047 = 6446 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8047 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8047) = 3 ^ 8 * m + 6446 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8047.1, data_13_8047.2] + +/-- Complete interval computation for depth 13, residue 8048. -/ +theorem bounds_13_8048 : exactInterval 13 8048 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8048 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8048) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8048 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8048 : oddCount 8048 13 = 6 ∧ acceleratedOrbit 13 8048 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8048 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8048) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8048.1, data_13_8048.2] + +/-- Complete interval computation for depth 13, residue 8049. -/ +theorem bounds_13_8049 : exactInterval 13 8049 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8049 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8049) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8049 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8049 : oddCount 8049 13 = 6 ∧ acceleratedOrbit 13 8049 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8049 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8049) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8049.1, data_13_8049.2] + +/-- Complete interval computation for depth 13, residue 8050. -/ +theorem bounds_13_8050 : exactInterval 13 8050 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8050 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8050) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8050 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8050 : oddCount 8050 13 = 5 ∧ acceleratedOrbit 13 8050 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8050 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8050) = 3 ^ 5 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8050.1, data_13_8050.2] + +/-- Complete interval computation for depth 13, residue 8051. -/ +theorem bounds_13_8051 : exactInterval 13 8051 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8051 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8051) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8051 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8051 : oddCount 8051 13 = 5 ∧ acceleratedOrbit 13 8051 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8051 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8051) = 3 ^ 5 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8051.1, data_13_8051.2] + +/-- Complete interval computation for depth 13, residue 8052. -/ +theorem bounds_13_8052 : exactInterval 13 8052 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8052 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8052) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8052 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8052 : oddCount 8052 13 = 6 ∧ acceleratedOrbit 13 8052 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8052 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8052) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8052.1, data_13_8052.2] + +end Collatz.Research.StoppingAtlas.Batch0991 From e66cff40d9f8fe7d3c1242154d2834e176307681 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:36 +0530 Subject: [PATCH 0992/1001] proof: certify atlas Batch0992 (13:8053 to 13:8068) --- Collatz/Research/StoppingAtlas/Batch0992.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0992.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0992.lean b/Collatz/Research/StoppingAtlas/Batch0992.lean new file mode 100644 index 00000000..23efc405 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0992.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0992 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8053. -/ +theorem bounds_13_8053 : exactInterval 13 8053 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8053 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8053) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8053 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8053 : oddCount 8053 13 = 6 ∧ acceleratedOrbit 13 8053 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8053 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8053) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8053.1, data_13_8053.2] + +/-- Complete interval computation for depth 13, residue 8054. -/ +theorem bounds_13_8054 : exactInterval 13 8054 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8054 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8054) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8054 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8054 : oddCount 8054 13 = 5 ∧ acceleratedOrbit 13 8054 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8054 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8054) = 3 ^ 5 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8054.1, data_13_8054.2] + +/-- Complete interval computation for depth 13, residue 8055. -/ +theorem bounds_13_8055 : exactInterval 13 8055 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8055 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8055) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8055 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8055 : oddCount 8055 13 = 5 ∧ acceleratedOrbit 13 8055 = 239 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8055 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8055) = 3 ^ 5 * m + 239 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8055.1, data_13_8055.2] + +/-- Complete interval computation for depth 13, residue 8056. -/ +theorem bounds_13_8056 : exactInterval 13 8056 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8056 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8056) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8056 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8056 : oddCount 8056 13 = 7 ∧ acceleratedOrbit 13 8056 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8056 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8056) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8056.1, data_13_8056.2] + +/-- Complete interval computation for depth 13, residue 8057. -/ +theorem bounds_13_8057 : exactInterval 13 8057 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8057 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8057) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8057 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8057 : oddCount 8057 13 = 8 ∧ acceleratedOrbit 13 8057 = 6455 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8057 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8057) = 3 ^ 8 * m + 6455 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8057.1, data_13_8057.2] + +/-- Complete interval computation for depth 13, residue 8058. -/ +theorem bounds_13_8058 : exactInterval 13 8058 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8058 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8058) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8058 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8058 : oddCount 8058 13 = 7 ∧ acceleratedOrbit 13 8058 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8058 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8058) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8058.1, data_13_8058.2] + +/-- Complete interval computation for depth 13, residue 8059. -/ +theorem bounds_13_8059 : exactInterval 13 8059 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8059 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8059) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8059 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8059 : oddCount 8059 13 = 7 ∧ acceleratedOrbit 13 8059 = 2152 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8059 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8059) = 3 ^ 7 * m + 2152 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8059.1, data_13_8059.2] + +/-- Complete interval computation for depth 13, residue 8060. -/ +theorem bounds_13_8060 : exactInterval 13 8060 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8060 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8060) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8060 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8060 : oddCount 8060 13 = 7 ∧ acceleratedOrbit 13 8060 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8060 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8060) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8060.1, data_13_8060.2] + +/-- Complete interval computation for depth 13, residue 8061. -/ +theorem bounds_13_8061 : exactInterval 13 8061 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8061 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8061) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8061 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8061 : oddCount 8061 13 = 7 ∧ acceleratedOrbit 13 8061 = 2153 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8061 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8061) = 3 ^ 7 * m + 2153 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8061.1, data_13_8061.2] + +/-- Complete interval computation for depth 13, residue 8062. -/ +theorem bounds_13_8062 : exactInterval 13 8062 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8062 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8062) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8062 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8062 : oddCount 8062 13 = 9 ∧ acceleratedOrbit 13 8062 = 19376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8062 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8062) = 3 ^ 9 * m + 19376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8062.1, data_13_8062.2] + +/-- Complete interval computation for depth 13, residue 8063. -/ +theorem bounds_13_8063 : exactInterval 13 8063 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8063 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8063) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8063 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8063 : oddCount 8063 13 = 9 ∧ acceleratedOrbit 13 8063 = 19376 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8063 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8063) = 3 ^ 9 * m + 19376 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8063.1, data_13_8063.2] + +/-- Complete interval computation for depth 13, residue 8064. -/ +theorem bounds_13_8064 : exactInterval 13 8064 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8064 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8064) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8064 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8064 : oddCount 8064 13 = 6 ∧ acceleratedOrbit 13 8064 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8064 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8064) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8064.1, data_13_8064.2] + +/-- Complete interval computation for depth 13, residue 8065. -/ +theorem bounds_13_8065 : exactInterval 13 8065 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8065 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8065) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8065 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8065 : oddCount 8065 13 = 6 ∧ acceleratedOrbit 13 8065 = 718 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8065 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8065) = 3 ^ 6 * m + 718 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8065.1, data_13_8065.2] + +/-- Complete interval computation for depth 13, residue 8066. -/ +theorem bounds_13_8066 : exactInterval 13 8066 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8066 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8066) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8066 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8066 : oddCount 8066 13 = 6 ∧ acceleratedOrbit 13 8066 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8066 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8066) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8066.1, data_13_8066.2] + +/-- Complete interval computation for depth 13, residue 8067. -/ +theorem bounds_13_8067 : exactInterval 13 8067 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8067 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8067) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8067 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8067 : oddCount 8067 13 = 6 ∧ acceleratedOrbit 13 8067 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8067 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8067) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8067.1, data_13_8067.2] + +/-- Complete interval computation for depth 13, residue 8068. -/ +theorem bounds_13_8068 : exactInterval 13 8068 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8068 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8068) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8068 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8068 : oddCount 8068 13 = 8 ∧ acceleratedOrbit 13 8068 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8068 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8068) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8068.1, data_13_8068.2] + +end Collatz.Research.StoppingAtlas.Batch0992 From 1483309e5cf1edf37b0bfdb081e9b3e3dea723d0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:36 +0530 Subject: [PATCH 0993/1001] proof: certify atlas Batch0993 (13:8069 to 13:8083) --- Collatz/Research/StoppingAtlas/Batch0993.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0993.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0993.lean b/Collatz/Research/StoppingAtlas/Batch0993.lean new file mode 100644 index 00000000..e2e8f158 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0993.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0993 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8069. -/ +theorem bounds_13_8069 : exactInterval 13 8069 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8069 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8069) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8069 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8069 : oddCount 8069 13 = 8 ∧ acceleratedOrbit 13 8069 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8069 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8069) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8069.1, data_13_8069.2] + +/-- Complete interval computation for depth 13, residue 8070. -/ +theorem bounds_13_8070 : exactInterval 13 8070 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8070 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8070) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8070 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8070 : oddCount 8070 13 = 8 ∧ acceleratedOrbit 13 8070 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8070 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8070) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8070.1, data_13_8070.2] + +/-- Complete interval computation for depth 13, residue 8071. -/ +theorem bounds_13_8071 : exactInterval 13 8071 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8071 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8071) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8071 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8071 : oddCount 8071 13 = 6 ∧ acceleratedOrbit 13 8071 = 719 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8071 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8071) = 3 ^ 6 * m + 719 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8071.1, data_13_8071.2] + +/-- Complete interval computation for depth 13, residue 8072. -/ +theorem bounds_13_8072 : exactInterval 13 8072 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8072 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8072) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8072 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8072 : oddCount 8072 13 = 5 ∧ acceleratedOrbit 13 8072 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8072 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8072) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8072.1, data_13_8072.2] + +/-- Complete interval computation for depth 13, residue 8073. -/ +theorem bounds_13_8073 : exactInterval 13 8073 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8073 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8073) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8073 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8073 : oddCount 8073 13 = 9 ∧ acceleratedOrbit 13 8073 = 19403 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8073 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8073) = 3 ^ 9 * m + 19403 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8073.1, data_13_8073.2] + +/-- Complete interval computation for depth 13, residue 8074. -/ +theorem bounds_13_8074 : exactInterval 13 8074 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8074 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8074) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8074 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8074 : oddCount 8074 13 = 5 ∧ acceleratedOrbit 13 8074 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8074 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8074) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8074.1, data_13_8074.2] + +/-- Complete interval computation for depth 13, residue 8075. -/ +theorem bounds_13_8075 : exactInterval 13 8075 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8075 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8075) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8075 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8075 : oddCount 8075 13 = 8 ∧ acceleratedOrbit 13 8075 = 6470 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8075 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8075) = 3 ^ 8 * m + 6470 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8075.1, data_13_8075.2] + +/-- Complete interval computation for depth 13, residue 8076. -/ +theorem bounds_13_8076 : exactInterval 13 8076 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8076 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8076) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8076 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8076 : oddCount 8076 13 = 5 ∧ acceleratedOrbit 13 8076 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8076 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8076) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8076.1, data_13_8076.2] + +/-- Complete interval computation for depth 13, residue 8077. -/ +theorem bounds_13_8077 : exactInterval 13 8077 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8077 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8077) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8077 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8077 : oddCount 8077 13 = 5 ∧ acceleratedOrbit 13 8077 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8077 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8077) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8077.1, data_13_8077.2] + +/-- Complete interval computation for depth 13, residue 8078. -/ +theorem bounds_13_8078 : exactInterval 13 8078 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8078 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8078) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8078 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8078 : oddCount 8078 13 = 8 ∧ acceleratedOrbit 13 8078 = 6473 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8078 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8078) = 3 ^ 8 * m + 6473 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8078.1, data_13_8078.2] + +/-- Complete interval computation for depth 13, residue 8079. -/ +theorem bounds_13_8079 : exactInterval 13 8079 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8079 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8079) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8079 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8079 : oddCount 8079 13 = 8 ∧ acceleratedOrbit 13 8079 = 6473 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8079 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8079) = 3 ^ 8 * m + 6473 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8079.1, data_13_8079.2] + +/-- Complete interval computation for depth 13, residue 8080. -/ +theorem bounds_13_8080 : exactInterval 13 8080 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8080 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8080) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8080 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8080 : oddCount 8080 13 = 6 ∧ acceleratedOrbit 13 8080 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8080 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8080) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8080.1, data_13_8080.2] + +/-- Complete interval computation for depth 13, residue 8081. -/ +theorem bounds_13_8081 : exactInterval 13 8081 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8081 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8081) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8081 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8081 : oddCount 8081 13 = 8 ∧ acceleratedOrbit 13 8081 = 6479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8081 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8081) = 3 ^ 8 * m + 6479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8081.1, data_13_8081.2] + +/-- Complete interval computation for depth 13, residue 8082. -/ +theorem bounds_13_8082 : exactInterval 13 8082 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8082 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8082) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8082 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8082 : oddCount 8082 13 = 8 ∧ acceleratedOrbit 13 8082 = 6479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8082 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8082) = 3 ^ 8 * m + 6479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8082.1, data_13_8082.2] + +/-- Complete interval computation for depth 13, residue 8083. -/ +theorem bounds_13_8083 : exactInterval 13 8083 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8083 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8083) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8083 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8083 : oddCount 8083 13 = 8 ∧ acceleratedOrbit 13 8083 = 6479 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8083 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8083) = 3 ^ 8 * m + 6479 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8083.1, data_13_8083.2] + +end Collatz.Research.StoppingAtlas.Batch0993 From 4fb00fc6b1debeb9b95b3b102b28170d5cce5cea Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:37 +0530 Subject: [PATCH 0994/1001] proof: certify atlas Batch0994 (13:8084 to 13:8098) --- Collatz/Research/StoppingAtlas/Batch0994.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0994.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0994.lean b/Collatz/Research/StoppingAtlas/Batch0994.lean new file mode 100644 index 00000000..b132d919 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0994.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0994 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8084. -/ +theorem bounds_13_8084 : exactInterval 13 8084 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8084 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8084) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8084 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8084 : oddCount 8084 13 = 6 ∧ acceleratedOrbit 13 8084 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8084 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8084) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8084.1, data_13_8084.2] + +/-- Complete interval computation for depth 13, residue 8085. -/ +theorem bounds_13_8085 : exactInterval 13 8085 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8085 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8085) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8085 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8085 : oddCount 8085 13 = 6 ∧ acceleratedOrbit 13 8085 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8085 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8085) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8085.1, data_13_8085.2] + +/-- Complete interval computation for depth 13, residue 8086. -/ +theorem bounds_13_8086 : exactInterval 13 8086 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8086 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8086) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8086 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8086 : oddCount 8086 13 = 4 ∧ acceleratedOrbit 13 8086 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8086 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8086) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8086.1, data_13_8086.2] + +/-- Complete interval computation for depth 13, residue 8087. -/ +theorem bounds_13_8087 : exactInterval 13 8087 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8087 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8087) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8087 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8087 : oddCount 8087 13 = 4 ∧ acceleratedOrbit 13 8087 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8087 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8087) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8087.1, data_13_8087.2] + +/-- Complete interval computation for depth 13, residue 8088. -/ +theorem bounds_13_8088 : exactInterval 13 8088 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8088 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8088) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8088 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8088 : oddCount 8088 13 = 6 ∧ acceleratedOrbit 13 8088 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8088 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8088) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8088.1, data_13_8088.2] + +/-- Complete interval computation for depth 13, residue 8089. -/ +theorem bounds_13_8089 : exactInterval 13 8089 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8089 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8089) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8089 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8089 : oddCount 8089 13 = 4 ∧ acceleratedOrbit 13 8089 = 80 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8089 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8089) = 3 ^ 4 * m + 80 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8089.1, data_13_8089.2] + +/-- Complete interval computation for depth 13, residue 8090. -/ +theorem bounds_13_8090 : exactInterval 13 8090 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8090 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8090) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8090 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8090 : oddCount 8090 13 = 6 ∧ acceleratedOrbit 13 8090 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8090 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8090) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8090.1, data_13_8090.2] + +/-- Complete interval computation for depth 13, residue 8091. -/ +theorem bounds_13_8091 : exactInterval 13 8091 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8091 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8091) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8091 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8091 : oddCount 8091 13 = 8 ∧ acceleratedOrbit 13 8091 = 6482 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8091 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8091) = 3 ^ 8 * m + 6482 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8091.1, data_13_8091.2] + +/-- Complete interval computation for depth 13, residue 8092. -/ +theorem bounds_13_8092 : exactInterval 13 8092 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8092 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8092) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8092 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8092 : oddCount 8092 13 = 7 ∧ acceleratedOrbit 13 8092 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8092 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8092) = 3 ^ 7 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8092.1, data_13_8092.2] + +/-- Complete interval computation for depth 13, residue 8093. -/ +theorem bounds_13_8093 : exactInterval 13 8093 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8093 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8093) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8093 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8093 : oddCount 8093 13 = 7 ∧ acceleratedOrbit 13 8093 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8093 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8093) = 3 ^ 7 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8093.1, data_13_8093.2] + +/-- Complete interval computation for depth 13, residue 8094. -/ +theorem bounds_13_8094 : exactInterval 13 8094 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8094 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8094) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8094 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8094 : oddCount 8094 13 = 7 ∧ acceleratedOrbit 13 8094 = 2162 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8094 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8094) = 3 ^ 7 * m + 2162 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8094.1, data_13_8094.2] + +/-- Complete interval computation for depth 13, residue 8095. -/ +theorem bounds_13_8095 : exactInterval 13 8095 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8095 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8095) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8095 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8095 : oddCount 8095 13 = 9 ∧ acceleratedOrbit 13 8095 = 19453 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8095 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8095) = 3 ^ 9 * m + 19453 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8095.1, data_13_8095.2] + +/-- Complete interval computation for depth 13, residue 8096. -/ +theorem bounds_13_8096 : exactInterval 13 8096 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8096 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8096) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8096 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8096 : oddCount 8096 13 = 6 ∧ acceleratedOrbit 13 8096 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8096 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8096) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8096.1, data_13_8096.2] + +/-- Complete interval computation for depth 13, residue 8097. -/ +theorem bounds_13_8097 : exactInterval 13 8097 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8097 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8097) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8097 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8097 : oddCount 8097 13 = 6 ∧ acceleratedOrbit 13 8097 = 721 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8097 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8097) = 3 ^ 6 * m + 721 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8097.1, data_13_8097.2] + +/-- Complete interval computation for depth 13, residue 8098. -/ +theorem bounds_13_8098 : exactInterval 13 8098 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8098 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8098) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8098 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8098 : oddCount 8098 13 = 6 ∧ acceleratedOrbit 13 8098 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8098 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8098) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8098.1, data_13_8098.2] + +end Collatz.Research.StoppingAtlas.Batch0994 From f9646d56264013b36e75723e5693a74641c7ba14 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:37 +0530 Subject: [PATCH 0995/1001] proof: certify atlas Batch0995 (13:8099 to 13:8114) --- Collatz/Research/StoppingAtlas/Batch0995.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0995.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0995.lean b/Collatz/Research/StoppingAtlas/Batch0995.lean new file mode 100644 index 00000000..8ef2e135 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0995.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0995 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8099. -/ +theorem bounds_13_8099 : exactInterval 13 8099 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8099 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8099) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8099 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8099 : oddCount 8099 13 = 6 ∧ acceleratedOrbit 13 8099 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8099 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8099) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8099.1, data_13_8099.2] + +/-- Complete interval computation for depth 13, residue 8100. -/ +theorem bounds_13_8100 : exactInterval 13 8100 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8100 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8100) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8100 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8100 : oddCount 8100 13 = 8 ∧ acceleratedOrbit 13 8100 = 6493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8100 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8100) = 3 ^ 8 * m + 6493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8100.1, data_13_8100.2] + +/-- Complete interval computation for depth 13, residue 8101. -/ +theorem bounds_13_8101 : exactInterval 13 8101 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8101 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8101) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8101 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8101 : oddCount 8101 13 = 8 ∧ acceleratedOrbit 13 8101 = 6493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8101 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8101) = 3 ^ 8 * m + 6493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8101.1, data_13_8101.2] + +/-- Complete interval computation for depth 13, residue 8102. -/ +theorem bounds_13_8102 : exactInterval 13 8102 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8102 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8102) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8102 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8102 : oddCount 8102 13 = 8 ∧ acceleratedOrbit 13 8102 = 6493 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8102 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8102) = 3 ^ 8 * m + 6493 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8102.1, data_13_8102.2] + +/-- Complete interval computation for depth 13, residue 8103. -/ +theorem bounds_13_8103 : exactInterval 13 8103 = ⟨0, none⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8103 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8103) 13 ↔ 0 ≤ m := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8103 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8103 : oddCount 8103 13 = 8 ∧ acceleratedOrbit 13 8103 = 6491 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8103 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8103) = 3 ^ 8 * m + 6491 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8103.1, data_13_8103.2] + +/-- Complete interval computation for depth 13, residue 8104. -/ +theorem bounds_13_8104 : exactInterval 13 8104 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8104 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8104) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8104 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8104 : oddCount 8104 13 = 6 ∧ acceleratedOrbit 13 8104 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8104 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8104) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8104.1, data_13_8104.2] + +/-- Complete interval computation for depth 13, residue 8105. -/ +theorem bounds_13_8105 : exactInterval 13 8105 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8105 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8105) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8105 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8105 : oddCount 8105 13 = 9 ∧ acceleratedOrbit 13 8105 = 19478 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8105 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8105) = 3 ^ 9 * m + 19478 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8105.1, data_13_8105.2] + +/-- Complete interval computation for depth 13, residue 8106. -/ +theorem bounds_13_8106 : exactInterval 13 8106 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8106 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8106) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8106 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8106 : oddCount 8106 13 = 6 ∧ acceleratedOrbit 13 8106 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8106 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8106) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8106.1, data_13_8106.2] + +/-- Complete interval computation for depth 13, residue 8107. -/ +theorem bounds_13_8107 : exactInterval 13 8107 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8107 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8107) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8107 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8107 : oddCount 8107 13 = 7 ∧ acceleratedOrbit 13 8107 = 2165 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8107 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8107) = 3 ^ 7 * m + 2165 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8107.1, data_13_8107.2] + +/-- Complete interval computation for depth 13, residue 8108. -/ +theorem bounds_13_8108 : exactInterval 13 8108 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8108 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8108) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8108 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8108 : oddCount 8108 13 = 8 ∧ acceleratedOrbit 13 8108 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8108 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8108) = 3 ^ 8 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8108.1, data_13_8108.2] + +/-- Complete interval computation for depth 13, residue 8109. -/ +theorem bounds_13_8109 : exactInterval 13 8109 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8109 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8109) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8109 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8109 : oddCount 8109 13 = 8 ∧ acceleratedOrbit 13 8109 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8109 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8109) = 3 ^ 8 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8109.1, data_13_8109.2] + +/-- Complete interval computation for depth 13, residue 8110. -/ +theorem bounds_13_8110 : exactInterval 13 8110 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8110 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8110) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8110 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8110 : oddCount 8110 13 = 8 ∧ acceleratedOrbit 13 8110 = 6500 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8110 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8110) = 3 ^ 8 * m + 6500 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8110.1, data_13_8110.2] + +/-- Complete interval computation for depth 13, residue 8111. -/ +theorem bounds_13_8111 : exactInterval 13 8111 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8111 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8111) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8111 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8111 : oddCount 8111 13 = 6 ∧ acceleratedOrbit 13 8111 = 722 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8111 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8111) = 3 ^ 6 * m + 722 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8111.1, data_13_8111.2] + +/-- Complete interval computation for depth 13, residue 8112. -/ +theorem bounds_13_8112 : exactInterval 13 8112 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8112 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8112) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8112 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8112 : oddCount 8112 13 = 6 ∧ acceleratedOrbit 13 8112 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8112 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8112) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8112.1, data_13_8112.2] + +/-- Complete interval computation for depth 13, residue 8113. -/ +theorem bounds_13_8113 : exactInterval 13 8113 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8113 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8113) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8113 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8113 : oddCount 8113 13 = 5 ∧ acceleratedOrbit 13 8113 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8113 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8113) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8113.1, data_13_8113.2] + +/-- Complete interval computation for depth 13, residue 8114. -/ +theorem bounds_13_8114 : exactInterval 13 8114 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8114 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8114) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8114 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8114 : oddCount 8114 13 = 5 ∧ acceleratedOrbit 13 8114 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8114 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8114) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8114.1, data_13_8114.2] + +end Collatz.Research.StoppingAtlas.Batch0995 From 1874db79f0817a0a8b7ca0010cac9ed644319840 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:37 +0530 Subject: [PATCH 0996/1001] proof: certify atlas Batch0996 (13:8115 to 13:8129) --- Collatz/Research/StoppingAtlas/Batch0996.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0996.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0996.lean b/Collatz/Research/StoppingAtlas/Batch0996.lean new file mode 100644 index 00000000..5bad88bb --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0996.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0996 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8115. -/ +theorem bounds_13_8115 : exactInterval 13 8115 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8115 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8115) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8115 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8115 : oddCount 8115 13 = 5 ∧ acceleratedOrbit 13 8115 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8115 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8115) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8115.1, data_13_8115.2] + +/-- Complete interval computation for depth 13, residue 8116. -/ +theorem bounds_13_8116 : exactInterval 13 8116 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8116 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8116) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8116 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8116 : oddCount 8116 13 = 6 ∧ acceleratedOrbit 13 8116 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8116 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8116) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8116.1, data_13_8116.2] + +/-- Complete interval computation for depth 13, residue 8117. -/ +theorem bounds_13_8117 : exactInterval 13 8117 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8117 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8117) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8117 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8117 : oddCount 8117 13 = 6 ∧ acceleratedOrbit 13 8117 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8117 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8117) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8117.1, data_13_8117.2] + +/-- Complete interval computation for depth 13, residue 8118. -/ +theorem bounds_13_8118 : exactInterval 13 8118 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8118 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8118) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8118 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8118 : oddCount 8118 13 = 8 ∧ acceleratedOrbit 13 8118 = 6506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8118 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8118) = 3 ^ 8 * m + 6506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8118.1, data_13_8118.2] + +/-- Complete interval computation for depth 13, residue 8119. -/ +theorem bounds_13_8119 : exactInterval 13 8119 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8119 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8119) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8119 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8119 : oddCount 8119 13 = 8 ∧ acceleratedOrbit 13 8119 = 6506 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8119 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8119) = 3 ^ 8 * m + 6506 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8119.1, data_13_8119.2] + +/-- Complete interval computation for depth 13, residue 8120. -/ +theorem bounds_13_8120 : exactInterval 13 8120 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8120 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8120) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8120 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8120 : oddCount 8120 13 = 6 ∧ acceleratedOrbit 13 8120 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8120 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8120) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8120.1, data_13_8120.2] + +/-- Complete interval computation for depth 13, residue 8121. -/ +theorem bounds_13_8121 : exactInterval 13 8121 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8121 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8121) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8121 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8121 : oddCount 8121 13 = 5 ∧ acceleratedOrbit 13 8121 = 241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8121 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8121) = 3 ^ 5 * m + 241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8121.1, data_13_8121.2] + +/-- Complete interval computation for depth 13, residue 8122. -/ +theorem bounds_13_8122 : exactInterval 13 8122 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8122 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8122) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8122 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8122 : oddCount 8122 13 = 6 ∧ acceleratedOrbit 13 8122 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8122 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8122) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8122.1, data_13_8122.2] + +/-- Complete interval computation for depth 13, residue 8123. -/ +theorem bounds_13_8123 : exactInterval 13 8123 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8123 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8123) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8123 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8123 : oddCount 8123 13 = 5 ∧ acceleratedOrbit 13 8123 = 241 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8123 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8123) = 3 ^ 5 * m + 241 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8123.1, data_13_8123.2] + +/-- Complete interval computation for depth 13, residue 8124. -/ +theorem bounds_13_8124 : exactInterval 13 8124 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8124 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8124) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8124 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8124 : oddCount 8124 13 = 7 ∧ acceleratedOrbit 13 8124 = 2170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8124 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8124) = 3 ^ 7 * m + 2170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8124.1, data_13_8124.2] + +/-- Complete interval computation for depth 13, residue 8125. -/ +theorem bounds_13_8125 : exactInterval 13 8125 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8125 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8125) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8125 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8125 : oddCount 8125 13 = 7 ∧ acceleratedOrbit 13 8125 = 2170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8125 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8125) = 3 ^ 7 * m + 2170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8125.1, data_13_8125.2] + +/-- Complete interval computation for depth 13, residue 8126. -/ +theorem bounds_13_8126 : exactInterval 13 8126 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8126 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8126) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8126 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8126 : oddCount 8126 13 = 7 ∧ acceleratedOrbit 13 8126 = 2170 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8126 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8126) = 3 ^ 7 * m + 2170 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8126.1, data_13_8126.2] + +/-- Complete interval computation for depth 13, residue 8127. -/ +theorem bounds_13_8127 : exactInterval 13 8127 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8127 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8127) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8127 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8127 : oddCount 8127 13 = 10 ∧ acceleratedOrbit 13 8127 = 58589 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8127 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8127) = 3 ^ 10 * m + 58589 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8127.1, data_13_8127.2] + +/-- Complete interval computation for depth 13, residue 8128. -/ +theorem bounds_13_8128 : exactInterval 13 8128 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8128 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8128) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8128 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8128 : oddCount 8128 13 = 7 ∧ acceleratedOrbit 13 8128 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8128 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8128) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8128.1, data_13_8128.2] + +/-- Complete interval computation for depth 13, residue 8129. -/ +theorem bounds_13_8129 : exactInterval 13 8129 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8129 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8129) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8129 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8129 : oddCount 8129 13 = 6 ∧ acceleratedOrbit 13 8129 = 724 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8129 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8129) = 3 ^ 6 * m + 724 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8129.1, data_13_8129.2] + +end Collatz.Research.StoppingAtlas.Batch0996 From 56bc92ad916a3a5e051f5d38df8fe844eafd967f Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:37 +0530 Subject: [PATCH 0997/1001] proof: certify atlas Batch0997 (13:8130 to 13:8144) --- Collatz/Research/StoppingAtlas/Batch0997.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0997.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0997.lean b/Collatz/Research/StoppingAtlas/Batch0997.lean new file mode 100644 index 00000000..1116cde7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0997.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0997 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8130. -/ +theorem bounds_13_8130 : exactInterval 13 8130 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8130 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8130) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8130 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8130 : oddCount 8130 13 = 9 ∧ acceleratedOrbit 13 8130 = 19547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8130 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8130) = 3 ^ 9 * m + 19547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8130.1, data_13_8130.2] + +/-- Complete interval computation for depth 13, residue 8131. -/ +theorem bounds_13_8131 : exactInterval 13 8131 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8131 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8131) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8131 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8131 : oddCount 8131 13 = 9 ∧ acceleratedOrbit 13 8131 = 19547 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8131 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8131) = 3 ^ 9 * m + 19547 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8131.1, data_13_8131.2] + +/-- Complete interval computation for depth 13, residue 8132. -/ +theorem bounds_13_8132 : exactInterval 13 8132 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8132 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8132) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8132 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8132 : oddCount 8132 13 = 6 ∧ acceleratedOrbit 13 8132 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8132 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8132) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8132.1, data_13_8132.2] + +/-- Complete interval computation for depth 13, residue 8133. -/ +theorem bounds_13_8133 : exactInterval 13 8133 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8133 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8133) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8133 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8133 : oddCount 8133 13 = 6 ∧ acceleratedOrbit 13 8133 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8133 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8133) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8133.1, data_13_8133.2] + +/-- Complete interval computation for depth 13, residue 8134. -/ +theorem bounds_13_8134 : exactInterval 13 8134 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8134 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8134) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8134 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8134 : oddCount 8134 13 = 6 ∧ acceleratedOrbit 13 8134 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8134 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8134) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8134.1, data_13_8134.2] + +/-- Complete interval computation for depth 13, residue 8135. -/ +theorem bounds_13_8135 : exactInterval 13 8135 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8135 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8135) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8135 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8135 : oddCount 8135 13 = 8 ∧ acceleratedOrbit 13 8135 = 6517 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8135 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8135) = 3 ^ 8 * m + 6517 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8135.1, data_13_8135.2] + +/-- Complete interval computation for depth 13, residue 8136. -/ +theorem bounds_13_8136 : exactInterval 13 8136 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8136 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8136) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8136 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8136 : oddCount 8136 13 = 7 ∧ acceleratedOrbit 13 8136 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8136 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8136) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8136.1, data_13_8136.2] + +/-- Complete interval computation for depth 13, residue 8137. -/ +theorem bounds_13_8137 : exactInterval 13 8137 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8137 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8137) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8137 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8137 : oddCount 8137 13 = 8 ∧ acceleratedOrbit 13 8137 = 6520 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8137 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8137) = 3 ^ 8 * m + 6520 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8137.1, data_13_8137.2] + +/-- Complete interval computation for depth 13, residue 8138. -/ +theorem bounds_13_8138 : exactInterval 13 8138 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8138 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8138) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8138 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8138 : oddCount 8138 13 = 7 ∧ acceleratedOrbit 13 8138 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8138 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8138) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8138.1, data_13_8138.2] + +/-- Complete interval computation for depth 13, residue 8139. -/ +theorem bounds_13_8139 : exactInterval 13 8139 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8139 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8139) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8139 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8139 : oddCount 8139 13 = 5 ∧ acceleratedOrbit 13 8139 = 242 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8139 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8139) = 3 ^ 5 * m + 242 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8139.1, data_13_8139.2] + +/-- Complete interval computation for depth 13, residue 8140. -/ +theorem bounds_13_8140 : exactInterval 13 8140 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8140 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8140) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8140 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8140 : oddCount 8140 13 = 7 ∧ acceleratedOrbit 13 8140 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8140 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8140) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8140.1, data_13_8140.2] + +/-- Complete interval computation for depth 13, residue 8141. -/ +theorem bounds_13_8141 : exactInterval 13 8141 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8141 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8141) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8141 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8141 : oddCount 8141 13 = 7 ∧ acceleratedOrbit 13 8141 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8141 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8141) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8141.1, data_13_8141.2] + +/-- Complete interval computation for depth 13, residue 8142. -/ +theorem bounds_13_8142 : exactInterval 13 8142 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8142 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8142) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8142 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8142 : oddCount 8142 13 = 8 ∧ acceleratedOrbit 13 8142 = 6524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8142 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8142) = 3 ^ 8 * m + 6524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8142.1, data_13_8142.2] + +/-- Complete interval computation for depth 13, residue 8143. -/ +theorem bounds_13_8143 : exactInterval 13 8143 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8143 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8143) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8143 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8143 : oddCount 8143 13 = 8 ∧ acceleratedOrbit 13 8143 = 6524 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8143 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8143) = 3 ^ 8 * m + 6524 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8143.1, data_13_8143.2] + +/-- Complete interval computation for depth 13, residue 8144. -/ +theorem bounds_13_8144 : exactInterval 13 8144 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8144 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8144) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8144 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8144 : oddCount 8144 13 = 7 ∧ acceleratedOrbit 13 8144 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8144 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8144) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8144.1, data_13_8144.2] + +end Collatz.Research.StoppingAtlas.Batch0997 From 465a4808edced455449fa5050c13476cc56f0798 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:37 +0530 Subject: [PATCH 0998/1001] proof: certify atlas Batch0998 (13:8145 to 13:8160) --- Collatz/Research/StoppingAtlas/Batch0998.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0998.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0998.lean b/Collatz/Research/StoppingAtlas/Batch0998.lean new file mode 100644 index 00000000..936cb524 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0998.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0998 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8145. -/ +theorem bounds_13_8145 : exactInterval 13 8145 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8145 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8145) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8145 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8145 : oddCount 8145 13 = 7 ∧ acceleratedOrbit 13 8145 = 2177 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8145 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8145) = 3 ^ 7 * m + 2177 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8145.1, data_13_8145.2] + +/-- Complete interval computation for depth 13, residue 8146. -/ +theorem bounds_13_8146 : exactInterval 13 8146 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8146 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8146) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8146 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8146 : oddCount 8146 13 = 8 ∧ acceleratedOrbit 13 8146 = 6527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8146 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8146) = 3 ^ 8 * m + 6527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8146.1, data_13_8146.2] + +/-- Complete interval computation for depth 13, residue 8147. -/ +theorem bounds_13_8147 : exactInterval 13 8147 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8147 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8147) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8147 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8147 : oddCount 8147 13 = 8 ∧ acceleratedOrbit 13 8147 = 6527 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8147 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8147) = 3 ^ 8 * m + 6527 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8147.1, data_13_8147.2] + +/-- Complete interval computation for depth 13, residue 8148. -/ +theorem bounds_13_8148 : exactInterval 13 8148 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8148 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8148) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8148 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8148 : oddCount 8148 13 = 7 ∧ acceleratedOrbit 13 8148 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8148 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8148) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8148.1, data_13_8148.2] + +/-- Complete interval computation for depth 13, residue 8149. -/ +theorem bounds_13_8149 : exactInterval 13 8149 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8149 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8149) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8149 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8149 : oddCount 8149 13 = 7 ∧ acceleratedOrbit 13 8149 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8149 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8149) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8149.1, data_13_8149.2] + +/-- Complete interval computation for depth 13, residue 8150. -/ +theorem bounds_13_8150 : exactInterval 13 8150 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8150 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8150) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8150 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8150 : oddCount 8150 13 = 9 ∧ acceleratedOrbit 13 8150 = 19592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8150 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8150) = 3 ^ 9 * m + 19592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8150.1, data_13_8150.2] + +/-- Complete interval computation for depth 13, residue 8151. -/ +theorem bounds_13_8151 : exactInterval 13 8151 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8151 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8151) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8151 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8151 : oddCount 8151 13 = 9 ∧ acceleratedOrbit 13 8151 = 19592 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8151 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8151) = 3 ^ 9 * m + 19592 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8151.1, data_13_8151.2] + +/-- Complete interval computation for depth 13, residue 8152. -/ +theorem bounds_13_8152 : exactInterval 13 8152 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8152 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8152) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8152 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8152 : oddCount 8152 13 = 7 ∧ acceleratedOrbit 13 8152 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8152 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8152) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8152.1, data_13_8152.2] + +/-- Complete interval computation for depth 13, residue 8153. -/ +theorem bounds_13_8153 : exactInterval 13 8153 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8153 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8153) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8153 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8153 : oddCount 8153 13 = 6 ∧ acceleratedOrbit 13 8153 = 728 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8153 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8153) = 3 ^ 6 * m + 728 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8153.1, data_13_8153.2] + +/-- Complete interval computation for depth 13, residue 8154. -/ +theorem bounds_13_8154 : exactInterval 13 8154 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8154 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8154) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8154 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8154 : oddCount 8154 13 = 7 ∧ acceleratedOrbit 13 8154 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8154 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8154) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8154.1, data_13_8154.2] + +/-- Complete interval computation for depth 13, residue 8155. -/ +theorem bounds_13_8155 : exactInterval 13 8155 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8155 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8155) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8155 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8155 : oddCount 8155 13 = 9 ∧ acceleratedOrbit 13 8155 = 19601 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8155 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8155) = 3 ^ 9 * m + 19601 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8155.1, data_13_8155.2] + +/-- Complete interval computation for depth 13, residue 8156. -/ +theorem bounds_13_8156 : exactInterval 13 8156 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8156 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8156) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8156 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8156 : oddCount 8156 13 = 7 ∧ acceleratedOrbit 13 8156 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8156 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8156) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8156.1, data_13_8156.2] + +/-- Complete interval computation for depth 13, residue 8157. -/ +theorem bounds_13_8157 : exactInterval 13 8157 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8157 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8157) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8157 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8157 : oddCount 8157 13 = 7 ∧ acceleratedOrbit 13 8157 = 2180 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8157 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8157) = 3 ^ 7 * m + 2180 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8157.1, data_13_8157.2] + +/-- Complete interval computation for depth 13, residue 8158. -/ +theorem bounds_13_8158 : exactInterval 13 8158 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8158 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8158) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8158 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8158 : oddCount 8158 13 = 8 ∧ acceleratedOrbit 13 8158 = 6536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8158 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8158) = 3 ^ 8 * m + 6536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8158.1, data_13_8158.2] + +/-- Complete interval computation for depth 13, residue 8159. -/ +theorem bounds_13_8159 : exactInterval 13 8159 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8159 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8159) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8159 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8159 : oddCount 8159 13 = 8 ∧ acceleratedOrbit 13 8159 = 6536 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8159 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8159) = 3 ^ 8 * m + 6536 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8159.1, data_13_8159.2] + +/-- Complete interval computation for depth 13, residue 8160. -/ +theorem bounds_13_8160 : exactInterval 13 8160 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8160 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8160) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8160 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8160 : oddCount 8160 13 = 8 ∧ acceleratedOrbit 13 8160 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8160 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8160) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8160.1, data_13_8160.2] + +end Collatz.Research.StoppingAtlas.Batch0998 From 89ec2072223065d08ac35c96e14904ba12b169d5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:38 +0530 Subject: [PATCH 0999/1001] proof: certify atlas Batch0999 (13:8161 to 13:8175) --- Collatz/Research/StoppingAtlas/Batch0999.lean | 295 ++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch0999.lean diff --git a/Collatz/Research/StoppingAtlas/Batch0999.lean b/Collatz/Research/StoppingAtlas/Batch0999.lean new file mode 100644 index 00000000..11e32283 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch0999.lean @@ -0,0 +1,295 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch0999 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8161. -/ +theorem bounds_13_8161 : exactInterval 13 8161 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8161 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8161) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8161 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8161 : oddCount 8161 13 = 9 ∧ acceleratedOrbit 13 8161 = 19615 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8161 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8161) = 3 ^ 9 * m + 19615 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8161.1, data_13_8161.2] + +/-- Complete interval computation for depth 13, residue 8162. -/ +theorem bounds_13_8162 : exactInterval 13 8162 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8162 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8162) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8162 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8162 : oddCount 8162 13 = 7 ∧ acceleratedOrbit 13 8162 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8162 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8162) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8162.1, data_13_8162.2] + +/-- Complete interval computation for depth 13, residue 8163. -/ +theorem bounds_13_8163 : exactInterval 13 8163 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8163 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8163) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8163 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8163 : oddCount 8163 13 = 7 ∧ acceleratedOrbit 13 8163 = 2186 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8163 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8163) = 3 ^ 7 * m + 2186 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8163.1, data_13_8163.2] + +/-- Complete interval computation for depth 13, residue 8164. -/ +theorem bounds_13_8164 : exactInterval 13 8164 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8164 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8164) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8164 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8164 : oddCount 8164 13 = 7 ∧ acceleratedOrbit 13 8164 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8164 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8164) = 3 ^ 7 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8164.1, data_13_8164.2] + +/-- Complete interval computation for depth 13, residue 8165. -/ +theorem bounds_13_8165 : exactInterval 13 8165 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8165 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8165) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8165 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8165 : oddCount 8165 13 = 7 ∧ acceleratedOrbit 13 8165 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8165 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8165) = 3 ^ 7 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8165.1, data_13_8165.2] + +/-- Complete interval computation for depth 13, residue 8166. -/ +theorem bounds_13_8166 : exactInterval 13 8166 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8166 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8166) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8166 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8166 : oddCount 8166 13 = 7 ∧ acceleratedOrbit 13 8166 = 2182 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8166 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8166) = 3 ^ 7 * m + 2182 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8166.1, data_13_8166.2] + +/-- Complete interval computation for depth 13, residue 8167. -/ +theorem bounds_13_8167 : exactInterval 13 8167 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8167 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8167) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8167 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8167 : oddCount 8167 13 = 9 ∧ acceleratedOrbit 13 8167 = 19628 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8167 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8167) = 3 ^ 9 * m + 19628 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8167.1, data_13_8167.2] + +/-- Complete interval computation for depth 13, residue 8168. -/ +theorem bounds_13_8168 : exactInterval 13 8168 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8168 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8168) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8168 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8168 : oddCount 8168 13 = 8 ∧ acceleratedOrbit 13 8168 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8168 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8168) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8168.1, data_13_8168.2] + +/-- Complete interval computation for depth 13, residue 8169. -/ +theorem bounds_13_8169 : exactInterval 13 8169 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8169 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8169) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8169 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8169 : oddCount 8169 13 = 8 ∧ acceleratedOrbit 13 8169 = 6544 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8169 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8169) = 3 ^ 8 * m + 6544 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8169.1, data_13_8169.2] + +/-- Complete interval computation for depth 13, residue 8170. -/ +theorem bounds_13_8170 : exactInterval 13 8170 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8170 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8170) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8170 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8170 : oddCount 8170 13 = 8 ∧ acceleratedOrbit 13 8170 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8170 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8170) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8170.1, data_13_8170.2] + +/-- Complete interval computation for depth 13, residue 8171. -/ +theorem bounds_13_8171 : exactInterval 13 8171 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8171 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8171) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8171 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8171 : oddCount 8171 13 = 10 ∧ acceleratedOrbit 13 8171 = 58913 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8171 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8171) = 3 ^ 10 * m + 58913 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8171.1, data_13_8171.2] + +/-- Complete interval computation for depth 13, residue 8172. -/ +theorem bounds_13_8172 : exactInterval 13 8172 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8172 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8172) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8172 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8172 : oddCount 8172 13 = 8 ∧ acceleratedOrbit 13 8172 = 6551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8172 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8172) = 3 ^ 8 * m + 6551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8172.1, data_13_8172.2] + +/-- Complete interval computation for depth 13, residue 8173. -/ +theorem bounds_13_8173 : exactInterval 13 8173 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8173 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8173) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8173 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8173 : oddCount 8173 13 = 8 ∧ acceleratedOrbit 13 8173 = 6551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8173 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8173) = 3 ^ 8 * m + 6551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8173.1, data_13_8173.2] + +/-- Complete interval computation for depth 13, residue 8174. -/ +theorem bounds_13_8174 : exactInterval 13 8174 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8174 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8174) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8174 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8174 : oddCount 8174 13 = 8 ∧ acceleratedOrbit 13 8174 = 6551 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8174 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8174) = 3 ^ 8 * m + 6551 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8174.1, data_13_8174.2] + +/-- Complete interval computation for depth 13, residue 8175. -/ +theorem bounds_13_8175 : exactInterval 13 8175 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8175 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8175) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8175 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8175 : oddCount 8175 13 = 9 ∧ acceleratedOrbit 13 8175 = 19646 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8175 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8175) = 3 ^ 9 * m + 19646 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8175.1, data_13_8175.2] + +end Collatz.Research.StoppingAtlas.Batch0999 From a99424ee3ee81c379c89fa17755f98b8380826ac Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:39:38 +0530 Subject: [PATCH 1000/1001] proof: certify atlas Batch1000 (13:8176 to 13:8191) --- Collatz/Research/StoppingAtlas/Batch1000.lean | 314 ++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/Batch1000.lean diff --git a/Collatz/Research/StoppingAtlas/Batch1000.lean b/Collatz/Research/StoppingAtlas/Batch1000.lean new file mode 100644 index 00000000..0f1a67ad --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Batch1000.lean @@ -0,0 +1,314 @@ +import Collatz.Research.DescentIntervals.Classifier + +namespace Collatz.Research.StoppingAtlas.Batch1000 + +open Collatz.Research.DescentIntervals + +set_option maxRecDepth 20000 +set_option maxHeartbeats 0 + +/-- Complete interval computation for depth 13, residue 8176. -/ +theorem bounds_13_8176 : exactInterval 13 8176 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8176 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8176) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8176 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8176 : oddCount 8176 13 = 9 ∧ acceleratedOrbit 13 8176 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8176 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8176) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8176.1, data_13_8176.2] + +/-- Complete interval computation for depth 13, residue 8177. -/ +theorem bounds_13_8177 : exactInterval 13 8177 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8177 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8177) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8177 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8177 : oddCount 8177 13 = 8 ∧ acceleratedOrbit 13 8177 = 6560 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8177 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8177) = 3 ^ 8 * m + 6560 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8177.1, data_13_8177.2] + +/-- Complete interval computation for depth 13, residue 8178. -/ +theorem bounds_13_8178 : exactInterval 13 8178 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8178 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8178) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8178 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8178 : oddCount 8178 13 = 8 ∧ acceleratedOrbit 13 8178 = 6554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8178 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8178) = 3 ^ 8 * m + 6554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8178.1, data_13_8178.2] + +/-- Complete interval computation for depth 13, residue 8179. -/ +theorem bounds_13_8179 : exactInterval 13 8179 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8179 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8179) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8179 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8179 : oddCount 8179 13 = 8 ∧ acceleratedOrbit 13 8179 = 6554 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8179 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8179) = 3 ^ 8 * m + 6554 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8179.1, data_13_8179.2] + +/-- Complete interval computation for depth 13, residue 8180. -/ +theorem bounds_13_8180 : exactInterval 13 8180 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8180 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8180) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8180 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8180 : oddCount 8180 13 = 9 ∧ acceleratedOrbit 13 8180 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8180 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8180) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8180.1, data_13_8180.2] + +/-- Complete interval computation for depth 13, residue 8181. -/ +theorem bounds_13_8181 : exactInterval 13 8181 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8181 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8181) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8181 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8181 : oddCount 8181 13 = 9 ∧ acceleratedOrbit 13 8181 = 19682 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8181 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8181) = 3 ^ 9 * m + 19682 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8181.1, data_13_8181.2] + +/-- Complete interval computation for depth 13, residue 8182. -/ +theorem bounds_13_8182 : exactInterval 13 8182 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8182 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8182) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8182 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8182 : oddCount 8182 13 = 8 ∧ acceleratedOrbit 13 8182 = 6556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8182 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8182) = 3 ^ 8 * m + 6556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8182.1, data_13_8182.2] + +/-- Complete interval computation for depth 13, residue 8183. -/ +theorem bounds_13_8183 : exactInterval 13 8183 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8183 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8183) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8183 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8183 : oddCount 8183 13 = 8 ∧ acceleratedOrbit 13 8183 = 6556 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8183 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8183) = 3 ^ 8 * m + 6556 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8183.1, data_13_8183.2] + +/-- Complete interval computation for depth 13, residue 8184. -/ +theorem bounds_13_8184 : exactInterval 13 8184 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8184 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8184) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8184 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8184 : oddCount 8184 13 = 10 ∧ acceleratedOrbit 13 8184 = 59048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8184 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8184) = 3 ^ 10 * m + 59048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8184.1, data_13_8184.2] + +/-- Complete interval computation for depth 13, residue 8185. -/ +theorem bounds_13_8185 : exactInterval 13 8185 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8185 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8185) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8185 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8185 : oddCount 8185 13 = 9 ∧ acceleratedOrbit 13 8185 = 19673 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8185 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8185) = 3 ^ 9 * m + 19673 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8185.1, data_13_8185.2] + +/-- Complete interval computation for depth 13, residue 8186. -/ +theorem bounds_13_8186 : exactInterval 13 8186 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8186 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8186) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8186 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8186 : oddCount 8186 13 = 10 ∧ acceleratedOrbit 13 8186 = 59048 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8186 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8186) = 3 ^ 10 * m + 59048 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8186.1, data_13_8186.2] + +/-- Complete interval computation for depth 13, residue 8187. -/ +theorem bounds_13_8187 : exactInterval 13 8187 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8187 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8187) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8187 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8187 : oddCount 8187 13 = 9 ∧ acceleratedOrbit 13 8187 = 19676 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8187 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8187) = 3 ^ 9 * m + 19676 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8187.1, data_13_8187.2] + +/-- Complete interval computation for depth 13, residue 8188. -/ +theorem bounds_13_8188 : exactInterval 13 8188 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8188 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8188) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8188 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8188 : oddCount 8188 13 = 11 ∧ acceleratedOrbit 13 8188 = 177146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8188 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8188) = 3 ^ 11 * m + 177146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8188.1, data_13_8188.2] + +/-- Complete interval computation for depth 13, residue 8189. -/ +theorem bounds_13_8189 : exactInterval 13 8189 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8189 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8189) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8189 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8189 : oddCount 8189 13 = 11 ∧ acceleratedOrbit 13 8189 = 177146 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8189 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8189) = 3 ^ 11 * m + 177146 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8189.1, data_13_8189.2] + +/-- Complete interval computation for depth 13, residue 8190. -/ +theorem bounds_13_8190 : exactInterval 13 8190 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8190 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8190) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8190 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8190 : oddCount 8190 13 = 12 ∧ acceleratedOrbit 13 8190 = 531440 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8190 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8190) = 3 ^ 12 * m + 531440 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8190.1, data_13_8190.2] + +/-- Complete interval computation for depth 13, residue 8191. -/ +theorem bounds_13_8191 : exactInterval 13 8191 = ⟨0, some 0⟩ := by + decide + +/-- Exact classification for every natural class index, not a finite sample. -/ +theorem exact_13_8191 (m : Nat) : + stoppingTime (2 ^ 13 * m + 8191) 13 ↔ 0 ≤ m ∧ m < 0 := by + simpa only [IndexInterval.Contains, and_true] using + exact_of_certificate bounds_13_8191 m + +/-- Independently checked base parity and endpoint arithmetic. -/ +theorem data_13_8191 : oddCount 8191 13 = 13 ∧ acceleratedOrbit 13 8191 = 1594322 := by + decide + +/-- Symbolic endpoint for the entire infinite dyadic class. -/ +theorem endpoint_13_8191 (m : Nat) : + acceleratedOrbit 13 (2 ^ 13 * m + 8191) = 3 ^ 13 * m + 1594322 := by + rw [Congruence.accOrbit_pow_two_mul_add, data_13_8191.1, data_13_8191.2] + +end Collatz.Research.StoppingAtlas.Batch1000 From b83c1d541031521bebb7c3cea76762aad9bf2f16 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 6 Oct 2026 16:44:09 +0530 Subject: [PATCH 1001/1001] feat: extend first-crossing descent to 1538 with audited stopping atlas --- .github/workflows/ci.yml | 3 + Collatz.lean | 1 + Collatz/Research/StoppingAtlas/All.lean | 5 + Collatz/Research/StoppingAtlas/Audit.lean | 61726 ++++++ Collatz/Research/StoppingAtlas/Bridge.lean | 68 + Collatz/Research/StoppingAtlas/Census.lean | 1127 + .../Research/StoppingAtlas/Certificates.lean | 1000 + .../Research/StoppingAtlas/Discrepancy.lean | 90 + Collatz/Research/StoppingAtlas/Events.lean | 124 + Collatz/Research/StoppingAtlas/Horizon.lean | 59 + Collatz/Research/StoppingAtlas/Timing.lean | 47 + README.md | 4 + RESEARCH.md | 12 + Research/StoppingAtlas/.gitignore | 8 + Research/StoppingAtlas/README.md | 171 + Research/StoppingAtlas/axioms.log | 61726 ++++++ Research/StoppingAtlas/batch-receipts.json | 8002 + Research/StoppingAtlas/build.log | 74 + Research/StoppingAtlas/history-check.log | 15 + .../StoppingAtlas/history-verification.json | 14 + Research/StoppingAtlas/manifest.json | 144256 +++++++++++++++ .../negative-insufficient_gap_bound.log | 3 + .../negative-late_descent_is_not_first.log | 3 + ...negative-missing_small_input_exception.log | 3 + .../StoppingAtlas/negative-wrong_cylinder.log | 3 + .../StoppingAtlas/proof-escape-screen.log | 1 + Research/StoppingAtlas/python-tests.json | 38 + Research/StoppingAtlas/python-tests.log | 39 + Research/StoppingAtlas/verification.json | 7148 + scripts/audit_stopping_atlas.py | 125 + scripts/check_stopping_atlas_history.py | 44 + scripts/generate_stopping_census.py | 57 + scripts/stopping_atlas.py | 125 + scripts/test_stopping_atlas.py | 87 + 34 files changed, 286208 insertions(+) create mode 100644 Collatz/Research/StoppingAtlas/All.lean create mode 100644 Collatz/Research/StoppingAtlas/Audit.lean create mode 100644 Collatz/Research/StoppingAtlas/Bridge.lean create mode 100644 Collatz/Research/StoppingAtlas/Census.lean create mode 100644 Collatz/Research/StoppingAtlas/Certificates.lean create mode 100644 Collatz/Research/StoppingAtlas/Discrepancy.lean create mode 100644 Collatz/Research/StoppingAtlas/Events.lean create mode 100644 Collatz/Research/StoppingAtlas/Horizon.lean create mode 100644 Collatz/Research/StoppingAtlas/Timing.lean create mode 100644 Research/StoppingAtlas/.gitignore create mode 100644 Research/StoppingAtlas/README.md create mode 100644 Research/StoppingAtlas/axioms.log create mode 100644 Research/StoppingAtlas/batch-receipts.json create mode 100644 Research/StoppingAtlas/build.log create mode 100644 Research/StoppingAtlas/history-check.log create mode 100644 Research/StoppingAtlas/history-verification.json create mode 100644 Research/StoppingAtlas/manifest.json create mode 100644 Research/StoppingAtlas/negative-insufficient_gap_bound.log create mode 100644 Research/StoppingAtlas/negative-late_descent_is_not_first.log create mode 100644 Research/StoppingAtlas/negative-missing_small_input_exception.log create mode 100644 Research/StoppingAtlas/negative-wrong_cylinder.log create mode 100644 Research/StoppingAtlas/proof-escape-screen.log create mode 100644 Research/StoppingAtlas/python-tests.json create mode 100644 Research/StoppingAtlas/python-tests.log create mode 100644 Research/StoppingAtlas/verification.json create mode 100644 scripts/audit_stopping_atlas.py create mode 100644 scripts/check_stopping_atlas_history.py create mode 100644 scripts/generate_stopping_census.py create mode 100644 scripts/stopping_atlas.py create mode 100644 scripts/test_stopping_atlas.py diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 69996a42..4f3aca62 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -40,3 +40,6 @@ jobs: - name: Check coefficient crossing and interval transfer run: python3 scripts/audit_coefficient_descent.py + + - name: Check stopping atlas and horizon extension + run: python3 scripts/audit_stopping_atlas.py diff --git a/Collatz.lean b/Collatz.lean index 00c82875..3eb0c917 100644 --- a/Collatz.lean +++ b/Collatz.lean @@ -2102,3 +2102,4 @@ import Collatz.Search.InverseIntervalLayers import Collatz.Search.InverseIntervalEarlyStop import Collatz.Strategy.StoppingCorrectionBounds import Collatz.Strategy.ProductDescentCheck +import Collatz.Research.StoppingAtlas.All diff --git a/Collatz/Research/StoppingAtlas/All.lean b/Collatz/Research/StoppingAtlas/All.lean new file mode 100644 index 00000000..f97efa3e --- /dev/null +++ b/Collatz/Research/StoppingAtlas/All.lean @@ -0,0 +1,5 @@ +import Collatz.Research.StoppingAtlas.Bridge +import Collatz.Research.StoppingAtlas.Discrepancy +import Collatz.Research.StoppingAtlas.Certificates +import Collatz.Research.StoppingAtlas.Timing +import Collatz.Research.StoppingAtlas.Census diff --git a/Collatz/Research/StoppingAtlas/Audit.lean b/Collatz/Research/StoppingAtlas/Audit.lean new file mode 100644 index 00000000..511a97a7 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Audit.lean @@ -0,0 +1,61726 @@ +import Collatz.Research.StoppingAtlas.All + +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.bounds_10_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.exact_10_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.data_10_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.bounds_10_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.exact_10_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.data_10_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.bounds_10_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.exact_10_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.data_10_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.bounds_10_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.exact_10_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.data_10_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.bounds_10_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.exact_10_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.data_10_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.bounds_10_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.exact_10_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.data_10_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.bounds_10_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.exact_10_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.data_10_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.bounds_10_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.exact_10_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.data_10_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.bounds_10_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.exact_10_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.data_10_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.bounds_10_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.exact_10_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.data_10_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.bounds_10_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.exact_10_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.data_10_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.bounds_10_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.exact_10_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.data_10_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.bounds_10_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.exact_10_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.data_10_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.bounds_10_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.exact_10_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.data_10_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.bounds_10_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.exact_10_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.data_10_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.bounds_10_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.exact_10_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.data_10_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.bounds_10_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.exact_10_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.data_10_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.bounds_10_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.exact_10_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.data_10_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.bounds_10_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.exact_10_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.data_10_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.bounds_10_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.exact_10_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.data_10_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.bounds_10_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.exact_10_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.data_10_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.bounds_10_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.exact_10_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.data_10_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.bounds_10_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.exact_10_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.data_10_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.bounds_10_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.exact_10_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.data_10_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.bounds_10_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.exact_10_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.data_10_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.bounds_10_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.exact_10_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.data_10_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.bounds_10_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.exact_10_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.data_10_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.bounds_10_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.exact_10_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.data_10_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.bounds_10_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.exact_10_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.data_10_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.bounds_10_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.exact_10_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.data_10_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.bounds_10_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.exact_10_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.data_10_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.bounds_10_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.exact_10_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.data_10_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.bounds_10_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.exact_10_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.data_10_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.bounds_10_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.exact_10_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.data_10_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.bounds_10_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.exact_10_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.data_10_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.bounds_10_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.exact_10_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.data_10_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.bounds_10_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.exact_10_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.data_10_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.bounds_10_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.exact_10_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.data_10_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.bounds_10_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.exact_10_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.data_10_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.bounds_10_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.exact_10_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.data_10_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.bounds_10_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.exact_10_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.data_10_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.bounds_10_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.exact_10_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.data_10_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.bounds_10_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.exact_10_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.data_10_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.bounds_10_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.exact_10_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.data_10_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.bounds_10_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.exact_10_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.data_10_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.bounds_10_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.exact_10_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.data_10_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.bounds_10_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.exact_10_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.data_10_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.bounds_10_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.exact_10_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.data_10_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.bounds_10_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.exact_10_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.data_10_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.bounds_10_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.exact_10_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.data_10_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.bounds_10_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.exact_10_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.data_10_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.bounds_10_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.exact_10_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.data_10_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.bounds_10_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.exact_10_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.data_10_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.bounds_10_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.exact_10_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.data_10_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.bounds_10_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.exact_10_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.data_10_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0055.endpoint_10_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.bounds_10_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.exact_10_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.data_10_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.bounds_10_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.exact_10_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.data_10_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.bounds_10_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.exact_10_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.data_10_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.bounds_10_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.exact_10_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.data_10_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.bounds_10_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.exact_10_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.data_10_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.bounds_10_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.exact_10_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.data_10_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.bounds_10_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.exact_10_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.data_10_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.bounds_10_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.exact_10_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.data_10_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.bounds_10_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.exact_10_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.data_10_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.bounds_10_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.exact_10_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.data_10_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.exact_10_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.data_10_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_10_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_10_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_11_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_11_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_11_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_11_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_11_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_11_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_11_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_11_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_11_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_11_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_11_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_11_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.bounds_11_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.exact_11_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.data_11_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.bounds_11_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.exact_11_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.data_11_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.bounds_11_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.exact_11_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.data_11_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.bounds_11_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.exact_11_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.data_11_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.bounds_11_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.exact_11_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.data_11_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.bounds_11_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.exact_11_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.data_11_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.bounds_11_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.exact_11_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.data_11_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.bounds_11_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.exact_11_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.data_11_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.bounds_11_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.exact_11_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.data_11_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.bounds_11_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.exact_11_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.data_11_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.bounds_11_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.exact_11_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.data_11_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.bounds_11_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.exact_11_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.data_11_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.bounds_11_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.exact_11_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.data_11_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.bounds_11_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.exact_11_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.data_11_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.bounds_11_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.exact_11_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.data_11_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.bounds_11_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.exact_11_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.data_11_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.bounds_11_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.exact_11_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.data_11_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.bounds_11_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.exact_11_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.data_11_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.bounds_11_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.exact_11_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.data_11_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.bounds_11_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.exact_11_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.data_11_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.bounds_11_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.exact_11_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.data_11_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.bounds_11_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.exact_11_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.data_11_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.bounds_11_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.exact_11_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.data_11_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.bounds_11_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.exact_11_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.data_11_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.bounds_11_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.exact_11_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.data_11_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.bounds_11_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.exact_11_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.data_11_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.bounds_11_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.exact_11_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.data_11_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.bounds_11_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.exact_11_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.data_11_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.bounds_11_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.exact_11_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.data_11_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.bounds_11_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.exact_11_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.data_11_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0096.endpoint_11_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.bounds_11_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.exact_11_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.data_11_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0097.endpoint_11_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.bounds_11_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.exact_11_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.data_11_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0098.endpoint_11_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.bounds_11_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.exact_11_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.data_11_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.bounds_11_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.exact_11_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.data_11_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.bounds_11_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.exact_11_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.data_11_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.bounds_11_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.exact_11_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.data_11_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.bounds_11_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.exact_11_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.data_11_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.bounds_11_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.exact_11_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.data_11_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.bounds_11_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.exact_11_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.data_11_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.bounds_11_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.exact_11_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.data_11_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.bounds_11_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.exact_11_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.data_11_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0107.endpoint_11_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.bounds_11_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.exact_11_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.data_11_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.bounds_11_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.exact_11_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.data_11_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.bounds_11_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.exact_11_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.data_11_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.bounds_11_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.exact_11_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.data_11_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.bounds_11_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.exact_11_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.data_11_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.bounds_11_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.exact_11_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.data_11_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.bounds_11_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.exact_11_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.data_11_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.bounds_11_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.exact_11_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.data_11_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.bounds_11_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.exact_11_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.data_11_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.bounds_11_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.exact_11_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.data_11_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.bounds_11_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.exact_11_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.data_11_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.bounds_11_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.exact_11_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.data_11_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.bounds_11_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.exact_11_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.data_11_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.bounds_11_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.exact_11_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.data_11_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.bounds_11_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.exact_11_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.data_11_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.bounds_11_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.exact_11_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.data_11_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.bounds_11_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.exact_11_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.data_11_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.bounds_11_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.exact_11_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.data_11_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.bounds_11_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.exact_11_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.data_11_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.bounds_11_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.exact_11_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.data_11_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.bounds_11_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.exact_11_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.data_11_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.bounds_11_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.exact_11_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.data_11_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.bounds_11_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.exact_11_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.data_11_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.bounds_11_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.exact_11_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.data_11_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.bounds_11_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.exact_11_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.data_11_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.exact_11_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.data_11_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.exact_11_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.data_11_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.exact_11_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.data_11_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.exact_11_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.data_11_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.exact_11_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.data_11_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.exact_11_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.data_11_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.exact_11_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.data_11_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.exact_11_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.data_11_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.exact_11_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.data_11_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.exact_11_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.data_11_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.exact_11_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.data_11_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.exact_11_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.data_11_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.exact_11_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.data_11_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.exact_11_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.data_11_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.exact_11_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.data_11_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.exact_11_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.data_11_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.exact_11_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.data_11_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.exact_11_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.data_11_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.exact_11_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.data_11_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.exact_11_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.data_11_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.exact_11_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.data_11_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.exact_11_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.data_11_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.exact_11_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.data_11_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.exact_11_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.data_11_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.exact_11_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.data_11_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.exact_11_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.data_11_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.exact_11_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.data_11_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.exact_11_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.data_11_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.exact_11_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.data_11_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.exact_11_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.data_11_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.exact_11_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.data_11_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.exact_11_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.data_11_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.exact_11_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.data_11_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.exact_11_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.data_11_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.exact_11_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.data_11_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.exact_11_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.data_11_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.exact_11_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.data_11_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.exact_11_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.data_11_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.exact_11_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.data_11_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.exact_11_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.data_11_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.exact_11_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.data_11_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.exact_11_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.data_11_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.exact_11_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.data_11_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.exact_11_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.data_11_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.exact_11_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.data_11_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.exact_11_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.data_11_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.exact_11_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.data_11_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.exact_11_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.data_11_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.exact_11_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.data_11_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.exact_11_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.data_11_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.exact_11_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.data_11_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.exact_11_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.data_11_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.exact_11_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.data_11_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.exact_11_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.data_11_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.exact_11_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.data_11_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.exact_11_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.data_11_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.exact_11_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.data_11_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.exact_11_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.data_11_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.exact_11_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.data_11_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.exact_11_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.data_11_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.exact_11_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.data_11_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.exact_11_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.data_11_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.exact_11_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.data_11_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.exact_11_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.data_11_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.bounds_11_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.exact_11_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.data_11_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.exact_11_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.data_11_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.exact_11_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.data_11_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.exact_11_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.data_11_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.bounds_12_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.exact_12_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.data_12_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.bounds_12_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.exact_12_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.data_12_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.bounds_12_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.exact_12_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.data_12_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.bounds_12_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.exact_12_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.data_12_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.bounds_12_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.exact_12_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.data_12_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.bounds_12_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.exact_12_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.data_12_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.bounds_12_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.exact_12_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.data_12_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.bounds_12_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.exact_12_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.data_12_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.bounds_12_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.exact_12_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.data_12_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.bounds_12_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.exact_12_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.data_12_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.bounds_12_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.exact_12_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.data_12_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.bounds_12_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.exact_12_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.data_12_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.bounds_12_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.exact_12_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.data_12_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0213.endpoint_12_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.bounds_12_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.exact_12_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.data_12_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.bounds_12_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.exact_12_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.data_12_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.bounds_12_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.exact_12_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.data_12_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.bounds_12_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.exact_12_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.data_12_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.bounds_12_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.exact_12_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.data_12_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.bounds_12_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.exact_12_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.data_12_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.bounds_12_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.exact_12_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.data_12_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.bounds_12_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.exact_12_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.data_12_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.bounds_12_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.exact_12_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.data_12_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.bounds_12_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.exact_12_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.data_12_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.bounds_12_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.exact_12_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.data_12_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.bounds_12_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.exact_12_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.data_12_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.bounds_12_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.exact_12_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.data_12_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.bounds_12_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.exact_12_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.data_12_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.bounds_12_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.exact_12_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.data_12_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.bounds_12_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.exact_12_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.data_12_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.bounds_12_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.exact_12_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.data_12_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.bounds_12_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.exact_12_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.data_12_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.bounds_12_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.exact_12_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.data_12_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.bounds_12_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.exact_12_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.data_12_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.bounds_12_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.exact_12_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.data_12_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.bounds_12_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.exact_12_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.data_12_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.bounds_12_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.exact_12_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.data_12_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.bounds_12_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.exact_12_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.data_12_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.bounds_12_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.exact_12_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.data_12_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.bounds_12_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.exact_12_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.data_12_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.bounds_12_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.exact_12_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.data_12_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.bounds_12_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.exact_12_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.data_12_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.bounds_12_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.exact_12_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.data_12_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.bounds_12_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.exact_12_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.data_12_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.bounds_12_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.exact_12_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.data_12_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.bounds_12_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.exact_12_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.data_12_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.bounds_12_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.exact_12_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.data_12_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.bounds_12_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.exact_12_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.data_12_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.bounds_12_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.exact_12_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.data_12_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.bounds_12_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.exact_12_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.data_12_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.bounds_12_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.exact_12_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.data_12_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.bounds_12_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.exact_12_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.data_12_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.bounds_12_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.exact_12_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.data_12_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.bounds_12_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.exact_12_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.data_12_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.bounds_12_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.exact_12_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.data_12_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.bounds_12_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.exact_12_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.data_12_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.bounds_12_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.exact_12_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.data_12_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.bounds_12_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.exact_12_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.data_12_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.bounds_12_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.exact_12_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.data_12_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.bounds_12_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.exact_12_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.data_12_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.bounds_12_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.exact_12_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.data_12_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.bounds_12_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.exact_12_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.data_12_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.bounds_12_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.exact_12_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.data_12_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.bounds_12_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.exact_12_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.data_12_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.bounds_12_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.exact_12_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.data_12_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.bounds_12_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.exact_12_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.data_12_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.exact_12_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.data_12_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.exact_12_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.data_12_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.exact_12_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.data_12_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.exact_12_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.data_12_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.exact_12_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.data_12_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.exact_12_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.data_12_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.exact_12_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.data_12_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.exact_12_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.data_12_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.exact_12_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.data_12_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.exact_12_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.data_12_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.exact_12_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.data_12_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.exact_12_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.data_12_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.exact_12_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.data_12_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.exact_12_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.data_12_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.exact_12_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.data_12_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.exact_12_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.data_12_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.exact_12_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.data_12_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.exact_12_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.data_12_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.exact_12_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.data_12_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.exact_12_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.data_12_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.exact_12_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.data_12_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.exact_12_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.data_12_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.exact_12_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.data_12_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.exact_12_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.data_12_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.exact_12_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.data_12_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.exact_12_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.data_12_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.exact_12_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.data_12_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.exact_12_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.data_12_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.exact_12_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.data_12_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.exact_12_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.data_12_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.exact_12_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.data_12_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.exact_12_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.data_12_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.exact_12_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.data_12_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.exact_12_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.data_12_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.exact_12_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.data_12_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.exact_12_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.data_12_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.exact_12_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.data_12_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.exact_12_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.data_12_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.exact_12_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.data_12_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.exact_12_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.data_12_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.exact_12_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.data_12_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.exact_12_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.data_12_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.exact_12_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.data_12_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.exact_12_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.data_12_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.exact_12_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.data_12_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.exact_12_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.data_12_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.exact_12_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.data_12_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.exact_12_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.data_12_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.exact_12_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.data_12_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.exact_12_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.data_12_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.bounds_12_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.exact_12_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.data_12_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0316.endpoint_12_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.exact_12_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.data_12_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.exact_12_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.data_12_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.exact_12_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.data_12_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.exact_12_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.data_12_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.exact_12_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.data_12_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.exact_12_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.data_12_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.exact_12_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.data_12_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.exact_12_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.data_12_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.exact_12_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.data_12_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.exact_12_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.data_12_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.exact_12_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.data_12_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.exact_12_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.data_12_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.exact_12_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.data_12_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.exact_12_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.data_12_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.exact_12_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.data_12_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.exact_12_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.data_12_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.exact_12_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.data_12_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.exact_12_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.data_12_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.exact_12_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.data_12_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.exact_12_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.data_12_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.exact_12_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.data_12_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.exact_12_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.data_12_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.exact_12_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.data_12_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.exact_12_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.data_12_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.exact_12_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.data_12_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.exact_12_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.data_12_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.exact_12_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.data_12_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.exact_12_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.data_12_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.exact_12_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.data_12_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.exact_12_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.data_12_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.exact_12_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.data_12_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.exact_12_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.data_12_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.exact_12_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.data_12_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.exact_12_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.data_12_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.exact_12_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.data_12_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.exact_12_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.data_12_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.exact_12_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.data_12_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.exact_12_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.data_12_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.exact_12_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.data_12_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.exact_12_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.data_12_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.exact_12_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.data_12_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.exact_12_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.data_12_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.exact_12_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.data_12_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.exact_12_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.data_12_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.exact_12_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.data_12_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.exact_12_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.data_12_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.exact_12_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.data_12_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.exact_12_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.data_12_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.exact_12_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.data_12_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.exact_12_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.data_12_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.exact_12_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.data_12_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.exact_12_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.data_12_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.exact_12_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.data_12_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.exact_12_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.data_12_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.exact_12_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.data_12_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.exact_12_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.data_12_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.exact_12_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.data_12_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.exact_12_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.data_12_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.exact_12_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.data_12_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.exact_12_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.data_12_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.exact_12_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.data_12_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.exact_12_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.data_12_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.exact_12_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.data_12_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.exact_12_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.data_12_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.exact_12_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.data_12_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.exact_12_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.data_12_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.exact_12_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.data_12_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.exact_12_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.data_12_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.exact_12_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.data_12_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.exact_12_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.data_12_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.exact_12_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.data_12_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.exact_12_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.data_12_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.exact_12_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.data_12_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.exact_12_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.data_12_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.exact_12_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.data_12_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.exact_12_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.data_12_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.exact_12_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.data_12_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.exact_12_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.data_12_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.exact_12_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.data_12_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.exact_12_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.data_12_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.exact_12_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.data_12_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.exact_12_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.data_12_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.exact_12_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.data_12_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.exact_12_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.data_12_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.exact_12_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.data_12_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.exact_12_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.data_12_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.exact_12_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.data_12_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.exact_12_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.data_12_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.exact_12_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.data_12_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.exact_12_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.data_12_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.exact_12_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.data_12_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.exact_12_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.data_12_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.exact_12_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.data_12_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.exact_12_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.data_12_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.exact_12_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.data_12_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.exact_12_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.data_12_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.exact_12_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.data_12_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.exact_12_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.data_12_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.exact_12_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.data_12_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.exact_12_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.data_12_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.exact_12_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.data_12_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.exact_12_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.data_12_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.exact_12_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.data_12_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.exact_12_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.data_12_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.exact_12_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.data_12_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.exact_12_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.data_12_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.exact_12_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.data_12_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.exact_12_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.data_12_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.exact_12_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.data_12_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.exact_12_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.data_12_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.exact_12_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.data_12_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.exact_12_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.data_12_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.exact_12_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.data_12_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.exact_12_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.data_12_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.exact_12_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.data_12_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.exact_12_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.data_12_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.exact_12_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.data_12_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.exact_12_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.data_12_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.exact_12_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.data_12_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.exact_12_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.data_12_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.exact_12_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.data_12_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.exact_12_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.data_12_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.exact_12_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.data_12_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.exact_12_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.data_12_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.exact_12_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.data_12_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.exact_12_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.data_12_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.exact_12_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.data_12_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.exact_12_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.data_12_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.exact_12_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.data_12_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.exact_12_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.data_12_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.exact_12_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.data_12_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.exact_12_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.data_12_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.exact_12_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.data_12_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.exact_12_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.data_12_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.exact_12_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.data_12_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.exact_12_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.data_12_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.exact_12_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.data_12_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.exact_12_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.data_12_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.exact_12_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.data_12_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.exact_12_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.data_12_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.exact_12_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.data_12_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.exact_12_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.data_12_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.exact_12_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.data_12_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.exact_12_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.data_12_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.exact_12_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.data_12_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.exact_12_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.data_12_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.exact_12_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.data_12_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.exact_12_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.data_12_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.exact_12_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.data_12_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.exact_12_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.data_12_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_12_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_12_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_13_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_13_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_13_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_0 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_13_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_13_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_13_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_1 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_13_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_13_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_13_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_2 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_13_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_13_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_13_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_3 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.bounds_13_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.exact_13_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.data_13_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_4 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_5 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_6 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_7 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_8 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_9 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_10 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_11 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_12 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_13 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_14 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_15 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_16 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_17 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_18 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.bounds_13_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.exact_13_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.data_13_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_19 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_20 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_21 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_22 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_23 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_24 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_25 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_26 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_27 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_28 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_29 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_30 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_31 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_32 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_33 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.bounds_13_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.exact_13_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.data_13_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_34 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_35 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_36 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_37 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_38 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_39 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_40 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_41 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_42 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_43 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_44 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_45 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_46 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_47 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_48 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_49 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.bounds_13_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.exact_13_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.data_13_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_50 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_51 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_52 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_53 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_54 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_55 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_56 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_57 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_58 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_59 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_60 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_61 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_62 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_63 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_64 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.bounds_13_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.exact_13_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.data_13_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_65 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_66 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_67 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_68 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_69 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_70 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_71 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_72 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_73 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_74 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_75 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_76 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_77 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_78 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_79 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.bounds_13_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.exact_13_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.data_13_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_80 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_81 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_82 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_83 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_84 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_85 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_86 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_87 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_88 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_89 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_90 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_91 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_92 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_93 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_94 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_95 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.bounds_13_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.exact_13_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.data_13_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_96 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_97 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_98 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_99 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_100 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_101 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_102 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_103 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_104 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_105 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_106 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_107 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_108 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_109 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_110 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.bounds_13_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.exact_13_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.data_13_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_111 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_112 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_113 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_114 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_115 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_116 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_117 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_118 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_119 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_120 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_121 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_122 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_123 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_124 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_125 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_126 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.bounds_13_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.exact_13_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.data_13_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_127 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_128 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_129 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_130 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_131 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_132 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_133 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_134 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_135 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_136 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_137 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_138 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_139 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_140 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_141 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.bounds_13_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.exact_13_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.data_13_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_142 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_143 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_144 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_145 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_146 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_147 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_148 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_149 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_150 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_151 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_152 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_153 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_154 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_155 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_156 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.bounds_13_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.exact_13_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.data_13_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_157 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_158 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_159 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_160 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_161 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_162 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_163 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_164 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_165 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_166 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_167 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_168 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_169 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_170 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_171 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_172 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.bounds_13_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.exact_13_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.data_13_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_173 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_174 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_175 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_176 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_177 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_178 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_179 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_180 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_181 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_182 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_183 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_184 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_185 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_186 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_187 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.bounds_13_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.exact_13_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.data_13_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_188 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_189 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_190 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_191 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_192 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_193 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_194 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_195 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_196 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_197 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_198 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_199 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_200 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_201 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_202 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.bounds_13_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.exact_13_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.data_13_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_203 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_204 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_205 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_206 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_207 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_208 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_209 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_210 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_211 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_212 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_213 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_214 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_215 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_216 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_217 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_218 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.bounds_13_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.exact_13_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.data_13_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_219 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_220 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_221 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_222 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_223 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_224 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_225 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_226 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_227 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_228 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_229 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_230 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_231 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_232 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_233 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.bounds_13_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.exact_13_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.data_13_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_234 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_235 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_236 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_237 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_238 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_239 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_240 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_241 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_242 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_243 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_244 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_245 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_246 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_247 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_248 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.bounds_13_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.exact_13_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.data_13_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_249 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_250 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_251 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_252 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_253 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_254 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_255 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_256 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_257 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_258 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_259 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_260 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_261 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_262 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_263 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_264 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.bounds_13_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.exact_13_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.data_13_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_265 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_266 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_267 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_268 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_269 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_270 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_271 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_272 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_273 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_274 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_275 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_276 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_277 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_278 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_279 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.bounds_13_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.exact_13_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.data_13_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_280 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_281 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_282 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_283 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_284 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_285 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_286 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_287 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_288 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_289 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_290 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_291 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_292 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_293 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_294 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.bounds_13_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.exact_13_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.data_13_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_295 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_296 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_297 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_298 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_299 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_300 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_301 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_302 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_303 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_304 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_305 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_306 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_307 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_308 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_309 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_310 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.bounds_13_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.exact_13_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.data_13_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_311 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_312 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_313 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_314 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_315 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_316 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_317 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_318 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_319 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_320 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_321 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_322 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_323 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_324 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_325 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.bounds_13_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.exact_13_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.data_13_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_326 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_327 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_328 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_329 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_330 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_331 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_332 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_333 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_334 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_335 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_336 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_337 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_338 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_339 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_340 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_341 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.bounds_13_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.exact_13_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.data_13_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_342 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_343 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_344 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_345 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_346 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_347 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_348 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_349 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_350 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_351 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_352 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_353 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_354 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_355 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_356 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.bounds_13_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.exact_13_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.data_13_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0490.endpoint_13_357 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_358 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_359 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_360 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_361 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_362 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_363 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_364 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_365 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_366 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_367 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_368 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_369 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_370 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_371 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.bounds_13_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.exact_13_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.data_13_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0491.endpoint_13_372 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_373 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_374 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_375 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_376 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_377 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_378 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_379 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_380 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_381 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_382 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_383 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_384 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_385 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_386 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_387 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.bounds_13_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.exact_13_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.data_13_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_388 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_389 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_390 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_391 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_392 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_393 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_394 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_395 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_396 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_397 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_398 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_399 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_400 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_401 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_402 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.bounds_13_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.exact_13_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.data_13_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_403 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_404 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_405 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_406 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_407 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_408 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_409 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_410 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_411 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_412 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_413 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_414 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_415 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_416 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_417 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.bounds_13_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.exact_13_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.data_13_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_418 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_419 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_420 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_421 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_422 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_423 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_424 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_425 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_426 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_427 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_428 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_429 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_430 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_431 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_432 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_433 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.bounds_13_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.exact_13_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.data_13_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_434 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_435 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_436 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_437 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_438 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_439 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_440 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_441 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_442 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_443 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_444 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_445 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_446 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_447 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_448 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.bounds_13_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.exact_13_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.data_13_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_449 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_450 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_451 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_452 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_453 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_454 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_455 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_456 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_457 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_458 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_459 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_460 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_461 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_462 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_463 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.bounds_13_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.exact_13_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.data_13_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0497.endpoint_13_464 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_465 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_466 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_467 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_468 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_469 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_470 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_471 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_472 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_473 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_474 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_475 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_476 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_477 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_478 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_479 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.bounds_13_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.exact_13_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.data_13_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_480 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_481 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_482 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_483 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_484 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_485 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_486 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_487 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_488 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_489 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_490 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_491 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_492 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_493 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_494 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.bounds_13_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.exact_13_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.data_13_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_495 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_496 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_497 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_498 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_499 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_500 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_501 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_502 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_503 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_504 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_505 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_506 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_507 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_508 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_509 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_510 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.bounds_13_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.exact_13_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.data_13_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_511 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_512 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_513 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_514 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_515 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_516 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_517 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_518 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_519 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_520 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_521 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_522 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_523 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_524 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_525 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.bounds_13_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.exact_13_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.data_13_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_526 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_527 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_528 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_529 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_530 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_531 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_532 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_533 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_534 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_535 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_536 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_537 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_538 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_539 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_540 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.bounds_13_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.exact_13_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.data_13_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_541 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_542 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_543 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_544 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_545 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_546 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_547 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_548 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_549 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_550 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_551 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_552 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_553 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_554 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_555 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_556 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.bounds_13_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.exact_13_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.data_13_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_557 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_558 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_559 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_560 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_561 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_562 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_563 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_564 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_565 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_566 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_567 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_568 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_569 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_570 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_571 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.bounds_13_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.exact_13_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.data_13_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_572 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_573 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_574 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_575 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_576 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_577 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_578 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_579 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_580 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_581 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_582 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_583 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_584 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_585 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_586 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.bounds_13_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.exact_13_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.data_13_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_587 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_588 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_589 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_590 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_591 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_592 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_593 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_594 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_595 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_596 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_597 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_598 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_599 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_600 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_601 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_602 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.bounds_13_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.exact_13_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.data_13_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_603 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_604 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_605 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_606 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_607 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_608 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_609 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_610 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_611 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_612 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_613 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_614 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_615 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_616 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_617 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.bounds_13_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.exact_13_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.data_13_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_618 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_619 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_620 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_621 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_622 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_623 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_624 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_625 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_626 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_627 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_628 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_629 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_630 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_631 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_632 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.bounds_13_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.exact_13_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.data_13_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_633 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_634 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_635 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_636 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_637 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_638 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_639 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_640 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_641 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_642 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_643 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_644 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_645 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_646 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_647 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_648 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.bounds_13_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.exact_13_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.data_13_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_649 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_650 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_651 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_652 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_653 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_654 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_655 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_656 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_657 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_658 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_659 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_660 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_661 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_662 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_663 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.bounds_13_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.exact_13_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.data_13_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_664 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_665 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_666 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_667 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_668 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_669 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_670 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_671 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_672 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_673 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_674 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_675 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_676 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_677 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_678 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.bounds_13_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.exact_13_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.data_13_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_679 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_680 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_681 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_682 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_683 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_684 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_685 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_686 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_687 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_688 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_689 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_690 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_691 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_692 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_693 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_694 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.bounds_13_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.exact_13_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.data_13_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_695 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_696 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_697 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_698 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_699 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_700 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_701 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_702 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_703 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_704 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_705 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_706 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_707 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_708 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_709 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.bounds_13_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.exact_13_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.data_13_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_710 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_711 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_712 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_713 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_714 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_715 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_716 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_717 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_718 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_719 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_720 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_721 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_722 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_723 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_724 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_725 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.bounds_13_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.exact_13_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.data_13_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_726 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_727 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_728 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_729 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_730 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_731 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_732 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_733 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_734 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_735 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_736 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_737 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_738 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_739 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_740 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.bounds_13_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.exact_13_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.data_13_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_741 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_742 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_743 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_744 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_745 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_746 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_747 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_748 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_749 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_750 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_751 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_752 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_753 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_754 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_755 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.bounds_13_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.exact_13_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.data_13_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_756 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_757 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_758 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_759 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_760 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_761 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_762 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_763 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_764 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_765 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_766 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_767 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_768 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_769 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_770 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_771 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.bounds_13_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.exact_13_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.data_13_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_772 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_773 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_774 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_775 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_776 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_777 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_778 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_779 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_780 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_781 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_782 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_783 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_784 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_785 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_786 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.bounds_13_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.exact_13_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.data_13_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_787 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_788 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_789 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_790 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_791 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_792 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_793 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_794 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_795 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_796 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_797 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_798 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_799 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_800 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_801 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.bounds_13_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.exact_13_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.data_13_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_802 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_803 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_804 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_805 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_806 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_807 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_808 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_809 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_810 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_811 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_812 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_813 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_814 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_815 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_816 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_817 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.bounds_13_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.exact_13_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.data_13_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_818 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_819 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_820 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_821 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_822 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_823 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_824 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_825 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_826 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_827 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_828 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_829 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_830 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_831 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_832 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.bounds_13_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.exact_13_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.data_13_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_833 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_834 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_835 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_836 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_837 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_838 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_839 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_840 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_841 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_842 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_843 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_844 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_845 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_846 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_847 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.bounds_13_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.exact_13_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.data_13_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_848 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_849 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_850 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_851 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_852 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_853 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_854 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_855 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_856 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_857 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_858 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_859 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_860 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_861 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_862 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_863 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.bounds_13_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.exact_13_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.data_13_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_864 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_865 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_866 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_867 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_868 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_869 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_870 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_871 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_872 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_873 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_874 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_875 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_876 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_877 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_878 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.bounds_13_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.exact_13_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.data_13_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_879 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_880 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_881 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_882 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_883 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_884 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_885 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_886 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_887 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_888 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_889 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_890 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_891 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_892 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_893 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_894 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.bounds_13_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.exact_13_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.data_13_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_895 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_896 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_897 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_898 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_899 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_900 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_901 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_902 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_903 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_904 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_905 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_906 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_907 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_908 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_909 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.bounds_13_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.exact_13_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.data_13_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_910 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_911 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_912 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_913 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_914 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_915 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_916 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_917 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_918 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_919 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_920 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_921 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_922 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_923 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_924 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.bounds_13_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.exact_13_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.data_13_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_925 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_926 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_927 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_928 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_929 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_930 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_931 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_932 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_933 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_934 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_935 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_936 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_937 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_938 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_939 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_940 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.bounds_13_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.exact_13_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.data_13_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_941 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_942 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_943 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_944 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_945 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_946 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_947 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_948 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_949 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_950 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_951 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_952 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_953 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_954 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_955 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.bounds_13_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.exact_13_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.data_13_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_956 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_957 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_958 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_959 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_960 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_961 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_962 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_963 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_964 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_965 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_966 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_967 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_968 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_969 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_970 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.bounds_13_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.exact_13_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.data_13_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_971 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_972 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_973 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_974 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_975 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_976 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_977 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_978 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_979 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_980 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_981 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_982 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_983 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_984 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_985 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_986 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.bounds_13_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.exact_13_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.data_13_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_987 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_988 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_989 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_990 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_991 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_992 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_993 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_994 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_995 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_996 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_997 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_998 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_999 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_1000 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_1001 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.bounds_13_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.exact_13_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.data_13_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_1002 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1003 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1004 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1005 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1006 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1007 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1008 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1009 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1010 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1011 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1012 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1013 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1014 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1015 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1016 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.exact_13_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.data_13_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1017 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1018 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1019 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1020 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1021 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1022 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1023 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1024 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1025 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1026 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1027 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1028 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1029 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1030 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1031 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1032 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.exact_13_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.data_13_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1033 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1034 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1035 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1036 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1037 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1038 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1039 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1040 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1041 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1042 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1043 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1044 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1045 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1046 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1047 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.exact_13_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.data_13_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1048 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1049 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1050 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1051 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1052 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1053 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1054 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1055 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1056 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1057 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1058 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1059 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1060 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1061 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1062 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.exact_13_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.data_13_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1063 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1064 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1065 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1066 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1067 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1068 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1069 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1070 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1071 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1072 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1073 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1074 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1075 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1076 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1077 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1078 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.exact_13_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.data_13_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1079 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1080 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1081 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1082 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1083 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1084 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1085 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1086 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1087 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1088 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1089 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1090 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1091 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1092 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1093 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.exact_13_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.data_13_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1094 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1095 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1096 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1097 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1098 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1099 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1100 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1101 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1102 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1103 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1104 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1105 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1106 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1107 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1108 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1109 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.exact_13_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.data_13_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1110 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1111 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1112 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1113 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1114 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1115 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1116 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1117 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1118 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1119 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1120 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1121 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1122 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1123 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1124 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.exact_13_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.data_13_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1125 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1126 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1127 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1128 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1129 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1130 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1131 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1132 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1133 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1134 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1135 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1136 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1137 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1138 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1139 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.exact_13_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.data_13_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1140 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1141 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1142 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1143 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1144 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1145 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1146 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1147 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1148 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1149 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1150 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1151 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1152 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1153 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1154 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1155 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.exact_13_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.data_13_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1156 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1157 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1158 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1159 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1160 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1161 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1162 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1163 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1164 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1165 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1166 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1167 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1168 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1169 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1170 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.exact_13_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.data_13_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1171 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1172 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1173 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1174 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1175 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1176 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1177 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1178 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1179 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1180 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1181 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1182 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1183 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1184 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1185 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.exact_13_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.data_13_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1186 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1187 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1188 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1189 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1190 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1191 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1192 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1193 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1194 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1195 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1196 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1197 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1198 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1199 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1200 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1201 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.exact_13_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.data_13_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1202 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1203 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1204 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1205 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1206 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1207 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1208 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1209 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1210 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1211 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1212 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1213 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1214 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1215 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1216 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.exact_13_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.data_13_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1217 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1218 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1219 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1220 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1221 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1222 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1223 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1224 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1225 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1226 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1227 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1228 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1229 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1230 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1231 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.exact_13_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.data_13_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1232 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1233 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1234 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1235 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1236 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1237 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1238 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1239 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1240 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1241 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1242 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1243 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1244 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1245 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1246 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1247 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.exact_13_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.data_13_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1248 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1249 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1250 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1251 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1252 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1253 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1254 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1255 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1256 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1257 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1258 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1259 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1260 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1261 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1262 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.exact_13_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.data_13_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1263 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1264 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1265 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1266 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1267 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1268 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1269 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1270 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1271 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1272 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1273 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1274 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1275 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1276 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1277 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1278 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.exact_13_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.data_13_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1279 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1280 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1281 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1282 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1283 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1284 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1285 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1286 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1287 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1288 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1289 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1290 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1291 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1292 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1293 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.exact_13_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.data_13_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1294 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1295 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1296 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1297 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1298 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1299 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1300 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1301 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1302 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1303 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1304 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1305 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1306 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1307 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1308 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.exact_13_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.data_13_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1309 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1310 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1311 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1312 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1313 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1314 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1315 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1316 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1317 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1318 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1319 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1320 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1321 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1322 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1323 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1324 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.exact_13_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.data_13_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1325 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1326 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1327 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1328 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1329 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1330 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1331 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1332 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1333 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1334 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1335 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1336 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1337 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1338 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1339 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.exact_13_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.data_13_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1340 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1341 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1342 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1343 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1344 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1345 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1346 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1347 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1348 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1349 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1350 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1351 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1352 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1353 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1354 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.exact_13_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.data_13_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1355 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1356 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1357 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1358 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1359 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1360 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1361 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1362 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1363 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1364 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1365 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1366 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1367 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1368 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1369 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1370 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.exact_13_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.data_13_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1371 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1372 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1373 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1374 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1375 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1376 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1377 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1378 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1379 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1380 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1381 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1382 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1383 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1384 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1385 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.exact_13_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.data_13_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1386 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1387 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1388 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1389 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1390 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1391 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1392 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1393 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1394 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1395 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1396 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1397 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1398 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1399 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1400 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.exact_13_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.data_13_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1401 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1402 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1403 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1404 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1405 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1406 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1407 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1408 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1409 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1410 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1411 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1412 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1413 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1414 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1415 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1416 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.exact_13_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.data_13_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1417 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1418 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1419 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1420 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1421 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1422 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1423 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1424 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1425 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1426 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1427 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1428 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1429 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1430 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1431 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.exact_13_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.data_13_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1432 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1433 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1434 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1435 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1436 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1437 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1438 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1439 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1440 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1441 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1442 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1443 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1444 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1445 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1446 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.exact_13_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.data_13_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1447 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1448 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1449 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1450 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1451 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1452 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1453 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1454 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1455 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1456 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1457 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1458 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1459 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1460 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1461 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1462 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.exact_13_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.data_13_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1463 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1464 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1465 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1466 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1467 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1468 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1469 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1470 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1471 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1472 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1473 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1474 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1475 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1476 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1477 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.exact_13_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.data_13_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1478 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1479 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1480 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1481 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1482 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1483 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1484 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1485 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1486 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1487 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1488 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1489 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1490 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1491 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1492 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1493 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.exact_13_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.data_13_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1494 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1495 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1496 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1497 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1498 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1499 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1500 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1501 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1502 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1503 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1504 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1505 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1506 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1507 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1508 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.exact_13_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.data_13_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1509 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1510 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1511 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1512 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1513 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1514 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1515 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1516 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1517 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1518 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1519 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1520 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1521 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1522 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1523 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.exact_13_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.data_13_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1524 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1525 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1526 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1527 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1528 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1529 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1530 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1531 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1532 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1533 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1534 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1535 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1536 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1537 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1538 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1539 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.exact_13_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.data_13_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1540 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1541 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1542 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1543 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1544 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1545 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1546 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1547 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1548 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1549 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1550 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1551 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1552 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1553 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1554 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.exact_13_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.data_13_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1555 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1556 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1557 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1558 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1559 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1560 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1561 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1562 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1563 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1564 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1565 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1566 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1567 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1568 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1569 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.exact_13_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.data_13_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1570 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1571 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1572 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1573 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1574 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1575 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1576 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1577 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1578 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1579 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1580 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1581 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1582 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1583 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1584 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1585 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.exact_13_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.data_13_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1586 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1587 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1588 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1589 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1590 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1591 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1592 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1593 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1594 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1595 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1596 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1597 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1598 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1599 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1600 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.exact_13_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.data_13_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1601 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1602 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1603 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1604 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1605 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1606 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1607 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1608 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1609 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1610 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1611 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1612 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1613 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1614 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1615 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.exact_13_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.data_13_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1616 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1617 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1618 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1619 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1620 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1621 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1622 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1623 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1624 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1625 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1626 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1627 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1628 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1629 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1630 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1631 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.exact_13_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.data_13_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1632 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1633 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1634 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1635 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1636 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1637 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1638 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1639 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1640 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1641 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1642 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1643 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1644 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1645 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1646 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.exact_13_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.data_13_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1647 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1648 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1649 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1650 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1651 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1652 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1653 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1654 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1655 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1656 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1657 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1658 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1659 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1660 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1661 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1662 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.exact_13_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.data_13_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1663 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1664 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1665 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1666 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1667 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1668 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1669 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1670 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1671 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1672 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1673 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1674 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1675 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1676 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1677 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.exact_13_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.data_13_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1678 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1679 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1680 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1681 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1682 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1683 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1684 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1685 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1686 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1687 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1688 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1689 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1690 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1691 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1692 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.exact_13_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.data_13_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1693 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1694 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1695 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1696 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1697 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1698 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1699 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1700 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1701 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1702 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1703 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1704 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1705 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1706 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1707 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1708 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.exact_13_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.data_13_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1709 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1710 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1711 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1712 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1713 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1714 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1715 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1716 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1717 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1718 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1719 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1720 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1721 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1722 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1723 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.exact_13_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.data_13_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1724 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1725 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1726 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1727 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1728 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1729 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1730 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1731 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1732 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1733 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1734 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1735 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1736 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1737 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1738 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.exact_13_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.data_13_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1739 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1740 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1741 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1742 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1743 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1744 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1745 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1746 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1747 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1748 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1749 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1750 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1751 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1752 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1753 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1754 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.exact_13_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.data_13_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1755 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1756 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1757 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1758 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1759 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1760 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1761 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1762 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1763 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1764 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1765 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1766 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1767 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1768 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1769 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.exact_13_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.data_13_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1770 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1771 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1772 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1773 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1774 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1775 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1776 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1777 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1778 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1779 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1780 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1781 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1782 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1783 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1784 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.exact_13_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.data_13_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1785 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1786 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1787 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1788 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1789 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1790 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1791 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1792 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1793 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1794 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1795 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1796 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1797 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1798 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1799 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1800 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.exact_13_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.data_13_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1801 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1802 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1803 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1804 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1805 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1806 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1807 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1808 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1809 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1810 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1811 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1812 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1813 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1814 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1815 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.exact_13_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.data_13_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1816 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1817 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1818 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1819 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1820 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1821 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1822 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1823 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1824 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1825 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1826 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1827 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1828 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1829 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1830 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.exact_13_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.data_13_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1831 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1832 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1833 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1834 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1835 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1836 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1837 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1838 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1839 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1840 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1841 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1842 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1843 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1844 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1845 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1846 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.exact_13_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.data_13_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1847 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1848 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1849 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1850 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1851 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1852 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1853 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1854 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1855 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1856 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1857 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1858 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1859 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1860 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1861 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.exact_13_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.data_13_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1862 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1863 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1864 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1865 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1866 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1867 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1868 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1869 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1870 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1871 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1872 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1873 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1874 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1875 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1876 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1877 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.exact_13_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.data_13_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1878 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1879 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1880 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1881 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1882 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1883 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1884 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1885 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1886 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1887 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1888 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1889 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1890 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1891 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1892 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.exact_13_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.data_13_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1893 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1894 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1895 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1896 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1897 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1898 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1899 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1900 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1901 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1902 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1903 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1904 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1905 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1906 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1907 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.exact_13_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.data_13_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1908 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1909 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1910 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1911 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1912 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1913 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1914 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1915 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1916 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1917 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1918 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1919 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1920 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1921 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1922 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1923 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.exact_13_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.data_13_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1924 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1925 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1926 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1927 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1928 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1929 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1930 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1931 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1932 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1933 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1934 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1935 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1936 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1937 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1938 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.exact_13_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.data_13_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1939 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1940 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1941 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1942 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1943 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1944 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1945 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1946 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1947 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1948 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1949 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1950 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1951 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1952 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1953 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.exact_13_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.data_13_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1954 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1955 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1956 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1957 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1958 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1959 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1960 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1961 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1962 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1963 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1964 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1965 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1966 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1967 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1968 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1969 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.exact_13_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.data_13_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1970 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1971 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1972 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1973 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1974 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1975 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1976 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1977 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1978 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1979 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1980 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1981 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1982 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1983 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1984 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.exact_13_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.data_13_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1985 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1986 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1987 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1988 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1989 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1990 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1991 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1992 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1993 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1994 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1995 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1996 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1997 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1998 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1999 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.bounds_13_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.exact_13_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.data_13_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_2000 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2001 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2002 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2003 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2004 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2005 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2006 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2007 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2008 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2009 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2010 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2011 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2012 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2013 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2014 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2015 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.exact_13_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.data_13_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2016 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2017 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2018 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2019 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2020 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2021 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2022 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2023 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2024 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2025 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2026 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2027 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2028 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2029 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2030 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.exact_13_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.data_13_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2031 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2032 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2033 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2034 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2035 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2036 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2037 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2038 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2039 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2040 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2041 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2042 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2043 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2044 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2045 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2046 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.exact_13_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.data_13_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2047 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2048 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2049 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2050 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2051 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2052 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2053 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2054 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2055 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2056 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2057 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2058 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2059 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2060 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2061 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.exact_13_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.data_13_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2062 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2063 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2064 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2065 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2066 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2067 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2068 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2069 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2070 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2071 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2072 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2073 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2074 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2075 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2076 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.exact_13_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.data_13_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2077 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2078 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2079 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2080 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2081 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2082 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2083 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2084 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2085 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2086 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2087 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2088 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2089 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2090 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2091 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2092 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.exact_13_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.data_13_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2093 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2094 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2095 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2096 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2097 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2098 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2099 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2100 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2101 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2102 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2103 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2104 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2105 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2106 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2107 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.exact_13_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.data_13_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2108 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2109 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2110 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2111 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2112 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2113 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2114 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2115 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2116 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2117 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2118 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2119 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2120 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2121 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2122 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.exact_13_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.data_13_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2123 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2124 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2125 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2126 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2127 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2128 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2129 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2130 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2131 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2132 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2133 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2134 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2135 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2136 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2137 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2138 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.exact_13_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.data_13_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2139 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2140 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2141 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2142 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2143 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2144 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2145 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2146 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2147 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2148 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2149 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2150 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2151 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2152 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2153 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.exact_13_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.data_13_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2154 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2155 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2156 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2157 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2158 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2159 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2160 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2161 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2162 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2163 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2164 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2165 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2166 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2167 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2168 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.exact_13_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.data_13_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2169 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2170 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2171 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2172 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2173 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2174 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2175 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2176 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2177 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2178 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2179 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2180 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2181 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2182 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2183 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2184 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.exact_13_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.data_13_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2185 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2186 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2187 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2188 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2189 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2190 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2191 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2192 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2193 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2194 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2195 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2196 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2197 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2198 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2199 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.exact_13_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.data_13_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2200 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2201 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2202 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2203 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2204 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2205 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2206 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2207 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2208 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2209 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2210 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2211 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2212 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2213 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2214 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.exact_13_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.data_13_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2215 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2216 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2217 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2218 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2219 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2220 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2221 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2222 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2223 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2224 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2225 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2226 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2227 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2228 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2229 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2230 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.exact_13_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.data_13_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2231 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2232 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2233 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2234 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2235 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2236 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2237 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2238 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2239 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2240 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2241 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2242 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2243 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2244 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2245 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.bounds_13_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.exact_13_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.data_13_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0613.endpoint_13_2246 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2247 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2248 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2249 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2250 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2251 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2252 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2253 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2254 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2255 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2256 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2257 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2258 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2259 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2260 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2261 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.exact_13_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.data_13_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2262 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2263 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2264 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2265 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2266 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2267 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2268 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2269 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2270 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2271 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2272 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2273 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2274 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2275 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2276 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.exact_13_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.data_13_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2277 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2278 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2279 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2280 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2281 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2282 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2283 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2284 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2285 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2286 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2287 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2288 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2289 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2290 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2291 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.exact_13_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.data_13_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2292 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2293 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2294 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2295 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2296 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2297 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2298 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2299 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2300 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2301 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2302 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2303 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2304 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2305 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2306 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2307 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.exact_13_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.data_13_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2308 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2309 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2310 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2311 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2312 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2313 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2314 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2315 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2316 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2317 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2318 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2319 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2320 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2321 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2322 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.exact_13_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.data_13_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2323 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2324 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2325 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2326 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2327 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2328 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2329 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2330 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2331 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2332 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2333 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2334 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2335 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2336 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2337 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.exact_13_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.data_13_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2338 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2339 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2340 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2341 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2342 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2343 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2344 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2345 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2346 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2347 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2348 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2349 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2350 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2351 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2352 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2353 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.exact_13_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.data_13_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2354 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2355 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2356 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2357 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2358 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2359 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2360 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2361 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2362 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2363 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2364 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2365 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2366 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2367 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2368 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.exact_13_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.data_13_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2369 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2370 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2371 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2372 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2373 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2374 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2375 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2376 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2377 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2378 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2379 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2380 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2381 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2382 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2383 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.exact_13_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.data_13_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2384 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2385 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2386 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2387 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2388 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2389 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2390 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2391 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2392 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2393 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2394 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2395 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2396 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2397 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2398 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2399 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.exact_13_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.data_13_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2400 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2401 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2402 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2403 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2404 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2405 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2406 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2407 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2408 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2409 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2410 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2411 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2412 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2413 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2414 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.exact_13_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.data_13_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2415 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2416 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2417 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2418 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2419 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2420 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2421 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2422 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2423 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2424 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2425 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2426 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2427 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2428 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2429 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2430 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.exact_13_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.data_13_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2431 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2432 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2433 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2434 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2435 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2436 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2437 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2438 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2439 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2440 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2441 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2442 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2443 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2444 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2445 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.exact_13_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.data_13_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2446 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2447 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2448 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2449 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2450 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2451 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2452 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2453 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2454 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2455 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2456 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2457 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2458 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2459 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2460 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.exact_13_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.data_13_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2461 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2462 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2463 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2464 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2465 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2466 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2467 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2468 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2469 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2470 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2471 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2472 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2473 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2474 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2475 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2476 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.exact_13_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.data_13_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2477 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2478 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2479 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2480 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2481 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2482 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2483 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2484 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2485 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2486 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2487 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2488 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2489 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2490 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2491 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.exact_13_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.data_13_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2492 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2493 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2494 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2495 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2496 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2497 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2498 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2499 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2500 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2501 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2502 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2503 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2504 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2505 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2506 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.exact_13_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.data_13_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2507 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2508 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2509 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2510 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2511 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2512 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2513 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2514 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2515 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2516 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2517 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2518 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2519 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2520 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2521 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2522 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.exact_13_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.data_13_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2523 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2524 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2525 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2526 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2527 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2528 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2529 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2530 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2531 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2532 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2533 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2534 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2535 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2536 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2537 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.exact_13_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.data_13_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2538 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2539 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2540 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2541 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2542 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2543 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2544 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2545 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2546 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2547 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2548 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2549 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2550 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2551 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2552 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.exact_13_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.data_13_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2553 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2554 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2555 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2556 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2557 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2558 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2559 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2560 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2561 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2562 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2563 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2564 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2565 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2566 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2567 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2568 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.exact_13_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.data_13_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2569 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2570 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2571 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2572 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2573 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2574 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2575 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2576 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2577 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2578 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2579 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2580 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2581 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2582 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2583 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.exact_13_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.data_13_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2584 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2585 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2586 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2587 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2588 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2589 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2590 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2591 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2592 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2593 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2594 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2595 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2596 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2597 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2598 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.exact_13_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.data_13_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2599 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2600 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2601 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2602 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2603 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2604 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2605 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2606 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2607 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2608 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2609 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2610 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2611 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2612 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2613 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2614 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.exact_13_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.data_13_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2615 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2616 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2617 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2618 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2619 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2620 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2621 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2622 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2623 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2624 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2625 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2626 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2627 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2628 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2629 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.exact_13_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.data_13_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2630 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2631 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2632 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2633 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2634 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2635 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2636 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2637 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2638 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2639 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2640 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2641 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2642 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2643 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2644 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2645 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.exact_13_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.data_13_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2646 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2647 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2648 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2649 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2650 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2651 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2652 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2653 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2654 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2655 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2656 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2657 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2658 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2659 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2660 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.exact_13_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.data_13_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2661 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2662 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2663 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2664 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2665 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2666 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2667 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2668 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2669 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2670 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2671 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2672 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2673 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2674 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2675 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.exact_13_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.data_13_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2676 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2677 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2678 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2679 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2680 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2681 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2682 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2683 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2684 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2685 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2686 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2687 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2688 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2689 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2690 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2691 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.exact_13_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.data_13_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2692 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2693 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2694 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2695 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2696 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2697 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2698 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2699 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2700 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2701 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2702 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2703 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2704 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2705 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2706 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.exact_13_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.data_13_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2707 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2708 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2709 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2710 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2711 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2712 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2713 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2714 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2715 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2716 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2717 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2718 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2719 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2720 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2721 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.exact_13_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.data_13_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2722 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2723 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2724 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2725 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2726 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2727 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2728 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2729 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2730 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2731 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2732 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2733 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2734 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2735 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2736 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2737 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.exact_13_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.data_13_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2738 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2739 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2740 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2741 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2742 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2743 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2744 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2745 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2746 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2747 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2748 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2749 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2750 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2751 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2752 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.exact_13_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.data_13_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2753 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2754 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2755 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2756 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2757 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2758 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2759 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2760 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2761 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2762 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2763 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2764 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2765 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2766 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2767 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.exact_13_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.data_13_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2768 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2769 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2770 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2771 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2772 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2773 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2774 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2775 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2776 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2777 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2778 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2779 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2780 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2781 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2782 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2783 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.exact_13_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.data_13_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2784 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2785 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2786 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2787 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2788 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2789 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2790 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2791 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2792 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2793 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2794 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2795 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2796 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2797 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2798 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.exact_13_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.data_13_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2799 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2800 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2801 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2802 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2803 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2804 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2805 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2806 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2807 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2808 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2809 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2810 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2811 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2812 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2813 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2814 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.exact_13_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.data_13_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2815 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2816 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2817 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2818 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2819 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2820 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2821 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2822 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2823 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2824 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2825 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2826 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2827 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2828 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2829 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.exact_13_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.data_13_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2830 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2831 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2832 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2833 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2834 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2835 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2836 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2837 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2838 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2839 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2840 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2841 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2842 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2843 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2844 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.exact_13_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.data_13_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2845 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2846 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2847 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2848 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2849 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2850 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2851 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2852 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2853 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2854 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2855 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2856 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2857 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2858 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2859 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2860 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.exact_13_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.data_13_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2861 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2862 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2863 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2864 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2865 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2866 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2867 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2868 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2869 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2870 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2871 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2872 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2873 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2874 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2875 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.exact_13_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.data_13_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2876 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2877 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2878 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2879 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2880 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2881 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2882 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2883 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2884 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2885 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2886 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2887 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2888 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2889 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2890 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.exact_13_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.data_13_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2891 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2892 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2893 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2894 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2895 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2896 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2897 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2898 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2899 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2900 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2901 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2902 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2903 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2904 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2905 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2906 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.exact_13_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.data_13_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2907 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2908 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2909 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2910 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2911 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2912 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2913 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2914 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2915 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2916 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2917 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2918 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2919 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2920 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2921 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.exact_13_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.data_13_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2922 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2923 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2924 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2925 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2926 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2927 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2928 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2929 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2930 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2931 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2932 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2933 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2934 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2935 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2936 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.exact_13_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.data_13_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2937 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2938 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2939 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2940 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2941 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2942 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2943 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2944 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2945 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2946 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2947 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2948 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2949 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2950 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2951 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2952 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.exact_13_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.data_13_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2953 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2954 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2955 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2956 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2957 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2958 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2959 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2960 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2961 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2962 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2963 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2964 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2965 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2966 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2967 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.exact_13_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.data_13_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2968 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2969 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2970 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2971 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2972 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2973 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2974 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2975 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2976 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2977 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2978 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2979 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2980 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2981 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2982 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.exact_13_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.data_13_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2983 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2984 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2985 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2986 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2987 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2988 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2989 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2990 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2991 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2992 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2993 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2994 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2995 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2996 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2997 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2998 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.exact_13_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.data_13_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2999 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3000 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3001 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3002 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3003 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3004 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3005 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3006 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3007 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3008 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3009 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3010 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3011 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3012 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3013 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.exact_13_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.data_13_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3014 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3015 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3016 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3017 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3018 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3019 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3020 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3021 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3022 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3023 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3024 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3025 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3026 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3027 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3028 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3029 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.exact_13_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.data_13_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3030 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3031 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3032 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3033 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3034 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3035 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3036 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3037 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3038 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3039 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3040 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3041 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3042 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3043 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3044 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.exact_13_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.data_13_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3045 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3046 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3047 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3048 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3049 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3050 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3051 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3052 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3053 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3054 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3055 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3056 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3057 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3058 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3059 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.exact_13_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.data_13_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3060 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3061 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3062 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3063 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3064 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3065 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3066 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3067 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3068 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3069 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3070 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3071 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3072 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3073 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3074 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3075 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.exact_13_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.data_13_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3076 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3077 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3078 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3079 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3080 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3081 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3082 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3083 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3084 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3085 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3086 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3087 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3088 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3089 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3090 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.exact_13_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.data_13_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3091 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3092 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3093 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3094 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3095 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3096 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3097 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3098 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3099 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3100 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3101 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3102 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3103 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3104 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3105 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.exact_13_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.data_13_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3106 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3107 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3108 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3109 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3110 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3111 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3112 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3113 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3114 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3115 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3116 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3117 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3118 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3119 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3120 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3121 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.exact_13_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.data_13_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3122 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3123 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3124 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3125 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3126 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3127 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3128 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3129 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3130 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3131 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3132 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3133 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3134 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3135 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3136 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.exact_13_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.data_13_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3137 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3138 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3139 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3140 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3141 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3142 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3143 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3144 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3145 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3146 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3147 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3148 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3149 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3150 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3151 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.exact_13_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.data_13_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3152 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3153 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3154 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3155 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3156 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3157 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3158 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3159 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3160 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3161 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3162 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3163 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3164 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3165 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3166 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3167 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.exact_13_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.data_13_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3168 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3169 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3170 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3171 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3172 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3173 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3174 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3175 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3176 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3177 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3178 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3179 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3180 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3181 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3182 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.exact_13_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.data_13_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3183 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3184 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3185 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3186 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3187 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3188 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3189 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3190 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3191 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3192 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3193 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3194 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3195 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3196 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3197 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3198 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.exact_13_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.data_13_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3199 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3200 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3201 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3202 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3203 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3204 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3205 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3206 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3207 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3208 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3209 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3210 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3211 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3212 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3213 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.exact_13_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.data_13_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3214 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3215 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3216 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3217 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3218 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3219 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3220 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3221 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3222 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3223 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3224 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3225 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3226 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3227 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3228 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.exact_13_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.data_13_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3229 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3230 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3231 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3232 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3233 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3234 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3235 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3236 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3237 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3238 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3239 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3240 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3241 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3242 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3243 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3244 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.exact_13_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.data_13_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3245 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3246 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3247 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3248 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3249 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3250 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3251 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3252 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3253 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3254 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3255 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3256 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3257 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3258 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3259 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.exact_13_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.data_13_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3260 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3261 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3262 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3263 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3264 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3265 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3266 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3267 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3268 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3269 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3270 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3271 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3272 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3273 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3274 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.exact_13_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.data_13_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3275 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3276 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3277 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3278 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3279 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3280 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3281 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3282 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3283 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3284 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3285 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3286 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3287 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3288 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3289 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3290 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.exact_13_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.data_13_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3291 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3292 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3293 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3294 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3295 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3296 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3297 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3298 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3299 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3300 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3301 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3302 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3303 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3304 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3305 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.exact_13_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.data_13_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3306 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3307 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3308 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3309 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3310 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3311 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3312 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3313 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3314 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3315 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3316 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3317 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3318 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3319 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3320 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.exact_13_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.data_13_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3321 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3322 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3323 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3324 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3325 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3326 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3327 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3328 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3329 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3330 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3331 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3332 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3333 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3334 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3335 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3336 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.exact_13_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.data_13_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3337 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3338 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3339 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3340 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3341 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3342 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3343 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3344 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3345 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3346 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3347 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3348 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3349 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3350 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3351 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.exact_13_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.data_13_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3352 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3353 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3354 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3355 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3356 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3357 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3358 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3359 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3360 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3361 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3362 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3363 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3364 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3365 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3366 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.exact_13_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.data_13_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3367 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3368 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3369 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3370 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3371 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3372 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3373 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3374 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3375 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3376 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3377 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3378 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3379 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3380 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3381 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3382 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.exact_13_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.data_13_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3383 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3384 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3385 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3386 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3387 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3388 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3389 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3390 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3391 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3392 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3393 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3394 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3395 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3396 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3397 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.exact_13_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.data_13_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3398 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3399 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3400 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3401 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3402 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3403 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3404 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3405 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3406 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3407 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3408 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3409 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3410 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3411 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3412 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3413 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.exact_13_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.data_13_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3414 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3415 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3416 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3417 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3418 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3419 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3420 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3421 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3422 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3423 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3424 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3425 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3426 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3427 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3428 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.exact_13_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.data_13_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3429 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3430 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3431 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3432 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3433 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3434 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3435 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3436 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3437 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3438 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3439 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3440 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3441 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3442 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3443 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.exact_13_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.data_13_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3444 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3445 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3446 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3447 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3448 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3449 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3450 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3451 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3452 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3453 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3454 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3455 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3456 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3457 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3458 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3459 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.exact_13_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.data_13_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3460 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3461 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3462 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3463 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3464 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3465 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3466 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3467 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3468 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3469 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3470 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3471 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3472 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3473 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3474 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.exact_13_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.data_13_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3475 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3476 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3477 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3478 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3479 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3480 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3481 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3482 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3483 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3484 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3485 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3486 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3487 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3488 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3489 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.exact_13_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.data_13_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3490 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3491 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3492 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3493 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3494 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3495 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3496 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3497 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3498 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3499 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3500 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3501 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3502 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3503 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3504 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3505 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.exact_13_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.data_13_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3506 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3507 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3508 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3509 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3510 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3511 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3512 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3513 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3514 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3515 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3516 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3517 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3518 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3519 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3520 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.exact_13_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.data_13_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3521 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3522 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3523 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3524 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3525 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3526 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3527 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3528 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3529 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3530 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3531 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3532 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3533 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3534 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3535 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.exact_13_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.data_13_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3536 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3537 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3538 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3539 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3540 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3541 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3542 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3543 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3544 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3545 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3546 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3547 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3548 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3549 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3550 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3551 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.exact_13_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.data_13_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3552 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3553 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3554 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3555 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3556 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3557 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3558 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3559 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3560 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3561 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3562 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3563 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3564 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3565 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3566 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.exact_13_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.data_13_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3567 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3568 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3569 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3570 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3571 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3572 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3573 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3574 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3575 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3576 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3577 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3578 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3579 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3580 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3581 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3582 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.exact_13_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.data_13_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3583 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3584 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3585 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3586 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3587 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3588 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3589 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3590 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3591 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3592 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3593 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3594 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3595 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3596 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3597 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.exact_13_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.data_13_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3598 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3599 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3600 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3601 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3602 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3603 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3604 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3605 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3606 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3607 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3608 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3609 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3610 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3611 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3612 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.exact_13_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.data_13_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3613 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3614 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3615 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3616 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3617 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3618 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3619 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3620 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3621 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3622 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3623 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3624 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3625 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3626 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3627 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3628 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.exact_13_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.data_13_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3629 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3630 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3631 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3632 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3633 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3634 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3635 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3636 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3637 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3638 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3639 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3640 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3641 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3642 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3643 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.exact_13_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.data_13_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3644 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3645 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3646 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3647 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3648 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3649 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3650 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3651 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3652 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3653 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3654 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3655 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3656 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3657 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3658 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.exact_13_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.data_13_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3659 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3660 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3661 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3662 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3663 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3664 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3665 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3666 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3667 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3668 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3669 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3670 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3671 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3672 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3673 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3674 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.exact_13_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.data_13_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3675 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3676 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3677 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3678 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3679 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3680 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3681 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3682 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3683 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3684 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3685 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3686 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3687 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3688 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3689 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.exact_13_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.data_13_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3690 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3691 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3692 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3693 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3694 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3695 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3696 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3697 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3698 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3699 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3700 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3701 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3702 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3703 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3704 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.exact_13_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.data_13_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3705 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3706 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3707 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3708 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3709 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3710 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3711 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3712 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3713 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3714 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3715 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3716 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3717 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3718 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3719 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3720 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.exact_13_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.data_13_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3721 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3722 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3723 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3724 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3725 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3726 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3727 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3728 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3729 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3730 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3731 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3732 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3733 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3734 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3735 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.exact_13_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.data_13_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3736 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3737 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3738 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3739 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3740 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3741 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3742 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3743 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3744 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3745 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3746 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3747 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3748 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3749 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3750 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.exact_13_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.data_13_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3751 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3752 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3753 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3754 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3755 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3756 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3757 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3758 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3759 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3760 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3761 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3762 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3763 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3764 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3765 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3766 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.exact_13_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.data_13_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3767 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3768 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3769 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3770 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3771 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3772 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3773 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3774 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3775 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3776 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3777 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3778 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3779 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3780 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3781 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.exact_13_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.data_13_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3782 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3783 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3784 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3785 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3786 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3787 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3788 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3789 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3790 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3791 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3792 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3793 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3794 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3795 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3796 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3797 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.exact_13_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.data_13_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3798 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3799 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3800 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3801 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3802 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3803 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3804 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3805 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3806 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3807 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3808 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3809 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3810 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3811 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3812 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.exact_13_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.data_13_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3813 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3814 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3815 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3816 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3817 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3818 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3819 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3820 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3821 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3822 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3823 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3824 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3825 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3826 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3827 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.exact_13_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.data_13_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3828 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3829 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3830 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3831 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3832 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3833 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3834 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3835 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3836 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3837 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3838 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3839 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3840 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3841 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3842 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3843 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.exact_13_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.data_13_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3844 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3845 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3846 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3847 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3848 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3849 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3850 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3851 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3852 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3853 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3854 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3855 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3856 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3857 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3858 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.exact_13_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.data_13_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3859 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3860 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3861 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3862 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3863 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3864 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3865 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3866 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3867 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3868 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3869 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3870 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3871 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3872 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3873 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.exact_13_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.data_13_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3874 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3875 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3876 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3877 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3878 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3879 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3880 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3881 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3882 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3883 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3884 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3885 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3886 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3887 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3888 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3889 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.exact_13_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.data_13_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3890 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3891 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3892 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3893 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3894 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3895 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3896 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3897 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3898 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3899 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3900 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3901 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3902 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3903 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3904 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.exact_13_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.data_13_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3905 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3906 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3907 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3908 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3909 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3910 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3911 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3912 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3913 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3914 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3915 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3916 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3917 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3918 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3919 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.exact_13_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.data_13_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3920 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3921 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3922 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3923 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3924 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3925 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3926 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3927 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3928 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3929 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3930 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3931 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3932 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3933 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3934 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3935 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.exact_13_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.data_13_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3936 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3937 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3938 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3939 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3940 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3941 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3942 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3943 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3944 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3945 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3946 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3947 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3948 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3949 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3950 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.exact_13_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.data_13_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3951 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3952 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3953 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3954 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3955 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3956 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3957 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3958 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3959 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3960 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3961 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3962 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3963 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3964 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3965 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3966 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.exact_13_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.data_13_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3967 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3968 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3969 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3970 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3971 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3972 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3973 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3974 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3975 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3976 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3977 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3978 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3979 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3980 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3981 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.exact_13_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.data_13_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3982 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3983 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3984 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3985 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3986 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3987 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3988 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3989 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3990 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3991 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3992 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3993 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3994 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3995 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3996 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.exact_13_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.data_13_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3997 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_3998 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_3999 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4000 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4001 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4002 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4003 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4004 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4005 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4006 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4007 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4008 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4009 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4010 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4011 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4012 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.exact_13_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.data_13_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4013 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4014 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4015 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4016 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4017 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4018 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4019 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4020 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4021 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4022 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4023 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4024 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4025 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4026 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4027 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.exact_13_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.data_13_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4028 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4029 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4030 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4031 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4032 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4033 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4034 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4035 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4036 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4037 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4038 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4039 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4040 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4041 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4042 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.exact_13_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.data_13_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4043 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4044 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4045 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4046 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4047 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4048 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4049 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4050 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4051 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4052 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4053 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4054 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4055 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4056 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4057 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4058 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.exact_13_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.data_13_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4059 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4060 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4061 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4062 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4063 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4064 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4065 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4066 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4067 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4068 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4069 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4070 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4071 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4072 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4073 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.exact_13_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.data_13_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4074 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4075 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4076 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4077 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4078 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4079 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4080 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4081 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4082 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4083 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4084 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4085 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4086 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4087 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4088 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.exact_13_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.data_13_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4089 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4090 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4091 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4092 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4093 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4094 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4095 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4096 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4096 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4096 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4096 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4097 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4097 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4097 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4097 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4098 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4098 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4098 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4098 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4099 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4099 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4099 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4099 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4100 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4100 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4100 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4100 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4101 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4101 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4101 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4101 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4102 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4102 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4102 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4102 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4103 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4103 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4103 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4103 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4104 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4104 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4104 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4104 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4105 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.exact_13_4105 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.data_13_4105 +#print axioms Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4105 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4106 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4106 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4106 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4106 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4107 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4107 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4107 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4107 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4108 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4108 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4108 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4108 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4109 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4109 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4109 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4109 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4110 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4110 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4110 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4110 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4111 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4111 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4111 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4111 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4112 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4112 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4112 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4112 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4113 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4113 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4113 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4113 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4114 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4114 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4114 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4114 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4115 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4115 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4115 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4115 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4116 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4116 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4116 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4116 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4117 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4117 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4117 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4117 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4118 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4118 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4118 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4118 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4119 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4119 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4119 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4119 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4120 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.exact_13_4120 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.data_13_4120 +#print axioms Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4120 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4121 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4121 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4121 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4121 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4122 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4122 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4122 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4122 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4123 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4123 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4123 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4123 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4124 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4124 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4124 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4124 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4125 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4125 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4125 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4125 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4126 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4126 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4126 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4126 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4127 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4127 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4127 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4127 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4128 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4128 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4128 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4128 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4129 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4129 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4129 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4129 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4130 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4130 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4130 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4130 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4131 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4131 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4131 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4131 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4132 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4132 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4132 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4132 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4133 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4133 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4133 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4133 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4134 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4134 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4134 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4134 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4135 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.exact_13_4135 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.data_13_4135 +#print axioms Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4135 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4136 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4136 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4136 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4136 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4137 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4137 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4137 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4137 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4138 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4138 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4138 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4138 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4139 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4139 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4139 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4139 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4140 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4140 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4140 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4140 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4141 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4141 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4141 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4141 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4142 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4142 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4142 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4142 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4143 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4143 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4143 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4143 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4144 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4144 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4144 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4144 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4145 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4145 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4145 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4145 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4146 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4146 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4146 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4146 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4147 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4147 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4147 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4147 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4148 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4148 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4148 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4148 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4149 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4149 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4149 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4149 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4150 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4150 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4150 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4150 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4151 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.exact_13_4151 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.data_13_4151 +#print axioms Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4151 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4152 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4152 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4152 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4152 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4153 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4153 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4153 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4153 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4154 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4154 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4154 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4154 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4155 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4155 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4155 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4155 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4156 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4156 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4156 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4156 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4157 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4157 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4157 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4157 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4158 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4158 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4158 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4158 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4159 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4159 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4159 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4159 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4160 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4160 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4160 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4160 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4161 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4161 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4161 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4161 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4162 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4162 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4162 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4162 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4163 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4163 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4163 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4163 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4164 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4164 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4164 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4164 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4165 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4165 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4165 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4165 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4166 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.exact_13_4166 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.data_13_4166 +#print axioms Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4166 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4167 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4167 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4167 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4167 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4168 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4168 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4168 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4168 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4169 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4169 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4169 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4169 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4170 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4170 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4170 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4170 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4171 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4171 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4171 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4171 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4172 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4172 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4172 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4172 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4173 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4173 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4173 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4173 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4174 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4174 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4174 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4174 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4175 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4175 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4175 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4175 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4176 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4176 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4176 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4176 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4177 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4177 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4177 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4177 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4178 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4178 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4178 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4178 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4179 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4179 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4179 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4179 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4180 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4180 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4180 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4180 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4181 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4181 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4181 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4181 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4182 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.exact_13_4182 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.data_13_4182 +#print axioms Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4182 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4183 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4183 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4183 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4183 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4184 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4184 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4184 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4184 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4185 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4185 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4185 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4185 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4186 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4186 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4186 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4186 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4187 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4187 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4187 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4187 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4188 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4188 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4188 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4188 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4189 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4189 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4189 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4189 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4190 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4190 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4190 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4190 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4191 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4191 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4191 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4191 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4192 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4192 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4192 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4192 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4193 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4193 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4193 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4193 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4194 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4194 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4194 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4194 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4195 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4195 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4195 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4195 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4196 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4196 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4196 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4196 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4197 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.exact_13_4197 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.data_13_4197 +#print axioms Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4197 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4198 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4198 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4198 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4198 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4199 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4199 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4199 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4199 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4200 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4200 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4200 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4200 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4201 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4201 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4201 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4201 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4202 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4202 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4202 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4202 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4203 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4203 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4203 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4203 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4204 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4204 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4204 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4204 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4205 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4205 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4205 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4205 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4206 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4206 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4206 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4206 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4207 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4207 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4207 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4207 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4208 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4208 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4208 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4208 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4209 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4209 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4209 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4209 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4210 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4210 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4210 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4210 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4211 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4211 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4211 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4211 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4212 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.exact_13_4212 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.data_13_4212 +#print axioms Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4212 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4213 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4213 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4213 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4213 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4214 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4214 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4214 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4214 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4215 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4215 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4215 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4215 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4216 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4216 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4216 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4216 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4217 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4217 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4217 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4217 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4218 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4218 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4218 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4218 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4219 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4219 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4219 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4219 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4220 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4220 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4220 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4220 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4221 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4221 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4221 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4221 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4222 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4222 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4222 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4222 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4223 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4223 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4223 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4223 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4224 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4224 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4224 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4224 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4225 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4225 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4225 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4225 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4226 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4226 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4226 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4226 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4227 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4227 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4227 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4227 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4228 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.exact_13_4228 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.data_13_4228 +#print axioms Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4228 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4229 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4229 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4229 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4229 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4230 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4230 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4230 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4230 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4231 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4231 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4231 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4231 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4232 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4232 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4232 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4232 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4233 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4233 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4233 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4233 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4234 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4234 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4234 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4234 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4235 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4235 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4235 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4235 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4236 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4236 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4236 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4236 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4237 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4237 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4237 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4237 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4238 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4238 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4238 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4238 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4239 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4239 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4239 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4239 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4240 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4240 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4240 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4240 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4241 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4241 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4241 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4241 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4242 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4242 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4242 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4242 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4243 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.exact_13_4243 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.data_13_4243 +#print axioms Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4243 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4244 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4244 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4244 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4244 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4245 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4245 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4245 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4245 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4246 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4246 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4246 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4246 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4247 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4247 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4247 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4247 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4248 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4248 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4248 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4248 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4249 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4249 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4249 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4249 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4250 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4250 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4250 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4250 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4251 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4251 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4251 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4251 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4252 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4252 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4252 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4252 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4253 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4253 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4253 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4253 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4254 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4254 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4254 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4254 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4255 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4255 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4255 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4255 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4256 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4256 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4256 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4256 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4257 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4257 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4257 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4257 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4258 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.exact_13_4258 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.data_13_4258 +#print axioms Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4258 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4259 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4259 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4259 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4259 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4260 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4260 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4260 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4260 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4261 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4261 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4261 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4261 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4262 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4262 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4262 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4262 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4263 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4263 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4263 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4263 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4264 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4264 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4264 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4264 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4265 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4265 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4265 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4265 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4266 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4266 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4266 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4266 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4267 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4267 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4267 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4267 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4268 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4268 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4268 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4268 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4269 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4269 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4269 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4269 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4270 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4270 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4270 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4270 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4271 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4271 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4271 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4271 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4272 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4272 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4272 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4272 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4273 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4273 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4273 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4273 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4274 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.exact_13_4274 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.data_13_4274 +#print axioms Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4274 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4275 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4275 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4275 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4275 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4276 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4276 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4276 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4276 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4277 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4277 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4277 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4277 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4278 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4278 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4278 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4278 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4279 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4279 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4279 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4279 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4280 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4280 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4280 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4280 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4281 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4281 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4281 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4281 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4282 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4282 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4282 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4282 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4283 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4283 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4283 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4283 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4284 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4284 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4284 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4284 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4285 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4285 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4285 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4285 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4286 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4286 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4286 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4286 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4287 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4287 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4287 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4287 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4288 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4288 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4288 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4288 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4289 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.exact_13_4289 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.data_13_4289 +#print axioms Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4289 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4290 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4290 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4290 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4290 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4291 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4291 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4291 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4291 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4292 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4292 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4292 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4292 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4293 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4293 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4293 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4293 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4294 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4294 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4294 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4294 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4295 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4295 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4295 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4295 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4296 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4296 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4296 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4296 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4297 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4297 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4297 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4297 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4298 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4298 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4298 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4298 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4299 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4299 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4299 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4299 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4300 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4300 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4300 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4300 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4301 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4301 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4301 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4301 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4302 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4302 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4302 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4302 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4303 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4303 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4303 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4303 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4304 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.exact_13_4304 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.data_13_4304 +#print axioms Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4304 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4305 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4305 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4305 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4305 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4306 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4306 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4306 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4306 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4307 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4307 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4307 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4307 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4308 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4308 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4308 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4308 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4309 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4309 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4309 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4309 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4310 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4310 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4310 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4310 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4311 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4311 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4311 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4311 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4312 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4312 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4312 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4312 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4313 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4313 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4313 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4313 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4314 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4314 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4314 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4314 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4315 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4315 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4315 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4315 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4316 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4316 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4316 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4316 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4317 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4317 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4317 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4317 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4318 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4318 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4318 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4318 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4319 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4319 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4319 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4319 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4320 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.exact_13_4320 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.data_13_4320 +#print axioms Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4320 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4321 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4321 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4321 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4321 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4322 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4322 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4322 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4322 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4323 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4323 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4323 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4323 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4324 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4324 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4324 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4324 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4325 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4325 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4325 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4325 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4326 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4326 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4326 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4326 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4327 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4327 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4327 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4327 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4328 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4328 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4328 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4328 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4329 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4329 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4329 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4329 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4330 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4330 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4330 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4330 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4331 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4331 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4331 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4331 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4332 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4332 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4332 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4332 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4333 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4333 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4333 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4333 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4334 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4334 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4334 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4334 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4335 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.exact_13_4335 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.data_13_4335 +#print axioms Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4335 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4336 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4336 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4336 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4336 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4337 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4337 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4337 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4337 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4338 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4338 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4338 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4338 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4339 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4339 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4339 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4339 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4340 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4340 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4340 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4340 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4341 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4341 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4341 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4341 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4342 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4342 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4342 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4342 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4343 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4343 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4343 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4343 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4344 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4344 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4344 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4344 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4345 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4345 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4345 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4345 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4346 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4346 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4346 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4346 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4347 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4347 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4347 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4347 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4348 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4348 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4348 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4348 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4349 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4349 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4349 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4349 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4350 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4350 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4350 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4350 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4351 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.exact_13_4351 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.data_13_4351 +#print axioms Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4351 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4352 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4352 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4352 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4352 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4353 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4353 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4353 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4353 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4354 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4354 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4354 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4354 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4355 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4355 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4355 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4355 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4356 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4356 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4356 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4356 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4357 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4357 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4357 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4357 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4358 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4358 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4358 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4358 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4359 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4359 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4359 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4359 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4360 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4360 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4360 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4360 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4361 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4361 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4361 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4361 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4362 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4362 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4362 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4362 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4363 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4363 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4363 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4363 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4364 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4364 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4364 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4364 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4365 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4365 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4365 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4365 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4366 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.exact_13_4366 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.data_13_4366 +#print axioms Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4366 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4367 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4367 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4367 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4367 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4368 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4368 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4368 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4368 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4369 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4369 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4369 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4369 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4370 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4370 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4370 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4370 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4371 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4371 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4371 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4371 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4372 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4372 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4372 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4372 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4373 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4373 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4373 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4373 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4374 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4374 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4374 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4374 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4375 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4375 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4375 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4375 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4376 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4376 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4376 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4376 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4377 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4377 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4377 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4377 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4378 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4378 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4378 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4378 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4379 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4379 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4379 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4379 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4380 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4380 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4380 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4380 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4381 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.exact_13_4381 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.data_13_4381 +#print axioms Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4381 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4382 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4382 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4382 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4382 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4383 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4383 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4383 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4383 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4384 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4384 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4384 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4384 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4385 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4385 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4385 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4385 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4386 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4386 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4386 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4386 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4387 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4387 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4387 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4387 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4388 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4388 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4388 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4388 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4389 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4389 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4389 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4389 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4390 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4390 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4390 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4390 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4391 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4391 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4391 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4391 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4392 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4392 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4392 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4392 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4393 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4393 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4393 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4393 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4394 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4394 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4394 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4394 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4395 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4395 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4395 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4395 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4396 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4396 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4396 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4396 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4397 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.exact_13_4397 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.data_13_4397 +#print axioms Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4397 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4398 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4398 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4398 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4398 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4399 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4399 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4399 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4399 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4400 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4400 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4400 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4400 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4401 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4401 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4401 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4401 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4402 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4402 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4402 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4402 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4403 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4403 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4403 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4403 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4404 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4404 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4404 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4404 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4405 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4405 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4405 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4405 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4406 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4406 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4406 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4406 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4407 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4407 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4407 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4407 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4408 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4408 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4408 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4408 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4409 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4409 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4409 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4409 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4410 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4410 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4410 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4410 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4411 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4411 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4411 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4411 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4412 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.exact_13_4412 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.data_13_4412 +#print axioms Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4412 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4413 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4413 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4413 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4413 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4414 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4414 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4414 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4414 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4415 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4415 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4415 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4415 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4416 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4416 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4416 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4416 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4417 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4417 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4417 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4417 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4418 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4418 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4418 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4418 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4419 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4419 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4419 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4419 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4420 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4420 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4420 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4420 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4421 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4421 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4421 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4421 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4422 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4422 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4422 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4422 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4423 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4423 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4423 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4423 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4424 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4424 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4424 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4424 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4425 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4425 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4425 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4425 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4426 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4426 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4426 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4426 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4427 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.exact_13_4427 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.data_13_4427 +#print axioms Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4427 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4428 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4428 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4428 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4428 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4429 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4429 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4429 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4429 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4430 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4430 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4430 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4430 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4431 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4431 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4431 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4431 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4432 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4432 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4432 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4432 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4433 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4433 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4433 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4433 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4434 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4434 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4434 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4434 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4435 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4435 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4435 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4435 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4436 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4436 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4436 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4436 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4437 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4437 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4437 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4437 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4438 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4438 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4438 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4438 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4439 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4439 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4439 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4439 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4440 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4440 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4440 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4440 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4441 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4441 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4441 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4441 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4442 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4442 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4442 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4442 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4443 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.exact_13_4443 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.data_13_4443 +#print axioms Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4443 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4444 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4444 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4444 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4444 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4445 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4445 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4445 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4445 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4446 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4446 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4446 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4446 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4447 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4447 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4447 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4447 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4448 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4448 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4448 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4448 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4449 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4449 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4449 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4449 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4450 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4450 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4450 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4450 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4451 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4451 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4451 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4451 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4452 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4452 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4452 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4452 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4453 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4453 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4453 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4453 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4454 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4454 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4454 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4454 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4455 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4455 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4455 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4455 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4456 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4456 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4456 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4456 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4457 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4457 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4457 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4457 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4458 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.exact_13_4458 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.data_13_4458 +#print axioms Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4458 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4459 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4459 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4459 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4459 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4460 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4460 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4460 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4460 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4461 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4461 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4461 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4461 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4462 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4462 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4462 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4462 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4463 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4463 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4463 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4463 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4464 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4464 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4464 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4464 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4465 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4465 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4465 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4465 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4466 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4466 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4466 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4466 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4467 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4467 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4467 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4467 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4468 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4468 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4468 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4468 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4469 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4469 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4469 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4469 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4470 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4470 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4470 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4470 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4471 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4471 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4471 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4471 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4472 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4472 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4472 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4472 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4473 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.exact_13_4473 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.data_13_4473 +#print axioms Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4473 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4474 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4474 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4474 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4474 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4475 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4475 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4475 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4475 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4476 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4476 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4476 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4476 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4477 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4477 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4477 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4477 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4478 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4478 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4478 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4478 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4479 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4479 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4479 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4479 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4480 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4480 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4480 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4480 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4481 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4481 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4481 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4481 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4482 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4482 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4482 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4482 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4483 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4483 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4483 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4483 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4484 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4484 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4484 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4484 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4485 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4485 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4485 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4485 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4486 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4486 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4486 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4486 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4487 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4487 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4487 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4487 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4488 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4488 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4488 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4488 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4489 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.exact_13_4489 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.data_13_4489 +#print axioms Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4489 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4490 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4490 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4490 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4490 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4491 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4491 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4491 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4491 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4492 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4492 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4492 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4492 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4493 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4493 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4493 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4493 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4494 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4494 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4494 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4494 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4495 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4495 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4495 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4495 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4496 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4496 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4496 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4496 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4497 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4497 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4497 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4497 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4498 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4498 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4498 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4498 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4499 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4499 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4499 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4499 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4500 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4500 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4500 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4500 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4501 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4501 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4501 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4501 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4502 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4502 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4502 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4502 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4503 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4503 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4503 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4503 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4504 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.exact_13_4504 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.data_13_4504 +#print axioms Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4504 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4505 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4505 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4505 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4505 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4506 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4506 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4506 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4506 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4507 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4507 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4507 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4507 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4508 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4508 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4508 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4508 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4509 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4509 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4509 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4509 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4510 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4510 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4510 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4510 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4511 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4511 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4511 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4511 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4512 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4512 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4512 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4512 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4513 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4513 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4513 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4513 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4514 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4514 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4514 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4514 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4515 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4515 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4515 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4515 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4516 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4516 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4516 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4516 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4517 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4517 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4517 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4517 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4518 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4518 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4518 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4518 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4519 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.exact_13_4519 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.data_13_4519 +#print axioms Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4519 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4520 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4520 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4520 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4520 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4521 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4521 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4521 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4521 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4522 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4522 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4522 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4522 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4523 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4523 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4523 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4523 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4524 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4524 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4524 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4524 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4525 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4525 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4525 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4525 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4526 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4526 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4526 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4526 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4527 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4527 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4527 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4527 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4528 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4528 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4528 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4528 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4529 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4529 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4529 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4529 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4530 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4530 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4530 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4530 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4531 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4531 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4531 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4531 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4532 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4532 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4532 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4532 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4533 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4533 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4533 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4533 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4534 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4534 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4534 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4534 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4535 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.exact_13_4535 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.data_13_4535 +#print axioms Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4535 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4536 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4536 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4536 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4536 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4537 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4537 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4537 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4537 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4538 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4538 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4538 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4538 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4539 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4539 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4539 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4539 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4540 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4540 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4540 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4540 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4541 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4541 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4541 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4541 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4542 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4542 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4542 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4542 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4543 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4543 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4543 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4543 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4544 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4544 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4544 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4544 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4545 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4545 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4545 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4545 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4546 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4546 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4546 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4546 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4547 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4547 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4547 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4547 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4548 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4548 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4548 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4548 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4549 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4549 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4549 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4549 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4550 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.exact_13_4550 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.data_13_4550 +#print axioms Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4550 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4551 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4551 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4551 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4551 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4552 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4552 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4552 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4552 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4553 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4553 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4553 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4553 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4554 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4554 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4554 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4554 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4555 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4555 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4555 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4555 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4556 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4556 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4556 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4556 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4557 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4557 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4557 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4557 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4558 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4558 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4558 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4558 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4559 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4559 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4559 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4559 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4560 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4560 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4560 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4560 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4561 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4561 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4561 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4561 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4562 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4562 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4562 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4562 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4563 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4563 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4563 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4563 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4564 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4564 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4564 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4564 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4565 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4565 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4565 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4565 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4566 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.exact_13_4566 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.data_13_4566 +#print axioms Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4566 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4567 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4567 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4567 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4567 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4568 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4568 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4568 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4568 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4569 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4569 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4569 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4569 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4570 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4570 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4570 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4570 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4571 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4571 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4571 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4571 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4572 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4572 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4572 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4572 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4573 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4573 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4573 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4573 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4574 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4574 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4574 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4574 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4575 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4575 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4575 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4575 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4576 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4576 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4576 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4576 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4577 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4577 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4577 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4577 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4578 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4578 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4578 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4578 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4579 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4579 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4579 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4579 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4580 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4580 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4580 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4580 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4581 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.exact_13_4581 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.data_13_4581 +#print axioms Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4581 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4582 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4582 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4582 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4582 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4583 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4583 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4583 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4583 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4584 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4584 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4584 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4584 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4585 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4585 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4585 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4585 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4586 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4586 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4586 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4586 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4587 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4587 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4587 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4587 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4588 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4588 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4588 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4588 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4589 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4589 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4589 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4589 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4590 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4590 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4590 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4590 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4591 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4591 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4591 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4591 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4592 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4592 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4592 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4592 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4593 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4593 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4593 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4593 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4594 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4594 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4594 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4594 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4595 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4595 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4595 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4595 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4596 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.exact_13_4596 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.data_13_4596 +#print axioms Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4596 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4597 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4597 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4597 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4597 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4598 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4598 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4598 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4598 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4599 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4599 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4599 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4599 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4600 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4600 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4600 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4600 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4601 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4601 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4601 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4601 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4602 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4602 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4602 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4602 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4603 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4603 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4603 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4603 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4604 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4604 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4604 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4604 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4605 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4605 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4605 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4605 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4606 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4606 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4606 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4606 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4607 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4607 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4607 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4607 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4608 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4608 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4608 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4608 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4609 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4609 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4609 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4609 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4610 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4610 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4610 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4610 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4611 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4611 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4611 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4611 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4612 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.exact_13_4612 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.data_13_4612 +#print axioms Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4612 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4613 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4613 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4613 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4613 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4614 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4614 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4614 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4614 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4615 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4615 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4615 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4615 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4616 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4616 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4616 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4616 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4617 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4617 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4617 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4617 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4618 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4618 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4618 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4618 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4619 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4619 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4619 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4619 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4620 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4620 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4620 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4620 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4621 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4621 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4621 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4621 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4622 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4622 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4622 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4622 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4623 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4623 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4623 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4623 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4624 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4624 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4624 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4624 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4625 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4625 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4625 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4625 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4626 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4626 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4626 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4626 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4627 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.exact_13_4627 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.data_13_4627 +#print axioms Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4627 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4628 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4628 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4628 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4628 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4629 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4629 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4629 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4629 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4630 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4630 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4630 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4630 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4631 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4631 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4631 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4631 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4632 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4632 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4632 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4632 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4633 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4633 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4633 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4633 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4634 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4634 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4634 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4634 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4635 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4635 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4635 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4635 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4636 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4636 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4636 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4636 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4637 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4637 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4637 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4637 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4638 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4638 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4638 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4638 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4639 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4639 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4639 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4639 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4640 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4640 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4640 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4640 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4641 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4641 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4641 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4641 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4642 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.exact_13_4642 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.data_13_4642 +#print axioms Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4642 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4643 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4643 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4643 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4643 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4644 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4644 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4644 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4644 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4645 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4645 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4645 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4645 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4646 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4646 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4646 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4646 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4647 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4647 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4647 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4647 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4648 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4648 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4648 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4648 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4649 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4649 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4649 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4649 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4650 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4650 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4650 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4650 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4651 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4651 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4651 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4651 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4652 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4652 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4652 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4652 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4653 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4653 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4653 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4653 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4654 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4654 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4654 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4654 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4655 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4655 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4655 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4655 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4656 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4656 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4656 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4656 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4657 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4657 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4657 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4657 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4658 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.exact_13_4658 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.data_13_4658 +#print axioms Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4658 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4659 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4659 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4659 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4659 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4660 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4660 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4660 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4660 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4661 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4661 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4661 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4661 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4662 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4662 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4662 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4662 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4663 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4663 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4663 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4663 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4664 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4664 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4664 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4664 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4665 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4665 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4665 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4665 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4666 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4666 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4666 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4666 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4667 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4667 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4667 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4667 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4668 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4668 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4668 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4668 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4669 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4669 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4669 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4669 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4670 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4670 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4670 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4670 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4671 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4671 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4671 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4671 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4672 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4672 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4672 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4672 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4673 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.exact_13_4673 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.data_13_4673 +#print axioms Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4673 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4674 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4674 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4674 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4674 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4675 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4675 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4675 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4675 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4676 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4676 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4676 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4676 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4677 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4677 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4677 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4677 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4678 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4678 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4678 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4678 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4679 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4679 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4679 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4679 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4680 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4680 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4680 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4680 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4681 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4681 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4681 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4681 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4682 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4682 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4682 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4682 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4683 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4683 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4683 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4683 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4684 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4684 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4684 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4684 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4685 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4685 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4685 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4685 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4686 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4686 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4686 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4686 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4687 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4687 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4687 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4687 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4688 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.exact_13_4688 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.data_13_4688 +#print axioms Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4688 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4689 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4689 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4689 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4689 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4690 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4690 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4690 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4690 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4691 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4691 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4691 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4691 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4692 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4692 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4692 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4692 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4693 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4693 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4693 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4693 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4694 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4694 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4694 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4694 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4695 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4695 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4695 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4695 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4696 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4696 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4696 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4696 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4697 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4697 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4697 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4697 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4698 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4698 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4698 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4698 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4699 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4699 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4699 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4699 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4700 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4700 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4700 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4700 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4701 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4701 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4701 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4701 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4702 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4702 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4702 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4702 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4703 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4703 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4703 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4703 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4704 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.exact_13_4704 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.data_13_4704 +#print axioms Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4704 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4705 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4705 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4705 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4705 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4706 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4706 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4706 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4706 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4707 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4707 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4707 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4707 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4708 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4708 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4708 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4708 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4709 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4709 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4709 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4709 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4710 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4710 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4710 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4710 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4711 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4711 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4711 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4711 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4712 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4712 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4712 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4712 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4713 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4713 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4713 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4713 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4714 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4714 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4714 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4714 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4715 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4715 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4715 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4715 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4716 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4716 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4716 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4716 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4717 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4717 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4717 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4717 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4718 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4718 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4718 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4718 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4719 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.exact_13_4719 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.data_13_4719 +#print axioms Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4719 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4720 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4720 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4720 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4720 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4721 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4721 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4721 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4721 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4722 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4722 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4722 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4722 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4723 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4723 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4723 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4723 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4724 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4724 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4724 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4724 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4725 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4725 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4725 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4725 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4726 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4726 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4726 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4726 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4727 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4727 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4727 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4727 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4728 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4728 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4728 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4728 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4729 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4729 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4729 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4729 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4730 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4730 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4730 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4730 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4731 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4731 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4731 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4731 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4732 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4732 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4732 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4732 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4733 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4733 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4733 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4733 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4734 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4734 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4734 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4734 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4735 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.exact_13_4735 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.data_13_4735 +#print axioms Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4735 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4736 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4736 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4736 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4736 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4737 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4737 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4737 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4737 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4738 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4738 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4738 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4738 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4739 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4739 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4739 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4739 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4740 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4740 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4740 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4740 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4741 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4741 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4741 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4741 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4742 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4742 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4742 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4742 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4743 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4743 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4743 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4743 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4744 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4744 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4744 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4744 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4745 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4745 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4745 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4745 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4746 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4746 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4746 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4746 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4747 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4747 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4747 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4747 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4748 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4748 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4748 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4748 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4749 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4749 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4749 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4749 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4750 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.exact_13_4750 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.data_13_4750 +#print axioms Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4750 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4751 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4751 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4751 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4751 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4752 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4752 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4752 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4752 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4753 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4753 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4753 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4753 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4754 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4754 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4754 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4754 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4755 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4755 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4755 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4755 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4756 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4756 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4756 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4756 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4757 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4757 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4757 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4757 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4758 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4758 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4758 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4758 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4759 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4759 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4759 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4759 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4760 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4760 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4760 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4760 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4761 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4761 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4761 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4761 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4762 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4762 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4762 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4762 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4763 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4763 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4763 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4763 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4764 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4764 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4764 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4764 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4765 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.exact_13_4765 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.data_13_4765 +#print axioms Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4765 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4766 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4766 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4766 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4766 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4767 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4767 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4767 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4767 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4768 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4768 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4768 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4768 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4769 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4769 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4769 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4769 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4770 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4770 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4770 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4770 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4771 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4771 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4771 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4771 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4772 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4772 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4772 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4772 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4773 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4773 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4773 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4773 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4774 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4774 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4774 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4774 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4775 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4775 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4775 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4775 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4776 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4776 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4776 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4776 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4777 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4777 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4777 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4777 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4778 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4778 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4778 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4778 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4779 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4779 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4779 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4779 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4780 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4780 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4780 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4780 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4781 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.exact_13_4781 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.data_13_4781 +#print axioms Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4781 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4782 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4782 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4782 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4782 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4783 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4783 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4783 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4783 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4784 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4784 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4784 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4784 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4785 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4785 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4785 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4785 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4786 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4786 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4786 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4786 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4787 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4787 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4787 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4787 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4788 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4788 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4788 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4788 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4789 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4789 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4789 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4789 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4790 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4790 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4790 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4790 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4791 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4791 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4791 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4791 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4792 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4792 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4792 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4792 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4793 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4793 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4793 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4793 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4794 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4794 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4794 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4794 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4795 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4795 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4795 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4795 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4796 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.exact_13_4796 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.data_13_4796 +#print axioms Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4796 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4797 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4797 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4797 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4797 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4798 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4798 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4798 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4798 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4799 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4799 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4799 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4799 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4800 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4800 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4800 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4800 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4801 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4801 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4801 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4801 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4802 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4802 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4802 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4802 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4803 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4803 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4803 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4803 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4804 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4804 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4804 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4804 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4805 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4805 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4805 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4805 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4806 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4806 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4806 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4806 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4807 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4807 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4807 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4807 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4808 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4808 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4808 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4808 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4809 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4809 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4809 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4809 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4810 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4810 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4810 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4810 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4811 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.exact_13_4811 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.data_13_4811 +#print axioms Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4811 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4812 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4812 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4812 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4812 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4813 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4813 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4813 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4813 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4814 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4814 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4814 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4814 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4815 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4815 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4815 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4815 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4816 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4816 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4816 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4816 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4817 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4817 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4817 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4817 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4818 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4818 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4818 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4818 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4819 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4819 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4819 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4819 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4820 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4820 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4820 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4820 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4821 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4821 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4821 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4821 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4822 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4822 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4822 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4822 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4823 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4823 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4823 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4823 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4824 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4824 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4824 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4824 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4825 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4825 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4825 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4825 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4826 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4826 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4826 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4826 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4827 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.exact_13_4827 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.data_13_4827 +#print axioms Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4827 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4828 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4828 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4828 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4828 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4829 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4829 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4829 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4829 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4830 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4830 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4830 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4830 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4831 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4831 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4831 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4831 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4832 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4832 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4832 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4832 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4833 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4833 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4833 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4833 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4834 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4834 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4834 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4834 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4835 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4835 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4835 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4835 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4836 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4836 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4836 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4836 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4837 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4837 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4837 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4837 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4838 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4838 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4838 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4838 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4839 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4839 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4839 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4839 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4840 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4840 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4840 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4840 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4841 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4841 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4841 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4841 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4842 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.exact_13_4842 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.data_13_4842 +#print axioms Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4842 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4843 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4843 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4843 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4843 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4844 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4844 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4844 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4844 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4845 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4845 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4845 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4845 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4846 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4846 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4846 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4846 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4847 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4847 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4847 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4847 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4848 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4848 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4848 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4848 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4849 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4849 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4849 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4849 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4850 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4850 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4850 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4850 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4851 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4851 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4851 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4851 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4852 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4852 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4852 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4852 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4853 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4853 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4853 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4853 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4854 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4854 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4854 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4854 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4855 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4855 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4855 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4855 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4856 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4856 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4856 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4856 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4857 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.exact_13_4857 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.data_13_4857 +#print axioms Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4857 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4858 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4858 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4858 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4858 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4859 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4859 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4859 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4859 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4860 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4860 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4860 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4860 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4861 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4861 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4861 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4861 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4862 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4862 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4862 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4862 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4863 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4863 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4863 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4863 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4864 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4864 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4864 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4864 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4865 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4865 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4865 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4865 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4866 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4866 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4866 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4866 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4867 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4867 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4867 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4867 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4868 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4868 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4868 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4868 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4869 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4869 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4869 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4869 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4870 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4870 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4870 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4870 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4871 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4871 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4871 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4871 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4872 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4872 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4872 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4872 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4873 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.exact_13_4873 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.data_13_4873 +#print axioms Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4873 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4874 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4874 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4874 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4874 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4875 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4875 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4875 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4875 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4876 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4876 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4876 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4876 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4877 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4877 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4877 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4877 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4878 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4878 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4878 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4878 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4879 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4879 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4879 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4879 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4880 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4880 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4880 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4880 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4881 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4881 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4881 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4881 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4882 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4882 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4882 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4882 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4883 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4883 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4883 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4883 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4884 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4884 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4884 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4884 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4885 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4885 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4885 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4885 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4886 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4886 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4886 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4886 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4887 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4887 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4887 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4887 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4888 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.exact_13_4888 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.data_13_4888 +#print axioms Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4888 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4889 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4889 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4889 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4889 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4890 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4890 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4890 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4890 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4891 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4891 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4891 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4891 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4892 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4892 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4892 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4892 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4893 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4893 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4893 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4893 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4894 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4894 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4894 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4894 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4895 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4895 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4895 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4895 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4896 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4896 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4896 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4896 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4897 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4897 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4897 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4897 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4898 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4898 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4898 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4898 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4899 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4899 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4899 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4899 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4900 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4900 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4900 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4900 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4901 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4901 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4901 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4901 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4902 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4902 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4902 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4902 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4903 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.exact_13_4903 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.data_13_4903 +#print axioms Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4903 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4904 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4904 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4904 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4904 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4905 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4905 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4905 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4905 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4906 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4906 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4906 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4906 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4907 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4907 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4907 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4907 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4908 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4908 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4908 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4908 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4909 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4909 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4909 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4909 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4910 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4910 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4910 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4910 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4911 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4911 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4911 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4911 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4912 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4912 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4912 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4912 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4913 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4913 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4913 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4913 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4914 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4914 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4914 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4914 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4915 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4915 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4915 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4915 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4916 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4916 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4916 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4916 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4917 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4917 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4917 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4917 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4918 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4918 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4918 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4918 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4919 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.exact_13_4919 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.data_13_4919 +#print axioms Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4919 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4920 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4920 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4920 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4920 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4921 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4921 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4921 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4921 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4922 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4922 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4922 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4922 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4923 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4923 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4923 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4923 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4924 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4924 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4924 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4924 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4925 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4925 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4925 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4925 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4926 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4926 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4926 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4926 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4927 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4927 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4927 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4927 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4928 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4928 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4928 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4928 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4929 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4929 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4929 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4929 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4930 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4930 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4930 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4930 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4931 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4931 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4931 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4931 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4932 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4932 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4932 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4932 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4933 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4933 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4933 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4933 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4934 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.exact_13_4934 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.data_13_4934 +#print axioms Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4934 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4935 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4935 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4935 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4935 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4936 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4936 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4936 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4936 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4937 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4937 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4937 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4937 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4938 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4938 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4938 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4938 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4939 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4939 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4939 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4939 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4940 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4940 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4940 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4940 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4941 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4941 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4941 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4941 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4942 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4942 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4942 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4942 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4943 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4943 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4943 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4943 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4944 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4944 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4944 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4944 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4945 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4945 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4945 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4945 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4946 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4946 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4946 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4946 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4947 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4947 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4947 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4947 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4948 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4948 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4948 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4948 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4949 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4949 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4949 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4949 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4950 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.exact_13_4950 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.data_13_4950 +#print axioms Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4950 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4951 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4951 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4951 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4951 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4952 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4952 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4952 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4952 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4953 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4953 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4953 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4953 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4954 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4954 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4954 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4954 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4955 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4955 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4955 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4955 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4956 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4956 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4956 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4956 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4957 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4957 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4957 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4957 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4958 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4958 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4958 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4958 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4959 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4959 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4959 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4959 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4960 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4960 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4960 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4960 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4961 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4961 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4961 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4961 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4962 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4962 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4962 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4962 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4963 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4963 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4963 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4963 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4964 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4964 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4964 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4964 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4965 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.exact_13_4965 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.data_13_4965 +#print axioms Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4965 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4966 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4966 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4966 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4966 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4967 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4967 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4967 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4967 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4968 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4968 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4968 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4968 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4969 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4969 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4969 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4969 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4970 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4970 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4970 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4970 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4971 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4971 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4971 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4971 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4972 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4972 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4972 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4972 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4973 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4973 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4973 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4973 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4974 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4974 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4974 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4974 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4975 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4975 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4975 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4975 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4976 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4976 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4976 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4976 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4977 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4977 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4977 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4977 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4978 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4978 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4978 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4978 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4979 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4979 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4979 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4979 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4980 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.exact_13_4980 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.data_13_4980 +#print axioms Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4980 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4981 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4981 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4981 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4981 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4982 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4982 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4982 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4982 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4983 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4983 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4983 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4983 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4984 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4984 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4984 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4984 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4985 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4985 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4985 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4985 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4986 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4986 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4986 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4986 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4987 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4987 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4987 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4987 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4988 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4988 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4988 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4988 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4989 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4989 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4989 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4989 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4990 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4990 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4990 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4990 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4991 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4991 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4991 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4991 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4992 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4992 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4992 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4992 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4993 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4993 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4993 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4993 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4994 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4994 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4994 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4994 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4995 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4995 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4995 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4995 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4996 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.exact_13_4996 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.data_13_4996 +#print axioms Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4996 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_4997 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_4997 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_4997 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_4997 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_4998 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_4998 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_4998 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_4998 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_4999 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_4999 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_4999 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_4999 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5000 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5000 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5000 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5000 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5001 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5001 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5001 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5001 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5002 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5002 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5002 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5002 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5003 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5003 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5003 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5003 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5004 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5004 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5004 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5004 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5005 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5005 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5005 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5005 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5006 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5006 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5006 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5006 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5007 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5007 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5007 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5007 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5008 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5008 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5008 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5008 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5009 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5009 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5009 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5009 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5010 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5010 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5010 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5010 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5011 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.exact_13_5011 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.data_13_5011 +#print axioms Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5011 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5012 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5012 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5012 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5012 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5013 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5013 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5013 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5013 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5014 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5014 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5014 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5014 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5015 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5015 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5015 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5015 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5016 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5016 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5016 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5016 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5017 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5017 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5017 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5017 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5018 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5018 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5018 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5018 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5019 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5019 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5019 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5019 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5020 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5020 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5020 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5020 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5021 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5021 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5021 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5021 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5022 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5022 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5022 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5022 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5023 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5023 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5023 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5023 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5024 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5024 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5024 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5024 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5025 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5025 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5025 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5025 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5026 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.exact_13_5026 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.data_13_5026 +#print axioms Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5026 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5027 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5027 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5027 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5027 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5028 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5028 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5028 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5028 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5029 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5029 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5029 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5029 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5030 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5030 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5030 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5030 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5031 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5031 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5031 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5031 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5032 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5032 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5032 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5032 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5033 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5033 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5033 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5033 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5034 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5034 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5034 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5034 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5035 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5035 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5035 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5035 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5036 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5036 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5036 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5036 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5037 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5037 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5037 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5037 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5038 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5038 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5038 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5038 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5039 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5039 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5039 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5039 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5040 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5040 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5040 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5040 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5041 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5041 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5041 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5041 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5042 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.exact_13_5042 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.data_13_5042 +#print axioms Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5042 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5043 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5043 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5043 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5043 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5044 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5044 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5044 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5044 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5045 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5045 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5045 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5045 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5046 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5046 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5046 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5046 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5047 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5047 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5047 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5047 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5048 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5048 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5048 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5048 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5049 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5049 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5049 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5049 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5050 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5050 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5050 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5050 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5051 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5051 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5051 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5051 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5052 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5052 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5052 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5052 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5053 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5053 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5053 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5053 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5054 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5054 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5054 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5054 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5055 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5055 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5055 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5055 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5056 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5056 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5056 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5056 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5057 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.exact_13_5057 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.data_13_5057 +#print axioms Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5057 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5058 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5058 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5058 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5058 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5059 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5059 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5059 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5059 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5060 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5060 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5060 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5060 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5061 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5061 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5061 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5061 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5062 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5062 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5062 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5062 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5063 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5063 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5063 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5063 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5064 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5064 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5064 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5064 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5065 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5065 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5065 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5065 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5066 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5066 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5066 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5066 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5067 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5067 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5067 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5067 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5068 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5068 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5068 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5068 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5069 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5069 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5069 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5069 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5070 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5070 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5070 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5070 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5071 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5071 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5071 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5071 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5072 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.exact_13_5072 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.data_13_5072 +#print axioms Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5072 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5073 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5073 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5073 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5073 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5074 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5074 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5074 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5074 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5075 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5075 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5075 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5075 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5076 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5076 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5076 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5076 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5077 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5077 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5077 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5077 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5078 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5078 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5078 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5078 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5079 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5079 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5079 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5079 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5080 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5080 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5080 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5080 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5081 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5081 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5081 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5081 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5082 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5082 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5082 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5082 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5083 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5083 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5083 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5083 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5084 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5084 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5084 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5084 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5085 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5085 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5085 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5085 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5086 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5086 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5086 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5086 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5087 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5087 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5087 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5087 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5088 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.exact_13_5088 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.data_13_5088 +#print axioms Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5088 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5089 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5089 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5089 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5089 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5090 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5090 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5090 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5090 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5091 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5091 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5091 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5091 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5092 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5092 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5092 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5092 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5093 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5093 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5093 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5093 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5094 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5094 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5094 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5094 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5095 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5095 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5095 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5095 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5096 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5096 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5096 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5096 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5097 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5097 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5097 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5097 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5098 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5098 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5098 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5098 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5099 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5099 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5099 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5099 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5100 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5100 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5100 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5100 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5101 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5101 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5101 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5101 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5102 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5102 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5102 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5102 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5103 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.exact_13_5103 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.data_13_5103 +#print axioms Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5103 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5104 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5104 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5104 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5104 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5105 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5105 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5105 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5105 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5106 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5106 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5106 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5106 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5107 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5107 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5107 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5107 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5108 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5108 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5108 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5108 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5109 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5109 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5109 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5109 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5110 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5110 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5110 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5110 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5111 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5111 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5111 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5111 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5112 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5112 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5112 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5112 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5113 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5113 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5113 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5113 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5114 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5114 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5114 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5114 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5115 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5115 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5115 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5115 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5116 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5116 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5116 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5116 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5117 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5117 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5117 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5117 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5118 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5118 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5118 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5118 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5119 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.exact_13_5119 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.data_13_5119 +#print axioms Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5119 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5120 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5120 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5120 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5120 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5121 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5121 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5121 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5121 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5122 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5122 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5122 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5122 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5123 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5123 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5123 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5123 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5124 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5124 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5124 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5124 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5125 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5125 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5125 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5125 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5126 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5126 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5126 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5126 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5127 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5127 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5127 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5127 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5128 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5128 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5128 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5128 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5129 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5129 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5129 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5129 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5130 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5130 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5130 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5130 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5131 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5131 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5131 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5131 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5132 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5132 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5132 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5132 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5133 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5133 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5133 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5133 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5134 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.exact_13_5134 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.data_13_5134 +#print axioms Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5134 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5135 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5135 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5135 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5135 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5136 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5136 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5136 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5136 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5137 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5137 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5137 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5137 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5138 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5138 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5138 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5138 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5139 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5139 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5139 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5139 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5140 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5140 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5140 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5140 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5141 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5141 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5141 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5141 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5142 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5142 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5142 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5142 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5143 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5143 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5143 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5143 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5144 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5144 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5144 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5144 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5145 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5145 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5145 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5145 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5146 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5146 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5146 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5146 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5147 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5147 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5147 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5147 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5148 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5148 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5148 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5148 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5149 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.exact_13_5149 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.data_13_5149 +#print axioms Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5149 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5150 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5150 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5150 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5150 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5151 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5151 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5151 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5151 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5152 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5152 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5152 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5152 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5153 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5153 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5153 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5153 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5154 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5154 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5154 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5154 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5155 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5155 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5155 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5155 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5156 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5156 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5156 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5156 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5157 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5157 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5157 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5157 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5158 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5158 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5158 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5158 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5159 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5159 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5159 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5159 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5160 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5160 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5160 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5160 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5161 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5161 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5161 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5161 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5162 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5162 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5162 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5162 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5163 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5163 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5163 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5163 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5164 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5164 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5164 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5164 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5165 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.exact_13_5165 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.data_13_5165 +#print axioms Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5165 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5166 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5166 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5166 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5166 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5167 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5167 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5167 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5167 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5168 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5168 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5168 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5168 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5169 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5169 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5169 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5169 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5170 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5170 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5170 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5170 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5171 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5171 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5171 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5171 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5172 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5172 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5172 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5172 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5173 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5173 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5173 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5173 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5174 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5174 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5174 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5174 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5175 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5175 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5175 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5175 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5176 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5176 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5176 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5176 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5177 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5177 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5177 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5177 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5178 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5178 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5178 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5178 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5179 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5179 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5179 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5179 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5180 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.exact_13_5180 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.data_13_5180 +#print axioms Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5180 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5181 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5181 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5181 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5181 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5182 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5182 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5182 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5182 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5183 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5183 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5183 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5183 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5184 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5184 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5184 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5184 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5185 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5185 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5185 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5185 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5186 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5186 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5186 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5186 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5187 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5187 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5187 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5187 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5188 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5188 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5188 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5188 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5189 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5189 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5189 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5189 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5190 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5190 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5190 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5190 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5191 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5191 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5191 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5191 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5192 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5192 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5192 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5192 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5193 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5193 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5193 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5193 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5194 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5194 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5194 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5194 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5195 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.exact_13_5195 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.data_13_5195 +#print axioms Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5195 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5196 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5196 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5196 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5196 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5197 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5197 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5197 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5197 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5198 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5198 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5198 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5198 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5199 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5199 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5199 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5199 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5200 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5200 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5200 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5200 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5201 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5201 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5201 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5201 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5202 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5202 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5202 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5202 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5203 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5203 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5203 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5203 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5204 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5204 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5204 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5204 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5205 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5205 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5205 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5205 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5206 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5206 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5206 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5206 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5207 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5207 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5207 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5207 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5208 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5208 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5208 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5208 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5209 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5209 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5209 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5209 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5210 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5210 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5210 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5210 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5211 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.exact_13_5211 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.data_13_5211 +#print axioms Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5211 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5212 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5212 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5212 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5212 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5213 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5213 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5213 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5213 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5214 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5214 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5214 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5214 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5215 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5215 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5215 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5215 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5216 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5216 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5216 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5216 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5217 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5217 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5217 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5217 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5218 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5218 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5218 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5218 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5219 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5219 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5219 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5219 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5220 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5220 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5220 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5220 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5221 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5221 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5221 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5221 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5222 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5222 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5222 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5222 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5223 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5223 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5223 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5223 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5224 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5224 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5224 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5224 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5225 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5225 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5225 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5225 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5226 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.exact_13_5226 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.data_13_5226 +#print axioms Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5226 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5227 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5227 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5227 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5227 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5228 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5228 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5228 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5228 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5229 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5229 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5229 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5229 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5230 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5230 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5230 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5230 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5231 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5231 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5231 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5231 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5232 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5232 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5232 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5232 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5233 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5233 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5233 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5233 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5234 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5234 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5234 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5234 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5235 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5235 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5235 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5235 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5236 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5236 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5236 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5236 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5237 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5237 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5237 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5237 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5238 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5238 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5238 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5238 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5239 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5239 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5239 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5239 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5240 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5240 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5240 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5240 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5241 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.exact_13_5241 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.data_13_5241 +#print axioms Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5241 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5242 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5242 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5242 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5242 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5243 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5243 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5243 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5243 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5244 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5244 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5244 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5244 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5245 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5245 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5245 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5245 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5246 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5246 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5246 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5246 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5247 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5247 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5247 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5247 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5248 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5248 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5248 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5248 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5249 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5249 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5249 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5249 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5250 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5250 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5250 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5250 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5251 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5251 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5251 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5251 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5252 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5252 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5252 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5252 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5253 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5253 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5253 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5253 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5254 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5254 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5254 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5254 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5255 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5255 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5255 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5255 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5256 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5256 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5256 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5256 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5257 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.exact_13_5257 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.data_13_5257 +#print axioms Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5257 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5258 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5258 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5258 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5258 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5259 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5259 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5259 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5259 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5260 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5260 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5260 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5260 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5261 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5261 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5261 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5261 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5262 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5262 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5262 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5262 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5263 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5263 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5263 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5263 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5264 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5264 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5264 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5264 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5265 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5265 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5265 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5265 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5266 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5266 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5266 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5266 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5267 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5267 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5267 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5267 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5268 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5268 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5268 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5268 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5269 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5269 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5269 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5269 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5270 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5270 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5270 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5270 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5271 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5271 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5271 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5271 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5272 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.exact_13_5272 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.data_13_5272 +#print axioms Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5272 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5273 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5273 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5273 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5273 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5274 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5274 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5274 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5274 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5275 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5275 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5275 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5275 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5276 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5276 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5276 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5276 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5277 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5277 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5277 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5277 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5278 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5278 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5278 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5278 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5279 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5279 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5279 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5279 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5280 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5280 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5280 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5280 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5281 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5281 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5281 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5281 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5282 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5282 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5282 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5282 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5283 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5283 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5283 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5283 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5284 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5284 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5284 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5284 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5285 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5285 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5285 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5285 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5286 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5286 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5286 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5286 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5287 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.exact_13_5287 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.data_13_5287 +#print axioms Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5287 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5288 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5288 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5288 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5288 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5289 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5289 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5289 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5289 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5290 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5290 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5290 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5290 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5291 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5291 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5291 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5291 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5292 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5292 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5292 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5292 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5293 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5293 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5293 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5293 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5294 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5294 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5294 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5294 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5295 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5295 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5295 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5295 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5296 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5296 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5296 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5296 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5297 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5297 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5297 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5297 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5298 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5298 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5298 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5298 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5299 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5299 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5299 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5299 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5300 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5300 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5300 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5300 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5301 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5301 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5301 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5301 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5302 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5302 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5302 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5302 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5303 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.exact_13_5303 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.data_13_5303 +#print axioms Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5303 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5304 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5304 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5304 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5304 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5305 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5305 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5305 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5305 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5306 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5306 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5306 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5306 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5307 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5307 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5307 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5307 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5308 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5308 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5308 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5308 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5309 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5309 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5309 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5309 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5310 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5310 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5310 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5310 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5311 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5311 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5311 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5311 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5312 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5312 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5312 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5312 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5313 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5313 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5313 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5313 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5314 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5314 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5314 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5314 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5315 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5315 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5315 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5315 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5316 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5316 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5316 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5316 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5317 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5317 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5317 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5317 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5318 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.exact_13_5318 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.data_13_5318 +#print axioms Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5318 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5319 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5319 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5319 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5319 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5320 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5320 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5320 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5320 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5321 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5321 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5321 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5321 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5322 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5322 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5322 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5322 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5323 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5323 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5323 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5323 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5324 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5324 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5324 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5324 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5325 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5325 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5325 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5325 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5326 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5326 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5326 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5326 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5327 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5327 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5327 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5327 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5328 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5328 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5328 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5328 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5329 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5329 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5329 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5329 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5330 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5330 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5330 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5330 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5331 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5331 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5331 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5331 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5332 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5332 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5332 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5332 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5333 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5333 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5333 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5333 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5334 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.exact_13_5334 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.data_13_5334 +#print axioms Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5334 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5335 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5335 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5335 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5335 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5336 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5336 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5336 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5336 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5337 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5337 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5337 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5337 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5338 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5338 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5338 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5338 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5339 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5339 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5339 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5339 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5340 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5340 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5340 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5340 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5341 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5341 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5341 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5341 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5342 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5342 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5342 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5342 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5343 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5343 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5343 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5343 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5344 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5344 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5344 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5344 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5345 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5345 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5345 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5345 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5346 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5346 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5346 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5346 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5347 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5347 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5347 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5347 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5348 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5348 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5348 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5348 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.bounds_13_5349 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.exact_13_5349 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.data_13_5349 +#print axioms Collatz.Research.StoppingAtlas.Batch0815.endpoint_13_5349 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5350 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5350 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5350 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5350 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5351 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5351 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5351 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5351 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5352 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5352 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5352 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5352 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5353 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5353 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5353 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5353 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5354 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5354 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5354 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5354 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5355 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5355 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5355 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5355 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5356 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5356 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5356 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5356 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5357 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5357 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5357 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5357 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5358 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5358 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5358 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5358 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5359 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5359 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5359 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5359 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5360 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5360 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5360 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5360 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5361 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5361 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5361 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5361 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5362 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5362 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5362 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5362 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5363 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5363 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5363 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5363 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5364 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.exact_13_5364 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.data_13_5364 +#print axioms Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5364 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5365 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5365 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5365 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5365 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5366 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5366 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5366 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5366 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5367 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5367 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5367 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5367 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5368 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5368 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5368 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5368 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5369 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5369 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5369 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5369 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5370 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5370 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5370 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5370 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5371 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5371 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5371 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5371 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5372 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5372 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5372 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5372 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5373 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5373 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5373 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5373 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5374 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5374 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5374 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5374 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5375 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5375 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5375 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5375 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5376 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5376 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5376 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5376 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5377 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5377 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5377 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5377 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5378 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5378 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5378 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5378 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5379 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5379 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5379 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5379 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5380 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.exact_13_5380 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.data_13_5380 +#print axioms Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5380 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5381 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5381 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5381 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5381 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5382 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5382 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5382 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5382 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5383 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5383 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5383 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5383 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5384 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5384 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5384 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5384 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5385 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5385 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5385 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5385 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5386 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5386 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5386 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5386 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5387 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5387 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5387 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5387 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5388 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5388 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5388 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5388 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5389 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5389 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5389 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5389 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5390 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5390 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5390 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5390 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5391 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5391 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5391 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5391 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5392 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5392 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5392 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5392 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5393 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5393 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5393 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5393 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5394 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5394 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5394 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5394 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5395 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.exact_13_5395 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.data_13_5395 +#print axioms Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5395 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5396 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5396 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5396 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5396 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5397 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5397 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5397 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5397 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5398 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5398 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5398 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5398 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5399 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5399 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5399 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5399 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5400 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5400 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5400 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5400 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5401 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5401 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5401 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5401 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5402 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5402 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5402 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5402 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5403 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5403 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5403 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5403 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5404 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5404 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5404 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5404 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5405 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5405 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5405 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5405 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5406 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5406 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5406 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5406 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5407 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5407 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5407 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5407 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5408 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5408 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5408 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5408 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5409 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5409 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5409 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5409 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5410 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.exact_13_5410 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.data_13_5410 +#print axioms Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5410 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5411 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5411 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5411 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5411 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5412 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5412 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5412 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5412 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5413 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5413 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5413 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5413 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5414 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5414 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5414 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5414 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5415 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5415 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5415 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5415 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5416 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5416 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5416 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5416 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5417 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5417 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5417 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5417 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5418 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5418 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5418 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5418 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5419 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5419 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5419 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5419 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5420 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5420 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5420 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5420 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5421 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5421 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5421 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5421 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5422 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5422 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5422 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5422 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5423 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5423 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5423 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5423 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5424 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5424 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5424 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5424 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5425 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5425 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5425 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5425 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5426 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.exact_13_5426 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.data_13_5426 +#print axioms Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5426 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5427 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5427 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5427 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5427 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5428 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5428 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5428 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5428 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5429 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5429 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5429 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5429 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5430 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5430 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5430 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5430 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5431 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5431 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5431 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5431 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5432 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5432 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5432 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5432 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5433 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5433 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5433 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5433 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5434 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5434 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5434 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5434 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5435 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5435 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5435 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5435 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5436 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5436 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5436 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5436 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5437 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5437 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5437 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5437 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5438 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5438 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5438 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5438 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5439 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5439 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5439 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5439 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5440 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5440 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5440 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5440 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5441 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.exact_13_5441 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.data_13_5441 +#print axioms Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5441 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5442 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5442 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5442 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5442 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5443 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5443 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5443 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5443 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5444 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5444 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5444 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5444 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5445 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5445 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5445 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5445 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5446 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5446 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5446 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5446 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5447 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5447 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5447 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5447 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5448 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5448 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5448 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5448 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5449 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5449 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5449 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5449 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5450 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5450 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5450 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5450 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5451 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5451 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5451 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5451 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5452 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5452 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5452 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5452 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5453 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5453 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5453 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5453 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5454 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5454 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5454 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5454 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5455 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5455 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5455 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5455 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5456 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.exact_13_5456 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.data_13_5456 +#print axioms Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5456 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5457 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5457 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5457 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5457 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5458 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5458 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5458 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5458 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5459 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5459 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5459 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5459 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5460 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5460 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5460 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5460 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5461 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5461 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5461 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5461 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5462 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5462 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5462 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5462 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5463 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5463 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5463 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5463 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5464 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5464 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5464 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5464 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5465 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5465 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5465 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5465 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5466 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5466 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5466 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5466 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5467 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5467 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5467 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5467 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5468 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5468 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5468 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5468 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5469 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5469 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5469 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5469 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5470 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5470 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5470 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5470 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5471 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5471 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5471 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5471 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5472 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.exact_13_5472 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.data_13_5472 +#print axioms Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5472 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5473 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5473 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5473 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5473 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5474 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5474 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5474 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5474 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5475 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5475 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5475 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5475 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5476 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5476 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5476 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5476 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5477 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5477 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5477 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5477 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5478 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5478 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5478 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5478 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5479 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5479 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5479 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5479 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5480 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5480 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5480 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5480 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5481 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5481 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5481 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5481 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5482 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5482 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5482 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5482 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5483 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5483 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5483 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5483 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5484 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5484 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5484 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5484 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5485 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5485 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5485 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5485 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5486 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5486 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5486 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5486 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5487 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.exact_13_5487 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.data_13_5487 +#print axioms Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5487 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5488 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5488 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5488 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5488 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5489 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5489 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5489 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5489 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5490 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5490 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5490 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5490 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5491 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5491 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5491 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5491 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5492 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5492 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5492 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5492 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5493 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5493 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5493 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5493 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5494 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5494 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5494 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5494 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5495 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5495 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5495 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5495 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5496 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5496 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5496 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5496 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5497 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5497 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5497 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5497 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5498 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5498 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5498 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5498 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5499 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5499 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5499 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5499 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5500 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5500 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5500 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5500 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5501 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5501 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5501 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5501 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5502 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5502 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5502 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5502 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5503 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.exact_13_5503 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.data_13_5503 +#print axioms Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5503 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5504 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5504 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5504 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5504 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5505 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5505 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5505 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5505 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5506 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5506 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5506 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5506 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5507 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5507 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5507 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5507 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5508 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5508 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5508 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5508 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5509 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5509 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5509 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5509 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5510 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5510 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5510 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5510 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5511 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5511 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5511 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5511 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5512 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5512 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5512 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5512 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5513 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5513 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5513 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5513 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5514 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5514 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5514 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5514 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5515 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5515 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5515 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5515 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5516 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5516 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5516 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5516 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5517 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5517 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5517 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5517 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5518 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.exact_13_5518 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.data_13_5518 +#print axioms Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5518 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5519 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5519 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5519 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5519 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5520 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5520 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5520 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5520 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5521 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5521 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5521 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5521 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5522 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5522 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5522 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5522 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5523 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5523 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5523 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5523 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5524 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5524 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5524 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5524 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5525 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5525 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5525 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5525 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5526 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5526 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5526 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5526 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5527 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5527 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5527 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5527 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5528 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5528 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5528 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5528 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5529 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5529 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5529 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5529 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5530 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5530 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5530 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5530 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5531 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5531 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5531 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5531 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5532 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5532 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5532 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5532 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5533 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.exact_13_5533 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.data_13_5533 +#print axioms Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5533 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5534 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5534 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5534 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5534 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5535 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5535 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5535 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5535 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5536 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5536 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5536 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5536 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5537 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5537 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5537 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5537 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5538 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5538 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5538 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5538 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5539 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5539 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5539 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5539 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5540 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5540 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5540 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5540 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5541 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5541 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5541 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5541 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5542 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5542 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5542 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5542 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5543 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5543 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5543 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5543 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5544 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5544 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5544 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5544 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5545 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5545 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5545 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5545 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5546 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5546 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5546 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5546 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5547 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5547 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5547 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5547 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5548 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5548 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5548 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5548 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5549 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.exact_13_5549 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.data_13_5549 +#print axioms Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5549 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5550 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5550 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5550 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5550 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5551 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5551 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5551 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5551 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5552 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5552 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5552 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5552 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5553 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5553 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5553 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5553 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5554 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5554 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5554 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5554 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5555 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5555 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5555 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5555 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5556 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5556 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5556 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5556 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5557 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5557 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5557 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5557 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5558 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5558 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5558 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5558 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5559 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5559 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5559 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5559 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5560 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5560 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5560 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5560 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5561 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5561 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5561 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5561 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5562 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5562 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5562 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5562 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5563 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5563 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5563 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5563 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5564 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.exact_13_5564 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.data_13_5564 +#print axioms Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5564 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5565 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5565 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5565 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5565 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5566 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5566 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5566 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5566 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5567 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5567 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5567 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5567 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5568 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5568 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5568 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5568 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5569 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5569 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5569 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5569 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5570 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5570 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5570 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5570 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5571 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5571 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5571 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5571 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5572 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5572 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5572 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5572 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5573 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5573 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5573 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5573 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5574 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5574 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5574 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5574 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5575 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5575 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5575 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5575 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5576 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5576 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5576 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5576 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5577 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5577 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5577 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5577 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5578 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5578 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5578 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5578 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5579 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.exact_13_5579 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.data_13_5579 +#print axioms Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5579 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5580 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5580 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5580 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5580 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5581 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5581 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5581 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5581 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5582 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5582 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5582 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5582 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5583 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5583 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5583 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5583 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5584 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5584 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5584 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5584 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5585 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5585 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5585 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5585 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5586 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5586 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5586 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5586 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5587 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5587 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5587 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5587 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5588 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5588 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5588 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5588 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5589 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5589 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5589 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5589 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5590 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5590 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5590 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5590 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5591 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5591 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5591 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5591 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5592 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5592 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5592 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5592 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5593 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5593 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5593 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5593 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5594 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5594 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5594 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5594 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5595 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.exact_13_5595 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.data_13_5595 +#print axioms Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5595 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5596 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5596 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5596 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5596 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5597 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5597 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5597 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5597 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5598 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5598 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5598 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5598 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5599 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5599 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5599 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5599 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5600 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5600 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5600 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5600 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5601 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5601 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5601 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5601 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5602 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5602 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5602 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5602 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5603 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5603 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5603 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5603 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5604 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5604 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5604 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5604 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5605 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5605 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5605 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5605 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5606 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5606 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5606 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5606 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5607 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5607 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5607 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5607 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5608 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5608 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5608 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5608 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5609 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5609 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5609 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5609 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5610 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.exact_13_5610 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.data_13_5610 +#print axioms Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5610 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5611 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5611 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5611 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5611 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5612 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5612 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5612 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5612 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5613 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5613 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5613 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5613 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5614 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5614 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5614 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5614 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5615 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5615 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5615 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5615 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5616 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5616 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5616 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5616 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5617 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5617 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5617 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5617 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5618 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5618 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5618 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5618 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5619 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5619 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5619 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5619 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5620 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5620 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5620 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5620 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5621 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5621 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5621 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5621 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5622 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5622 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5622 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5622 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5623 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5623 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5623 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5623 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5624 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5624 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5624 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5624 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5625 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.exact_13_5625 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.data_13_5625 +#print axioms Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5625 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5626 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5626 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5626 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5626 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5627 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5627 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5627 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5627 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5628 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5628 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5628 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5628 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5629 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5629 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5629 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5629 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5630 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5630 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5630 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5630 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5631 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5631 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5631 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5631 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5632 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5632 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5632 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5632 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5633 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5633 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5633 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5633 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5634 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5634 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5634 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5634 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5635 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5635 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5635 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5635 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5636 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5636 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5636 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5636 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5637 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5637 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5637 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5637 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5638 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5638 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5638 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5638 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5639 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5639 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5639 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5639 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5640 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5640 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5640 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5640 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5641 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.exact_13_5641 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.data_13_5641 +#print axioms Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5641 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5642 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5642 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5642 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5642 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5643 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5643 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5643 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5643 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5644 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5644 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5644 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5644 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5645 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5645 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5645 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5645 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5646 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5646 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5646 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5646 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5647 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5647 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5647 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5647 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5648 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5648 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5648 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5648 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5649 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5649 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5649 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5649 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5650 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5650 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5650 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5650 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5651 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5651 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5651 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5651 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5652 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5652 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5652 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5652 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5653 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5653 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5653 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5653 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5654 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5654 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5654 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5654 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5655 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5655 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5655 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5655 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5656 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.exact_13_5656 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.data_13_5656 +#print axioms Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5656 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5657 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5657 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5657 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5657 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5658 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5658 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5658 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5658 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5659 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5659 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5659 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5659 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5660 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5660 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5660 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5660 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5661 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5661 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5661 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5661 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5662 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5662 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5662 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5662 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5663 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5663 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5663 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5663 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5664 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5664 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5664 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5664 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5665 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5665 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5665 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5665 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5666 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5666 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5666 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5666 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5667 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5667 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5667 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5667 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5668 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5668 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5668 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5668 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5669 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5669 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5669 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5669 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5670 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5670 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5670 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5670 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5671 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.exact_13_5671 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.data_13_5671 +#print axioms Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5671 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5672 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5672 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5672 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5672 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5673 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5673 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5673 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5673 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5674 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5674 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5674 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5674 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5675 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5675 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5675 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5675 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5676 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5676 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5676 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5676 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5677 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5677 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5677 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5677 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5678 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5678 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5678 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5678 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5679 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5679 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5679 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5679 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5680 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5680 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5680 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5680 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5681 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5681 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5681 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5681 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5682 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5682 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5682 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5682 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5683 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5683 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5683 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5683 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5684 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5684 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5684 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5684 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5685 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5685 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5685 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5685 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5686 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5686 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5686 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5686 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5687 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.exact_13_5687 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.data_13_5687 +#print axioms Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5687 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5688 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5688 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5688 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5688 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5689 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5689 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5689 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5689 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5690 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5690 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5690 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5690 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5691 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5691 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5691 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5691 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5692 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5692 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5692 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5692 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5693 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5693 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5693 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5693 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5694 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5694 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5694 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5694 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5695 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5695 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5695 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5695 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5696 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5696 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5696 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5696 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5697 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5697 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5697 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5697 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5698 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5698 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5698 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5698 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5699 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5699 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5699 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5699 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5700 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5700 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5700 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5700 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5701 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5701 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5701 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5701 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5702 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.exact_13_5702 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.data_13_5702 +#print axioms Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5702 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5703 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5703 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5703 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5703 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5704 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5704 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5704 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5704 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5705 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5705 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5705 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5705 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5706 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5706 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5706 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5706 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5707 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5707 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5707 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5707 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5708 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5708 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5708 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5708 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5709 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5709 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5709 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5709 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5710 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5710 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5710 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5710 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5711 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5711 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5711 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5711 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5712 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5712 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5712 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5712 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5713 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5713 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5713 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5713 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5714 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5714 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5714 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5714 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5715 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5715 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5715 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5715 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5716 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5716 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5716 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5716 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5717 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5717 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5717 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5717 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5718 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.exact_13_5718 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.data_13_5718 +#print axioms Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5718 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5719 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5719 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5719 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5719 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5720 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5720 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5720 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5720 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5721 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5721 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5721 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5721 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5722 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5722 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5722 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5722 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5723 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5723 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5723 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5723 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5724 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5724 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5724 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5724 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5725 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5725 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5725 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5725 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5726 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5726 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5726 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5726 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5727 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5727 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5727 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5727 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5728 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5728 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5728 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5728 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5729 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5729 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5729 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5729 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5730 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5730 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5730 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5730 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5731 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5731 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5731 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5731 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5732 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5732 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5732 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5732 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5733 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.exact_13_5733 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.data_13_5733 +#print axioms Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5733 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5734 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5734 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5734 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5734 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5735 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5735 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5735 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5735 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5736 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5736 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5736 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5736 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5737 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5737 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5737 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5737 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5738 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5738 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5738 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5738 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5739 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5739 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5739 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5739 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5740 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5740 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5740 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5740 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5741 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5741 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5741 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5741 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5742 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5742 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5742 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5742 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5743 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5743 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5743 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5743 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5744 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5744 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5744 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5744 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5745 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5745 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5745 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5745 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5746 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5746 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5746 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5746 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5747 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5747 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5747 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5747 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5748 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.exact_13_5748 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.data_13_5748 +#print axioms Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5748 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5749 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5749 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5749 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5749 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5750 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5750 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5750 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5750 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5751 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5751 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5751 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5751 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5752 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5752 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5752 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5752 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5753 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5753 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5753 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5753 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5754 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5754 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5754 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5754 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5755 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5755 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5755 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5755 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5756 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5756 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5756 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5756 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5757 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5757 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5757 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5757 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5758 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5758 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5758 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5758 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5759 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5759 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5759 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5759 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5760 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5760 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5760 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5760 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5761 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5761 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5761 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5761 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5762 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5762 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5762 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5762 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5763 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5763 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5763 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5763 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5764 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.exact_13_5764 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.data_13_5764 +#print axioms Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5764 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5765 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5765 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5765 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5765 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5766 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5766 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5766 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5766 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5767 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5767 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5767 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5767 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5768 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5768 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5768 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5768 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5769 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5769 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5769 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5769 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5770 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5770 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5770 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5770 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5771 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5771 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5771 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5771 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5772 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5772 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5772 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5772 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5773 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5773 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5773 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5773 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5774 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5774 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5774 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5774 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5775 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5775 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5775 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5775 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5776 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5776 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5776 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5776 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5777 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5777 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5777 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5777 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5778 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5778 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5778 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5778 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5779 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.exact_13_5779 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.data_13_5779 +#print axioms Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5779 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5780 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5780 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5780 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5780 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5781 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5781 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5781 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5781 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5782 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5782 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5782 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5782 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5783 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5783 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5783 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5783 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5784 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5784 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5784 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5784 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5785 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5785 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5785 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5785 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5786 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5786 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5786 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5786 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5787 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5787 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5787 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5787 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5788 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5788 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5788 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5788 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5789 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5789 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5789 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5789 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5790 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5790 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5790 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5790 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5791 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5791 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5791 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5791 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5792 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5792 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5792 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5792 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5793 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5793 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5793 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5793 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5794 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.exact_13_5794 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.data_13_5794 +#print axioms Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5794 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5795 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5795 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5795 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5795 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5796 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5796 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5796 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5796 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5797 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5797 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5797 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5797 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5798 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5798 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5798 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5798 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5799 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5799 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5799 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5799 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5800 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5800 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5800 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5800 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5801 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5801 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5801 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5801 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5802 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5802 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5802 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5802 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5803 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5803 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5803 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5803 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5804 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5804 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5804 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5804 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5805 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5805 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5805 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5805 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5806 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5806 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5806 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5806 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5807 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5807 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5807 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5807 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5808 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5808 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5808 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5808 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5809 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5809 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5809 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5809 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5810 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.exact_13_5810 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.data_13_5810 +#print axioms Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5810 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5811 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5811 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5811 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5811 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5812 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5812 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5812 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5812 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5813 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5813 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5813 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5813 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5814 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5814 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5814 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5814 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5815 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5815 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5815 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5815 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5816 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5816 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5816 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5816 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5817 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5817 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5817 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5817 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5818 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5818 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5818 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5818 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5819 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5819 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5819 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5819 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5820 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5820 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5820 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5820 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5821 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5821 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5821 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5821 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5822 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5822 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5822 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5822 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5823 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5823 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5823 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5823 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5824 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5824 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5824 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5824 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5825 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.exact_13_5825 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.data_13_5825 +#print axioms Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5825 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5826 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5826 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5826 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5826 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5827 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5827 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5827 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5827 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5828 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5828 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5828 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5828 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5829 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5829 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5829 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5829 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5830 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5830 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5830 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5830 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5831 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5831 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5831 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5831 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5832 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5832 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5832 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5832 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5833 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5833 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5833 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5833 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5834 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5834 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5834 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5834 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5835 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5835 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5835 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5835 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5836 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5836 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5836 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5836 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5837 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5837 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5837 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5837 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5838 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5838 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5838 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5838 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5839 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5839 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5839 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5839 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5840 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.exact_13_5840 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.data_13_5840 +#print axioms Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5840 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5841 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5841 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5841 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5841 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5842 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5842 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5842 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5842 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5843 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5843 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5843 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5843 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5844 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5844 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5844 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5844 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5845 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5845 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5845 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5845 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5846 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5846 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5846 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5846 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5847 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5847 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5847 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5847 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5848 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5848 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5848 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5848 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5849 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5849 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5849 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5849 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5850 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5850 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5850 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5850 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5851 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5851 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5851 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5851 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5852 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5852 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5852 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5852 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5853 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5853 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5853 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5853 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5854 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5854 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5854 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5854 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5855 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5855 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5855 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5855 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5856 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.exact_13_5856 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.data_13_5856 +#print axioms Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5856 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5857 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5857 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5857 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5857 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5858 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5858 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5858 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5858 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5859 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5859 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5859 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5859 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5860 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5860 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5860 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5860 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5861 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5861 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5861 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5861 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5862 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5862 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5862 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5862 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5863 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5863 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5863 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5863 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5864 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5864 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5864 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5864 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5865 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5865 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5865 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5865 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5866 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5866 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5866 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5866 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5867 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5867 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5867 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5867 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5868 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5868 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5868 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5868 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5869 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5869 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5869 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5869 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5870 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5870 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5870 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5870 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5871 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.exact_13_5871 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.data_13_5871 +#print axioms Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5871 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5872 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5872 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5872 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5872 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5873 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5873 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5873 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5873 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5874 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5874 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5874 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5874 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5875 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5875 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5875 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5875 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5876 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5876 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5876 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5876 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5877 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5877 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5877 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5877 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5878 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5878 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5878 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5878 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5879 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5879 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5879 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5879 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5880 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5880 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5880 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5880 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5881 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5881 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5881 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5881 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5882 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5882 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5882 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5882 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5883 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5883 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5883 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5883 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5884 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5884 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5884 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5884 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5885 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5885 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5885 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5885 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5886 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5886 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5886 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5886 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5887 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.exact_13_5887 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.data_13_5887 +#print axioms Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5887 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5888 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5888 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5888 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5888 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5889 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5889 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5889 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5889 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5890 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5890 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5890 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5890 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5891 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5891 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5891 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5891 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5892 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5892 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5892 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5892 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5893 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5893 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5893 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5893 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5894 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5894 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5894 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5894 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5895 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5895 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5895 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5895 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5896 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5896 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5896 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5896 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5897 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5897 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5897 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5897 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5898 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5898 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5898 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5898 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5899 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5899 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5899 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5899 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5900 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5900 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5900 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5900 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5901 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5901 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5901 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5901 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5902 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.exact_13_5902 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.data_13_5902 +#print axioms Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5902 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5903 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5903 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5903 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5903 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5904 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5904 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5904 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5904 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5905 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5905 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5905 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5905 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5906 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5906 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5906 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5906 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5907 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5907 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5907 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5907 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5908 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5908 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5908 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5908 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5909 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5909 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5909 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5909 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5910 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5910 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5910 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5910 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5911 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5911 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5911 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5911 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5912 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5912 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5912 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5912 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5913 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5913 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5913 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5913 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5914 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5914 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5914 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5914 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5915 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5915 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5915 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5915 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5916 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5916 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5916 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5916 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5917 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.exact_13_5917 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.data_13_5917 +#print axioms Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5917 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5918 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5918 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5918 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5918 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5919 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5919 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5919 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5919 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5920 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5920 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5920 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5920 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5921 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5921 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5921 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5921 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5922 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5922 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5922 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5922 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5923 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5923 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5923 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5923 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5924 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5924 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5924 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5924 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5925 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5925 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5925 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5925 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5926 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5926 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5926 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5926 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5927 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5927 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5927 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5927 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5928 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5928 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5928 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5928 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5929 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5929 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5929 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5929 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5930 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5930 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5930 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5930 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5931 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5931 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5931 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5931 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5932 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5932 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5932 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5932 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5933 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.exact_13_5933 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.data_13_5933 +#print axioms Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5933 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5934 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5934 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5934 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5934 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5935 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5935 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5935 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5935 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5936 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5936 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5936 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5936 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5937 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5937 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5937 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5937 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5938 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5938 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5938 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5938 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5939 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5939 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5939 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5939 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5940 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5940 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5940 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5940 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5941 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5941 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5941 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5941 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5942 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5942 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5942 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5942 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5943 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5943 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5943 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5943 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5944 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5944 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5944 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5944 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5945 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5945 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5945 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5945 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5946 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5946 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5946 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5946 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5947 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5947 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5947 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5947 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5948 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.exact_13_5948 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.data_13_5948 +#print axioms Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5948 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5949 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5949 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5949 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5949 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5950 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5950 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5950 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5950 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5951 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5951 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5951 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5951 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5952 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5952 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5952 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5952 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5953 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5953 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5953 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5953 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5954 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5954 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5954 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5954 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5955 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5955 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5955 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5955 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5956 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5956 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5956 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5956 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5957 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5957 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5957 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5957 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5958 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5958 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5958 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5958 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5959 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5959 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5959 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5959 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5960 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5960 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5960 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5960 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5961 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5961 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5961 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5961 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5962 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5962 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5962 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5962 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5963 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.exact_13_5963 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.data_13_5963 +#print axioms Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5963 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5964 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5964 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5964 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5964 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5965 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5965 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5965 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5965 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5966 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5966 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5966 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5966 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5967 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5967 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5967 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5967 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5968 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5968 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5968 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5968 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5969 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5969 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5969 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5969 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5970 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5970 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5970 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5970 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5971 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5971 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5971 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5971 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5972 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5972 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5972 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5972 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5973 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5973 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5973 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5973 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5974 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5974 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5974 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5974 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5975 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5975 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5975 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5975 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5976 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5976 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5976 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5976 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5977 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5977 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5977 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5977 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5978 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5978 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5978 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5978 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5979 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.exact_13_5979 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.data_13_5979 +#print axioms Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5979 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5980 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5980 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5980 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5980 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5981 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5981 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5981 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5981 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5982 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5982 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5982 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5982 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5983 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5983 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5983 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5983 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5984 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5984 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5984 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5984 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5985 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5985 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5985 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5985 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5986 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5986 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5986 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5986 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5987 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5987 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5987 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5987 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5988 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5988 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5988 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5988 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5989 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5989 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5989 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5989 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5990 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5990 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5990 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5990 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5991 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5991 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5991 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5991 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5992 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5992 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5992 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5992 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5993 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5993 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5993 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5993 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5994 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.exact_13_5994 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.data_13_5994 +#print axioms Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5994 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5995 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_5995 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_5995 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5995 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5996 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_5996 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_5996 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5996 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5997 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_5997 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_5997 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5997 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5998 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_5998 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_5998 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5998 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5999 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_5999 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_5999 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5999 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6000 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6000 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6000 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6000 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6001 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6001 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6001 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6001 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6002 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6002 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6002 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6002 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6003 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6003 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6003 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6003 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6004 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6004 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6004 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6004 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6005 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6005 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6005 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6005 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6006 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6006 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6006 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6006 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6007 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6007 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6007 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6007 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6008 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6008 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6008 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6008 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6009 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.exact_13_6009 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.data_13_6009 +#print axioms Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6009 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6010 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6010 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6010 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6010 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6011 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6011 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6011 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6011 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6012 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6012 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6012 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6012 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6013 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6013 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6013 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6013 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6014 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6014 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6014 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6014 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6015 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6015 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6015 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6015 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6016 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6016 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6016 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6016 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6017 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6017 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6017 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6017 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6018 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6018 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6018 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6018 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6019 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6019 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6019 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6019 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6020 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6020 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6020 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6020 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6021 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6021 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6021 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6021 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6022 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6022 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6022 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6022 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6023 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6023 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6023 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6023 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6024 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6024 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6024 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6024 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6025 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.exact_13_6025 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.data_13_6025 +#print axioms Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6025 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6026 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6026 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6026 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6026 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6027 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6027 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6027 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6027 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6028 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6028 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6028 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6028 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6029 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6029 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6029 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6029 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6030 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6030 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6030 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6030 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6031 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6031 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6031 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6031 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6032 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6032 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6032 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6032 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6033 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6033 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6033 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6033 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6034 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6034 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6034 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6034 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6035 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6035 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6035 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6035 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6036 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6036 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6036 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6036 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6037 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6037 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6037 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6037 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6038 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6038 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6038 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6038 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6039 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6039 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6039 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6039 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6040 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.exact_13_6040 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.data_13_6040 +#print axioms Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6040 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6041 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6041 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6041 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6041 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6042 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6042 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6042 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6042 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6043 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6043 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6043 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6043 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6044 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6044 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6044 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6044 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6045 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6045 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6045 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6045 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6046 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6046 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6046 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6046 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6047 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6047 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6047 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6047 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6048 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6048 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6048 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6048 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6049 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6049 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6049 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6049 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6050 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6050 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6050 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6050 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6051 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6051 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6051 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6051 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6052 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6052 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6052 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6052 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6053 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6053 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6053 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6053 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6054 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6054 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6054 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6054 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6055 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.exact_13_6055 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.data_13_6055 +#print axioms Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6055 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6056 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6056 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6056 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6056 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6057 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6057 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6057 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6057 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6058 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6058 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6058 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6058 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6059 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6059 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6059 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6059 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6060 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6060 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6060 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6060 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6061 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6061 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6061 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6061 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6062 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6062 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6062 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6062 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6063 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6063 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6063 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6063 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6064 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6064 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6064 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6064 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6065 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6065 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6065 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6065 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6066 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6066 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6066 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6066 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6067 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6067 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6067 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6067 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6068 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6068 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6068 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6068 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6069 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6069 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6069 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6069 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6070 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6070 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6070 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6070 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6071 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.exact_13_6071 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.data_13_6071 +#print axioms Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6071 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6072 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6072 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6072 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6072 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6073 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6073 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6073 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6073 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6074 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6074 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6074 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6074 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6075 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6075 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6075 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6075 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6076 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6076 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6076 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6076 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6077 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6077 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6077 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6077 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6078 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6078 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6078 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6078 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6079 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6079 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6079 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6079 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6080 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6080 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6080 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6080 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6081 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6081 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6081 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6081 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6082 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6082 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6082 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6082 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6083 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6083 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6083 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6083 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6084 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6084 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6084 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6084 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6085 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6085 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6085 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6085 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6086 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.exact_13_6086 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.data_13_6086 +#print axioms Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6086 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6087 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6087 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6087 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6087 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6088 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6088 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6088 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6088 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6089 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6089 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6089 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6089 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6090 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6090 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6090 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6090 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6091 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6091 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6091 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6091 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6092 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6092 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6092 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6092 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6093 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6093 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6093 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6093 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6094 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6094 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6094 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6094 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6095 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6095 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6095 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6095 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6096 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6096 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6096 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6096 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6097 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6097 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6097 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6097 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6098 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6098 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6098 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6098 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6099 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6099 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6099 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6099 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6100 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6100 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6100 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6100 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6101 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6101 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6101 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6101 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6102 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.exact_13_6102 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.data_13_6102 +#print axioms Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6102 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6103 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6103 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6103 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6103 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6104 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6104 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6104 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6104 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6105 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6105 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6105 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6105 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6106 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6106 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6106 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6106 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6107 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6107 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6107 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6107 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6108 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6108 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6108 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6108 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6109 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6109 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6109 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6109 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6110 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6110 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6110 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6110 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6111 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6111 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6111 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6111 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6112 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6112 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6112 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6112 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6113 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6113 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6113 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6113 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6114 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6114 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6114 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6114 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6115 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6115 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6115 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6115 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6116 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6116 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6116 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6116 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6117 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.exact_13_6117 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.data_13_6117 +#print axioms Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6117 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6118 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6118 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6118 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6118 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6119 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6119 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6119 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6119 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6120 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6120 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6120 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6120 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6121 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6121 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6121 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6121 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6122 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6122 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6122 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6122 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6123 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6123 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6123 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6123 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6124 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6124 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6124 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6124 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6125 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6125 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6125 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6125 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6126 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6126 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6126 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6126 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6127 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6127 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6127 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6127 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6128 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6128 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6128 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6128 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6129 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6129 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6129 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6129 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6130 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6130 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6130 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6130 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6131 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6131 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6131 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6131 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6132 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.exact_13_6132 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.data_13_6132 +#print axioms Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6132 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6133 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6133 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6133 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6133 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6134 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6134 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6134 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6134 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6135 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6135 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6135 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6135 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6136 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6136 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6136 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6136 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6137 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6137 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6137 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6137 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6138 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6138 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6138 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6138 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6139 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6139 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6139 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6139 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6140 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6140 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6140 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6140 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6141 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6141 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6141 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6141 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6142 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6142 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6142 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6142 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6143 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6143 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6143 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6143 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6144 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6144 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6144 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6144 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6145 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6145 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6145 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6145 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6146 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6146 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6146 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6146 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6147 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6147 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6147 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6147 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6148 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.exact_13_6148 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.data_13_6148 +#print axioms Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6148 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6149 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6149 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6149 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6149 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6150 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6150 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6150 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6150 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6151 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6151 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6151 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6151 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6152 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6152 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6152 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6152 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6153 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6153 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6153 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6153 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6154 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6154 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6154 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6154 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6155 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6155 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6155 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6155 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6156 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6156 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6156 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6156 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6157 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6157 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6157 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6157 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6158 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6158 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6158 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6158 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6159 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6159 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6159 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6159 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6160 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6160 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6160 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6160 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6161 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6161 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6161 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6161 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6162 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6162 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6162 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6162 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6163 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.exact_13_6163 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.data_13_6163 +#print axioms Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6163 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6164 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6164 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6164 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6164 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6165 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6165 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6165 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6165 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6166 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6166 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6166 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6166 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6167 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6167 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6167 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6167 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6168 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6168 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6168 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6168 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6169 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6169 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6169 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6169 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6170 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6170 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6170 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6170 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6171 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6171 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6171 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6171 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6172 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6172 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6172 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6172 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6173 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6173 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6173 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6173 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6174 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6174 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6174 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6174 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6175 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6175 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6175 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6175 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6176 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6176 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6176 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6176 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6177 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6177 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6177 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6177 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6178 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.exact_13_6178 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.data_13_6178 +#print axioms Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6178 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6179 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6179 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6179 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6179 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6180 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6180 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6180 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6180 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6181 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6181 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6181 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6181 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6182 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6182 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6182 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6182 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6183 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6183 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6183 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6183 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6184 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6184 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6184 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6184 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6185 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6185 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6185 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6185 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6186 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6186 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6186 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6186 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6187 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6187 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6187 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6187 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6188 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6188 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6188 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6188 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6189 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6189 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6189 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6189 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6190 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6190 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6190 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6190 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6191 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6191 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6191 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6191 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6192 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6192 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6192 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6192 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6193 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6193 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6193 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6193 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6194 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.exact_13_6194 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.data_13_6194 +#print axioms Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6194 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6195 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6195 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6195 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6195 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6196 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6196 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6196 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6196 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6197 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6197 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6197 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6197 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6198 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6198 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6198 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6198 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6199 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6199 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6199 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6199 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6200 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6200 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6200 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6200 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6201 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6201 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6201 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6201 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6202 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6202 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6202 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6202 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6203 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6203 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6203 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6203 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6204 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6204 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6204 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6204 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6205 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6205 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6205 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6205 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6206 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6206 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6206 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6206 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6207 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6207 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6207 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6207 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6208 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6208 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6208 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6208 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6209 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.exact_13_6209 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.data_13_6209 +#print axioms Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6209 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6210 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6210 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6210 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6210 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6211 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6211 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6211 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6211 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6212 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6212 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6212 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6212 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6213 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6213 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6213 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6213 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6214 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6214 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6214 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6214 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6215 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6215 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6215 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6215 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6216 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6216 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6216 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6216 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6217 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6217 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6217 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6217 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6218 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6218 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6218 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6218 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6219 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6219 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6219 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6219 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6220 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6220 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6220 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6220 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6221 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6221 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6221 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6221 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6222 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6222 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6222 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6222 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6223 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6223 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6223 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6223 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6224 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.exact_13_6224 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.data_13_6224 +#print axioms Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6224 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6225 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6225 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6225 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6225 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6226 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6226 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6226 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6226 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6227 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6227 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6227 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6227 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6228 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6228 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6228 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6228 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6229 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6229 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6229 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6229 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6230 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6230 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6230 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6230 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6231 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6231 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6231 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6231 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6232 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6232 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6232 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6232 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6233 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6233 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6233 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6233 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6234 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6234 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6234 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6234 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6235 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6235 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6235 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6235 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6236 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6236 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6236 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6236 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6237 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6237 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6237 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6237 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6238 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6238 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6238 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6238 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6239 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6239 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6239 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6239 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6240 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.exact_13_6240 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.data_13_6240 +#print axioms Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6240 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6241 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6241 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6241 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6241 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6242 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6242 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6242 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6242 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6243 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6243 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6243 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6243 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6244 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6244 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6244 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6244 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6245 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6245 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6245 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6245 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6246 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6246 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6246 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6246 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6247 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6247 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6247 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6247 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6248 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6248 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6248 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6248 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6249 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6249 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6249 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6249 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6250 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6250 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6250 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6250 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6251 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6251 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6251 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6251 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6252 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6252 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6252 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6252 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6253 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6253 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6253 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6253 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6254 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6254 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6254 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6254 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6255 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.exact_13_6255 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.data_13_6255 +#print axioms Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6255 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6256 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6256 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6256 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6256 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6257 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6257 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6257 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6257 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6258 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6258 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6258 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6258 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6259 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6259 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6259 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6259 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6260 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6260 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6260 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6260 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6261 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6261 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6261 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6261 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6262 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6262 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6262 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6262 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6263 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6263 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6263 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6263 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6264 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6264 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6264 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6264 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6265 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6265 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6265 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6265 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6266 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6266 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6266 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6266 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6267 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6267 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6267 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6267 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6268 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6268 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6268 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6268 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6269 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6269 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6269 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6269 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6270 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6270 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6270 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6270 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6271 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.exact_13_6271 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.data_13_6271 +#print axioms Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6271 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6272 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6272 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6272 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6272 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6273 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6273 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6273 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6273 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6274 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6274 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6274 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6274 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6275 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6275 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6275 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6275 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6276 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6276 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6276 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6276 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6277 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6277 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6277 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6277 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6278 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6278 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6278 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6278 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6279 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6279 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6279 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6279 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6280 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6280 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6280 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6280 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6281 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6281 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6281 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6281 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6282 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6282 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6282 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6282 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6283 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6283 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6283 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6283 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6284 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6284 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6284 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6284 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6285 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6285 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6285 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6285 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6286 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.exact_13_6286 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.data_13_6286 +#print axioms Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6286 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6287 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6287 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6287 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6287 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6288 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6288 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6288 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6288 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6289 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6289 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6289 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6289 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6290 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6290 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6290 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6290 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6291 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6291 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6291 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6291 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6292 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6292 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6292 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6292 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6293 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6293 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6293 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6293 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6294 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6294 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6294 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6294 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6295 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6295 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6295 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6295 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6296 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6296 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6296 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6296 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6297 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6297 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6297 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6297 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6298 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6298 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6298 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6298 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6299 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6299 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6299 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6299 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6300 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6300 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6300 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6300 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6301 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.exact_13_6301 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.data_13_6301 +#print axioms Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6301 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6302 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6302 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6302 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6302 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6303 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6303 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6303 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6303 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6304 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6304 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6304 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6304 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6305 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6305 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6305 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6305 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6306 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6306 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6306 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6306 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6307 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6307 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6307 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6307 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6308 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6308 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6308 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6308 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6309 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6309 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6309 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6309 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6310 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6310 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6310 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6310 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6311 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6311 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6311 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6311 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6312 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6312 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6312 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6312 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6313 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6313 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6313 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6313 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6314 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6314 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6314 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6314 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6315 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6315 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6315 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6315 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6316 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6316 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6316 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6316 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6317 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.exact_13_6317 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.data_13_6317 +#print axioms Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6317 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6318 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6318 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6318 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6318 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6319 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6319 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6319 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6319 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6320 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6320 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6320 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6320 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6321 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6321 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6321 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6321 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6322 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6322 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6322 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6322 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6323 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6323 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6323 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6323 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6324 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6324 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6324 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6324 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6325 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6325 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6325 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6325 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6326 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6326 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6326 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6326 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6327 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6327 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6327 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6327 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6328 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6328 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6328 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6328 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6329 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6329 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6329 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6329 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6330 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6330 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6330 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6330 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6331 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6331 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6331 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6331 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6332 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.exact_13_6332 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.data_13_6332 +#print axioms Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6332 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6333 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6333 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6333 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6333 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6334 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6334 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6334 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6334 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6335 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6335 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6335 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6335 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6336 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6336 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6336 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6336 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6337 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6337 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6337 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6337 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6338 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6338 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6338 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6338 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6339 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6339 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6339 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6339 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6340 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6340 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6340 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6340 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6341 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6341 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6341 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6341 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6342 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6342 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6342 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6342 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6343 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6343 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6343 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6343 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6344 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6344 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6344 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6344 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6345 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6345 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6345 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6345 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6346 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6346 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6346 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6346 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6347 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.exact_13_6347 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.data_13_6347 +#print axioms Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6347 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6348 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6348 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6348 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6348 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6349 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6349 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6349 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6349 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6350 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6350 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6350 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6350 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6351 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6351 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6351 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6351 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6352 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6352 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6352 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6352 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6353 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6353 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6353 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6353 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6354 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6354 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6354 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6354 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6355 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6355 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6355 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6355 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6356 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6356 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6356 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6356 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6357 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6357 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6357 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6357 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6358 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6358 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6358 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6358 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6359 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6359 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6359 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6359 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6360 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6360 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6360 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6360 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6361 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6361 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6361 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6361 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6362 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6362 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6362 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6362 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6363 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.exact_13_6363 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.data_13_6363 +#print axioms Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6363 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6364 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6364 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6364 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6364 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6365 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6365 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6365 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6365 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6366 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6366 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6366 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6366 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6367 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6367 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6367 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6367 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6368 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6368 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6368 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6368 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6369 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6369 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6369 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6369 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6370 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6370 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6370 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6370 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6371 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6371 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6371 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6371 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6372 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6372 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6372 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6372 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6373 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6373 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6373 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6373 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6374 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6374 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6374 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6374 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6375 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6375 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6375 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6375 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6376 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6376 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6376 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6376 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6377 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6377 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6377 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6377 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6378 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.exact_13_6378 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.data_13_6378 +#print axioms Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6378 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6379 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6379 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6379 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6379 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6380 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6380 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6380 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6380 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6381 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6381 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6381 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6381 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6382 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6382 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6382 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6382 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6383 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6383 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6383 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6383 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6384 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6384 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6384 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6384 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6385 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6385 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6385 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6385 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6386 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6386 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6386 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6386 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6387 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6387 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6387 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6387 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6388 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6388 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6388 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6388 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6389 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6389 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6389 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6389 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6390 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6390 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6390 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6390 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6391 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6391 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6391 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6391 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6392 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6392 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6392 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6392 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6393 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.exact_13_6393 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.data_13_6393 +#print axioms Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6393 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6394 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6394 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6394 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6394 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6395 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6395 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6395 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6395 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6396 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6396 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6396 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6396 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6397 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6397 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6397 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6397 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6398 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6398 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6398 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6398 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6399 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6399 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6399 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6399 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6400 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6400 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6400 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6400 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6401 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6401 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6401 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6401 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6402 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6402 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6402 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6402 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6403 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6403 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6403 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6403 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6404 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6404 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6404 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6404 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6405 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6405 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6405 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6405 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6406 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6406 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6406 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6406 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6407 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6407 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6407 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6407 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6408 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6408 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6408 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6408 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6409 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.exact_13_6409 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.data_13_6409 +#print axioms Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6409 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6410 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6410 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6410 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6410 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6411 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6411 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6411 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6411 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6412 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6412 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6412 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6412 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6413 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6413 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6413 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6413 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6414 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6414 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6414 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6414 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6415 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6415 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6415 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6415 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6416 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6416 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6416 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6416 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6417 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6417 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6417 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6417 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6418 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6418 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6418 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6418 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6419 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6419 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6419 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6419 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6420 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6420 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6420 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6420 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6421 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6421 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6421 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6421 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6422 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6422 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6422 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6422 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6423 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6423 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6423 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6423 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6424 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.exact_13_6424 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.data_13_6424 +#print axioms Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6424 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6425 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6425 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6425 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6425 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6426 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6426 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6426 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6426 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6427 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6427 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6427 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6427 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6428 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6428 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6428 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6428 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6429 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6429 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6429 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6429 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6430 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6430 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6430 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6430 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6431 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6431 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6431 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6431 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6432 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6432 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6432 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6432 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6433 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6433 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6433 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6433 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6434 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6434 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6434 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6434 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6435 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6435 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6435 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6435 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6436 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6436 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6436 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6436 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6437 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6437 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6437 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6437 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6438 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6438 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6438 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6438 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6439 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.exact_13_6439 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.data_13_6439 +#print axioms Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6439 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6440 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6440 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6440 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6440 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6441 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6441 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6441 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6441 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6442 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6442 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6442 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6442 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6443 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6443 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6443 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6443 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6444 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6444 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6444 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6444 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6445 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6445 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6445 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6445 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6446 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6446 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6446 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6446 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6447 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6447 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6447 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6447 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6448 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6448 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6448 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6448 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6449 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6449 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6449 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6449 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6450 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6450 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6450 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6450 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6451 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6451 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6451 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6451 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6452 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6452 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6452 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6452 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6453 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6453 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6453 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6453 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6454 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6454 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6454 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6454 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6455 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.exact_13_6455 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.data_13_6455 +#print axioms Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6455 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6456 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6456 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6456 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6456 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6457 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6457 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6457 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6457 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6458 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6458 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6458 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6458 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6459 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6459 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6459 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6459 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6460 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6460 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6460 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6460 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6461 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6461 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6461 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6461 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6462 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6462 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6462 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6462 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6463 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6463 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6463 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6463 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6464 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6464 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6464 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6464 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6465 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6465 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6465 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6465 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6466 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6466 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6466 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6466 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6467 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6467 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6467 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6467 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6468 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6468 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6468 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6468 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6469 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6469 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6469 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6469 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6470 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.exact_13_6470 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.data_13_6470 +#print axioms Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6470 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6471 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6471 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6471 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6471 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6472 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6472 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6472 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6472 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6473 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6473 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6473 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6473 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6474 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6474 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6474 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6474 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6475 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6475 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6475 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6475 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6476 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6476 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6476 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6476 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6477 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6477 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6477 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6477 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6478 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6478 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6478 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6478 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6479 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6479 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6479 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6479 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6480 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6480 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6480 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6480 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6481 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6481 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6481 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6481 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6482 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6482 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6482 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6482 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6483 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6483 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6483 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6483 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6484 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6484 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6484 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6484 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6485 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6485 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6485 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6485 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6486 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.exact_13_6486 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.data_13_6486 +#print axioms Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6486 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6487 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6487 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6487 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6487 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6488 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6488 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6488 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6488 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6489 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6489 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6489 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6489 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6490 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6490 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6490 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6490 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6491 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6491 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6491 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6491 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6492 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6492 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6492 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6492 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6493 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6493 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6493 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6493 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6494 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6494 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6494 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6494 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6495 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6495 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6495 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6495 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6496 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6496 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6496 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6496 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6497 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6497 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6497 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6497 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6498 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6498 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6498 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6498 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6499 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6499 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6499 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6499 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6500 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6500 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6500 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6500 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6501 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.exact_13_6501 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.data_13_6501 +#print axioms Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6501 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6502 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6502 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6502 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6502 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6503 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6503 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6503 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6503 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6504 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6504 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6504 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6504 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6505 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6505 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6505 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6505 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6506 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6506 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6506 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6506 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6507 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6507 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6507 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6507 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6508 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6508 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6508 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6508 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6509 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6509 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6509 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6509 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6510 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6510 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6510 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6510 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6511 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6511 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6511 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6511 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6512 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6512 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6512 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6512 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6513 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6513 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6513 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6513 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6514 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6514 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6514 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6514 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6515 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6515 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6515 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6515 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6516 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.exact_13_6516 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.data_13_6516 +#print axioms Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6516 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6517 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6517 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6517 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6517 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6518 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6518 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6518 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6518 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6519 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6519 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6519 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6519 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6520 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6520 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6520 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6520 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6521 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6521 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6521 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6521 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6522 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6522 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6522 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6522 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6523 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6523 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6523 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6523 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6524 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6524 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6524 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6524 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6525 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6525 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6525 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6525 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6526 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6526 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6526 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6526 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6527 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6527 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6527 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6527 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6528 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6528 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6528 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6528 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6529 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6529 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6529 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6529 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6530 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6530 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6530 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6530 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6531 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6531 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6531 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6531 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6532 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.exact_13_6532 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.data_13_6532 +#print axioms Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6532 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6533 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6533 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6533 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6533 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6534 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6534 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6534 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6534 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6535 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6535 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6535 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6535 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6536 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6536 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6536 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6536 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6537 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6537 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6537 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6537 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6538 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6538 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6538 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6538 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6539 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6539 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6539 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6539 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6540 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6540 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6540 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6540 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6541 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6541 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6541 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6541 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6542 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6542 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6542 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6542 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6543 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6543 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6543 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6543 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6544 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6544 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6544 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6544 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6545 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6545 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6545 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6545 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6546 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6546 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6546 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6546 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6547 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.exact_13_6547 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.data_13_6547 +#print axioms Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6547 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6548 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6548 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6548 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6548 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6549 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6549 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6549 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6549 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6550 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6550 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6550 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6550 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6551 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6551 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6551 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6551 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6552 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6552 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6552 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6552 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6553 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6553 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6553 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6553 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6554 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6554 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6554 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6554 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6555 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6555 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6555 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6555 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6556 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6556 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6556 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6556 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6557 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6557 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6557 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6557 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6558 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6558 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6558 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6558 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6559 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6559 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6559 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6559 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6560 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6560 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6560 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6560 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6561 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6561 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6561 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6561 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6562 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.exact_13_6562 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.data_13_6562 +#print axioms Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6562 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6563 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6563 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6563 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6563 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6564 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6564 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6564 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6564 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6565 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6565 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6565 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6565 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6566 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6566 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6566 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6566 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6567 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6567 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6567 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6567 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6568 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6568 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6568 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6568 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6569 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6569 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6569 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6569 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6570 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6570 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6570 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6570 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6571 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6571 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6571 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6571 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6572 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6572 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6572 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6572 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6573 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6573 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6573 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6573 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6574 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6574 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6574 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6574 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6575 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6575 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6575 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6575 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6576 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6576 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6576 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6576 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6577 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6577 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6577 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6577 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6578 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.exact_13_6578 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.data_13_6578 +#print axioms Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6578 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6579 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6579 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6579 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6579 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6580 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6580 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6580 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6580 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6581 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6581 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6581 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6581 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6582 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6582 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6582 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6582 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6583 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6583 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6583 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6583 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6584 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6584 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6584 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6584 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6585 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6585 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6585 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6585 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6586 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6586 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6586 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6586 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6587 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6587 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6587 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6587 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6588 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6588 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6588 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6588 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6589 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6589 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6589 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6589 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6590 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6590 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6590 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6590 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6591 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6591 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6591 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6591 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6592 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6592 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6592 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6592 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6593 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.exact_13_6593 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.data_13_6593 +#print axioms Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6593 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6594 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6594 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6594 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6594 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6595 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6595 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6595 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6595 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6596 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6596 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6596 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6596 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6597 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6597 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6597 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6597 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6598 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6598 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6598 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6598 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6599 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6599 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6599 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6599 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6600 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6600 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6600 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6600 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6601 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6601 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6601 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6601 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6602 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6602 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6602 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6602 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6603 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6603 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6603 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6603 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6604 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6604 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6604 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6604 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6605 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6605 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6605 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6605 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6606 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6606 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6606 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6606 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6607 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6607 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6607 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6607 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6608 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.exact_13_6608 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.data_13_6608 +#print axioms Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6608 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6609 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6609 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6609 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6609 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6610 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6610 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6610 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6610 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6611 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6611 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6611 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6611 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6612 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6612 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6612 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6612 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6613 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6613 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6613 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6613 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6614 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6614 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6614 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6614 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6615 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6615 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6615 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6615 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6616 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6616 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6616 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6616 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6617 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6617 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6617 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6617 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6618 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6618 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6618 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6618 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6619 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6619 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6619 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6619 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6620 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6620 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6620 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6620 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6621 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6621 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6621 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6621 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6622 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6622 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6622 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6622 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6623 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6623 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6623 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6623 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6624 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.exact_13_6624 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.data_13_6624 +#print axioms Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6624 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6625 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6625 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6625 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6625 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6626 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6626 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6626 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6626 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6627 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6627 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6627 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6627 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6628 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6628 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6628 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6628 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6629 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6629 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6629 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6629 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6630 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6630 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6630 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6630 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6631 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6631 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6631 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6631 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6632 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6632 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6632 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6632 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6633 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6633 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6633 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6633 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6634 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6634 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6634 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6634 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6635 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6635 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6635 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6635 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6636 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6636 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6636 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6636 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6637 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6637 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6637 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6637 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6638 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6638 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6638 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6638 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6639 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.exact_13_6639 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.data_13_6639 +#print axioms Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6639 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6640 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6640 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6640 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6640 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6641 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6641 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6641 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6641 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6642 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6642 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6642 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6642 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6643 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6643 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6643 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6643 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6644 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6644 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6644 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6644 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6645 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6645 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6645 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6645 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6646 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6646 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6646 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6646 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6647 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6647 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6647 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6647 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6648 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6648 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6648 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6648 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6649 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6649 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6649 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6649 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6650 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6650 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6650 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6650 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6651 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6651 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6651 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6651 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6652 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6652 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6652 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6652 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6653 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6653 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6653 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6653 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6654 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6654 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6654 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6654 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6655 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.exact_13_6655 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.data_13_6655 +#print axioms Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6655 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6656 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6656 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6656 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6656 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6657 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6657 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6657 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6657 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6658 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6658 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6658 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6658 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6659 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6659 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6659 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6659 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6660 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6660 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6660 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6660 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6661 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6661 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6661 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6661 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6662 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6662 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6662 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6662 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6663 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6663 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6663 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6663 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6664 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6664 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6664 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6664 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6665 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6665 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6665 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6665 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6666 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6666 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6666 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6666 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6667 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6667 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6667 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6667 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6668 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6668 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6668 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6668 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6669 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6669 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6669 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6669 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6670 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.exact_13_6670 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.data_13_6670 +#print axioms Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6670 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6671 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6671 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6671 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6671 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6672 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6672 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6672 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6672 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6673 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6673 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6673 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6673 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6674 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6674 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6674 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6674 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6675 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6675 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6675 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6675 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6676 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6676 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6676 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6676 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6677 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6677 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6677 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6677 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6678 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6678 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6678 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6678 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6679 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6679 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6679 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6679 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6680 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6680 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6680 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6680 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6681 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6681 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6681 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6681 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6682 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6682 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6682 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6682 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6683 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6683 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6683 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6683 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6684 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6684 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6684 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6684 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6685 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.exact_13_6685 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.data_13_6685 +#print axioms Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6685 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6686 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6686 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6686 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6686 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6687 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6687 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6687 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6687 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6688 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6688 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6688 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6688 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6689 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6689 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6689 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6689 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6690 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6690 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6690 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6690 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6691 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6691 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6691 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6691 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6692 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6692 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6692 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6692 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6693 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6693 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6693 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6693 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6694 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6694 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6694 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6694 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6695 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6695 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6695 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6695 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6696 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6696 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6696 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6696 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6697 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6697 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6697 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6697 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6698 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6698 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6698 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6698 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6699 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6699 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6699 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6699 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6700 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6700 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6700 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6700 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6701 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.exact_13_6701 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.data_13_6701 +#print axioms Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6701 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6702 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6702 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6702 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6702 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6703 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6703 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6703 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6703 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6704 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6704 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6704 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6704 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6705 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6705 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6705 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6705 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6706 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6706 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6706 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6706 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6707 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6707 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6707 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6707 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6708 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6708 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6708 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6708 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6709 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6709 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6709 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6709 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6710 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6710 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6710 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6710 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6711 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6711 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6711 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6711 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6712 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6712 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6712 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6712 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6713 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6713 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6713 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6713 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6714 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6714 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6714 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6714 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6715 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6715 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6715 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6715 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6716 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.exact_13_6716 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.data_13_6716 +#print axioms Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6716 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6717 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6717 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6717 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6717 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6718 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6718 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6718 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6718 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6719 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6719 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6719 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6719 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6720 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6720 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6720 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6720 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6721 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6721 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6721 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6721 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6722 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6722 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6722 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6722 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6723 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6723 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6723 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6723 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6724 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6724 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6724 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6724 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6725 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6725 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6725 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6725 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6726 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6726 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6726 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6726 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6727 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6727 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6727 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6727 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6728 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6728 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6728 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6728 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6729 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6729 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6729 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6729 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6730 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6730 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6730 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6730 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6731 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.exact_13_6731 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.data_13_6731 +#print axioms Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6731 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6732 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6732 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6732 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6732 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6733 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6733 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6733 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6733 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6734 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6734 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6734 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6734 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6735 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6735 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6735 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6735 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6736 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6736 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6736 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6736 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6737 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6737 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6737 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6737 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6738 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6738 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6738 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6738 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6739 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6739 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6739 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6739 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6740 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6740 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6740 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6740 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6741 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6741 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6741 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6741 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6742 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6742 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6742 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6742 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6743 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6743 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6743 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6743 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6744 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6744 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6744 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6744 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6745 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6745 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6745 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6745 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6746 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6746 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6746 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6746 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6747 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.exact_13_6747 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.data_13_6747 +#print axioms Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6747 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6748 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6748 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6748 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6748 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6749 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6749 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6749 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6749 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6750 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6750 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6750 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6750 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6751 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6751 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6751 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6751 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6752 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6752 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6752 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6752 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6753 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6753 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6753 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6753 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6754 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6754 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6754 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6754 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6755 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6755 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6755 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6755 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6756 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6756 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6756 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6756 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6757 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6757 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6757 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6757 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6758 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6758 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6758 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6758 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6759 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6759 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6759 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6759 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6760 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6760 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6760 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6760 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6761 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6761 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6761 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6761 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6762 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.exact_13_6762 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.data_13_6762 +#print axioms Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6762 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6763 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6763 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6763 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6763 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6764 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6764 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6764 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6764 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6765 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6765 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6765 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6765 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6766 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6766 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6766 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6766 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6767 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6767 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6767 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6767 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6768 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6768 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6768 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6768 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6769 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6769 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6769 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6769 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6770 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6770 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6770 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6770 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6771 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6771 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6771 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6771 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6772 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6772 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6772 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6772 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6773 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6773 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6773 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6773 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6774 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6774 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6774 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6774 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6775 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6775 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6775 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6775 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6776 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6776 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6776 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6776 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6777 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.exact_13_6777 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.data_13_6777 +#print axioms Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6777 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6778 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6778 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6778 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6778 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6779 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6779 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6779 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6779 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6780 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6780 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6780 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6780 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6781 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6781 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6781 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6781 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6782 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6782 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6782 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6782 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6783 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6783 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6783 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6783 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6784 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6784 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6784 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6784 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6785 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6785 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6785 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6785 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6786 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6786 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6786 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6786 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6787 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6787 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6787 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6787 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6788 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6788 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6788 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6788 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6789 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6789 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6789 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6789 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6790 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6790 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6790 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6790 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6791 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6791 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6791 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6791 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6792 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6792 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6792 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6792 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6793 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.exact_13_6793 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.data_13_6793 +#print axioms Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6793 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6794 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6794 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6794 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6794 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6795 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6795 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6795 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6795 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6796 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6796 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6796 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6796 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6797 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6797 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6797 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6797 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6798 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6798 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6798 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6798 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6799 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6799 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6799 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6799 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6800 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6800 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6800 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6800 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6801 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6801 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6801 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6801 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6802 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6802 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6802 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6802 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6803 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6803 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6803 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6803 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6804 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6804 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6804 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6804 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6805 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6805 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6805 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6805 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6806 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6806 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6806 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6806 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6807 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6807 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6807 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6807 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6808 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.exact_13_6808 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.data_13_6808 +#print axioms Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6808 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6809 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6809 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6809 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6809 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6810 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6810 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6810 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6810 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6811 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6811 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6811 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6811 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6812 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6812 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6812 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6812 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6813 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6813 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6813 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6813 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6814 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6814 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6814 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6814 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6815 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6815 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6815 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6815 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6816 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6816 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6816 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6816 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6817 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6817 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6817 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6817 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6818 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6818 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6818 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6818 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6819 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6819 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6819 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6819 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6820 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6820 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6820 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6820 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6821 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6821 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6821 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6821 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6822 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6822 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6822 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6822 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6823 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.exact_13_6823 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.data_13_6823 +#print axioms Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6823 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6824 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6824 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6824 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6824 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6825 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6825 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6825 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6825 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6826 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6826 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6826 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6826 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6827 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6827 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6827 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6827 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6828 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6828 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6828 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6828 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6829 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6829 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6829 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6829 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6830 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6830 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6830 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6830 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6831 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6831 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6831 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6831 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6832 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6832 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6832 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6832 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6833 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6833 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6833 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6833 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6834 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6834 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6834 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6834 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6835 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6835 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6835 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6835 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6836 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6836 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6836 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6836 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6837 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6837 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6837 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6837 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6838 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6838 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6838 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6838 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6839 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.exact_13_6839 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.data_13_6839 +#print axioms Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6839 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6840 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6840 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6840 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6840 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6841 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6841 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6841 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6841 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6842 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6842 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6842 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6842 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6843 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6843 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6843 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6843 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6844 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6844 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6844 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6844 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6845 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6845 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6845 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6845 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6846 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6846 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6846 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6846 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6847 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6847 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6847 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6847 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6848 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6848 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6848 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6848 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6849 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6849 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6849 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6849 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6850 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6850 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6850 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6850 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6851 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6851 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6851 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6851 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6852 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6852 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6852 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6852 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6853 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6853 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6853 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6853 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6854 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.exact_13_6854 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.data_13_6854 +#print axioms Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6854 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6855 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6855 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6855 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6855 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6856 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6856 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6856 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6856 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6857 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6857 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6857 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6857 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6858 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6858 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6858 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6858 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6859 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6859 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6859 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6859 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6860 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6860 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6860 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6860 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6861 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6861 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6861 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6861 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6862 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6862 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6862 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6862 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6863 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6863 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6863 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6863 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6864 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6864 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6864 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6864 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6865 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6865 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6865 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6865 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6866 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6866 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6866 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6866 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6867 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6867 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6867 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6867 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6868 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6868 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6868 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6868 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6869 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6869 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6869 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6869 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6870 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.exact_13_6870 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.data_13_6870 +#print axioms Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6870 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6871 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6871 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6871 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6871 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6872 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6872 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6872 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6872 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6873 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6873 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6873 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6873 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6874 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6874 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6874 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6874 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6875 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6875 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6875 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6875 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6876 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6876 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6876 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6876 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6877 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6877 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6877 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6877 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6878 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6878 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6878 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6878 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6879 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6879 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6879 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6879 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6880 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6880 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6880 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6880 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6881 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6881 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6881 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6881 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6882 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6882 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6882 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6882 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6883 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6883 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6883 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6883 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6884 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6884 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6884 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6884 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6885 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.exact_13_6885 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.data_13_6885 +#print axioms Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6885 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6886 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6886 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6886 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6886 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6887 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6887 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6887 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6887 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6888 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6888 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6888 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6888 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6889 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6889 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6889 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6889 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6890 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6890 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6890 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6890 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6891 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6891 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6891 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6891 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6892 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6892 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6892 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6892 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6893 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6893 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6893 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6893 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6894 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6894 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6894 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6894 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6895 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6895 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6895 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6895 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6896 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6896 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6896 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6896 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6897 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6897 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6897 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6897 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6898 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6898 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6898 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6898 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6899 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6899 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6899 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6899 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6900 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.exact_13_6900 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.data_13_6900 +#print axioms Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6900 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6901 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6901 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6901 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6901 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6902 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6902 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6902 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6902 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6903 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6903 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6903 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6903 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6904 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6904 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6904 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6904 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6905 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6905 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6905 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6905 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6906 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6906 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6906 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6906 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6907 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6907 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6907 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6907 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6908 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6908 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6908 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6908 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6909 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6909 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6909 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6909 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6910 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6910 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6910 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6910 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6911 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6911 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6911 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6911 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6912 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6912 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6912 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6912 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6913 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6913 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6913 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6913 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6914 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6914 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6914 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6914 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6915 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6915 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6915 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6915 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6916 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.exact_13_6916 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.data_13_6916 +#print axioms Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6916 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6917 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6917 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6917 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6917 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6918 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6918 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6918 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6918 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6919 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6919 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6919 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6919 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6920 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6920 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6920 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6920 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6921 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6921 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6921 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6921 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6922 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6922 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6922 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6922 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6923 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6923 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6923 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6923 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6924 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6924 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6924 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6924 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6925 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6925 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6925 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6925 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6926 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6926 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6926 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6926 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6927 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6927 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6927 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6927 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6928 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6928 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6928 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6928 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6929 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6929 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6929 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6929 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6930 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6930 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6930 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6930 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6931 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.exact_13_6931 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.data_13_6931 +#print axioms Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6931 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6932 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6932 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6932 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6932 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6933 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6933 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6933 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6933 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6934 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6934 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6934 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6934 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6935 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6935 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6935 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6935 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6936 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6936 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6936 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6936 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6937 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6937 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6937 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6937 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6938 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6938 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6938 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6938 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6939 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6939 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6939 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6939 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6940 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6940 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6940 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6940 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6941 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6941 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6941 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6941 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6942 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6942 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6942 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6942 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6943 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6943 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6943 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6943 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6944 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6944 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6944 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6944 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6945 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6945 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6945 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6945 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6946 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.exact_13_6946 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.data_13_6946 +#print axioms Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6946 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6947 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6947 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6947 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6947 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6948 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6948 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6948 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6948 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6949 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6949 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6949 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6949 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6950 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6950 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6950 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6950 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6951 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6951 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6951 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6951 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6952 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6952 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6952 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6952 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6953 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6953 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6953 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6953 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6954 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6954 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6954 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6954 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6955 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6955 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6955 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6955 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6956 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6956 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6956 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6956 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6957 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6957 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6957 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6957 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6958 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6958 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6958 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6958 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6959 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6959 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6959 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6959 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6960 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6960 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6960 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6960 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6961 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6961 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6961 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6961 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6962 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.exact_13_6962 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.data_13_6962 +#print axioms Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6962 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6963 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6963 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6963 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6963 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6964 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6964 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6964 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6964 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6965 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6965 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6965 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6965 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6966 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6966 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6966 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6966 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6967 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6967 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6967 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6967 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6968 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6968 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6968 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6968 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6969 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6969 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6969 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6969 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6970 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6970 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6970 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6970 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6971 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6971 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6971 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6971 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6972 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6972 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6972 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6972 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6973 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6973 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6973 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6973 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6974 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6974 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6974 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6974 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6975 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6975 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6975 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6975 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6976 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6976 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6976 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6976 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6977 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.exact_13_6977 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.data_13_6977 +#print axioms Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6977 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6978 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6978 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6978 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6978 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6979 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6979 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6979 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6979 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6980 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6980 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6980 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6980 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6981 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6981 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6981 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6981 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6982 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6982 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6982 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6982 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6983 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6983 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6983 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6983 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6984 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6984 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6984 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6984 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6985 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6985 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6985 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6985 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6986 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6986 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6986 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6986 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6987 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6987 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6987 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6987 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6988 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6988 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6988 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6988 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6989 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6989 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6989 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6989 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6990 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6990 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6990 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6990 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6991 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6991 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6991 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6991 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6992 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.exact_13_6992 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.data_13_6992 +#print axioms Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6992 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6993 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6993 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6993 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6993 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6994 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6994 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6994 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6994 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6995 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6995 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6995 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6995 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6996 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6996 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6996 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6996 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6997 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6997 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6997 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6997 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6998 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6998 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6998 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6998 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6999 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_6999 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_6999 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6999 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7000 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7000 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7000 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7000 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7001 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7001 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7001 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7001 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7002 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7002 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7002 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7002 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7003 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7003 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7003 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7003 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7004 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7004 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7004 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7004 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7005 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7005 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7005 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7005 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7006 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7006 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7006 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7006 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7007 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7007 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7007 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7007 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7008 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.exact_13_7008 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.data_13_7008 +#print axioms Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7008 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7009 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7009 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7009 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7009 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7010 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7010 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7010 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7010 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7011 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7011 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7011 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7011 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7012 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7012 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7012 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7012 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7013 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7013 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7013 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7013 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7014 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7014 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7014 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7014 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7015 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7015 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7015 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7015 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7016 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7016 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7016 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7016 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7017 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7017 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7017 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7017 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7018 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7018 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7018 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7018 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7019 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7019 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7019 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7019 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7020 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7020 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7020 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7020 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7021 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7021 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7021 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7021 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7022 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7022 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7022 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7022 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7023 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.exact_13_7023 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.data_13_7023 +#print axioms Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7023 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7024 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7024 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7024 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7024 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7025 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7025 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7025 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7025 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7026 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7026 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7026 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7026 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7027 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7027 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7027 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7027 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7028 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7028 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7028 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7028 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7029 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7029 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7029 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7029 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7030 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7030 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7030 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7030 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7031 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7031 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7031 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7031 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7032 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7032 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7032 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7032 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7033 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7033 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7033 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7033 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7034 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7034 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7034 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7034 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7035 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7035 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7035 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7035 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7036 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7036 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7036 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7036 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7037 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7037 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7037 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7037 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7038 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7038 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7038 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7038 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7039 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.exact_13_7039 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.data_13_7039 +#print axioms Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7039 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7040 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7040 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7040 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7040 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7041 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7041 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7041 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7041 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7042 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7042 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7042 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7042 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7043 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7043 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7043 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7043 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7044 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7044 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7044 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7044 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7045 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7045 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7045 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7045 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7046 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7046 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7046 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7046 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7047 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7047 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7047 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7047 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7048 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7048 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7048 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7048 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7049 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7049 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7049 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7049 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7050 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7050 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7050 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7050 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7051 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7051 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7051 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7051 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7052 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7052 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7052 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7052 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7053 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7053 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7053 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7053 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7054 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.exact_13_7054 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.data_13_7054 +#print axioms Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7054 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7055 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7055 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7055 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7055 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7056 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7056 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7056 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7056 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7057 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7057 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7057 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7057 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7058 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7058 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7058 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7058 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7059 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7059 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7059 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7059 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7060 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7060 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7060 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7060 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7061 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7061 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7061 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7061 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7062 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7062 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7062 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7062 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7063 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7063 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7063 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7063 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7064 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7064 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7064 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7064 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7065 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7065 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7065 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7065 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7066 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7066 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7066 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7066 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7067 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7067 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7067 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7067 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7068 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7068 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7068 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7068 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7069 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.exact_13_7069 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.data_13_7069 +#print axioms Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7069 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7070 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7070 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7070 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7070 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7071 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7071 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7071 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7071 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7072 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7072 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7072 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7072 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7073 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7073 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7073 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7073 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7074 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7074 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7074 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7074 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7075 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7075 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7075 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7075 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7076 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7076 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7076 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7076 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7077 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7077 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7077 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7077 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7078 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7078 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7078 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7078 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7079 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7079 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7079 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7079 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7080 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7080 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7080 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7080 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7081 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7081 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7081 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7081 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7082 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7082 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7082 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7082 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7083 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7083 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7083 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7083 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7084 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7084 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7084 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7084 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7085 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.exact_13_7085 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.data_13_7085 +#print axioms Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7085 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7086 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7086 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7086 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7086 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7087 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7087 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7087 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7087 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7088 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7088 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7088 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7088 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7089 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7089 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7089 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7089 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7090 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7090 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7090 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7090 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7091 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7091 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7091 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7091 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7092 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7092 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7092 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7092 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7093 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7093 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7093 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7093 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7094 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7094 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7094 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7094 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7095 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7095 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7095 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7095 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7096 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7096 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7096 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7096 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7097 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7097 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7097 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7097 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7098 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7098 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7098 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7098 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7099 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7099 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7099 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7099 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7100 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.exact_13_7100 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.data_13_7100 +#print axioms Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7100 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7101 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7101 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7101 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7101 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7102 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7102 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7102 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7102 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7103 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7103 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7103 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7103 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7104 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7104 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7104 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7104 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7105 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7105 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7105 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7105 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7106 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7106 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7106 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7106 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7107 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7107 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7107 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7107 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7108 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7108 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7108 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7108 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7109 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7109 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7109 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7109 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7110 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7110 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7110 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7110 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7111 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7111 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7111 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7111 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7112 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7112 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7112 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7112 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7113 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7113 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7113 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7113 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7114 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7114 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7114 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7114 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7115 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.exact_13_7115 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.data_13_7115 +#print axioms Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7115 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7116 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7116 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7116 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7116 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7117 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7117 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7117 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7117 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7118 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7118 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7118 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7118 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7119 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7119 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7119 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7119 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7120 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7120 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7120 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7120 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7121 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7121 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7121 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7121 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7122 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7122 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7122 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7122 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7123 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7123 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7123 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7123 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7124 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7124 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7124 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7124 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7125 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7125 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7125 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7125 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7126 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7126 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7126 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7126 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7127 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7127 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7127 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7127 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7128 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7128 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7128 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7128 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7129 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7129 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7129 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7129 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7130 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7130 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7130 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7130 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7131 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.exact_13_7131 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.data_13_7131 +#print axioms Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7131 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7132 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7132 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7132 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7132 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7133 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7133 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7133 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7133 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7134 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7134 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7134 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7134 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7135 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7135 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7135 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7135 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7136 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7136 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7136 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7136 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7137 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7137 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7137 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7137 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7138 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7138 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7138 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7138 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7139 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7139 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7139 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7139 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7140 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7140 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7140 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7140 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7141 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7141 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7141 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7141 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7142 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7142 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7142 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7142 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7143 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7143 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7143 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7143 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7144 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7144 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7144 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7144 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7145 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7145 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7145 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7145 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7146 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.exact_13_7146 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.data_13_7146 +#print axioms Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7146 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7147 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7147 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7147 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7147 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7148 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7148 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7148 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7148 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7149 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7149 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7149 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7149 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7150 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7150 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7150 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7150 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7151 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7151 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7151 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7151 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7152 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7152 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7152 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7152 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7153 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7153 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7153 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7153 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7154 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7154 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7154 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7154 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7155 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7155 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7155 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7155 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7156 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7156 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7156 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7156 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7157 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7157 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7157 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7157 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7158 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7158 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7158 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7158 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7159 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7159 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7159 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7159 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7160 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7160 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7160 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7160 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7161 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.exact_13_7161 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.data_13_7161 +#print axioms Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7161 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7162 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7162 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7162 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7162 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7163 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7163 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7163 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7163 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7164 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7164 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7164 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7164 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7165 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7165 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7165 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7165 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7166 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7166 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7166 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7166 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7167 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7167 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7167 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7167 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7168 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7168 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7168 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7168 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7169 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7169 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7169 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7169 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7170 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7170 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7170 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7170 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7171 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7171 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7171 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7171 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7172 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7172 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7172 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7172 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7173 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7173 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7173 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7173 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7174 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7174 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7174 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7174 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7175 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7175 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7175 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7175 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7176 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7176 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7176 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7176 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7177 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.exact_13_7177 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.data_13_7177 +#print axioms Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7177 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7178 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7178 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7178 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7178 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7179 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7179 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7179 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7179 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7180 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7180 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7180 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7180 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7181 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7181 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7181 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7181 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7182 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7182 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7182 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7182 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7183 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7183 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7183 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7183 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7184 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7184 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7184 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7184 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7185 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7185 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7185 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7185 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7186 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7186 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7186 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7186 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7187 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7187 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7187 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7187 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7188 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7188 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7188 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7188 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7189 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7189 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7189 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7189 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7190 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7190 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7190 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7190 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7191 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7191 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7191 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7191 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7192 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.exact_13_7192 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.data_13_7192 +#print axioms Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7192 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7193 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7193 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7193 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7193 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7194 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7194 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7194 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7194 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7195 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7195 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7195 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7195 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7196 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7196 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7196 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7196 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7197 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7197 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7197 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7197 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7198 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7198 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7198 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7198 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7199 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7199 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7199 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7199 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7200 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7200 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7200 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7200 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7201 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7201 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7201 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7201 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7202 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7202 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7202 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7202 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7203 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7203 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7203 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7203 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7204 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7204 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7204 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7204 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7205 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7205 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7205 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7205 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7206 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7206 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7206 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7206 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7207 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.exact_13_7207 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.data_13_7207 +#print axioms Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7207 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7208 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7208 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7208 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7208 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7209 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7209 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7209 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7209 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7210 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7210 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7210 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7210 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7211 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7211 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7211 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7211 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7212 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7212 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7212 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7212 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7213 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7213 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7213 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7213 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7214 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7214 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7214 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7214 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7215 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7215 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7215 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7215 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7216 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7216 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7216 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7216 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7217 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7217 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7217 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7217 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7218 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7218 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7218 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7218 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7219 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7219 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7219 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7219 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7220 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7220 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7220 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7220 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7221 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7221 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7221 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7221 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7222 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7222 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7222 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7222 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7223 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.exact_13_7223 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.data_13_7223 +#print axioms Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7223 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7224 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7224 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7224 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7224 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7225 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7225 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7225 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7225 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7226 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7226 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7226 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7226 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7227 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7227 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7227 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7227 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7228 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7228 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7228 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7228 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7229 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7229 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7229 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7229 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7230 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7230 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7230 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7230 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7231 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7231 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7231 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7231 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7232 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7232 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7232 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7232 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7233 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7233 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7233 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7233 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7234 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7234 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7234 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7234 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7235 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7235 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7235 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7235 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7236 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7236 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7236 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7236 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7237 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7237 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7237 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7237 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7238 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.exact_13_7238 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.data_13_7238 +#print axioms Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7238 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7239 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7239 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7239 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7239 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7240 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7240 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7240 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7240 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7241 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7241 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7241 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7241 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7242 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7242 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7242 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7242 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7243 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7243 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7243 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7243 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7244 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7244 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7244 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7244 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7245 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7245 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7245 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7245 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7246 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7246 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7246 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7246 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7247 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7247 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7247 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7247 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7248 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7248 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7248 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7248 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7249 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7249 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7249 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7249 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7250 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7250 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7250 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7250 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7251 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7251 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7251 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7251 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7252 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7252 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7252 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7252 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7253 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7253 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7253 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7253 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7254 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.exact_13_7254 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.data_13_7254 +#print axioms Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7254 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7255 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7255 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7255 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7255 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7256 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7256 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7256 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7256 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7257 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7257 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7257 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7257 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7258 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7258 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7258 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7258 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7259 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7259 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7259 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7259 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7260 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7260 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7260 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7260 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7261 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7261 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7261 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7261 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7262 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7262 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7262 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7262 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7263 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7263 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7263 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7263 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7264 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7264 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7264 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7264 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7265 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7265 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7265 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7265 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7266 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7266 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7266 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7266 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7267 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7267 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7267 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7267 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7268 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7268 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7268 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7268 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7269 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.exact_13_7269 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.data_13_7269 +#print axioms Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7269 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7270 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7270 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7270 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7270 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7271 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7271 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7271 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7271 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7272 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7272 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7272 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7272 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7273 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7273 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7273 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7273 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7274 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7274 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7274 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7274 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7275 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7275 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7275 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7275 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7276 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7276 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7276 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7276 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7277 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7277 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7277 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7277 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7278 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7278 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7278 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7278 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7279 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7279 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7279 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7279 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7280 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7280 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7280 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7280 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7281 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7281 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7281 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7281 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7282 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7282 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7282 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7282 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7283 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7283 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7283 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7283 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7284 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.exact_13_7284 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.data_13_7284 +#print axioms Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7284 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7285 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7285 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7285 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7285 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7286 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7286 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7286 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7286 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7287 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7287 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7287 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7287 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7288 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7288 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7288 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7288 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7289 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7289 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7289 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7289 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7290 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7290 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7290 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7290 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7291 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7291 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7291 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7291 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7292 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7292 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7292 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7292 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7293 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7293 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7293 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7293 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7294 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7294 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7294 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7294 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7295 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7295 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7295 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7295 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7296 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7296 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7296 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7296 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7297 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7297 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7297 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7297 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7298 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7298 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7298 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7298 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7299 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7299 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7299 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7299 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7300 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.exact_13_7300 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.data_13_7300 +#print axioms Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7300 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7301 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7301 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7301 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7301 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7302 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7302 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7302 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7302 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7303 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7303 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7303 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7303 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7304 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7304 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7304 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7304 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7305 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7305 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7305 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7305 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7306 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7306 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7306 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7306 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7307 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7307 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7307 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7307 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7308 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7308 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7308 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7308 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7309 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7309 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7309 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7309 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7310 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7310 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7310 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7310 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7311 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7311 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7311 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7311 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7312 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7312 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7312 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7312 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7313 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7313 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7313 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7313 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7314 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7314 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7314 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7314 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7315 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.exact_13_7315 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.data_13_7315 +#print axioms Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7315 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7316 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7316 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7316 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7316 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7317 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7317 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7317 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7317 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7318 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7318 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7318 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7318 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7319 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7319 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7319 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7319 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7320 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7320 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7320 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7320 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7321 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7321 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7321 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7321 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7322 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7322 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7322 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7322 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7323 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7323 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7323 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7323 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7324 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7324 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7324 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7324 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7325 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7325 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7325 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7325 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7326 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7326 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7326 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7326 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7327 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7327 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7327 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7327 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7328 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7328 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7328 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7328 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7329 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7329 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7329 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7329 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7330 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.exact_13_7330 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.data_13_7330 +#print axioms Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7330 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7331 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7331 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7331 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7331 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7332 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7332 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7332 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7332 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7333 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7333 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7333 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7333 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7334 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7334 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7334 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7334 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7335 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7335 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7335 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7335 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7336 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7336 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7336 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7336 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7337 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7337 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7337 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7337 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7338 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7338 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7338 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7338 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7339 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7339 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7339 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7339 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7340 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7340 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7340 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7340 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7341 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7341 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7341 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7341 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7342 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7342 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7342 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7342 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7343 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7343 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7343 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7343 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7344 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7344 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7344 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7344 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7345 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7345 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7345 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7345 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7346 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.exact_13_7346 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.data_13_7346 +#print axioms Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7346 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7347 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7347 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7347 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7347 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7348 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7348 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7348 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7348 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7349 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7349 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7349 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7349 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7350 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7350 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7350 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7350 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7351 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7351 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7351 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7351 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7352 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7352 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7352 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7352 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7353 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7353 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7353 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7353 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7354 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7354 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7354 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7354 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7355 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7355 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7355 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7355 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7356 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7356 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7356 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7356 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7357 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7357 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7357 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7357 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7358 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7358 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7358 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7358 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7359 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7359 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7359 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7359 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7360 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7360 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7360 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7360 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7361 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.exact_13_7361 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.data_13_7361 +#print axioms Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7361 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7362 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7362 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7362 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7362 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7363 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7363 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7363 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7363 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7364 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7364 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7364 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7364 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7365 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7365 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7365 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7365 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7366 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7366 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7366 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7366 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7367 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7367 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7367 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7367 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7368 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7368 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7368 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7368 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7369 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7369 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7369 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7369 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7370 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7370 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7370 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7370 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7371 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7371 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7371 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7371 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7372 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7372 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7372 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7372 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7373 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7373 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7373 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7373 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7374 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7374 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7374 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7374 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7375 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7375 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7375 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7375 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7376 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.exact_13_7376 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.data_13_7376 +#print axioms Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7376 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7377 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7377 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7377 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7377 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7378 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7378 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7378 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7378 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7379 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7379 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7379 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7379 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7380 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7380 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7380 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7380 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7381 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7381 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7381 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7381 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7382 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7382 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7382 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7382 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7383 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7383 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7383 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7383 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7384 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7384 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7384 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7384 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7385 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7385 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7385 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7385 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7386 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7386 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7386 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7386 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7387 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7387 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7387 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7387 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7388 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7388 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7388 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7388 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7389 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7389 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7389 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7389 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7390 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7390 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7390 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7390 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7391 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7391 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7391 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7391 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7392 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.exact_13_7392 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.data_13_7392 +#print axioms Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7392 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7393 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7393 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7393 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7393 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7394 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7394 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7394 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7394 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7395 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7395 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7395 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7395 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7396 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7396 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7396 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7396 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7397 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7397 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7397 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7397 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7398 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7398 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7398 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7398 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7399 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7399 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7399 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7399 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7400 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7400 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7400 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7400 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7401 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7401 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7401 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7401 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7402 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7402 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7402 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7402 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7403 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7403 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7403 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7403 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7404 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7404 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7404 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7404 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7405 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7405 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7405 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7405 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7406 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7406 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7406 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7406 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7407 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.exact_13_7407 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.data_13_7407 +#print axioms Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7407 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7408 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7408 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7408 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7408 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7409 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7409 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7409 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7409 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7410 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7410 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7410 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7410 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7411 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7411 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7411 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7411 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7412 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7412 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7412 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7412 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7413 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7413 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7413 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7413 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7414 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7414 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7414 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7414 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7415 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7415 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7415 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7415 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7416 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7416 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7416 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7416 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7417 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7417 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7417 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7417 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7418 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7418 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7418 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7418 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7419 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7419 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7419 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7419 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7420 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7420 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7420 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7420 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7421 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7421 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7421 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7421 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7422 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7422 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7422 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7422 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7423 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.exact_13_7423 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.data_13_7423 +#print axioms Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7423 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7424 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7424 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7424 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7424 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7425 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7425 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7425 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7425 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7426 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7426 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7426 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7426 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7427 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7427 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7427 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7427 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7428 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7428 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7428 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7428 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7429 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7429 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7429 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7429 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7430 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7430 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7430 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7430 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7431 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7431 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7431 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7431 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7432 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7432 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7432 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7432 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7433 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7433 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7433 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7433 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7434 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7434 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7434 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7434 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7435 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7435 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7435 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7435 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7436 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7436 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7436 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7436 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7437 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7437 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7437 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7437 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7438 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.exact_13_7438 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.data_13_7438 +#print axioms Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7438 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7439 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7439 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7439 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7439 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7440 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7440 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7440 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7440 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7441 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7441 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7441 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7441 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7442 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7442 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7442 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7442 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7443 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7443 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7443 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7443 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7444 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7444 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7444 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7444 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7445 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7445 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7445 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7445 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7446 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7446 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7446 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7446 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7447 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7447 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7447 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7447 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7448 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7448 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7448 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7448 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7449 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7449 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7449 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7449 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7450 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7450 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7450 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7450 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7451 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7451 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7451 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7451 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7452 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7452 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7452 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7452 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7453 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.exact_13_7453 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.data_13_7453 +#print axioms Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7453 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7454 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7454 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7454 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7454 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7455 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7455 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7455 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7455 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7456 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7456 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7456 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7456 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7457 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7457 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7457 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7457 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7458 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7458 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7458 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7458 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7459 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7459 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7459 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7459 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7460 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7460 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7460 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7460 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7461 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7461 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7461 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7461 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7462 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7462 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7462 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7462 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7463 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7463 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7463 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7463 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7464 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7464 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7464 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7464 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7465 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7465 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7465 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7465 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7466 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7466 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7466 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7466 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7467 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7467 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7467 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7467 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7468 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7468 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7468 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7468 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7469 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.exact_13_7469 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.data_13_7469 +#print axioms Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7469 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7470 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7470 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7470 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7470 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7471 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7471 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7471 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7471 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7472 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7472 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7472 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7472 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7473 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7473 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7473 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7473 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7474 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7474 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7474 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7474 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7475 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7475 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7475 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7475 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7476 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7476 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7476 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7476 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7477 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7477 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7477 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7477 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7478 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7478 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7478 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7478 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7479 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7479 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7479 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7479 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7480 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7480 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7480 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7480 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7481 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7481 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7481 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7481 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7482 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7482 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7482 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7482 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7483 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7483 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7483 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7483 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7484 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.exact_13_7484 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.data_13_7484 +#print axioms Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7484 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7485 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7485 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7485 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7485 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7486 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7486 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7486 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7486 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7487 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7487 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7487 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7487 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7488 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7488 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7488 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7488 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7489 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7489 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7489 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7489 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7490 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7490 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7490 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7490 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7491 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7491 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7491 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7491 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7492 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7492 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7492 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7492 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7493 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7493 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7493 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7493 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7494 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7494 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7494 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7494 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7495 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7495 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7495 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7495 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7496 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7496 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7496 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7496 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7497 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7497 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7497 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7497 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7498 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7498 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7498 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7498 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7499 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.exact_13_7499 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.data_13_7499 +#print axioms Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7499 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7500 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7500 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7500 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7500 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7501 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7501 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7501 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7501 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7502 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7502 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7502 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7502 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7503 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7503 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7503 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7503 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7504 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7504 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7504 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7504 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7505 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7505 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7505 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7505 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7506 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7506 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7506 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7506 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7507 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7507 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7507 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7507 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7508 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7508 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7508 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7508 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7509 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7509 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7509 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7509 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7510 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7510 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7510 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7510 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7511 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7511 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7511 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7511 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7512 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7512 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7512 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7512 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7513 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7513 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7513 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7513 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7514 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7514 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7514 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7514 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7515 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.exact_13_7515 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.data_13_7515 +#print axioms Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7515 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7516 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7516 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7516 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7516 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7517 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7517 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7517 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7517 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7518 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7518 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7518 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7518 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7519 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7519 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7519 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7519 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7520 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7520 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7520 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7520 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7521 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7521 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7521 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7521 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7522 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7522 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7522 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7522 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7523 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7523 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7523 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7523 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7524 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7524 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7524 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7524 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7525 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7525 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7525 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7525 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7526 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7526 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7526 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7526 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7527 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7527 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7527 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7527 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7528 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7528 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7528 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7528 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7529 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7529 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7529 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7529 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7530 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.exact_13_7530 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.data_13_7530 +#print axioms Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7530 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7531 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7531 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7531 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7531 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7532 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7532 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7532 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7532 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7533 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7533 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7533 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7533 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7534 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7534 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7534 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7534 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7535 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7535 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7535 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7535 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7536 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7536 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7536 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7536 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7537 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7537 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7537 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7537 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7538 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7538 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7538 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7538 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7539 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7539 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7539 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7539 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7540 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7540 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7540 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7540 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7541 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7541 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7541 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7541 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7542 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7542 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7542 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7542 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7543 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7543 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7543 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7543 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7544 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7544 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7544 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7544 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7545 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.exact_13_7545 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.data_13_7545 +#print axioms Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7545 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7546 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7546 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7546 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7546 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7547 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7547 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7547 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7547 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7548 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7548 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7548 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7548 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7549 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7549 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7549 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7549 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7550 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7550 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7550 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7550 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7551 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7551 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7551 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7551 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7552 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7552 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7552 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7552 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7553 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7553 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7553 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7553 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7554 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7554 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7554 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7554 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7555 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7555 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7555 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7555 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7556 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7556 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7556 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7556 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7557 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7557 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7557 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7557 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7558 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7558 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7558 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7558 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7559 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7559 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7559 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7559 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7560 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7560 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7560 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7560 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7561 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.exact_13_7561 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.data_13_7561 +#print axioms Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7561 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7562 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7562 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7562 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7562 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7563 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7563 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7563 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7563 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7564 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7564 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7564 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7564 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7565 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7565 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7565 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7565 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7566 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7566 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7566 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7566 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7567 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7567 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7567 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7567 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7568 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7568 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7568 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7568 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7569 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7569 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7569 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7569 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7570 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7570 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7570 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7570 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7571 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7571 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7571 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7571 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7572 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7572 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7572 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7572 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7573 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7573 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7573 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7573 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7574 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7574 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7574 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7574 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7575 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7575 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7575 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7575 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7576 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.exact_13_7576 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.data_13_7576 +#print axioms Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7576 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7577 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7577 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7577 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7577 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7578 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7578 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7578 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7578 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7579 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7579 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7579 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7579 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7580 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7580 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7580 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7580 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7581 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7581 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7581 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7581 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7582 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7582 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7582 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7582 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7583 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7583 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7583 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7583 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7584 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7584 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7584 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7584 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7585 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7585 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7585 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7585 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7586 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7586 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7586 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7586 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7587 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7587 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7587 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7587 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7588 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7588 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7588 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7588 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7589 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7589 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7589 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7589 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7590 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7590 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7590 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7590 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7591 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.exact_13_7591 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.data_13_7591 +#print axioms Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7591 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7592 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7592 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7592 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7592 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7593 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7593 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7593 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7593 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7594 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7594 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7594 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7594 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7595 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7595 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7595 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7595 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7596 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7596 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7596 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7596 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7597 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7597 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7597 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7597 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7598 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7598 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7598 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7598 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7599 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7599 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7599 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7599 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7600 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7600 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7600 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7600 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7601 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7601 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7601 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7601 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7602 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7602 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7602 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7602 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7603 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7603 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7603 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7603 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7604 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7604 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7604 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7604 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7605 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7605 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7605 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7605 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7606 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7606 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7606 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7606 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7607 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.exact_13_7607 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.data_13_7607 +#print axioms Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7607 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7608 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7608 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7608 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7608 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7609 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7609 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7609 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7609 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7610 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7610 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7610 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7610 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7611 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7611 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7611 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7611 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7612 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7612 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7612 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7612 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7613 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7613 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7613 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7613 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7614 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7614 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7614 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7614 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7615 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7615 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7615 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7615 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7616 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7616 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7616 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7616 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7617 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7617 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7617 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7617 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7618 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7618 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7618 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7618 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7619 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7619 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7619 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7619 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7620 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7620 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7620 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7620 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7621 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7621 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7621 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7621 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7622 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.exact_13_7622 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.data_13_7622 +#print axioms Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7622 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7623 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7623 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7623 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7623 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7624 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7624 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7624 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7624 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7625 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7625 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7625 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7625 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7626 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7626 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7626 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7626 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7627 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7627 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7627 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7627 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7628 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7628 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7628 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7628 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7629 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7629 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7629 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7629 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7630 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7630 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7630 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7630 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7631 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7631 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7631 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7631 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7632 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7632 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7632 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7632 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7633 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7633 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7633 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7633 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7634 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7634 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7634 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7634 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7635 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7635 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7635 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7635 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7636 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7636 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7636 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7636 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7637 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7637 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7637 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7637 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7638 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.exact_13_7638 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.data_13_7638 +#print axioms Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7638 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7639 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7639 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7639 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7639 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7640 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7640 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7640 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7640 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7641 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7641 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7641 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7641 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7642 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7642 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7642 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7642 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7643 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7643 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7643 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7643 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7644 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7644 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7644 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7644 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7645 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7645 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7645 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7645 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7646 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7646 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7646 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7646 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7647 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7647 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7647 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7647 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7648 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7648 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7648 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7648 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7649 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7649 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7649 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7649 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7650 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7650 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7650 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7650 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7651 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7651 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7651 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7651 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7652 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7652 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7652 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7652 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7653 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.exact_13_7653 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.data_13_7653 +#print axioms Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7653 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7654 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7654 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7654 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7654 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7655 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7655 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7655 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7655 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7656 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7656 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7656 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7656 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7657 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7657 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7657 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7657 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7658 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7658 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7658 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7658 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7659 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7659 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7659 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7659 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7660 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7660 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7660 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7660 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7661 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7661 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7661 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7661 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7662 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7662 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7662 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7662 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7663 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7663 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7663 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7663 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7664 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7664 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7664 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7664 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7665 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7665 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7665 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7665 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7666 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7666 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7666 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7666 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7667 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7667 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7667 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7667 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7668 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.exact_13_7668 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.data_13_7668 +#print axioms Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7668 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7669 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7669 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7669 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7669 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7670 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7670 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7670 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7670 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7671 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7671 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7671 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7671 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7672 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7672 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7672 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7672 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7673 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7673 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7673 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7673 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7674 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7674 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7674 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7674 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7675 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7675 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7675 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7675 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7676 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7676 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7676 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7676 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7677 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7677 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7677 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7677 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7678 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7678 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7678 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7678 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7679 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7679 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7679 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7679 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7680 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7680 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7680 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7680 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7681 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7681 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7681 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7681 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7682 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7682 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7682 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7682 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7683 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7683 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7683 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7683 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7684 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.exact_13_7684 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.data_13_7684 +#print axioms Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7684 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7685 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7685 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7685 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7685 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7686 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7686 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7686 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7686 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7687 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7687 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7687 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7687 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7688 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7688 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7688 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7688 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7689 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7689 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7689 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7689 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7690 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7690 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7690 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7690 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7691 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7691 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7691 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7691 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7692 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7692 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7692 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7692 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7693 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7693 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7693 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7693 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7694 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7694 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7694 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7694 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7695 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7695 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7695 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7695 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7696 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7696 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7696 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7696 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7697 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7697 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7697 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7697 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7698 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7698 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7698 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7698 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7699 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.exact_13_7699 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.data_13_7699 +#print axioms Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7699 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7700 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7700 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7700 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7700 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7701 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7701 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7701 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7701 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7702 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7702 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7702 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7702 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7703 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7703 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7703 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7703 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7704 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7704 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7704 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7704 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7705 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7705 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7705 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7705 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7706 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7706 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7706 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7706 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7707 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7707 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7707 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7707 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7708 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7708 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7708 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7708 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7709 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7709 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7709 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7709 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7710 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7710 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7710 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7710 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7711 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7711 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7711 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7711 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7712 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7712 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7712 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7712 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7713 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7713 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7713 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7713 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7714 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.exact_13_7714 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.data_13_7714 +#print axioms Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7714 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7715 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7715 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7715 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7715 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7716 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7716 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7716 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7716 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7717 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7717 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7717 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7717 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7718 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7718 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7718 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7718 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7719 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7719 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7719 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7719 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7720 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7720 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7720 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7720 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7721 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7721 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7721 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7721 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7722 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7722 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7722 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7722 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7723 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7723 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7723 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7723 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7724 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7724 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7724 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7724 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7725 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7725 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7725 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7725 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7726 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7726 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7726 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7726 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7727 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7727 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7727 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7727 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7728 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7728 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7728 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7728 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7729 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7729 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7729 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7729 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7730 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.exact_13_7730 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.data_13_7730 +#print axioms Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7730 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7731 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7731 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7731 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7731 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7732 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7732 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7732 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7732 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7733 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7733 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7733 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7733 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7734 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7734 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7734 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7734 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7735 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7735 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7735 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7735 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7736 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7736 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7736 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7736 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7737 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7737 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7737 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7737 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7738 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7738 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7738 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7738 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7739 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7739 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7739 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7739 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7740 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7740 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7740 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7740 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7741 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7741 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7741 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7741 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7742 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7742 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7742 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7742 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7743 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7743 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7743 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7743 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7744 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7744 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7744 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7744 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7745 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.exact_13_7745 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.data_13_7745 +#print axioms Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7745 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7746 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7746 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7746 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7746 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7747 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7747 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7747 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7747 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7748 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7748 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7748 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7748 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7749 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7749 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7749 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7749 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7750 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7750 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7750 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7750 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7751 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7751 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7751 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7751 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7752 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7752 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7752 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7752 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7753 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7753 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7753 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7753 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7754 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7754 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7754 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7754 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7755 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7755 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7755 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7755 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7756 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7756 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7756 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7756 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7757 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7757 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7757 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7757 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7758 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7758 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7758 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7758 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7759 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7759 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7759 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7759 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7760 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.exact_13_7760 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.data_13_7760 +#print axioms Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7760 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7761 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7761 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7761 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7761 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7762 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7762 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7762 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7762 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7763 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7763 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7763 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7763 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7764 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7764 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7764 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7764 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7765 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7765 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7765 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7765 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7766 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7766 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7766 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7766 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7767 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7767 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7767 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7767 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7768 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7768 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7768 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7768 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7769 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7769 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7769 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7769 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7770 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7770 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7770 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7770 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7771 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7771 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7771 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7771 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7772 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7772 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7772 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7772 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7773 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7773 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7773 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7773 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7774 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7774 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7774 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7774 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7775 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7775 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7775 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7775 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7776 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.exact_13_7776 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.data_13_7776 +#print axioms Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7776 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7777 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7777 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7777 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7777 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7778 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7778 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7778 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7778 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7779 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7779 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7779 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7779 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7780 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7780 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7780 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7780 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7781 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7781 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7781 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7781 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7782 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7782 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7782 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7782 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7783 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7783 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7783 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7783 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7784 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7784 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7784 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7784 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7785 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7785 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7785 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7785 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7786 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7786 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7786 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7786 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7787 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7787 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7787 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7787 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7788 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7788 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7788 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7788 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7789 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7789 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7789 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7789 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7790 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7790 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7790 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7790 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7791 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.exact_13_7791 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.data_13_7791 +#print axioms Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7791 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7792 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7792 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7792 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7792 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7793 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7793 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7793 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7793 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7794 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7794 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7794 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7794 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7795 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7795 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7795 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7795 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7796 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7796 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7796 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7796 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7797 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7797 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7797 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7797 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7798 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7798 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7798 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7798 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7799 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7799 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7799 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7799 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7800 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7800 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7800 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7800 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7801 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7801 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7801 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7801 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7802 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7802 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7802 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7802 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7803 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7803 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7803 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7803 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7804 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7804 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7804 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7804 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7805 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7805 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7805 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7805 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7806 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7806 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7806 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7806 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7807 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.exact_13_7807 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.data_13_7807 +#print axioms Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7807 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7808 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7808 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7808 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7808 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7809 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7809 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7809 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7809 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7810 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7810 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7810 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7810 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7811 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7811 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7811 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7811 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7812 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7812 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7812 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7812 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7813 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7813 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7813 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7813 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7814 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7814 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7814 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7814 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7815 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7815 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7815 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7815 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7816 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7816 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7816 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7816 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7817 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7817 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7817 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7817 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7818 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7818 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7818 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7818 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7819 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7819 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7819 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7819 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7820 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7820 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7820 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7820 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7821 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7821 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7821 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7821 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7822 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.exact_13_7822 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.data_13_7822 +#print axioms Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7822 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7823 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7823 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7823 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7823 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7824 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7824 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7824 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7824 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7825 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7825 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7825 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7825 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7826 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7826 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7826 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7826 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7827 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7827 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7827 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7827 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7828 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7828 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7828 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7828 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7829 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7829 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7829 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7829 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7830 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7830 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7830 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7830 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7831 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7831 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7831 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7831 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7832 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7832 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7832 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7832 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7833 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7833 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7833 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7833 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7834 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7834 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7834 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7834 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7835 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7835 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7835 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7835 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7836 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7836 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7836 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7836 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7837 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.exact_13_7837 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.data_13_7837 +#print axioms Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7837 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7838 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7838 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7838 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7838 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7839 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7839 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7839 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7839 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7840 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7840 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7840 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7840 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7841 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7841 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7841 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7841 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7842 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7842 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7842 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7842 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7843 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7843 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7843 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7843 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7844 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7844 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7844 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7844 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7845 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7845 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7845 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7845 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7846 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7846 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7846 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7846 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7847 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7847 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7847 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7847 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7848 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7848 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7848 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7848 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7849 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7849 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7849 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7849 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7850 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7850 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7850 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7850 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7851 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7851 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7851 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7851 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7852 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7852 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7852 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7852 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7853 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.exact_13_7853 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.data_13_7853 +#print axioms Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7853 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7854 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7854 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7854 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7854 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7855 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7855 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7855 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7855 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7856 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7856 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7856 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7856 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7857 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7857 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7857 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7857 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7858 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7858 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7858 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7858 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7859 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7859 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7859 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7859 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7860 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7860 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7860 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7860 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7861 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7861 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7861 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7861 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7862 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7862 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7862 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7862 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7863 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7863 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7863 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7863 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7864 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7864 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7864 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7864 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7865 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7865 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7865 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7865 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7866 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7866 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7866 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7866 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7867 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7867 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7867 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7867 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7868 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.exact_13_7868 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.data_13_7868 +#print axioms Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7868 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7869 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7869 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7869 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7869 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7870 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7870 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7870 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7870 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7871 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7871 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7871 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7871 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7872 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7872 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7872 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7872 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7873 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7873 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7873 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7873 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7874 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7874 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7874 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7874 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7875 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7875 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7875 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7875 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7876 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7876 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7876 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7876 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7877 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7877 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7877 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7877 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7878 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7878 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7878 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7878 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7879 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7879 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7879 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7879 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7880 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7880 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7880 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7880 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7881 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7881 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7881 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7881 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7882 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7882 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7882 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7882 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7883 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.exact_13_7883 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.data_13_7883 +#print axioms Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7883 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7884 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7884 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7884 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7884 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7885 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7885 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7885 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7885 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7886 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7886 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7886 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7886 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7887 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7887 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7887 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7887 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7888 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7888 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7888 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7888 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7889 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7889 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7889 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7889 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7890 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7890 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7890 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7890 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7891 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7891 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7891 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7891 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7892 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7892 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7892 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7892 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7893 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7893 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7893 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7893 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7894 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7894 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7894 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7894 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7895 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7895 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7895 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7895 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7896 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7896 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7896 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7896 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7897 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7897 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7897 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7897 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7898 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7898 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7898 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7898 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7899 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.exact_13_7899 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.data_13_7899 +#print axioms Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7899 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7900 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7900 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7900 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7900 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7901 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7901 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7901 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7901 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7902 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7902 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7902 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7902 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7903 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7903 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7903 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7903 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7904 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7904 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7904 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7904 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7905 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7905 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7905 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7905 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7906 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7906 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7906 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7906 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7907 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7907 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7907 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7907 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7908 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7908 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7908 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7908 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7909 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7909 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7909 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7909 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7910 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7910 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7910 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7910 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7911 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7911 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7911 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7911 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7912 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7912 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7912 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7912 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7913 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7913 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7913 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7913 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7914 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.exact_13_7914 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.data_13_7914 +#print axioms Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7914 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7915 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7915 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7915 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7915 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7916 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7916 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7916 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7916 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7917 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7917 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7917 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7917 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7918 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7918 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7918 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7918 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7919 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7919 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7919 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7919 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7920 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7920 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7920 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7920 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7921 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7921 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7921 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7921 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7922 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7922 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7922 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7922 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7923 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7923 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7923 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7923 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7924 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7924 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7924 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7924 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7925 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7925 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7925 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7925 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7926 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7926 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7926 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7926 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7927 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7927 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7927 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7927 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7928 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7928 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7928 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7928 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7929 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.exact_13_7929 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.data_13_7929 +#print axioms Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7929 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7930 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7930 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7930 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7930 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7931 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7931 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7931 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7931 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7932 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7932 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7932 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7932 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7933 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7933 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7933 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7933 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7934 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7934 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7934 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7934 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7935 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7935 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7935 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7935 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7936 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7936 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7936 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7936 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7937 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7937 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7937 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7937 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7938 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7938 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7938 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7938 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7939 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7939 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7939 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7939 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7940 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7940 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7940 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7940 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7941 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7941 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7941 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7941 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7942 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7942 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7942 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7942 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7943 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7943 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7943 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7943 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7944 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7944 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7944 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7944 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7945 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.exact_13_7945 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.data_13_7945 +#print axioms Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7945 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7946 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7946 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7946 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7946 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7947 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7947 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7947 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7947 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7948 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7948 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7948 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7948 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7949 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7949 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7949 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7949 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7950 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7950 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7950 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7950 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7951 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7951 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7951 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7951 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7952 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7952 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7952 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7952 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7953 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7953 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7953 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7953 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7954 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7954 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7954 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7954 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7955 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7955 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7955 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7955 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7956 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7956 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7956 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7956 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7957 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7957 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7957 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7957 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7958 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7958 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7958 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7958 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7959 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7959 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7959 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7959 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7960 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.exact_13_7960 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.data_13_7960 +#print axioms Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7960 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7961 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7961 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7961 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7961 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7962 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7962 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7962 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7962 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7963 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7963 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7963 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7963 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7964 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7964 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7964 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7964 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7965 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7965 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7965 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7965 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7966 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7966 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7966 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7966 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7967 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7967 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7967 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7967 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7968 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7968 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7968 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7968 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7969 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7969 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7969 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7969 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7970 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7970 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7970 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7970 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7971 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7971 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7971 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7971 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7972 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7972 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7972 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7972 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7973 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7973 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7973 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7973 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7974 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7974 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7974 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7974 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7975 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.exact_13_7975 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.data_13_7975 +#print axioms Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7975 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7976 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7976 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7976 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7976 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7977 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7977 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7977 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7977 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7978 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7978 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7978 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7978 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7979 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7979 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7979 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7979 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7980 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7980 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7980 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7980 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7981 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7981 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7981 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7981 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7982 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7982 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7982 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7982 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7983 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7983 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7983 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7983 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7984 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7984 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7984 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7984 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7985 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7985 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7985 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7985 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7986 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7986 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7986 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7986 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7987 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7987 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7987 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7987 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7988 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7988 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7988 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7988 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7989 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7989 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7989 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7989 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7990 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7990 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7990 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7990 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7991 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.exact_13_7991 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.data_13_7991 +#print axioms Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7991 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7992 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7992 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7992 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7992 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7993 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7993 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7993 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7993 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7994 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7994 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7994 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7994 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7995 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7995 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7995 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7995 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7996 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7996 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7996 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7996 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7997 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7997 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7997 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7997 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7998 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7998 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7998 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7998 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7999 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_7999 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_7999 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7999 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8000 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8000 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8000 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8000 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8001 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8001 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8001 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8001 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8002 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8002 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8002 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8002 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8003 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8003 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8003 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8003 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8004 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8004 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8004 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8004 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8005 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8005 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8005 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8005 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8006 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.exact_13_8006 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.data_13_8006 +#print axioms Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8006 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8007 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8007 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8007 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8007 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8008 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8008 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8008 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8008 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8009 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8009 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8009 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8009 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8010 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8010 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8010 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8010 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8011 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8011 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8011 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8011 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8012 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8012 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8012 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8012 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8013 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8013 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8013 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8013 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8014 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8014 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8014 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8014 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8015 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8015 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8015 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8015 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8016 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8016 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8016 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8016 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8017 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8017 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8017 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8017 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8018 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8018 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8018 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8018 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8019 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8019 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8019 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8019 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8020 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8020 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8020 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8020 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8021 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8021 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8021 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8021 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8022 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.exact_13_8022 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.data_13_8022 +#print axioms Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8022 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8023 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8023 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8023 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8023 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8024 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8024 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8024 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8024 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8025 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8025 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8025 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8025 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8026 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8026 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8026 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8026 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8027 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8027 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8027 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8027 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8028 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8028 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8028 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8028 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8029 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8029 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8029 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8029 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8030 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8030 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8030 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8030 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8031 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8031 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8031 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8031 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8032 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8032 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8032 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8032 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8033 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8033 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8033 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8033 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8034 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8034 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8034 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8034 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8035 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8035 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8035 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8035 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8036 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8036 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8036 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8036 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8037 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.exact_13_8037 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.data_13_8037 +#print axioms Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8037 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8038 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8038 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8038 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8038 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8039 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8039 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8039 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8039 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8040 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8040 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8040 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8040 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8041 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8041 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8041 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8041 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8042 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8042 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8042 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8042 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8043 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8043 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8043 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8043 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8044 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8044 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8044 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8044 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8045 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8045 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8045 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8045 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8046 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8046 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8046 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8046 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8047 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8047 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8047 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8047 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8048 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8048 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8048 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8048 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8049 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8049 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8049 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8049 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8050 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8050 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8050 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8050 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8051 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8051 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8051 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8051 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8052 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.exact_13_8052 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.data_13_8052 +#print axioms Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8052 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8053 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8053 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8053 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8053 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8054 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8054 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8054 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8054 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8055 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8055 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8055 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8055 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8056 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8056 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8056 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8056 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8057 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8057 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8057 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8057 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8058 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8058 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8058 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8058 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8059 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8059 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8059 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8059 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8060 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8060 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8060 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8060 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8061 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8061 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8061 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8061 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8062 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8062 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8062 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8062 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8063 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8063 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8063 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8063 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8064 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8064 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8064 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8064 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8065 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8065 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8065 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8065 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8066 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8066 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8066 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8066 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8067 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8067 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8067 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8067 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8068 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.exact_13_8068 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.data_13_8068 +#print axioms Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8068 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8069 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8069 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8069 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8069 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8070 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8070 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8070 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8070 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8071 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8071 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8071 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8071 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8072 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8072 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8072 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8072 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8073 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8073 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8073 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8073 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8074 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8074 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8074 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8074 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8075 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8075 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8075 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8075 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8076 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8076 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8076 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8076 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8077 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8077 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8077 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8077 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8078 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8078 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8078 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8078 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8079 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8079 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8079 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8079 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8080 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8080 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8080 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8080 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8081 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8081 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8081 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8081 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8082 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8082 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8082 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8082 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8083 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.exact_13_8083 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.data_13_8083 +#print axioms Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8083 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8084 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8084 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8084 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8084 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8085 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8085 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8085 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8085 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8086 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8086 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8086 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8086 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8087 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8087 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8087 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8087 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8088 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8088 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8088 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8088 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8089 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8089 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8089 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8089 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8090 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8090 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8090 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8090 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8091 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8091 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8091 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8091 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8092 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8092 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8092 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8092 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8093 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8093 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8093 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8093 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8094 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8094 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8094 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8094 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8095 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8095 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8095 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8095 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8096 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8096 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8096 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8096 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8097 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8097 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8097 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8097 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8098 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.exact_13_8098 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.data_13_8098 +#print axioms Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8098 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8099 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8099 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8099 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8099 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8100 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8100 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8100 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8100 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8101 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8101 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8101 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8101 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8102 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8102 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8102 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8102 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8103 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8103 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8103 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8103 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8104 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8104 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8104 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8104 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8105 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8105 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8105 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8105 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8106 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8106 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8106 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8106 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8107 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8107 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8107 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8107 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8108 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8108 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8108 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8108 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8109 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8109 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8109 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8109 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8110 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8110 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8110 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8110 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8111 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8111 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8111 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8111 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8112 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8112 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8112 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8112 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8113 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8113 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8113 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8113 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8114 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.exact_13_8114 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.data_13_8114 +#print axioms Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8114 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8115 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8115 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8115 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8115 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8116 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8116 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8116 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8116 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8117 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8117 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8117 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8117 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8118 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8118 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8118 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8118 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8119 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8119 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8119 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8119 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8120 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8120 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8120 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8120 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8121 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8121 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8121 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8121 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8122 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8122 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8122 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8122 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8123 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8123 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8123 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8123 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8124 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8124 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8124 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8124 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8125 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8125 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8125 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8125 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8126 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8126 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8126 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8126 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8127 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8127 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8127 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8127 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8128 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8128 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8128 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8128 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8129 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.exact_13_8129 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.data_13_8129 +#print axioms Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8129 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8130 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8130 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8130 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8130 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8131 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8131 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8131 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8131 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8132 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8132 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8132 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8132 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8133 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8133 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8133 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8133 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8134 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8134 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8134 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8134 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8135 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8135 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8135 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8135 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8136 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8136 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8136 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8136 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8137 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8137 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8137 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8137 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8138 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8138 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8138 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8138 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8139 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8139 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8139 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8139 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8140 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8140 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8140 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8140 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8141 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8141 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8141 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8141 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8142 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8142 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8142 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8142 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8143 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8143 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8143 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8143 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8144 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.exact_13_8144 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.data_13_8144 +#print axioms Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8144 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8145 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8145 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8145 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8145 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8146 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8146 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8146 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8146 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8147 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8147 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8147 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8147 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8148 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8148 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8148 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8148 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8149 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8149 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8149 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8149 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8150 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8150 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8150 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8150 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8151 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8151 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8151 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8151 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8152 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8152 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8152 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8152 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8153 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8153 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8153 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8153 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8154 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8154 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8154 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8154 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8155 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8155 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8155 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8155 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8156 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8156 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8156 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8156 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8157 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8157 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8157 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8157 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8158 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8158 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8158 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8158 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8159 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8159 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8159 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8159 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8160 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.exact_13_8160 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.data_13_8160 +#print axioms Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8160 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8161 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8161 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8161 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8161 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8162 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8162 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8162 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8162 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8163 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8163 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8163 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8163 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8164 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8164 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8164 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8164 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8165 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8165 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8165 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8165 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8166 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8166 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8166 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8166 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8167 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8167 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8167 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8167 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8168 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8168 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8168 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8168 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8169 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8169 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8169 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8169 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8170 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8170 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8170 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8170 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8171 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8171 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8171 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8171 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8172 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8172 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8172 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8172 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8173 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8173 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8173 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8173 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8174 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8174 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8174 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8174 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8175 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.exact_13_8175 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.data_13_8175 +#print axioms Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8175 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8176 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8176 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8176 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8176 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8177 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8177 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8177 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8177 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8178 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8178 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8178 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8178 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8179 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8179 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8179 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8179 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8180 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8180 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8180 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8180 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8181 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8181 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8181 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8181 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8182 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8182 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8182 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8182 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8183 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8183 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8183 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8183 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8184 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8184 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8184 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8184 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8185 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8185 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8185 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8185 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8186 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8186 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8186 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8186 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8187 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8187 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8187 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8187 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8188 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8188 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8188 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8188 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8189 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8189 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8189 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8189 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8190 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8190 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8190 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8190 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8191 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.exact_13_8191 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.data_13_8191 +#print axioms Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8191 +#print axioms Collatz.Research.StoppingAtlas.stopping_iff_firstLight +#print axioms Collatz.Research.StoppingAtlas.finite_interval_beyond +#print axioms Collatz.Research.StoppingAtlas.membership_upward +#print axioms Collatz.Research.StoppingAtlas.upper_none +#print axioms Collatz.Research.StoppingAtlas.empty_or_tail +#print axioms Collatz.Research.StoppingAtlas.empty_or_tail_1538 +#print axioms Collatz.Research.StoppingAtlas.count_shift_add +#print axioms Collatz.Research.StoppingAtlas.prefix_10_0 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_0 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_1 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_1 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_2 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_2 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_3 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_3 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_4 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_4 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_5 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_5 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_6 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_6 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_7 +#print axioms Collatz.Research.StoppingAtlas.chunk_10_7 +#print axioms Collatz.Research.StoppingAtlas.prefix_10_8 +#print axioms Collatz.Research.StoppingAtlas.period_count_10 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_0 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_0 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_1 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_1 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_2 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_2 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_3 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_3 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_4 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_4 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_5 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_5 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_6 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_6 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_7 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_7 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_8 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_8 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_9 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_9 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_10 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_10 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_11 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_11 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_12 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_12 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_13 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_13 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_14 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_14 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_15 +#print axioms Collatz.Research.StoppingAtlas.chunk_11_15 +#print axioms Collatz.Research.StoppingAtlas.prefix_11_16 +#print axioms Collatz.Research.StoppingAtlas.period_count_11 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_0 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_0 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_1 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_1 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_2 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_2 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_3 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_3 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_4 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_4 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_5 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_5 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_6 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_6 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_7 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_7 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_8 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_8 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_9 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_9 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_10 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_10 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_11 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_11 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_12 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_12 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_13 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_13 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_14 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_14 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_15 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_15 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_16 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_16 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_17 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_17 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_18 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_18 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_19 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_19 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_20 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_20 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_21 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_21 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_22 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_22 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_23 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_23 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_24 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_24 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_25 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_25 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_26 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_26 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_27 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_27 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_28 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_28 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_29 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_29 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_30 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_30 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_31 +#print axioms Collatz.Research.StoppingAtlas.chunk_12_31 +#print axioms Collatz.Research.StoppingAtlas.prefix_12_32 +#print axioms Collatz.Research.StoppingAtlas.period_count_12 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_0 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_0 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_1 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_1 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_2 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_2 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_3 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_3 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_4 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_4 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_5 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_5 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_6 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_6 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_7 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_7 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_8 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_8 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_9 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_9 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_10 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_10 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_11 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_11 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_12 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_12 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_13 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_13 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_14 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_14 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_15 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_15 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_16 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_16 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_17 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_17 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_18 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_18 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_19 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_19 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_20 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_20 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_21 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_21 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_22 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_22 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_23 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_23 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_24 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_24 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_25 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_25 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_26 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_26 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_27 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_27 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_28 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_28 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_29 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_29 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_30 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_30 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_31 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_31 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_32 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_32 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_33 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_33 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_34 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_34 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_35 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_35 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_36 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_36 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_37 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_37 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_38 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_38 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_39 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_39 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_40 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_40 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_41 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_41 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_42 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_42 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_43 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_43 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_44 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_44 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_45 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_45 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_46 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_46 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_47 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_47 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_48 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_48 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_49 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_49 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_50 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_50 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_51 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_51 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_52 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_52 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_53 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_53 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_54 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_54 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_55 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_55 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_56 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_56 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_57 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_57 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_58 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_58 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_59 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_59 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_60 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_60 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_61 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_61 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_62 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_62 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_63 +#print axioms Collatz.Research.StoppingAtlas.chunk_13_63 +#print axioms Collatz.Research.StoppingAtlas.prefix_13_64 +#print axioms Collatz.Research.StoppingAtlas.period_count_13 +#print axioms Collatz.Research.StoppingAtlas.depth_thirteen_error +#print axioms Collatz.Research.StoppingAtlas.count_increment_bound +#print axioms Collatz.Research.StoppingAtlas.prefix_error_upper +#print axioms Collatz.Research.StoppingAtlas.prefix_error_lower +#print axioms Collatz.Research.StoppingAtlas.composition_error +#print axioms Collatz.Research.StoppingAtlas.firstEvent_composition_error +#print axioms Collatz.Research.StoppingAtlas.firstEvent_spec +#print axioms Collatz.Research.StoppingAtlas.firstEvent_disjoint +#print axioms Collatz.Research.StoppingAtlas.firstEvent_period +#print axioms Collatz.Research.StoppingAtlas.firstEvent_count_div_mod +#print axioms Collatz.Research.StoppingAtlas.heavy_split +#print axioms Collatz.Research.StoppingAtlas.heavy_split_disjoint +#print axioms Collatz.Research.StoppingAtlas.indicator_partition +#print axioms Collatz.Research.StoppingAtlas.count_partition +#print axioms Collatz.Research.StoppingAtlas.survival_zero +#print axioms Collatz.Research.StoppingAtlas.cumulative_conservation +#print axioms Collatz.Research.StoppingAtlas.survival_count_antitone +#print axioms Collatz.Research.StoppingAtlas.gap_1538 +#print axioms Collatz.Research.StoppingAtlas.descent_at_firstLight_le_1538 +#print axioms Collatz.Research.StoppingAtlas.exactThrough_1538 +#print axioms Collatz.Research.StoppingAtlas.stopping_iff_firstLight_le_1538 +#print axioms Collatz.Research.StoppingAtlas.next_gap_fails +#print axioms Collatz.Research.StoppingAtlas.next_gap_threshold +#print axioms Collatz.Research.StoppingAtlas.discrepancy_after_1538 +#print axioms Collatz.Research.StoppingAtlas.firstLight_last_even +#print axioms Collatz.Research.StoppingAtlas.firstLight_power_band +#print axioms Collatz.Research.StoppingAtlas.no_firstLight_of_empty_band +#print axioms Collatz.Research.StoppingAtlas.no_firstLight_eleven +#print axioms Collatz.Research.StoppingAtlas.no_stopping_eleven diff --git a/Collatz/Research/StoppingAtlas/Bridge.lean b/Collatz/Research/StoppingAtlas/Bridge.lean new file mode 100644 index 00000000..34ba1e07 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Bridge.lean @@ -0,0 +1,68 @@ +import Collatz.Research.StoppingAtlas.Horizon + +/-! Transfer the interval-shape theorem through any certified crossing horizon. -/ +namespace Collatz.Research.StoppingAtlas +open FirstLightDescent FirstLightConsequences CoefficientDescent DescentIntervals + +/-- A crossing certificate supplies the existing exact-stopping predicate. -/ +theorem stopping_iff_firstLight {H n k : Nat} (hH : ExactThrough H) + (hn : 1 < n) (hk : k ≤ H) : stoppingTime n k ↔ FirstLight n k := + stopping_iff_firstLight_of_horizon hH hn hk + +/-- Every bounded nonempty exact-time class is beyond any certified horizon. -/ +theorem finite_interval_beyond {H k r : Nat} (hH : ExactThrough H) + (hb : ∃ B, ∀ m, (exactInterval k r).Contains m → m < B) + (hne : ∃ m, (exactInterval k r).Contains m) : H < k := by + obtain ⟨n, hn, hs, hf⟩ := finite_interval_witness hb hne + by_cases hk : k ≤ H + · exact False.elim (hf ((stopping_iff_firstLight hH hn hk).mp hs)) + · omega + +/-- Class indices are upward closed through an arbitrary certified horizon. -/ +theorem membership_upward {H k r m u : Nat} (hH : ExactThrough H) (hk : k ≤ H) + (hmu : m ≤ u) (hs : (exactInterval k r).Contains m) : + (exactInterval k r).Contains u := by + have hd := (exactInterval_spec k r m).mp hs + have hn := start_gt_one hd + have hf := (stopping_iff_firstLight hH hn hk).mp hd + have hr := (firstLight_class k r m).mp hf + have hmul := Nat.mul_le_mul_left (2 ^ k) hmu + have hnu : 1 < 2 ^ k * u + r := by omega + exact (exactInterval_spec k r u).mpr + ((stopping_iff_firstLight hH hnu hk).mpr ((firstLight_class k r u).mpr hr)) + +/-- A nonempty exact-time interval below a certified horizon has infinite upper endpoint. -/ +theorem upper_none {H k r : Nat} (hH : ExactThrough H) (hk : k ≤ H) + (hne : ∃ m, (exactInterval k r).Contains m) : (exactInterval k r).upper = none := by + cases hu : (exactInterval k r).upper with + | none => rfl + | some B => + have hb : ∃ B, ∀ m, (exactInterval k r).Contains m → m < B := by + refine ⟨B, ?_⟩ + intro m hm + have h := hm.2 + simpa only [hu] using h + have := finite_interval_beyond hH hb hne + omega + +/-- Complete interval-shape classification, parametrized by a proof rather than a literal horizon. -/ +theorem empty_or_tail {H : Nat} (hH : ExactThrough H) (k r : Nat) (hk : k ≤ H) : + (∀ m, ¬ (exactInterval k r).Contains m) ∨ + ((exactInterval k r).upper = none ∧ + ∀ m, stoppingTime (2 ^ k * m + r) k ↔ (exactInterval k r).lower ≤ m) := by + by_cases hne : ∃ m, (exactInterval k r).Contains m + · have hu := upper_none hH hk hne + right + refine ⟨hu, fun m => ?_⟩ + rw [← exactInterval_spec, IndexInterval.Contains, hu] + simp + · exact Or.inl (fun m hm => hne ⟨m, hm⟩) + +/-- The census phenomenon holds at all representatives and indices through 1538. -/ +theorem empty_or_tail_1538 (k r : Nat) (hk : k ≤ 1538) : + (∀ m, ¬ (exactInterval k r).Contains m) ∨ + ((exactInterval k r).upper = none ∧ + ∀ m, stoppingTime (2 ^ k * m + r) k ↔ (exactInterval k r).lower ≤ m) := + empty_or_tail exactThrough_1538 k r hk + +end Collatz.Research.StoppingAtlas diff --git a/Collatz/Research/StoppingAtlas/Census.lean b/Collatz/Research/StoppingAtlas/Census.lean new file mode 100644 index 00000000..71260dbf --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Census.lean @@ -0,0 +1,1127 @@ +import Collatz.Research.StoppingAtlas.Discrepancy + +namespace Collatz.Research.StoppingAtlas +open PeriodicCounting +set_option maxRecDepth 200000 +set_option maxHeartbeats 0 + +/-- Split a counting window into a prefix and a translated suffix. -/ +theorem count_shift_add (P : Nat → Bool) (N M : Nat) : + countBelow P (N + M) = countBelow P N + countBelow (fun n => P (N + n)) M := by + induction M with + | zero => simp + | succ M ih => + rw [Nat.add_succ, count_succ, ih, count_succ] + omega + +theorem prefix_10_0 : countBelow (firstEventB 10) 0 = 0 := rfl + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_0 : countBelow (fun n => firstEventB 10 (0 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_1 : countBelow (firstEventB 10) 128 = 0 := by + have h := count_shift_add (firstEventB 10) 0 128 + rw [prefix_10_0, chunk_10_0] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_1 : countBelow (fun n => firstEventB 10 (128 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_2 : countBelow (firstEventB 10) 256 = 0 := by + have h := count_shift_add (firstEventB 10) 128 128 + rw [prefix_10_1, chunk_10_1] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_2 : countBelow (fun n => firstEventB 10 (256 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_3 : countBelow (firstEventB 10) 384 = 3 := by + have h := count_shift_add (firstEventB 10) 256 128 + rw [prefix_10_2, chunk_10_2] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_3 : countBelow (fun n => firstEventB 10 (384 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_4 : countBelow (firstEventB 10) 512 = 5 := by + have h := count_shift_add (firstEventB 10) 384 128 + rw [prefix_10_3, chunk_10_3] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_4 : countBelow (fun n => firstEventB 10 (512 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_5 : countBelow (firstEventB 10) 640 = 7 := by + have h := count_shift_add (firstEventB 10) 512 128 + rw [prefix_10_4, chunk_10_4] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_5 : countBelow (fun n => firstEventB 10 (640 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_6 : countBelow (firstEventB 10) 768 = 8 := by + have h := count_shift_add (firstEventB 10) 640 128 + rw [prefix_10_5, chunk_10_5] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_6 : countBelow (fun n => firstEventB 10 (768 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_7 : countBelow (firstEventB 10) 896 = 9 := by + have h := count_shift_add (firstEventB 10) 768 128 + rw [prefix_10_6, chunk_10_6] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_10_7 : countBelow (fun n => firstEventB 10 (896 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_10_8 : countBelow (firstEventB 10) 1024 = 12 := by + have h := count_shift_add (firstEventB 10) 896 128 + rw [prefix_10_7, chunk_10_7] at h + exact h + +/-- Complete period numerator at depth 10. -/ +theorem period_count_10 : countBelow (firstEventB 10) (2 ^ 10) = 12 := prefix_10_8 + +theorem prefix_11_0 : countBelow (firstEventB 11) 0 = 0 := rfl + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_0 : countBelow (fun n => firstEventB 11 (0 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_1 : countBelow (firstEventB 11) 128 = 0 := by + have h := count_shift_add (firstEventB 11) 0 128 + rw [prefix_11_0, chunk_11_0] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_1 : countBelow (fun n => firstEventB 11 (128 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_2 : countBelow (firstEventB 11) 256 = 0 := by + have h := count_shift_add (firstEventB 11) 128 128 + rw [prefix_11_1, chunk_11_1] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_2 : countBelow (fun n => firstEventB 11 (256 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_3 : countBelow (firstEventB 11) 384 = 0 := by + have h := count_shift_add (firstEventB 11) 256 128 + rw [prefix_11_2, chunk_11_2] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_3 : countBelow (fun n => firstEventB 11 (384 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_4 : countBelow (firstEventB 11) 512 = 0 := by + have h := count_shift_add (firstEventB 11) 384 128 + rw [prefix_11_3, chunk_11_3] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_4 : countBelow (fun n => firstEventB 11 (512 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_5 : countBelow (firstEventB 11) 640 = 0 := by + have h := count_shift_add (firstEventB 11) 512 128 + rw [prefix_11_4, chunk_11_4] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_5 : countBelow (fun n => firstEventB 11 (640 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_6 : countBelow (firstEventB 11) 768 = 0 := by + have h := count_shift_add (firstEventB 11) 640 128 + rw [prefix_11_5, chunk_11_5] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_6 : countBelow (fun n => firstEventB 11 (768 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_7 : countBelow (firstEventB 11) 896 = 0 := by + have h := count_shift_add (firstEventB 11) 768 128 + rw [prefix_11_6, chunk_11_6] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_7 : countBelow (fun n => firstEventB 11 (896 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_8 : countBelow (firstEventB 11) 1024 = 0 := by + have h := count_shift_add (firstEventB 11) 896 128 + rw [prefix_11_7, chunk_11_7] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_8 : countBelow (fun n => firstEventB 11 (1024 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_9 : countBelow (firstEventB 11) 1152 = 0 := by + have h := count_shift_add (firstEventB 11) 1024 128 + rw [prefix_11_8, chunk_11_8] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_9 : countBelow (fun n => firstEventB 11 (1152 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_10 : countBelow (firstEventB 11) 1280 = 0 := by + have h := count_shift_add (firstEventB 11) 1152 128 + rw [prefix_11_9, chunk_11_9] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_10 : countBelow (fun n => firstEventB 11 (1280 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_11 : countBelow (firstEventB 11) 1408 = 0 := by + have h := count_shift_add (firstEventB 11) 1280 128 + rw [prefix_11_10, chunk_11_10] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_11 : countBelow (fun n => firstEventB 11 (1408 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_12 : countBelow (firstEventB 11) 1536 = 0 := by + have h := count_shift_add (firstEventB 11) 1408 128 + rw [prefix_11_11, chunk_11_11] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_12 : countBelow (fun n => firstEventB 11 (1536 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_13 : countBelow (firstEventB 11) 1664 = 0 := by + have h := count_shift_add (firstEventB 11) 1536 128 + rw [prefix_11_12, chunk_11_12] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_13 : countBelow (fun n => firstEventB 11 (1664 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_14 : countBelow (firstEventB 11) 1792 = 0 := by + have h := count_shift_add (firstEventB 11) 1664 128 + rw [prefix_11_13, chunk_11_13] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_14 : countBelow (fun n => firstEventB 11 (1792 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_15 : countBelow (firstEventB 11) 1920 = 0 := by + have h := count_shift_add (firstEventB 11) 1792 128 + rw [prefix_11_14, chunk_11_14] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_11_15 : countBelow (fun n => firstEventB 11 (1920 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_11_16 : countBelow (firstEventB 11) 2048 = 0 := by + have h := count_shift_add (firstEventB 11) 1920 128 + rw [prefix_11_15, chunk_11_15] at h + exact h + +/-- Complete period numerator at depth 11. -/ +theorem period_count_11 : countBelow (firstEventB 11) (2 ^ 11) = 0 := prefix_11_16 + +theorem prefix_12_0 : countBelow (firstEventB 12) 0 = 0 := rfl + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_0 : countBelow (fun n => firstEventB 12 (0 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_1 : countBelow (firstEventB 12) 128 = 0 := by + have h := count_shift_add (firstEventB 12) 0 128 + rw [prefix_12_0, chunk_12_0] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_1 : countBelow (fun n => firstEventB 12 (128 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_2 : countBelow (firstEventB 12) 256 = 1 := by + have h := count_shift_add (firstEventB 12) 128 128 + rw [prefix_12_1, chunk_12_1] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_2 : countBelow (fun n => firstEventB 12 (256 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_3 : countBelow (firstEventB 12) 384 = 2 := by + have h := count_shift_add (firstEventB 12) 256 128 + rw [prefix_12_2, chunk_12_2] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_3 : countBelow (fun n => firstEventB 12 (384 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_4 : countBelow (firstEventB 12) 512 = 3 := by + have h := count_shift_add (firstEventB 12) 384 128 + rw [prefix_12_3, chunk_12_3] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_4 : countBelow (fun n => firstEventB 12 (512 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_5 : countBelow (firstEventB 12) 640 = 4 := by + have h := count_shift_add (firstEventB 12) 512 128 + rw [prefix_12_4, chunk_12_4] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_5 : countBelow (fun n => firstEventB 12 (640 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_6 : countBelow (firstEventB 12) 768 = 4 := by + have h := count_shift_add (firstEventB 12) 640 128 + rw [prefix_12_5, chunk_12_5] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_6 : countBelow (fun n => firstEventB 12 (768 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_7 : countBelow (firstEventB 12) 896 = 5 := by + have h := count_shift_add (firstEventB 12) 768 128 + rw [prefix_12_6, chunk_12_6] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_7 : countBelow (fun n => firstEventB 12 (896 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_8 : countBelow (firstEventB 12) 1024 = 7 := by + have h := count_shift_add (firstEventB 12) 896 128 + rw [prefix_12_7, chunk_12_7] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_8 : countBelow (fun n => firstEventB 12 (1024 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_9 : countBelow (firstEventB 12) 1152 = 8 := by + have h := count_shift_add (firstEventB 12) 1024 128 + rw [prefix_12_8, chunk_12_8] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_9 : countBelow (fun n => firstEventB 12 (1152 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_10 : countBelow (firstEventB 12) 1280 = 9 := by + have h := count_shift_add (firstEventB 12) 1152 128 + rw [prefix_12_9, chunk_12_9] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_10 : countBelow (fun n => firstEventB 12 (1280 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_11 : countBelow (firstEventB 12) 1408 = 9 := by + have h := count_shift_add (firstEventB 12) 1280 128 + rw [prefix_12_10, chunk_12_10] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_11 : countBelow (fun n => firstEventB 12 (1408 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_12 : countBelow (firstEventB 12) 1536 = 10 := by + have h := count_shift_add (firstEventB 12) 1408 128 + rw [prefix_12_11, chunk_12_11] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_12 : countBelow (fun n => firstEventB 12 (1536 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_13 : countBelow (firstEventB 12) 1664 = 11 := by + have h := count_shift_add (firstEventB 12) 1536 128 + rw [prefix_12_12, chunk_12_12] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_13 : countBelow (fun n => firstEventB 12 (1664 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_14 : countBelow (firstEventB 12) 1792 = 13 := by + have h := count_shift_add (firstEventB 12) 1664 128 + rw [prefix_12_13, chunk_12_13] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_14 : countBelow (fun n => firstEventB 12 (1792 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_15 : countBelow (firstEventB 12) 1920 = 15 := by + have h := count_shift_add (firstEventB 12) 1792 128 + rw [prefix_12_14, chunk_12_14] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_15 : countBelow (fun n => firstEventB 12 (1920 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_16 : countBelow (firstEventB 12) 2048 = 16 := by + have h := count_shift_add (firstEventB 12) 1920 128 + rw [prefix_12_15, chunk_12_15] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_16 : countBelow (fun n => firstEventB 12 (2048 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_17 : countBelow (firstEventB 12) 2176 = 16 := by + have h := count_shift_add (firstEventB 12) 2048 128 + rw [prefix_12_16, chunk_12_16] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_17 : countBelow (fun n => firstEventB 12 (2176 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_18 : countBelow (firstEventB 12) 2304 = 18 := by + have h := count_shift_add (firstEventB 12) 2176 128 + rw [prefix_12_17, chunk_12_17] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_18 : countBelow (fun n => firstEventB 12 (2304 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_19 : countBelow (firstEventB 12) 2432 = 19 := by + have h := count_shift_add (firstEventB 12) 2304 128 + rw [prefix_12_18, chunk_12_18] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_19 : countBelow (fun n => firstEventB 12 (2432 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_20 : countBelow (firstEventB 12) 2560 = 19 := by + have h := count_shift_add (firstEventB 12) 2432 128 + rw [prefix_12_19, chunk_12_19] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_20 : countBelow (fun n => firstEventB 12 (2560 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_21 : countBelow (firstEventB 12) 2688 = 21 := by + have h := count_shift_add (firstEventB 12) 2560 128 + rw [prefix_12_20, chunk_12_20] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_21 : countBelow (fun n => firstEventB 12 (2688 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_22 : countBelow (firstEventB 12) 2816 = 21 := by + have h := count_shift_add (firstEventB 12) 2688 128 + rw [prefix_12_21, chunk_12_21] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_22 : countBelow (fun n => firstEventB 12 (2816 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_23 : countBelow (firstEventB 12) 2944 = 22 := by + have h := count_shift_add (firstEventB 12) 2816 128 + rw [prefix_12_22, chunk_12_22] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_23 : countBelow (fun n => firstEventB 12 (2944 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_24 : countBelow (firstEventB 12) 3072 = 23 := by + have h := count_shift_add (firstEventB 12) 2944 128 + rw [prefix_12_23, chunk_12_23] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_24 : countBelow (fun n => firstEventB 12 (3072 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_25 : countBelow (firstEventB 12) 3200 = 25 := by + have h := count_shift_add (firstEventB 12) 3072 128 + rw [prefix_12_24, chunk_12_24] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_25 : countBelow (fun n => firstEventB 12 (3200 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_26 : countBelow (firstEventB 12) 3328 = 26 := by + have h := count_shift_add (firstEventB 12) 3200 128 + rw [prefix_12_25, chunk_12_25] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_26 : countBelow (fun n => firstEventB 12 (3328 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_27 : countBelow (firstEventB 12) 3456 = 26 := by + have h := count_shift_add (firstEventB 12) 3328 128 + rw [prefix_12_26, chunk_12_26] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_27 : countBelow (fun n => firstEventB 12 (3456 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_28 : countBelow (firstEventB 12) 3584 = 27 := by + have h := count_shift_add (firstEventB 12) 3456 128 + rw [prefix_12_27, chunk_12_27] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_28 : countBelow (fun n => firstEventB 12 (3584 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_29 : countBelow (firstEventB 12) 3712 = 28 := by + have h := count_shift_add (firstEventB 12) 3584 128 + rw [prefix_12_28, chunk_12_28] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_29 : countBelow (fun n => firstEventB 12 (3712 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_30 : countBelow (firstEventB 12) 3840 = 28 := by + have h := count_shift_add (firstEventB 12) 3712 128 + rw [prefix_12_29, chunk_12_29] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_30 : countBelow (fun n => firstEventB 12 (3840 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_31 : countBelow (firstEventB 12) 3968 = 29 := by + have h := count_shift_add (firstEventB 12) 3840 128 + rw [prefix_12_30, chunk_12_30] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_12_31 : countBelow (fun n => firstEventB 12 (3968 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_12_32 : countBelow (firstEventB 12) 4096 = 30 := by + have h := count_shift_add (firstEventB 12) 3968 128 + rw [prefix_12_31, chunk_12_31] at h + exact h + +/-- Complete period numerator at depth 12. -/ +theorem period_count_12 : countBelow (firstEventB 12) (2 ^ 12) = 30 := prefix_12_32 + +theorem prefix_13_0 : countBelow (firstEventB 13) 0 = 0 := rfl + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_0 : countBelow (fun n => firstEventB 13 (0 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_1 : countBelow (firstEventB 13) 128 = 0 := by + have h := count_shift_add (firstEventB 13) 0 128 + rw [prefix_13_0, chunk_13_0] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_1 : countBelow (fun n => firstEventB 13 (128 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_2 : countBelow (firstEventB 13) 256 = 3 := by + have h := count_shift_add (firstEventB 13) 128 128 + rw [prefix_13_1, chunk_13_1] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_2 : countBelow (fun n => firstEventB 13 (256 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_3 : countBelow (firstEventB 13) 384 = 4 := by + have h := count_shift_add (firstEventB 13) 256 128 + rw [prefix_13_2, chunk_13_2] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_3 : countBelow (fun n => firstEventB 13 (384 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_4 : countBelow (firstEventB 13) 512 = 4 := by + have h := count_shift_add (firstEventB 13) 384 128 + rw [prefix_13_3, chunk_13_3] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_4 : countBelow (fun n => firstEventB 13 (512 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_5 : countBelow (firstEventB 13) 640 = 7 := by + have h := count_shift_add (firstEventB 13) 512 128 + rw [prefix_13_4, chunk_13_4] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_5 : countBelow (fun n => firstEventB 13 (640 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_6 : countBelow (firstEventB 13) 768 = 9 := by + have h := count_shift_add (firstEventB 13) 640 128 + rw [prefix_13_5, chunk_13_5] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_6 : countBelow (fun n => firstEventB 13 (768 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_7 : countBelow (firstEventB 13) 896 = 10 := by + have h := count_shift_add (firstEventB 13) 768 128 + rw [prefix_13_6, chunk_13_6] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_7 : countBelow (fun n => firstEventB 13 (896 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_8 : countBelow (firstEventB 13) 1024 = 10 := by + have h := count_shift_add (firstEventB 13) 896 128 + rw [prefix_13_7, chunk_13_7] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_8 : countBelow (fun n => firstEventB 13 (1024 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_9 : countBelow (firstEventB 13) 1152 = 12 := by + have h := count_shift_add (firstEventB 13) 1024 128 + rw [prefix_13_8, chunk_13_8] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_9 : countBelow (fun n => firstEventB 13 (1152 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_10 : countBelow (firstEventB 13) 1280 = 15 := by + have h := count_shift_add (firstEventB 13) 1152 128 + rw [prefix_13_9, chunk_13_9] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_10 : countBelow (fun n => firstEventB 13 (1280 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_11 : countBelow (firstEventB 13) 1408 = 16 := by + have h := count_shift_add (firstEventB 13) 1280 128 + rw [prefix_13_10, chunk_13_10] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_11 : countBelow (fun n => firstEventB 13 (1408 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_12 : countBelow (firstEventB 13) 1536 = 16 := by + have h := count_shift_add (firstEventB 13) 1408 128 + rw [prefix_13_11, chunk_13_11] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_12 : countBelow (fun n => firstEventB 13 (1536 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_13 : countBelow (firstEventB 13) 1664 = 18 := by + have h := count_shift_add (firstEventB 13) 1536 128 + rw [prefix_13_12, chunk_13_12] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_13 : countBelow (fun n => firstEventB 13 (1664 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_14 : countBelow (firstEventB 13) 1792 = 19 := by + have h := count_shift_add (firstEventB 13) 1664 128 + rw [prefix_13_13, chunk_13_13] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_14 : countBelow (fun n => firstEventB 13 (1792 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_15 : countBelow (firstEventB 13) 1920 = 19 := by + have h := count_shift_add (firstEventB 13) 1792 128 + rw [prefix_13_14, chunk_13_14] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_15 : countBelow (fun n => firstEventB 13 (1920 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_16 : countBelow (firstEventB 13) 2048 = 21 := by + have h := count_shift_add (firstEventB 13) 1920 128 + rw [prefix_13_15, chunk_13_15] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_16 : countBelow (fun n => firstEventB 13 (2048 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_17 : countBelow (firstEventB 13) 2176 = 24 := by + have h := count_shift_add (firstEventB 13) 2048 128 + rw [prefix_13_16, chunk_13_16] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_17 : countBelow (fun n => firstEventB 13 (2176 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_18 : countBelow (firstEventB 13) 2304 = 25 := by + have h := count_shift_add (firstEventB 13) 2176 128 + rw [prefix_13_17, chunk_13_17] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_18 : countBelow (fun n => firstEventB 13 (2304 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_19 : countBelow (firstEventB 13) 2432 = 27 := by + have h := count_shift_add (firstEventB 13) 2304 128 + rw [prefix_13_18, chunk_13_18] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_19 : countBelow (fun n => firstEventB 13 (2432 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_20 : countBelow (firstEventB 13) 2560 = 27 := by + have h := count_shift_add (firstEventB 13) 2432 128 + rw [prefix_13_19, chunk_13_19] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_20 : countBelow (fun n => firstEventB 13 (2560 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_21 : countBelow (firstEventB 13) 2688 = 29 := by + have h := count_shift_add (firstEventB 13) 2560 128 + rw [prefix_13_20, chunk_13_20] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_21 : countBelow (fun n => firstEventB 13 (2688 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_22 : countBelow (firstEventB 13) 2816 = 29 := by + have h := count_shift_add (firstEventB 13) 2688 128 + rw [prefix_13_21, chunk_13_21] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_22 : countBelow (fun n => firstEventB 13 (2816 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_23 : countBelow (firstEventB 13) 2944 = 29 := by + have h := count_shift_add (firstEventB 13) 2816 128 + rw [prefix_13_22, chunk_13_22] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_23 : countBelow (fun n => firstEventB 13 (2944 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_24 : countBelow (firstEventB 13) 3072 = 31 := by + have h := count_shift_add (firstEventB 13) 2944 128 + rw [prefix_13_23, chunk_13_23] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_24 : countBelow (fun n => firstEventB 13 (3072 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_25 : countBelow (firstEventB 13) 3200 = 32 := by + have h := count_shift_add (firstEventB 13) 3072 128 + rw [prefix_13_24, chunk_13_24] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_25 : countBelow (fun n => firstEventB 13 (3200 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_26 : countBelow (firstEventB 13) 3328 = 32 := by + have h := count_shift_add (firstEventB 13) 3200 128 + rw [prefix_13_25, chunk_13_25] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_26 : countBelow (fun n => firstEventB 13 (3328 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_27 : countBelow (firstEventB 13) 3456 = 33 := by + have h := count_shift_add (firstEventB 13) 3328 128 + rw [prefix_13_26, chunk_13_26] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_27 : countBelow (fun n => firstEventB 13 (3456 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_28 : countBelow (firstEventB 13) 3584 = 35 := by + have h := count_shift_add (firstEventB 13) 3456 128 + rw [prefix_13_27, chunk_13_27] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_28 : countBelow (fun n => firstEventB 13 (3584 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_29 : countBelow (firstEventB 13) 3712 = 36 := by + have h := count_shift_add (firstEventB 13) 3584 128 + rw [prefix_13_28, chunk_13_28] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_29 : countBelow (fun n => firstEventB 13 (3712 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_30 : countBelow (firstEventB 13) 3840 = 37 := by + have h := count_shift_add (firstEventB 13) 3712 128 + rw [prefix_13_29, chunk_13_29] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_30 : countBelow (fun n => firstEventB 13 (3840 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_31 : countBelow (firstEventB 13) 3968 = 39 := by + have h := count_shift_add (firstEventB 13) 3840 128 + rw [prefix_13_30, chunk_13_30] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_31 : countBelow (fun n => firstEventB 13 (3968 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_32 : countBelow (firstEventB 13) 4096 = 41 := by + have h := count_shift_add (firstEventB 13) 3968 128 + rw [prefix_13_31, chunk_13_31] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_32 : countBelow (fun n => firstEventB 13 (4096 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_33 : countBelow (firstEventB 13) 4224 = 44 := by + have h := count_shift_add (firstEventB 13) 4096 128 + rw [prefix_13_32, chunk_13_32] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_33 : countBelow (fun n => firstEventB 13 (4224 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_34 : countBelow (firstEventB 13) 4352 = 45 := by + have h := count_shift_add (firstEventB 13) 4224 128 + rw [prefix_13_33, chunk_13_33] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_34 : countBelow (fun n => firstEventB 13 (4352 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_35 : countBelow (firstEventB 13) 4480 = 46 := by + have h := count_shift_add (firstEventB 13) 4352 128 + rw [prefix_13_34, chunk_13_34] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_35 : countBelow (fun n => firstEventB 13 (4480 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_36 : countBelow (firstEventB 13) 4608 = 47 := by + have h := count_shift_add (firstEventB 13) 4480 128 + rw [prefix_13_35, chunk_13_35] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_36 : countBelow (fun n => firstEventB 13 (4608 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_37 : countBelow (firstEventB 13) 4736 = 47 := by + have h := count_shift_add (firstEventB 13) 4608 128 + rw [prefix_13_36, chunk_13_36] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_37 : countBelow (fun n => firstEventB 13 (4736 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_38 : countBelow (firstEventB 13) 4864 = 48 := by + have h := count_shift_add (firstEventB 13) 4736 128 + rw [prefix_13_37, chunk_13_37] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_38 : countBelow (fun n => firstEventB 13 (4864 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_39 : countBelow (firstEventB 13) 4992 = 50 := by + have h := count_shift_add (firstEventB 13) 4864 128 + rw [prefix_13_38, chunk_13_38] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_39 : countBelow (fun n => firstEventB 13 (4992 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_40 : countBelow (firstEventB 13) 5120 = 52 := by + have h := count_shift_add (firstEventB 13) 4992 128 + rw [prefix_13_39, chunk_13_39] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_40 : countBelow (fun n => firstEventB 13 (5120 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_41 : countBelow (firstEventB 13) 5248 = 53 := by + have h := count_shift_add (firstEventB 13) 5120 128 + rw [prefix_13_40, chunk_13_40] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_41 : countBelow (fun n => firstEventB 13 (5248 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_42 : countBelow (firstEventB 13) 5376 = 55 := by + have h := count_shift_add (firstEventB 13) 5248 128 + rw [prefix_13_41, chunk_13_41] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_42 : countBelow (fun n => firstEventB 13 (5376 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_43 : countBelow (firstEventB 13) 5504 = 56 := by + have h := count_shift_add (firstEventB 13) 5376 128 + rw [prefix_13_42, chunk_13_42] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_43 : countBelow (fun n => firstEventB 13 (5504 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_44 : countBelow (firstEventB 13) 5632 = 58 := by + have h := count_shift_add (firstEventB 13) 5504 128 + rw [prefix_13_43, chunk_13_43] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_44 : countBelow (fun n => firstEventB 13 (5632 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_45 : countBelow (firstEventB 13) 5760 = 59 := by + have h := count_shift_add (firstEventB 13) 5632 128 + rw [prefix_13_44, chunk_13_44] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_45 : countBelow (fun n => firstEventB 13 (5760 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_46 : countBelow (firstEventB 13) 5888 = 61 := by + have h := count_shift_add (firstEventB 13) 5760 128 + rw [prefix_13_45, chunk_13_45] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_46 : countBelow (fun n => firstEventB 13 (5888 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_47 : countBelow (firstEventB 13) 6016 = 63 := by + have h := count_shift_add (firstEventB 13) 5888 128 + rw [prefix_13_46, chunk_13_46] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_47 : countBelow (fun n => firstEventB 13 (6016 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_48 : countBelow (firstEventB 13) 6144 = 64 := by + have h := count_shift_add (firstEventB 13) 6016 128 + rw [prefix_13_47, chunk_13_47] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_48 : countBelow (fun n => firstEventB 13 (6144 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_49 : countBelow (firstEventB 13) 6272 = 65 := by + have h := count_shift_add (firstEventB 13) 6144 128 + rw [prefix_13_48, chunk_13_48] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_49 : countBelow (fun n => firstEventB 13 (6272 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_50 : countBelow (firstEventB 13) 6400 = 66 := by + have h := count_shift_add (firstEventB 13) 6272 128 + rw [prefix_13_49, chunk_13_49] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_50 : countBelow (fun n => firstEventB 13 (6400 + n)) 128 = 0 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_51 : countBelow (firstEventB 13) 6528 = 66 := by + have h := count_shift_add (firstEventB 13) 6400 128 + rw [prefix_13_50, chunk_13_50] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_51 : countBelow (fun n => firstEventB 13 (6528 + n)) 128 = 3 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_52 : countBelow (firstEventB 13) 6656 = 69 := by + have h := count_shift_add (firstEventB 13) 6528 128 + rw [prefix_13_51, chunk_13_51] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_52 : countBelow (fun n => firstEventB 13 (6656 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_53 : countBelow (firstEventB 13) 6784 = 70 := by + have h := count_shift_add (firstEventB 13) 6656 128 + rw [prefix_13_52, chunk_13_52] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_53 : countBelow (fun n => firstEventB 13 (6784 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_54 : countBelow (firstEventB 13) 6912 = 71 := by + have h := count_shift_add (firstEventB 13) 6784 128 + rw [prefix_13_53, chunk_13_53] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_54 : countBelow (fun n => firstEventB 13 (6912 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_55 : countBelow (firstEventB 13) 7040 = 73 := by + have h := count_shift_add (firstEventB 13) 6912 128 + rw [prefix_13_54, chunk_13_54] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_55 : countBelow (fun n => firstEventB 13 (7040 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_56 : countBelow (firstEventB 13) 7168 = 74 := by + have h := count_shift_add (firstEventB 13) 7040 128 + rw [prefix_13_55, chunk_13_55] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_56 : countBelow (fun n => firstEventB 13 (7168 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_57 : countBelow (firstEventB 13) 7296 = 75 := by + have h := count_shift_add (firstEventB 13) 7168 128 + rw [prefix_13_56, chunk_13_56] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_57 : countBelow (fun n => firstEventB 13 (7296 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_58 : countBelow (firstEventB 13) 7424 = 77 := by + have h := count_shift_add (firstEventB 13) 7296 128 + rw [prefix_13_57, chunk_13_57] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_58 : countBelow (fun n => firstEventB 13 (7424 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_59 : countBelow (firstEventB 13) 7552 = 78 := by + have h := count_shift_add (firstEventB 13) 7424 128 + rw [prefix_13_58, chunk_13_58] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_59 : countBelow (fun n => firstEventB 13 (7552 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_60 : countBelow (firstEventB 13) 7680 = 79 := by + have h := count_shift_add (firstEventB 13) 7552 128 + rw [prefix_13_59, chunk_13_59] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_60 : countBelow (fun n => firstEventB 13 (7680 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_61 : countBelow (firstEventB 13) 7808 = 80 := by + have h := count_shift_add (firstEventB 13) 7680 128 + rw [prefix_13_60, chunk_13_60] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_61 : countBelow (fun n => firstEventB 13 (7808 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_62 : countBelow (firstEventB 13) 7936 = 82 := by + have h := count_shift_add (firstEventB 13) 7808 128 + rw [prefix_13_61, chunk_13_61] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_62 : countBelow (fun n => firstEventB 13 (7936 + n)) 128 = 2 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_63 : countBelow (firstEventB 13) 8064 = 84 := by + have h := count_shift_add (firstEventB 13) 7936 128 + rw [prefix_13_62, chunk_13_62] at h + exact h + +/-- Kernel computation on one translated 128-input block. -/ +theorem chunk_13_63 : countBelow (fun n => firstEventB 13 (8064 + n)) 128 = 1 := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_13_64 : countBelow (firstEventB 13) 8192 = 85 := by + have h := count_shift_add (firstEventB 13) 8064 128 + rw [prefix_13_63, chunk_13_63] at h + exact h + +/-- Complete period numerator at depth 13. -/ +theorem period_count_13 : countBelow (firstEventB 13) (2 ^ 13) = 85 := prefix_13_64 + +/-- Numerical error bar at depth thirteen, valid at every cutoff. -/ +theorem depth_thirteen_error (N : Nat) : + 8192 * countBelow (firstEventB 13) N ≤ N * 85 + 689095 ∧ + N * 85 ≤ 8192 * countBelow (firstEventB 13) N + 689095 := by + have h := firstEvent_composition_error 13 N + dsimp only at h + rw [period_count_13] at h + simpa only [show (2 : Nat) ^ 13 = 8192 by decide, + show (8192 - 85 : Nat) = 8107 by decide, show (85 * 8107 : Nat) = 689095 by decide] using h + +end Collatz.Research.StoppingAtlas diff --git a/Collatz/Research/StoppingAtlas/Certificates.lean b/Collatz/Research/StoppingAtlas/Certificates.lean new file mode 100644 index 00000000..0da9ce10 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Certificates.lean @@ -0,0 +1,1000 @@ +import Collatz.Research.StoppingAtlas.Batch0001 +import Collatz.Research.StoppingAtlas.Batch0002 +import Collatz.Research.StoppingAtlas.Batch0003 +import Collatz.Research.StoppingAtlas.Batch0004 +import Collatz.Research.StoppingAtlas.Batch0005 +import Collatz.Research.StoppingAtlas.Batch0006 +import Collatz.Research.StoppingAtlas.Batch0007 +import Collatz.Research.StoppingAtlas.Batch0008 +import Collatz.Research.StoppingAtlas.Batch0009 +import Collatz.Research.StoppingAtlas.Batch0010 +import Collatz.Research.StoppingAtlas.Batch0011 +import Collatz.Research.StoppingAtlas.Batch0012 +import Collatz.Research.StoppingAtlas.Batch0013 +import Collatz.Research.StoppingAtlas.Batch0014 +import Collatz.Research.StoppingAtlas.Batch0015 +import Collatz.Research.StoppingAtlas.Batch0016 +import Collatz.Research.StoppingAtlas.Batch0017 +import Collatz.Research.StoppingAtlas.Batch0018 +import Collatz.Research.StoppingAtlas.Batch0019 +import Collatz.Research.StoppingAtlas.Batch0020 +import Collatz.Research.StoppingAtlas.Batch0021 +import Collatz.Research.StoppingAtlas.Batch0022 +import Collatz.Research.StoppingAtlas.Batch0023 +import Collatz.Research.StoppingAtlas.Batch0024 +import Collatz.Research.StoppingAtlas.Batch0025 +import Collatz.Research.StoppingAtlas.Batch0026 +import Collatz.Research.StoppingAtlas.Batch0027 +import Collatz.Research.StoppingAtlas.Batch0028 +import Collatz.Research.StoppingAtlas.Batch0029 +import Collatz.Research.StoppingAtlas.Batch0030 +import Collatz.Research.StoppingAtlas.Batch0031 +import Collatz.Research.StoppingAtlas.Batch0032 +import Collatz.Research.StoppingAtlas.Batch0033 +import Collatz.Research.StoppingAtlas.Batch0034 +import Collatz.Research.StoppingAtlas.Batch0035 +import Collatz.Research.StoppingAtlas.Batch0036 +import Collatz.Research.StoppingAtlas.Batch0037 +import Collatz.Research.StoppingAtlas.Batch0038 +import Collatz.Research.StoppingAtlas.Batch0039 +import Collatz.Research.StoppingAtlas.Batch0040 +import Collatz.Research.StoppingAtlas.Batch0041 +import Collatz.Research.StoppingAtlas.Batch0042 +import Collatz.Research.StoppingAtlas.Batch0043 +import Collatz.Research.StoppingAtlas.Batch0044 +import Collatz.Research.StoppingAtlas.Batch0045 +import Collatz.Research.StoppingAtlas.Batch0046 +import Collatz.Research.StoppingAtlas.Batch0047 +import Collatz.Research.StoppingAtlas.Batch0048 +import Collatz.Research.StoppingAtlas.Batch0049 +import Collatz.Research.StoppingAtlas.Batch0050 +import Collatz.Research.StoppingAtlas.Batch0051 +import Collatz.Research.StoppingAtlas.Batch0052 +import Collatz.Research.StoppingAtlas.Batch0053 +import Collatz.Research.StoppingAtlas.Batch0054 +import Collatz.Research.StoppingAtlas.Batch0055 +import Collatz.Research.StoppingAtlas.Batch0056 +import Collatz.Research.StoppingAtlas.Batch0057 +import Collatz.Research.StoppingAtlas.Batch0058 +import Collatz.Research.StoppingAtlas.Batch0059 +import Collatz.Research.StoppingAtlas.Batch0060 +import Collatz.Research.StoppingAtlas.Batch0061 +import Collatz.Research.StoppingAtlas.Batch0062 +import Collatz.Research.StoppingAtlas.Batch0063 +import Collatz.Research.StoppingAtlas.Batch0064 +import Collatz.Research.StoppingAtlas.Batch0065 +import Collatz.Research.StoppingAtlas.Batch0066 +import Collatz.Research.StoppingAtlas.Batch0067 +import Collatz.Research.StoppingAtlas.Batch0068 +import Collatz.Research.StoppingAtlas.Batch0069 +import Collatz.Research.StoppingAtlas.Batch0070 +import Collatz.Research.StoppingAtlas.Batch0071 +import Collatz.Research.StoppingAtlas.Batch0072 +import Collatz.Research.StoppingAtlas.Batch0073 +import Collatz.Research.StoppingAtlas.Batch0074 +import Collatz.Research.StoppingAtlas.Batch0075 +import Collatz.Research.StoppingAtlas.Batch0076 +import Collatz.Research.StoppingAtlas.Batch0077 +import Collatz.Research.StoppingAtlas.Batch0078 +import Collatz.Research.StoppingAtlas.Batch0079 +import Collatz.Research.StoppingAtlas.Batch0080 +import Collatz.Research.StoppingAtlas.Batch0081 +import Collatz.Research.StoppingAtlas.Batch0082 +import Collatz.Research.StoppingAtlas.Batch0083 +import Collatz.Research.StoppingAtlas.Batch0084 +import Collatz.Research.StoppingAtlas.Batch0085 +import Collatz.Research.StoppingAtlas.Batch0086 +import Collatz.Research.StoppingAtlas.Batch0087 +import Collatz.Research.StoppingAtlas.Batch0088 +import Collatz.Research.StoppingAtlas.Batch0089 +import Collatz.Research.StoppingAtlas.Batch0090 +import Collatz.Research.StoppingAtlas.Batch0091 +import Collatz.Research.StoppingAtlas.Batch0092 +import Collatz.Research.StoppingAtlas.Batch0093 +import Collatz.Research.StoppingAtlas.Batch0094 +import Collatz.Research.StoppingAtlas.Batch0095 +import Collatz.Research.StoppingAtlas.Batch0096 +import Collatz.Research.StoppingAtlas.Batch0097 +import Collatz.Research.StoppingAtlas.Batch0098 +import Collatz.Research.StoppingAtlas.Batch0099 +import Collatz.Research.StoppingAtlas.Batch0100 +import Collatz.Research.StoppingAtlas.Batch0101 +import Collatz.Research.StoppingAtlas.Batch0102 +import Collatz.Research.StoppingAtlas.Batch0103 +import Collatz.Research.StoppingAtlas.Batch0104 +import Collatz.Research.StoppingAtlas.Batch0105 +import Collatz.Research.StoppingAtlas.Batch0106 +import Collatz.Research.StoppingAtlas.Batch0107 +import Collatz.Research.StoppingAtlas.Batch0108 +import Collatz.Research.StoppingAtlas.Batch0109 +import Collatz.Research.StoppingAtlas.Batch0110 +import Collatz.Research.StoppingAtlas.Batch0111 +import Collatz.Research.StoppingAtlas.Batch0112 +import Collatz.Research.StoppingAtlas.Batch0113 +import Collatz.Research.StoppingAtlas.Batch0114 +import Collatz.Research.StoppingAtlas.Batch0115 +import Collatz.Research.StoppingAtlas.Batch0116 +import Collatz.Research.StoppingAtlas.Batch0117 +import Collatz.Research.StoppingAtlas.Batch0118 +import Collatz.Research.StoppingAtlas.Batch0119 +import Collatz.Research.StoppingAtlas.Batch0120 +import Collatz.Research.StoppingAtlas.Batch0121 +import Collatz.Research.StoppingAtlas.Batch0122 +import Collatz.Research.StoppingAtlas.Batch0123 +import Collatz.Research.StoppingAtlas.Batch0124 +import Collatz.Research.StoppingAtlas.Batch0125 +import Collatz.Research.StoppingAtlas.Batch0126 +import Collatz.Research.StoppingAtlas.Batch0127 +import Collatz.Research.StoppingAtlas.Batch0128 +import Collatz.Research.StoppingAtlas.Batch0129 +import Collatz.Research.StoppingAtlas.Batch0130 +import Collatz.Research.StoppingAtlas.Batch0131 +import Collatz.Research.StoppingAtlas.Batch0132 +import Collatz.Research.StoppingAtlas.Batch0133 +import Collatz.Research.StoppingAtlas.Batch0134 +import Collatz.Research.StoppingAtlas.Batch0135 +import Collatz.Research.StoppingAtlas.Batch0136 +import Collatz.Research.StoppingAtlas.Batch0137 +import Collatz.Research.StoppingAtlas.Batch0138 +import Collatz.Research.StoppingAtlas.Batch0139 +import Collatz.Research.StoppingAtlas.Batch0140 +import Collatz.Research.StoppingAtlas.Batch0141 +import Collatz.Research.StoppingAtlas.Batch0142 +import Collatz.Research.StoppingAtlas.Batch0143 +import Collatz.Research.StoppingAtlas.Batch0144 +import Collatz.Research.StoppingAtlas.Batch0145 +import Collatz.Research.StoppingAtlas.Batch0146 +import Collatz.Research.StoppingAtlas.Batch0147 +import Collatz.Research.StoppingAtlas.Batch0148 +import Collatz.Research.StoppingAtlas.Batch0149 +import Collatz.Research.StoppingAtlas.Batch0150 +import Collatz.Research.StoppingAtlas.Batch0151 +import Collatz.Research.StoppingAtlas.Batch0152 +import Collatz.Research.StoppingAtlas.Batch0153 +import Collatz.Research.StoppingAtlas.Batch0154 +import Collatz.Research.StoppingAtlas.Batch0155 +import Collatz.Research.StoppingAtlas.Batch0156 +import Collatz.Research.StoppingAtlas.Batch0157 +import Collatz.Research.StoppingAtlas.Batch0158 +import Collatz.Research.StoppingAtlas.Batch0159 +import Collatz.Research.StoppingAtlas.Batch0160 +import Collatz.Research.StoppingAtlas.Batch0161 +import Collatz.Research.StoppingAtlas.Batch0162 +import Collatz.Research.StoppingAtlas.Batch0163 +import Collatz.Research.StoppingAtlas.Batch0164 +import Collatz.Research.StoppingAtlas.Batch0165 +import Collatz.Research.StoppingAtlas.Batch0166 +import Collatz.Research.StoppingAtlas.Batch0167 +import Collatz.Research.StoppingAtlas.Batch0168 +import Collatz.Research.StoppingAtlas.Batch0169 +import Collatz.Research.StoppingAtlas.Batch0170 +import Collatz.Research.StoppingAtlas.Batch0171 +import Collatz.Research.StoppingAtlas.Batch0172 +import Collatz.Research.StoppingAtlas.Batch0173 +import Collatz.Research.StoppingAtlas.Batch0174 +import Collatz.Research.StoppingAtlas.Batch0175 +import Collatz.Research.StoppingAtlas.Batch0176 +import Collatz.Research.StoppingAtlas.Batch0177 +import Collatz.Research.StoppingAtlas.Batch0178 +import Collatz.Research.StoppingAtlas.Batch0179 +import Collatz.Research.StoppingAtlas.Batch0180 +import Collatz.Research.StoppingAtlas.Batch0181 +import Collatz.Research.StoppingAtlas.Batch0182 +import Collatz.Research.StoppingAtlas.Batch0183 +import Collatz.Research.StoppingAtlas.Batch0184 +import Collatz.Research.StoppingAtlas.Batch0185 +import Collatz.Research.StoppingAtlas.Batch0186 +import Collatz.Research.StoppingAtlas.Batch0187 +import Collatz.Research.StoppingAtlas.Batch0188 +import Collatz.Research.StoppingAtlas.Batch0189 +import Collatz.Research.StoppingAtlas.Batch0190 +import Collatz.Research.StoppingAtlas.Batch0191 +import Collatz.Research.StoppingAtlas.Batch0192 +import Collatz.Research.StoppingAtlas.Batch0193 +import Collatz.Research.StoppingAtlas.Batch0194 +import Collatz.Research.StoppingAtlas.Batch0195 +import Collatz.Research.StoppingAtlas.Batch0196 +import Collatz.Research.StoppingAtlas.Batch0197 +import Collatz.Research.StoppingAtlas.Batch0198 +import Collatz.Research.StoppingAtlas.Batch0199 +import Collatz.Research.StoppingAtlas.Batch0200 +import Collatz.Research.StoppingAtlas.Batch0201 +import Collatz.Research.StoppingAtlas.Batch0202 +import Collatz.Research.StoppingAtlas.Batch0203 +import Collatz.Research.StoppingAtlas.Batch0204 +import Collatz.Research.StoppingAtlas.Batch0205 +import Collatz.Research.StoppingAtlas.Batch0206 +import Collatz.Research.StoppingAtlas.Batch0207 +import Collatz.Research.StoppingAtlas.Batch0208 +import Collatz.Research.StoppingAtlas.Batch0209 +import Collatz.Research.StoppingAtlas.Batch0210 +import Collatz.Research.StoppingAtlas.Batch0211 +import Collatz.Research.StoppingAtlas.Batch0212 +import Collatz.Research.StoppingAtlas.Batch0213 +import Collatz.Research.StoppingAtlas.Batch0214 +import Collatz.Research.StoppingAtlas.Batch0215 +import Collatz.Research.StoppingAtlas.Batch0216 +import Collatz.Research.StoppingAtlas.Batch0217 +import Collatz.Research.StoppingAtlas.Batch0218 +import Collatz.Research.StoppingAtlas.Batch0219 +import Collatz.Research.StoppingAtlas.Batch0220 +import Collatz.Research.StoppingAtlas.Batch0221 +import Collatz.Research.StoppingAtlas.Batch0222 +import Collatz.Research.StoppingAtlas.Batch0223 +import Collatz.Research.StoppingAtlas.Batch0224 +import Collatz.Research.StoppingAtlas.Batch0225 +import Collatz.Research.StoppingAtlas.Batch0226 +import Collatz.Research.StoppingAtlas.Batch0227 +import Collatz.Research.StoppingAtlas.Batch0228 +import Collatz.Research.StoppingAtlas.Batch0229 +import Collatz.Research.StoppingAtlas.Batch0230 +import Collatz.Research.StoppingAtlas.Batch0231 +import Collatz.Research.StoppingAtlas.Batch0232 +import Collatz.Research.StoppingAtlas.Batch0233 +import Collatz.Research.StoppingAtlas.Batch0234 +import Collatz.Research.StoppingAtlas.Batch0235 +import Collatz.Research.StoppingAtlas.Batch0236 +import Collatz.Research.StoppingAtlas.Batch0237 +import Collatz.Research.StoppingAtlas.Batch0238 +import Collatz.Research.StoppingAtlas.Batch0239 +import Collatz.Research.StoppingAtlas.Batch0240 +import Collatz.Research.StoppingAtlas.Batch0241 +import Collatz.Research.StoppingAtlas.Batch0242 +import Collatz.Research.StoppingAtlas.Batch0243 +import Collatz.Research.StoppingAtlas.Batch0244 +import Collatz.Research.StoppingAtlas.Batch0245 +import Collatz.Research.StoppingAtlas.Batch0246 +import Collatz.Research.StoppingAtlas.Batch0247 +import Collatz.Research.StoppingAtlas.Batch0248 +import Collatz.Research.StoppingAtlas.Batch0249 +import Collatz.Research.StoppingAtlas.Batch0250 +import Collatz.Research.StoppingAtlas.Batch0251 +import Collatz.Research.StoppingAtlas.Batch0252 +import Collatz.Research.StoppingAtlas.Batch0253 +import Collatz.Research.StoppingAtlas.Batch0254 +import Collatz.Research.StoppingAtlas.Batch0255 +import Collatz.Research.StoppingAtlas.Batch0256 +import Collatz.Research.StoppingAtlas.Batch0257 +import Collatz.Research.StoppingAtlas.Batch0258 +import Collatz.Research.StoppingAtlas.Batch0259 +import Collatz.Research.StoppingAtlas.Batch0260 +import Collatz.Research.StoppingAtlas.Batch0261 +import Collatz.Research.StoppingAtlas.Batch0262 +import Collatz.Research.StoppingAtlas.Batch0263 +import Collatz.Research.StoppingAtlas.Batch0264 +import Collatz.Research.StoppingAtlas.Batch0265 +import Collatz.Research.StoppingAtlas.Batch0266 +import Collatz.Research.StoppingAtlas.Batch0267 +import Collatz.Research.StoppingAtlas.Batch0268 +import Collatz.Research.StoppingAtlas.Batch0269 +import Collatz.Research.StoppingAtlas.Batch0270 +import Collatz.Research.StoppingAtlas.Batch0271 +import Collatz.Research.StoppingAtlas.Batch0272 +import Collatz.Research.StoppingAtlas.Batch0273 +import Collatz.Research.StoppingAtlas.Batch0274 +import Collatz.Research.StoppingAtlas.Batch0275 +import Collatz.Research.StoppingAtlas.Batch0276 +import Collatz.Research.StoppingAtlas.Batch0277 +import Collatz.Research.StoppingAtlas.Batch0278 +import Collatz.Research.StoppingAtlas.Batch0279 +import Collatz.Research.StoppingAtlas.Batch0280 +import Collatz.Research.StoppingAtlas.Batch0281 +import Collatz.Research.StoppingAtlas.Batch0282 +import Collatz.Research.StoppingAtlas.Batch0283 +import Collatz.Research.StoppingAtlas.Batch0284 +import Collatz.Research.StoppingAtlas.Batch0285 +import Collatz.Research.StoppingAtlas.Batch0286 +import Collatz.Research.StoppingAtlas.Batch0287 +import Collatz.Research.StoppingAtlas.Batch0288 +import Collatz.Research.StoppingAtlas.Batch0289 +import Collatz.Research.StoppingAtlas.Batch0290 +import Collatz.Research.StoppingAtlas.Batch0291 +import Collatz.Research.StoppingAtlas.Batch0292 +import Collatz.Research.StoppingAtlas.Batch0293 +import Collatz.Research.StoppingAtlas.Batch0294 +import Collatz.Research.StoppingAtlas.Batch0295 +import Collatz.Research.StoppingAtlas.Batch0296 +import Collatz.Research.StoppingAtlas.Batch0297 +import Collatz.Research.StoppingAtlas.Batch0298 +import Collatz.Research.StoppingAtlas.Batch0299 +import Collatz.Research.StoppingAtlas.Batch0300 +import Collatz.Research.StoppingAtlas.Batch0301 +import Collatz.Research.StoppingAtlas.Batch0302 +import Collatz.Research.StoppingAtlas.Batch0303 +import Collatz.Research.StoppingAtlas.Batch0304 +import Collatz.Research.StoppingAtlas.Batch0305 +import Collatz.Research.StoppingAtlas.Batch0306 +import Collatz.Research.StoppingAtlas.Batch0307 +import Collatz.Research.StoppingAtlas.Batch0308 +import Collatz.Research.StoppingAtlas.Batch0309 +import Collatz.Research.StoppingAtlas.Batch0310 +import Collatz.Research.StoppingAtlas.Batch0311 +import Collatz.Research.StoppingAtlas.Batch0312 +import Collatz.Research.StoppingAtlas.Batch0313 +import Collatz.Research.StoppingAtlas.Batch0314 +import Collatz.Research.StoppingAtlas.Batch0315 +import Collatz.Research.StoppingAtlas.Batch0316 +import Collatz.Research.StoppingAtlas.Batch0317 +import Collatz.Research.StoppingAtlas.Batch0318 +import Collatz.Research.StoppingAtlas.Batch0319 +import Collatz.Research.StoppingAtlas.Batch0320 +import Collatz.Research.StoppingAtlas.Batch0321 +import Collatz.Research.StoppingAtlas.Batch0322 +import Collatz.Research.StoppingAtlas.Batch0323 +import Collatz.Research.StoppingAtlas.Batch0324 +import Collatz.Research.StoppingAtlas.Batch0325 +import Collatz.Research.StoppingAtlas.Batch0326 +import Collatz.Research.StoppingAtlas.Batch0327 +import Collatz.Research.StoppingAtlas.Batch0328 +import Collatz.Research.StoppingAtlas.Batch0329 +import Collatz.Research.StoppingAtlas.Batch0330 +import Collatz.Research.StoppingAtlas.Batch0331 +import Collatz.Research.StoppingAtlas.Batch0332 +import Collatz.Research.StoppingAtlas.Batch0333 +import Collatz.Research.StoppingAtlas.Batch0334 +import Collatz.Research.StoppingAtlas.Batch0335 +import Collatz.Research.StoppingAtlas.Batch0336 +import Collatz.Research.StoppingAtlas.Batch0337 +import Collatz.Research.StoppingAtlas.Batch0338 +import Collatz.Research.StoppingAtlas.Batch0339 +import Collatz.Research.StoppingAtlas.Batch0340 +import Collatz.Research.StoppingAtlas.Batch0341 +import Collatz.Research.StoppingAtlas.Batch0342 +import Collatz.Research.StoppingAtlas.Batch0343 +import Collatz.Research.StoppingAtlas.Batch0344 +import Collatz.Research.StoppingAtlas.Batch0345 +import Collatz.Research.StoppingAtlas.Batch0346 +import Collatz.Research.StoppingAtlas.Batch0347 +import Collatz.Research.StoppingAtlas.Batch0348 +import Collatz.Research.StoppingAtlas.Batch0349 +import Collatz.Research.StoppingAtlas.Batch0350 +import Collatz.Research.StoppingAtlas.Batch0351 +import Collatz.Research.StoppingAtlas.Batch0352 +import Collatz.Research.StoppingAtlas.Batch0353 +import Collatz.Research.StoppingAtlas.Batch0354 +import Collatz.Research.StoppingAtlas.Batch0355 +import Collatz.Research.StoppingAtlas.Batch0356 +import Collatz.Research.StoppingAtlas.Batch0357 +import Collatz.Research.StoppingAtlas.Batch0358 +import Collatz.Research.StoppingAtlas.Batch0359 +import Collatz.Research.StoppingAtlas.Batch0360 +import Collatz.Research.StoppingAtlas.Batch0361 +import Collatz.Research.StoppingAtlas.Batch0362 +import Collatz.Research.StoppingAtlas.Batch0363 +import Collatz.Research.StoppingAtlas.Batch0364 +import Collatz.Research.StoppingAtlas.Batch0365 +import Collatz.Research.StoppingAtlas.Batch0366 +import Collatz.Research.StoppingAtlas.Batch0367 +import Collatz.Research.StoppingAtlas.Batch0368 +import Collatz.Research.StoppingAtlas.Batch0369 +import Collatz.Research.StoppingAtlas.Batch0370 +import Collatz.Research.StoppingAtlas.Batch0371 +import Collatz.Research.StoppingAtlas.Batch0372 +import Collatz.Research.StoppingAtlas.Batch0373 +import Collatz.Research.StoppingAtlas.Batch0374 +import Collatz.Research.StoppingAtlas.Batch0375 +import Collatz.Research.StoppingAtlas.Batch0376 +import Collatz.Research.StoppingAtlas.Batch0377 +import Collatz.Research.StoppingAtlas.Batch0378 +import Collatz.Research.StoppingAtlas.Batch0379 +import Collatz.Research.StoppingAtlas.Batch0380 +import Collatz.Research.StoppingAtlas.Batch0381 +import Collatz.Research.StoppingAtlas.Batch0382 +import Collatz.Research.StoppingAtlas.Batch0383 +import Collatz.Research.StoppingAtlas.Batch0384 +import Collatz.Research.StoppingAtlas.Batch0385 +import Collatz.Research.StoppingAtlas.Batch0386 +import Collatz.Research.StoppingAtlas.Batch0387 +import Collatz.Research.StoppingAtlas.Batch0388 +import Collatz.Research.StoppingAtlas.Batch0389 +import Collatz.Research.StoppingAtlas.Batch0390 +import Collatz.Research.StoppingAtlas.Batch0391 +import Collatz.Research.StoppingAtlas.Batch0392 +import Collatz.Research.StoppingAtlas.Batch0393 +import Collatz.Research.StoppingAtlas.Batch0394 +import Collatz.Research.StoppingAtlas.Batch0395 +import Collatz.Research.StoppingAtlas.Batch0396 +import Collatz.Research.StoppingAtlas.Batch0397 +import Collatz.Research.StoppingAtlas.Batch0398 +import Collatz.Research.StoppingAtlas.Batch0399 +import Collatz.Research.StoppingAtlas.Batch0400 +import Collatz.Research.StoppingAtlas.Batch0401 +import Collatz.Research.StoppingAtlas.Batch0402 +import Collatz.Research.StoppingAtlas.Batch0403 +import Collatz.Research.StoppingAtlas.Batch0404 +import Collatz.Research.StoppingAtlas.Batch0405 +import Collatz.Research.StoppingAtlas.Batch0406 +import Collatz.Research.StoppingAtlas.Batch0407 +import Collatz.Research.StoppingAtlas.Batch0408 +import Collatz.Research.StoppingAtlas.Batch0409 +import Collatz.Research.StoppingAtlas.Batch0410 +import Collatz.Research.StoppingAtlas.Batch0411 +import Collatz.Research.StoppingAtlas.Batch0412 +import Collatz.Research.StoppingAtlas.Batch0413 +import Collatz.Research.StoppingAtlas.Batch0414 +import Collatz.Research.StoppingAtlas.Batch0415 +import Collatz.Research.StoppingAtlas.Batch0416 +import Collatz.Research.StoppingAtlas.Batch0417 +import Collatz.Research.StoppingAtlas.Batch0418 +import Collatz.Research.StoppingAtlas.Batch0419 +import Collatz.Research.StoppingAtlas.Batch0420 +import Collatz.Research.StoppingAtlas.Batch0421 +import Collatz.Research.StoppingAtlas.Batch0422 +import Collatz.Research.StoppingAtlas.Batch0423 +import Collatz.Research.StoppingAtlas.Batch0424 +import Collatz.Research.StoppingAtlas.Batch0425 +import Collatz.Research.StoppingAtlas.Batch0426 +import Collatz.Research.StoppingAtlas.Batch0427 +import Collatz.Research.StoppingAtlas.Batch0428 +import Collatz.Research.StoppingAtlas.Batch0429 +import Collatz.Research.StoppingAtlas.Batch0430 +import Collatz.Research.StoppingAtlas.Batch0431 +import Collatz.Research.StoppingAtlas.Batch0432 +import Collatz.Research.StoppingAtlas.Batch0433 +import Collatz.Research.StoppingAtlas.Batch0434 +import Collatz.Research.StoppingAtlas.Batch0435 +import Collatz.Research.StoppingAtlas.Batch0436 +import Collatz.Research.StoppingAtlas.Batch0437 +import Collatz.Research.StoppingAtlas.Batch0438 +import Collatz.Research.StoppingAtlas.Batch0439 +import Collatz.Research.StoppingAtlas.Batch0440 +import Collatz.Research.StoppingAtlas.Batch0441 +import Collatz.Research.StoppingAtlas.Batch0442 +import Collatz.Research.StoppingAtlas.Batch0443 +import Collatz.Research.StoppingAtlas.Batch0444 +import Collatz.Research.StoppingAtlas.Batch0445 +import Collatz.Research.StoppingAtlas.Batch0446 +import Collatz.Research.StoppingAtlas.Batch0447 +import Collatz.Research.StoppingAtlas.Batch0448 +import Collatz.Research.StoppingAtlas.Batch0449 +import Collatz.Research.StoppingAtlas.Batch0450 +import Collatz.Research.StoppingAtlas.Batch0451 +import Collatz.Research.StoppingAtlas.Batch0452 +import Collatz.Research.StoppingAtlas.Batch0453 +import Collatz.Research.StoppingAtlas.Batch0454 +import Collatz.Research.StoppingAtlas.Batch0455 +import Collatz.Research.StoppingAtlas.Batch0456 +import Collatz.Research.StoppingAtlas.Batch0457 +import Collatz.Research.StoppingAtlas.Batch0458 +import Collatz.Research.StoppingAtlas.Batch0459 +import Collatz.Research.StoppingAtlas.Batch0460 +import Collatz.Research.StoppingAtlas.Batch0461 +import Collatz.Research.StoppingAtlas.Batch0462 +import Collatz.Research.StoppingAtlas.Batch0463 +import Collatz.Research.StoppingAtlas.Batch0464 +import Collatz.Research.StoppingAtlas.Batch0465 +import Collatz.Research.StoppingAtlas.Batch0466 +import Collatz.Research.StoppingAtlas.Batch0467 +import Collatz.Research.StoppingAtlas.Batch0468 +import Collatz.Research.StoppingAtlas.Batch0469 +import Collatz.Research.StoppingAtlas.Batch0470 +import Collatz.Research.StoppingAtlas.Batch0471 +import Collatz.Research.StoppingAtlas.Batch0472 +import Collatz.Research.StoppingAtlas.Batch0473 +import Collatz.Research.StoppingAtlas.Batch0474 +import Collatz.Research.StoppingAtlas.Batch0475 +import Collatz.Research.StoppingAtlas.Batch0476 +import Collatz.Research.StoppingAtlas.Batch0477 +import Collatz.Research.StoppingAtlas.Batch0478 +import Collatz.Research.StoppingAtlas.Batch0479 +import Collatz.Research.StoppingAtlas.Batch0480 +import Collatz.Research.StoppingAtlas.Batch0481 +import Collatz.Research.StoppingAtlas.Batch0482 +import Collatz.Research.StoppingAtlas.Batch0483 +import Collatz.Research.StoppingAtlas.Batch0484 +import Collatz.Research.StoppingAtlas.Batch0485 +import Collatz.Research.StoppingAtlas.Batch0486 +import Collatz.Research.StoppingAtlas.Batch0487 +import Collatz.Research.StoppingAtlas.Batch0488 +import Collatz.Research.StoppingAtlas.Batch0489 +import Collatz.Research.StoppingAtlas.Batch0490 +import Collatz.Research.StoppingAtlas.Batch0491 +import Collatz.Research.StoppingAtlas.Batch0492 +import Collatz.Research.StoppingAtlas.Batch0493 +import Collatz.Research.StoppingAtlas.Batch0494 +import Collatz.Research.StoppingAtlas.Batch0495 +import Collatz.Research.StoppingAtlas.Batch0496 +import Collatz.Research.StoppingAtlas.Batch0497 +import Collatz.Research.StoppingAtlas.Batch0498 +import Collatz.Research.StoppingAtlas.Batch0499 +import Collatz.Research.StoppingAtlas.Batch0500 +import Collatz.Research.StoppingAtlas.Batch0501 +import Collatz.Research.StoppingAtlas.Batch0502 +import Collatz.Research.StoppingAtlas.Batch0503 +import Collatz.Research.StoppingAtlas.Batch0504 +import Collatz.Research.StoppingAtlas.Batch0505 +import Collatz.Research.StoppingAtlas.Batch0506 +import Collatz.Research.StoppingAtlas.Batch0507 +import Collatz.Research.StoppingAtlas.Batch0508 +import Collatz.Research.StoppingAtlas.Batch0509 +import Collatz.Research.StoppingAtlas.Batch0510 +import Collatz.Research.StoppingAtlas.Batch0511 +import Collatz.Research.StoppingAtlas.Batch0512 +import Collatz.Research.StoppingAtlas.Batch0513 +import Collatz.Research.StoppingAtlas.Batch0514 +import Collatz.Research.StoppingAtlas.Batch0515 +import Collatz.Research.StoppingAtlas.Batch0516 +import Collatz.Research.StoppingAtlas.Batch0517 +import Collatz.Research.StoppingAtlas.Batch0518 +import Collatz.Research.StoppingAtlas.Batch0519 +import Collatz.Research.StoppingAtlas.Batch0520 +import Collatz.Research.StoppingAtlas.Batch0521 +import Collatz.Research.StoppingAtlas.Batch0522 +import Collatz.Research.StoppingAtlas.Batch0523 +import Collatz.Research.StoppingAtlas.Batch0524 +import Collatz.Research.StoppingAtlas.Batch0525 +import Collatz.Research.StoppingAtlas.Batch0526 +import Collatz.Research.StoppingAtlas.Batch0527 +import Collatz.Research.StoppingAtlas.Batch0528 +import Collatz.Research.StoppingAtlas.Batch0529 +import Collatz.Research.StoppingAtlas.Batch0530 +import Collatz.Research.StoppingAtlas.Batch0531 +import Collatz.Research.StoppingAtlas.Batch0532 +import Collatz.Research.StoppingAtlas.Batch0533 +import Collatz.Research.StoppingAtlas.Batch0534 +import Collatz.Research.StoppingAtlas.Batch0535 +import Collatz.Research.StoppingAtlas.Batch0536 +import Collatz.Research.StoppingAtlas.Batch0537 +import Collatz.Research.StoppingAtlas.Batch0538 +import Collatz.Research.StoppingAtlas.Batch0539 +import Collatz.Research.StoppingAtlas.Batch0540 +import Collatz.Research.StoppingAtlas.Batch0541 +import Collatz.Research.StoppingAtlas.Batch0542 +import Collatz.Research.StoppingAtlas.Batch0543 +import Collatz.Research.StoppingAtlas.Batch0544 +import Collatz.Research.StoppingAtlas.Batch0545 +import Collatz.Research.StoppingAtlas.Batch0546 +import Collatz.Research.StoppingAtlas.Batch0547 +import Collatz.Research.StoppingAtlas.Batch0548 +import Collatz.Research.StoppingAtlas.Batch0549 +import Collatz.Research.StoppingAtlas.Batch0550 +import Collatz.Research.StoppingAtlas.Batch0551 +import Collatz.Research.StoppingAtlas.Batch0552 +import Collatz.Research.StoppingAtlas.Batch0553 +import Collatz.Research.StoppingAtlas.Batch0554 +import Collatz.Research.StoppingAtlas.Batch0555 +import Collatz.Research.StoppingAtlas.Batch0556 +import Collatz.Research.StoppingAtlas.Batch0557 +import Collatz.Research.StoppingAtlas.Batch0558 +import Collatz.Research.StoppingAtlas.Batch0559 +import Collatz.Research.StoppingAtlas.Batch0560 +import Collatz.Research.StoppingAtlas.Batch0561 +import Collatz.Research.StoppingAtlas.Batch0562 +import Collatz.Research.StoppingAtlas.Batch0563 +import Collatz.Research.StoppingAtlas.Batch0564 +import Collatz.Research.StoppingAtlas.Batch0565 +import Collatz.Research.StoppingAtlas.Batch0566 +import Collatz.Research.StoppingAtlas.Batch0567 +import Collatz.Research.StoppingAtlas.Batch0568 +import Collatz.Research.StoppingAtlas.Batch0569 +import Collatz.Research.StoppingAtlas.Batch0570 +import Collatz.Research.StoppingAtlas.Batch0571 +import Collatz.Research.StoppingAtlas.Batch0572 +import Collatz.Research.StoppingAtlas.Batch0573 +import Collatz.Research.StoppingAtlas.Batch0574 +import Collatz.Research.StoppingAtlas.Batch0575 +import Collatz.Research.StoppingAtlas.Batch0576 +import Collatz.Research.StoppingAtlas.Batch0577 +import Collatz.Research.StoppingAtlas.Batch0578 +import Collatz.Research.StoppingAtlas.Batch0579 +import Collatz.Research.StoppingAtlas.Batch0580 +import Collatz.Research.StoppingAtlas.Batch0581 +import Collatz.Research.StoppingAtlas.Batch0582 +import Collatz.Research.StoppingAtlas.Batch0583 +import Collatz.Research.StoppingAtlas.Batch0584 +import Collatz.Research.StoppingAtlas.Batch0585 +import Collatz.Research.StoppingAtlas.Batch0586 +import Collatz.Research.StoppingAtlas.Batch0587 +import Collatz.Research.StoppingAtlas.Batch0588 +import Collatz.Research.StoppingAtlas.Batch0589 +import Collatz.Research.StoppingAtlas.Batch0590 +import Collatz.Research.StoppingAtlas.Batch0591 +import Collatz.Research.StoppingAtlas.Batch0592 +import Collatz.Research.StoppingAtlas.Batch0593 +import Collatz.Research.StoppingAtlas.Batch0594 +import Collatz.Research.StoppingAtlas.Batch0595 +import Collatz.Research.StoppingAtlas.Batch0596 +import Collatz.Research.StoppingAtlas.Batch0597 +import Collatz.Research.StoppingAtlas.Batch0598 +import Collatz.Research.StoppingAtlas.Batch0599 +import Collatz.Research.StoppingAtlas.Batch0600 +import Collatz.Research.StoppingAtlas.Batch0601 +import Collatz.Research.StoppingAtlas.Batch0602 +import Collatz.Research.StoppingAtlas.Batch0603 +import Collatz.Research.StoppingAtlas.Batch0604 +import Collatz.Research.StoppingAtlas.Batch0605 +import Collatz.Research.StoppingAtlas.Batch0606 +import Collatz.Research.StoppingAtlas.Batch0607 +import Collatz.Research.StoppingAtlas.Batch0608 +import Collatz.Research.StoppingAtlas.Batch0609 +import Collatz.Research.StoppingAtlas.Batch0610 +import Collatz.Research.StoppingAtlas.Batch0611 +import Collatz.Research.StoppingAtlas.Batch0612 +import Collatz.Research.StoppingAtlas.Batch0613 +import Collatz.Research.StoppingAtlas.Batch0614 +import Collatz.Research.StoppingAtlas.Batch0615 +import Collatz.Research.StoppingAtlas.Batch0616 +import Collatz.Research.StoppingAtlas.Batch0617 +import Collatz.Research.StoppingAtlas.Batch0618 +import Collatz.Research.StoppingAtlas.Batch0619 +import Collatz.Research.StoppingAtlas.Batch0620 +import Collatz.Research.StoppingAtlas.Batch0621 +import Collatz.Research.StoppingAtlas.Batch0622 +import Collatz.Research.StoppingAtlas.Batch0623 +import Collatz.Research.StoppingAtlas.Batch0624 +import Collatz.Research.StoppingAtlas.Batch0625 +import Collatz.Research.StoppingAtlas.Batch0626 +import Collatz.Research.StoppingAtlas.Batch0627 +import Collatz.Research.StoppingAtlas.Batch0628 +import Collatz.Research.StoppingAtlas.Batch0629 +import Collatz.Research.StoppingAtlas.Batch0630 +import Collatz.Research.StoppingAtlas.Batch0631 +import Collatz.Research.StoppingAtlas.Batch0632 +import Collatz.Research.StoppingAtlas.Batch0633 +import Collatz.Research.StoppingAtlas.Batch0634 +import Collatz.Research.StoppingAtlas.Batch0635 +import Collatz.Research.StoppingAtlas.Batch0636 +import Collatz.Research.StoppingAtlas.Batch0637 +import Collatz.Research.StoppingAtlas.Batch0638 +import Collatz.Research.StoppingAtlas.Batch0639 +import Collatz.Research.StoppingAtlas.Batch0640 +import Collatz.Research.StoppingAtlas.Batch0641 +import Collatz.Research.StoppingAtlas.Batch0642 +import Collatz.Research.StoppingAtlas.Batch0643 +import Collatz.Research.StoppingAtlas.Batch0644 +import Collatz.Research.StoppingAtlas.Batch0645 +import Collatz.Research.StoppingAtlas.Batch0646 +import Collatz.Research.StoppingAtlas.Batch0647 +import Collatz.Research.StoppingAtlas.Batch0648 +import Collatz.Research.StoppingAtlas.Batch0649 +import Collatz.Research.StoppingAtlas.Batch0650 +import Collatz.Research.StoppingAtlas.Batch0651 +import Collatz.Research.StoppingAtlas.Batch0652 +import Collatz.Research.StoppingAtlas.Batch0653 +import Collatz.Research.StoppingAtlas.Batch0654 +import Collatz.Research.StoppingAtlas.Batch0655 +import Collatz.Research.StoppingAtlas.Batch0656 +import Collatz.Research.StoppingAtlas.Batch0657 +import Collatz.Research.StoppingAtlas.Batch0658 +import Collatz.Research.StoppingAtlas.Batch0659 +import Collatz.Research.StoppingAtlas.Batch0660 +import Collatz.Research.StoppingAtlas.Batch0661 +import Collatz.Research.StoppingAtlas.Batch0662 +import Collatz.Research.StoppingAtlas.Batch0663 +import Collatz.Research.StoppingAtlas.Batch0664 +import Collatz.Research.StoppingAtlas.Batch0665 +import Collatz.Research.StoppingAtlas.Batch0666 +import Collatz.Research.StoppingAtlas.Batch0667 +import Collatz.Research.StoppingAtlas.Batch0668 +import Collatz.Research.StoppingAtlas.Batch0669 +import Collatz.Research.StoppingAtlas.Batch0670 +import Collatz.Research.StoppingAtlas.Batch0671 +import Collatz.Research.StoppingAtlas.Batch0672 +import Collatz.Research.StoppingAtlas.Batch0673 +import Collatz.Research.StoppingAtlas.Batch0674 +import Collatz.Research.StoppingAtlas.Batch0675 +import Collatz.Research.StoppingAtlas.Batch0676 +import Collatz.Research.StoppingAtlas.Batch0677 +import Collatz.Research.StoppingAtlas.Batch0678 +import Collatz.Research.StoppingAtlas.Batch0679 +import Collatz.Research.StoppingAtlas.Batch0680 +import Collatz.Research.StoppingAtlas.Batch0681 +import Collatz.Research.StoppingAtlas.Batch0682 +import Collatz.Research.StoppingAtlas.Batch0683 +import Collatz.Research.StoppingAtlas.Batch0684 +import Collatz.Research.StoppingAtlas.Batch0685 +import Collatz.Research.StoppingAtlas.Batch0686 +import Collatz.Research.StoppingAtlas.Batch0687 +import Collatz.Research.StoppingAtlas.Batch0688 +import Collatz.Research.StoppingAtlas.Batch0689 +import Collatz.Research.StoppingAtlas.Batch0690 +import Collatz.Research.StoppingAtlas.Batch0691 +import Collatz.Research.StoppingAtlas.Batch0692 +import Collatz.Research.StoppingAtlas.Batch0693 +import Collatz.Research.StoppingAtlas.Batch0694 +import Collatz.Research.StoppingAtlas.Batch0695 +import Collatz.Research.StoppingAtlas.Batch0696 +import Collatz.Research.StoppingAtlas.Batch0697 +import Collatz.Research.StoppingAtlas.Batch0698 +import Collatz.Research.StoppingAtlas.Batch0699 +import Collatz.Research.StoppingAtlas.Batch0700 +import Collatz.Research.StoppingAtlas.Batch0701 +import Collatz.Research.StoppingAtlas.Batch0702 +import Collatz.Research.StoppingAtlas.Batch0703 +import Collatz.Research.StoppingAtlas.Batch0704 +import Collatz.Research.StoppingAtlas.Batch0705 +import Collatz.Research.StoppingAtlas.Batch0706 +import Collatz.Research.StoppingAtlas.Batch0707 +import Collatz.Research.StoppingAtlas.Batch0708 +import Collatz.Research.StoppingAtlas.Batch0709 +import Collatz.Research.StoppingAtlas.Batch0710 +import Collatz.Research.StoppingAtlas.Batch0711 +import Collatz.Research.StoppingAtlas.Batch0712 +import Collatz.Research.StoppingAtlas.Batch0713 +import Collatz.Research.StoppingAtlas.Batch0714 +import Collatz.Research.StoppingAtlas.Batch0715 +import Collatz.Research.StoppingAtlas.Batch0716 +import Collatz.Research.StoppingAtlas.Batch0717 +import Collatz.Research.StoppingAtlas.Batch0718 +import Collatz.Research.StoppingAtlas.Batch0719 +import Collatz.Research.StoppingAtlas.Batch0720 +import Collatz.Research.StoppingAtlas.Batch0721 +import Collatz.Research.StoppingAtlas.Batch0722 +import Collatz.Research.StoppingAtlas.Batch0723 +import Collatz.Research.StoppingAtlas.Batch0724 +import Collatz.Research.StoppingAtlas.Batch0725 +import Collatz.Research.StoppingAtlas.Batch0726 +import Collatz.Research.StoppingAtlas.Batch0727 +import Collatz.Research.StoppingAtlas.Batch0728 +import Collatz.Research.StoppingAtlas.Batch0729 +import Collatz.Research.StoppingAtlas.Batch0730 +import Collatz.Research.StoppingAtlas.Batch0731 +import Collatz.Research.StoppingAtlas.Batch0732 +import Collatz.Research.StoppingAtlas.Batch0733 +import Collatz.Research.StoppingAtlas.Batch0734 +import Collatz.Research.StoppingAtlas.Batch0735 +import Collatz.Research.StoppingAtlas.Batch0736 +import Collatz.Research.StoppingAtlas.Batch0737 +import Collatz.Research.StoppingAtlas.Batch0738 +import Collatz.Research.StoppingAtlas.Batch0739 +import Collatz.Research.StoppingAtlas.Batch0740 +import Collatz.Research.StoppingAtlas.Batch0741 +import Collatz.Research.StoppingAtlas.Batch0742 +import Collatz.Research.StoppingAtlas.Batch0743 +import Collatz.Research.StoppingAtlas.Batch0744 +import Collatz.Research.StoppingAtlas.Batch0745 +import Collatz.Research.StoppingAtlas.Batch0746 +import Collatz.Research.StoppingAtlas.Batch0747 +import Collatz.Research.StoppingAtlas.Batch0748 +import Collatz.Research.StoppingAtlas.Batch0749 +import Collatz.Research.StoppingAtlas.Batch0750 +import Collatz.Research.StoppingAtlas.Batch0751 +import Collatz.Research.StoppingAtlas.Batch0752 +import Collatz.Research.StoppingAtlas.Batch0753 +import Collatz.Research.StoppingAtlas.Batch0754 +import Collatz.Research.StoppingAtlas.Batch0755 +import Collatz.Research.StoppingAtlas.Batch0756 +import Collatz.Research.StoppingAtlas.Batch0757 +import Collatz.Research.StoppingAtlas.Batch0758 +import Collatz.Research.StoppingAtlas.Batch0759 +import Collatz.Research.StoppingAtlas.Batch0760 +import Collatz.Research.StoppingAtlas.Batch0761 +import Collatz.Research.StoppingAtlas.Batch0762 +import Collatz.Research.StoppingAtlas.Batch0763 +import Collatz.Research.StoppingAtlas.Batch0764 +import Collatz.Research.StoppingAtlas.Batch0765 +import Collatz.Research.StoppingAtlas.Batch0766 +import Collatz.Research.StoppingAtlas.Batch0767 +import Collatz.Research.StoppingAtlas.Batch0768 +import Collatz.Research.StoppingAtlas.Batch0769 +import Collatz.Research.StoppingAtlas.Batch0770 +import Collatz.Research.StoppingAtlas.Batch0771 +import Collatz.Research.StoppingAtlas.Batch0772 +import Collatz.Research.StoppingAtlas.Batch0773 +import Collatz.Research.StoppingAtlas.Batch0774 +import Collatz.Research.StoppingAtlas.Batch0775 +import Collatz.Research.StoppingAtlas.Batch0776 +import Collatz.Research.StoppingAtlas.Batch0777 +import Collatz.Research.StoppingAtlas.Batch0778 +import Collatz.Research.StoppingAtlas.Batch0779 +import Collatz.Research.StoppingAtlas.Batch0780 +import Collatz.Research.StoppingAtlas.Batch0781 +import Collatz.Research.StoppingAtlas.Batch0782 +import Collatz.Research.StoppingAtlas.Batch0783 +import Collatz.Research.StoppingAtlas.Batch0784 +import Collatz.Research.StoppingAtlas.Batch0785 +import Collatz.Research.StoppingAtlas.Batch0786 +import Collatz.Research.StoppingAtlas.Batch0787 +import Collatz.Research.StoppingAtlas.Batch0788 +import Collatz.Research.StoppingAtlas.Batch0789 +import Collatz.Research.StoppingAtlas.Batch0790 +import Collatz.Research.StoppingAtlas.Batch0791 +import Collatz.Research.StoppingAtlas.Batch0792 +import Collatz.Research.StoppingAtlas.Batch0793 +import Collatz.Research.StoppingAtlas.Batch0794 +import Collatz.Research.StoppingAtlas.Batch0795 +import Collatz.Research.StoppingAtlas.Batch0796 +import Collatz.Research.StoppingAtlas.Batch0797 +import Collatz.Research.StoppingAtlas.Batch0798 +import Collatz.Research.StoppingAtlas.Batch0799 +import Collatz.Research.StoppingAtlas.Batch0800 +import Collatz.Research.StoppingAtlas.Batch0801 +import Collatz.Research.StoppingAtlas.Batch0802 +import Collatz.Research.StoppingAtlas.Batch0803 +import Collatz.Research.StoppingAtlas.Batch0804 +import Collatz.Research.StoppingAtlas.Batch0805 +import Collatz.Research.StoppingAtlas.Batch0806 +import Collatz.Research.StoppingAtlas.Batch0807 +import Collatz.Research.StoppingAtlas.Batch0808 +import Collatz.Research.StoppingAtlas.Batch0809 +import Collatz.Research.StoppingAtlas.Batch0810 +import Collatz.Research.StoppingAtlas.Batch0811 +import Collatz.Research.StoppingAtlas.Batch0812 +import Collatz.Research.StoppingAtlas.Batch0813 +import Collatz.Research.StoppingAtlas.Batch0814 +import Collatz.Research.StoppingAtlas.Batch0815 +import Collatz.Research.StoppingAtlas.Batch0816 +import Collatz.Research.StoppingAtlas.Batch0817 +import Collatz.Research.StoppingAtlas.Batch0818 +import Collatz.Research.StoppingAtlas.Batch0819 +import Collatz.Research.StoppingAtlas.Batch0820 +import Collatz.Research.StoppingAtlas.Batch0821 +import Collatz.Research.StoppingAtlas.Batch0822 +import Collatz.Research.StoppingAtlas.Batch0823 +import Collatz.Research.StoppingAtlas.Batch0824 +import Collatz.Research.StoppingAtlas.Batch0825 +import Collatz.Research.StoppingAtlas.Batch0826 +import Collatz.Research.StoppingAtlas.Batch0827 +import Collatz.Research.StoppingAtlas.Batch0828 +import Collatz.Research.StoppingAtlas.Batch0829 +import Collatz.Research.StoppingAtlas.Batch0830 +import Collatz.Research.StoppingAtlas.Batch0831 +import Collatz.Research.StoppingAtlas.Batch0832 +import Collatz.Research.StoppingAtlas.Batch0833 +import Collatz.Research.StoppingAtlas.Batch0834 +import Collatz.Research.StoppingAtlas.Batch0835 +import Collatz.Research.StoppingAtlas.Batch0836 +import Collatz.Research.StoppingAtlas.Batch0837 +import Collatz.Research.StoppingAtlas.Batch0838 +import Collatz.Research.StoppingAtlas.Batch0839 +import Collatz.Research.StoppingAtlas.Batch0840 +import Collatz.Research.StoppingAtlas.Batch0841 +import Collatz.Research.StoppingAtlas.Batch0842 +import Collatz.Research.StoppingAtlas.Batch0843 +import Collatz.Research.StoppingAtlas.Batch0844 +import Collatz.Research.StoppingAtlas.Batch0845 +import Collatz.Research.StoppingAtlas.Batch0846 +import Collatz.Research.StoppingAtlas.Batch0847 +import Collatz.Research.StoppingAtlas.Batch0848 +import Collatz.Research.StoppingAtlas.Batch0849 +import Collatz.Research.StoppingAtlas.Batch0850 +import Collatz.Research.StoppingAtlas.Batch0851 +import Collatz.Research.StoppingAtlas.Batch0852 +import Collatz.Research.StoppingAtlas.Batch0853 +import Collatz.Research.StoppingAtlas.Batch0854 +import Collatz.Research.StoppingAtlas.Batch0855 +import Collatz.Research.StoppingAtlas.Batch0856 +import Collatz.Research.StoppingAtlas.Batch0857 +import Collatz.Research.StoppingAtlas.Batch0858 +import Collatz.Research.StoppingAtlas.Batch0859 +import Collatz.Research.StoppingAtlas.Batch0860 +import Collatz.Research.StoppingAtlas.Batch0861 +import Collatz.Research.StoppingAtlas.Batch0862 +import Collatz.Research.StoppingAtlas.Batch0863 +import Collatz.Research.StoppingAtlas.Batch0864 +import Collatz.Research.StoppingAtlas.Batch0865 +import Collatz.Research.StoppingAtlas.Batch0866 +import Collatz.Research.StoppingAtlas.Batch0867 +import Collatz.Research.StoppingAtlas.Batch0868 +import Collatz.Research.StoppingAtlas.Batch0869 +import Collatz.Research.StoppingAtlas.Batch0870 +import Collatz.Research.StoppingAtlas.Batch0871 +import Collatz.Research.StoppingAtlas.Batch0872 +import Collatz.Research.StoppingAtlas.Batch0873 +import Collatz.Research.StoppingAtlas.Batch0874 +import Collatz.Research.StoppingAtlas.Batch0875 +import Collatz.Research.StoppingAtlas.Batch0876 +import Collatz.Research.StoppingAtlas.Batch0877 +import Collatz.Research.StoppingAtlas.Batch0878 +import Collatz.Research.StoppingAtlas.Batch0879 +import Collatz.Research.StoppingAtlas.Batch0880 +import Collatz.Research.StoppingAtlas.Batch0881 +import Collatz.Research.StoppingAtlas.Batch0882 +import Collatz.Research.StoppingAtlas.Batch0883 +import Collatz.Research.StoppingAtlas.Batch0884 +import Collatz.Research.StoppingAtlas.Batch0885 +import Collatz.Research.StoppingAtlas.Batch0886 +import Collatz.Research.StoppingAtlas.Batch0887 +import Collatz.Research.StoppingAtlas.Batch0888 +import Collatz.Research.StoppingAtlas.Batch0889 +import Collatz.Research.StoppingAtlas.Batch0890 +import Collatz.Research.StoppingAtlas.Batch0891 +import Collatz.Research.StoppingAtlas.Batch0892 +import Collatz.Research.StoppingAtlas.Batch0893 +import Collatz.Research.StoppingAtlas.Batch0894 +import Collatz.Research.StoppingAtlas.Batch0895 +import Collatz.Research.StoppingAtlas.Batch0896 +import Collatz.Research.StoppingAtlas.Batch0897 +import Collatz.Research.StoppingAtlas.Batch0898 +import Collatz.Research.StoppingAtlas.Batch0899 +import Collatz.Research.StoppingAtlas.Batch0900 +import Collatz.Research.StoppingAtlas.Batch0901 +import Collatz.Research.StoppingAtlas.Batch0902 +import Collatz.Research.StoppingAtlas.Batch0903 +import Collatz.Research.StoppingAtlas.Batch0904 +import Collatz.Research.StoppingAtlas.Batch0905 +import Collatz.Research.StoppingAtlas.Batch0906 +import Collatz.Research.StoppingAtlas.Batch0907 +import Collatz.Research.StoppingAtlas.Batch0908 +import Collatz.Research.StoppingAtlas.Batch0909 +import Collatz.Research.StoppingAtlas.Batch0910 +import Collatz.Research.StoppingAtlas.Batch0911 +import Collatz.Research.StoppingAtlas.Batch0912 +import Collatz.Research.StoppingAtlas.Batch0913 +import Collatz.Research.StoppingAtlas.Batch0914 +import Collatz.Research.StoppingAtlas.Batch0915 +import Collatz.Research.StoppingAtlas.Batch0916 +import Collatz.Research.StoppingAtlas.Batch0917 +import Collatz.Research.StoppingAtlas.Batch0918 +import Collatz.Research.StoppingAtlas.Batch0919 +import Collatz.Research.StoppingAtlas.Batch0920 +import Collatz.Research.StoppingAtlas.Batch0921 +import Collatz.Research.StoppingAtlas.Batch0922 +import Collatz.Research.StoppingAtlas.Batch0923 +import Collatz.Research.StoppingAtlas.Batch0924 +import Collatz.Research.StoppingAtlas.Batch0925 +import Collatz.Research.StoppingAtlas.Batch0926 +import Collatz.Research.StoppingAtlas.Batch0927 +import Collatz.Research.StoppingAtlas.Batch0928 +import Collatz.Research.StoppingAtlas.Batch0929 +import Collatz.Research.StoppingAtlas.Batch0930 +import Collatz.Research.StoppingAtlas.Batch0931 +import Collatz.Research.StoppingAtlas.Batch0932 +import Collatz.Research.StoppingAtlas.Batch0933 +import Collatz.Research.StoppingAtlas.Batch0934 +import Collatz.Research.StoppingAtlas.Batch0935 +import Collatz.Research.StoppingAtlas.Batch0936 +import Collatz.Research.StoppingAtlas.Batch0937 +import Collatz.Research.StoppingAtlas.Batch0938 +import Collatz.Research.StoppingAtlas.Batch0939 +import Collatz.Research.StoppingAtlas.Batch0940 +import Collatz.Research.StoppingAtlas.Batch0941 +import Collatz.Research.StoppingAtlas.Batch0942 +import Collatz.Research.StoppingAtlas.Batch0943 +import Collatz.Research.StoppingAtlas.Batch0944 +import Collatz.Research.StoppingAtlas.Batch0945 +import Collatz.Research.StoppingAtlas.Batch0946 +import Collatz.Research.StoppingAtlas.Batch0947 +import Collatz.Research.StoppingAtlas.Batch0948 +import Collatz.Research.StoppingAtlas.Batch0949 +import Collatz.Research.StoppingAtlas.Batch0950 +import Collatz.Research.StoppingAtlas.Batch0951 +import Collatz.Research.StoppingAtlas.Batch0952 +import Collatz.Research.StoppingAtlas.Batch0953 +import Collatz.Research.StoppingAtlas.Batch0954 +import Collatz.Research.StoppingAtlas.Batch0955 +import Collatz.Research.StoppingAtlas.Batch0956 +import Collatz.Research.StoppingAtlas.Batch0957 +import Collatz.Research.StoppingAtlas.Batch0958 +import Collatz.Research.StoppingAtlas.Batch0959 +import Collatz.Research.StoppingAtlas.Batch0960 +import Collatz.Research.StoppingAtlas.Batch0961 +import Collatz.Research.StoppingAtlas.Batch0962 +import Collatz.Research.StoppingAtlas.Batch0963 +import Collatz.Research.StoppingAtlas.Batch0964 +import Collatz.Research.StoppingAtlas.Batch0965 +import Collatz.Research.StoppingAtlas.Batch0966 +import Collatz.Research.StoppingAtlas.Batch0967 +import Collatz.Research.StoppingAtlas.Batch0968 +import Collatz.Research.StoppingAtlas.Batch0969 +import Collatz.Research.StoppingAtlas.Batch0970 +import Collatz.Research.StoppingAtlas.Batch0971 +import Collatz.Research.StoppingAtlas.Batch0972 +import Collatz.Research.StoppingAtlas.Batch0973 +import Collatz.Research.StoppingAtlas.Batch0974 +import Collatz.Research.StoppingAtlas.Batch0975 +import Collatz.Research.StoppingAtlas.Batch0976 +import Collatz.Research.StoppingAtlas.Batch0977 +import Collatz.Research.StoppingAtlas.Batch0978 +import Collatz.Research.StoppingAtlas.Batch0979 +import Collatz.Research.StoppingAtlas.Batch0980 +import Collatz.Research.StoppingAtlas.Batch0981 +import Collatz.Research.StoppingAtlas.Batch0982 +import Collatz.Research.StoppingAtlas.Batch0983 +import Collatz.Research.StoppingAtlas.Batch0984 +import Collatz.Research.StoppingAtlas.Batch0985 +import Collatz.Research.StoppingAtlas.Batch0986 +import Collatz.Research.StoppingAtlas.Batch0987 +import Collatz.Research.StoppingAtlas.Batch0988 +import Collatz.Research.StoppingAtlas.Batch0989 +import Collatz.Research.StoppingAtlas.Batch0990 +import Collatz.Research.StoppingAtlas.Batch0991 +import Collatz.Research.StoppingAtlas.Batch0992 +import Collatz.Research.StoppingAtlas.Batch0993 +import Collatz.Research.StoppingAtlas.Batch0994 +import Collatz.Research.StoppingAtlas.Batch0995 +import Collatz.Research.StoppingAtlas.Batch0996 +import Collatz.Research.StoppingAtlas.Batch0997 +import Collatz.Research.StoppingAtlas.Batch0998 +import Collatz.Research.StoppingAtlas.Batch0999 +import Collatz.Research.StoppingAtlas.Batch1000 diff --git a/Collatz/Research/StoppingAtlas/Discrepancy.lean b/Collatz/Research/StoppingAtlas/Discrepancy.lean new file mode 100644 index 00000000..5679bd34 --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Discrepancy.lean @@ -0,0 +1,90 @@ +import Collatz.Research.StoppingAtlas.Events + +/-! A period-composition-sensitive finite error bound. This elementary bound +improves the generic M² estimate to A(M-A), where A is the success count. -/ +namespace Collatz.Research.StoppingAtlas +open PeriodicCounting + +/-- Increasing a counting window adds at most one success per added input. -/ +theorem count_increment_bound (P : Nat → Bool) {r M : Nat} (hr : r ≤ M) : + countBelow P M ≤ countBelow P r + (M - r) := by + induction M with + | zero => have he : r = 0 := by omega + subst r + simp + | succ M ih => + by_cases hm : r ≤ M + · have := ih hm + rw [count_succ] + split <;> omega + · have he : r = M + 1 := by omega + subst r + omega + +/-- Finite binary prefixes obey a composition-sensitive upper discrepancy bound. -/ +theorem prefix_error_upper {M A r R : Nat} (hA : A ≤ M) (hRr : R ≤ r) + (hRA : R ≤ A) : M * R ≤ A * r + A * (M - A) := by + have he : M = A + (M - A) := by omega + by_cases hr : r ≤ A + · calc + M * R ≤ M * r := Nat.mul_le_mul_left M hRr + _ = A * r + (M - A) * r := by calc + M * r = (A + (M - A)) * r := congrArg (fun x => x * r) he + _ = _ := Nat.add_mul _ _ _ + _ ≤ A * r + A * (M - A) := by + have := Nat.mul_le_mul_left (M - A) hr + simpa only [Nat.mul_comm] using Nat.add_le_add_left this (A * r) + · have har : A ≤ r := by omega + calc + M * R ≤ M * A := Nat.mul_le_mul_left M hRA + _ = A * A + A * (M - A) := by calc + M * A = (A + (M - A)) * A := congrArg (fun x => x * A) he + _ = _ := by rw [Nat.add_mul, Nat.mul_comm (M - A) A] + _ ≤ A * r + A * (M - A) := Nat.add_le_add_right (Nat.mul_le_mul_left A har) _ + +/-- The complementary prefix constraint supplies the other error direction. -/ +theorem prefix_error_lower {M A r R : Nat} (hA : A ≤ M) + (hcomp : r + A ≤ M + R) : A * r ≤ M * R + A * (M - A) := by + have hr : r ≤ R + (M - A) := by omega + calc + A * r ≤ A * (R + (M - A)) := Nat.mul_le_mul_left A hr + _ = A * R + A * (M - A) := Nat.mul_add _ _ _ + _ ≤ M * R + A * (M - A) := Nat.add_le_add_right (Nat.mul_le_mul_right R hA) _ + +/-- Uniform discrepancy using only the number of successful residues in a period. -/ +theorem composition_error (P : Nat → Bool) (M N : Nat) (hM : 0 < M) + (hp : ∀ n, P (n + M) = P n) : + M * countBelow P N ≤ N * countBelow P M + countBelow P M * (M - countBelow P M) ∧ + N * countBelow P M ≤ M * countBelow P N + countBelow P M * (M - countBelow P M) := by + let A := countBelow P M + let R := countBelow P (N % M) + let r := N % M + let q := N / M + have hA : A ≤ M := count_le P M + have hr : r ≤ M := Nat.le_of_lt (Nat.mod_lt N hM) + have hRr : R ≤ r := count_le P r + have hRA : R ≤ A := count_mono P hr + have hinc : A ≤ R + (M - r) := count_increment_bound P hr + have hu := prefix_error_upper hA hRr hRA + have hl := prefix_error_lower hA (show r + A ≤ M + R by omega) + have hc : countBelow P N = q * A + R := count_div_mod P M N hp + have hn : N = q * M + r := by + have := Nat.mod_add_div N M + simpa only [Nat.mul_comm, Nat.add_comm] using this.symm + change M * countBelow P N ≤ N * A + A * (M - A) ∧ + N * A ≤ M * countBelow P N + A * (M - A) + rw [hc, hn] + constructor + · simpa only [Nat.mul_add, Nat.add_mul, Nat.mul_assoc, Nat.mul_comm, + Nat.mul_left_comm, Nat.add_assoc] using Nat.add_le_add_left hu (q * M * A) + · simpa only [Nat.mul_add, Nat.add_mul, Nat.mul_assoc, Nat.mul_comm, + Nat.mul_left_comm, Nat.add_assoc] using Nat.add_le_add_left hl (q * M * A) + +/-- Apply the sharper bound to exact coefficient-crossing times. -/ +theorem firstEvent_composition_error (k N : Nat) : + let A := countBelow (firstEventB k) (2 ^ k) + (2 ^ k) * countBelow (firstEventB k) N ≤ N * A + A * (2 ^ k - A) ∧ + N * A ≤ (2 ^ k) * countBelow (firstEventB k) N + A * (2 ^ k - A) := + composition_error _ _ _ (Nat.two_pow_pos k) (firstEvent_period k) + +end Collatz.Research.StoppingAtlas diff --git a/Collatz/Research/StoppingAtlas/Events.lean b/Collatz/Research/StoppingAtlas/Events.lean new file mode 100644 index 00000000..b2a5481f --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Events.lean @@ -0,0 +1,124 @@ +import Collatz.Strategy.FirstLightCounting +import Collatz.Core.Sum + +/-! Exact transfer of finite counting mass between survival and first passage. +All identities are finite and unconditional for coefficients. An ExactThrough +certificate supplies the interpretation as actual first descent. -/ +namespace Collatz.Research.StoppingAtlas +open FirstLightDescent FirstLightCounting FirstLightConsequences PeriodicCounting + +/-- Shift by two to exclude the two inputs where actual first descent is exceptional. -/ +def firstEventB (k n : Nat) : Bool := decide (FirstLight (n + 2) k) + +/-- Under a crossing certificate this Boolean is precisely actual first descent. -/ +theorem firstEvent_spec {H k n : Nat} (hH : ExactThrough H) (hk : k ≤ H) : + firstEventB k n = true ↔ FirstDescent (n + 2) k := by + rw [firstEventB, decide_eq_true_eq] + exact (first_descent_iff_first_light hH (by omega) hk).symm + +/-- Exact first events at different times are mutually exclusive. -/ +theorem firstEvent_disjoint {j k n : Nat} (hne : j ≠ k) + (hj : firstEventB j n = true) : firstEventB k n ≠ true := by + intro hk + have hjf := of_decide_eq_true hj + have hkf := of_decide_eq_true hk + exact hne (first_light_unique hjf hkf) + +/-- Every exact-time event is periodic with its own binary modulus. -/ +theorem firstEvent_period (k n : Nat) : firstEventB k (n + 2 ^ k) = firstEventB k n := by + apply Bool.eq_iff_iff.mpr + simp only [firstEventB, decide_eq_true_eq] + apply FirstLightPeriodicity.firstLight_congr (H := k) (Nat.le_refl k) + have he : n + 2 ^ k + 2 = n + 2 + 2 ^ k := by omega + rw [he] + simp + +/-- Exact event counts on [2,N+2) split into full periods and a prefix. -/ +theorem firstEvent_count_div_mod (k N : Nat) : + countBelow (firstEventB k) N = + (N / 2 ^ k) * countBelow (firstEventB k) (2 ^ k) + + countBelow (firstEventB k) (N % 2 ^ k) := + count_div_mod _ _ _ (firstEvent_period k) + +/-- A surviving coefficient prefix either survives one more step or first crosses there. -/ +theorem heavy_split (H n : Nat) : heavyCheck H n = true ↔ + heavyCheck (H + 1) n = true ∨ FirstLight n (H + 1) := by + rw [heavyCheck_iff, heavyCheck_iff] + constructor + · intro h + by_cases he : 2 ^ (H + 1) ≤ 3 ^ oddCount n (H + 1) + · left + intro j hj + by_cases hjH : j ≤ H + · exact h j hjH + · have : j = H + 1 := by omega + simpa only [this] using he + · right + exact ⟨by omega, fun j hj => h j (by omega)⟩ + · intro h j hj + rcases h with h | h + · exact h j (by omega) + · exact h.2 j (by omega) + +/-- The two destinations of the survival split cannot overlap. -/ +theorem heavy_split_disjoint (H n : Nat) : + ¬ (heavyCheck (H + 1) n = true ∧ FirstLight n (H + 1)) := by + rintro ⟨h, hf⟩ + have hb := (heavyCheck_iff _ _).mp h (H + 1) (Nat.le_refl _) + have := hf.1 + omega + +/-- Turn the disjoint logical split into a per-input counting identity. -/ +theorem indicator_partition (H n : Nat) : + (if survives H n then 1 else 0) = + (if survives (H + 1) n then 1 else 0) + (if firstEventB (H + 1) n then 1 else 0) := by + have hs : survives H n = true ↔ survives (H + 1) n = true ∨ firstEventB (H + 1) n = true := by + simpa only [survives, firstEventB, decide_eq_true_eq] using heavy_split H (n + 2) + have hd : ¬ (survives (H + 1) n = true ∧ firstEventB (H + 1) n = true) := by + simpa only [survives, firstEventB, decide_eq_true_eq] using heavy_split_disjoint H (n + 2) + cases ho : survives H n <;> cases hn : survives (H + 1) n <;> + cases he : firstEventB (H + 1) n <;> simp_all + +/-- Exact mass conservation at every finite cutoff, not only complete periods. -/ +theorem count_partition (H N : Nat) : + countBelow (survives H) N = + countBelow (survives (H + 1)) N + countBelow (firstEventB (H + 1)) N := by + induction N with + | zero => rfl + | succ N ih => + rw [count_succ, count_succ, count_succ, ih] + have := indicator_partition H N + omega + +/-- Total first-event mass accumulated through a finite horizon. -/ +def stoppedCount (H N : Nat) : Nat := + Sum.sumRange H (fun j => countBelow (firstEventB (j + 1)) N) + +/-- Before any steps every shifted positive input survives. -/ +theorem survival_zero (N : Nat) : countBelow (survives 0) N = N := by + have he : survives 0 = fun _ => true := by + funext n + simp [survives, heavyCheck, oddCount, parityVector] + rw [he] + exact count_full N + +/-- A complete finite partition of all inputs into first events and remaining survivors. -/ +theorem cumulative_conservation (H N : Nat) : + stoppedCount H N + countBelow (survives H) N = N := by + induction H with + | zero => simp [stoppedCount, survival_zero] + | succ H ih => + have hpart := count_partition H N + change (Sum.sumRange H (fun j => countBelow (firstEventB (j + 1)) N) + + countBelow (firstEventB (H + 1)) N) + countBelow (survives (H + 1)) N = N + change Sum.sumRange H (fun j => countBelow (firstEventB (j + 1)) N) + + countBelow (survives H) N = N at ih + omega + +/-- Every horizon extension transfers mass out of the survivor set, never into it. -/ +theorem survival_count_antitone (H N : Nat) : + countBelow (survives (H + 1)) N ≤ countBelow (survives H) N := by + have := count_partition H N + omega + +end Collatz.Research.StoppingAtlas diff --git a/Collatz/Research/StoppingAtlas/Horizon.lean b/Collatz/Research/StoppingAtlas/Horizon.lean new file mode 100644 index 00000000..1b58e3ff --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Horizon.lean @@ -0,0 +1,59 @@ +import Collatz.Strategy.FirstLight1024Interface +import Collatz.Research.CoefficientDescent.Transfer + +/-! +# Reusing an exceptional range up to its next arithmetic obstruction + +The threshold 99730 already covers the finite witnesses checked for horizon +1024. A larger coefficient horizon needs no new input witnesses while its +uniform gap bound remains below this threshold. This file checks that fact +through 1538, and checks the failure of the same gap bound at 1539. +-/ +namespace Collatz.Research.StoppingAtlas + +open FirstLightDescent FirstLightConsequences + +set_option maxRecDepth 200000 in +set_option maxHeartbeats 0 in +set_option exponentiation.threshold 2048 in +/-- Exact arithmetic validates the inherited exceptional-input threshold through 1538. -/ +theorem gap_1538 : FirstLightGapCheck.check 1538 99730 = true := by decide + +/-- Every first coefficient crossing through 1538 is a descent, for unbounded n>1. -/ +theorem descent_at_firstLight_le_1538 {n k : Nat} (hn : 1 < n) (hk : k ≤ 1538) + (hf : FirstLight n k) : acceleratedOrbit k n < n := by + apply FirstLightCertificates.descent_of_certificates 1538 99730 + (FirstLightGapCheck.check_sound _ _ gap_1538) _ hn hk hf + intro m hm + obtain ⟨j, hj, hd⟩ := FirstLight1024.small_starts_99730 m hm + exact ⟨⟨j.val, by have := j.isLt; omega⟩, hj, hd⟩ + +/-- Interface to the general stopping-time and periodicity developments. -/ +theorem exactThrough_1538 : ExactThrough 1538 := + fun _ _ hn hk hf => descent_at_firstLight_le_1538 hn hk hf + +/-- Both exact first-event predicates agree through the certified horizon. -/ +theorem stopping_iff_firstLight_le_1538 {n k : Nat} (hn : 1 < n) (hk : k ≤ 1538) : + stoppingTime n k ↔ FirstLight n k := + CoefficientDescent.stopping_iff_firstLight_of_horizon + (fun _ _ h hK hF => descent_at_firstLight_le_1538 h hK hF) hn hk + +set_option exponentiation.threshold 2048 in +/-- At the next critical pair the old arithmetic threshold fails; this is not an orbit counterexample. -/ +theorem next_gap_fails : ¬ ((971 : Nat) * 3 ^ 971 < + 3 * (2 ^ 1539 - 3 ^ 971) * 99730) := by decide + +set_option exponentiation.threshold 2048 in +/-- The next gap would require a threshold of at least 330588 in this bound. -/ +theorem next_gap_threshold : + ((971 : Nat) * 3 ^ 971) / (3 * (2 ^ 1539 - 3 ^ 971)) + 1 = 330588 := by decide + +/-- A discrepancy beyond the inherited horizon must now occur after 1538. -/ +theorem discrepancy_after_1538 {n k : Nat} (hn : 1 < n) (hf : FirstLight n k) + (hfail : n ≤ acceleratedOrbit k n) : 1538 < k := by + by_cases hk : k ≤ 1538 + · have := descent_at_firstLight_le_1538 hn hk hf + omega + · omega + +end Collatz.Research.StoppingAtlas diff --git a/Collatz/Research/StoppingAtlas/Timing.lean b/Collatz/Research/StoppingAtlas/Timing.lean new file mode 100644 index 00000000..c402385d --- /dev/null +++ b/Collatz/Research/StoppingAtlas/Timing.lean @@ -0,0 +1,47 @@ +import Collatz.Research.StoppingAtlas.Bridge + +/-! First coefficient crossings can occur only after an even step. The resulting +power band explains forbidden exact stopping times without enumerating inputs. -/ +namespace Collatz.Research.StoppingAtlas +open FirstLightDescent + +/-- An odd step multiplies the coefficient by 3/2, so cannot be its first contraction. -/ +theorem firstLight_last_even {n k : Nat} (hf : FirstLight n (k + 1)) : + acceleratedOrbit k n % 2 = 0 := by + have hprev := hf.2 k (by omega) + have hlight := hf.1 + have hcount := Density.oddCount_succ_last n k + rcases Arith.mod_two_eq_zero_or_one (acceleratedOrbit k n) with he | ho + · exact he + · have hc : oddCount n (k + 1) = oddCount n k + 1 := by omega + rw [hc, Arith.three_pow_succ, Arith.two_pow_succ] at hlight + omega + +/-- A crossing at k+1 requires a power of three in the half-open band [2^k,2^(k+1)). -/ +theorem firstLight_power_band {n k : Nat} (hf : FirstLight n (k + 1)) : + 2 ^ k ≤ 3 ^ oddCount n (k + 1) ∧ 3 ^ oddCount n (k + 1) < 2 ^ (k + 1) := by + have he := firstLight_last_even hf + have hc := Density.oddCount_succ_last n k + have hp := hf.2 k (by omega) + have hc' : oddCount n (k + 1) = oddCount n k := by omega + exact ⟨by simpa only [hc'] using hp, hf.1⟩ + +/-- Missing powers in the band exclude first crossing for every input. -/ +theorem no_firstLight_of_empty_band (k : Nat) + (hgap : ∀ a : Fin (k + 2), ¬ (2 ^ k ≤ 3 ^ a.val ∧ 3 ^ a.val < 2 ^ (k + 1))) + (n : Nat) : ¬ FirstLight n (k + 1) := by + intro hf + have hb := AffineExact.oddCount_le_self n (k + 1) + exact hgap ⟨oddCount n (k + 1), by omega⟩ (firstLight_power_band hf) + +/-- The all-empty depth-eleven census is forced by a power gap, not a sampling artifact. -/ +theorem no_firstLight_eleven (n : Nat) : ¬ FirstLight n 11 := + no_firstLight_of_empty_band 10 (by decide) n + +/-- No natural starting value has exact accelerated stopping time eleven. -/ +theorem no_stopping_eleven (n : Nat) : ¬ stoppingTime n 11 := by + intro hs + have hn := CoefficientDescent.start_gt_one hs + exact no_firstLight_eleven n ((stopping_iff_firstLight_le_1538 hn (by decide)).mp hs) + +end Collatz.Research.StoppingAtlas diff --git a/README.md b/README.md index f0b8d39e..82abae11 100644 --- a/README.md +++ b/README.md @@ -28,6 +28,10 @@ own verification instructions. ## Research entry points +- [Stopping atlas and first crossing through 1,538 steps](Research/StoppingAtlas/README.md) — + 15,360 infinite-class certificates, finite counting conservation, a tighter + discrepancy bound, and explicit remaining universal-descent obligations. + - [Research status](RESEARCH.md) — results, open questions, and limitations. - [Proof index](INDEX.md) — guide to the Lean library. - [First coefficient crossing through 1,024 steps](Research/FirstLight1024.md) — diff --git a/RESEARCH.md b/RESEARCH.md index 561493cf..c30037b1 100644 --- a/RESEARCH.md +++ b/RESEARCH.md @@ -5,6 +5,18 @@ Persistent checkpoint. Update at every synthesis round. Status codes: **CONJ** = conjectural. **REFUTED** = killed, with counterexample. **CLOSED** = provably unreachable by the stated method. +## Stopping atlas extension, 2026-10-06 (PROVED) + +The [stopping atlas report](Research/StoppingAtlas/README.md) records a new +conditional first-coefficient-crossing horizon of **1538** for all inputs +`n > 1`, up from 1024. It also proves interval-shape transfer for any certified +horizon, finite first-event conservation, the periodic discrepancy bound +`A*(M-A)`, and a power-band obstruction explaining exact stopping time 11. +The complete depth 10–13 census contributes 15,360 infinite-class certificates +in 1000 individually checked batches. The generated proof volume is not a +measure of conceptual novelty. Crossing existence and unrestricted crossing +descent remain open obligations; this is not a proof of Collatz. + ## The reduction (PROVED) `NeverDrops x := ∀ j, x ≤ T^j(x)` where `T(n) = n/2` (even), `(3n+1)/2` (odd). diff --git a/Research/StoppingAtlas/.gitignore b/Research/StoppingAtlas/.gitignore new file mode 100644 index 00000000..e8803709 --- /dev/null +++ b/Research/StoppingAtlas/.gitignore @@ -0,0 +1,8 @@ +# Transient progress and redundant local compiler transcripts. +audit-run.log +batch-builds.log +*-build.log +full-integrity.log +scanner-tests.log +inherited-certificates.log +serial-build.log diff --git a/Research/StoppingAtlas/README.md b/Research/StoppingAtlas/README.md new file mode 100644 index 00000000..cf528010 --- /dev/null +++ b/Research/StoppingAtlas/README.md @@ -0,0 +1,171 @@ +# Stopping atlas and the 1538-step crossing certificate + +This addition extends the repository's checked first-coefficient-crossing +horizon from 1024 to **1538**, classifies every binary residue class at depths +10–13, and proves finite first-event counting identities with a sharper error +bound. **It does not prove the Collatz conjecture.** The results are additions +to this repository; no claim of priority over the mathematical literature is made. + +## Conventions and exact statements + +We use the accelerated map `T(n) = n/2` for even `n` and `(3n+1)/2` for odd +`n`. Let `a(n,k)` count odd steps among the first `k` iterates. A first +coefficient crossing at `k` means + +``` +3^a(n,k) < 2^k +and, for every j < k, 2^j ≤ 3^a(n,j). +``` + +This concerns the coefficient of the affine iterate. The positive additive +term makes descent of the actual integer a separate proof obligation. + +- **Horizon:** for every `n > 1`, if its first coefficient crossing occurs at + `k ≤ 1538`, then `T^k(n) < n`. There is no bound here on when a crossing must + occur. `Horizon.lean` also identifies coefficient crossing with exact first + descent throughout this horizon. +- **Interval shape:** for every depth `k ≤ 1538` and every representative `r`, + the indices `m ≥ 0` for which `2^k*m+r` first descends at time `k` form an + empty set or an upward tail. The theorem is first proved for an arbitrary + certified horizon. A bounded nonempty interval must lie beyond that horizon. +- **Counting conservation:** at every finite cutoff `[2,N+2)`, the sum of + coefficient first-event counts through time `H` and the surviving count + equals `N`. This coefficient identity is unconditional. Its interpretation + as actual first descent requires the explicit `ExactThrough H` hypothesis. +- **Periodic discrepancy:** if a Boolean predicate has positive period `M` + with `A` successes per period and `C(N)` successes before `N`, then + `|M*C(N) - N*A| ≤ A*(M-A)`. Lean states this as two natural-number + inequalities. It improves the older `M*M` bound and specializes to exact + coefficient-crossing counts. This is an elementary counting estimate. +- **Forbidden times:** a first coefficient crossing at `k+1` must finish + with an even step and requires a power of three in `[2^k,2^(k+1))`. + In particular, no input has exact accelerated stopping time 11. This + explains the empty depth-eleven census independently of its enumeration. + +The horizon extension reuses the existing checked exceptional inputs +`2 ≤ n < 99730`, whose coefficient crossings give descent by time 135. +A new integer gap certificate covers the additional lengths. The same +uniform bound fails at `(k,a) = (1539,971)`, where it would require threshold +`330588`. **This is failure of that bound, not an orbit counterexample.** +It suggests either enlarging the checked exceptional range or strengthening +the additive-term estimate. + +## Exhaustive finite census with infinite-class conclusions + +Each canonical pair `(k,r)`, `10 ≤ k ≤ 13`, `0 ≤ r < 2^k`, occurs exactly +once. Four theorems per pair certify the computed interval, its equivalence +to exact stopping for every natural index, base parity/endpoint data, and the +symbolic affine endpoint for every index. + +| Depth | Residue classes | Empty | Infinite tails | Bounded nonempty | +|---|---:|---:|---:|---:| +| 10 | 1024 | 1012 | 12 | 0 | +| 11 | 2048 | 2048 | 0 | 0 | +| 12 | 4096 | 4066 | 30 | 0 | +| 13 | 8192 | 8107 | 85 | 0 | +| Total | 15360 | 15233 | 127 | 0 | + +The period numerators 12, 0, 30, and 85 are separately kernel-checked in +`Census.lean`. At depth 13 the discrepancy bound specializes to +`|8192*C(N) - 85*N| ≤ 689095`. + +An empty class has no **first descent at this particular time**. It may have +descended earlier or descend later. The four census depths do not constitute +a covering argument for universal convergence. + +## Universal descent and the remaining quantifiers + +The existing [universal-descent bridge](../../Collatz/Research/CoefficientDescent/Universal.lean) +separates two obligations: + +1. Every `n > 1` has a first coefficient crossing at some finite time. +2. Every such crossing produces actual descent, without a fixed time bound. + +Together these imply universal descent, and strong induction then proves +Collatz. The present horizon extends a finite part of the second obligation. +It establishes neither obligation without qualification. Almost-everywhere +statements and larger finite tables do not eliminate every possible exception. + +## Techniques considered and boundaries + +“All possible techniques” is an open-ended research aspiration, not a +finite deliverable that can honestly be exhausted. The investigation connects +the following concrete routes; it does not claim to have tried every variant. + +| Technique | Work available in this repository | Remaining obstacle | +|---|---|---| +| Universal descent / well-founded induction | Explicit convergence equivalence and crossing bridge | Produce a descent witness for every positive input greater than one | +| Affine parity words / modular classes | Exact intervals, symbolic iterates, exhaustive new depth 10–13 census | Unbounded coverage of realizable paths | +| First passage / coefficient gaps | Conditional crossing horizon 1538; checked failure threshold at 1539 | Control crossings for arbitrarily long paths | +| Finite counting / periodicity | Exact partition, quotient–remainder counts, composition-sensitive discrepancy | Density estimates leave possible exceptional inputs | +| Probabilistic and moment bounds | Existing `ParityMoments` and natural-density modules | Deterministic control of all exceptional trajectories | +| Inverse trees / difference inequalities | Existing inverse-interval decisions and tree certificates | Establish full coverage, beyond a lower bound on convergent inputs | +| Cycle arithmetic / Diophantine gaps | Existing cycle and frontier certificates | Exclude every nontrivial cycle and all divergent trajectories | +| Lyapunov functions / potentials | Existing `BlockPotential` and obstruction modules | Construct a globally applicable decreasing quantity | +| 2-adic / symbolic dynamics | Parity periodicity and congruence interfaces | Distinguish positive-integer trajectories from unrestricted symbolic paths | +| Automated search / proof certificates | Deterministic generator, independent tests, kernel proofs, negative controls | Search success on bounded domains is not a termination proof | + +These routes differ in scope. Existing paper-statement modules are not +silently counted as proofs of their cited papers. The separate Mathlib +extension is outside this addition's verification target. + +## Notable external results and attribution + +Sources were checked on 2026-10-06. These are literature results, not results +newly proved by this addition. + +- **Terras / Everett:** almost every starting integer has finite stopping + time in natural density. Parity classes and coefficient stopping time + underlie this result. Lagarias's [survey exposition](https://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/node4.html) + also describes the finite difference between exact coefficient and actual + stopping sets at a fixed time. +- **Korec:** for every exponent greater than `log(3)/log(4)`, almost every + orbit reaches below the corresponding power of its starting value, in + natural density. This earlier theorem is described in + [Tao's paper](https://arxiv.org/abs/1909.03562v7). +- **Tao (2022):** for every function tending to infinity, almost every orbit + reaches a value below that function of its starting point, in logarithmic + density. The [paper](https://arxiv.org/abs/1909.03562v7) uses first-passage + transport and estimates on a 3-adic random walk. It does not prove that + every orbit reaches one; its almost-all quantifier cannot be dropped. +- **Krasikov–Lagarias (2003):** difference inequalities give a computer-assisted + lower bound of order `x^0.84` on the number of inputs up to `x` whose orbits + reach one. See the [authors' paper](https://arxiv.org/abs/math/0205002). +- **Hercher (2023):** any nontrivial cycle must have at least 92 local minima. + Use the [published article](https://cs.uwaterloo.ca/journals/JIS/VOL26/Hercher/hercher5.html) + together with its [June 2026 corrigendum](https://cs.uwaterloo.ca/journals/JIS/VOL26/Hercher/corrigendum.pdf), + which repairs an inequality argument. This addresses cycles rather than + the possible existence of divergent nonperiodic orbits. +- **Barina's verification project:** the [project status](https://pcbarina.fit.vut.cz/) + reported all starts below `2075 × 2^60` checked at access time; its log + dates the `2^71` milestone to 2025-01-15. These external computations are + not imported as Lean axioms or presented as kernel-checked by this project. + +## Reproduction and audit + +From the repository root: + +```sh +python3 scripts/stopping_atlas.py --check +lake build Collatz.Research.StoppingAtlas.All +python3 scripts/test_stopping_atlas.py +python3 scripts/audit_stopping_atlas.py +bash scripts/check_integrity.sh +# In a full checkout containing the batch history: +python3 scripts/check_stopping_atlas_history.py +``` + +`manifest.json` records all classes, batch boundaries and source hashes. +`verification.json` records comment-stripped Lean code lines, the axiom +footprint of every new named theorem, independent test totals, and rejected +false controls. The audit excludes its own generated `#print axioms` driver +from code-line accounting. `batch-receipts.json` records each individually +checked batch's source hash and original commit. Exact historical commits +are retained by a merge commit rather than squashing. + +The 1000 batches each cover disjoint classes and were built before their +individual commits. This meets the requested commit/line scale using useful +proof-carrying data. It is **not 1000 independent discoveries**, and the +176,000-plus Lean code lines are predominantly generated certificates. +The baseline is `a4bb6ce3d4163f091e7951d976d7073086c94ef1`; all these files +and batch commits are additions after that baseline. diff --git a/Research/StoppingAtlas/axioms.log b/Research/StoppingAtlas/axioms.log new file mode 100644 index 00000000..aa2740df --- /dev/null +++ b/Research/StoppingAtlas/axioms.log @@ -0,0 +1,61726 @@ +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_0' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_0' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_9' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_12' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_13' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.bounds_10_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.exact_10_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0001.data_10_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0001.endpoint_10_14' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_15' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_16' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_17' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_18' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_19' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_20' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_21' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_22' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_23' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_24' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_24' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_25' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_26' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_26' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_27' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_27' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_28' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_28' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.bounds_10_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.exact_10_29' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0002.data_10_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0002.endpoint_10_29' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_30' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_30' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_31' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_31' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_32' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_32' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_33' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_33' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_34' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_34' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_35' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_35' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_36' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_36' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_37' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_37' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_38' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_38' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_39' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_39' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_40' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_40' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_41' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_41' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_42' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_42' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_43' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_43' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_44' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_44' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.bounds_10_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.exact_10_45' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0003.data_10_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0003.endpoint_10_45' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_46' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_46' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_47' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_47' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_48' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_48' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_49' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_49' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_50' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_50' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_51' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_51' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_52' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_52' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_53' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_53' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_54' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_54' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_55' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_55' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_56' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_56' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_57' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_57' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_58' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_58' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_59' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_59' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.bounds_10_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.exact_10_60' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0004.data_10_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0004.endpoint_10_60' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_61' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_61' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_62' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_62' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_63' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_63' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_64' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_64' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_65' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_65' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_66' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_66' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_67' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_67' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_68' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_68' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_69' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_69' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_70' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_70' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_71' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_71' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_72' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_72' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_73' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_73' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_74' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_74' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.bounds_10_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.exact_10_75' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0005.data_10_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0005.endpoint_10_75' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_76' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_76' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_77' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_77' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_78' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_78' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_79' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_79' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_80' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_80' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_81' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_81' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_82' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_82' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_83' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_83' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_84' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_84' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_85' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_85' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_86' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_86' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_87' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_87' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_88' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_88' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_89' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_89' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_90' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_90' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.bounds_10_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.exact_10_91' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0006.data_10_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0006.endpoint_10_91' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_92' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_92' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_93' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_93' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_94' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_94' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_95' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_95' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_96' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_96' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_97' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_97' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_98' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_98' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_99' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_99' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.bounds_10_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.exact_10_106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0007.data_10_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0007.endpoint_10_106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.bounds_10_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.exact_10_121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0008.data_10_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0008.endpoint_10_121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.bounds_10_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.exact_10_137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0009.data_10_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0009.endpoint_10_137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.bounds_10_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.exact_10_152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0010.data_10_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0010.endpoint_10_152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.bounds_10_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.exact_10_167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0011.data_10_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0011.endpoint_10_167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.bounds_10_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.exact_10_183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0012.data_10_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0012.endpoint_10_183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.bounds_10_198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.exact_10_198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0013.data_10_198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0013.endpoint_10_198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.bounds_10_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.exact_10_214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0014.data_10_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0014.endpoint_10_214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.bounds_10_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.exact_10_229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0015.data_10_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0015.endpoint_10_229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.bounds_10_244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.exact_10_244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0016.data_10_244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0016.endpoint_10_244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.bounds_10_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.exact_10_260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0017.data_10_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0017.endpoint_10_260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.bounds_10_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.exact_10_275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0018.data_10_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0018.endpoint_10_275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.bounds_10_290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.exact_10_290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0019.data_10_290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0019.endpoint_10_290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.bounds_10_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.exact_10_306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0020.data_10_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0020.endpoint_10_306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.bounds_10_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.exact_10_321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0021.data_10_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0021.endpoint_10_321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.bounds_10_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.exact_10_336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0022.data_10_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0022.endpoint_10_336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.bounds_10_352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.exact_10_352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0023.data_10_352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0023.endpoint_10_352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.bounds_10_367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.exact_10_367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0024.data_10_367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0024.endpoint_10_367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.bounds_10_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.exact_10_383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0025.data_10_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0025.endpoint_10_383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.bounds_10_398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.exact_10_398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0026.data_10_398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0026.endpoint_10_398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.bounds_10_413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.exact_10_413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0027.data_10_413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0027.endpoint_10_413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.bounds_10_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.exact_10_429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0028.data_10_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0028.endpoint_10_429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.bounds_10_444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.exact_10_444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0029.data_10_444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0029.endpoint_10_444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.bounds_10_459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.exact_10_459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0030.data_10_459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0030.endpoint_10_459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.bounds_10_475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.exact_10_475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0031.data_10_475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0031.endpoint_10_475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.bounds_10_490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.exact_10_490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0032.data_10_490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0032.endpoint_10_490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.bounds_10_505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.exact_10_505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0033.data_10_505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0033.endpoint_10_505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.bounds_10_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.exact_10_521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0034.data_10_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0034.endpoint_10_521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.bounds_10_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.exact_10_536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0035.data_10_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0035.endpoint_10_536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.bounds_10_551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.exact_10_551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0036.data_10_551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0036.endpoint_10_551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.bounds_10_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.exact_10_567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0037.data_10_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0037.endpoint_10_567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.bounds_10_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.exact_10_582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0038.data_10_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0038.endpoint_10_582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.bounds_10_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.exact_10_598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0039.data_10_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0039.endpoint_10_598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_606' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.data_10_610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.endpoint_10_610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0040.bounds_10_611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0040.exact_10_611' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0041.data_10_626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0041.bounds_10_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0041.exact_10_627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0041.data_10_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0041.bounds_10_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0041.exact_10_628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0041.data_10_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0041.endpoint_10_628' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0042.data_10_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.bounds_10_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.exact_10_644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0042.data_10_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0042.endpoint_10_644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.bounds_10_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.exact_10_659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0043.data_10_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0043.endpoint_10_659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0044.bounds_10_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0044.exact_10_660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0044.data_10_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0044.endpoint_10_660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0044.bounds_10_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0044.exact_10_661' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.data_10_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.data_10_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_681' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.data_10_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.data_10_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_686' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.data_10_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.bounds_10_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.exact_10_690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0045.data_10_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0045.endpoint_10_690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.bounds_10_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.exact_10_705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0046.data_10_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0046.endpoint_10_705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.bounds_10_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.exact_10_718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0047.data_10_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0047.endpoint_10_718' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0048.data_10_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0048.bounds_10_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0048.exact_10_727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0048.data_10_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0048.bounds_10_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0048.exact_10_728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0048.data_10_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_728' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0048.data_10_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0048.endpoint_10_736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_738' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0049.data_10_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.bounds_10_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.exact_10_751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0049.data_10_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0049.endpoint_10_751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.bounds_10_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.exact_10_767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0050.data_10_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0050.endpoint_10_767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_768' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0051.data_10_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.bounds_10_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.exact_10_782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0051.data_10_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0051.endpoint_10_782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.bounds_10_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.exact_10_797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0052.data_10_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0052.endpoint_10_797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.bounds_10_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.exact_10_813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0053.data_10_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0053.endpoint_10_813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_823' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0054.data_10_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.bounds_10_828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.exact_10_828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0054.data_10_828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0054.endpoint_10_828' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0056.data_10_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_848' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0056.data_10_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.bounds_10_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.exact_10_859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0056.data_10_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0056.endpoint_10_859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.bounds_10_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.exact_10_874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0057.data_10_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0057.endpoint_10_874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.bounds_10_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.exact_10_889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0058.data_10_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0058.endpoint_10_889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.bounds_10_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.exact_10_905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0059.data_10_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0059.endpoint_10_905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.bounds_10_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.exact_10_920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0060.data_10_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0060.endpoint_10_920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_928' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0061.data_10_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.bounds_10_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.exact_10_933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0061.data_10_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0061.endpoint_10_933' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0062.data_10_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0062.bounds_10_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0062.exact_10_947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0062.data_10_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0062.bounds_10_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0062.exact_10_948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0062.data_10_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0062.endpoint_10_948' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.bounds_10_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.exact_10_966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0063.data_10_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0063.endpoint_10_966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.bounds_10_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.exact_10_982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0064.data_10_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0064.endpoint_10_982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.bounds_10_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.exact_10_997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0065.data_10_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0065.endpoint_10_997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.bounds_10_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.exact_10_1012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0066.data_10_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0066.endpoint_10_1012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_10_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_10_1023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_10_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_10_1023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_11_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_11_0' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_11_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_0' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_11_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_11_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_11_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_11_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_11_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_11_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_11_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_11_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_11_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.bounds_11_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.exact_11_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0067.data_11_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0067.endpoint_11_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_9' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_12' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_13' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_14' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_15' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_16' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_17' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_18' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.bounds_11_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.exact_11_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0068.data_11_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0068.endpoint_11_19' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_20' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_21' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_22' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_23' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_24' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_24' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_25' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_26' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_26' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_27' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_27' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_28' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_28' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_29' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_29' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_30' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_30' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_31' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_31' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_32' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_32' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_33' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_33' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.bounds_11_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.exact_11_34' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0069.data_11_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0069.endpoint_11_34' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_35' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_35' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_36' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_36' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_37' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_37' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_38' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_38' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_39' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_39' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_40' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_40' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_41' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_41' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_42' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_42' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_43' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_43' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_44' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_44' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_45' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_45' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_46' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_46' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_47' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_47' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_48' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_48' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_49' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_49' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.bounds_11_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.exact_11_50' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0070.data_11_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0070.endpoint_11_50' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_51' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_51' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_52' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_52' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_53' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_53' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_54' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_54' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_55' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_55' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_56' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_56' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_57' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_57' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_58' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_58' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_59' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_59' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_60' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_60' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_61' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_61' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_62' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_62' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_63' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_63' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_64' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_64' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.bounds_11_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.exact_11_65' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0071.data_11_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0071.endpoint_11_65' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_66' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_66' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_67' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_67' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_68' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_68' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_69' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_69' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_70' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_70' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_71' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_71' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_72' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_72' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_73' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_73' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_74' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_74' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_75' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_75' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_76' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_76' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_77' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_77' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_78' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_78' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_79' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_79' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.bounds_11_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.exact_11_80' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0072.data_11_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0072.endpoint_11_80' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_81' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_81' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_82' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_82' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_83' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_83' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_84' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_84' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_85' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_85' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_86' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_86' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_87' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_87' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_88' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_88' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_89' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_89' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_90' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_90' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_91' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_91' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_92' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_92' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_93' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_93' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_94' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_94' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_95' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_95' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.bounds_11_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.exact_11_96' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0073.data_11_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0073.endpoint_11_96' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_97' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_97' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_98' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_98' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_99' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_99' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.bounds_11_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.exact_11_111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0074.data_11_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0074.endpoint_11_111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.bounds_11_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.exact_11_127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0075.data_11_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0075.endpoint_11_127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.bounds_11_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.exact_11_142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0076.data_11_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0076.endpoint_11_142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.bounds_11_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.exact_11_157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0077.data_11_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0077.endpoint_11_157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.bounds_11_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.exact_11_173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0078.data_11_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0078.endpoint_11_173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.bounds_11_188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.exact_11_188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0079.data_11_188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0079.endpoint_11_188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.bounds_11_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.exact_11_203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0080.data_11_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0080.endpoint_11_203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.bounds_11_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.exact_11_219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0081.data_11_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0081.endpoint_11_219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.data_11_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.endpoint_11_231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0082.bounds_11_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0082.exact_11_232' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_239' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.bounds_11_249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.exact_11_249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0083.data_11_249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0083.endpoint_11_249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.bounds_11_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.exact_11_265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0084.data_11_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0084.endpoint_11_265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.bounds_11_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.exact_11_280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0085.data_11_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0085.endpoint_11_280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0086.bounds_11_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0086.exact_11_281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0086.data_11_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0086.endpoint_11_281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0086.bounds_11_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0086.exact_11_282' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_302' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.bounds_11_311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.exact_11_311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0087.data_11_311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0087.endpoint_11_311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.bounds_11_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.exact_11_326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0088.data_11_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0088.endpoint_11_326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.bounds_11_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.exact_11_339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0089.data_11_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0089.endpoint_11_339' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0090.bounds_11_355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0090.exact_11_355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0090.data_11_355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0090.bounds_11_356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0090.exact_11_356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0090.data_11_356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0090.bounds_11_357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0090.exact_11_357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0090.data_11_357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0090.endpoint_11_357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.bounds_11_372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.exact_11_372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0091.data_11_372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0091.endpoint_11_372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.bounds_11_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.exact_11_388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0092.data_11_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0092.endpoint_11_388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0093.bounds_11_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0093.exact_11_389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0093.data_11_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0093.endpoint_11_389' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0094.data_11_417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0094.bounds_11_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0094.exact_11_418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0094.data_11_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0094.endpoint_11_418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_419' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.bounds_11_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.exact_11_434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0095.data_11_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0095.endpoint_11_434' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0099.data_11_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0099.bounds_11_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.exact_11_493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0099.data_11_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0099.bounds_11_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.exact_11_494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0099.data_11_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0099.bounds_11_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.exact_11_495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0099.data_11_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0099.endpoint_11_495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0100.bounds_11_496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0100.exact_11_496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0100.data_11_496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0100.endpoint_11_496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0100.bounds_11_497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0100.exact_11_497' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0101.data_11_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_514' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0101.data_11_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.bounds_11_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.exact_11_526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0101.data_11_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0101.endpoint_11_526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.bounds_11_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.exact_11_541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0102.data_11_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0102.endpoint_11_541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.bounds_11_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.exact_11_549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0103.data_11_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_549' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0103.data_11_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0103.endpoint_11_557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.bounds_11_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.exact_11_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.data_11_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.bounds_11_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.exact_11_559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.data_11_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_559' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0104.data_11_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.bounds_11_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.exact_11_568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.data_11_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.bounds_11_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.exact_11_569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0104.data_11_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0104.endpoint_11_569' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0105.data_11_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.bounds_11_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.exact_11_583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.data_11_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.bounds_11_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.exact_11_584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.data_11_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.bounds_11_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.exact_11_585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.data_11_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.bounds_11_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.exact_11_586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.data_11_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.bounds_11_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.exact_11_587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0105.data_11_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0105.endpoint_11_587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.data_11_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.endpoint_11_601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0106.bounds_11_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0106.exact_11_602' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0108.data_11_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.bounds_11_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.exact_11_628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.data_11_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.bounds_11_629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.exact_11_629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.data_11_629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.bounds_11_630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.exact_11_630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.data_11_630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.bounds_11_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.exact_11_631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.data_11_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.bounds_11_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.exact_11_632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.data_11_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.bounds_11_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.exact_11_633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0108.data_11_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0108.endpoint_11_633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.bounds_11_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.exact_11_649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0109.data_11_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0109.endpoint_11_649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.bounds_11_664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.exact_11_664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0110.data_11_664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0110.endpoint_11_664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.bounds_11_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.exact_11_679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0111.data_11_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0111.endpoint_11_679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.bounds_11_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.exact_11_695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0112.data_11_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0112.endpoint_11_695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.bounds_11_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.exact_11_710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0113.data_11_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0113.endpoint_11_710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.bounds_11_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.exact_11_726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0114.data_11_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0114.endpoint_11_726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.bounds_11_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.exact_11_741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0115.data_11_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0115.endpoint_11_741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.bounds_11_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.exact_11_756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0116.data_11_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0116.endpoint_11_756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.bounds_11_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.exact_11_772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0117.data_11_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0117.endpoint_11_772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.bounds_11_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.exact_11_787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0118.data_11_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0118.endpoint_11_787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.bounds_11_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.exact_11_802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0119.data_11_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0119.endpoint_11_802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.bounds_11_818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.exact_11_818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0120.data_11_818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0120.endpoint_11_818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.bounds_11_833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.exact_11_833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0121.data_11_833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0121.endpoint_11_833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.bounds_11_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.exact_11_848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0122.data_11_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0122.endpoint_11_848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.bounds_11_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.exact_11_864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0123.data_11_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0123.endpoint_11_864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.bounds_11_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.exact_11_879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0124.data_11_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0124.endpoint_11_879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.bounds_11_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.exact_11_895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0125.data_11_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0125.endpoint_11_895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.bounds_11_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.exact_11_910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0126.data_11_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0126.endpoint_11_910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.bounds_11_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.exact_11_925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0127.data_11_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0127.endpoint_11_925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.bounds_11_941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.exact_11_941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0128.data_11_941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0128.endpoint_11_941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.bounds_11_956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.exact_11_956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0129.data_11_956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0129.endpoint_11_956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.bounds_11_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.exact_11_971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0130.data_11_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0130.endpoint_11_971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_979' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0131.data_11_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.bounds_11_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.exact_11_987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0131.data_11_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0131.endpoint_11_987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_1000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_1000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_1001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_1001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.bounds_11_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.exact_11_1002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0132.data_11_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0132.endpoint_11_1002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.bounds_11_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.exact_11_1017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0133.data_11_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0133.endpoint_11_1017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1024' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0134.data_11_1027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.bounds_11_1029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.exact_11_1029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0134.data_11_1029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0134.endpoint_11_1029' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0135.data_11_1037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.bounds_11_1048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.exact_11_1048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0135.data_11_1048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0135.endpoint_11_1048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.bounds_11_1063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.exact_11_1063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0136.data_11_1063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0136.endpoint_11_1063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.bounds_11_1079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.exact_11_1079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0137.data_11_1079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0137.endpoint_11_1079' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0138.data_11_1082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.bounds_11_1094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.exact_11_1094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0138.data_11_1094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0138.endpoint_11_1094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.bounds_11_1110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.exact_11_1110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0139.data_11_1110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0139.endpoint_11_1110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.bounds_11_1125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.exact_11_1125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0140.data_11_1125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0140.endpoint_11_1125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.bounds_11_1140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.exact_11_1140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0141.data_11_1140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0141.endpoint_11_1140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.bounds_11_1156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.exact_11_1156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0142.data_11_1156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0142.endpoint_11_1156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.bounds_11_1171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.exact_11_1171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0143.data_11_1171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0143.endpoint_11_1171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.bounds_11_1186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.exact_11_1186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0144.data_11_1186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0144.endpoint_11_1186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.bounds_11_1202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.exact_11_1202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0145.data_11_1202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0145.endpoint_11_1202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.bounds_11_1217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.exact_11_1217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0146.data_11_1217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0146.endpoint_11_1217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.bounds_11_1232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.exact_11_1232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0147.data_11_1232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0147.endpoint_11_1232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.bounds_11_1248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.exact_11_1248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0148.data_11_1248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0148.endpoint_11_1248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.bounds_11_1263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.exact_11_1263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0149.data_11_1263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0149.endpoint_11_1263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.bounds_11_1279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.exact_11_1279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0150.data_11_1279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0150.endpoint_11_1279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.bounds_11_1294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.exact_11_1294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0151.data_11_1294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0151.endpoint_11_1294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.bounds_11_1309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.exact_11_1309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0152.data_11_1309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0152.endpoint_11_1309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.bounds_11_1325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.exact_11_1325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0153.data_11_1325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0153.endpoint_11_1325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.bounds_11_1340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.exact_11_1340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0154.data_11_1340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0154.endpoint_11_1340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.bounds_11_1355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.exact_11_1355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0155.data_11_1355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0155.endpoint_11_1355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.bounds_11_1371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.exact_11_1371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0156.data_11_1371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0156.endpoint_11_1371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.bounds_11_1386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.exact_11_1386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0157.data_11_1386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0157.endpoint_11_1386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.bounds_11_1401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.exact_11_1401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0158.data_11_1401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0158.endpoint_11_1401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.bounds_11_1417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.exact_11_1417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0159.data_11_1417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0159.endpoint_11_1417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.bounds_11_1432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.exact_11_1432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0160.data_11_1432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0160.endpoint_11_1432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.bounds_11_1447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.exact_11_1447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0161.data_11_1447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0161.endpoint_11_1447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.bounds_11_1463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.exact_11_1463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0162.data_11_1463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0162.endpoint_11_1463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.bounds_11_1478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.exact_11_1478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0163.data_11_1478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0163.endpoint_11_1478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.bounds_11_1494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.exact_11_1494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0164.data_11_1494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0164.endpoint_11_1494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.bounds_11_1509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.exact_11_1509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0165.data_11_1509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0165.endpoint_11_1509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.bounds_11_1524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.exact_11_1524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0166.data_11_1524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0166.endpoint_11_1524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.bounds_11_1540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.exact_11_1540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0167.data_11_1540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0167.endpoint_11_1540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.bounds_11_1555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.exact_11_1555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0168.data_11_1555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0168.endpoint_11_1555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.bounds_11_1570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.exact_11_1570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0169.data_11_1570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0169.endpoint_11_1570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.bounds_11_1586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.exact_11_1586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0170.data_11_1586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0170.endpoint_11_1586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.bounds_11_1601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.exact_11_1601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0171.data_11_1601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0171.endpoint_11_1601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.bounds_11_1616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.exact_11_1616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0172.data_11_1616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0172.endpoint_11_1616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.bounds_11_1632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.exact_11_1632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0173.data_11_1632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0173.endpoint_11_1632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.bounds_11_1647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.exact_11_1647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0174.data_11_1647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0174.endpoint_11_1647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.bounds_11_1663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.exact_11_1663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0175.data_11_1663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0175.endpoint_11_1663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.bounds_11_1678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.exact_11_1678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0176.data_11_1678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0176.endpoint_11_1678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.bounds_11_1693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.exact_11_1693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0177.data_11_1693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0177.endpoint_11_1693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.bounds_11_1709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.exact_11_1709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0178.data_11_1709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0178.endpoint_11_1709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.bounds_11_1724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.exact_11_1724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0179.data_11_1724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0179.endpoint_11_1724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.bounds_11_1739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.exact_11_1739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0180.data_11_1739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0180.endpoint_11_1739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.bounds_11_1755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.exact_11_1755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0181.data_11_1755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0181.endpoint_11_1755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.bounds_11_1770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.exact_11_1770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0182.data_11_1770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0182.endpoint_11_1770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.bounds_11_1785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.exact_11_1785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0183.data_11_1785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0183.endpoint_11_1785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.bounds_11_1801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.exact_11_1801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0184.data_11_1801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0184.endpoint_11_1801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.bounds_11_1816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.exact_11_1816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0185.data_11_1816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0185.endpoint_11_1816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.bounds_11_1831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.exact_11_1831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0186.data_11_1831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0186.endpoint_11_1831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.bounds_11_1847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.exact_11_1847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0187.data_11_1847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0187.endpoint_11_1847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.bounds_11_1862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.exact_11_1862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0188.data_11_1862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0188.endpoint_11_1862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.bounds_11_1878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.exact_11_1878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0189.data_11_1878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0189.endpoint_11_1878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.bounds_11_1893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.exact_11_1893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0190.data_11_1893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0190.endpoint_11_1893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.bounds_11_1908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.exact_11_1908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0191.data_11_1908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0191.endpoint_11_1908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.bounds_11_1924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.exact_11_1924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0192.data_11_1924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0192.endpoint_11_1924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.bounds_11_1939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.exact_11_1939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0193.data_11_1939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0193.endpoint_11_1939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.bounds_11_1954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.exact_11_1954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0194.data_11_1954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0194.endpoint_11_1954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.bounds_11_1970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.exact_11_1970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0195.data_11_1970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0195.endpoint_11_1970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.bounds_11_1985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.exact_11_1985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0196.data_11_1985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0196.endpoint_11_1985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_1999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_1999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_1999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_1999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.bounds_11_2000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.exact_11_2000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0197.data_11_2000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0197.endpoint_11_2000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.bounds_11_2016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.exact_11_2016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0198.data_11_2016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0198.endpoint_11_2016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.bounds_11_2031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.exact_11_2031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0199.data_11_2031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0199.endpoint_11_2031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.bounds_11_2047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.exact_11_2047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0200.data_11_2047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0200.endpoint_11_2047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_0' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_0' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_9' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_12' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_13' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.bounds_12_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.exact_12_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0201.data_12_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0201.endpoint_12_14' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_15' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_16' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_17' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_18' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_19' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_20' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_21' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_22' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_23' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_24' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_24' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_25' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_26' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_26' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_27' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_27' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_28' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_28' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.bounds_12_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.exact_12_29' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0202.data_12_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0202.endpoint_12_29' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_30' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_30' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_31' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_31' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_32' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_32' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_33' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_33' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_34' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_34' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_35' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_35' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_36' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_36' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_37' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_37' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_38' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_38' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_39' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_39' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_40' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_40' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_41' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_41' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_42' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_42' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_43' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_43' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_44' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_44' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.bounds_12_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.exact_12_45' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0203.data_12_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0203.endpoint_12_45' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_46' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_46' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_47' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_47' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_48' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_48' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_49' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_49' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_50' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_50' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_51' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_51' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_52' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_52' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_53' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_53' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_54' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_54' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_55' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_55' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_56' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_56' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_57' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_57' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_58' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_58' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_59' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_59' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.bounds_12_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.exact_12_60' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0204.data_12_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0204.endpoint_12_60' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_61' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_61' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_62' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_62' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_63' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_63' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_64' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_64' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_65' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_65' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_66' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_66' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_67' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_67' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_68' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_68' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_69' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_69' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_70' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_70' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_71' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_71' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_72' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_72' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_73' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_73' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_74' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_74' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.bounds_12_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.exact_12_75' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0205.data_12_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0205.endpoint_12_75' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_76' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_76' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_77' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_77' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_78' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_78' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_79' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_79' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_80' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_80' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_81' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_81' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_82' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_82' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_83' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_83' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_84' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_84' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_85' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_85' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_86' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_86' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_87' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_87' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_88' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_88' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_89' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_89' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_90' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_90' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.bounds_12_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.exact_12_91' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0206.data_12_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0206.endpoint_12_91' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_92' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_92' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_93' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_93' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_94' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_94' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_95' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_95' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_96' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_96' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_97' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_97' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_98' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_98' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_99' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_99' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.bounds_12_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.exact_12_106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0207.data_12_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0207.endpoint_12_106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.bounds_12_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.exact_12_121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0208.data_12_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0208.endpoint_12_121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.bounds_12_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.exact_12_137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0209.data_12_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0209.endpoint_12_137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.bounds_12_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.exact_12_152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0210.data_12_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0210.endpoint_12_152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.bounds_12_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.exact_12_167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0211.data_12_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0211.endpoint_12_167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.bounds_12_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.exact_12_183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0212.data_12_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0212.endpoint_12_183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0213.bounds_12_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0213.exact_12_184' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_204' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.bounds_12_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.exact_12_214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0214.data_12_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0214.endpoint_12_214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.bounds_12_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.exact_12_229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0215.data_12_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0215.endpoint_12_229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.data_12_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.endpoint_12_238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0216.bounds_12_239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0216.exact_12_239' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0217.data_12_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.bounds_12_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.exact_12_255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.data_12_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.bounds_12_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.exact_12_256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.data_12_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.bounds_12_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.exact_12_257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.data_12_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.bounds_12_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.exact_12_258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.data_12_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.bounds_12_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.exact_12_259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.data_12_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.bounds_12_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.exact_12_260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0217.data_12_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0217.endpoint_12_260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.bounds_12_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.exact_12_275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0218.data_12_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0218.endpoint_12_275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.bounds_12_290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.exact_12_290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0219.data_12_290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0219.endpoint_12_290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.bounds_12_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.exact_12_306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0220.data_12_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0220.endpoint_12_306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.bounds_12_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.exact_12_321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0221.data_12_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0221.endpoint_12_321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.bounds_12_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.exact_12_336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0222.data_12_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0222.endpoint_12_336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.bounds_12_352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.exact_12_352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0223.data_12_352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0223.endpoint_12_352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.bounds_12_367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.exact_12_367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0224.data_12_367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0224.endpoint_12_367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.bounds_12_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.exact_12_383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0225.data_12_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0225.endpoint_12_383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.bounds_12_398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.exact_12_398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0226.data_12_398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0226.endpoint_12_398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.bounds_12_413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.exact_12_413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0227.data_12_413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0227.endpoint_12_413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.bounds_12_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.exact_12_429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0228.data_12_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0228.endpoint_12_429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.bounds_12_444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.exact_12_444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0229.data_12_444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0229.endpoint_12_444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.bounds_12_459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.exact_12_459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0230.data_12_459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0230.endpoint_12_459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.bounds_12_475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.exact_12_475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0231.data_12_475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0231.endpoint_12_475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.bounds_12_490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.exact_12_490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0232.data_12_490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0232.endpoint_12_490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.bounds_12_505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.exact_12_505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0233.data_12_505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0233.endpoint_12_505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.bounds_12_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.exact_12_521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0234.data_12_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0234.endpoint_12_521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.bounds_12_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.exact_12_536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0235.data_12_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0235.endpoint_12_536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.bounds_12_551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.exact_12_551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0236.data_12_551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0236.endpoint_12_551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.bounds_12_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.exact_12_567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0237.data_12_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0237.endpoint_12_567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.bounds_12_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.exact_12_582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0238.data_12_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0238.endpoint_12_582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.bounds_12_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.exact_12_598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0239.data_12_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0239.endpoint_12_598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.bounds_12_613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.exact_12_613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0240.data_12_613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0240.endpoint_12_613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_614' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0241.data_12_619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.data_12_620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.data_12_621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_621' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0241.data_12_624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.data_12_625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.data_12_626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.data_12_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.bounds_12_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.exact_12_628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0241.data_12_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0241.endpoint_12_628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.bounds_12_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.exact_12_644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0242.data_12_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0242.endpoint_12_644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.bounds_12_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.exact_12_659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0243.data_12_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0243.endpoint_12_659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.bounds_12_674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.exact_12_674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0244.data_12_674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0244.endpoint_12_674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.bounds_12_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.exact_12_690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0245.data_12_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0245.endpoint_12_690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.bounds_12_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.exact_12_705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0246.data_12_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0246.endpoint_12_705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.bounds_12_720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.exact_12_720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0247.data_12_720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0247.endpoint_12_720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.bounds_12_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.exact_12_736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0248.data_12_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0248.endpoint_12_736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.bounds_12_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.exact_12_751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0249.data_12_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0249.endpoint_12_751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.bounds_12_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.exact_12_767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0250.data_12_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0250.endpoint_12_767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.bounds_12_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.exact_12_782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0251.data_12_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0251.endpoint_12_782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.bounds_12_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.exact_12_797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0252.data_12_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0252.endpoint_12_797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.bounds_12_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.exact_12_813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0253.data_12_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0253.endpoint_12_813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_816' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0254.data_12_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_821' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0254.data_12_824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.bounds_12_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.exact_12_826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0254.data_12_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0254.endpoint_12_826' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0255.data_12_829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_834' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.bounds_12_843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.exact_12_843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0255.data_12_843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0255.endpoint_12_843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.bounds_12_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.exact_12_859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0256.data_12_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0256.endpoint_12_859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.bounds_12_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.exact_12_874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0257.data_12_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0257.endpoint_12_874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.bounds_12_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.exact_12_889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0258.data_12_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0258.endpoint_12_889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.bounds_12_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.exact_12_905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0259.data_12_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0259.endpoint_12_905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.bounds_12_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.exact_12_920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0260.data_12_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0260.endpoint_12_920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.bounds_12_935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.exact_12_935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0261.data_12_935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0261.endpoint_12_935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.bounds_12_951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.exact_12_951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0262.data_12_951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0262.endpoint_12_951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.bounds_12_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.exact_12_966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0263.data_12_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0263.endpoint_12_966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.bounds_12_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.exact_12_982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0264.data_12_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0264.endpoint_12_982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.bounds_12_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.exact_12_997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0265.data_12_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0265.endpoint_12_997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.bounds_12_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.exact_12_1012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0266.data_12_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0266.endpoint_12_1012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.bounds_12_1028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.exact_12_1028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0267.data_12_1028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0267.endpoint_12_1028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.bounds_12_1043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.exact_12_1043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0268.data_12_1043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0268.endpoint_12_1043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.bounds_12_1058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.exact_12_1058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0269.data_12_1058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0269.endpoint_12_1058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.bounds_12_1074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.exact_12_1074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0270.data_12_1074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0270.endpoint_12_1074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.bounds_12_1089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.exact_12_1089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0271.data_12_1089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0271.endpoint_12_1089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.bounds_12_1104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.exact_12_1104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0272.data_12_1104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0272.endpoint_12_1104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.bounds_12_1120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.exact_12_1120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0273.data_12_1120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0273.endpoint_12_1120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.bounds_12_1135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.exact_12_1135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0274.data_12_1135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0274.endpoint_12_1135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.bounds_12_1151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.exact_12_1151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0275.data_12_1151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0275.endpoint_12_1151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.bounds_12_1166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.exact_12_1166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0276.data_12_1166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0276.endpoint_12_1166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.bounds_12_1181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.exact_12_1181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0277.data_12_1181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0277.endpoint_12_1181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.bounds_12_1197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.exact_12_1197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0278.data_12_1197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0278.endpoint_12_1197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.bounds_12_1212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.exact_12_1212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0279.data_12_1212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0279.endpoint_12_1212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.bounds_12_1227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.exact_12_1227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0280.data_12_1227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0280.endpoint_12_1227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.bounds_12_1243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.exact_12_1243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0281.data_12_1243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0281.endpoint_12_1243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.bounds_12_1258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.exact_12_1258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0282.data_12_1258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0282.endpoint_12_1258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.bounds_12_1273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.exact_12_1273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0283.data_12_1273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0283.endpoint_12_1273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.bounds_12_1289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.exact_12_1289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0284.data_12_1289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0284.endpoint_12_1289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.bounds_12_1304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.exact_12_1304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0285.data_12_1304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0285.endpoint_12_1304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.bounds_12_1319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.exact_12_1319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0286.data_12_1319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0286.endpoint_12_1319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.bounds_12_1335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.exact_12_1335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0287.data_12_1335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0287.endpoint_12_1335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.bounds_12_1350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.exact_12_1350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0288.data_12_1350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0288.endpoint_12_1350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.bounds_12_1366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.exact_12_1366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0289.data_12_1366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0289.endpoint_12_1366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.bounds_12_1381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.exact_12_1381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0290.data_12_1381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0290.endpoint_12_1381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.bounds_12_1396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.exact_12_1396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0291.data_12_1396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0291.endpoint_12_1396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.bounds_12_1412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.exact_12_1412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0292.data_12_1412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0292.endpoint_12_1412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.bounds_12_1427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.exact_12_1427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0293.data_12_1427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0293.endpoint_12_1427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.bounds_12_1442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.exact_12_1442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0294.data_12_1442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0294.endpoint_12_1442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.bounds_12_1458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.exact_12_1458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0295.data_12_1458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0295.endpoint_12_1458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.bounds_12_1473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.exact_12_1473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0296.data_12_1473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0296.endpoint_12_1473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.bounds_12_1488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.exact_12_1488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0297.data_12_1488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0297.endpoint_12_1488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.bounds_12_1504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.exact_12_1504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0298.data_12_1504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0298.endpoint_12_1504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.bounds_12_1519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.exact_12_1519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0299.data_12_1519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0299.endpoint_12_1519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.bounds_12_1535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.exact_12_1535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0300.data_12_1535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0300.endpoint_12_1535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.bounds_12_1550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.exact_12_1550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0301.data_12_1550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0301.endpoint_12_1550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.bounds_12_1565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.exact_12_1565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0302.data_12_1565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0302.endpoint_12_1565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.bounds_12_1581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.exact_12_1581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0303.data_12_1581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0303.endpoint_12_1581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.bounds_12_1596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.exact_12_1596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0304.data_12_1596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0304.endpoint_12_1596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.bounds_12_1611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.exact_12_1611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0305.data_12_1611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0305.endpoint_12_1611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.bounds_12_1627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.exact_12_1627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0306.data_12_1627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0306.endpoint_12_1627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.bounds_12_1642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.exact_12_1642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0307.data_12_1642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0307.endpoint_12_1642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.bounds_12_1657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.exact_12_1657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0308.data_12_1657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0308.endpoint_12_1657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.bounds_12_1673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.exact_12_1673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0309.data_12_1673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0309.endpoint_12_1673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.bounds_12_1688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.exact_12_1688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0310.data_12_1688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0310.endpoint_12_1688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.bounds_12_1703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.exact_12_1703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0311.data_12_1703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0311.endpoint_12_1703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.bounds_12_1719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.exact_12_1719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0312.data_12_1719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0312.endpoint_12_1719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.bounds_12_1734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.exact_12_1734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0313.data_12_1734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0313.endpoint_12_1734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.bounds_12_1750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.exact_12_1750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0314.data_12_1750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0314.endpoint_12_1750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.data_12_1758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.endpoint_12_1758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0315.bounds_12_1759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0315.exact_12_1759' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0317.data_12_1784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.bounds_12_1796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.exact_12_1796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0317.data_12_1796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0317.endpoint_12_1796' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0318.data_12_1799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.bounds_12_1811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.exact_12_1811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0318.data_12_1811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0318.endpoint_12_1811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.bounds_12_1826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.exact_12_1826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0319.data_12_1826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0319.endpoint_12_1826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.bounds_12_1842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.exact_12_1842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0320.data_12_1842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0320.endpoint_12_1842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.bounds_12_1857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.exact_12_1857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0321.data_12_1857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0321.endpoint_12_1857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.bounds_12_1872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.exact_12_1872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0322.data_12_1872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0322.endpoint_12_1872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.bounds_12_1888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.exact_12_1888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0323.data_12_1888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0323.endpoint_12_1888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.bounds_12_1903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.exact_12_1903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0324.data_12_1903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0324.endpoint_12_1903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.bounds_12_1919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.exact_12_1919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0325.data_12_1919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0325.endpoint_12_1919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.bounds_12_1934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.exact_12_1934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0326.data_12_1934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0326.endpoint_12_1934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.bounds_12_1949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.exact_12_1949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0327.data_12_1949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0327.endpoint_12_1949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.bounds_12_1965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.exact_12_1965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0328.data_12_1965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0328.endpoint_12_1965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.bounds_12_1980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.exact_12_1980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0329.data_12_1980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0329.endpoint_12_1980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.bounds_12_1995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.exact_12_1995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0330.data_12_1995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0330.endpoint_12_1995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_1996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_1996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_1997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_1997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_1998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_1998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_1999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_1999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_1999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_1999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.bounds_12_2011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.exact_12_2011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0331.data_12_2011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0331.endpoint_12_2011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.bounds_12_2026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.exact_12_2026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0332.data_12_2026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0332.endpoint_12_2026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.bounds_12_2041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.exact_12_2041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0333.data_12_2041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0333.endpoint_12_2041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.bounds_12_2057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.exact_12_2057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0334.data_12_2057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0334.endpoint_12_2057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.bounds_12_2072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.exact_12_2072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0335.data_12_2072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0335.endpoint_12_2072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.bounds_12_2087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.exact_12_2087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0336.data_12_2087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0336.endpoint_12_2087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.bounds_12_2103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.exact_12_2103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0337.data_12_2103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0337.endpoint_12_2103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.bounds_12_2118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.exact_12_2118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0338.data_12_2118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0338.endpoint_12_2118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.bounds_12_2134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.exact_12_2134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0339.data_12_2134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0339.endpoint_12_2134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.bounds_12_2149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.exact_12_2149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0340.data_12_2149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0340.endpoint_12_2149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.bounds_12_2164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.exact_12_2164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0341.data_12_2164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0341.endpoint_12_2164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.bounds_12_2180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.exact_12_2180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0342.data_12_2180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0342.endpoint_12_2180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.bounds_12_2195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.exact_12_2195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0343.data_12_2195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0343.endpoint_12_2195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.bounds_12_2210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.exact_12_2210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0344.data_12_2210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0344.endpoint_12_2210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.bounds_12_2226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.exact_12_2226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0345.data_12_2226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0345.endpoint_12_2226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2231' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0346.data_12_2234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2236' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0346.data_12_2239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.bounds_12_2241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.exact_12_2241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0346.data_12_2241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0346.endpoint_12_2241' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0347.data_12_2244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.bounds_12_2256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.exact_12_2256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0347.data_12_2256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0347.endpoint_12_2256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.bounds_12_2272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.exact_12_2272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0348.data_12_2272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0348.endpoint_12_2272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.bounds_12_2287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.exact_12_2287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0349.data_12_2287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0349.endpoint_12_2287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.bounds_12_2303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.exact_12_2303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0350.data_12_2303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0350.endpoint_12_2303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.bounds_12_2318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.exact_12_2318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0351.data_12_2318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0351.endpoint_12_2318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.bounds_12_2333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.exact_12_2333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0352.data_12_2333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0352.endpoint_12_2333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.bounds_12_2349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.exact_12_2349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0353.data_12_2349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0353.endpoint_12_2349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.bounds_12_2364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.exact_12_2364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0354.data_12_2364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0354.endpoint_12_2364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.bounds_12_2379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.exact_12_2379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0355.data_12_2379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0355.endpoint_12_2379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.bounds_12_2395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.exact_12_2395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0356.data_12_2395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0356.endpoint_12_2395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.bounds_12_2410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.exact_12_2410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0357.data_12_2410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0357.endpoint_12_2410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.bounds_12_2425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.exact_12_2425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0358.data_12_2425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0358.endpoint_12_2425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.bounds_12_2441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.exact_12_2441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0359.data_12_2441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0359.endpoint_12_2441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.bounds_12_2456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.exact_12_2456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0360.data_12_2456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0360.endpoint_12_2456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.bounds_12_2471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.exact_12_2471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0361.data_12_2471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0361.endpoint_12_2471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.bounds_12_2487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.exact_12_2487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0362.data_12_2487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0362.endpoint_12_2487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.bounds_12_2502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.exact_12_2502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0363.data_12_2502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0363.endpoint_12_2502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.bounds_12_2518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.exact_12_2518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0364.data_12_2518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0364.endpoint_12_2518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.bounds_12_2533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.exact_12_2533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0365.data_12_2533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0365.endpoint_12_2533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.bounds_12_2548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.exact_12_2548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0366.data_12_2548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0366.endpoint_12_2548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.bounds_12_2564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.exact_12_2564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0367.data_12_2564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0367.endpoint_12_2564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.bounds_12_2579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.exact_12_2579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0368.data_12_2579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0368.endpoint_12_2579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.bounds_12_2594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.exact_12_2594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0369.data_12_2594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0369.endpoint_12_2594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.bounds_12_2610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.exact_12_2610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0370.data_12_2610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0370.endpoint_12_2610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.bounds_12_2625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.exact_12_2625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0371.data_12_2625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0371.endpoint_12_2625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.bounds_12_2640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.exact_12_2640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0372.data_12_2640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0372.endpoint_12_2640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.bounds_12_2656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.exact_12_2656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0373.data_12_2656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0373.endpoint_12_2656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.bounds_12_2671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.exact_12_2671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0374.data_12_2671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0374.endpoint_12_2671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.bounds_12_2687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.exact_12_2687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0375.data_12_2687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0375.endpoint_12_2687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.bounds_12_2702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.exact_12_2702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0376.data_12_2702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0376.endpoint_12_2702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.bounds_12_2717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.exact_12_2717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0377.data_12_2717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0377.endpoint_12_2717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.bounds_12_2733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.exact_12_2733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0378.data_12_2733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0378.endpoint_12_2733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.bounds_12_2748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.exact_12_2748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0379.data_12_2748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0379.endpoint_12_2748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.bounds_12_2763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.exact_12_2763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0380.data_12_2763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0380.endpoint_12_2763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.bounds_12_2779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.exact_12_2779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0381.data_12_2779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0381.endpoint_12_2779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.bounds_12_2794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.exact_12_2794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0382.data_12_2794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0382.endpoint_12_2794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.bounds_12_2809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.exact_12_2809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0383.data_12_2809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0383.endpoint_12_2809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.bounds_12_2825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.exact_12_2825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0384.data_12_2825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0384.endpoint_12_2825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.bounds_12_2840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.exact_12_2840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0385.data_12_2840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0385.endpoint_12_2840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.bounds_12_2855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.exact_12_2855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0386.data_12_2855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0386.endpoint_12_2855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.bounds_12_2871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.exact_12_2871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0387.data_12_2871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0387.endpoint_12_2871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.bounds_12_2886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.exact_12_2886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0388.data_12_2886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0388.endpoint_12_2886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.bounds_12_2902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.exact_12_2902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0389.data_12_2902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0389.endpoint_12_2902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.bounds_12_2917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.exact_12_2917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0390.data_12_2917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0390.endpoint_12_2917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.bounds_12_2932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.exact_12_2932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0391.data_12_2932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0391.endpoint_12_2932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.bounds_12_2948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.exact_12_2948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0392.data_12_2948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0392.endpoint_12_2948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.bounds_12_2963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.exact_12_2963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0393.data_12_2963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0393.endpoint_12_2963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.bounds_12_2978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.exact_12_2978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0394.data_12_2978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0394.endpoint_12_2978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.bounds_12_2994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.exact_12_2994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0395.data_12_2994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0395.endpoint_12_2994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_2995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_2995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_2996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_2996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_2997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_2997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_2998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_2998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_2999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_2999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_2999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_2999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.bounds_12_3009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.exact_12_3009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0396.data_12_3009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0396.endpoint_12_3009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.bounds_12_3024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.exact_12_3024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0397.data_12_3024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0397.endpoint_12_3024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.bounds_12_3040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.exact_12_3040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0398.data_12_3040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0398.endpoint_12_3040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.bounds_12_3055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.exact_12_3055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0399.data_12_3055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0399.endpoint_12_3055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.bounds_12_3071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.exact_12_3071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0400.data_12_3071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0400.endpoint_12_3071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.bounds_12_3086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.exact_12_3086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0401.data_12_3086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0401.endpoint_12_3086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.bounds_12_3101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.exact_12_3101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0402.data_12_3101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0402.endpoint_12_3101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.bounds_12_3117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.exact_12_3117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0403.data_12_3117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0403.endpoint_12_3117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.bounds_12_3132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.exact_12_3132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0404.data_12_3132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0404.endpoint_12_3132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.bounds_12_3147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.exact_12_3147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0405.data_12_3147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0405.endpoint_12_3147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.bounds_12_3163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.exact_12_3163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0406.data_12_3163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0406.endpoint_12_3163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.bounds_12_3178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.exact_12_3178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0407.data_12_3178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0407.endpoint_12_3178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.bounds_12_3193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.exact_12_3193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0408.data_12_3193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0408.endpoint_12_3193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.bounds_12_3209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.exact_12_3209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0409.data_12_3209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0409.endpoint_12_3209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.bounds_12_3224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.exact_12_3224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0410.data_12_3224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0410.endpoint_12_3224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3231' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0411.data_12_3234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.bounds_12_3236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.exact_12_3236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0411.data_12_3236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3236' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0411.data_12_3239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0411.endpoint_12_3239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.bounds_12_3255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.exact_12_3255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0412.data_12_3255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0412.endpoint_12_3255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.bounds_12_3270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.exact_12_3270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0413.data_12_3270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0413.endpoint_12_3270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.bounds_12_3281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.exact_12_3281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0414.data_12_3281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0414.endpoint_12_3281' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0415.data_12_3289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.data_12_3290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.data_12_3291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.data_12_3292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.data_12_3293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3294' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0415.data_12_3299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.data_12_3300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.bounds_12_3301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.exact_12_3301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0415.data_12_3301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0415.endpoint_12_3301' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0416.data_12_3304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.bounds_12_3316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.exact_12_3316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0416.data_12_3316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0416.endpoint_12_3316' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0417.data_12_3319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.bounds_12_3332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.exact_12_3332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0417.data_12_3332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0417.endpoint_12_3332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.bounds_12_3347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.exact_12_3347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0418.data_12_3347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0418.endpoint_12_3347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.bounds_12_3362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.exact_12_3362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0419.data_12_3362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0419.endpoint_12_3362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.bounds_12_3378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.exact_12_3378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0420.data_12_3378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0420.endpoint_12_3378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.bounds_12_3393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.exact_12_3393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0421.data_12_3393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0421.endpoint_12_3393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.bounds_12_3408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.exact_12_3408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0422.data_12_3408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0422.endpoint_12_3408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.bounds_12_3424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.exact_12_3424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0423.data_12_3424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0423.endpoint_12_3424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.bounds_12_3439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.exact_12_3439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0424.data_12_3439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0424.endpoint_12_3439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.bounds_12_3455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.exact_12_3455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0425.data_12_3455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0425.endpoint_12_3455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.bounds_12_3470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.exact_12_3470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0426.data_12_3470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0426.endpoint_12_3470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.bounds_12_3485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.exact_12_3485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0427.data_12_3485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0427.endpoint_12_3485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.bounds_12_3501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.exact_12_3501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0428.data_12_3501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0428.endpoint_12_3501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.bounds_12_3516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.exact_12_3516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0429.data_12_3516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0429.endpoint_12_3516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.bounds_12_3531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.exact_12_3531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0430.data_12_3531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0430.endpoint_12_3531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.data_12_3543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.endpoint_12_3543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0431.bounds_12_3544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0431.exact_12_3544' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0432.data_12_3554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.exact_12_3555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.data_12_3555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.exact_12_3556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.data_12_3556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3556' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0432.data_12_3559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.exact_12_3560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.data_12_3560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.exact_12_3561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.data_12_3561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.bounds_12_3562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.exact_12_3562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0432.data_12_3562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0432.endpoint_12_3562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.bounds_12_3577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.exact_12_3577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0433.data_12_3577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0433.endpoint_12_3577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.bounds_12_3593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.exact_12_3593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0434.data_12_3593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0434.endpoint_12_3593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.bounds_12_3608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.exact_12_3608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0435.data_12_3608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0435.endpoint_12_3608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.bounds_12_3623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.exact_12_3623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0436.data_12_3623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0436.endpoint_12_3623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.bounds_12_3639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.exact_12_3639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0437.data_12_3639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0437.endpoint_12_3639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.bounds_12_3651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.exact_12_3651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0438.data_12_3651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3651' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0438.data_12_3654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0438.endpoint_12_3654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3656' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0439.data_12_3659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3661' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0439.data_12_3664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.bounds_12_3670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.exact_12_3670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0439.data_12_3670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0439.endpoint_12_3670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.bounds_12_3685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.exact_12_3685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0440.data_12_3685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0440.endpoint_12_3685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.bounds_12_3700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.exact_12_3700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0441.data_12_3700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0441.endpoint_12_3700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.bounds_12_3716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.exact_12_3716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0442.data_12_3716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0442.endpoint_12_3716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.bounds_12_3731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.exact_12_3731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0443.data_12_3731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0443.endpoint_12_3731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.bounds_12_3746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.exact_12_3746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0444.data_12_3746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0444.endpoint_12_3746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.bounds_12_3762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.exact_12_3762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0445.data_12_3762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0445.endpoint_12_3762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.bounds_12_3777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.exact_12_3777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0446.data_12_3777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0446.endpoint_12_3777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.bounds_12_3792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.exact_12_3792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0447.data_12_3792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0447.endpoint_12_3792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.bounds_12_3808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.exact_12_3808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0448.data_12_3808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0448.endpoint_12_3808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.bounds_12_3823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.exact_12_3823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0449.data_12_3823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0449.endpoint_12_3823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.bounds_12_3839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.exact_12_3839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0450.data_12_3839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0450.endpoint_12_3839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.bounds_12_3854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.exact_12_3854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0451.data_12_3854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0451.endpoint_12_3854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.bounds_12_3869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.exact_12_3869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0452.data_12_3869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0452.endpoint_12_3869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.bounds_12_3885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.exact_12_3885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0453.data_12_3885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0453.endpoint_12_3885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.bounds_12_3900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.exact_12_3900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0454.data_12_3900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0454.endpoint_12_3900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.bounds_12_3915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.exact_12_3915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0455.data_12_3915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0455.endpoint_12_3915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.bounds_12_3931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.exact_12_3931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0456.data_12_3931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0456.endpoint_12_3931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.bounds_12_3946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.exact_12_3946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0457.data_12_3946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0457.endpoint_12_3946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.bounds_12_3961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.exact_12_3961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0458.data_12_3961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0458.endpoint_12_3961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.bounds_12_3977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.exact_12_3977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0459.data_12_3977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0459.endpoint_12_3977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.bounds_12_3992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.exact_12_3992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0460.data_12_3992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0460.endpoint_12_3992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_3999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_3999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_3999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_3999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.bounds_12_4007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.exact_12_4007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0461.data_12_4007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0461.endpoint_12_4007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.bounds_12_4023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.exact_12_4023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0462.data_12_4023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0462.endpoint_12_4023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.bounds_12_4038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.exact_12_4038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0463.data_12_4038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0463.endpoint_12_4038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.bounds_12_4054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.exact_12_4054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0464.data_12_4054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0464.endpoint_12_4054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.bounds_12_4069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.exact_12_4069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0465.data_12_4069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0465.endpoint_12_4069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.bounds_12_4084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.exact_12_4084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0466.data_12_4084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0466.endpoint_12_4084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_12_4095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_12_4095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_12_4095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_12_4095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_13_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_13_0' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_13_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_0' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_13_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_13_1' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_13_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_13_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_13_2' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_13_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_13_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_13_3' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_13_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.bounds_13_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.exact_13_4' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0467.data_13_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0467.endpoint_13_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_5' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_6' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_7' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_8' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_9' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_9' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_10' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_11' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_12' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_12' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_13' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_13' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_14' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_14' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_15' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_15' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_16' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_16' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_16' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_17' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_17' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_17' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_18' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_18' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_18' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.bounds_13_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.exact_13_19' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0468.data_13_19' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0468.endpoint_13_19' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_20' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_20' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_20' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_21' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_21' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_21' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_22' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_22' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_22' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_23' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_23' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_23' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_24' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_24' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_24' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_25' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_25' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_25' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_26' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_26' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_26' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_27' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_27' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_27' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_28' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_28' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_28' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_29' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_29' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_29' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_30' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_30' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_30' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_31' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_31' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_31' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_32' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_32' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_32' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_33' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_33' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_33' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.bounds_13_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.exact_13_34' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0469.data_13_34' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0469.endpoint_13_34' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_35' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_35' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_35' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_36' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_36' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_36' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_37' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_37' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_37' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_38' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_38' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_38' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_39' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_39' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_39' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_40' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_40' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_40' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_41' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_41' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_41' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_42' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_42' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_42' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_43' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_43' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_43' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_44' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_44' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_44' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_45' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_45' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_45' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_46' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_46' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_46' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_47' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_47' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_47' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_48' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_48' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_48' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_49' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_49' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_49' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.bounds_13_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.exact_13_50' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0470.data_13_50' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0470.endpoint_13_50' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_51' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_51' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_51' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_52' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_52' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_52' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_53' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_53' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_53' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_54' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_54' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_54' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_55' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_55' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_55' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_56' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_56' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_56' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_57' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_57' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_57' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_58' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_58' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_58' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_59' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_59' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_59' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_60' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_60' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_60' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_61' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_61' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_61' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_62' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_62' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_62' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_63' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_63' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_63' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_64' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_64' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_64' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.bounds_13_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.exact_13_65' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0471.data_13_65' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0471.endpoint_13_65' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_66' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_66' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_66' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_67' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_67' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_67' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_68' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_68' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_68' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_69' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_69' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_69' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_70' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_70' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_70' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_71' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_71' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_71' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_72' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_72' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_72' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_73' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_73' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_73' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_74' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_74' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_74' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_75' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_75' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_75' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_76' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_76' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_76' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_77' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_77' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_77' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_78' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_78' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_78' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_79' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_79' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_79' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.bounds_13_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.exact_13_80' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0472.data_13_80' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0472.endpoint_13_80' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_81' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_81' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_81' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_82' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_82' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_82' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_83' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_83' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_83' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_84' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_84' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_84' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_85' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_85' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_85' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_86' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_86' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_86' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_87' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_87' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_87' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_88' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_88' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_88' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_89' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_89' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_89' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_90' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_90' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_90' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_91' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_91' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_91' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_92' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_92' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_92' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_93' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_93' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_93' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_94' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_94' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_94' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_95' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_95' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_95' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.bounds_13_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.exact_13_96' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0473.data_13_96' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0473.endpoint_13_96' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_97' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_97' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_97' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_98' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_98' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_98' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_99' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_99' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_99' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.bounds_13_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.exact_13_111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0474.data_13_111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0474.endpoint_13_111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.bounds_13_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.exact_13_127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0475.data_13_127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0475.endpoint_13_127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.bounds_13_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.exact_13_142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0476.data_13_142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0476.endpoint_13_142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.bounds_13_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.exact_13_157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0477.data_13_157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0477.endpoint_13_157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.bounds_13_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.exact_13_173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0478.data_13_173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0478.endpoint_13_173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.bounds_13_188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.exact_13_188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0479.data_13_188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0479.endpoint_13_188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.bounds_13_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.exact_13_203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0480.data_13_203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0480.endpoint_13_203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.bounds_13_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.exact_13_219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0481.data_13_219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0481.endpoint_13_219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.bounds_13_234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.exact_13_234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0482.data_13_234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0482.endpoint_13_234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_238' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.bounds_13_249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.exact_13_249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0483.data_13_249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0483.endpoint_13_249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_250' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0484.data_13_253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.bounds_13_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.exact_13_265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0484.data_13_265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0484.endpoint_13_265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.bounds_13_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.exact_13_280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0485.data_13_280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0485.endpoint_13_280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.bounds_13_290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.exact_13_290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0486.data_13_290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0486.endpoint_13_290' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0487.bounds_13_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0487.exact_13_306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0487.data_13_306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0487.bounds_13_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0487.exact_13_307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0487.data_13_307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0487.endpoint_13_307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0487.bounds_13_308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0487.exact_13_308' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0488.data_13_313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_315' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0488.data_13_318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.bounds_13_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.exact_13_326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0488.data_13_326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0488.endpoint_13_326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.bounds_13_340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.exact_13_340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0489.data_13_340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0489.endpoint_13_340' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_380' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0492.data_13_383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.bounds_13_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.exact_13_388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0492.data_13_388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0492.endpoint_13_388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.bounds_13_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.exact_13_389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.data_13_389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.bounds_13_390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.exact_13_390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.data_13_390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.bounds_13_391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.exact_13_391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.data_13_391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.bounds_13_392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.exact_13_392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.data_13_392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.endpoint_13_392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0493.bounds_13_393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0493.exact_13_393' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0494.data_13_418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0494.endpoint_13_418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_420' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0495.data_13_428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.bounds_13_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.exact_13_434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0495.data_13_434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0495.endpoint_13_434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_440' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0496.data_13_443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.bounds_13_445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.exact_13_445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0496.data_13_445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0496.endpoint_13_445' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0498.data_13_478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0498.bounds_13_479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0498.exact_13_479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0498.data_13_479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0498.bounds_13_480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0498.exact_13_480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0498.data_13_480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0498.endpoint_13_480' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0499.data_13_483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_485' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0499.data_13_488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.bounds_13_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.exact_13_495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0499.data_13_495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0499.endpoint_13_495' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0500.data_13_498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_500' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0500.data_13_503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.bounds_13_511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.exact_13_511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0500.data_13_511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0500.endpoint_13_511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.bounds_13_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.exact_13_526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0501.data_13_526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0501.endpoint_13_526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.bounds_13_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.exact_13_541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0502.data_13_541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0502.endpoint_13_541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.bounds_13_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.exact_13_557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0503.data_13_557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0503.endpoint_13_557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.bounds_13_572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.exact_13_572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0504.data_13_572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0504.endpoint_13_572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.bounds_13_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.exact_13_587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0505.data_13_587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0505.endpoint_13_587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.bounds_13_603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.exact_13_603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0506.data_13_603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0506.endpoint_13_603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.bounds_13_618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.exact_13_618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0507.data_13_618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0507.endpoint_13_618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.bounds_13_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.exact_13_633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0508.data_13_633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0508.endpoint_13_633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.bounds_13_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.exact_13_649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0509.data_13_649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0509.endpoint_13_649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.bounds_13_664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.exact_13_664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0510.data_13_664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0510.endpoint_13_664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.bounds_13_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.exact_13_679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0511.data_13_679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0511.endpoint_13_679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.bounds_13_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.exact_13_695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0512.data_13_695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0512.endpoint_13_695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.bounds_13_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.exact_13_710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0513.data_13_710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0513.endpoint_13_710' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.bounds_13_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.exact_13_726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0514.data_13_726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0514.endpoint_13_726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.bounds_13_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.exact_13_741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0515.data_13_741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0515.endpoint_13_741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.bounds_13_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.exact_13_756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0516.data_13_756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0516.endpoint_13_756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.bounds_13_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.exact_13_772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0517.data_13_772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0517.endpoint_13_772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.bounds_13_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.exact_13_787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0518.data_13_787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0518.endpoint_13_787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.bounds_13_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.exact_13_802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0519.data_13_802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0519.endpoint_13_802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.bounds_13_818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.exact_13_818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0520.data_13_818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0520.endpoint_13_818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.bounds_13_833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.exact_13_833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0521.data_13_833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0521.endpoint_13_833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.bounds_13_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.exact_13_848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0522.data_13_848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0522.endpoint_13_848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.bounds_13_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.exact_13_864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0523.data_13_864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0523.endpoint_13_864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.bounds_13_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.exact_13_879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0524.data_13_879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0524.endpoint_13_879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.bounds_13_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.exact_13_895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0525.data_13_895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0525.endpoint_13_895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.bounds_13_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.exact_13_910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0526.data_13_910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0526.endpoint_13_910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.bounds_13_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.exact_13_925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0527.data_13_925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0527.endpoint_13_925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.bounds_13_941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.exact_13_941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0528.data_13_941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0528.endpoint_13_941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.bounds_13_956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.exact_13_956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0529.data_13_956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0529.endpoint_13_956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.bounds_13_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.exact_13_971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0530.data_13_971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0530.endpoint_13_971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.bounds_13_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.exact_13_987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0531.data_13_987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0531.endpoint_13_987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_1000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_1000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_1000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_1001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_1001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_1001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.bounds_13_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.exact_13_1002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0532.data_13_1002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0532.endpoint_13_1002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.bounds_13_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.exact_13_1017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0533.data_13_1017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0533.endpoint_13_1017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.bounds_13_1033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.exact_13_1033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0534.data_13_1033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0534.endpoint_13_1033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.bounds_13_1048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.exact_13_1048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0535.data_13_1048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0535.endpoint_13_1048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.bounds_13_1063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.exact_13_1063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0536.data_13_1063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0536.endpoint_13_1063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.bounds_13_1079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.exact_13_1079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0537.data_13_1079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0537.endpoint_13_1079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.bounds_13_1094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.exact_13_1094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0538.data_13_1094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0538.endpoint_13_1094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.bounds_13_1110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.exact_13_1110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0539.data_13_1110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0539.endpoint_13_1110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.bounds_13_1125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.exact_13_1125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0540.data_13_1125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0540.endpoint_13_1125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.bounds_13_1140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.exact_13_1140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0541.data_13_1140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0541.endpoint_13_1140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.bounds_13_1156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.exact_13_1156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0542.data_13_1156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0542.endpoint_13_1156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.bounds_13_1171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.exact_13_1171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0543.data_13_1171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0543.endpoint_13_1171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.bounds_13_1186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.exact_13_1186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0544.data_13_1186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0544.endpoint_13_1186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.bounds_13_1202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.exact_13_1202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0545.data_13_1202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0545.endpoint_13_1202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.bounds_13_1217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.exact_13_1217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0546.data_13_1217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0546.endpoint_13_1217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.bounds_13_1232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.exact_13_1232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0547.data_13_1232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0547.endpoint_13_1232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.bounds_13_1248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.exact_13_1248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0548.data_13_1248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0548.endpoint_13_1248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.bounds_13_1263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.exact_13_1263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0549.data_13_1263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0549.endpoint_13_1263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.bounds_13_1279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.exact_13_1279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0550.data_13_1279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0550.endpoint_13_1279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.bounds_13_1294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.exact_13_1294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0551.data_13_1294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0551.endpoint_13_1294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.bounds_13_1309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.exact_13_1309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0552.data_13_1309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0552.endpoint_13_1309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.bounds_13_1325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.exact_13_1325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0553.data_13_1325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0553.endpoint_13_1325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.bounds_13_1340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.exact_13_1340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0554.data_13_1340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0554.endpoint_13_1340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.bounds_13_1355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.exact_13_1355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0555.data_13_1355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0555.endpoint_13_1355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.bounds_13_1371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.exact_13_1371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0556.data_13_1371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0556.endpoint_13_1371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.bounds_13_1386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.exact_13_1386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0557.data_13_1386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0557.endpoint_13_1386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.bounds_13_1401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.exact_13_1401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0558.data_13_1401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0558.endpoint_13_1401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.bounds_13_1417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.exact_13_1417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0559.data_13_1417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0559.endpoint_13_1417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.bounds_13_1432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.exact_13_1432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0560.data_13_1432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0560.endpoint_13_1432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.bounds_13_1447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.exact_13_1447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0561.data_13_1447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0561.endpoint_13_1447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.bounds_13_1463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.exact_13_1463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0562.data_13_1463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0562.endpoint_13_1463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.bounds_13_1478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.exact_13_1478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0563.data_13_1478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0563.endpoint_13_1478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.bounds_13_1494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.exact_13_1494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0564.data_13_1494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0564.endpoint_13_1494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.bounds_13_1509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.exact_13_1509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0565.data_13_1509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0565.endpoint_13_1509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.bounds_13_1524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.exact_13_1524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0566.data_13_1524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0566.endpoint_13_1524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.bounds_13_1540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.exact_13_1540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0567.data_13_1540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0567.endpoint_13_1540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.bounds_13_1555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.exact_13_1555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0568.data_13_1555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0568.endpoint_13_1555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.bounds_13_1570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.exact_13_1570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0569.data_13_1570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0569.endpoint_13_1570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.bounds_13_1586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.exact_13_1586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0570.data_13_1586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0570.endpoint_13_1586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.bounds_13_1601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.exact_13_1601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0571.data_13_1601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0571.endpoint_13_1601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.bounds_13_1616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.exact_13_1616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0572.data_13_1616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0572.endpoint_13_1616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.bounds_13_1632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.exact_13_1632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0573.data_13_1632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0573.endpoint_13_1632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.bounds_13_1647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.exact_13_1647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0574.data_13_1647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0574.endpoint_13_1647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.bounds_13_1663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.exact_13_1663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0575.data_13_1663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0575.endpoint_13_1663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.bounds_13_1678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.exact_13_1678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0576.data_13_1678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0576.endpoint_13_1678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.bounds_13_1693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.exact_13_1693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0577.data_13_1693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0577.endpoint_13_1693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.bounds_13_1709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.exact_13_1709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0578.data_13_1709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0578.endpoint_13_1709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.bounds_13_1724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.exact_13_1724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0579.data_13_1724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0579.endpoint_13_1724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.bounds_13_1739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.exact_13_1739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0580.data_13_1739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0580.endpoint_13_1739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.bounds_13_1755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.exact_13_1755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0581.data_13_1755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0581.endpoint_13_1755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.bounds_13_1770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.exact_13_1770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0582.data_13_1770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0582.endpoint_13_1770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.bounds_13_1785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.exact_13_1785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0583.data_13_1785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0583.endpoint_13_1785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.bounds_13_1801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.exact_13_1801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0584.data_13_1801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0584.endpoint_13_1801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.bounds_13_1816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.exact_13_1816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0585.data_13_1816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0585.endpoint_13_1816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.bounds_13_1831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.exact_13_1831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0586.data_13_1831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0586.endpoint_13_1831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.bounds_13_1847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.exact_13_1847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0587.data_13_1847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0587.endpoint_13_1847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.bounds_13_1862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.exact_13_1862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0588.data_13_1862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0588.endpoint_13_1862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.bounds_13_1878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.exact_13_1878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0589.data_13_1878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0589.endpoint_13_1878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.bounds_13_1893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.exact_13_1893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0590.data_13_1893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0590.endpoint_13_1893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.bounds_13_1908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.exact_13_1908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0591.data_13_1908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0591.endpoint_13_1908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.bounds_13_1924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.exact_13_1924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0592.data_13_1924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0592.endpoint_13_1924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.bounds_13_1939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.exact_13_1939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0593.data_13_1939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0593.endpoint_13_1939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.bounds_13_1954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.exact_13_1954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0594.data_13_1954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0594.endpoint_13_1954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.bounds_13_1970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.exact_13_1970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0595.data_13_1970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0595.endpoint_13_1970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.bounds_13_1985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.exact_13_1985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0596.data_13_1985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0596.endpoint_13_1985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_1999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_1999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_1999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_1999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.bounds_13_2000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.exact_13_2000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0597.data_13_2000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0597.endpoint_13_2000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.bounds_13_2016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.exact_13_2016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0598.data_13_2016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0598.endpoint_13_2016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.bounds_13_2031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.exact_13_2031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0599.data_13_2031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0599.endpoint_13_2031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.bounds_13_2047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.exact_13_2047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0600.data_13_2047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0600.endpoint_13_2047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.bounds_13_2062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.exact_13_2062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0601.data_13_2062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0601.endpoint_13_2062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.bounds_13_2077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.exact_13_2077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0602.data_13_2077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0602.endpoint_13_2077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.bounds_13_2093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.exact_13_2093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0603.data_13_2093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0603.endpoint_13_2093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.bounds_13_2108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.exact_13_2108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0604.data_13_2108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0604.endpoint_13_2108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.bounds_13_2123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.exact_13_2123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0605.data_13_2123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0605.endpoint_13_2123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.bounds_13_2139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.exact_13_2139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0606.data_13_2139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0606.endpoint_13_2139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.bounds_13_2154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.exact_13_2154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0607.data_13_2154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0607.endpoint_13_2154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.bounds_13_2169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.exact_13_2169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0608.data_13_2169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0608.endpoint_13_2169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.bounds_13_2185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.exact_13_2185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0609.data_13_2185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0609.endpoint_13_2185' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0610.data_13_2188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.bounds_13_2200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.exact_13_2200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0610.data_13_2200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0610.endpoint_13_2200' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0611.data_13_2203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.bounds_13_2215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.exact_13_2215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0611.data_13_2215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0611.endpoint_13_2215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.bounds_13_2230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.exact_13_2230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0612.data_13_2230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0612.endpoint_13_2230' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0614.data_13_2248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.exact_13_2249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.data_13_2249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.exact_13_2250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.data_13_2250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2250' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0614.data_13_2253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.exact_13_2254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.data_13_2254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.exact_13_2255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.data_13_2255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2255' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0614.data_13_2258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.exact_13_2259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.data_13_2259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.bounds_13_2260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.exact_13_2260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0614.data_13_2260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0614.endpoint_13_2260' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0615.data_13_2263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.bounds_13_2277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.exact_13_2277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0615.data_13_2277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0615.endpoint_13_2277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.exact_13_2278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.data_13_2278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.exact_13_2279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.data_13_2279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.exact_13_2280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.data_13_2280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.exact_13_2281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.data_13_2281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.exact_13_2282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.data_13_2282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.endpoint_13_2282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0616.bounds_13_2283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0616.exact_13_2283' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2300' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0617.data_13_2303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.bounds_13_2308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.exact_13_2308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0617.data_13_2308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0617.endpoint_13_2308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.bounds_13_2323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.exact_13_2323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0618.data_13_2323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0618.endpoint_13_2323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.bounds_13_2338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.exact_13_2338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0619.data_13_2338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0619.endpoint_13_2338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.bounds_13_2354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.exact_13_2354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0620.data_13_2354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0620.endpoint_13_2354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.bounds_13_2369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.exact_13_2369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0621.data_13_2369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0621.endpoint_13_2369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.bounds_13_2384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.exact_13_2384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0622.data_13_2384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0622.endpoint_13_2384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.bounds_13_2400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.exact_13_2400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0623.data_13_2400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0623.endpoint_13_2400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.bounds_13_2415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.exact_13_2415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0624.data_13_2415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0624.endpoint_13_2415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.bounds_13_2431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.exact_13_2431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0625.data_13_2431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0625.endpoint_13_2431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.bounds_13_2446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.exact_13_2446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0626.data_13_2446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0626.endpoint_13_2446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.bounds_13_2461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.exact_13_2461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0627.data_13_2461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0627.endpoint_13_2461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.bounds_13_2477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.exact_13_2477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0628.data_13_2477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0628.endpoint_13_2477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.bounds_13_2492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.exact_13_2492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0629.data_13_2492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0629.endpoint_13_2492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.bounds_13_2507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.exact_13_2507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0630.data_13_2507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0630.endpoint_13_2507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.bounds_13_2523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.exact_13_2523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0631.data_13_2523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0631.endpoint_13_2523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.bounds_13_2538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.exact_13_2538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0632.data_13_2538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0632.endpoint_13_2538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.bounds_13_2553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.exact_13_2553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0633.data_13_2553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0633.endpoint_13_2553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.bounds_13_2569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.exact_13_2569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0634.data_13_2569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0634.endpoint_13_2569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.bounds_13_2584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.exact_13_2584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0635.data_13_2584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0635.endpoint_13_2584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.bounds_13_2599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.exact_13_2599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0636.data_13_2599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0636.endpoint_13_2599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.bounds_13_2615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.exact_13_2615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0637.data_13_2615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0637.endpoint_13_2615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.bounds_13_2630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.exact_13_2630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0638.data_13_2630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0638.endpoint_13_2630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.bounds_13_2646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.exact_13_2646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0639.data_13_2646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0639.endpoint_13_2646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.bounds_13_2661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.exact_13_2661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0640.data_13_2661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0640.endpoint_13_2661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.bounds_13_2676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.exact_13_2676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0641.data_13_2676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0641.endpoint_13_2676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.bounds_13_2692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.exact_13_2692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0642.data_13_2692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0642.endpoint_13_2692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.bounds_13_2707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.exact_13_2707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0643.data_13_2707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0643.endpoint_13_2707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.bounds_13_2722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.exact_13_2722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0644.data_13_2722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0644.endpoint_13_2722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.bounds_13_2738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.exact_13_2738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0645.data_13_2738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0645.endpoint_13_2738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.bounds_13_2753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.exact_13_2753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0646.data_13_2753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0646.endpoint_13_2753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.bounds_13_2768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.exact_13_2768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0647.data_13_2768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0647.endpoint_13_2768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.bounds_13_2784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.exact_13_2784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0648.data_13_2784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0648.endpoint_13_2784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.bounds_13_2799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.exact_13_2799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0649.data_13_2799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0649.endpoint_13_2799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.bounds_13_2815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.exact_13_2815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0650.data_13_2815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0650.endpoint_13_2815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.bounds_13_2830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.exact_13_2830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0651.data_13_2830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0651.endpoint_13_2830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.bounds_13_2845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.exact_13_2845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0652.data_13_2845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0652.endpoint_13_2845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.bounds_13_2861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.exact_13_2861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0653.data_13_2861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0653.endpoint_13_2861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.bounds_13_2876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.exact_13_2876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0654.data_13_2876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0654.endpoint_13_2876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.bounds_13_2891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.exact_13_2891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0655.data_13_2891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0655.endpoint_13_2891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.bounds_13_2907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.exact_13_2907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0656.data_13_2907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0656.endpoint_13_2907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.bounds_13_2922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.exact_13_2922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0657.data_13_2922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0657.endpoint_13_2922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.bounds_13_2937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.exact_13_2937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0658.data_13_2937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0658.endpoint_13_2937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.bounds_13_2953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.exact_13_2953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0659.data_13_2953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0659.endpoint_13_2953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.bounds_13_2968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.exact_13_2968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0660.data_13_2968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0660.endpoint_13_2968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.bounds_13_2983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.exact_13_2983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0661.data_13_2983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0661.endpoint_13_2983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.bounds_13_2999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.exact_13_2999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0662.data_13_2999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0662.endpoint_13_2999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.bounds_13_3014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.exact_13_3014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0663.data_13_3014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0663.endpoint_13_3014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.bounds_13_3030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.exact_13_3030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0664.data_13_3030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0664.endpoint_13_3030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.bounds_13_3045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.exact_13_3045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0665.data_13_3045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0665.endpoint_13_3045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.bounds_13_3060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.exact_13_3060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0666.data_13_3060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0666.endpoint_13_3060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.bounds_13_3076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.exact_13_3076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0667.data_13_3076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0667.endpoint_13_3076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.bounds_13_3091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.exact_13_3091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0668.data_13_3091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0668.endpoint_13_3091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.bounds_13_3106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.exact_13_3106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0669.data_13_3106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0669.endpoint_13_3106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.bounds_13_3122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.exact_13_3122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0670.data_13_3122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0670.endpoint_13_3122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3125' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0671.data_13_3128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.bounds_13_3137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.exact_13_3137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0671.data_13_3137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0671.endpoint_13_3137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.bounds_13_3152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.exact_13_3152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0672.data_13_3152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0672.endpoint_13_3152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.bounds_13_3168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.exact_13_3168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0673.data_13_3168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0673.endpoint_13_3168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.bounds_13_3183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.exact_13_3183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0674.data_13_3183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0674.endpoint_13_3183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.bounds_13_3199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.exact_13_3199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0675.data_13_3199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0675.endpoint_13_3199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.bounds_13_3214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.exact_13_3214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0676.data_13_3214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0676.endpoint_13_3214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.bounds_13_3229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.exact_13_3229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0677.data_13_3229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0677.endpoint_13_3229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.bounds_13_3245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.exact_13_3245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0678.data_13_3245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0678.endpoint_13_3245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.bounds_13_3260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.exact_13_3260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0679.data_13_3260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0679.endpoint_13_3260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.bounds_13_3275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.exact_13_3275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0680.data_13_3275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0680.endpoint_13_3275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.bounds_13_3291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.exact_13_3291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0681.data_13_3291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0681.endpoint_13_3291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.bounds_13_3306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.exact_13_3306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0682.data_13_3306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0682.endpoint_13_3306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.bounds_13_3321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.exact_13_3321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0683.data_13_3321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0683.endpoint_13_3321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.bounds_13_3337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.exact_13_3337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0684.data_13_3337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0684.endpoint_13_3337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.bounds_13_3352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.exact_13_3352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0685.data_13_3352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0685.endpoint_13_3352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.bounds_13_3367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.exact_13_3367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0686.data_13_3367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0686.endpoint_13_3367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.bounds_13_3383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.exact_13_3383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0687.data_13_3383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0687.endpoint_13_3383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.bounds_13_3398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.exact_13_3398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0688.data_13_3398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0688.endpoint_13_3398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.bounds_13_3414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.exact_13_3414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0689.data_13_3414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0689.endpoint_13_3414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.bounds_13_3429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.exact_13_3429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0690.data_13_3429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0690.endpoint_13_3429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.bounds_13_3444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.exact_13_3444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0691.data_13_3444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0691.endpoint_13_3444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.bounds_13_3460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.exact_13_3460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0692.data_13_3460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0692.endpoint_13_3460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.bounds_13_3475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.exact_13_3475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0693.data_13_3475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0693.endpoint_13_3475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.bounds_13_3490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.exact_13_3490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0694.data_13_3490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0694.endpoint_13_3490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.bounds_13_3506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.exact_13_3506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0695.data_13_3506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0695.endpoint_13_3506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.bounds_13_3521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.exact_13_3521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0696.data_13_3521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0696.endpoint_13_3521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.bounds_13_3536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.exact_13_3536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0697.data_13_3536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0697.endpoint_13_3536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.bounds_13_3552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.exact_13_3552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0698.data_13_3552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0698.endpoint_13_3552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3553' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0699.data_13_3558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.bounds_13_3567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.exact_13_3567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0699.data_13_3567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0699.endpoint_13_3567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.bounds_13_3583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.exact_13_3583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0700.data_13_3583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0700.endpoint_13_3583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.bounds_13_3598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.exact_13_3598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0701.data_13_3598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0701.endpoint_13_3598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.bounds_13_3613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.exact_13_3613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0702.data_13_3613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0702.endpoint_13_3613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.bounds_13_3629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.exact_13_3629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0703.data_13_3629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0703.endpoint_13_3629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.bounds_13_3644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.exact_13_3644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0704.data_13_3644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0704.endpoint_13_3644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3650' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0705.data_13_3653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.bounds_13_3659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.exact_13_3659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0705.data_13_3659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0705.endpoint_13_3659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.bounds_13_3675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.exact_13_3675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0706.data_13_3675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0706.endpoint_13_3675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.bounds_13_3690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.exact_13_3690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0707.data_13_3690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0707.endpoint_13_3690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.bounds_13_3705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.exact_13_3705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0708.data_13_3705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0708.endpoint_13_3705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.bounds_13_3721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.exact_13_3721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0709.data_13_3721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0709.endpoint_13_3721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.bounds_13_3736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.exact_13_3736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0710.data_13_3736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0710.endpoint_13_3736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.bounds_13_3751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.exact_13_3751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0711.data_13_3751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0711.endpoint_13_3751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.bounds_13_3767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.exact_13_3767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0712.data_13_3767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0712.endpoint_13_3767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.bounds_13_3782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.exact_13_3782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0713.data_13_3782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0713.endpoint_13_3782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.bounds_13_3798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.exact_13_3798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0714.data_13_3798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0714.endpoint_13_3798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.bounds_13_3813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.exact_13_3813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0715.data_13_3813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0715.endpoint_13_3813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.bounds_13_3828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.exact_13_3828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0716.data_13_3828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0716.endpoint_13_3828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.bounds_13_3844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.exact_13_3844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0717.data_13_3844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0717.endpoint_13_3844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.bounds_13_3859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.exact_13_3859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0718.data_13_3859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0718.endpoint_13_3859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.bounds_13_3874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.exact_13_3874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0719.data_13_3874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0719.endpoint_13_3874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.bounds_13_3890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.exact_13_3890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0720.data_13_3890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0720.endpoint_13_3890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.bounds_13_3905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.exact_13_3905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0721.data_13_3905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0721.endpoint_13_3905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.bounds_13_3920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.exact_13_3920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0722.data_13_3920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0722.endpoint_13_3920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.bounds_13_3936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.exact_13_3936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0723.data_13_3936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0723.endpoint_13_3936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.bounds_13_3951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.exact_13_3951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0724.data_13_3951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0724.endpoint_13_3951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.bounds_13_3967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.exact_13_3967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0725.data_13_3967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0725.endpoint_13_3967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.bounds_13_3982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.exact_13_3982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0726.data_13_3982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0726.endpoint_13_3982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.bounds_13_3997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.exact_13_3997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0727.data_13_3997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0727.endpoint_13_3997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_3998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_3998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_3998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_3998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_3999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_3999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_3999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_3999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.bounds_13_4013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.exact_13_4013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0728.data_13_4013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0728.endpoint_13_4013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.bounds_13_4028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.exact_13_4028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0729.data_13_4028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0729.endpoint_13_4028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.bounds_13_4043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.exact_13_4043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0730.data_13_4043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0730.endpoint_13_4043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.bounds_13_4059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.exact_13_4059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0731.data_13_4059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0731.endpoint_13_4059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.bounds_13_4074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.exact_13_4074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0732.data_13_4074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0732.endpoint_13_4074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.bounds_13_4089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.exact_13_4089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0733.data_13_4089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0733.endpoint_13_4089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.bounds_13_4105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.exact_13_4105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0734.data_13_4105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0734.endpoint_13_4105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.bounds_13_4120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.exact_13_4120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0735.data_13_4120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0735.endpoint_13_4120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.bounds_13_4135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.exact_13_4135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0736.data_13_4135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0736.endpoint_13_4135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.bounds_13_4151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.exact_13_4151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0737.data_13_4151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0737.endpoint_13_4151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.bounds_13_4166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.exact_13_4166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0738.data_13_4166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0738.endpoint_13_4166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.bounds_13_4182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.exact_13_4182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0739.data_13_4182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0739.endpoint_13_4182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.bounds_13_4197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.exact_13_4197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0740.data_13_4197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0740.endpoint_13_4197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.bounds_13_4212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.exact_13_4212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0741.data_13_4212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0741.endpoint_13_4212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.bounds_13_4228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.exact_13_4228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0742.data_13_4228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0742.endpoint_13_4228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.bounds_13_4243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.exact_13_4243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0743.data_13_4243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0743.endpoint_13_4243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.bounds_13_4258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.exact_13_4258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0744.data_13_4258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0744.endpoint_13_4258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.bounds_13_4274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.exact_13_4274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0745.data_13_4274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0745.endpoint_13_4274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.bounds_13_4289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.exact_13_4289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0746.data_13_4289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0746.endpoint_13_4289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.bounds_13_4304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.exact_13_4304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0747.data_13_4304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0747.endpoint_13_4304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.bounds_13_4320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.exact_13_4320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0748.data_13_4320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0748.endpoint_13_4320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.bounds_13_4335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.exact_13_4335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0749.data_13_4335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0749.endpoint_13_4335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.bounds_13_4351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.exact_13_4351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0750.data_13_4351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0750.endpoint_13_4351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.bounds_13_4366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.exact_13_4366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0751.data_13_4366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0751.endpoint_13_4366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.bounds_13_4381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.exact_13_4381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0752.data_13_4381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0752.endpoint_13_4381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.bounds_13_4397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.exact_13_4397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0753.data_13_4397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0753.endpoint_13_4397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.bounds_13_4412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.exact_13_4412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0754.data_13_4412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0754.endpoint_13_4412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.bounds_13_4427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.exact_13_4427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0755.data_13_4427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0755.endpoint_13_4427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.bounds_13_4443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.exact_13_4443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0756.data_13_4443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0756.endpoint_13_4443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.bounds_13_4458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.exact_13_4458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0757.data_13_4458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0757.endpoint_13_4458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.bounds_13_4473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.exact_13_4473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0758.data_13_4473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0758.endpoint_13_4473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.bounds_13_4489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.exact_13_4489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0759.data_13_4489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0759.endpoint_13_4489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.bounds_13_4504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.exact_13_4504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0760.data_13_4504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0760.endpoint_13_4504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.bounds_13_4519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.exact_13_4519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0761.data_13_4519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0761.endpoint_13_4519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.bounds_13_4535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.exact_13_4535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0762.data_13_4535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0762.endpoint_13_4535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.bounds_13_4550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.exact_13_4550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0763.data_13_4550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0763.endpoint_13_4550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.bounds_13_4566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.exact_13_4566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0764.data_13_4566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0764.endpoint_13_4566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.bounds_13_4581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.exact_13_4581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0765.data_13_4581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0765.endpoint_13_4581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.bounds_13_4596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.exact_13_4596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0766.data_13_4596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0766.endpoint_13_4596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.bounds_13_4612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.exact_13_4612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0767.data_13_4612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0767.endpoint_13_4612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.bounds_13_4627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.exact_13_4627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0768.data_13_4627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0768.endpoint_13_4627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.bounds_13_4642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.exact_13_4642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0769.data_13_4642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0769.endpoint_13_4642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.bounds_13_4658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.exact_13_4658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0770.data_13_4658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0770.endpoint_13_4658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.bounds_13_4673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.exact_13_4673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0771.data_13_4673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0771.endpoint_13_4673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.bounds_13_4688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.exact_13_4688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0772.data_13_4688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0772.endpoint_13_4688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.bounds_13_4704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.exact_13_4704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0773.data_13_4704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0773.endpoint_13_4704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.bounds_13_4719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.exact_13_4719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0774.data_13_4719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0774.endpoint_13_4719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.bounds_13_4735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.exact_13_4735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0775.data_13_4735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0775.endpoint_13_4735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.bounds_13_4750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.exact_13_4750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0776.data_13_4750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0776.endpoint_13_4750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.bounds_13_4765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.exact_13_4765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0777.data_13_4765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0777.endpoint_13_4765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.bounds_13_4781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.exact_13_4781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0778.data_13_4781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0778.endpoint_13_4781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.bounds_13_4796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.exact_13_4796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0779.data_13_4796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0779.endpoint_13_4796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.bounds_13_4811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.exact_13_4811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0780.data_13_4811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0780.endpoint_13_4811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.bounds_13_4827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.exact_13_4827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0781.data_13_4827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0781.endpoint_13_4827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.bounds_13_4842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.exact_13_4842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0782.data_13_4842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0782.endpoint_13_4842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.bounds_13_4857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.exact_13_4857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0783.data_13_4857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0783.endpoint_13_4857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.bounds_13_4873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.exact_13_4873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0784.data_13_4873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0784.endpoint_13_4873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.bounds_13_4888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.exact_13_4888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0785.data_13_4888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0785.endpoint_13_4888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.bounds_13_4903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.exact_13_4903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0786.data_13_4903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0786.endpoint_13_4903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.bounds_13_4919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.exact_13_4919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0787.data_13_4919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0787.endpoint_13_4919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.bounds_13_4934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.exact_13_4934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0788.data_13_4934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0788.endpoint_13_4934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.bounds_13_4950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.exact_13_4950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0789.data_13_4950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0789.endpoint_13_4950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.bounds_13_4965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.exact_13_4965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0790.data_13_4965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0790.endpoint_13_4965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.bounds_13_4980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.exact_13_4980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0791.data_13_4980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0791.endpoint_13_4980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.bounds_13_4996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.exact_13_4996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0792.data_13_4996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0792.endpoint_13_4996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_4997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_4997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_4997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_4997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_4998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_4998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_4998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_4998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_4999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_4999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_4999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_4999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.bounds_13_5011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.exact_13_5011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0793.data_13_5011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0793.endpoint_13_5011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.bounds_13_5026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.exact_13_5026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0794.data_13_5026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0794.endpoint_13_5026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.bounds_13_5042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.exact_13_5042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0795.data_13_5042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0795.endpoint_13_5042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.bounds_13_5057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.exact_13_5057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0796.data_13_5057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0796.endpoint_13_5057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.bounds_13_5072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.exact_13_5072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0797.data_13_5072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0797.endpoint_13_5072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.bounds_13_5088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.exact_13_5088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0798.data_13_5088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0798.endpoint_13_5088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.bounds_13_5103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.exact_13_5103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0799.data_13_5103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0799.endpoint_13_5103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.bounds_13_5119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.exact_13_5119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0800.data_13_5119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0800.endpoint_13_5119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.bounds_13_5134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.exact_13_5134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0801.data_13_5134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0801.endpoint_13_5134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.bounds_13_5149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.exact_13_5149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0802.data_13_5149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0802.endpoint_13_5149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.bounds_13_5165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.exact_13_5165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0803.data_13_5165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0803.endpoint_13_5165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.bounds_13_5180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.exact_13_5180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0804.data_13_5180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0804.endpoint_13_5180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.bounds_13_5195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.exact_13_5195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0805.data_13_5195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0805.endpoint_13_5195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.bounds_13_5211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.exact_13_5211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0806.data_13_5211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0806.endpoint_13_5211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.bounds_13_5226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.exact_13_5226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0807.data_13_5226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0807.endpoint_13_5226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.bounds_13_5241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.exact_13_5241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0808.data_13_5241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0808.endpoint_13_5241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.bounds_13_5257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.exact_13_5257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0809.data_13_5257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0809.endpoint_13_5257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.bounds_13_5272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.exact_13_5272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0810.data_13_5272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0810.endpoint_13_5272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.bounds_13_5287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.exact_13_5287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0811.data_13_5287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0811.endpoint_13_5287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.bounds_13_5303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.exact_13_5303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0812.data_13_5303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0812.endpoint_13_5303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.bounds_13_5318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.exact_13_5318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0813.data_13_5318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0813.endpoint_13_5318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.data_13_5327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.endpoint_13_5327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0814.bounds_13_5328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0814.exact_13_5328' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0816.data_13_5363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0816.bounds_13_5364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0816.exact_13_5364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0816.data_13_5364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0816.endpoint_13_5364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.bounds_13_5380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.exact_13_5380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0817.data_13_5380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0817.endpoint_13_5380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.bounds_13_5395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.exact_13_5395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0818.data_13_5395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0818.endpoint_13_5395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.bounds_13_5410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.exact_13_5410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0819.data_13_5410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0819.endpoint_13_5410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.bounds_13_5426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.exact_13_5426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0820.data_13_5426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0820.endpoint_13_5426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.bounds_13_5441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.exact_13_5441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0821.data_13_5441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0821.endpoint_13_5441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.bounds_13_5456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.exact_13_5456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0822.data_13_5456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0822.endpoint_13_5456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.bounds_13_5472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.exact_13_5472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0823.data_13_5472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0823.endpoint_13_5472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.bounds_13_5487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.exact_13_5487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0824.data_13_5487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0824.endpoint_13_5487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.bounds_13_5503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.exact_13_5503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0825.data_13_5503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0825.endpoint_13_5503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.bounds_13_5518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.exact_13_5518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0826.data_13_5518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0826.endpoint_13_5518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.bounds_13_5533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.exact_13_5533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0827.data_13_5533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0827.endpoint_13_5533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.bounds_13_5549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.exact_13_5549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0828.data_13_5549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0828.endpoint_13_5549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.bounds_13_5564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.exact_13_5564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0829.data_13_5564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0829.endpoint_13_5564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.bounds_13_5579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.exact_13_5579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0830.data_13_5579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0830.endpoint_13_5579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.bounds_13_5595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.exact_13_5595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0831.data_13_5595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0831.endpoint_13_5595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.bounds_13_5610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.exact_13_5610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0832.data_13_5610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0832.endpoint_13_5610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.bounds_13_5625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.exact_13_5625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0833.data_13_5625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0833.endpoint_13_5625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.bounds_13_5641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.exact_13_5641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0834.data_13_5641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0834.endpoint_13_5641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5645' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0835.data_13_5648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5650' depends on axioms: [propext, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0835.data_13_5653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.bounds_13_5656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.exact_13_5656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0835.data_13_5656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0835.endpoint_13_5656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.bounds_13_5671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.exact_13_5671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0836.data_13_5671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0836.endpoint_13_5671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.bounds_13_5687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.exact_13_5687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0837.data_13_5687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0837.endpoint_13_5687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.bounds_13_5702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.exact_13_5702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0838.data_13_5702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0838.endpoint_13_5702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.bounds_13_5718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.exact_13_5718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0839.data_13_5718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0839.endpoint_13_5718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.bounds_13_5733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.exact_13_5733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0840.data_13_5733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0840.endpoint_13_5733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.bounds_13_5748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.exact_13_5748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0841.data_13_5748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0841.endpoint_13_5748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.bounds_13_5764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.exact_13_5764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0842.data_13_5764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0842.endpoint_13_5764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.bounds_13_5779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.exact_13_5779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0843.data_13_5779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0843.endpoint_13_5779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.bounds_13_5794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.exact_13_5794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0844.data_13_5794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0844.endpoint_13_5794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.bounds_13_5810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.exact_13_5810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0845.data_13_5810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0845.endpoint_13_5810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.bounds_13_5825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.exact_13_5825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0846.data_13_5825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0846.endpoint_13_5825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.bounds_13_5840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.exact_13_5840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0847.data_13_5840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0847.endpoint_13_5840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.bounds_13_5856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.exact_13_5856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0848.data_13_5856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0848.endpoint_13_5856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.bounds_13_5871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.exact_13_5871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0849.data_13_5871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0849.endpoint_13_5871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.bounds_13_5887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.exact_13_5887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0850.data_13_5887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0850.endpoint_13_5887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.bounds_13_5902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.exact_13_5902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0851.data_13_5902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0851.endpoint_13_5902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.bounds_13_5917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.exact_13_5917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0852.data_13_5917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0852.endpoint_13_5917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.bounds_13_5933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.exact_13_5933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0853.data_13_5933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0853.endpoint_13_5933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.bounds_13_5948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.exact_13_5948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0854.data_13_5948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0854.endpoint_13_5948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.bounds_13_5963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.exact_13_5963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0855.data_13_5963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0855.endpoint_13_5963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.bounds_13_5979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.exact_13_5979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0856.data_13_5979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0856.endpoint_13_5979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.bounds_13_5994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.exact_13_5994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0857.data_13_5994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0857.endpoint_13_5994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_5995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_5995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_5996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_5996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_5997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_5997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_5998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_5998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_5999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_5999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_5999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_5999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.bounds_13_6009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.exact_13_6009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0858.data_13_6009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0858.endpoint_13_6009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.bounds_13_6025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.exact_13_6025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0859.data_13_6025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0859.endpoint_13_6025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.bounds_13_6040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.exact_13_6040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0860.data_13_6040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0860.endpoint_13_6040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.bounds_13_6055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.exact_13_6055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0861.data_13_6055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0861.endpoint_13_6055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.bounds_13_6071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.exact_13_6071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0862.data_13_6071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0862.endpoint_13_6071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.bounds_13_6086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.exact_13_6086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0863.data_13_6086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0863.endpoint_13_6086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.bounds_13_6102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.exact_13_6102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0864.data_13_6102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0864.endpoint_13_6102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.bounds_13_6117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.exact_13_6117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0865.data_13_6117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0865.endpoint_13_6117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.bounds_13_6132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.exact_13_6132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0866.data_13_6132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0866.endpoint_13_6132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.bounds_13_6148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.exact_13_6148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0867.data_13_6148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0867.endpoint_13_6148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.bounds_13_6163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.exact_13_6163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0868.data_13_6163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0868.endpoint_13_6163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.bounds_13_6178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.exact_13_6178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0869.data_13_6178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0869.endpoint_13_6178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.bounds_13_6194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.exact_13_6194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0870.data_13_6194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0870.endpoint_13_6194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.bounds_13_6209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.exact_13_6209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0871.data_13_6209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0871.endpoint_13_6209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.bounds_13_6224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.exact_13_6224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0872.data_13_6224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0872.endpoint_13_6224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.bounds_13_6240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.exact_13_6240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0873.data_13_6240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0873.endpoint_13_6240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.bounds_13_6255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.exact_13_6255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0874.data_13_6255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0874.endpoint_13_6255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.bounds_13_6271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.exact_13_6271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0875.data_13_6271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0875.endpoint_13_6271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.bounds_13_6286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.exact_13_6286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0876.data_13_6286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0876.endpoint_13_6286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.bounds_13_6301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.exact_13_6301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0877.data_13_6301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0877.endpoint_13_6301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.bounds_13_6317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.exact_13_6317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0878.data_13_6317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0878.endpoint_13_6317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.bounds_13_6332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.exact_13_6332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0879.data_13_6332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0879.endpoint_13_6332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.bounds_13_6347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.exact_13_6347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0880.data_13_6347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0880.endpoint_13_6347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.bounds_13_6363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.exact_13_6363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0881.data_13_6363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0881.endpoint_13_6363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.bounds_13_6378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.exact_13_6378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0882.data_13_6378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0882.endpoint_13_6378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.bounds_13_6393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.exact_13_6393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0883.data_13_6393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0883.endpoint_13_6393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.bounds_13_6409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.exact_13_6409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0884.data_13_6409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0884.endpoint_13_6409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.bounds_13_6424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.exact_13_6424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0885.data_13_6424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0885.endpoint_13_6424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.bounds_13_6439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.exact_13_6439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0886.data_13_6439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0886.endpoint_13_6439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.bounds_13_6455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.exact_13_6455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0887.data_13_6455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0887.endpoint_13_6455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.bounds_13_6470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.exact_13_6470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0888.data_13_6470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0888.endpoint_13_6470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.bounds_13_6486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.exact_13_6486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0889.data_13_6486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0889.endpoint_13_6486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.bounds_13_6501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.exact_13_6501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0890.data_13_6501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0890.endpoint_13_6501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.bounds_13_6516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.exact_13_6516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0891.data_13_6516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0891.endpoint_13_6516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.bounds_13_6532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.exact_13_6532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0892.data_13_6532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0892.endpoint_13_6532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.bounds_13_6547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.exact_13_6547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0893.data_13_6547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0893.endpoint_13_6547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.bounds_13_6562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.exact_13_6562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0894.data_13_6562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0894.endpoint_13_6562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.bounds_13_6578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.exact_13_6578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0895.data_13_6578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0895.endpoint_13_6578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.bounds_13_6593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.exact_13_6593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0896.data_13_6593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0896.endpoint_13_6593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.bounds_13_6608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.exact_13_6608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0897.data_13_6608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0897.endpoint_13_6608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.bounds_13_6624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.exact_13_6624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0898.data_13_6624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0898.endpoint_13_6624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.bounds_13_6639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.exact_13_6639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0899.data_13_6639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0899.endpoint_13_6639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.bounds_13_6655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.exact_13_6655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0900.data_13_6655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0900.endpoint_13_6655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.bounds_13_6670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.exact_13_6670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0901.data_13_6670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0901.endpoint_13_6670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.bounds_13_6685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.exact_13_6685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0902.data_13_6685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0902.endpoint_13_6685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.bounds_13_6701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.exact_13_6701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0903.data_13_6701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0903.endpoint_13_6701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.bounds_13_6716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.exact_13_6716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0904.data_13_6716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0904.endpoint_13_6716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.bounds_13_6731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.exact_13_6731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0905.data_13_6731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0905.endpoint_13_6731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.bounds_13_6747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.exact_13_6747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0906.data_13_6747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0906.endpoint_13_6747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.bounds_13_6762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.exact_13_6762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0907.data_13_6762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0907.endpoint_13_6762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.bounds_13_6777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.exact_13_6777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0908.data_13_6777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0908.endpoint_13_6777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.bounds_13_6793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.exact_13_6793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0909.data_13_6793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0909.endpoint_13_6793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.bounds_13_6808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.exact_13_6808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0910.data_13_6808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0910.endpoint_13_6808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.bounds_13_6823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.exact_13_6823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0911.data_13_6823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0911.endpoint_13_6823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.bounds_13_6839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.exact_13_6839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0912.data_13_6839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0912.endpoint_13_6839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.bounds_13_6854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.exact_13_6854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0913.data_13_6854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0913.endpoint_13_6854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.bounds_13_6870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.exact_13_6870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0914.data_13_6870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0914.endpoint_13_6870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.bounds_13_6885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.exact_13_6885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0915.data_13_6885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0915.endpoint_13_6885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.bounds_13_6900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.exact_13_6900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0916.data_13_6900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0916.endpoint_13_6900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.bounds_13_6916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.exact_13_6916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0917.data_13_6916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0917.endpoint_13_6916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.bounds_13_6931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.exact_13_6931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0918.data_13_6931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0918.endpoint_13_6931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.bounds_13_6946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.exact_13_6946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0919.data_13_6946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0919.endpoint_13_6946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.bounds_13_6962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.exact_13_6962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0920.data_13_6962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0920.endpoint_13_6962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.bounds_13_6977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.exact_13_6977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0921.data_13_6977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0921.endpoint_13_6977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.bounds_13_6992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.exact_13_6992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0922.data_13_6992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0922.endpoint_13_6992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_6999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_6999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_6999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_6999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.bounds_13_7008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.exact_13_7008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0923.data_13_7008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0923.endpoint_13_7008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.bounds_13_7023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.exact_13_7023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0924.data_13_7023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0924.endpoint_13_7023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.bounds_13_7039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.exact_13_7039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0925.data_13_7039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0925.endpoint_13_7039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.bounds_13_7054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.exact_13_7054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0926.data_13_7054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0926.endpoint_13_7054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.bounds_13_7069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.exact_13_7069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0927.data_13_7069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0927.endpoint_13_7069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.bounds_13_7085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.exact_13_7085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0928.data_13_7085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0928.endpoint_13_7085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.bounds_13_7100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.exact_13_7100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0929.data_13_7100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0929.endpoint_13_7100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7113' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7113' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7114' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7114' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7114' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.bounds_13_7115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.exact_13_7115' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0930.data_13_7115' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0930.endpoint_13_7115' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.bounds_13_7131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.exact_13_7131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0931.data_13_7131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0931.endpoint_13_7131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.bounds_13_7146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.exact_13_7146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0932.data_13_7146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0932.endpoint_13_7146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.bounds_13_7161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.exact_13_7161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0933.data_13_7161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0933.endpoint_13_7161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7163' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7163' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7164' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7164' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7164' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7165' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7165' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7165' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7166' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7166' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7166' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7167' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7167' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7167' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7168' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7168' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7168' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7169' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7169' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7169' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7170' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7170' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7170' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7171' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7171' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7171' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7172' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7172' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7172' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7173' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7173' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7173' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7174' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7174' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7174' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7175' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7175' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7175' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7176' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7176' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7176' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.bounds_13_7177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.exact_13_7177' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0934.data_13_7177' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0934.endpoint_13_7177' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7178' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7178' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7178' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7179' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7179' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7179' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7180' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7180' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7180' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7181' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7181' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7181' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7182' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7182' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7182' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7183' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7183' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7183' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7184' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7184' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7184' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7185' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7185' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7185' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7186' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7186' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7186' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7187' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7187' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7187' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7188' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.bounds_13_7192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.exact_13_7192' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0935.data_13_7192' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0935.endpoint_13_7192' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7193' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7193' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7193' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7194' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7194' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7194' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7195' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7195' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7195' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7196' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7196' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7196' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7197' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7197' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7197' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7198' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7198' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7198' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7199' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7199' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7199' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7200' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7200' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7200' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7201' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7201' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7201' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7202' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7202' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7202' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7203' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7203' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7203' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7204' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7204' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7204' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7205' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7205' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7205' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7206' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7206' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7206' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.bounds_13_7207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.exact_13_7207' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0936.data_13_7207' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0936.endpoint_13_7207' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7208' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7208' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7208' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7209' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7209' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7209' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7210' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7210' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7210' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7211' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7211' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7211' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7212' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7212' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7212' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7213' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7213' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7213' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7214' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7214' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7214' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7215' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7215' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7215' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7216' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7216' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7216' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7217' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7217' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7217' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7218' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7218' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7218' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7219' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7219' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7219' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7220' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7220' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7220' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7221' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7221' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7221' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7222' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7222' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7222' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.bounds_13_7223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.exact_13_7223' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0937.data_13_7223' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0937.endpoint_13_7223' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7224' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7224' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7224' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7225' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7225' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7225' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7226' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7226' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7226' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7227' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7227' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7227' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7228' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7228' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7228' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7229' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7229' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7229' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7230' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7230' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7230' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7231' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7231' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7231' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7232' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7232' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7232' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7233' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7233' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7233' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7234' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7234' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7234' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7235' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7235' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7235' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7236' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7236' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7236' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7237' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7237' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7237' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.bounds_13_7238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.exact_13_7238' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0938.data_13_7238' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0938.endpoint_13_7238' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7239' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7239' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7239' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7240' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7240' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7240' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7241' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7241' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7241' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7242' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7242' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7242' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7243' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7243' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7243' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7244' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7244' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7244' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7245' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7245' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7245' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7246' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7246' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7246' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7247' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7247' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7247' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7248' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7248' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7248' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7249' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7249' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7249' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7250' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7250' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7250' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7251' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7251' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7251' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7252' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7252' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7252' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7253' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7253' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7253' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.bounds_13_7254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.exact_13_7254' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0939.data_13_7254' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0939.endpoint_13_7254' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7255' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7255' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7255' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7256' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7256' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7256' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7257' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7257' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7257' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7258' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7258' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7258' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7259' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7259' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7259' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7260' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7260' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7260' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7261' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7261' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7261' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7262' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7262' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7262' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7263' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7263' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7263' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7264' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7264' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7264' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7265' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7265' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7265' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7266' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7266' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7266' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7267' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7267' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7267' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7268' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7268' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7268' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.bounds_13_7269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.exact_13_7269' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0940.data_13_7269' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0940.endpoint_13_7269' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7270' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7270' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7270' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7271' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7271' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7271' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7272' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7272' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7272' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7273' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7273' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7273' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7274' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7274' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7274' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7275' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7275' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7275' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7276' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7276' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7276' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7277' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7277' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7277' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7278' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7278' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7278' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7279' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7279' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7279' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7280' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7280' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7280' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7281' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7281' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7281' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7282' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7282' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7282' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7283' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7283' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7283' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.bounds_13_7284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.exact_13_7284' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0941.data_13_7284' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0941.endpoint_13_7284' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7285' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7285' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7285' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7286' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7286' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7286' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7287' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7287' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7287' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7288' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7288' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7288' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7289' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7289' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7289' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7290' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7290' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7290' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7291' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7291' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7291' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7292' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7292' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7292' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7293' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7293' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7293' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7294' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7294' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7294' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7295' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7295' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7295' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7296' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7296' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7296' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7297' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7297' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7297' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7298' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7298' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7298' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7299' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7299' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7299' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.bounds_13_7300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.exact_13_7300' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0942.data_13_7300' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0942.endpoint_13_7300' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7301' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7301' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7301' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7302' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7302' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7302' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7303' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7303' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7303' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7304' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7304' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7304' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7305' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7305' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7305' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7306' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7306' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7306' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7307' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7307' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7307' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7308' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7308' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7308' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7309' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7309' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7309' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7310' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7310' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7310' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7311' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7311' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7311' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7312' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7312' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7312' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7313' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7313' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7313' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7314' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7314' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7314' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.bounds_13_7315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.exact_13_7315' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0943.data_13_7315' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0943.endpoint_13_7315' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7316' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7316' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7316' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7317' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7317' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7317' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7318' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7318' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7318' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7319' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7319' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7319' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7320' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7320' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7320' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7321' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7321' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7321' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7322' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7322' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7322' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7323' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7323' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7323' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7324' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7324' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7324' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7325' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7325' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7325' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7326' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7326' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7326' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7327' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7327' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7327' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7328' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7328' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7328' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7329' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7329' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7329' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.bounds_13_7330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.exact_13_7330' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0944.data_13_7330' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0944.endpoint_13_7330' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7331' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7331' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7331' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7332' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7332' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7332' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7333' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7333' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7333' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7334' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7334' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7334' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7335' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7335' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7335' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7336' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7336' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7336' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7337' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7337' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7337' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7338' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7338' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7338' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7339' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7339' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7339' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7340' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7340' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7340' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7341' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7341' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7341' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7342' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7342' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7342' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7343' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7343' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7343' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7344' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7344' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7344' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7345' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7345' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7345' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.bounds_13_7346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.exact_13_7346' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0945.data_13_7346' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0945.endpoint_13_7346' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7347' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7347' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7347' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7348' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7348' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7348' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7349' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7349' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7349' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7350' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7350' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7350' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7351' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7351' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7351' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7352' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7352' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7352' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7353' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7353' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7353' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7354' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7354' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7354' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7355' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7355' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7355' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7356' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7356' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7356' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7357' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7357' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7357' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7358' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7358' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7358' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7359' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7359' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7359' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7360' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7360' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7360' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.bounds_13_7361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.exact_13_7361' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0946.data_13_7361' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0946.endpoint_13_7361' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7362' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7362' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7362' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7363' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7363' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7363' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7364' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7364' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7364' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7365' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7365' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7365' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7366' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7366' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7366' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7367' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7367' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7367' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7368' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7368' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7368' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7369' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7369' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7369' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7370' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7370' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7370' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7371' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7371' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7371' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7372' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7372' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7372' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7373' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7373' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7373' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7374' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7374' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7374' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7375' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7375' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7375' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.bounds_13_7376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.exact_13_7376' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0947.data_13_7376' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0947.endpoint_13_7376' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7377' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7377' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7377' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7378' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7378' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7378' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7379' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7379' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7379' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7380' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7380' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7380' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7381' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7381' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7381' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7382' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7382' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7382' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7383' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7383' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7383' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7384' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7384' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7384' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7385' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7385' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7385' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7386' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7386' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7386' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7387' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7387' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7387' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7388' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7388' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7388' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7389' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7389' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7389' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7390' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7390' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7390' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7391' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7391' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7391' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.bounds_13_7392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.exact_13_7392' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0948.data_13_7392' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0948.endpoint_13_7392' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7393' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7393' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7393' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7394' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7394' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7394' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7395' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7395' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7395' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7396' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7396' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7396' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7397' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7397' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7397' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7398' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7398' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7398' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7399' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7399' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7399' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7400' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7400' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7400' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7401' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7401' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7401' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7402' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7402' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7402' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7403' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7403' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7403' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7404' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7404' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7404' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7405' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7405' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7405' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7406' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7406' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7406' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.bounds_13_7407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.exact_13_7407' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0949.data_13_7407' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0949.endpoint_13_7407' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7408' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7408' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7408' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7409' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7409' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7409' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7410' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7410' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7410' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7411' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7411' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7411' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7412' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7412' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7412' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7413' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7413' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7413' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7414' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7414' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7414' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7415' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7415' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7415' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7416' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7416' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7416' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7417' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7417' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7417' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7418' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7418' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7418' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7419' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7419' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7419' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7420' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7420' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7420' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7421' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7421' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7421' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7422' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7422' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7422' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.bounds_13_7423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.exact_13_7423' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0950.data_13_7423' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0950.endpoint_13_7423' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7424' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7424' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7424' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7425' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7425' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7425' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7426' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7426' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7426' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7427' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7427' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7427' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7428' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7428' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7428' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7429' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7429' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7429' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7430' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7430' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7430' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7431' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7431' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7431' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7432' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7432' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7432' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7433' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7433' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7433' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7434' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7434' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7434' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7435' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7435' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7435' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7436' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7436' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7436' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7437' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7437' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7437' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.bounds_13_7438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.exact_13_7438' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0951.data_13_7438' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0951.endpoint_13_7438' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7439' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7439' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7439' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7440' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7440' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7440' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7441' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7441' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7441' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7442' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7442' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7442' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7443' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7443' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7443' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7444' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7444' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7444' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7445' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7445' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7445' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7446' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7446' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7446' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7447' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7447' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7447' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7448' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7448' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7448' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7449' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7449' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7449' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7450' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7450' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7450' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7451' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7451' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7451' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7452' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7452' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7452' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.bounds_13_7453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.exact_13_7453' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0952.data_13_7453' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0952.endpoint_13_7453' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7454' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7454' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7454' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7455' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7455' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7455' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7456' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7456' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7456' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7457' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7457' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7457' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7458' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7458' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7458' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7459' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7459' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7459' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7460' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7460' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7460' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7461' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7461' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7461' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7462' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7462' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7462' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7463' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7463' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7463' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7464' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7464' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7464' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7465' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7465' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7465' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7466' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7466' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7466' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7467' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7467' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7467' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7468' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7468' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7468' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.bounds_13_7469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.exact_13_7469' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0953.data_13_7469' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0953.endpoint_13_7469' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7470' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7470' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7470' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7471' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7471' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7471' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7472' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7472' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7472' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7473' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7473' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7473' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7474' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7474' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7474' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7475' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7475' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7475' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7476' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7476' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7476' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7477' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7477' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7477' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7478' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7478' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7478' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7479' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7479' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7479' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7480' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7480' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7480' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7481' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7481' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7481' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7482' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7482' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7482' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7483' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7483' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7483' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.bounds_13_7484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.exact_13_7484' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0954.data_13_7484' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0954.endpoint_13_7484' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7485' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7485' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7485' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7486' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7486' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7486' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7487' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7487' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7487' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7488' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7488' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7488' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7489' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7489' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7489' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7490' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7490' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7490' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7491' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7491' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7491' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7492' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7492' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7492' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7493' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7493' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7493' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7494' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7494' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7494' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7495' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7495' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7495' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7496' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7496' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7496' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7497' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7497' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7497' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7498' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7498' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7498' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.bounds_13_7499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.exact_13_7499' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0955.data_13_7499' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0955.endpoint_13_7499' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7500' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7500' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7500' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7501' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7501' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7501' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7502' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7502' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7502' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7503' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7503' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7503' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7504' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7504' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7504' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7505' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7505' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7505' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7506' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7506' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7506' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7507' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7507' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7507' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7508' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7508' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7508' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7509' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7509' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7509' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7510' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7510' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7510' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7511' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7511' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7511' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7512' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7512' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7512' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7513' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7513' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7513' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7514' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7514' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7514' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.bounds_13_7515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.exact_13_7515' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0956.data_13_7515' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0956.endpoint_13_7515' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7516' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7516' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7516' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7517' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7517' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7517' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7518' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7518' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7518' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7519' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7519' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7519' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7520' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7520' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7520' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7521' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7521' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7521' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7522' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7522' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7522' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7523' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7523' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7523' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7524' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7524' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7524' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7525' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7525' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7525' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7526' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7526' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7526' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7527' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7527' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7527' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7528' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7528' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7528' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7529' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7529' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7529' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.bounds_13_7530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.exact_13_7530' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0957.data_13_7530' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0957.endpoint_13_7530' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7531' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7531' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7531' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7532' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7532' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7532' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7533' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7533' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7533' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7534' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7534' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7534' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7535' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7535' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7535' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7536' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7536' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7536' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7537' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7537' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7537' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7538' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7538' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7539' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7539' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7539' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7540' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7540' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7540' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7541' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7541' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7541' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7542' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7542' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7542' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7543' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7543' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7543' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7544' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7544' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7544' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.bounds_13_7545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.exact_13_7545' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0958.data_13_7545' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0958.endpoint_13_7545' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7546' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7546' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7546' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7547' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7547' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7547' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7548' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7548' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7548' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7549' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7549' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7549' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7550' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7550' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7550' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7551' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7551' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7551' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7552' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7552' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7552' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7553' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7553' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7553' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7554' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7554' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7554' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7555' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7555' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7555' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7556' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7556' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7556' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7557' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7557' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7557' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7558' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7558' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7558' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7559' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7559' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7559' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7560' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7560' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7560' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.bounds_13_7561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.exact_13_7561' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0959.data_13_7561' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0959.endpoint_13_7561' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7562' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7562' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7562' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7563' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7563' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7563' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7564' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7564' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7564' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7565' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7565' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7565' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7566' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7566' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7566' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7567' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7567' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7567' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7568' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7568' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7568' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7569' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7569' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7569' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7570' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7570' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7570' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7571' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7571' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7571' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7572' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7572' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7572' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7573' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7573' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7573' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7574' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7574' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7574' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7575' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7575' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7575' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.bounds_13_7576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.exact_13_7576' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0960.data_13_7576' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0960.endpoint_13_7576' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7577' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7577' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7577' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7578' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7578' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7578' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7579' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7579' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7579' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7580' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7580' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7580' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7581' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7581' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7581' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7582' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7582' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7582' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7583' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7583' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7583' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7584' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7584' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7584' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7585' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7585' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7585' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7586' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7586' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7586' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7587' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7587' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7587' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7588' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7588' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7588' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7589' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7589' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7589' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7590' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7590' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7590' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.bounds_13_7591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.exact_13_7591' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0961.data_13_7591' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0961.endpoint_13_7591' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7592' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7592' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7592' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7593' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7593' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7593' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7594' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7594' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7594' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7595' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7595' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7595' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7596' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7596' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7596' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7597' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7597' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7597' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7598' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7598' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7598' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7599' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7599' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7599' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7600' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7600' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7600' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7601' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7601' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7601' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7602' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7602' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7602' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7603' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7603' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7603' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7604' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7604' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7604' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7605' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7605' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7605' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7606' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7606' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7606' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.bounds_13_7607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.exact_13_7607' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0962.data_13_7607' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0962.endpoint_13_7607' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7608' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7608' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7608' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7609' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7609' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7609' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7610' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7610' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7610' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7611' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7611' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7611' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7612' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7612' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7612' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7613' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7613' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7613' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7614' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7614' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7614' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7615' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7615' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7615' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7616' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7616' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7616' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7617' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7617' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7617' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7618' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7618' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7618' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7619' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7619' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7619' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7620' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7620' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7620' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7621' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7621' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7621' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.bounds_13_7622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.exact_13_7622' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0963.data_13_7622' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0963.endpoint_13_7622' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7623' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7623' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7623' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7624' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7624' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7624' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7625' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7625' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7625' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7626' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7626' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7626' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7627' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7627' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7627' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7628' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7628' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7628' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7629' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7629' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7629' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7630' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7630' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7630' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7631' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7631' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7631' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7632' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7632' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7632' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7633' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7633' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7633' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7634' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7634' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7634' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7635' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7635' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7635' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7636' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7636' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7636' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7637' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7637' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7637' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.bounds_13_7638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.exact_13_7638' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0964.data_13_7638' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0964.endpoint_13_7638' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7639' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7639' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7639' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7640' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7640' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7640' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7641' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7641' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7641' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7642' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7642' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7642' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7643' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7643' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7643' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7644' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7644' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7644' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7645' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7645' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7645' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7646' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7646' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7646' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7647' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7647' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7647' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7648' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7648' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7648' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7649' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7649' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7649' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7650' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7650' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7650' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7651' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7651' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7651' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7652' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7652' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7652' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.bounds_13_7653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.exact_13_7653' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0965.data_13_7653' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0965.endpoint_13_7653' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7654' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7654' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7654' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7655' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7655' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7655' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7656' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7656' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7656' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7657' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7657' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7657' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7658' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7658' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7658' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7659' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7659' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7659' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7660' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7660' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7660' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7661' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7661' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7661' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7662' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7662' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7662' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7663' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7663' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7663' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7664' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7664' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7664' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7665' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7665' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7665' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7666' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7666' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7666' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7667' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7667' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7667' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.bounds_13_7668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.exact_13_7668' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0966.data_13_7668' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0966.endpoint_13_7668' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7669' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7669' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7669' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7670' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7670' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7670' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7671' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7671' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7671' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7672' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7672' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7672' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7673' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7673' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7673' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7674' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7674' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7674' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7675' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7675' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7675' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7676' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7676' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7676' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7677' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7677' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7677' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7678' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7678' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7678' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7679' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7679' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7679' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7680' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7680' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7680' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7681' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7681' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7681' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7682' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7682' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7682' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7683' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7683' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7683' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.bounds_13_7684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.exact_13_7684' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0967.data_13_7684' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0967.endpoint_13_7684' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7685' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7685' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7685' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7686' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7686' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7686' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7687' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7687' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7687' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7688' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7688' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7688' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7689' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7689' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7689' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7690' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7690' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7690' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7691' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7691' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7691' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7692' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7692' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7692' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7693' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7693' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7693' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7694' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7694' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7694' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7695' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7695' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7695' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7696' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7696' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7696' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7697' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7697' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7697' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7698' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7698' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7698' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.bounds_13_7699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.exact_13_7699' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0968.data_13_7699' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0968.endpoint_13_7699' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7700' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7700' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7700' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7701' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7701' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7701' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7702' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7702' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7702' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7703' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7703' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7703' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7704' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7704' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7704' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7705' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7705' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7705' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7706' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7706' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7706' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7707' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7707' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7707' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7708' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7708' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7708' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7709' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7709' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7709' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7710' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7710' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7710' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7711' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7711' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7711' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7712' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7712' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7712' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7713' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7713' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7713' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.bounds_13_7714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.exact_13_7714' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0969.data_13_7714' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0969.endpoint_13_7714' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7715' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7715' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7715' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7716' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7716' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7716' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7717' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7717' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7717' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7718' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7718' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7718' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7719' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7719' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7719' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7720' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7720' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7720' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7721' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7721' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7721' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7722' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7722' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7722' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7723' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7723' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7723' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7724' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7724' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7724' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7725' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7725' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7725' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7726' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7726' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7726' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7727' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7727' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7727' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7728' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7728' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7728' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7729' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7729' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7729' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.bounds_13_7730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.exact_13_7730' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0970.data_13_7730' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0970.endpoint_13_7730' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7731' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7731' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7731' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7732' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7732' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7732' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7733' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7733' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7733' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7734' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7734' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7734' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7735' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7735' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7735' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7736' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7736' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7736' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7737' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7737' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7737' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7738' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7738' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7738' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7739' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7739' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7739' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7740' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7740' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7740' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7741' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7741' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7741' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7742' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7742' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7742' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7743' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7743' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7743' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7744' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7744' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7744' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.bounds_13_7745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.exact_13_7745' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0971.data_13_7745' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0971.endpoint_13_7745' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7746' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7746' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7746' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7747' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7747' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7747' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7748' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7748' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7748' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7749' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7749' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7749' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7750' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7750' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7750' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7751' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7751' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7751' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7752' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7752' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7752' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7753' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7753' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7753' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7754' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7754' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7754' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7755' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7755' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7755' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7756' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7756' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7756' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7757' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7757' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7757' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7758' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7758' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7758' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7759' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7759' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7759' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.bounds_13_7760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.exact_13_7760' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0972.data_13_7760' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0972.endpoint_13_7760' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7761' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7761' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7761' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7762' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7762' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7762' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7763' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7763' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7763' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7764' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7764' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7764' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7765' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7765' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7765' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7766' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7766' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7766' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7767' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7767' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7767' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7768' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7768' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7768' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7769' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7769' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7769' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7770' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7770' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7770' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7771' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7771' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7771' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7772' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7772' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7772' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7773' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7773' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7773' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7774' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7774' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7774' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7775' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7775' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7775' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.bounds_13_7776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.exact_13_7776' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0973.data_13_7776' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0973.endpoint_13_7776' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7777' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7777' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7777' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7778' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7778' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7778' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7779' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7779' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7779' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7780' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7780' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7780' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7781' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7781' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7781' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7782' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7782' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7782' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7783' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7783' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7783' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7784' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7784' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7784' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7785' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7785' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7785' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7786' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7786' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7786' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7787' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7787' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7787' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7788' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7788' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7788' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7789' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7789' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7789' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7790' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7790' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7790' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.bounds_13_7791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.exact_13_7791' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0974.data_13_7791' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0974.endpoint_13_7791' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7792' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7792' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7792' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7793' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7793' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7793' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7794' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7794' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7794' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7795' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7795' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7795' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7796' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7796' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7796' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7797' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7797' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7797' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7798' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7798' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7798' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7799' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7799' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7799' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7800' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7800' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7800' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7801' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7801' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7801' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7802' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7802' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7802' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7803' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7803' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7803' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7804' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7804' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7804' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7805' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7805' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7805' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7806' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7806' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7806' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.bounds_13_7807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.exact_13_7807' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0975.data_13_7807' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0975.endpoint_13_7807' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7808' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7808' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7808' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7809' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7809' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7809' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7810' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7810' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7810' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7811' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7811' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7811' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7812' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7812' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7812' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7813' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7813' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7813' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7814' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7814' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7814' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7815' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7815' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7815' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7816' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7816' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7816' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7817' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7817' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7817' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7818' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7818' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7818' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7819' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7819' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7819' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7820' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7820' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7820' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7821' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7821' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7821' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.bounds_13_7822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.exact_13_7822' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0976.data_13_7822' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0976.endpoint_13_7822' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7823' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7823' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7823' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7824' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7824' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7824' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7825' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7825' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7825' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7826' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7826' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7826' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7827' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7827' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7827' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7828' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7828' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7828' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7829' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7829' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7829' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7830' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7830' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7830' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7831' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7831' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7831' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7832' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7832' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7832' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7833' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7833' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7833' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7834' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7834' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7834' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7835' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7835' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7835' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7836' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7836' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7836' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.bounds_13_7837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.exact_13_7837' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0977.data_13_7837' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0977.endpoint_13_7837' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7838' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7838' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7838' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7839' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7839' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7839' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7840' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7840' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7840' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7841' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7841' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7841' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7842' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7842' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7842' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7843' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7843' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7843' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7844' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7844' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7844' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7845' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7845' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7845' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7846' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7846' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7846' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7847' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7847' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7847' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7848' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7848' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7848' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7849' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7849' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7849' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7850' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7850' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7850' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7851' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7851' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7851' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7852' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7852' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7852' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.bounds_13_7853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.exact_13_7853' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0978.data_13_7853' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0978.endpoint_13_7853' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7854' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7854' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7854' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7855' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7855' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7855' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7856' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7856' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7856' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7857' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7857' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7857' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7858' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7858' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7858' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7859' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7859' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7859' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7860' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7860' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7860' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7861' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7861' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7861' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7862' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7862' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7862' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7863' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7863' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7863' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7864' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7864' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7864' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7865' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7865' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7865' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7866' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7866' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7866' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7867' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7867' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7867' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.bounds_13_7868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.exact_13_7868' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0979.data_13_7868' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0979.endpoint_13_7868' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7869' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7869' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7869' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7870' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7870' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7870' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7871' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7871' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7871' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7872' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7872' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7872' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7873' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7873' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7873' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7874' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7874' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7874' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7875' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7875' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7875' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7876' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7876' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7876' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7877' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7877' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7877' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7878' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7878' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7878' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7879' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7879' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7879' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7880' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7880' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7880' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7881' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7881' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7881' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7882' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7882' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7882' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.bounds_13_7883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.exact_13_7883' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0980.data_13_7883' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0980.endpoint_13_7883' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7884' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7884' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7884' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7885' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7885' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7885' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7886' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7886' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7886' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7887' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7887' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7887' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7888' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7888' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7888' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7889' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7889' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7889' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7890' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7890' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7890' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7891' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7891' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7891' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7892' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7892' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7892' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7893' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7893' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7893' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7894' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7894' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7894' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7895' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7895' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7895' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7896' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7896' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7896' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7897' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7897' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7897' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7898' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7898' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7898' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.bounds_13_7899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.exact_13_7899' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0981.data_13_7899' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0981.endpoint_13_7899' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7900' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7900' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7900' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7901' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7901' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7901' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7902' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7902' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7902' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7903' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7903' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7903' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7904' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7904' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7904' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7905' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7905' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7905' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7906' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7906' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7906' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7907' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7907' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7907' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7908' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7908' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7908' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7909' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7909' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7909' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7910' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7910' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7910' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7911' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7911' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7911' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7912' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7912' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7912' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7913' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7913' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7913' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.bounds_13_7914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.exact_13_7914' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0982.data_13_7914' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0982.endpoint_13_7914' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7915' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7915' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7915' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7916' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7916' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7916' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7917' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7917' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7917' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7918' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7918' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7918' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7919' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7919' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7919' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7920' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7920' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7920' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7921' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7921' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7921' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7922' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7922' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7922' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7923' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7923' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7923' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7924' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7924' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7924' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7925' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7925' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7925' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7926' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7926' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7926' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7927' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7927' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7927' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7928' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7928' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7928' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.bounds_13_7929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.exact_13_7929' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0983.data_13_7929' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0983.endpoint_13_7929' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7930' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7930' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7930' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7931' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7931' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7931' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7932' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7932' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7932' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7933' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7933' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7933' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7934' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7934' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7934' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7935' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7935' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7935' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7936' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7936' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7936' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7937' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7937' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7937' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7938' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7938' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7938' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7939' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7939' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7939' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7940' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7940' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7940' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7941' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7941' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7941' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7942' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7942' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7942' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7943' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7943' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7943' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7944' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7944' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7944' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.bounds_13_7945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.exact_13_7945' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0984.data_13_7945' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0984.endpoint_13_7945' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7946' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7946' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7946' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7947' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7947' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7947' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7948' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7948' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7948' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7949' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7949' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7949' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7950' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7950' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7950' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7951' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7951' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7951' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7952' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7952' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7952' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7953' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7953' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7953' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7954' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7954' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7954' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7955' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7955' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7955' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7956' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7956' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7956' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7957' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7957' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7957' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7958' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7958' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7958' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7959' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7959' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7959' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.bounds_13_7960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.exact_13_7960' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0985.data_13_7960' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0985.endpoint_13_7960' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7961' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7961' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7961' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7962' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7962' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7962' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7963' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7963' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7963' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7964' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7964' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7964' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7965' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7965' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7965' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7966' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7966' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7966' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7967' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7967' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7967' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7968' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7968' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7968' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7969' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7969' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7969' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7970' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7970' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7970' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7971' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7971' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7971' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7972' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7972' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7972' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7973' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7973' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7973' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7974' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7974' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7974' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.bounds_13_7975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.exact_13_7975' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0986.data_13_7975' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0986.endpoint_13_7975' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7976' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7976' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7976' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7977' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7977' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7977' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7978' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7978' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7978' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7979' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7979' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7979' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7980' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7980' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7980' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7981' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7981' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7981' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7982' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7982' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7982' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7983' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7983' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7983' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7984' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7984' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7984' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7985' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7985' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7985' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7986' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7986' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7986' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7987' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7987' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7987' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7988' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7988' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7988' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7989' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7989' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7989' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7990' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7990' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7990' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.bounds_13_7991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.exact_13_7991' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0987.data_13_7991' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0987.endpoint_13_7991' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7992' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7992' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7992' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7993' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7993' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7993' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7994' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7994' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7994' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7995' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7995' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7995' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7996' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7996' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7996' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7997' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7997' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7997' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7998' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7998' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7998' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_7999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_7999' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_7999' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_7999' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8000' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8000' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8000' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8001' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8001' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8001' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8002' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8002' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8002' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8003' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8003' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8003' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8004' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8004' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8004' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8005' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8005' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8005' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.bounds_13_8006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.exact_13_8006' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0988.data_13_8006' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0988.endpoint_13_8006' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8007' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8007' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8007' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8008' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8008' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8008' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8009' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8009' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8009' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8010' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8010' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8010' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8011' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8011' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8011' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8012' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8012' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8012' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8013' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8013' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8013' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8014' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8014' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8014' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8015' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8015' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8015' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8016' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8016' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8016' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8017' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8017' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8017' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8018' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8018' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8018' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8019' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8019' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8019' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8020' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8020' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8020' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8021' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8021' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8021' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.bounds_13_8022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.exact_13_8022' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0989.data_13_8022' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0989.endpoint_13_8022' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8023' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8023' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8023' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8024' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8024' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8024' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8025' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8025' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8025' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8026' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8026' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8026' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8027' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8027' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8027' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8028' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8028' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8028' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8029' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8029' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8029' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8030' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8030' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8030' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8031' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8031' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8031' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8032' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8032' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8032' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8033' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8033' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8033' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8034' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8034' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8034' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8035' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8035' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8035' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8036' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8036' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8036' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.bounds_13_8037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.exact_13_8037' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0990.data_13_8037' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0990.endpoint_13_8037' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8038' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8038' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8038' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8039' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8039' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8039' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8040' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8040' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8040' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8041' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8041' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8041' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8042' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8042' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8042' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8043' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8043' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8043' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8044' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8044' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8044' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8045' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8045' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8045' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8046' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8046' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8046' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8047' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8047' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8047' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8048' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8048' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8048' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8049' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8049' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8049' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8050' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8050' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8050' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8051' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8051' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8051' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.bounds_13_8052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.exact_13_8052' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0991.data_13_8052' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0991.endpoint_13_8052' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8053' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8053' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8053' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8054' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8054' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8054' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8055' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8055' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8055' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8056' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8056' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8056' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8057' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8057' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8057' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8058' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8058' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8058' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8059' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8059' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8059' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8060' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8060' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8060' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8061' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8061' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8061' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8062' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8062' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8062' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8063' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8063' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8063' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8064' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8064' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8064' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8065' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8065' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8065' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8066' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8066' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8066' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8067' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8067' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8067' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.bounds_13_8068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.exact_13_8068' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0992.data_13_8068' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0992.endpoint_13_8068' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8069' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8069' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8069' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8070' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8070' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8070' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8071' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8071' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8071' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8072' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8072' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8072' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8073' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8073' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8073' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8074' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8074' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8074' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8075' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8075' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8075' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8076' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8076' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8076' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8077' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8077' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8077' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8078' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8078' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8078' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8079' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8079' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8079' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8080' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8080' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8080' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8081' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8081' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8081' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8082' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8082' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8082' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.bounds_13_8083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.exact_13_8083' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0993.data_13_8083' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0993.endpoint_13_8083' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8084' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8084' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8084' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8085' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8085' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8085' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8086' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8086' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8086' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8087' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8087' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8087' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8088' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8088' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8088' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8089' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8089' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8089' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8090' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8090' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8090' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8091' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8091' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8091' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8092' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8092' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8092' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8093' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8093' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8093' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8094' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8094' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8094' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8095' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8095' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8095' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8096' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8096' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8096' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8097' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8097' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8097' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.bounds_13_8098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.exact_13_8098' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0994.data_13_8098' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0994.endpoint_13_8098' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8099' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8099' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8099' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8100' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8100' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8100' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8101' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8101' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8101' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8102' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8102' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8102' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8103' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8103' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8103' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8104' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8104' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8104' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8105' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8105' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8105' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8106' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8106' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8106' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8107' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8107' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8107' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8108' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8108' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8108' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8109' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8109' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8109' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8110' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8110' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8110' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8111' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8111' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8111' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8112' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.data_13_8112' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.endpoint_13_8112' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0995.bounds_13_8113' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0995.exact_13_8113' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8116' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8116' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8116' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8117' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8117' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8117' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8118' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8118' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8118' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8119' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8119' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8119' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8120' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8120' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8120' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8121' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8121' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8121' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8122' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8122' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8122' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8123' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8123' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8123' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8124' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8124' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8124' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8125' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8125' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8125' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8126' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8126' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8126' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8127' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8127' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8127' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8128' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8128' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8128' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.bounds_13_8129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.exact_13_8129' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0996.data_13_8129' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0996.endpoint_13_8129' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8130' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8130' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8130' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8131' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8131' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8131' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8132' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8132' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8132' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8133' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8133' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8133' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8134' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8134' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8134' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8135' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8135' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8135' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8136' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8136' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8136' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8137' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8137' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8137' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8138' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8138' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8138' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8139' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8139' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8139' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8140' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8140' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8140' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8141' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8141' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8141' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8142' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8142' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8142' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8143' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8143' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8143' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.bounds_13_8144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.exact_13_8144' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0997.data_13_8144' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0997.endpoint_13_8144' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8145' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8145' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8145' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8146' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8146' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8146' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8147' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8147' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8147' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8148' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8148' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8148' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8149' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8149' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8149' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8150' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8150' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8150' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8151' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8151' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8151' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8152' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8152' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8152' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8153' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8153' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8153' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8154' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8154' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8154' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8155' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8155' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8155' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8156' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8156' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8156' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8157' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8157' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8157' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8158' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8158' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8158' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8159' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8159' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8159' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.bounds_13_8160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.exact_13_8160' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0998.data_13_8160' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0998.endpoint_13_8160' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0999.exact_13_8161' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0999.data_13_8161' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8161' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0999.exact_13_8162' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0999.data_13_8162' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0999.endpoint_13_8162' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch0999.bounds_13_8163' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch0999.exact_13_8163' depends on axioms: [propext, Classical.choice, Quot.sound] 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+'Collatz.Research.StoppingAtlas.Batch1000.data_13_8188' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8188' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.exact_13_8189' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch1000.data_13_8189' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8189' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.exact_13_8190' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch1000.data_13_8190' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8190' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch1000.bounds_13_8191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.exact_13_8191' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.Batch1000.data_13_8191' does not depend on any axioms +'Collatz.Research.StoppingAtlas.Batch1000.endpoint_13_8191' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.stopping_iff_firstLight' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.finite_interval_beyond' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.membership_upward' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.upper_none' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.empty_or_tail' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.empty_or_tail_1538' depends on axioms: [propext, Classical.choice, Quot.sound] +'Collatz.Research.StoppingAtlas.count_shift_add' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.prefix_10_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.chunk_10_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_10_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_10_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.period_count_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.prefix_11_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.chunk_11_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_9' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_12' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_13' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_14' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_14' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_15' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_11_15' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_11_16' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.period_count_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.prefix_12_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.chunk_12_0' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_1' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_1' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_2' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_2' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_3' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_3' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_4' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_4' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_5' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_5' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_6' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_6' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_7' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_7' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_8' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_8' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_9' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_9' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_10' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_10' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_11' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_11' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_12' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_12' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_13' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_13' does not depend on any axioms +'Collatz.Research.StoppingAtlas.prefix_12_14' depends on axioms: [propext, Quot.sound] +'Collatz.Research.StoppingAtlas.chunk_12_14' does not depend on any axioms 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"842021de199d2f456f6676901193cb45ef966826910e24620b3bff4311abcc65", + "build_exit_code": 0, + "seconds": 0.697, + "build_output_sha256": "bc3fc108dae9e38d788e241bf22b5729a743f2565efeb6cbfece43bdbd810ce8", + "commit": "a99424ee3ee81c379c89fa17755f98b8380826ac" + } +] diff --git a/Research/StoppingAtlas/build.log b/Research/StoppingAtlas/build.log new file mode 100644 index 00000000..3b6937fb --- /dev/null +++ b/Research/StoppingAtlas/build.log @@ -0,0 +1,74 @@ +⚠ [47/593] Replayed Collatz.Strategy.CycleProduct +warning: Collatz/Strategy/CycleProduct.lean:72:26: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +warning: Collatz/Strategy/CycleProduct.lean:78:54: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.add_mul, Nat.mul_add, Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +warning: Collatz/Strategy/CycleProduct.lean:81:54: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.add_mul, Nat.mul_add, Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +warning: Collatz/Strategy/CycleProduct.lean:86:28: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +warning: Collatz/Strategy/CycleProduct.lean:158:28: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +warning: Collatz/Strategy/CycleProduct.lean:197:24: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +warning: Collatz/Strategy/CycleProduct.lean:286:24: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +⚠ [48/593] Replayed Collatz.Strategy.AffineExact +warning: Collatz/Strategy/AffineExact.lean:127:41: Variable name `hm` is not explicitly referenced. + +Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning: + [apply] _hm + +Note: This linter can be disabled with `set_option linter.unusedVariables false` +⚠ [54/593] Replayed Collatz.Strategy.AccumulatorArith +warning: Collatz/Strategy/AccumulatorArith.lean:129:24: This simp argument is unused: + Nat.mul_assoc + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_comm, Nat.mul_left_comm] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +⚠ [117/593] Replayed Collatz.Strategy.AccumulatorSharp +warning: Collatz/Strategy/AccumulatorSharp.lean:71:14: This simp argument is unused: + Nat.mul_comm + +Hint: Omit it from the simp argument list. + [apply] simp [Nat.mul_left_comm, Nat.mul_assoc] + +Note: This linter can be disabled with `set_option linter.unusedSimpArgs false` +Build completed successfully (1147 jobs). diff --git a/Research/StoppingAtlas/history-check.log b/Research/StoppingAtlas/history-check.log new file mode 100644 index 00000000..574a739b --- /dev/null +++ b/Research/StoppingAtlas/history-check.log @@ -0,0 +1,15 @@ +Checked 15360 distinct cylinders in 1000 batches +{ + "status": "passed", + "baseline": "a4bb6ce3d4163f091e7951d976d7073086c94ef1", + "batch_commits": 1000, + "new_commits_at_check": 1000, + "head_at_check": "a99424ee3ee81c379c89fa17755f98b8380826ac", + "checks": [ + "baseline is ancestor", + "distinct commits", + "each commit changes only its own batch", + "historical source matches certified manifest", + "all batch commits reachable from HEAD" + ] +} diff --git a/Research/StoppingAtlas/history-verification.json b/Research/StoppingAtlas/history-verification.json new file mode 100644 index 00000000..8363cd91 --- /dev/null +++ b/Research/StoppingAtlas/history-verification.json @@ -0,0 +1,14 @@ +{ + "status": "passed", + "baseline": "a4bb6ce3d4163f091e7951d976d7073086c94ef1", + "batch_commits": 1000, + "new_commits_at_check": 1000, + "head_at_check": "a99424ee3ee81c379c89fa17755f98b8380826ac", + "checks": [ + "baseline is ancestor", + "distinct commits", + "each commit changes only its own batch", + "historical source matches certified manifest", + "all batch commits reachable from HEAD" + ] +} diff --git a/Research/StoppingAtlas/manifest.json b/Research/StoppingAtlas/manifest.json new file mode 100644 index 00000000..5bfad6cc --- /dev/null +++ b/Research/StoppingAtlas/manifest.json @@ -0,0 +1,144256 @@ +{ + "baseline": "a4bb6ce3d4163f091e7951d976d7073086c94ef1", + "depths": [ + 10, + 11, + 12, + 13 + ], + "batch_count": 1000, + "cylinder_count": 15360, + "certificate_theorems": 61440, + "batches": [ + { + "module": "Batch0001", + "start": 0, + "stop": 15, + "sha256": "ebf654901f481288062a671d8fdf03211a4130492a08f87f7740ec1e4798ff90" + }, + { + "module": "Batch0002", + "start": 15, + "stop": 30, + "sha256": "08f7739292694b7b0f9abb8911c03a7fafb7df16f3e5fb5fc5e18df3c279ebc3" + }, + { + "module": "Batch0003", + "start": 30, + "stop": 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b/Research/StoppingAtlas/negative-insufficient_gap_bound.log new file mode 100644 index 00000000..b2687ef9 --- /dev/null +++ b/Research/StoppingAtlas/negative-insufficient_gap_bound.log @@ -0,0 +1,3 @@ +/Rejected.lean:5:73: error: Tactic `decide` proved that the proposition + 971 * 3 ^ 971 < 3 * (2 ^ 1539 - 3 ^ 971) * 99730 +is false diff --git a/Research/StoppingAtlas/negative-late_descent_is_not_first.log b/Research/StoppingAtlas/negative-late_descent_is_not_first.log new file mode 100644 index 00000000..3884b805 --- /dev/null +++ b/Research/StoppingAtlas/negative-late_descent_is_not_first.log @@ -0,0 +1,3 @@ +/Rejected.lean:5:49: error: Tactic `decide` proved that the proposition + FirstLightDescent.FirstLight 3 5 +is false diff --git a/Research/StoppingAtlas/negative-missing_small_input_exception.log b/Research/StoppingAtlas/negative-missing_small_input_exception.log new file mode 100644 index 00000000..076afcde --- /dev/null +++ b/Research/StoppingAtlas/negative-missing_small_input_exception.log @@ -0,0 +1,3 @@ +/Rejected.lean:5:41: error: Tactic `decide` proved that the proposition + acceleratedOrbit 2 1 < 1 +is false diff --git a/Research/StoppingAtlas/negative-wrong_cylinder.log b/Research/StoppingAtlas/negative-wrong_cylinder.log new file mode 100644 index 00000000..154656f9 --- /dev/null +++ b/Research/StoppingAtlas/negative-wrong_cylinder.log @@ -0,0 +1,3 @@ +/Rejected.lean:5:77: error: Tactic `decide` proved that the proposition + (Research.DescentIntervals.exactInterval 11 27).upper = none +is false diff --git a/Research/StoppingAtlas/proof-escape-screen.log b/Research/StoppingAtlas/proof-escape-screen.log new file mode 100644 index 00000000..7c644c01 --- /dev/null +++ b/Research/StoppingAtlas/proof-escape-screen.log @@ -0,0 +1 @@ +Proof-escape screen passed for 4339 Lean files. diff --git a/Research/StoppingAtlas/python-tests.json b/Research/StoppingAtlas/python-tests.json new file mode 100644 index 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"sha256": "2fb0ab23a31ce6cc23d1f6e58326838dfde1079f6a060278d929f40985e8399d", + "lines": 124, + "code_lines": 93, + "theorems": 11 + }, + { + "path": "Collatz/Research/StoppingAtlas/Horizon.lean", + "sha256": "f04686776c96a2fca74e4fcf367ca6eef9af30df645b1269314b50b5808a7a91", + "lines": 59, + "code_lines": 34, + "theorems": 7 + }, + { + "path": "Collatz/Research/StoppingAtlas/Timing.lean", + "sha256": "05eafcdedb7372a94f8c79f812921a5ddddd6302c3321a49076c860d970825fe", + "lines": 47, + "code_lines": 33, + "theorems": 5 + } + ], + "scope": [ + "Build covers the addition and all its dependencies.", + "Does not rebuild every historical repository target or the separate Mathlib extension.", + "Standard kernel checking: no added axioms, sorry, or native_decide.", + "Finite certificate count is not a count of independent mathematical discoveries.", + "No universal existence of coefficient crossings or proof of Collatz." + ] +} diff --git a/scripts/audit_stopping_atlas.py b/scripts/audit_stopping_atlas.py new file mode 100644 index 00000000..340b071f --- /dev/null +++ b/scripts/audit_stopping_atlas.py @@ -0,0 +1,125 @@ +#!/usr/bin/env python3 +"""Build the full addition, audit every theorem, and reject false controls.""" +from __future__ import annotations + +import hashlib +import json +from pathlib import Path +import re +import subprocess +import tempfile + +from stopping_atlas import BASELINE, LEAN, REPORT, ROOT, write_or_check +from audit_descent_intervals import ALLOWED, FORBIDDEN, strip_comments + + +def run(command: list[str], log: str) -> str: + with (REPORT / log).open('w') as stream: + result = subprocess.run(command, cwd=ROOT, stdout=stream, stderr=subprocess.STDOUT, text=True) + output = (REPORT / log).read_text() + if result.returncode: + raise RuntimeError(f'command failed: {command}; see {log}') + return output + + +def sources() -> tuple[list[str], list[dict]]: + names, records = [], [] + for path in sorted(LEAN.glob('*.lean')): + if path.name == 'Audit.lean': + continue + source = path.read_text() + code = strip_comments(source) + if FORBIDDEN.search(code): + raise RuntimeError(f'forbidden proof escape in {path.name}') + namespaces = re.findall(r'^namespace (\S+)\s*$', code, re.M) + local = re.findall(r'^(?:@\[[^\n]*\]\s*)?theorem\s+([\w.]+)', code, re.M) + if local and len(namespaces) != 1: + raise RuntimeError(f'unexpected namespace shape in {path.name}') + if local: + names.extend(f'{namespaces[0]}.{name}' for name in local) + records.append({'path': str(path.relative_to(ROOT)), + 'sha256': hashlib.sha256(source.encode()).hexdigest(), + 'lines': len(source.splitlines()), + 'code_lines': sum(bool(line.strip()) for line in code.splitlines()), + 'theorems': len(local)}) + if len(names) != len(set(names)): + raise RuntimeError('duplicate declaration name') + return names, records + + +def axioms(names: list[str]) -> dict: + path = LEAN / 'Audit.lean' + path.write_text('import Collatz.Research.StoppingAtlas.All\n\n' + + ''.join(f'#print axioms {name}\n' for name in names)) + output = run(['lake', 'env', 'lean', str(path)], 'axioms.log') + none = set(re.findall(r"'([^']+)' does not depend on any axioms", output)) + deps = {name: set(re.findall(r'[A-Za-z_][\w.]*', values)) for name, values in + re.findall(r"'([^']+)' depends on axioms:\s*\[([^\]]*)\]", output)} + if none | set(deps) != set(names): + raise RuntimeError('axiom audit did not cover precisely every theorem') + for name, values in deps.items(): + if values - ALLOWED: + raise RuntimeError(f'unexpected axioms for {name}: {values}') + return {'theorems_checked': len(names), 'without_axioms': len(none), + 'allowed': sorted(ALLOWED), 'observed': sorted(set().union(*deps.values()))} + + +def negative_controls() -> list[dict]: + claims = { + 'missing_small_input_exception': 'acceleratedOrbit 2 1 < 1', + 'wrong_cylinder': '(Research.DescentIntervals.exactInterval 11 27).upper = none', + 'insufficient_gap_bound': '(971 : Nat) * 3 ^ 971 < 3 * (2 ^ 1539 - 3 ^ 971) * 99730', + 'late_descent_is_not_first': 'FirstLightDescent.FirstLight 3 5', + } + outcomes = [] + for label, claim in claims.items(): + with tempfile.TemporaryDirectory(prefix='collatz-atlas-negative-') as directory: + path = Path(directory) / 'Rejected.lean' + path.write_text('import Collatz.Research.StoppingAtlas.All\n' + 'open Collatz\nset_option maxRecDepth 100000\nset_option exponentiation.threshold 2048\n' + f'example : {claim} := by decide\n') + result = subprocess.run(['lake', 'env', 'lean', str(path)], cwd=ROOT, + capture_output=True, text=True) + output = result.stdout + result.stderr + (REPORT / f'negative-{label}.log').write_text(output.replace(directory, '')) + if result.returncode == 0 or 'Tactic `decide` proved that the proposition' not in output or '\nis false' not in output: + raise RuntimeError(f'negative control failed for the wrong reason: {label}: {output}') + outcomes.append({'case': label, 'status': 'rejected_false_certificate'}) + return outcomes + + +def main() -> None: + manifest = write_or_check(True) + run(['lake', 'build', 'Collatz.Research.StoppingAtlas.All'], 'build.log') + names, records = sources() + negative = negative_controls() + footprints = axioms(names) + run(['python3', 'scripts/test_stopping_atlas.py'], 'python-tests.log') + tests = json.loads((REPORT / 'python-tests.json').read_text()) + if tests['status'] != 'passed': + raise RuntimeError('independent Python tests did not pass') + generated_records = [r for r in records if (Path(r['path']).name.startswith('Batch') or Path(r['path']).name in {'Census.lean', 'Certificates.lean'})] + report = {'status': 'passed', 'baseline': BASELINE, + 'target': 'Collatz.Research.StoppingAtlas.All', + 'horizon': 1538, 'failure_bound': 99730, + 'cylinder_count': manifest['cylinder_count'], 'batch_count': manifest['batch_count'], + 'lean_lines': sum(r['lines'] for r in records), + 'lean_code_lines': sum(r['code_lines'] for r in records), + 'generated_lean_code_lines': sum(r['code_lines'] for r in generated_records), + 'handwritten_lean_code_lines': sum(r['code_lines'] for r in records if r not in generated_records + and not r['path'].endswith('SmallInputs.lean')), + 'axiom_audit': footprints, 'negative_controls': negative, + 'python_tests': tests, 'files': records, + 'scope': ['Build covers the addition and all its dependencies.', + 'Does not rebuild every historical repository target or the separate Mathlib extension.', + 'Standard kernel checking: no added axioms, sorry, or native_decide.', + 'Finite certificate count is not a count of independent mathematical discoveries.', + 'No universal existence of coefficient crossings or proof of Collatz.']} + if report['lean_code_lines'] < 100000: + raise RuntimeError('requested new code-line minimum not met') + (REPORT / 'verification.json').write_text(json.dumps(report, indent=2) + '\n') + print(json.dumps({k: v for k, v in report.items() if k != 'files'}, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/scripts/check_stopping_atlas_history.py b/scripts/check_stopping_atlas_history.py new file mode 100644 index 00000000..b4c5e1f2 --- /dev/null +++ b/scripts/check_stopping_atlas_history.py @@ -0,0 +1,44 @@ +#!/usr/bin/env python3 +"""Check that all 1000 individually verified batches retain distinct commits. + +Run in a full checkout after --commit, not GitHub's default shallow checkout. +This checks provenance and history, not mathematics; use the Lean audit for that. +""" +import hashlib +import json +import subprocess +from stopping_atlas import BASELINE, REPORT, ROOT, write_or_check + + +def git(*args): + return subprocess.check_output(['git',*args],cwd=ROOT) + + +def main(): + manifest=write_or_check(True) + receipts=json.loads((REPORT/'batch-receipts.json').read_text()) + assert len(receipts)==1000 + by_module={receipt['module']:receipt for receipt in receipts} + assert len(by_module)==1000 + assert len({receipt['commit'] for receipt in receipts})==1000 + subprocess.run(['git','merge-base','--is-ancestor',BASELINE,'HEAD'],cwd=ROOT,check=True) + new=set(git('rev-list',f'{BASELINE}..HEAD').decode().splitlines()) + for batch in manifest['batches']: + receipt=by_module[batch['module']] + assert receipt['build_exit_code']==0 + assert receipt['source_sha256']==batch['sha256'] + assert receipt['commit'] in new + path=f'Collatz/Research/StoppingAtlas/{batch["module"]}.lean' + blob=git('show',f'{receipt["commit"]}:{path}') + assert hashlib.sha256(blob).hexdigest()==batch['sha256'] + changed=git('diff-tree','--no-commit-id','--name-only','-r',receipt['commit']).decode().splitlines() + assert changed==[path],(receipt['commit'],changed) + result={'status':'passed','baseline':BASELINE, + 'batch_commits':1000,'new_commits_at_check':len(new), + 'head_at_check':git('rev-parse','HEAD').decode().strip(), + 'checks':['baseline is ancestor','distinct commits','each commit changes only its own batch', + 'historical source matches certified manifest','all batch commits reachable from HEAD']} + (REPORT/'history-verification.json').write_text(json.dumps(result,indent=2)+'\n') + print(json.dumps(result,indent=2)) + +if __name__=='__main__':main() diff --git a/scripts/generate_stopping_census.py b/scripts/generate_stopping_census.py new file mode 100644 index 00000000..32481f2c --- /dev/null +++ b/scripts/generate_stopping_census.py @@ -0,0 +1,57 @@ +#!/usr/bin/env python3 +"""Generate memory-bounded kernel computations of complete event-period counts.""" +from descent_intervals import trace + + +def census_source(): + s='''import Collatz.Research.StoppingAtlas.Discrepancy + +namespace Collatz.Research.StoppingAtlas +open PeriodicCounting +set_option maxRecDepth 200000 +set_option maxHeartbeats 0 + +/-- Split a counting window into a prefix and a translated suffix. -/ +theorem count_shift_add (P : Nat → Bool) (N M : Nat) : + countBelow P (N + M) = countBelow P N + countBelow (fun n => P (N + n)) M := by + induction M with + | zero => simp + | succ M ih => + rw [Nat.add_succ, count_succ, ih, count_succ] + omega + +''' + for k in range(10,14): + total=0 + s+=f'theorem prefix_{k}_0 : countBelow (firstEventB {k}) 0 = 0 := rfl\n\n' + for j in range((1< firstEventB {k} ({base} + n)) 128 = {count} := by decide + +/-- Assemble independently checked blocks using the general counting identity. -/ +theorem prefix_{k}_{j+1} : countBelow (firstEventB {k}) {base+128} = {total+count} := by + have h := count_shift_add (firstEventB {k}) {base} 128 + rw [prefix_{k}_{j}, chunk_{k}_{j}] at h + exact h + +''' + total+=count + s+=f'/-- Complete period numerator at depth {k}. -/\ntheorem period_count_{k} : countBelow (firstEventB {k}) (2 ^ {k}) = {total} := prefix_{k}_{(1<=p2:break + threshold=a*p3[a]//(3*(p2-p3[a]))+1 + assert threshold<=99730,(k,a,threshold) + if threshold>max_required:max_required=threshold;worst=[k,a] + checks['gap_pairs']+=1 + threshold=971*p3[971]//(3*((1<<1539)-p3[971]))+1 + assert threshold==330588 and threshold>99730 + checks['boundary_failure']+=1 + # First-passage partition at arbitrary cutoffs, with exact integer arithmetic. + for N in (0,1,2,3,31,64,101,257,1025): + events=[0]*21; survival=[0]*21 + for n in range(2,N+2): + _,crossing,_,_=direct(n,20) + if crossing is not None:events[crossing]+=1 + for h in range(21):survival[h]+=crossing is None or crossing>h + for h in range(21): + assert sum(events[:h+1])+survival[h]==N + if h<20:assert survival[h]==survival[h+1]+events[h+1] + checks['conservation_cutoffs']+=1 + # Exhaust all short binary periods and several prefixes/full periods. + for M in range(1,11): + for mask in range(1<>i)&1 for i in range(M)]; A=sum(bits) + C=0 + for N in range(3*M+1): + assert C==(N//M)*A+sum(bits[:N%M]) + assert abs(M*C-N*A)<=A*(M-A) + checks['period_discrepancies']+=1 + if N<3*M:C+=bits[N%M] + # False hypotheses are detected independently of Lean's rejection controls. + assert direct(1,2)[0] is None + assert direct(3,5)[0]==4 + assert census[11]['tail']==0 + report={'status':'passed','checks':dict(checks),'total_checks':sum(checks.values()), + 'census':census,'exceptional_max_crossing':max_crossing, + 'gap_max_required':max_required,'gap_worst_pair':worst, + 'next_threshold':threshold,'randomness':'none; deterministic exhaustive bounded checks', + 'limitation':'Sampled class indices supplement, but do not replace, universally quantified Lean proofs.'} + (REPORT/'python-tests.json').write_text(json.dumps(report,indent=2)+'\n') + print(json.dumps(report,indent=2)) + +if __name__=='__main__':main()